Ece198l Questionaire Sale

ECE198L SALE, MHIKO I. GEAS SET1 CHEMISTRY

1.) What are found in the nucleus of an atom? A. Eledctrions and Protons B. Protons and Neutrons C. Cations and Anions D. Electrons and Neutrons 2.) What is the negatively charged particle of an atom? A. Electrons B. Protons C. Neutron D. Molecule 3.) What is the positively charged particle of an atom? A. Electrons B. Protons C. Neutron D. Molecule 4. What is the particle of an atom that has no electrical charge? A. Electrons B. Protons C. Neutron D. Molecule 5. The word “atom” comes from Greek “Atomos” which means what? A. Extremely Small B. Invisible C. Indivisible D. Microscopic 6. Who was the first person to propose that atoms have weights? A. Ernest Rutherford B. Democritus C. John Dalton D. Joseph John Thomson

7. What is the result from the combination, in definite proportion of mass, of two or more elements? A. Mixture B. Compound C. Substance D. Chemical Reaction 8. How are mixtures classified? A. Elements or Compounds B. Metals, Nonmetals or Metalloids C. Homogeneous or Heterogeneous D. Suspension, Colloids or Solutions 9. The mixture of soil and water is an example of what classification of a mixture? A. Homogeneous B. Suspension C. Colloid D. Solution 10. A very fine particle of soil when mixed to water will form a cloudy mixture. How is this mixture classified? A. Colloid B. Suspension C. Solution D. Compound 11. The particles of sugar dispersed in water are so small that a clear homogeneous mixture. What is this homogeneous mixture called? A. Colloid B. Compound C. Suspension D. Solution 12. What are the three states of matter?

A. Solid, Liquid and Gas B. Metals, Nonmetals and Metalloids C. Suspension, Colloid and Solution D. Quarks, Photons and Quasar 13. Compounds are mostly classified as: A. Homogeneous and Heterogeneous B. Acids and Bases C. Gases, Liquids and Solids D. Metals and Nonmetals 14. What is the property of metals that allow them to be rolled without breaking? A. Ductility B. Malleability C. Luster D. Elasticity 15. What is the property of metals that reflects the light that strikes their surfaces, making them appear shiny? A. Malleability B. Ductility C. Luster D. Plasticity 16. An acid can react with base to produce a __________. A. hydrogen gas B. salt C. oxide D. hydroxide 17. Vinegar is a solution of water and what kind of acid? A. Phosphoric acid B. Sulfuric acid C. Nitric acid D. Acetic acid 18. What acid is added to

carbonated drinks to produce a tart test? A. Citric acid B. Phosphoric acid C. Sulfuric acid D. Nitric acid 19. What occurs when a substance changes it appearance without changing its composition? A. Chemical reaction B. Chemical change C. Physical change D. Catalyst 20. What is another term for “chemical change”? A. Chemical reaction B. Phase change C. State change D. Composition change 21. A material is said to be ______ if its composition and properties are uniform throughout. A. homogeneous B. heterogeneous C. pure substance D. pure compound 22. The properties of a material that changes when the amount of substance changes are called _______ properties. A. intensive B. extensive C. physical D. chemical 23. The properties of a material that do not change when the amount of substance changes are called _______ properties. A. intensive B. extensive

C. chemical D. physical 24. Which of the following is NOT an intensive property of a material? A. Color B. Surface area C. Melting point D. Taste 25. Which of the following is NOT an extensive property of a material? A. Length B. Volume C. Density D. Weight

A. molecules B. ions C. nuclides D. isotopes 31.) Calculate the moles of magnesium present in 93.5g of Mg? A.3.85 C.5.38 B.4.15 D.3.35 32.) How many number of atoms are there in 1.32x10^3 g of lead? Pb atomic mass is 207.2g. A.3.84x10^24 C.4.38x10^2 B.3.84^23

26. What is the charge of an electron in charge unit? A. 0 B. 1 + C. 1 – D. 0 –

D.4.38x10^2

33.) How many grams are there in 4.57x0^21 amu? A.6.8x10^-3 C.5.96x10^-3 B.5.45x10^-3 D.7.59x10^-3

27. What is the charge of a proton in coulombs? A. + 1.70217733 x 10^-19 B. + 1.60217733 x 10^-19 C. + 1.50217733 x 10^-19 D. + 1.40217733 x 10^-19

34.)Calculate the number of moles of cobalt atom in 7 billion Co atom

28. What is the charge of a proton in charge unit? A. 0 B. 1 + C. 1 – D. 0 –

35.) Given 16.7 moles of gold, how many grams of Au are there? atomic mass of Au is 197.0g

29. What is the mass of an electron in gram? A. 10203 x 10^-23 B. 8.218290 x 10^-25 C. 1.672623 x 10^-24 D. 9.109387 x 10^-28

B.3.29x10^3 D.3.6x10^13

A.1.16x10^-14 C.1.6x10^13 B.1.61x10^-13 D.1.3x10^-14

A.3.51x10^3 C.2.9x10^13

36.) Determine the mass in grams of a single atom of Ge which has an atomic mass of 72.59 A.3.51x10^3

30. Atoms of the same element which have different masses are called _______.

C.2.9x10^13

B.1.21x10^-22 D.3.6x10^13

37.)Solve for the volume occupied by 3.12 moles of nitric oxide which exerts 5.43 atm of pressure at a temperature of 82 A. 16.75L

C.15.76L

B.13.84L

D.16.48L

38.) Calculate the final pressusre if a sample of a certain gas is cooled from 34C to -73C, with an initial pressure of 1.45atm A.1.42atm

C.0.94atm

B.0.94atm

D.1.63atm

39.) Caffeine (C8H10N402) is a stimulant found in tea and coffee. what is its empirical formula? A.C4H5N20

C.C5H3NO2

B.CHN02

D.C1H2N40

40.) calculate the mass of a piece of platinum metal with a density of 34.1 g/cm^3 and has a volume of 5.2cm^3 A.17.732g

C.1773.2g

B.177.32 g

D.1.7732g

41.) What volume of concentrated sulfuric acid would weigh 0.82kg if its density us 1.85g/ml A. 2343.56ml

C.458.34 ml

B.443.24 ml

D.326.84ml

42.) Determine the number of moles present in 151.99g magnesium A.3.45 moles

C.9.21 moles

B.6.25 moles

D. 5.6 moles

43.) What is the molality of a solution containing 75.5g sucrose in 400g of water A. 0.553

C.0.38

B.0.421

D.0.421

44.) Find the mass of 3 moles of platinum in pounds A.1.3

C.1.8

B.2.1

D.2.5

45. Zinc (Zn) atom has atomic mass of 65.39. Calculate the number of atoms present in 4.22 g of zinc (Zn). A. 3.75 x 10^22 Zn atoms B. 3.93 x 10^22 Zn atoms C. 3.89 x 10^22 Zn atoms D. 4.04 x 10^22 Zn atoms 46. Calculate for the number of molecules of ethane (C2H6) present in 0.431 g of C2H6. (C atomic mass = 12.01g; H atomic mass = 1.008 g) A. 8.63 x 10^21 C2H6 molecules B. 8.75 x 10^21 C2H6 molecules C. 7.69 x 10^21 C2H6 molecules D. 9.13 x 10^21 C2H6 molecules

47. How many oxygen (O) atoms are there in 2.31 x 10^4 g of urea [(NH2)2CO]. Given molar mass of urea is 60.062g. A. 2.43 x 10^26 atoms B. 2.12 x 10^26 atoms C. 2.32 x 10^26 atoms D. 2.52 x 10^26 atoms

48. How many water molecules are present in 5.34 mL of water at a temperature of 4oC, which the density of water at this temperature is 1.00 g/mL? Atomic masses of H and O are 1.008 g and 16.00 g respectively. A. 1.84 x 10^23 molecules B. 1.78 x 10^23 molecules C. 1.74 x 10^23 molecules D. 1.87 x 10^23 molecules 49. Calculate the molecular mass of methanol (CH4O), given the atomic masses of C = 12.01 g, H = 1.008 g and O = 16 g. A. 29.018 amu B. 34.241 amu C. 32.042 amu D. 30.026 amu

50. How many moles of chloroform (CHCl3) are there in 210.45 g of chloroform? C = 12.01 amu, H = 1.008 amu and Cl = 35.45 amu. A. 1.76 CHCl3 moles B. 2.12 CHCl3 moles C. 4.34 CHCl3 moles D. 2.51 CHCl3 moles

51. What is the percent composition by mass of oxygen (O) element in sulfuric acid (H2SO4)? H = 1.008 amu, S = 32.07 amu, S = 32.07 amu and O = 16.00 amu. A. 62.25 % B. 63.34 % C. 64.45 % D. 65.25 %

52. Solve for the volume occupied by 3.12 moles of nitric oxide (NO) which exerts 5.43 atm of pressure at a temperature of 82oC. A. 16.75 L B. 13.84 L C. 15.76 L D. 16.48 L 53. Calculate the volume occupied by 50.6 g of HCl at STP. H = 1.008 amu and Cl = 35.45 amu. A. 83.2 L B. 31.1 L C. 27.4 L D. 1.38 L 54. Calculate the final pressure if a sample of a certain gas is cooled from 34oC to -73oC, with an initial pressure of 2.45 atm. A. 1.42 atm B. 1.58 atm C. 0.94 atm D. 1.63 atm 55. An 867-mL sample of chlorine gas exerts a pressure of 738 mmHg. Determine the pressure of the gas if the volume is reduced to 321 mL at constant temperature. A. 1.99 x 103 mm Hg B. 2.73 x 103 mm Hg C. 1.21 x 103 mm Hg D. 2.13 x 103 mm Hg 56. Determine the final pressure of a gas, initially at 3.0 L, 2.2 atm, and 72oC, which undergoes a change so that its final volume and temperature are 0.9 L and 41oC.

A. 7.66 atm B. 6.67 atm C. 4.18 atm D. 5.73 atm 57. A certain sample of natural gas contains 0.377 mole of ethane (C2H6), 7.48 moles of methane (CH4), and 0.134 mole of propane (C3H8). Calculate the partial pressure of propane gas, if the total pressure of the gases is 1.79 atm. A. 1.68 atm B. 0.084 atm C. 0.94 atm D. 0.03 atm 58. Calculate the number of molecules of oxygen gas present in 1.5 L of air at STP. Assuming that air contains 31% O2, 67% N2 and 2% Ar, all by volume. A. 1.87 x 10^23 molecules B. 4.18 x 10^24 molecules C. 2.81 x 10^23 molecules D. 1.25 x 10^22 molecules 59. Which of the following is the molar mass of the gas at 752 torr and 41oC? Ten grams of a gas occupy a volume of 5.12 L. A. 51 g/mol B. 1.96 g/mol C. 149 g/mol D. 1144 g/mol 60. What is the pressure required to compress 3 liters of a gas at 720 mm of pressure and 20 degree Celsius temperature into a vessel with a 0.5 liter capacity at a temperature of 100 degree Celsius? A. 5499 mm

B. 2956 mm C. 3314 mm D. 3585 mm

ECE198L SALE, MHIKO I. GEAS SET2 PHYSICS 1. What is the purpose of a unit vector? A. To describe the direction in space B. To indicate a magnitude without reference to direction C. To serve as comparison with other vectors D. To set a standard among vectors 2. What is another term for a scalar product of two vectors? A. Cross product B. Vector product C. Dot product D. Plus product 3. What refers to physical quantities that have a magnitude and a direction? A. Scalar quantities B. Vector quantities C. Dot product D. Vector quantities 4. The rate at which velocity changes with time is known as ________. A. acceleration B. instantaneous speed C. average speed D. instantaneous velocity

5. What is defined as any influence that can change the velocity of an object? A. Impulse B. Force C. Energy D. Work 6. “When an object exerts a force on another object, the second object exerts on the first a force of the same magnitude but in the opposite direction”. This statement is the _____. A. first law of motion B. second law of motion C. third law of motion D. d‟Alembert‟s principle 7. When the vector sum of the external forces acting on the system of particles equals zero, the total linear momentum of the system __________. A. becomes zero B. maximizes C. changes abruptly D. remains constant 8. “The force one charge exerts on another is directly proportional to the magnitudes of the charges and inversely proportional to the square of the distance between them”. This statement is known as ________. A. Coulomb’s law B. Kirchhoff‟s law

C. Lenz‟s law D. Faraday‟s law 9. The potential difference across a battery, a generator or other source of electric energy when it is not connected to any external circuit is called its ________. A. electromechanical force B. electrostatic force C. electromotive force D. internal resistance 10. What is defined as the luminous flux per unit area? A. Luminous intensity B. Luminous efficiency C. Illumination D. Lumen 11. What refers to the ratio between the speed of light in free space and its speed in a particular medium? A. Index of refection B. Total internal reflection C. Index of dispersion D. Index of refraction 12. “The ratio of the sines of the angles of incidence and refraction is equal to the ratio of the speeds of light in the two media”. This statement is known as ________. A. Huygen‟s principle B. Snell’s law C. Maxwell‟s hypothesis

D. Doppler‟s effect 13. The emission of electrons from a metal surface when light shines on it is called _______. A. Absorption effect B. Spectrum emission C. Quantum effect D. Photoelectric effect 14. If the forces acting on a falling body balance one another, the body continues to fall at a constant velocity. What is thus constant velocity called? A. Instantaneous velocity B. Free-falling body C. Gravitational velocity D. Terminal velocity

B. any torque acting on it C. velocity D. acceleration 18. The centripetal acceleration of a particle in uniform motion is __________ to the radius of its path. A. directly proportional B. equal C. inversely proportional D. not related to any way

A. Kelvin stress B. Hydraulic stress C. Thermal stress D. Humid stress 23. The English term “slug” is a unit of A. mass B. force C. weight D. energy

19. In a simple harmonic motion there is always a constant ratio between the displacement of the mass and its _______. A. speed B. acceleration C. period D. mass

24. An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies after the encounter is ____ to their total kinetic before the encounter A. Equal B. Not equal C. Less than compared D. Greater than compared

16. If you double the mass of a cart while undergoing constant unbalanced force the acceleration will be ________. A. double B. increased fourfold C. half as much D. one-fourth as much

20. If the buoyancy of an object exceeds to weight, the object ______________ A. tends to sink B. tends to rise C. A or B D. none of the above 21. What happens to wave velocity as it passes from the ionosphere? A. increases B. remain the same C. decreases D. not a factor

25. In mechanics, it refers to the force that makes a body followed a curved path. A. Centripetal force B. Normal force C. Gravitational force D. Centrifugal force 26. An object in equilibrium may have the following EXCEPT: A. Any force acting on it B. Any torque acting on it C. Velocity D. Acceleration

17. An object in equilibrium may not have A. any force acting on it

22. Stresses arising when a change in temperature affects the original length of a body

27. Light traveling at some angle as it moves from water into the air is refracted away

15. What is the velocity of light in meters per second? A. 3 x 10^6 B. 3 x 10^9 C. 3 x 10^7 D. 3 x 10^8

from the normal as it enters the air, so the fish you see under water is actually A. Above the refracted image B. Below the refracted image C. Beside the refracted image D. In the same place as the refracted image 28. It is the tendency of a body at rest to remain at rest, and of a body in motion to continue moving with unchanged velocity. A. Inertia B. Mass C. Moment of Inertia D. Moment of Mass 29. These are forces whose lines of action all pass through a common point. A. Concurrent forces B. Coplanar forces C. Reaction forces D. Parallel forces 30. It is a tangential force acting on an object that opposes the sliding of that object across an adjacent surface with which it is in contact. A. Normal force B. Frictional force C. Perpendicular force D. Opposing force 5. A system that can exchange neither

31.) Find the rate at which pulses will propagate aong a string that has mass per unit length of 150g/m when it is under tension A.13.85 m/s B. 15.38 m/s C.14.15 m/s D.18.26 m/s 32.) A Horizontal string 4m long has a mass of 20 grams. What is the tension on the string if the wavelength of a 100hz wave on the string is 40cm?

source that emits 800hz. Assuming that the listener is directly at the jet’s plane path, what sound frequency is heard before the jet plane pass the listener? A. 1400 Hz B. 830 Hz C. 1333.33 Hz D. 1420.22Hz

B. 800 N

36.) A jet plane flying at Mach 0.4, carries a sound source that emits 800hz. Assuming that the listener is directly at the jet’s plane path, what sound frequency is heard before the jet plane pass the listener?

C.1415 N

A. 571.43 Hz

D.1826 N

B. 830 Hz

33.) What is the velocity of sound at room temperature which is at 27 deg Celsius?

C. 600 Hz

A.1385 N

A. 349 m/s B. 347.1 m/s C.390 m/s N D. 348.2 m/s 34.) What is the frequency of a 4cm sound wave in air? Speed of sound is 332 m/s A. 840 Hz B. 830 Hz C. 860 Hz D. 835 Hz 35.) A jet plane flying at Mach 0.4, carries a sound

D. 1420.22Hz 37.) A light ray is incident at an angle of 20 deg on the surface between air and water. At what angle does the refracted rray make with the perpendicular to the surface when the ray is incident from the air side? Air=1 Water=1.333 A. 13.12 deg B. 15 deg C. 9 deg D. 14.87 deg

38.) A light ray is incident at an angle of 25 deg on one side of glass plane. At what angle will the light ray emerges from the other side of the glass plate? Glass and air is 1.6 and 1 respectively. A. 13.12 deg B. 15.3 deg C. 9 deg D. 16 deg 39.) What is the index of refraction of a certain medium if the speed of light in that medium is only half the speed of light of the vacuum? A. 2 B. 1.85 C. 2.21 D. 1.8 40.) A flint glass plate(n=1.8) has a thickness of 20mm. How long will it take for a pulse of light to pass through the glass plate? A. 4.2 x 10^-10 s B. 3.2 x 10^-10 s C. 1.2 x 10^-10 s D. 2.2 x 10^-10 s 41.) A ray of light passes from the heavy flint glass to water. What is the critical angle for this ray of light to pass the glass? Flint glass=1.650 and water=1.33 A. 50.81 deg

B. 51.71 deg C. 52.81 deg D. 53.71 deg 42.) A uniform steel beam is 12 feet long is suspended from one end by a construction crane. Determine the period of oscillation of the beam. A. 3.13 sec B. 4.13 sec C. 5.13 sec D. 6.13 sec 43.) A 5-lb weight hangs at the end of a spring (k=30 lb/ft). at what frequency will it vibrate if the weight is displaced slightly and released? A. 2.86 Hz B. 2.46 Hz C. 3.86 Hz D. 1.86 Hz 44.) The mariana Trench, which is also known as the Philippine Deep measures 10863 m depth. What is the pressure at the bottom of the Mariana Trench? Use specific gravity of sea water=1.03 A. 1.320x10^8 Pa B. 1.098x10^8 Pa C. 1.500x10^8 Pa D. 1.320x10^8 Pa

45. What is the absolute pressure (in Pa) if a pressure gauge registers 60 psig in a region where the barometer is 14.30 psia? A. 530128 Pa B. 512283 Pa C. 541290 Pa D. 521830 Pa 46. An iceberg(sp.gr.=0.92) floats in seawater (sp.gr=1.03). What percentage is the visible volume (volume of the iceberg above the surface) to the total volume of the iceberh? A. 85% B. 87% C. 80% D. 89% 47. A 2000-kg truck accelerates from the 20kph t 120kph in 10 seconds. Find its engine’s power output in watts. A. 2666 watts B. 2999 watts C. 2888 watts D. 2777 watts 48. The elevator at Excel Review Center’s building is powered by and electric motor with an output of 10kW. Determine the minimum time required for its to rise the 18m from the ground floor to roof deck, if the total mass of the loaded elevator is 800kg. A. 13.22 sec B. 14.13 sec C. 15.68 sec D. 16.80 sec

49. During a race, Jan Micheal’s sport car develops a 250 hp at 4000 rpm. What is the amount of torque exerted on the crankshaft? A. 328.25 ft-lb B. 342.78 ft-lb C. 332.12 ft-lb D. 350.80 ft-lb 50. Tiger woods hit a golf ball at a velocity of 80 m/s. The head of his club was in contact with the 50g ball of 0.4 ms. What is the average force acting on the golf ball during impact? A. 25 kN B. 20 kN C. 10 kN D. 15 kN 51. An apple can provide a person about 20000J of work. To what height can a 50-kg man climb uptairs of he eats one apple? A. 36.8 m B. 38.6 m C. 40.8 m D. 42.6 m 52. Using a wheel and axle, a 500N load can be raised by a force of 60N applied to the rim of the wheel. What is the efficiency of the machine if the radii of the wheel and axle are 80cm and 5cm, respectively? A. 50% B. 52% C. 54% D. 56%

53. A rubber ball is dropped to the floor from a height of 3m. It rebounds to a height of 1.8m. what is the coefficient of restitution. A. 0.625 B. 0.825 C. 0.665 D. 0.775 54. The wavelength of sound wave in a certain material as measured is 18cm. The frequency of the wave is 1900Hz. Compute the speed of sound wave? A. 342 m/s B. 400 m/s C. 542 m/s D. 300 m/s 55. A horizontal cord 5m long has a mass of 2.5 grams. What must be the tension in the cord if the wavelength of a 120Hz wave on it is to be 50cm? A. 1.50 N B. 1.80 N C. 2.50 N D. 4.30 N 56. A 3-m string is driven by a 240Hz vibrator at its end. Determine the speed of transverse waves on the string if its four segments? A. 340 m/s B. 360 m/s C. 430 m/s D. 420 m/s 57. A guitar string 30cm long resonates in its fundamental to a frequency of 250Hz. What is the tension in the string if 80cm of the string weighs 0.80 grams? A. 20N

B 30N C. 10N D. 40N 58. A piano string with a length of 1.17 m and a mass of 21 g in under tension of 6.4x10^3 N, what is the fundamental frequency? A. 225 Hz B. 187 Hz C. 255 Hz D. 290 Hz 59. A rope of 4ft long weighs 0.7 lb. A blow on the rope produces a transverse wave. Determine the velocity of the wave considering that the tension is 40lb. A. 75.8 ft/s B. 95.7 ft/s C. 78.5 ft/s D. 85.5 ft/s 60. What is the relative intensity level of sound in decibles if its intensity is 3x10^-7 W/cm^2? A. 94.8 B. 78.7 C. 80.5 D. 75.4

ECE198L SALE, MHIKO I. GEAS SET3 THERMODYNAMICS

1. The term “thermodynamics” comes from Greek words “therme” and “dynamis” which means _______. A. Heat power B. Heat transfer C. Heat energy D. Heat motion 2. The term “thermodynamics” was first used in 1849 in the publication of a. A. Rudolph Clausius B. William Rankine C. Lord Kelvin D. Thomas Savery 3. What law asserts that energy is a thermodynamic property? A. First law of Thermodynamics B. Second law of Thermodynamics C. Third law of Thermodynamics D. Zeroth law of Thermodynamics 4. What law asserts that energy has quality as well as quantity? A. First law of Thermodynamics B. Second law of Thermodynamics C. Third law of Thermodynamics

D. Zeroth law of Thermodynamics 5. What is defined as the energy required to raise the temperature of a unit mass of a substance by one degree? A. Latent heat of fusion B. Molar heat C. Specific heat capacity D. Specific heat 6. The ______ of a substance is the amount of heat that must be added or removed from a unit mass of the substance to change its temperature by one degree. A. Latent heat of fusion B. Molar heat C. Specific heat capacity D. Specific heat 7. What is defined a region in space chosen for study? A. Surroundings B. System C. Boundary D. Volume 8. The first law of thermodynamics is based on which of the following principles? A. Conservation of mass B. Conservation of energy C. Action and reaction D. The entropy-temperature relationship 9. What is the mass or region outside the system called? A. Surroundings B. Boundary C. Volume D. Environment

10. A system which consists of fixed amount of mass and no mass can cross its boundary called _____. A. Equilibrium system B. Thermal equilibrium system C. Open system D. Closed system 11. A system in which even energy is not allowed to cross the boundary is called ____. A. Closed system B. Exclusive system C. Isolated system D. Special system 12. A system in which there is a flow of mass is known as _____. A. Equilibrium system B. Isolated system C. Open system D. Closed system 13. If there is no heat transferred during the process, it is called a ______ process. A. Static B. Isobaric C. Polytropic D. Adiabatic 14. How are thermodynamic properties classified? A. Physical and chemical B. Intensive and extensive C. Real and imaginary D. Homogeneous and heterogeneous 15. The thermodynamic properties that are independent on the size of the system is called _____. A. Extensive property B. Intensive property

C. Open property D. Closed property 16. The thermodynamic properties that are dependent on the size or extent of the system is called ____. A. Extensive property B. Intensive property C. Open property D. Closed property 17. What states that if two bodies are in thermal equilibrium with a third body, they are also in equilibrium with each other? A. Zeroth law of thermodynamics B. First law of thermodynamics C. Second law of thermodynamics D. Third law of thermodynamics 18. 1 British thermal unit (BTU) is equivalent to how many joules? A. 1016 B. 1043 C. 1023 D. 1054 19. What is the thermodynamic temperature scale in the SI system? A. Kelvin scale B. Celsius scale C. Fahrenheit scale D. Rankine scale 20. What is the thermodynamic temperature scale in the English system? A. Kelvin scale B. Celsius scale C. Fahrenheit scale D. Rankine scale

21. What temperature scale is identical to the Kelvin scale? A. Ideal gas temperature scale B. Ideal temperature scale C. Absolute gas temperature scale D. Triple point temperature scale 22. The unit “pascal” is equivalent to ______. A. N/m^2 B. N/m C. N-m D. N-m^2 23. Which of the following is NOT a value of the standard atmospheric pressure? A. 1 bar B. 1 atm C. 1 kgf/cm^2 D. 14.223 psi 24. What is the SI unit of pressure? A. Atm B. Bar C. Pa D. Psi 25. 1 bar is equivalent to how many pascals? A. 10^3 B. 10^4 C. 10^5 D. 10^6 26. 1 atm is equivalent to how many pascals? A. 101,325 B. 101,689 C. 101,102 D. 101,812 27. What is considered as the actual pressure at a given

position and is measured relative to absolute vacuum? A. Gage pressure B. Absolute pressure C. Atmospheric pressure D. Vacuum pressure 28. What is the pressure below atmospheric pressure called? A. Gage pressure B. Absolute pressure C. Atmospheric pressure D. Vacuum pressure 29. The difference between the absolute pressure and the atmospheric pressure is called the _____ pressure. A. Gage B. Normal C. Standard D. Vacuum 30. Which of the following is NOT an instrument used to measure pressure? A. Bourdon tube B. Pitot tube C. Aneroid D. Manometer 31. A chef heated a bowl of soup of 30 deg C to 45 deg C, what is the change in the temperature in the Fahrenheit scale? A. 15 deg F B. 27 deg F C. 30 deg F D. 42 deg F 32. What is the new length of a bar made of pure gold at 75 ℃ if it has a length of 0.3 meters at 10℃? A. 3.00273 B. 3.0273 C. 3.00385 D. 3.0385

33.) A steel tank is filled with 15 gallons of gasoline when the temperature is 22 deg . the tnak and gasoline inside are then heated by the Sun’s rays to a temperatre of 40 deg C. How much of the gasoline will spill from the tank? Steel=12x10^-6 gasoline=0.95x10^-3 A. 0.13889 gallons B. 0.1938 gallons

Calories each), scrambled egg(75 Calories) and 2 pieces of bread(70 Calories each). Aside from that, he also drank 1 glass of milk(165 Calories). Believing that this is getting him fat, he wishes to do an equivalent amount of work at school by using the stairs on his way to the classrooms. Assuming that one step of the stairways is 0.2 meters, how many steps must he make?

C. 0.2479 gallons A. 5000 steps D. 0.2565 gallons B. 6500 steps 34.) What is the increase in temperature necessary for a hydrogen gas, initially at 0℃, to increase its volume by 5% at constant pressure? A. 4.5℃ B. 7.8℃ C. 12.5℃ D. 13.7℃ 35.) On a very hot day in Manila, an oil tanker loaded 50,000 liters of fuel. It traveled to Baguio, which is 20K colder than Manila How many liters were delivered to Baguio? Gasoline=0.95x10^3 A. 49,000 liters B. 49,050 liters C. 50,950 liters D. 51,000 liters

C. 8000 steps D. 9600 steps 37.) How much heat(calories) is required to raise the temperature of 5 liters of acetone from 20 deg C to 40 deg C? acetone=0.58g/cm^3, spec. heat of methyl=2118 J/kg-deg A. 25 kcal B. 29 kcal C. 32 kcal D. 40 kcal 38.) A tank contains 2.0 kg of water at 25 deg C. Into this tank, a person dropped a 0.90-kg piece of metal that has temperature of 75 deg C. What will be the equilibrium temperature of the mixture? Spec heat=448J/kg-deg A. 27.3 deg C

36. For a breakfast, a 100 kg ate 2 slices of bacon(35

B. 29.5 deg C

C. 34.6 deg C D. 38 deg C 39.) How much heat is required to raise the temperature of 1 mol of nitrogen gas by 1 degree at constant temperature? (Cp = 1037 J/kg-℃; Cv = 749 J/kg℃) A. 25 J B. 29 J C. 38 J D. 45 J 40.) A 5 liter amount of water at a temperature of 25℃ will be raised to what temperature if 3000 calories of heat is applied? A.25.05 ℃ B.25.15℃ C.25.30℃ D.25.45℃ 41.) How much heat is required to transform a 500 gram ice at -15 deg C into liquid water at 55 deg C? A. 280 kJ B. 292 kJ C. 304 kJ D. 453 kJ 42.) Using the first law of thermodynamics, what is the change in internal energy of a substance if it does 300 J of work while absorbing 450 J of heat? A.150J B.300J C.450J D.750J 43.) What is the specific heat of an unknown substance if the temperature of 30℃

doubles after applying an energy rated at 50 kilocalories? A.1.67 kcal/kg℃ B.2.14 kcal/kg℃ C.2.56 kcal/kg℃ D.3.12 kcal/kg℃

conductivity is 205 J/m-sdeg/.

44.) What is the change in internal energy of an ideal gas if it expands by 20 liters after applying 5kJ of heat? Assume the this is constantpressure process.

48. What temperature gradient must be applied to a gold bar(2 cm x 4cm) if the heat flow is to be 100J/s? gold conductivity=397 J/m-sdeg. A. 245 degC/m B. 289 degC/m C. 315 degC/m D. 362 degC/m

A. 2.03 kJ B. 2.97 kJ

A. 4.62 cal B. 8.97 cal C. 15.75 cal D. 19.33 cal

C. 3.75 kJ D. 5 kJ 45. Determine the work done on a 0.5 m^3 gas if it is compressed at constant temperature to 0.3 m^3. When the gas was at its initial state, the pressure was 5 atm while the temperature was 20℃ room temperature. A. -24.56 kJ B. -25.13 kJ C. -25.88 kJ D. -26.88 kJ 46. How much heat is required to convert 4 kg of water at 20℃ into vapor at 100 ℃. A.1.34 kJ B.1.34 kcal C.3.17 kJ D.3.17 kcal 47. An aluminum rod has a diameter of 4 cm and a length of 8cm. One end of the rod is placed in an ice bath. How much heat in calories is conduct through the bar in 1 minute? The thermal

49. A gas cylinder contains 15 L of oxygen gas at room temperature and 15 atm. The Temperature is doubled and the volume is reduced to half of the original volume. What is the pressure (atm) assuming the gas resembles ideal condition A. 7.5 atm B. 15.8 atm C. 32.1 atm D. 44.6 atm 50. An ideal gas at 100 deg F has a pressure of 32psig. It is heated in fixed, rigid and closed vessel to raise its temperature of 160 deg F. what is its final pressure A. 24 psia B. 52 psia C. 64 psia D. 67 psia 51. What is the rms velocity of oxygen gas molecules at room temperature? A. 274 m/s

B. 478 m/s C. 696 m/s D. 7713 m/s 52. What is the mass of air inside a closed vessel with dimensions 2.5m x 5m x 8m at a temperature and pressure of 50degC and 500000 Pa, respectively? A. 144 kg B. 298 kg C. 456 kg D. 540 kg 53. An engine transfers 2500J of energy from a hot reservoir during the cycle and transfers 2000J of energy to the cold reservoir. What s the power output of the engine if it operates at 2000 revolutions per minute assuming ther is a one thermodynamics cycle per revolution? A. 16.67 kW B. 23.33 kW C. 43.33 kW D. 46.67 kW 54. What is the coefficient of performance of a brand new refrigerator which as a capacity of 3500 W and an input rating of 750W? A. 3.56 B. 4.67 C. 5.87 D. 8.93 55. What is the efficiency of a Carnot engine operating between 500degF and 1700degF? A. 32% B. 44% C. 56% D. 68%

56. A steam engine has a boiler that operates at 600 K. The energy from the burning fuel changes water to steam, and this steam then drives the piston. The cold reservoir’s temperature is that of the outside air, which is estimated to be 300 K. What is the maximum thermal efficiency of this steam engine? A. 50% B. 75% C. 80% D. 100% 57. A piston-cylinder device contains liquid-vapor mixture at 300 K. During a constant pressure process, 800 kJ of heat was transferred to the water. As a result, part of the liquid in the cylinder vaporized. The changed in entropy of the water during the whole process is closest to which of the following values? A.0.38 B.1.38 C.2.67 D.4.22 58. A piano string with a length of 1.17 m and a mass of 21 g in under tension of 6.4x10^3 N, what is the fundamental frequency? A. 225 Hz B. 187 Hz C. 255 Hz D. 290 Hz 59. A high-altitude balloon that is designed to carry a 500-kg payload to an altitude of 30km is filled with 400 cubic meters of helium at sea level when the temperature is

15 degC. How many times will the volume of the balloon increase when it reaches maximum altitude? At an altitude of 30 km, the pressure is about 1% of the sae level pressure and temp may reach as low -50 centigrade. A. 34 times B. 55 times C. 62 times D. 77 times 60. What is the sonic velocity at 50,000 feet altitude in the upper standard atmosphere with a frequency of -70degF and a pressure of 1.7psi? A. 560 ft/s B. 770 ft/s C. 840 ft/s D. 970 ft/s

ECE198L SALE, MHIKO I. GEAS SET4 Engineering Mechanics

1. In Mechanics, what refers to the study of stationary rigid body? A. Statics B. Kinectics C. Associative D. Commutative 2. What is the study of the rigid body in motion under the action of forces. A. Consistent B.Strength of mamterials C.Dynamics D. Kinematics 3. What is the branch of engineering mechanics which refers to the study of rigid body in motion without reference to the force the causes the motion. A. Dynamics B. Statics C. Kinematics D. Kinetics 4. What refers to the force that holds part of the rigid body together. A. Natural force B. External force C. Internal force D. Concentrated force

5. What refers to a pair of equal, opposite and parallel forces? A. Couple B. Moment C. Torque D. All of the above 6. What is concurrent force system? A. All of forces act at the same point B. All forces have the same line of action C. All of forces are parallel with one another. D. All forces are in the same place. 7. When will a three-force member be considered in equilibrium? A. When the sum of the two forces equal to the third force. B. When they are cocurrent or parallel C. When they are coplanar D. All of the above. 8. A roller support has how many reactions? A. None B. 1 C. 2 D. 3 9. A link or cable support has how many support? A. None B. 1 C. 2

D. 3 10. A build-in, Fixed support has how many reactions and moment? A. 1 reaction and 1 moment B. 2 reactions and 1 moment C. 1 reactions and 2 moments D. 2 reactions and no moment 11. Which has one moment? A. Fricitionless guide B. Pin connection C. Fixed support D. Roller 12. What is the science that describes and predicts the effect on bodies at rest or in motion by forces acting on it. A. Engineering Mechanics B. Theory of structures C. Mechanics of Materials D. Strength of Materials 13. What refers to a negligible body when compared to the distances involved regarding motion. A. Particle B. Atomic substance C. Element D. Quarks 14. The resulting force of a distributed load is always acting at:

A. the center of the beam subjected to the distributed load B. the centroid of the area of the loading curve C. the 1/3 point from the higher intensity side of the loading curve D. the 2/3 point from the higher intensity side of the loading curve. 15. What equilibrium states exists when a body remains in its displaced state after being moved from its original equilibrium position? A. Neutral B. Stable C. Static D. Dynamic 16. What are the three types of equilibrium A. Neutral, Stable, Unstable B. Static, Kinetic, Dynamic C. Kinetic, Kinematic, Dynamic D. Static, Kinetic, Kinematic 17. What refers to the branch of mathematics which deals with the dimensions of quantities? A. Unit Analysis B. Dimension analysis C. system analysis D. Homogeneity analysis 18. What is “simple beam”? A. A beam supported only at its ends

B. A beam supported only. C. A beam with two supports D. A beam with only one support at the mid span. 19. What is the assumption is used in the analysis of uniform flexible cable? A. Cable is flexible B. Cable is inextensible C. The weight og the cable is very small when compared to the loads supported by the cable D. All of the above. 20. The forces acting internally on rigid bodies are due to____. A. electronics forces holding the molecules together. B. intermodular forces C. compressive and tensile forces holding the bodies together D. atomic bondage 21. A beam with more than one supports is called ___. A. Cantilever beam B. Simple beam C. Complex beam D. Continuous beam 22. A truss consisting of coplanar members is called ____. A. Plane truss B. space truss C. ideal truss D. rigid truss

23. A truss consisting of noncoplanar members is called ___. A. Plane truss B. space truss C. ideal truss D. rigid truss 24. What method of determining the bar force of a truss of only few members are required? A. Method of joints B. Method of section C. Maxwell Diagram D. Method of Superposition

25. The frictional force is ____ area of the contact. A. inversely proportional to B. dependent on C. independent on D. directly proportional to 26. What is usually used to move heavy loads by applying a force which is unusually smaller that the weight of the load? A. Axle B. Incline Plane C. Wedge D. Belt 27. The angle of inclined plane of a jack screw is also known as A. angle of thread B. angle of lead C. angle of friction D. angle of pitch

28. Center of gravity for a two dimensional body is the point at which the entire ___ acts regardless of the orientation of the body. A. mass B. weight C. mass or weight D. volume 29. What is the unit mass of moment of inertia? A. kg-m^4 B. kg-m^3 C. kg-m D. kg-m^2 30. The principle of kinetics of particles are derived from which law? A. Newton’s first law B. Newton’s second law C. Newton’s third law D. d’Alembert’s principle 31. What is the maginitdue and direction of the resultant of two forces, both with different directions with a 50N magnitude, but with different directins, first one 30deg while the other is 50deg? A. 98.48N at 40deg B. 98.48N at 10deg C. 98.48N at 10deg D. 98.48N at 10deg 32. If the resultant of two vectors is 2kN and is acting vertically to the south, what is the magnitude and direction of the second force

is he first force is 10kN acting directly to the east? A. 2.24kN,63.49 south of west B. 2.24kN,63.49 west of north C. 2.24kN,63.49 south of east D. 2.24kN,63.49 east of north 33.) If two forces, 30kN and 20kN are separated by 50 degrees, what is the resultant force? A. 43.54kN B. 44.45kN C. 45.51 kN D. 46.64 kN 34.) An airplane has speed of 120 miles per hour is heading in a direction due north. There is a crosswind of 30 miles per hour 15 degrees east of north. What is the speed of the airplane and what its direction relative to the ground? A. 133.201 mph to the north B. 133.201 mph to the north, 3.23 deg east of north C. 133.201 mph to the west D. 133.201 mph to the east 35.) Given three vectors: Vector 1 is 500 N at 30 deg, Vector 2 is 300 N at 150 deg and Vector 3 is 400 N at 270, what is the magnitude of the resultant vector? A. 137.21 N B. 143.71 N C. 173.21 N D. 177.31 N

36. If you are given two forces at right angles to each other, what os the magnitude of the resultant force is the two forces are each 50N? A. 0 B. 50N C. 70.7 N D. 100N 37.) A 10kg- box is being pulled by a 50N force that is inclined 20 deg with respect to the horizontal What is the component of the force that is parallel with the surface in whuc te box is being pulled? A. 17.10 N B. 27.10 N C. 36.98 N D. 46.98 N 38.) If you are given two vectors: A= 5i + 8j + 3k and B= 35i + 4j +-9k, what is the angle between the two vectors? A. 30deg B. 45deg C. 35deg D. 60deg 39.) What is the dot product of the vectors: A=6i+4j-5k and B=5i+3j+7k A. 4 B. 5 C. 6 D. 7

40.) In a 10 feet cantilever beam, find the reactions if there are two forces, each 50lb, applied at a point 3 feet and 6 feet from the end of the bean with the support/ A.HA:0; VA;100lb;MA=300lb-ft B. HA:0; VA;100lb;MA=450lb-ft C. HA:100; VA=0lb;MA=300lb-ft D. HA:100; VA;100lb;MA=300lb-ft 41.) What is the reaction at the roller if one endof a 10 meter beam is attached to a hinge while the other end is attached to a roller that is inclined to the horizontal at anangle of 20deg? Ther is a 50jn force concentrated halgwa across the beam. A. 9.81 kN B. 25kN C. 26.6kN D. 29.9kN 42.) Find the reactions of a simply supported beam that is 10 m in length with a concentrated load of 250 N, 4 meters from the left end, and a uniformly distributed load of 75N/m. A. 400N and 600N B. 425N and 575N C. 450N and 600N D. 475N and 525N 43.) Find the reacitns of a simply supported beam with a length of 8m if it has a uniformly varying load starting at 30N/m at the left end and goes up to 60 N/m at the right end.

A. 120N and 240 N B. 140N and 220 N C. 160 N and 200 N D. 180N and 180 N

that the angle that the rope makes with the horizontal is 7 degrees. What is the tension In the rope?

44.) A block weighs 100kg and is resting on a plane that is onlcined to tehe horizontal at an angle of 20 deg. What is the force that tends to move the block down the plane?

A. 1620N B. 2580N C. 2750N D. 3220N

A. 336N B. 632N C. 922N D. 982N 45. A 4000-lb truck is stationary. What are the normal forces exerted on the fron tire and rear tire, respectively, if both tires are separated by 15 ft and the rear tire is 5 ft from the end of the 25 foot truck. A. 1500lb, 2500lb B. 2000lb, 2000lb C. 2500 lb, 1500lb D. 1000lb, 3000lb 46. To maintain the box in equilibrium, a 75 N tension in is required that is inclied at 45 degrees with respect to the horizontal. Calculate the value of the horiznontal equilibrant. A.53.03 B.56.75 C.62.83 D.75 47. An 80kg acrobat is dangerously standing n balance at the middle of a tightly stretched rope such

48. A horizontal rod is 10 ft long. a 10lb force is applied vertically downwards 3ft from the right end. What is the sim of magnitudes of the torque about the two ends of the rod? A. 10 lbft B. 30 lb-ft C. 70 lb-ft D. 100 lb-ft 49. A block is placed in an inclined plane at an angle teta with respect to the horizontall. What is the value of teta such that the block will start to move doen the plane at a constant velocity? Coefficient of fricitn is 0.45 and the mass of the block is 100kg. A. 24.2 deg B. 28.9 deg C. 33.1 deg D. 34.9 deg 50. Solve the coefficient of friction between a 1500kg block and the surface if the block is being pulled along the surface at uniform speed wit a rope that is inclinedat 30deg assume that the tension in the rope is 500N A. 0.03 B. 0.08

C. 0.15 D. 0.30 51. Find the coefficent of static friction for a 50 lbf block resting on a horizontal surface being pulled horizontally using a rope if it needs around 6 lb of tension to keen on moving once it already started to move. A. 0.12 B. 0.2 C. 0.25 D. 0.30 52. For the block on the previous problem what is the coefficient of kinetic friction once it is now moving at constant velocity? A. 0.08 B. 0.1 C. 0.12 D. 0.18 53. A fisherman’s boat moves at a speed of 15 kph in calm water. The fisherman steers the boat staraight across a river in which the current is 7kph. What is the velocity of the boat A. 85 kph B. 13.4 kph C. 16.6 kph D. 18.9 kph 54. What is the coefficient of the starting friction if the force required to over a mass of 100 kg over a rough surface is around 460N? A. 0.35 B. 0.47 C. 0.52 D. 0.59

55. Calculate the mass moment of inertia of a cylinder wit hraduis of 4m and has a mass of 12kg? A. 96 B. 192 C. 288 D. 312 56. Solve for the second moment of area of a circle with respect to an axis 1 meter away from the circumference. The radios of the circle is 3 units. A. 257 B. 516 C. 624 D. 728 57. An 800 N box hangs on a vertical rope. A man pushes the box horizontally ultil the rope now hangs 45 deg. With respect to the vertical. Solve for the tension in the rope. A.1131 B.1435 C. 1600 D. 1895 58What is the mass moment of inertia of a ball if it has a mass of 2kg, radius of 0.3 metrs and is rotating at a speed of 15 rpm A. 0.036 B. 0.048 C. 0.060 D. 0.072 59. A ball with a mass of 5kg is suspended from a ceiling by any means of a cord. When a horizontal force F is applied to the ball the ball hangs motionless with the cord making an angle of 35deg with respect to the

vertical. What is the magnitude of the force F.? A. 32.57 B. 34.35 C. 47.68 D. 51.43 60. What is the mass moment of inertia of a 15 kg solid cone hwose circular base has a diameter of 10 meters A. 112.5 B. 156.7 C. 254.8 D. 268.5

ECE198L Sale, Mhiko GEAS SET 5 STRENGTH OF MATERIALS 1. What is the ratio of the transverse strain to the corresponding axial strain in a body subjected to uniaxial stress? A. Poisson’s ratio B. Euler‟s ratio C. Refractive index D. Dielectric index

2. What are the four basic forms of deformation of solid bodies? A. Tension, compression, bending and twisting B. Tension, compression, elongation and bending C. Tension, compression, plastic and elastic D. Tension, compression, elongation and torsion 3. What is a structural member supported horizontally and carries transverse loading? A. Beam B. Column C. Arch D. Shaft 4. What refers to a slender member which prevents parts of a structure moving towards each other under compressive force? A. Tie B. Column C. Panel D. Strut

5. What refers to a slender member which prevents parts of a structure moving towards each other under compressive force? A. Tie B. Column C. Strut D. Arch

10. Which of the following materials has the least modulus of elasticity? A. Steel B. Glass C. Copper D. Aluminum

6. What refers to the point in which the bending moment changes sign through a zero value? A. Critical point B. Point of inflection C. Point of contraflexure D. Point of zero stress

11. Within elastic limit, the shear stress is proportional to shear strain. What is the constant of proportionality of this statement called? A. Modulus of rigidity B. Modulus of elasticity C. Young‟s modulus D. Bulk modulus

7. What is the unit of strain? A. Pascal B. Unitless C. N-m D. N-m/s

12. What is the unit of the modulus of elasticity? A. N-m B. Unitless C. Pa D. N-m/s

8. Volumetric stain is the: A. change in volume per unit time B. square root of difference of original volume and change in volume C. original volume minus change in volume D. ratio of change in volume to original volume

13. Within elastic limit, the volumetric strain is proportional to the hydrostatic stress. What is the constant that relates these two quantities called? A. Modulus of rigidity B. Modulus of elasticity C. Young‟s modulus D. Bulk modulus

9. What refers to the stress in the material at the elastic limit? A. Working stress B. Yield stress C. Ultimate stress D. Maximum stress

14. What is another term for modulus of rigidity? A. Shear modulus B. Young‟s modulus C. Bulk modulus D. Modulus of elasticity 15. How many times greater is the plastic range

of strain as compared to the elastic range of strain? A. 100 B. 200 C. 300 D. 400 16. What does it means when the material is said to be “yielding”? A. The material has pass through plastic range and enter the elastic range B. The material has pass through elastic range and enter the plastic range C. The material is in the elastic range only D. The material is in the plastic range only

17. What refers to the parallel axis theorem for second moment of area? A. Mohr‟s theorem B. Steiner’s theorem C. Maxwell‟s theorem D. Young‟s theorem 18. The elastic deformation of a material is: A. directly proportional to cross-sectional area of the material B. inversely proportional to the modulus of elasticity of material C. inversely proportional to the force acting on the material D. inversely proportional to the initial length of the material 19. The strain energy of a member is:

A. inversely proportional to the square of the force acting on the member B. directly proportional to the modulus of elasticity C. inversely proportional to the cross-sectional area of the member D. inversely proportional to the initial length of the member

20. Stiffness is: A. ratio of force to deformation B. ratio of force to modulus of elasticity C. ratio of product of crosssectional area and initial length to deformation D. ratio of initial length to cross-sectional area 21. Which of the following substances has the least average coefficient of linear thermal expansion? A. Copper B. Concrete C. Steel D. Tin 22. Steel has a modulus of elasticity of _____ MPa. A. 200 B. 2,000 C. 20,000 D. 200,000

23. What is the maximum moment of a beam supported at both ends and carries a uniform load of w throughout its entire length? A. wL / 2

B. wL / 8 C. wL2 / 8 D. wL2 / 4

24. ____ is the stress beyond which the material will not return to its original shape when unloaded but will retain a permanent deformation. A. Elastic limit B. Proportional limit C. Yield limit D. Yield strength 25. All are methods of determining the bar force of a truss member except one. Which one? A. Method of joints B. Method of section C. Method of virtual work D. Maxwell diagram 26. What is the range of Poisson’s ratio for most metals A. 0.25 to 0.35 B. 0.35 to 0.45 C. 0.10 to 0.25 D. 0.15 to 0.20 27. A cylinder is said to be a “thin-walled” cylinder if the ratio of the wall thickness to the internal diameter of the cylinder is less than _________. A. 1/10 B. 1/5 C. 1/2 D. 1/20

28. The strain energy of a member is: A. inversely proportional to the square of the force acting on the member B. directly proportional to the modulus of elasticity C. inversely proportional to the cross-sectional area of the member D. inversely proportional to the initial length of the member 29. When an axial stress is applied eccentrically to a beam, the combined stress due to compression and bending can be computed by ____________. A. using frame theory B. using finite stress analysis C. adding the compression and bending stresses D. using Maxwell’s diagram 30. What does it means when the material is said to be “yielding”? A. The material has pass through plastic range and enter elastic range B. The material has pass through elastic range and enter the plastic range C. The material is in the elastic range only D. The material is in the plastic range only 31. What is the maximum normal stress on an element of a thin hollow sphere with a radius of 15 inches and a thickness of 0.15 inches that is subjected to an internal pressure of 200 psi

D.88.1 MPa A.5000 psi B.7500 psi C.10000 psi D.15000 psi 32.What is the maximum thickness of a steel plate in which a 4.2 inch diameter hole can be drilled? Assume that for this material, the maximum shearing strength is 50 ksi and the maximum compressive strength is 60 ksi. A.1.26 in B.1.53 in C.2.23 in D.2.87 in 33. Solve for the smallest hole diameter that can be drilled on a plate with maximum shear strength of 50 ksi and a maximum compressive strength of 60 ksi. Assume that the thickness of the plate is half an inch. A.1.22 in B.1.67 in C.2.45 in D.2.88 in 34. For a steel shaft with a cross sectional diameter of 100 mm that is installed in between fixed walls with a distance of 4 meter, solve for the stress in the shaft if the temperature changes by 30 degrees. For steel, the coefficient of linear expansion is 11.7x10-6 /C A.35.6 MPa B.53.4 MPa C.70.2 MPa

35.What is the force required in you want to drill a 0.75-in hole on a 1-in steel plate? For this specific plate, the maximum shearing stress and the maximum compressive stress is 30,000 psi and 60,000 psi, respectively. A.40,000 lb B.63,000 lb C.71,000 lb D.84,000 lb 36. If a bar is under a stress of 250 MPa, determine the elongation assuming it is made from steel that is 10 m long. A.12.5 mm B.23.1 mm C.43.5 mm D.50.1 mm 37. What is the increase in length of a steel pipe, 10 m long, if it’s temperature is doubled from 20 degree Celsius? A.2.34 mm B.3.45 mm C.4.13 mm D.5.86 mm 38. What is the diameter of a bolt if it is used to join two steel bars together under a tensile force of 10 kN if the maximum bearing stress if 55 MPa? Assume that the thickness of the plate is 10 mm. A.1.5 mm B.1.8 mm C.2.3 mm D.2.9 mm

39. If a tank in the shape of a sphere with a diameter of 10 m contains gas with a pressure of 50 MPa, what should be the thickness if it is put under stress of 500 MPa? A.125 mm B.250 mm C.350 mm D.400 mm 40. What is the total stress in a 3-m long steel rod with a diameter of 35 mm if it is pulled at both ends by a pair of 3500 N force at 20 ℃ A.33.4 MPa B.48.7 MPa C.50.4 MPa D.53.1 MPa 41.Solve for the maximum internal pressure inside a thin-walled steel cylinder if the maximum stress is 200 MPa. The 30-mm thick container has a diameter of half a meter and has a length of 2.5 m. A.12 MPa B.16 MPa C.20 MPa D.24 MPa 42. What is the section modulus of a rectangle with a diameter of 12 m and a base of 4 m? A.24 m^3 B.96 m^3 C.53 m^3 D.59 m^3 43.Solve for the modulus of elasticity of a material if, during the stress-strain test, it was found to have a stress

45 MPa at a unit deformation of 314x10-3 m. A.143.3 MPa B.153 MPa C.67 MPa D. 126 MPa

minute. Find the amount of torque in its crankshaft. A.202 ft-lb B.244 ft-lb C.218 ft-lb D.263 ft-lb

44. What is the increase in length of a steel pipe, 10 m long, if it’s temperature is doubled from 20 degree Celsius? A.2.34 mm B.3.45 mm C.4.13 mm D.5.86 mm

49. A steel bar 40 ft long has a cross-sectional area of 3 sq. inches. How much is it stretched when supporting a load of 2000 lb. Modulus of elasticity of steel is 29, 000,000 lb per sq. in. A.0.00092 ft B.0.00032 ft C.0.00042 ft D.0.00082 ft

45. If a bar is under a stress of 250 MPa, determine the elongation assuming it is made from steel that is 10 m long. A.12.5 mm B.23.1 mm C.43.5 mm D.50.1 mm 46.What is the section modulus of a beam with a circle cross-section with a 0.85-m radius? A.0.48 m^3 B.0.89 m^3 C.0.22 m^3 D. 0.77 m^3 47. What is the diameter of a bolt if it is used to join two steel bars together under a tensile force of 10 kN if the maximum bearing stress if 55 MPa? Assume that the thickness of the plate is 10 mm. A.1.5 mm B.1.8 mm C.2.3 mm D.2.9 mm 48. A race car develops 200 hp at 4000 revolution per

50. A solid circular shaft generates 100 kW while turning 1.5 rps. Find the twisting moment (in N-m) of the shaft if the allowable shearing stress is 40 MPa. A.10,610 B.11,111 C.12,232 D.21,222 51. A cylindrical pressure vessel is fabricated from steel plates which have a thickness of 20 mm. The diameter of the pressure vessel is 500 mm and its length is 3 m. Determine the maximum internal pressure which can be applied if the stress in the steel is limited to 140 MPa. A.1.12 MPa B.1.36 MPa C.1.22 MPa D.1.33 MPa 52. If a bar is under a stress of 250 MPa, determine the elongation assuming it is

made from steel that is 10 m long. A.12.5 mm B.23.1 mm C.43.5 mm D.50.1 mm 53. Solve for the modulus of elasticity of a material if, during the stress-strain test, it was found to have a stress 45 MPa at a unit deformation of 314x10-3 m. A.143.3 MPa B.153 MPa C.67 MPa D. 126 MPa 54. What is the section modulus of a beam with a circle cross-section with a 0.85-m radius? A.0.48 m^3 B.0.89 m^3 C.0.22 m^3 D. 0.77 m^3 55. For a steel shaft with a cross sectional diameter of 100 mm that is installed in between fixed walls with a distance of 4 meter, solve for the stress in the shaft if the temperature changes by 30 degrees. For steel, the coefficient of linear expansion is 11.7x10-6 /C A.35.6 MPa B.53.4 MPa C.70.2 MPa D.88.1 MPa 56. What is the increase in length of a steel pipe, 10 m long, if it’s temperature is doubled from 20 degree Celsius? A.2.34 mm B.3.45 mm C.4.13 mm

D.5.86 mm 57. What is the total stress in a 3-m long steel rod with a diameter of 35 mm if it is pulled at both ends by a pair of 3500 N force at 20 ℃ A.33.4 MPa B.48.7 MPa C.50.4 MPa D.53.1 MPa 58. If a bar is under a stress of 250 MPa, determine the elongation assuming it is made from steel that is 10 m long. A.12.5 mm B.23.1 mm C.43.5 mm D.50.1 mm 59.What is the section modulus of a beam with a circle cross-section with a 0.85-m radius? A.0.48 m^3 B.0.89 m^3 C.0.22 m^3 D. 0.77 m^3

60. A race car develops 200 hp at 4000 revolution per minute. Find the amount of torque in its crankshaft. A.202 ft-lb B.244 ft-lb C.218 ft-lb D.263 ft-lb

ECE198L Sale, Mhiko I. GEAS SET 6 PHYSICS 2

1.The number 175.00 has how many significant numbers? A.3 B. 5 C.4 D.6 2.How many basic units are there in the International SI units? A.6 B. 8 C.7 D.9 3.What is the standard unit of mass? A.Kilogram B.Gram C.Pound D.Newton 4.What is another term for vector product of two vectors? A.Cross product B.dot product C.Vector product D.plus product 5. Which is NOT a vector quantity? A.Displacement B.Acceleration C.Velocity D.Time 6.The _____ of a particle is defined as its change in position in some time interval. A.Distance

B.speed C.Displacement D.acceleration 7.The rate at which velocity changes with time is known as A.Acceleration B.average speed C.Instantaneous speed D. instantaneous velocity 8.What is used to determine the type of flow of a liquid? A.Reynold’s number B.Froude’s number C.Kutter’s number D.Bernoulli’s number 9.Work is defined as the product of: A.Force and displacement B.displacement and time C.Force and time D.power and time 10.What is the third law of motion? A.Law of inertia B.law of impulse and momentum C.Law of acceleration D.law of reaction 11.What refers to the product of the force and the time during which a force acts? A.Impulse B.power C.Momentum D.energy 12.Momentum is the product of: A.Mass and time B.force and time C.Velocity and mass D. force and mass

13.In mechanics, it refers to the imaginary force that is always pointing outwards of the circular path. A.Centripetal force B. gravitational force C.Normal force D. centrifugal force 14.Which of the following is not an SI derived unit? A.°C B. Pascal C.Joules D. Watt 15.What is the property of matter that causes it to resist a change in its state of motion? A.Weight B.mass C.Inertia D.elasticity 16.One horsepower is equivalent to how many watts? A.550 B.33,000 C.746 D. 250 17.Infrasound refers to sounds whose frequencies are below _____. A.20 Hz B.40 Hz C.30 Hz D.50 Hz 18.What refers to the change in frequency of a wave when there is relative motion between its source and an observer? A.Superposition principle B.Doppler effect C.Shock effect D.wave motion

19.It is the bouncing off of a wave as it hits the barrier. A.Dispersion B. refraction C.Reflection D.incidence 20.Which one states that each point on a wavefront maybe regarded as a new source of disturbance? A.Foucault’s theory B. newton’s wave theory C.Huygen’s principle D. hertz’s theory of wave motion 21.What is the distance from a lens to its focal point called? A.Focal index B. focal length C.Focal factor D. all of the above 22.What refers to the ability of waves to bend around the edges of obstacles in their paths? A.Coherence B.refraction C.Reflection D. diffraction 23.The second law of motion is also known a A.Law of acceleration B.law of interaction C.Law of inertia D. law of momentum 24.What refers to a measure of the energy of sound? A.Intensity B. pitch C.Loudness D.sone

25.In which medium do sound waves travel the fastest? A.Liquids B.gases C.Solids D. vacuum 26.What color has the longest wavelength? A.Orange B.yellow C.Red D. green 27.What color has the shortest wavelength? A.Indigo B. blue C.Violet D. green 28.What is the speed of sound in air at 0 degrees Celsius? A.300 m/s B 332 m/s C.330 m/s D. 338 m/s 29.What is the unit of electric current? A.Volt B. ampere C.Watt D. coulomb 30.What is the unit of luminous intensity? A.Footcandle B.candela C.Lumen D.Lux 31. The wavelength of a source wave in a certain material as measured is 18

cm. The frequency of the wave is 1900 Hz. Compute the speed of sound wave? A. 342 m/s B. 400 m/s C. 542 m/s D. 300 m/s 32. A sound wave on a certain material has wavelength of 10 cm and frequency of 2000 Hz. What is the velocity of sound wave? A.202 m/s B.208 m/s C.212 m/s D.200 m/s 33. What is the velocity of sound t room temperature which is a 27 ℃? A.347.1 m/s B. 345.9 m/s C. 346.8 m/s D. 348.2 m/s 34. Find the angle of refraction of light as a beam of parallel light enters a block of ice at an incident angle of 35 degrees. Use index of refraction of air and ice as 1.0 and 1.31, respectively. A.33 B.32 C.31 D.30 35. What is the index of refraction of a certain medium if the speed of flight in that medium is only half he speed of light in a vacuum? A.2.00

B.1.85 C.2.21 D.1.80 36. A flint glass plate (index of refraction = 1.8) has a thickness of 20 mm. How long it take for a pulse of light to pass through the glass plate? A.4.2x10-10 s B.2.2x10-10 s C.1.2x10-10 s D.3.2x10-10 s

C.11.81 D.11.11

B.35 cm C.40 cm D.45 cm

40. An object is placed 10 cm to the left of the lens that has a focal length of 6 cm. What is the magnification of the lens? A.-1.0 B.-1.5 C.-2.5 D.-2.0

45.Find the location of the image of an object placed 10 cm to the left of the lens that as a focal length of 6 cm. A.13 cm B.15 cm C.12 cm D.14 cm

37. A ray of light passes from the heavy flint glass to water. What is the critical angle for this ray of light to pass the glass? Use index of refraction of heavy flint glass and water as 1.650 and 1.33, respectively. A.50.81 B.51.71 C.52.81 D.53.71

41. Find the frequency of a photon having an energy of 3 eV? A.724 THz B.732 THz C.741 THz D.745 THz

38. A light ray passing through air, strikes a glass surface at an angle of 50 degrees from the normal surface. What is the angle between the glass surface and the reflected light ray? A.42 B.36 C.38 D.40 39. A double convex lens has faces of radii 15 and 30 cm. When an object is 20 cm from the lens, a real image is formed 25 cm from the lens. What is the focal length of the lens? A.12.81 B.12.12

42. A concave shaving mirror has a focal length of 40 cm. How far away from it should one’s face be for the reflected image to be erect and twice its actual size? A.18 cm B.20 cm C.22 cm D.24 cm 43. An object is placed 8 cm from the lens with a focal length of 10 cm. Where is the image located from the lens? A.-30 cm B.-35 cm C.-40 cm D.-45 cm 44. A converging lens of focal length of 15 cm is placed 30 cm in front of a screen. At what distance should the object be placed in order that the image will appear exactly on the screen? A.30 cm

46. An object is placed 8 cm from the lens with a focal length of 10 cm. Where is the image located from the lens? A.-30 cm B.-35 cm C.-40 cm D.-45 cm 47. A uniform steel beam is 12 feet long is suspended from one end by a construction crane. Determine the period of oscillation of the beam. A. 3.13 s B. 4.13 s C.5.13 s D. 6.13 s 48. A 2000-kg truck accelerates from 20 kph to 120 kph in 10 s. Find its engine power output in watts. A.22666 W B.22999 W C.12888 W D.107998 W 49. During a race, Jan Michael’s sports car develops a 250 hp at 4000 rpm. What is the amount of torque exerted on the crankshaft? A.328.25 B.329 C.330

D.340 50. Tiger woods hit a golf ball at a velocity of 80 m/s. The head of his club was in contact with the 50 g ball for 0.40 ms. What is the average force acting on the golf ball during impact? A.25 kN B.20 kN C.10 kN D.15 kN 51. An apple can provide a person about 20000 J of work. To what height can a 50-kg man climb upstairs if he eats one apple? A.36.8 m B.38.6 m C.40.8 m D.42.6 m 52. A rubber ball is dropped to the floor from a height of 3 m. It rebounds to a height of 1.8 m. What is the coefficient of restitution? A.0.625 B.0.825 C.0.665 D.0.775 53. What is the wavelength of yellow light whose frequency is 5 x 10^14 Hz A.800 nm B.200 nm C.600 nm D.700 nm 54. A rubber ball is dropped to the floor from a height of 3 m. It rebounds to a height of 1.9 m. What is the coefficient of restitution? A.0.625 B.0.825 C.0.665 D.0.796

55. Find the frequency of a photon having an energy of 3 eV? A.724 THz B.732 THz C.741 THz D.745 THz

56. The wavelength of a source wave in a certain material as measured is 18 cm. The frequency of the wave is 1900 Hz. Compute the speed of sound wave? A. 342 m/s B. 400 m/s C. 542 m/s D. 300 m/s 57. An object is placed 8 cm from the lens with a focal length of 10 cm. Where is the image located from the lens? A.-30 cm B.-35 cm C.-40 cm D.-45 cm 58. What is the wavelength of yellow light whose frequency is 5 x 10^14 Hz A.800 nm B.200 nm C.600 nm D.700 nm 59. An apple can provide a person about 20000 J of work. To what height can a 50-kg man climb upstairs if he eats one apple? A.36.8 m B.38.6 m C.40.8 m D.42.6 m

60. What is the velocity of sound t room temperature which is a 27 ℃? A.347.1 m/s B. 345.9 m/s C. 346.8 m/s D. 348.2 m/s

ECE198L Sale, Mhiko I. GEAS SET 7 Engineering Economics 1.What is defined as analysis and evaluation of monetary consequences by using the theories and principles of economics to engineering applications, designed and projects? A. Economic Analysis B. Engnieering cost analysis C. Engineering economy D. Design cost analysis 2. What is considered as the standard unit which forms the basis of a country’s domestic money supply? A. B. C. D.

Monetary unit Currency Foreign exchange Cash or check

3.What is defined as the analysis defined as any tangile economic product that contributes directly or indirectly to the satisfaction of human want? A. B. C. D.

Services Goods Commodities Goods or commodites

4.What is defined as any tangible economic activity that contributes directly or

indirectly to the satisfaction of human want? A. B. C. D.

Services Goods Commodites Goods or commodities

5.What are the two classification of goods and services? A. Local and imported B. Raw and Finisned C. Consumer and producer D. Ready-made and made-to-order

6.What refers to the goods and services that are required to support human life, needsa and activites? A. B. C. D.

Producer products Consumer products Luxury Necissities

7. What refers to the goods and services that are desired by human and will be acquired only after all the needs have been satisfied? A. B. C. D.

Producer products Consumer products Luxury Necissities

8.What refers to the exchange mechanism that brings together sellers and the buyers of a product, factor of production or financial security?

A. B. C. D.

Mall Market Store Office

9. What is considered as the basic consuming or demanding unit of commodity? A. B. C. D.

seller manufacturer producer buyer or consumer

10. What is defined as an entity which makes product, good or services available buyer or consumer in exchange of monetary consideration? A. B. C. D.

seller manufacturer producer buyer or consumer

11. What is the market situation whereby there is only one buyer of an item for which there is no goods substitute? A. B. C. D.

Monopsony Monopoly Oligopoly Oligopsony

12. What market situation exists where there are few sellers and few buyers? A. B. C. D.

Oligopoly Oligsopoly Bilateral Oligopoly Bilateral Oligopsony

13. What market situation exists where there is only one buyer and only one seller? A. B. C. D.

Monopsony Monopoly Bilateral monopsony Bilateral monopoly

14. What is the market situation exists when there are many buyers and many sellers? A. B. C. D.

Perfect competition Monopoly Oligopoly Oligopsony

15. If there is only one seller and many buyers, the market situation is ___. A. B. C. D.

Duapsony Oligopoly Oligposony Monopoly

16. IF there are many sellers and few buyers, the market situation is ____. A. B. C. D.

Duapsony Oligopoly Oligposony Monopoly

17. Oligopoly exists when there is/are: A. Few sellers and few buyers B. Few sellers and many buyers

C. Many sellers and few buyers D. One seller and few buyers

18. Duopsony is a market where there is/are: A. Few sellers and few buyers B. Few sellers and many buyers C. Many sellers and few buyers D. One seller and few buyers 19. Doupoly is a market situation where there is/are: A. Few sellers and few buyers B. two sellers and many buyers C. Many sellers and few buyers D. One seller and few buyers

20. What is another term for “perfect competion”? A. Atomistic competion B. No-limit competion C. Free-for-all market D. Heterogenous market 21. what refers to the market situation in which any given product is supplied by a very large number of vendors and there is no restriction against additional vendors from entering the market? A. Perfect competition

B. Oligopoly C. Oligposony D. Monopoly

22. Aside from many sellers and may buyers, which one is a characteristic of perfect competition? A. Homogenous product B. Free market entry and exit C. Perfect information and absence of all economic friction D. All of the above

23. What is the opposite of perfect competition? A. B. C. D.

Monopsony Oligopoly Oligposony Monopoly

24. What refers to the need, want or desire for a product backed by the money to purchase it? A. B. C. D.

Supply Demand Product Good

25. What refers to the amount of a product made available for sale? A. B. C. D.

Supply Demand Product Good

26. Under ordinary simple interest, how many days in one year? A. B. C. D.

300 360 365 366

27. One banker’s year equivalent to ___ days. A. B. C. D.

300 360 365 366

28. What refers to the present worth of the probable future net earnings? A. B. C. D.

Total fair value Total market value Going concern value Earning value

29. What refers to the amount of money paid for the used of borrowed capital? A. B. C. D.

Interest Rate of interest Simple interest Principal

30. What refers to the cost of borrowing money or the amount earned by a unit principal per unit time? A. B. C. D.

Yield rate Rate of return Rate of interest Economic Return

31. First Benchamrk Publishing’s gross margin is 50% of sales. The operating costs of the publishing are estimated at 15% of sales. If the company is within the 40% tax bracket, determine the percent of sales is their profit after taxes? A. B. C. D.

21% 20% 19% 18%

32. A farmer selling eggs at 50 esos a dozen gains 20%. If he ssells the eggs at the same price after the cost of the eggs rises by 12.5%, how much will his new gain in percent? A. B. C. D.

6.89% 6.65% 6.58% 6.12%

33. A feasibility study shows that a fixed capital investment of P 10,000,000 is required for a proposed construction firm and an estimated working capital of P 2,000,000. Annual Depriciation is estimated to be 10% of the fixed capital investment. Determine the rate of return on the total investment if the annual profit is P 3,500,000. A. B. C. D.

28.33% 29.17% 30.12% 30.78%

34. The monthly demand for ice cans being manufactured by MR. Camus is 3200 pieces. With a manual operated guillotine, the unit cutting cost is P 25.00. An electrically operated hydraulic guillotine was offered to MR. Camus at a price of P 275,000 and which cuts by 30% the unit cutting cost. Disregarding the cost of money, how many months will MR. Camus be able to recover the cost of the machine if he decides to buy now? A. B. C. D.

10 months 11 months 12 months 13 months

35. Engr. Trinidad loans from a loan firm an amount of P 100,00 with a rate of simple interest of 20% but the interest was deducted fro the loan at the time of the money was borrowed. If at the end of one year, she has to pay the full amount of P 100,000 what is the actual rate? A. B. C. D.

23.5% 24.7% 25% 25.8%

36. A loan of P 5,000 is made for a period of 15 months at a simpe interest rate of 15%, what future amount is due at the end of the loan period? A. 5,937.60

B. 5,873.20 C. 5,712.40 D. 5,690.12

37. Mr. Bacani borrowed money from the bank he received from the bank P 1,842 and promised to repay P2,000 at te end of the 10 months. Determine the rate of simple interest. A. B. C. D.

12.19% 12.03% 11.54% 10.29%

38. A college freshman borrowed P2,000 from a bank for his tition fee and promised to pay the amount for one year. He received only the amount of P1,920 after the bank collected an advance interest of P80,000. What was the rate of discount? A. B. C. D.

3.67% 4.00% 4.15% 4.25%

39. It is the practice of almost all the banks in the Philippines that when they are grant a loan, the interest for one year is automatically deducted from the principal amount upon release of mney to a borrower. Let us therefore assume that you applied for a loan with a bank an the P 80,000 was approved

at an interest rate of 14% of which P 11,200 was deducted and you were given a check of P 68,800. Since you have to pay the amount of P 80,000 one year after, what then will be the effective interest rate? A. B. C. D.

16.02% 16.28% 16.32% 16.47%

40. A man invested P 110,000 for 31 days. The net interest after deducting 20% withholding tax is P 890.36. Find the rate of return annually. A. B. C. D.

11.50% 11.75% 11.95% 12.32%

41. The investor wishes to earn 7% on his capital after payment of taxes. If the income form an available investment will be taxed at an average rate of 42%, what minimum rate of return, before payment of taxes, must the investment offer to be justified? A. B. C. D.

12.07% 12.34% 12.67% 12.87%

42. Mr Jun Ramos was granted a loan of P 20,000 by his employer excel first

review and training center, Inc. witn an interest of 6% for 180 days on the principal collected in advance. The corporation would accept a promissory note of P 20,000 non-interest for 180 days. If discounted at once, find the proceeds of the note. A. B. C. D.

P 18,800 P 18,900 P 19,000 P 19,100

43. Miss Evilla borrowed money from the bank. She receives from the bank P1,340.00 and promised to pay P1,500.00 at the end of 9 months. Determine the corresponding discount rate or often referred to as the “banker;s discount”. A. B. C. D.

13.15% 13.32% 13.46% 13.73%

44. The exact simple interest of P 5,000 invested from June 21, 1995 to December 25,1995 is P100. What is the rate of interest? A. B. C. D.

3.90% 3.92% 3.95% 3.98%

45. What is the ordinary interest on P 1,500.50 for 182 days at 5.2%?

A. B. C. D.

P 39.01 P 39.82 P 39.45 P 39.99

46. A loan for P 50,000 is to be paid in 3 years at the amount of P 65,000. What is the effective rate of money? A. B. C. D.

9.01% 9.14% 9.31% 9.41%

47. What is the effective rate corresponding to 18% compounded daily? Take 1 year to equal to 360 days. A. B. C. D.

19.61% 19.44% 19.31% 19.72%

48. What rate of interest compounded annually is the same as the rate of interest of 8% compounded quarterly? A. B. C. D.

8.07% 8.12% 8.16% 8.24%

49. Which of these gives the lowest effective rate of interest? A. 12.35% compounded annually B. 11.90% compounded semi-annually

C. 12.24% compounded quarterly D. 11.60% compounded monthly

50. An amount of P 1,000 becomes P 1608.44 after 4 years compounded bimonthly. Find the nominal interest. A. B. C. D.

11.89% 12% 12.08% 12.32%

51. How long will it take money to double itsel if invested at 5% compounded annually? A. B. C. D.

13.7 years 14.7 years 14.2 years 15.3 years

52. By the condition of a will, the sum of P 20,000 is left to a girl to be held in trust fund by her guardian until it amounts to P50,000. When will the girl receive the money if the fund is invested at 8% compounded quarterly? A. B. C. D.

11.23 years 11.46 years 11.57 years 11.87 years

53. A sum of P 1,000 is invested now and left for

eight years, at which time the principal is withdrawn. The interest has accursed is left for another eight years. If the effective annual interest rate is 5%, what will be the withdrawal amount at the end of the 16th year? A. B. C. D.

P 693.12 P 700.12 P 702.15 P 705.42

54. Mandarin bank advertises 9.5% account that yields 9.84% annually. Find how often the interest is compounded. A. B. C. D.

Monthly Bimonthly Quarterly Annually

55. A student plans to deposit P 1,500 in the bank now and another P 3,000 for the next 2 years. If he plans to withdraw P 5,000 three years form after his last deposit for the purpose of buying shoes, what will be the amount of money left in the bank after one year of his withdrawal? Effective annual interest rate is 10%. A. B. C. D.

P 1,549.64 P 1,459.64 P 1,345.98 P 1,945.64

56. You borrow P 3,500.00 for one year from a friend at

an interest rate of 1.5% per month instead of taking a loan from a bank at a rate of 18% per year. How much lesser you will pay by borrowing the money from the bank? A. B. C. D.

P 62.44 P 44.55 P 54.66 P 37.56

57. What is the present with of two P 100 payments at the end of the third year and fourth year? The annual interest rate of 8%. A. B. C. D.

P 150.56 P 152.88 P 153.89 P 151.09

58. A firm borrows P 2,000 for 6 years at 8%. At the end of 6 years it renews the loan for the amount due plus P 2,000 for 2 years at 8%. What is the lump sum due? A. B. C. D.

P 3,260.34 P 3,280.34 P 3,270.34 P 3,250.34

59. What annuity is required over 12 years to equate with a future amount f P20,000? Assume i=6% annually. A. B. C. D.

P 1,290.34 P 1,185.54 P 1,107.34 P 1,205.74

60. What is the present worth of a 3 year annuity paying P 3,000.00 at the end of each year, with interest of 8% compounded annually? A. B. C. D.

P 7,654.04 P 7,731.29 P 7,420.89 P 7,590.12

ECE198L SALE, MHIKO I. SET1 Algebra 1. The _____ property of addition says we can add number in any order A. Closure B. Distributive C. Associative D. Commutative 2. A/an ______ equation is an equation that is true for any number substituted to the variable. A. Consistent B. Independent C. Identity D. Conditional 3. These are solution that satisfy a transformed equation but do not satisfy the original equation. A. Pertinent Solutions B. Extraneous Solutions C. Intrinsic Solutions D. Primitive Solutions 4. In the equation ax^2 + bx + c = 0, the product of the roots is ______. A. -c/a B. -b/a C. c/a D. b/a 5. This method for solving linear systems is a systematic process of elimination that reduces to triangular form

because the system can then be easily solved by back substitutions. A. Runge-Kutta Method B. Gaussian Elimination C. Gauss-Jordan Elimination D. Gauss-Seidal Method 6. In the equation ‘n x m = q’, the multiplicand is A. n B. m C. q D. none of the above 7. If x is an irrational number not equal to zero and x^2 = N, then which of the following best describes N? A. N is a natural number B. N is a positive rational number C. N is any rational number D. N is a positive integral number

D. -4 is not the domain of the function 10. In the Gauss elimination method for solving a system of linear algebraic equations, triangulations leads tto A. Singular matrix B. Upper triangular matrix C. Diagonal matrix D. Lower diagonal matrix 11. It is a sequence same as Fibonacci sequence but with different initial conditions. A. Euler sequence B. Lucas sequence C. Sloane sequence D. Fermat sequence 12. The power set of empty set has many subsets? A. 1 B. 2 C. 3 D. 4

𝑛

8. In the expression √𝑎 , the number n is call the A. Power B. Exponent C. Radicand D. Index 9. Which statement is true for the function f(x) 1/(x+4). A. 4 is not the range of the function B. 4 is not the domain of the function C. -4 is not the range of the function

13. If he discriminant of a quadratic equation is _____ the roots are complex. A. a rational number B. greater than zero C. less than zero D. an irrational number 14. Given a function y = f(x) from set A to set B, denoted as f: A B, B is called ______ of f. A. domain B. limit C. range

D. codomain 15. The intensity of sound varies directly as the strength of the source and inversely as the square of the distance from the source. Which of the following best describes this relation? A. I = k(d^2/S) B. I = k(kSd^2) C. I = k(S/d^2) D. I = k(S/sqrt(d)) 16. What is sequence of numbers such that successive terms differ by a constant. A. Arithmetic progression B. Infinite geometric progression C. Geometric progression D. Harmonic progression 17. Convergent series is a sequence of decreasing numbers or when succeeding term is _____ the preceding term. A. equal to B. less than C. greater than D. twice

19. What refers to the fraction part of a logarithm? A. Characteristics B. Mantissa C. Cologarithm D. Natural logarithm 20. What is the equivalent of the Roman numeral MCMXCIV? A. 1964 B. 1974 C. 1984 D. 1994 21. If 𝑎⃗ + 𝑏⃗⃗ + 𝑐⃗ = 0 then 𝑎⃗ 𝑥 𝑏⃗⃗ is equal to A. 𝑐⃗ 𝑥 𝑎⃗ B. 𝑐⃗ C. ⃗𝒃⃗ 𝒙 ⃗𝒄⃗ D. 𝑎⃗ 𝑥 𝑐 22. The position vector of the points which divides internally in the ratio 2 : 3 the join of the points 2a – 3b and 3a – 2b, is 12 13 𝑎+ 𝑏 5 5 𝟏𝟐 𝟏𝟑 B. 𝒂 − 𝒃 𝟓 𝟓 3 2 C. 𝑎 − 𝑏 5 5

A.

D. None of these 18. What refers to a sequence of numbers where the succeeding term is greater than the preceding term? A. Divergent sequence B. Isometric sequence C. Convergent sequence D. Dissonant sequence

23. If the roots of an equation are zero, then these roots are classified as what type of solutions? A. Conditional solutions B. Extraneous solutions C. Hypergolic solutions D. Trivial solutions

24. If a = b, then b=a. This illustrates which axiom in algebra. A. Transitive axiom B. Replacement axiom C. Reflexive axiom D. Symmetric axiom 25. Zero raise to any number is equal to A. Zero B. Indeterminate C. Infinity D. 1 26. The set of all real numbers under the usual multiplication operation is not a group since A. multiplication is not a binary operation B. multiplication is not associative C. identity element does not exist D. zero has no inverse 27. What refers to the smallest natural number for which 2 natural numbers are factors? A. Least common divisor B. Least common denominator C. Least common factor D. Least common multiple 28. In algebra, what refers to the operation of root extraction? A. Evolution B. Resolution

C. Revolution D. Involution

D. 0

29. The number 0.123123123… is what type of number? A. Rational Number B. Irrational Number C. Imaginary Number D. Complex Number 30. What refers to the difference between an approximate value of a quantity and its exact value or true value? A. Relative error B. Absolute Error C. Mistake D. Difference

34.) Find the value of x and y from the equations: x-4y+2=0 2x+y-4=0

2 − 2 1 1 3 − − 2 −2 ((𝑥 3 (𝑥 3 𝑥 2 (𝑥 𝑥 ) )^1

/2)^6

𝟓

A. 11/7, -5/7 B. 11/, 8/9 C. 14/9, 8/9 D. 11/7, -5/7 35.) Find the value of x and y from the equations: 4x+2y= 5 13x-3=2

A.

𝒚𝟐 𝒙 5

B.-

𝑦2 𝑥 5

C.

𝑦2 𝑥+𝑥

A. ½, 3/2

D.

𝑦2 𝑥+𝑦

B. 0

39.)

5

(𝑥 2 𝑦 3 𝑧 −2 )^−3 (𝑥 −3 𝑦𝑧 3 )^−1/2

C. 1

5

(𝑥𝑦𝑧 −3 )−2 𝟏

A. 𝒙𝟐𝒚𝟕𝒛𝟑

D. 2

2

B. 𝑥 2 𝑦7 𝑧3

1 𝑥 2 𝑦−7 𝑧 3 3 D. 𝑥 2 𝑦7 𝑧3

C. 31. IF 16 is 4 more than 4x, find 5x-1 A. 14 B. 3 C. 12 D. 5

3𝑥 2 + 2𝑦 2 = 35

A. +- 3, +-sqrt(2)

32. Find the value of x in (x+1)/3 + 2x/4 = 47-2x A. 16.47 B. 12.87 C. 18.27 D. 20.17 33.) Find the value of the following 2 (3 A. 50/9 B. 80/9 C. 70/9

36. Solve the simultaneous equations 2𝑥 2 − 3𝑦 2 = 6

𝐴 10 (𝑥

+

𝐴 ) 𝑦

=𝐴

𝐴 𝐴 −4 ) = 𝐴 𝑥 𝑦

B. 3 C. 4 D. sqrt(2) 37.) Multiply the following (2x+5y)(5x-2y) A. -10x^2 +21xy-10y^2 B. 10x^2 -21xy-10y^2 C. 10x^2 +21xy-10y^2

40.) if p-q=5 and pq=k/2, then 𝑝2 + 𝑞 2 equals A. k B. 25k C. 25+k 𝑘 D. 25 41.) √𝑥 − 2 = √𝑥 + 2. A. none of these B. x+2 C. 2 D. 4 𝑎𝑏

42.) √ 3

√𝑎𝑏

𝟑

A. √𝒂𝒃

D. -10x^2 -21xy-10y^2

B. √𝑎𝑏

38. simplify:

C. ab D. a

3

1

43.) If to the ¾ power equals 8, x is A. 2 B. 3 C. 4 D. 16 44.) Find the quotient 3𝑥 5 − 4𝑥 2 + 2𝑥 2 + 36𝑥 + 48 divided by 𝑋 3 − 2𝑥 2 + 6

𝟓

𝟏

A. 𝟑 𝒐𝒓 − 𝟐 5

1

B. − 3 𝑜𝑟 2 2 3 1 D. 3

C.

1 2 1 −2

𝑜𝑟 − 𝑜𝑟

49. Solve: 10𝑥 2 + 10𝑥 + 1=0

A. −𝑋 3 − 2𝑥 2 + 6 B. 𝑋 3 − 2𝑥 2 − 6 C. 𝑋 3 + 2𝑥 2 + 6 D. 𝑿𝟑 − 𝟐𝒙𝟐 + 𝟔 45. The mean of x and y is a, the mean of y and z and the mean of x and z is c, what is the mean of x,y, and z? A.

𝒂+𝒃+𝒄 𝟑

B.

𝑎+𝑏+𝑐 2

C.

𝑎+𝑏+𝑐 3𝑎

D.

𝑎+𝑏+𝑐 3𝑏

46. Find the mean proportional of4 and 36 A.72 B.24 C.12 D.20 47. The equation of whose roots are the reciprocal of the 2𝑥 2 − 3𝑥 − 5 = 0 A. 𝟓𝒙𝟐 + 𝟑𝒙 − 𝟐 = 𝟎 B. 2𝑥 2 − 3𝑥 − 5 = 0 C. 3𝑥 2 − 3𝑥 − 5 = 0 D. 2𝑥 2 − 3𝑥 + 5 = 0 48. Solve for x that satisfies the equation 6x^2-7x-5=0

A. -0.113, -0.887 B. -0.123, -0.887 C. -0.113, -0.807 D. -0.1, -0.87 50. In the expression (x+4y)^12, the numerical coefficiecnt of the 5th term is, A. 63,360 B. 126,720 C. 21,000 D. 36,000 51. What is the fourth term of the expansion (𝑥 + 𝑥 2 )100 A. 1650x^3 B. 161700x^103 C. 161600x^103 D. 60000x^103 52. Find the value of 𝑙𝑜𝑔8 48 A. 1.86 B. 1.69 C. 0.12 D. 0.18 53. Evaluate the ff: 𝑙𝑜𝑔6 845 = 𝑥 A. 3.76 B. 13.4 C. 16.6 D. 18.9 54. What is the value of log to ase 10 of 1000^3.3?

A. 10.9 B. 99.9 C. 9.9 D. 9 55. what is the valie of (log 5 to the base 2) + (log 5 to the base 3)? A. 7.39 B. 3.79 C. 2.88 D. 3.12 56. Mary is 24 years old. Mary is twice as old as ann was when mary was as old as ann is now. How old is Ann now? A. 16 B. 18 C. 17 D. 12 57. The sum of kim’s and kevin’s ages is 18. In 3 years, kim will be twice as old as kevin. What are their ages now? A.4,12 B.5,13 C. 8,9 D. 2,5 58. Robert is 15 years older than his brother stan. However y years ago, rober was twice as old as stan. If stan is now b year old and b>y, find the value of (b-y) A. 15 B. 13 C. 14 D. 12 59. A 400mm pipe can fill the tank alone in 5hrs and another 600mm pipe can fill the tnak alone in 4 hrs. a drain pipe 300 mm can empty the tank in 20 hrs. with all the

three pipes open how long will it take to fill te tank? A. 2 hrs B. 2.5 hrs C. 3 hrs D. 1.5 hrs 60. A tank can be filled in 9hrs by one pipe, 12 hrs by a second pope and can be drained when full by a third pipe in 15 hrs. how long will it take to fill and empty tank will all pipes in operation. A. 8hrs B. 7 hrs C. 7 hrs and 40 mins D. 7 hrs and 50 mins

ECE198L SALE, MHIKO I. Mathematics SET2 Probability and Statistics 1. What is the square of the standard deviation? A. Variance B. Frequency C. Class Mark D. Mode 2. A pictogram is a representation of data by symbols usually pictures. What is another term for pictogram? A. Histogram B. Ogive C. Illustrated Diagram D. Isotype Diagram 3. What is the good way of displaying data that is in a frequency distribution which is represented by a circle and divided into sectors? A. Pictogram B. Pie Chart C. Isotype Diagram D. Histogram

difference between the largest and smallest values? A. Limits B. Distribution C. Range D. Class Mark 6. Who introduced the concepts of combinatorics into calculations of probability and now regarded as the father of the theory of probability A. Blaise Pascal B. Gerolamo Cardano C. Jakob Bernoulli D. Pierre de Fermat 7. The total probability of favorable and unfavorable outcomes is: A. May have a value of zero B. Maybe greater than 1 C. always 1 D. all of the above

4. What is the square root of Variance? A. Mean B. Mode C. Standard Deviation D. Median

8. A tree diagram is used to find the probability of: A. Mutually exclusive events B. Independent events C. Dependent events D. Combined events 9. Which refers to a graph where each vertex is connected to every other vertex? A. Real Graph B. Whole Graph C. Complete Graph D. General Graph

5. What is the measure of dispersion which refers to the

10. What is a random variable?

A. It is a variable with a random value B. It is a variable which is randomly selected C. It is a numeric quantity that cannot be measured in a random experiment D. It is a numeric quantity that can be measured in a random experiment 11. What type of error is committed if the null hypothesis is rejected when in fact true? A. Type III error B. Type II error C. Type I error D. Type IV error 12. What type of error is committed when a null hypothesis is accepted despites being false? A. Type I error B. Type II error C. Type III error D. Type IV error 13. The _________ of a test is the probability of committing Type I error A. Accuracy level B. Random level C. Precision level D. Significance level 14. The probability of distribution of a continuous random variable x is a function of the: A. absolute value of x B. numeric value of x

C. imaginary value of x D. alphanumeric value of x 15. What is the immediate consequence of the law of large numbers? A. Score theorem B. Chebyshev’s theorem C. Deviation theorem D. Galton theorem 16. The set of all possible outcomes of a probability experiment is the _____ space. A. sample B. outcome C. event D. experiment 17. The conditional probability of B given A is denoted symbolically by P(B/A)=P(B), then the events A and B are A. dependent B. independent C. mutually exclusive D. disjoint 18. It is the character of a population which is measurable. A. sample B. distribution C. frequency D. parameter 19. It is a measure of relationship between two variables. A. Function

B. Relation C. Correlation D. Equation 20. What is a frequency curve which is composed of series of rectangles connected with the steps as the base and the frequency as the height? A. Histogram B. Bar graph C. Ogive D. Frequency distribution 21. Considering normal distribution, spread is increased, and height of the curve is decreased for A. smaller standard deviation B. larger standard deviation C. smaller mean value D. larger mean value 22. It is the value of the observation in a dataset that appears most frequently. A. median B. mean C. mode D. midrange 23. It is a formula which is always true for every value of propositional variables. A. equivalence B. tautology C. synthesis D. contingency

24. It is a finite sequence of precise instruction for performing a computation or for solving problem. A. time complexity B. algorithm C. quick counting D. sorting 25. A compound proposition that is always false for all possible truth values of the constituent proposition is called a/an _____. A. contingency B. tautology C. contradiction D. contingency 26. Probability if an impossible event. A. ½ B. ¼ C. 0 D. 1 27. In a set of 4 numbers, what happens to the variance if each number is multiplied by 2? A. It becomes half B. It remains the same C. It doubles D. It quadruples 28. [~q^(p q)] ____. A. invalid B. tautology C. satisfiable D. unsatisfiable

~p is

29. A compound proposition that is always false is called A. idealogy B. contradiction C. contigency D. imaginary 30. The probability distribution of discrete random variable is classified as A. probability mass function B. posterior mass function C. interior mass function D. continuous mass function 31. in a class of 40 students, 27 like calclulus and 25 like chemistry. How many like both calculus and chemistry? A. 10 B. 11 C. 12 D. 13 32. A club of 40 executives, 33 like to smoke Marlboro and 20 like to smoke Philip morris. How many like both A. 10 B. 11 C. 12 D. 13 33.) A survey of 100 persons revealed that 72 of them had eaten at retstaurant P and that 52 of them had eaten at restaurant Q. Which of the following could not be th e numer of persons in the surveyed group who had eatn at both P and Q? A. 21

B. 22 C. 23 D. 24 34.) The probability for the ECE board examniees from a certain school to pass the subject Math is 3/7 and for the subject comms is 5/7. If none of the examniees fails both subject and there are 4 examinees hwo pass both subjects, find the number of examinees form that school who took the examinations. A. 22 B. 21 C. 30 D. 28 35.) In commercial survey involving 1000 persons on brand preference, 120 were found o prefer brand x only, 200 prefer brand y only, 150 prefer brand zonly, 370 prefer either brand x or y but not z, 450 prefer brand y or z but not x and 370 prefer either brand z or x but not y. how many persons have no brand preference, satisfied with ay of the three brands? A. 280 B. 230 C.180 D.130

36. If 15 people won prizes in the state lottery assuming that

there are no ties, how many ways can these 15 people win first, second, third, fourth, and fifth prizes

A. 4845 B. 116260 C. 360,360 D. 3003 37.) How many 4 digit numbers can be formed without repeating any digit from the following digits, 1,2,3,4 and 6 A. 120 B. 130 C. 140 D. 150 38. What is the number of permutaitons of the letters in the word BANANA? A. 36 B. 60 C. 20 D. 10

39.) A PSME unit has 10 ME’s, 8 PME’s and 6 CPM’s. if a committee of 3 members, one form each group is to be formed, how many such communities can be formed? A. 2024 B. 12144 C. 480 D. 60

40.) Four different colored flags can be hung in a row to make a coded signal How many signals can be made if a signal consists of the display of one or more flags? A. 64 B. 60 C. 66 D. 67 41.) In how many ways can 4 boys and 4 girls be seated alternately in a row of 8 seats? A. 576 B. 1152 C. 203 D. 589 42.) There are four balls of four different colors. Two balls are taken at a time and arranged in a definite order. For example, if a white and a red balls are taken, one definite arrangement is white firstmred second m and another arrangement is red first, white second. How many such arrangements are possible A. 24 B. 3 C. 12 D. 9 43.) There are four balls of different colors. Tow balls at a time are taken and arranged any way. How many such combination are possible. A. 36 B. 3 C. 4 D. 6 44.) How many 6 number combinations can be

generated from the numbers from 1 to 42 inclusive, without repetition and with no regards to the order of the numbers?

drawing a prize of he owns 5 tickets?

A. 850,668

C. 𝟐𝟎% D. 100%

A. 60% B. 40%

B. 𝟓, 𝟐𝟒𝟓, 𝟕𝟖𝟔 C. 300,000 D. 260,000 45. Find the total number of cominations of three letters J R T taken 1 2 3 at a time. A. 𝟕 B. 0 C. 3 D. 4 46. IN how many ways can you invite one or more of your five friends at a party? A.72 B.31 C.12 D.20 47. In how many ways can a committee of three consisting of two chemical engineers and one mechanical engineer can be formed from four chemical engineers and three mechanical engineers? A. 𝟏𝟖 B. 30 C. 20 D. 19 48.There are 50 tickets in a lottery in which there is a first and second prize. What is the probability of a man

49. Roll a pair of dice. What is the probability that the sum of two number is 11? A. 1/36 B. -1/24 C. 1/18 D. 1/14 50. Roll two dice once, what is the probability that the sum is 7? A. 1/3 B. 1/6 C. 1/5 D. 1/7 51. Determine the probability of drawing either a king or a diamond in a single draw from a pack of 52 playing cards. A. 8/9 B. 5/13 C. 4/13 D. 6/18 52. A card is drawn from the deck of 52 playing cards. Find the probability of rawing a king or red card A. 0.5385 B. 0.5345 C. 0.5585 D. 0.5389 53. A coin is tossed 3 times. What is the probability of getting 3 tails up?

A. 1/8 B. 1/3 C. 1/5 D. 1/6

both balls are white. Assume that the first ball is returned before the second ball is drawn.

54. The probability of getting at leat 2 heads when a coin is tossed is four times is A. 11/16 B. 13/16 C. 1/4 D. 3/8

A. 25/81 B. 13/81 C. 14/67 D. 12/90

55. A fair coin is tossed three times. What is the probability of getting either 3 heads or 3 tail? A. 1/8 B. 1/5 C. 1/4 D. 1/3 56. In multiple choices test, each questions is to be answered by selecting 1 out of 5 choices, of which only 1 is right. IF there are 10 questions in a test, what is the probability of getting 6 right of pure guesswork A. 10% B. 0.87% C. 7% D. 0.55% 57. From a box containing 6 red balls, 8 white balls and 10 blue balls, one ball is drawn at random. Determine the probability that it is red and white. A.1/3 B. 7/12 C. 5/12 D. 2/5 58. From a bag containing 4 black balls and 5 white balls, two balls are drawn one at a time. Find the probability that

59. A bag contains 3 white and 5 black balls. If two balls are drawn in succession without replacement, wat is the probability that both balls are black? A. 5/31 B. 5/81 C. 5/32 D. 5/14 60. In ECE Board exam, the probability that an examinee will pass each subject is 0.8. what is the probability that an examinee will pass at least two subjects out of the three board subjects. A. 90% B. 80 % C. 80.7% D. 89.6 %

ECE198L SALE, MHIKO I. Mathematics SET3 Solid Geometry 1. It is a polyhedron containing triangular faces with a common vertex and a base which is a polygon. A. pyramid B. triangular prism C. dodecahedron D. icosahedron 2. It is a type of polygon in which every interior angle is less than 180 degrees. A. irregular polygon B. convex polygon C. concave polygon D. regular polygon 3. How many edges does a tetrahedron have? A. 4 B. 20 C. 12 D. 6 4. How many faces does a regular dodecahedron have? A. 12 B. 20 C. 32 D. 18 5. A polygon is said to be convex if every interior angle is A. more than 90 B. less than 90

C. less than 180 D. more than 180 6. The face of a regular tetrahedron is a A. Triangle B. Pentagon C. Square D. Hexagon 7. The volume of solids of revolution is governed by what theorem? A. Pappus B. Newton C. Varignon’s D. Archimedes 8. To find the interior angles of a triangle whose sides are given, use the law of A. sine B. cosine C. tangent D. secant 9. A polyhedron possessing two congruent polygon faces and all remaining faces parallelograms. A. Prismatoid B. Conoid C. Prism D. Frustum 10. What is the maximum value for a longitude? A. 270 B. 90 C. 180 D. 360

11. A regular polygon has 27 diagonals, then it is a? A. pentagon B. heptagon C. hexagon D. nonagon 12. The volume of a solid of revolution is equal to the generating times the circumference of the circle described by the centroid of the arc provided that the axis of revolution does not cross the generating arc. A. First Proposition of Pappus B. Second Proposition of Pappus C. Third Proposition of Pappus D. Fourth Proposition of Pappus 13. It is a polyhedron of which two faces ae equal polygon in parallel planes and the other faces area parallelograms. A. Tetrahedron B. Prism C. Frustum D. Prismatoid 14. Each of the faces of a regular hexahedron is a ______. A. square B. triangle C. rectangle D. hexagon

15. What refers to a negativeheight (inward pointing) pyramid used in cumulation? A. Apex B. Elevatum C. Cumulatum D. Invaginatum 16. When two planes intersect with each othe, the amount of divergence between the two plane is expressed by measuring the ____. A. dihedral angle B. polyhedral angle C. reflex angle D. plane angle 17. 17 4degrees is equivalent to ____ mils. A. 3094 B. 2044 C. 3421 D. 2845 18. What is the reference angle of -510 degrees? A. 30 B. 10 C. 40 D. 20 19. The measure of 2.25 revolutions counterclockwise is _____ degrees. A. -810 B. -730 C. 810 D. 730

20. 4800 mills is equivalent to ____ degrees. A. 135 B. 270 C. 235 D. 142

a set of points is projected onto a second plane. A. Plane Geometry B. Solid Geometry C. Euclidean Geometry D. Projective Geometry

21. Surface area of hollow cylinder with radius ‘r’ and height ‘h’ is measured by A. 2πr - h B. 2πr + h C.πrh D.2πrh

26. Two angle with a common leg is called A. Adjacent angles B. Complementary angles C. Supplementary angles D. Vertical angles

22. A line segment is defined by A. 1 point B. 3 points C. 2 points D. 4 points 23. The sum of length of two sides of a triangle is always A. Less than third. B. Greater than third. C. Equal to third. D. 2/3 to third. 24. Deals with the properties of plane figures or geometrical shapes of two – dimensions A. Plane Geometry B. Solid Geometry C. Euclidean Geometry D. Projective Geometry 25. Deals with the study of those properties of plane figures that unchanged when

27. Are angles formed by two intersecting lines. A. Adjacent angles B. Complementary angles C. Supplementary angles D. Vertical angles 28. A _______ is straight line which divides a geometric figure into two equal figures. A. reciprocal B. explementary C. bisector D. conjugate 29. The area of the region bounded by two concentric circles is called ________. A. circular disk B. annulus C. ring D. washer 30. The area bounded by a chord of a parabola that is perpendicular to its axis and the curve, cur off by the chord.

A. Spherical segment B. Spherical sector C. Parabolic sector D. Parabolic segment

A. 2.80 B. 2.30 C. 2.45 D.1.30

31. Find the angle in mils subtended by a line 10 yards long at a distance of 5000 yards. A. 1 B. 2 C. 2.5 D. 3 32. Each angle of a regular dodecagon is equal to A. 130 deg B. 150 deg C. 120 deg D. 135 deg

36. What is the radius of the circle circumscribing an isosceles right triangle having an area of 162 sqm?

A. 12.73 B. 11.6 C. 14.18 D. 15.55

33.) Given a triangle ,C=100deg, a=15m,b=20m, Find c. A. 21 B. 22 C. 23 D. 27 34.) In triangle ABC, angle C=70 deg, A=45 deg, AB=40m. What is the ength of the median drawn form vertex A to side BC? A. 36.3 B. 21 C. 30 D. 28 35.) The sides of a triangle are 8cm, 10cm, and 14cm. Determine the radius of the inscribed circle.

37.) Two sides of a triangle are 50 m and 60 m long. The angle included between these sides is 30 deg. What is the interior angle opposite the longest side?

39. The area of a triangle inscribed in a circle is 39.19 cm^2 and the radios of the circumscribed circle is 7.14 cm. If the two sides of the inscribed triangle are 8cm and 10cm, respectively, find the third side. A. 16 B. 12 C. 22 D. 14 40.) What is the area in sq cm of the circle circumscribed about an equilateral triangle with a side 10 cm long? A. 104.7 B. 105.6 C. 103.9 D. 106.7 41.) The angle of a sector is 30deg and the radius is 15cm. What is the area of the sector in cm^2? A. 58.9 B. 115.2

A. 86.38 deg

C. 60.7

B. 90 deg

D. 85.9

C. 92.34 deg

42.) A trapezoid has an area of 36 m^2 and an altitude of 2m. Its two bases have ratio of 4:5. What are the lengths of the bases A. 12,15 B. 7,11 C. 8,10 D. 16,20

D. 91.2 deg 38. The area of a circle is 89.42 sq.inchs what is the circumference? A. 32.25 B. 33.52 C. 20 D. 10

43.) A regular hexagon is inscribed in a circle whose diameter is 20m. Find the area of the 6 segments of the circle formed by the sides of hexagon. A. 36.45

B. 63.54 C. 45.63 D. 54.36 44.) Find the area (in cm^2) of a regular octagon inscribed in a circle of radius 10cm? A. 𝟐𝟖𝟑 B. 289 C. 298

48. A circular cone having an altitude of 9m is divided into 2 segments having the same vertex. If the smaller altitude is m, find the ratio of the volume of the small cone to the big cone. A. 0.186 B. 0.296 C. 0.386 D. 0.486

D. 238 45. Find the area of a regular pentagon whose side is 25m and apothem is 17.2m. A. 1075 B. 1165 C. 1178 D. 1095 46. A circular piece of cardboard with a diameter of 1m will be made into a conical hat 40 cm high by cutting a sector off and joining the edges to form a cone. Determine the angle subtended by the sector removed A.144 B. 145 C. 158 D. 154 47. What is the area in sq.m of the zone of a spherical segment having volume of 1470.265 cu.mif the diameter of the sphere is 30m. A. 565.5 m^2 B. 465.5 𝑚^2 C. 665.5 𝑚^2 D. 19

49. Find the volume of the cone to be constructed from a sector having a diameter of 72 cm and a central angle of 150 A. 12367.32 B. 13232.6 C. 7710.82 D. 14682.5 50. A conical vessel has a height of 24 cm and a base diameter of 12 cm. It holds water to a depth of 18 cm above its vertex. Find the volume (in cm^3) of its content. A. 118.4 B. 381.7 C. 298.4 D. 412.6 51. What is the height of a right circular cone having a slant height of sqrt(10x) and a base of diameter of 2x? A. 2x B. 3x C. 4x/13 D. 3.162x 52. The ratio of the volume to the lateral area of a right

circular cone is 2:1. If the altitude is 15 cm, what is the ratio of the slant height to the radius. A. 5:6 B. 5:4 C. 4:3 D. 5:2 53. What is the vole of a frustum of a cone whose upper base is 15 cm in diameter and lower base 10cm. in diameter with an altitude of 25cm? A. 3018.87 B. 3180.87 C. 3108.87 D. 3081.87 54. The central angle of a spherical wedge is 1 radian. Find its volume if tits radius is 1 unit. A. 2/3 B. 1.2 C. 3/4 D. 2/5 55. A circular cylinder with a volume of 6.54 cu. m is circumscribed about the right prism whose base is an equilateral triangle of side 1.25m. What is the altitude of the cylinder in meters? A. 3.5 B. 3.75 C. 4 D. 4.26 56. The base of a right prism are hexagons with one of each side equal to 6 cm. The bases are 12 cm apart. What is the volume of the right prism? A. 2211.7

B. 1211.6 C. 1212.5 D. 1122.4 57. Determine the volume of a right truncated triangular prism with the ff definition: Let the corners of the triangular base be defined by A, B and C. The length of AB=10ft, BC=9ft, and CA=12ft, the sides A, B, and C are perpendicular to the triangular base and have the height of 8:6 ft., 7.1ft, and 5.5 ft. respectively A.413 B. 311 C. 313 D. 391 58. A regular octahedron has an edge 2m. Finds its volume (in m^3) A. 3.77 B. 1.88 C. 3.22 D. 2.44 59. A regular triangular pyramid has an altitude of 9m and a volume of 187.0 cu. m. What is the base edge in meters? A. 12 B. 13 C. 14 D. 15 60. How many times do the volime of a sphere increases if the radius is doubled A. 4 times B. 2 times C. 6 times D. 8 times

c) degree d) radius ECE198L SALE, MHIKO I. Mathematics SET4 Trigonometry 1) Angles between 0° and 90° lies in a) 2nd quadrant b) 3rd quadrant c) 1st quadrant d) 4th quadrant 1) System in which angles are measured in radians is called a) CGS system b) MKS system c) circular system d) sexagesimal system 2) Value of 240° into radians should be a) 4π⁄3 b) 3π⁄4 c) π⁄4 d) π⁄6 3) We can divide circumference of a circle into a) 180 equal arcs b) 360 equal arcs c) 270 equal arcs d) 90 equal arcs 4) Union of two non-collinear rays with some common end point is called a) vertex b) angle

5) A part of circumference of a circle is called a) segment b) radius c) sector d) arc 6) In an angle, rays of angle are known as a) arms b) vertex c) point of intersection d) initial side 7) π radians are equal to a) 180° b) 360° c) 90° d) 270° 8) Cosec²θ - cot²θ equals to a) 1 b) -1 c) 0 d) tanθ 9) Tanθ equals to a) 1⁄cosecθ b) 1⁄secθ c) 1⁄cosθ d) 1⁄cotθ 10) Angles between 90° and 180° lies in a) 1st quadrant b) 2nd quadrant c) 3rd quadrant d) 4th quadrant

11) 3π⁄2 radians are equal to a) 270° b) 180° c) 90° d) 60° 12) 1 + tan²θ equals to a) cosec²θ b) sec²θ c) sin²θ d) cos²θ 13) By rotating a ray from one position to another to make an angle, original position is called a) initial side b) terminal side c) point of intersection d) vertex 14) Angles between 270° and 360° lies in a) 1st quadrant b) 2nd quadrant c) 3rd quadrant d) 4th quadrant 15) By rotating a ray from one position to another to make an angle, final position is called a) vertex b) initial side c) terminal side d) point of intersection 16) The study of triangles by applying the relations between the sides and the angles a) Algebra

b) Digit c) Geometry d) Trigonometry 17) Deals with triangles in two dimensions of the plane a) Plane Trigo b) Digit c) Spherical Trigo d) Trigonometry 18) A triangle that has a right angle a) Right Triangle b) Oblique triangle c) Obtuse triangle d) None 19) A triangle that does not have right angle a) Right Triangle b) Oblique triangle c) Obtuse triangle d) None 20) Part of trigonometry which deals with the triangles on the sphere a) Plane Trigo b) Digit c) Spherical Trigo d) Trigonometry 21) The study of triangles by applying the relations between the sides and the angles a) Algebra b) Digit c) Geometry d) Trigonometry

22) Is a circle whose center coincides with the center of the sphere? a) Spherical b) Circle c ) Square d) Great Circle 23) It is the example of great circle a) meridians b) Equator c) A&B d) NONE 24) Deals with triangles in two dimensions of the plane a) Plane Trigo b) Digit c) Spherical Trigo d) Trigonometry 25) It is the circle construccted by a plane crossing the sphere not in its center a) Small Circle b) Big Circle c) Great Circle d) NONE 26) Deals with triangles in two dimensions of the plane a) Spherical triangle b) Digit c) Spherical Trigo d) Trigonometry 27) Part of trigonometry which deals with the triangles on the sphere a) Plane Trigo

b) Digit c) Spherical Trigo d) Trigonometry 28) what is the equivalent of sin^2x+cos^x a) 1 b) 2 c) 0.5 d) 0 29) What is the equivalent of 1/secx a) Tanx b) cosx c) cotx d) SinX 30) In an angle, common end point is known as a) vertex b) point of intersection c) initial side d) terminal side

31) sin(B-A) is equal to___, when B=270 deg and A is an acute angle A.-cosA C. -sinA B..cosA D. sin A 32) if sec^2 A 5/2, the quantity 1-sin^2 A is equivalent to A. 2.5 B. 1.5

C.0.4 D.0.6

33.) If sin3A = cos 6B, then A. A+B=90 B.A+B=180

C. A+2B=30 D.none 34.) If cos 65 + cos 55 = cos𝜃, find 𝜃 in radians A. 0.765 B. 0.087 C. 1.213 D. 1.421 35.) Find the value of sin(arccos(15/17)) A.8/11 B.8/15 C.8/19 D.8/17

36. The sine of a certain angle is 0.6, calculate the cotangent of the angle A.4/3 B.5/4

C.4/5 D.3/4

37.) If tan x = ½, tan y =1/3, what is the value of tan(x+y)? A.1/2 B.1/6

C.2 D.1

38. Find the value of (sin𝜽+cos𝜽tan𝜽)/cos𝜽 A. 2sin𝜽 B. 2cos𝜽

C.2tan𝜽 D.2cot𝜽

39. Simplify the equation: sin^2𝜽 (1+cot^2𝜽) A.1 B.sin^2x C.sin^2xsec^2x D.sec^2x

40.) Simplify the equation sec 𝜽 – (sec 𝜽) sin^2 𝜽 A. cos^2 𝜽 B. cos 𝜽 C. sin^2 𝜽 D. sin 𝜽 41.) A man is standing on a 48.5 meter building high, has an eyesight height of 1.5 m from the top of the building, took a depression reading from the top of another nearby building and nearest wall, which are 50 deg and 80 deg respectively. Find the height of the nearby building in meters. The man is standing at the edge of the building and both buildings lie on the same horizontal plane.

A. 54.23 m B. 42.44 m C. 48.23 m D. 46.21 m 44.) A wire supporting a pole is fastened to it 20 feet from the ground and to the ground 15 feet from the pole. Determine the length of the wire and the angle it makes with the pole. A. 24 ft, 53.13 B. 25 ft, 53.13 C. 24 ft, 36.87 D. 25ft, 36.87 45. The two legs of a triangle are 300 and 150 m each, respectively, The angle opposite the 150m side is 26 deg. What is the third side? A. 197.49

A. 39.49

B. 218.61

B. 35.50

C. 𝟑𝟒𝟏. 𝟕𝟖

C. 30.74

D. 282.15

D. 42.55 42.) A man finds the angle of elevation of the top of a tower to be 30. H walks 85m nearer the tower and finds its angle of elevation to be 60. What is the height of the tower? A. 76.31m B. 73.16 m C. 73.31 m D. 73.61 m 43.) A pole cast a shadow 15 m long when the angle of elevation of the sun is 61. If the pole is leaned 15 from the vertical directly towards the sun, determine the length of the pole.

46. If Greenwich Mean time (GMT) is 6 A.M, what is the anime at a place located 30deg east longitude? A. 7 AM B. 8 AM C. 9 AM D. 4 AM 47. If the longitude of Tokyo is 139 deg E and that of manila is 121 deg E, what is the time difference between tokoy and Manila A. 1 hour and 12 min B. 1 hour and 21 min C. 1 hour and 23 min D. 1 hour and 24 min

48. One degree on the equator of the earth is equivalent to ____ in time. A. 1 minute B. 4 minutes C. 30 minute D. 1 hr 49. The sides of a triangle are 8, 15 and 17 units. If each side is doubled, how many square unitss will the area of the new triangle be. A. 240 B. 420 C. 320 D. 200 50. The sides of a triangle are 195, 157 and 210, respectively. What is the area of the traiangle? A. 73250 B. 10250 C. 14586 D. 11260 51. The slides of a triangular lot are 130 m, 180m and 190 m. The lot is to be divided by a line bisecting the longest side and drawn from the opposite vertex. Find the length of the line A.120 B. 130 C. 125 D. 128 52. If an equilateral triangle is circumscribed about a circle of radius 10 cm, determine the side of the triangle. A. 34.64 cm B. 36.44 cm

C. 64.12 cm D.32.10 cm 53. Points A and B 1000 m apart are plotted on a straight highway running east and west. From A., the bearing of a tower C is 32 degW of N and from B the bearing og C is 26degN of E. Approximate the shortest distance of tower C to the highway. A. 364 B. 374 C. 384 D. 394 54. Two triangles have equal bases. The altitude of one triangle is 3 units more than its base and the altitude of the other triangle is 3 units less than its base. Fine the altitudes, if the areas of the triangles differ by 21 square units. A. 6 and 12 C. 5 and 11 B. 3 and 9 D. 4 and 10 55. A ship started sailing S 42°35’ W at the rate of 5kph. After 2hours, ship B started at the same port going N 46°20’W at the rate of 7kph. After how many hours will the second ship be exactly north of ship A.? A. 3.68 B. 4.03 C. 5.12 D. 4.83 56. Evaluate : 2𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜃−𝑐𝑜𝑠𝜃 1−𝑠𝑖𝑛𝜃+sin2 𝜃−cos2 𝜃

A. sin𝜃

B. 𝑐𝑜𝑠𝜃 C. 𝑡𝑎𝑛𝜃 D. 𝒄𝒐𝒕𝜽

57. If sec2A=1/(sin13A), determine the angle A in degrees A.5° B. 6° C. 3° D. 7° 58. Solve for 𝜽 in the ff equation : sin 2𝜽= 𝒄𝒐𝒔𝜽 A. 30° B. 45° C. 60° D. 15° 59. Find the value of A between 270 and 360 if 2 sin^2 -sinA=1 A. 300° B. 320° C. 310° D. 330° 60. Find the value of y in the given : y=(1+cos𝜃) tan𝜃 A. sin𝜃 B. cos𝜃 C. sin𝟐𝜽 D. cos2𝜃

ECE198L SALE, MHIKO I. Mathematics SET5 Differential Calculus 1. A function F(x) is called ____ of f(x) if F’(x) = f(x) a. Explicit function b. Derivative c. Implicit function d. Antiderivative 2. When f’(x) is negative, the curve of y = f(x) is concave _____. a. Downward b. To the right c. Upward d. To the left 3. At maximum point, the value of y’’ is: a. Zero b. Infinite c. Positive d. Negative 4. At the inflection point where x = a, a. F’’(a) > 0 b. F’’(a) < 0 c. F’’(a) = 0 d. F’’(a) is not equal to 0 5. Points of derivatives which do not exist (and so equals zero) are called a. Stationary points b. Minimum points c. Maximum points d. Minimum and maximum points 6. If the first derivative is a constant then the function is _____

7.

8.

9.

10.

a. Sinusoidal b. Logarithmic c. Linear d. Quadratic If the second derivative of the equation of a curve is equal to the negative of the equation of the same curve, the curve is a. A sinusoidal b. A paraboloid c. A cissoid d. An exponential Equations relating x and y that cannot readily be solved explicitly for y as a function of x or for x as a function of y. such equation may nonetheless determine y as the function of x or vice versa. Such a function is called a. Logarithmic function b. Implicit function c. Continuous function d. Explicit function Largest rectangle that can be inscribed in a circle a. Square b. Parallelogram c. Rhombus d. Rectangle If lim 𝑓(𝑥) exists, then it 𝑥→𝑎

is a. b. c. d.

Unique Zero Infinity Undefined

11. If functions f and g have domains Df and Dg respectively, then the domain of f / g is given by a. the union of Df and Dg b. the intersection of Df and Dg c. the intersection of Df and Dg without the zeros of function g d. None of the above 12. Let the closed interval [a , b] be the domain of function f. The domain of f(x - 3) is given by a. the open interval (a , b) b. the closed interval [a , b] c. the closed interval [a - 3 , b - 3] d. the closed interval [a + 3 , b + 3] 13. Let the interval (a , +infinity) be the range of function f. The range of f(x) - 4 is given by a. the interval (a - 4 , +infinity) b. the interval (a + 4, +infinity) c. the interval (a, +infinity) d. None of the above 14. A branch of mathematics that deals with derivatives and limits a. Algebra b. Trigonometry

15.

16.

17.

18.

19.

c. Integral calculus d. Differential calculus The _______ of a function expresses its rate of change with respect to an independent variable a. Derivative b. Integral c. Power d. None of the above The first derivative of a function is the ________ to that curve defined by the function. a. Slope of the tangent line b. Origin of the line c. Limit of the function d. Length of the tangent line It is a function win which one variable is defined only in terms of another variable. a. Logarithmic function b. Implicit function c. Continuous function d. Explicit function It is a formula for finding the derivative of a composition of functions a. Limits b. Related rates c. Derivative d. Chain rule One of the applications of differential calculus a. Related rate problems b. System of equation problems

c. Age problems d. Probability problems 20. If the first derivative of a function is linear, then the function is ______. a. Sinusoidal b. Logarithmic c. Linear d. Quadratic 21. Which of the following is correct? sin 𝑥 𝑥 𝐬𝐢𝐧 𝒙 𝐥𝐢𝐦 𝒙→𝟎 𝒙 sin 𝑥 lim 𝑥→0 𝑥 sin 𝑥 lim 𝑥 𝑥→0

a. lim

=0

b.

=𝟏

𝑥→0

c. d.

=2 = ∞

22. Which of the following is correct? 𝟏−𝐜𝐨𝐬 𝒙 𝒙 1−cos 𝑥 lim 𝑥 𝑥→0 1−cos 𝑥 lim 𝑥 𝑥→0 1−cos 𝑥 lim 𝑥 𝑥→0

a. 𝐥𝐢𝐦

=𝟎

b.

=1

𝒙→𝟎

c. d.

=𝑒 =∞

23. Which of the following is correct? 𝟏 𝒏 1 𝑛 ) 𝑛 1 𝑛 ) 𝑛 1 𝑛 ) 𝑛

a. 𝐥𝐢𝐦(𝟏 + )𝒏 = 𝒆 𝒙→𝟎

b. lim (1 + 𝑥→0

c. lim (1 + 𝑥→0

d. lim (1 + 𝑥→0

=1 =0 = 2𝑒

24. Which of the following is correct? 1

a. lim (1 + 𝑛)𝑛 = 1 𝑥→0

𝟏

b. 𝐥𝐢𝐦(𝟏 + 𝒏)𝒏 = 𝒆 𝒙→𝟎

1

c. lim (1 + 𝑛)𝑛 = 0 𝑥→0

1

d. lim (1 + 𝑛)𝑛 = 2𝑒 𝑥→0

25. For a>1, then:

a. b. c. d.

𝐥𝐢𝐦 𝒂𝒙 = +∞

𝒙→+∞

lim 𝑎 𝑥 = −∞

𝑥→+∞

lim 𝑎 𝑥 = 0

𝑥→+∞

lim 𝑎 𝑥 = 1

𝑥→+∞

26. F(c) is a local _____ value if f(x) ≤ f(c) for all x in I. a. Maximum b. Minimum c. Inflection d. Power 27. F(c) is a local _____ value if f(x) ≥ f(c) for all x in I. a. Maximum b. Minimum c. Inflection d. Power 28. What is the fifth step in solving maxima/minima problems? a. Equate to zero b. Differentiate c. Formulate equation d. Reduce to one variable 29. What is the fourth step in solving maxima/minima problems? a. Equate to zero b. Differentiate c. Formulate equation d. Reduce to one variable 30. ______ are the inverse operations of derivatives or the backward operation which goes from the derivative of a function to the original function itself in addition with a constant.

a. b. c. d.

Explicit function Derivative Implicit function Antiderivative 4𝑥 3 +2𝑥 2 −3 𝑥→∞ 5𝑥 3 +1

31. Evaluate: lim a. b. c. d.

3/4 4/5 3/5 4/3

32. Evaluate: a. b. c. d.

∞ 0 1 2

33. Evaluate: a. b. c. d.

2𝑥 5 −𝑥 3 −1 lim 6𝑥3 +2𝑥2 −7 𝑥→∞

ln 𝑥 lim 𝑥 𝑥→∞

0 1 -1 Infinite ln 𝑥

34. Evaluate: lim

𝑥→1 𝑠𝑖𝑛𝜋𝑥

a. 1/x b. 1 c. X d. -1/x 35. Evaluate: lim (1 + 𝑥→∞

1 𝑥𝑙𝑛8 ) 𝑥

a. b. c. d.

1 2 4 8 𝑠𝑖𝑛𝑥 𝑥→0 𝑥

36. Evaluate: lim a. b. c. d.

0 1 2 ½

39. Evaluate: lim

𝑥→0

a. b. c. d.

𝜃→0

𝑠𝑖𝑛7𝜃 𝜃

𝑐𝑜𝑠𝑥−1 𝑥

0 1 2 ½

40. Evaluate: lim

𝜃→0

𝑐𝑜𝑠8𝜃−1 2𝜃

a. 0 b. 1 c. 2 d. ½ 41. If ln(ln y) + ln y, find y’ a. b. c. d.

𝒚 𝒙+𝒚 𝑦 𝑥−𝑦 𝑥 𝑥+𝑦 𝑥 𝑥−𝑦

42. Find dy/dx of y = 3sin2x. a. 6sin2x b. 6cos2x c. 6tan2x d. 6sec2x 43. Given: y=x²lnx, find dy/dx a. x(1+2ln2x) b. 2x(1+lnx) c. x(1+2lnx) d. x(1-2lnx) ln 𝑥 , find 𝑥 1+𝑙𝑛𝑥 𝑥2 𝟏−𝒍𝒏𝒙 𝒙² 1−𝑙𝑛𝑥 𝑥

44. if y =

37. Evaluate: lim a. 7 b. 14

c. 28 d. 1 38. What is the limit of cos 1/y as y approaches infinity? a. 0 b. 1 c. -1 d. Infinity

a. b. c.

dy/dx

d.

1+𝑙𝑛𝑥 2𝑥²

𝑥

45. Find the derivative of 𝑒 𝑥 a. b. c. d.

𝟏−𝒙 𝒆𝒙 1−𝑙𝑛𝑒 𝑒² 1−𝑥 𝑒 1+𝑙𝑛𝑥 2𝑒²

46. Given: y = 𝑒 −𝑥 sin x. Find dy/dx a. 𝒆−𝒙(cos x – sin x) b. 𝑒 −𝑥 (cos x + sin x) c. 𝑒 −𝑥 (sin x – cos x) d. 𝑒 𝑥 (cos x – sin x) 47. What is the second derivative of a function y = 5x³ +2x +1? a. 15x b. 20x c. 25x d. 30x 48. If y = x ln x, find d²y/dx² a. 1/x b. 1/2x c. X d. 2x 49. Find the second derivative of the function y(x) = x(x²-1)² a. 4x(5x²-3) b. (x²-1)(5x²-1) c. 2x(5x²-6) d. (2x-1)(5x²-3) 50. Find d²y/dx² if x = 3-2z and y = z²-3z³ a. 0.5-4.5z b. 1.5+9z c. 0.5+9z d. 1.5-4.5z 𝑥−4

51. The function y = 𝑥+2 is discontinuous at x = ?

52.

53.

54.

55.

a. 0 b. -2 c. 2 d. -4 The distance a body travel is a function of time t and is defined by: x(t) = 18t+9t². What is its velocity at t = 3? a. 70 b. 72 c. 74 d. 76 If the distance x from the point of departure at time t is defined by the equation x = -16t² + 5000t + 5000, what is the initial velocity? a. 2,500 b. 5,000 c. 3,500 d. 4,000 A stone is thrown straight up a time, t = 0 so that its distance above the ground at time t is given s(t) = 112t-16t², with s in feet and t in seconds. How high does the stone rise and when will it hit the ground? a. 196 ft, 8s b. 192 ft, 7s c. 196 ft, 7s d. 192 ft, 8s Find the change in y = 2x3 if x changes from 3.3 to 3.5 a. 0.1 b. 0.2 c. 0.3

56.

57.

58.

59.

60.

d. 0.4 What is the allowable error in measure the edge of the cue that is intended to hold 8 cubic meters if the error of the compound volume is not to exceed 0.02 cubic meter? a. 0.00167 m b. 0.00217 m c. 0.00365 m d. 0.00453 m If y = 2x + sin 2x, find x if y’ = 0. a. π/2 b. π c. 3 π/2 d. π/4 Find the slope of x²y = 8 at the point (2,2) a. -1 b. 1 c. -2 d. 2 Find the slope of the curve y = x³-x+5 at (2,1) a. 11 b. 12 c. -11 d. -12 What is the slope of the curve y = x²/4 – 2x + 1 at a point (1,1)? a. 0.25 b. -1.25 c. 1.25 d. -0.25

ECE198L SALE, MHIKO I. Mathematics SET6 Analytic Geometry

1. A horizontal line has a slope of _____. a. Negative b. Infinity c. Positive d. Zero 2. A vertical line has a slope of ____. a. Negative b. Infinity c. Positive d. Zero 3. A line, which is perpendicular to the xaxis has a slop equal to ____. a. 1 b. 0 c. Infinity d. -1 4. If all the y-terms have even exponents the curve is symmetric with respect to the ____. a. Line 45 deg with the axis b. X-axis c. Origin d. Y-axis 5. Which of the following best describes the graph of the equation x² + y² + 2x – 4y + 5 = 0 in the xy plane? a. Circle

6.

7.

8.

9.

10.

b. Parabola c. Point d. Ellipse In general quadratic equation, if the discriminant is zero, the curve is figure that represents a /an _____. a. Circle b. Parabola c. Point d. Ellipse What is the line that passes through the focus and is perpendicular to the matrix of a parabola? a. Tangent line b. Directrix c. Latus Rectum d. Axis of Parabola What is a line that passes through the focus and perpendicular to the axis of the parabola? a. Tangent line b. Directrix c. Latus Rectum d. Axis of Parabola A locus of a point which moves is that it is always equidistant from a fixed point to a fix line is a ____. a. Circle b. Ellipse c. Parabola d. Hyperbola A locus of a point which moves so that it is always equidistant to a fixed point called center. a. Circle

11.

12.

13.

14.

15.

b. Ellipse c. Parabola d. Hyperbola A locus of a point which moves so that the sum of the distances to the fixed points called foci is constant and equal to the length of the major axis. a. Circle b. Ellipse c. Parabola d. Hyperbola A locus of a point which moves so that the difference of the distances to the fixed points called foci. a. Circle b. Ellipse c. Parabola d. Hyperbola 3x² + 2x -5y + 7 = 0. Determine the curve. a. Circle b. Ellipse c. Parabola d. Hyperbola 4x² - 256 = 0 is the equation of ____. a. Parallel lines b. Parabola c. Circle d. Ellipse A parabola y = -x² -6x -9 opens _____. a. To the right b. Upward c. To the left d. Downward

16. It is defined as the set of all points in the plane the sum of whose distances from two fixed points is a constant. a. Circle b. Hyperbola c. Parabola d. Ellipse 17. The chords of an ellipse which passes through the center, are known as ____. a. Asymptote b. Major axis c. Minor axis d. Diameter 18. A line that approaches a curve but never touches. a. Asymptote b. Major axis c. Minor axis d. Diameter 19. In an ellipse, a chord which contains a focus and is in a line perpendicular to the major axis is called ___. a. Focal width b. Latus rectum c. Conjugate axis d. Minor axis 20. _____ of an ellipse is one that is perpendicular to the major axis but does not pass through the focus but its center. a. Focal width b. Latus rectum c. Conjugate axis d. Minor axis

21. It is an axis of hyperbola that passes through its center and perpendicular to the transverse axis. a. Focal width b. Latus rectum c. Conjugate axis d. Minor axis 22. A line which a curve approaches indefinitely near as its tracing point passes off to the infinity is called the ____. a. Tangent b. Asymptote c. Directrix d. Latus Rectum 23. It is a line which intersects the curve in one and only one point. a. Tangent b. Asymptote c. Directrix d. Latus Rectum 24. It is a fixed line opposite the focus of a conic section which the eccentricity of the conic is defined. a. Tangent b. Asymptote c. Directrix d. Latus Rectum 25. In polar coordinate system, the length of the ray segment from a fixed origin is known as ____. a. Amplitude b. Radius vector c. Hypotenuse d. Minimum point

26. It refers to the nonnegative scalar measure of a wave’s magnitude of oscillation, i.e. the magnitude of the maximum disturbance of the medium during one wave cycle. a. Amplitude b. Radius vector c. Hypotenuse d. Minimum point 27. The graph of r = a + bcosθ is a ____ a. Lemniscate b. Limacon c. Cardiod d. Lituus 28. The graph of r² = a²cos(2θ) is a ____ a. Lemniscate b. Limacon c. Cardiod d. Lituus 29. The graph of r = 2a[1 + cos(θ)] is a ____ a. Lemniscate b. Limacon c. Cardiod d. Lituus 30. The graph of r² = a²/ θ is a ____ a. Lemniscate b. Limacon c. Cardiod d. Lituus 31. Find the distance between A(4,-3) and B(-2,5). A.11 B.9 C.10 D.8

32. If the distance between points (3,y) and (8,7) is 13, then y is equal to A.5 or -5 B.5 or 19 C.19 D.-5 or 19 33. If (-2,-4) is the midpoint of (6,-7) and (x,y), then the values of x and y are A.x=2,y=1 B.x=-10,y=-1 C.x=10,y=-1 D.x=-8,y=-1 34. Find the inclination of the line passing through (-5,3) and (10,7). A.14.73 B.14.93 C.14.83 D.14.63 35. If the slope of the line connecting the origin and point P is ¾, find the abscissa of P if its ordinate is 6. A.2 B.6 C.7 D.8 36. Find the angle formed by the lines 2x+y-8=0 and x+3y+4=0. A.30 B.35 C.45 D.60 37. What is the acute angle between the lines y=3x+2 and y=4x+9? A.4.4 B.28.3

C.5.2 D.18.6 38. Find the distance of the line 3x+4y=5 from the origin. A.4 B.3 C.2 D.1 39. Determine the distance from (5,10) to the line x-y=0. A.3.33 B.3.54 C.4.23 D.5.45 40. Find the slope of the line defined by y-x=5. A.1 B.1/4 C.-1/2 D.5+x 41. What is the slope of the line 3x+2y+1=0? A.3/2 B.2/3 C.-3/2 D.-2/3 42. Given three vertices of a triangle whose coordinates are A(1,1), B(3,-3) and (5,-3). Find the area of the triangle. A.3 B.4 C.5 D.6 43. Find the equation of a straight line with a slope of 3 and a y-intercept of 1. A.3X+Y-1=0 B.3X-Y+1=0 C.X+3Y+1=0

D.X-3Y-1=0 44. If the points (-2,3), (x,y) and (-3,5) lie on a straight line, then the equation of the line is A.X-2Y-1=0 B.2X+Y-1=0 C.X+2Y-1=0 D.2X+Y+1=0 45. Find the equation of the line passing through the origin and with a slope of 6. A.Y-6X=0 B.Y=-6 C.X+Y=-6 D.6X+Y=0 46. Find the equation if the line if the x-intercept and yintercept are -2 and 4, respectively. A.Y-2X-4=0 B.Y+2X-4=0 C.Y-2X-4=0 D.Y+2X+4=0 47. What is the equation of the line that passes thru (4,0) and is parallel to the line x-y2=0? A.X-Y+4=0 B.X+Y+4=0 C.X-Y-4=0 D.X-Y=0 48. Find the equation of the line through point (3,1) and is perpendicular to the line x+5y+5=0. A.5X-2Y=14 B.5X-Y=14 C.2X-5Y=14 D.2X+5Y=14

49. What is the equation of the line joining the points (3,2) and (-7,6)? A.2X+3Y=0 B.4X-5Y=22 C.4X+5Y=2 D.5X+4Y=7

55. What is the length of the latus rectum of the curve x2=20y? A.√20 B.20 C.5 D. √5

50. Find the slope of the line having a parametric equation of x=2+t and y=5-3t A.2 B.3 C.-2 D.-3

56. Find the eccentricity of the curve 9x2-4y2-36x+8y=4. A.1.80 B.1.92 C.1.86 D.1.76

51. What is the radius of the circle x2+y2-6y=0? A.2 B.3 C.4 D.5

57. What is the area enclosed by the curve 9x2+25y2225=0? A.47.1 B.50.2 C.63.8 D.72.3

52. A circle whose equation x2+y2+4x+6y-23=0 has its center at: A.(2,3) B.(3,2) C.(-3,2) D.(-2,-3) 53. Find the area (in square units) of the circle whose equation is x2+y2=6x-8y. A.20 pi B.22 pi C.25 pi D.27 pi 54. The focus of the parabola y2=16x is at A.(4,0) B.(0,4) C.(3,0) D.(0,3)

58. The length of the latus rectum for the ellipse 𝑦2 16

𝑥2 64

+

= 1 is equal to:

A.2 B.3 C.4 D.5 59. What is the radius of the sphere center at the origin that passes the point 8,1,6? A.10 B.9 C. √𝟏𝟎𝟏 D.1 60.Find the polar equation of the circle if its center is at (4,0) and the radius 4. A.r-8 cos 𝜽 =0 B. r-6 cos 𝜃 = 0 C. r-12 cos 𝜃 = 0

D. r-4 cos 𝜃 = 0 31. 32.

ECE198L Sale, Mhiko I. MATH SET 7 GEOMETRY 1) Who is the father of Algebra? A. John Dalton B.Diophantus Alexandria C.JJ Thompson D.none 2) Term used to describe the numbers in a given sequence? A.Element B.Series C.Alternating Series D.none 3) Sum of the terms in sequence? A.Element B.Series C.Alternating Series D.none 4) Has positive and negative terms arranged alternately? A.Element B.Series C.Alternating Series D.none 5) Another term for a sequence? A.Element C.Alternating Series B.Series D.Progression 6) Is an item that describes a magnitude or a position A.Element B.Series C.Alternating Series D.number 7) Numberse which allow us to cunt the objects or ideas in a given collection A.Element C.Cardinal number B.Series D.number 8) Sum of the terms in sequence? A.Element C.Alternating Series B.Series D.none 9) How many sifes have a polygon if the sum of the interior angle is 1080? A.5 C.7 B.6 D.8 10) The most widely used numerals

A.Element C.Alternating Series B.Arabic number D.none 11) Is a specific symbol used alone to denote a number A.Element C.Alternating Series B.Series D.Digit 12) Who is the father of ALgebra? A. John Dalto B.Diophantus Alexandria C.JJ Thompson D.none 13) an expression of both real and imaginary number combined A.Complex D.digit B.Real C.none 14) A real number is the numerical value of the number neglecting sign A.Complex C.digit B.Real D.Absolute Value 15) A single location in space is called a A. Line C. Plane B. Point D. ray 16) Vertical angles that are opposite to each other are also a)

not equal

19) A polygon having 10 sides is called a) decagon b) heptagon c)

quadrilateral

d) hexagon 20) A polygon having 8 sides is called a)

hexagon

b) nonagon c)

decagon

d) octagon 21) A triangle that has no equal sides and no equal angles is known as a)

isosceles triangle

b) scalene triangle c)

equilateral triangle

d) right angle 22) Perimeter of a rectangle with base ‘b’ and height ‘h’ is measured by

b) opposite

a)

c)

b) 2(h + b)

scalene

d) equal 17) Two lines that make an angle are called a)

scalene

c)

2 × b⁄h 2(b - h)

d) 2(h - b) 23) Area of a rectangle with base ‘b’ and height ‘h’ is measured

b) rays

by

c)

a) b × h

segment

d) vertex 18) Surface area of hollow cylinder with radius ‘r’ and height ‘h’ is measured by a)

2πr - h

b) 2πr + h c)

πrh

d) 2πrh

b) b + h c)

b⁄h

d) h⁄b 24) A line going through midpoint from one side to other side of a circle is called a)

angle

b) area

c)

radius

d) diameter 25) Exterior angles of any polygon sum up to a)

90°

b) 180° c)

270°

d) 360° 26) A polygon having 4 sides is called a)

hexagon

b) nonagon c)

heptagon

d) quadrilateral 27) Sum of all angles around a main point equals to a) 360°

31) Assuming that the earth is a sphere whose radius is 6400km. Find the distance along a 3 deg arc at the equator of the earths surface. A.335.10 km C.353.10km B.533.10km D.353.01km 32) Each angle of a regular dodecagon is equal to A.135 C.125 B.150 D.105 33) How many sifes have a polygon if the sum of the interior angle is 1080? A.5 C.7 B.6 D.8 34) The sum of the interior angle of a polygon is 540. Find the number of sides? A.3 C.5 B.4 D.6

b) 180° c)

270°

d) 90° 28) A line which connects any two points on a circle is known as a)

perimeter

b) diameter c)

chord

35) How many sides are in a polygon if each interior angle is 165 deg? A.12 C.20 B.24 D.48 36) How many diagonals are in a polygon of 20 sides? A.200 C.100 B.170 D.158

d) radius 29) Angles that are opposite to each other are called a) vertical angles b) complementary angles c)

reflective angles

d) supplementary angles 30) Angles that sum up to 90° are

37) Given a triangle, C=100, a=15. b=20. Find C A.26 C.28 B.27 D.29 38) The sides of a triangle are 8. 10 an 14. Determine the radius of the inscribed circle A.2.25 C.2.45 B.2.35 D.2.55

known as a)

vertical angles

b) complementary angles c)

reflective angles

d) supplementary angles

39) What is the radius of the circle circumscribing an an isosceles right triangle having an area of 162 sq.cm A.12.73 C.14.18 B.13.52 D.15.55

40) The sides of a triangle are 8, 10 and 14. Determine the radius of the circumscribing circle A.7.14 C.7.54 B.7.34 D.7.64 41) The area of a circle is 89.42 sq inches what is the circumference? A.32.25 C.35.33 B.33.52 D.35.55 42) The angle of a sector is 30 and the radius is 16cm. What is the area of the sector? A.59.8 C.67.02 B.89.5 D.85.9 43) The area of a regular hexagon inscribed in a circle of radius of 2 is A.1.31 C.10.39 B.2.945 D.3.816 44) The area of a triangle inscribed in a circle is 39.19 cm^2 and the radius of the circumscribed circle is 6.14 cm. If the two sides of the inscribed triangle are 8 cm and 10 cm, respectively, find the third side. A.11 cm C. 13 cm B. 12 cm D. 14 cm 45) Two perpendicular chords both 5 cm from the center of a circle divide the circle into four parts. If the radius of the circle is 13 cm, find the area of the smallest part. A. 30 C. 32 B. 31 D. 33 46) The arc of a sector is 9 units and its radius is 3 units. What is the area of the sector in square units A. 12.5 C. 14. B. 13.5 D. 15.5 47) A circle having an area of 452 sq. m is cut into two segments by a chord which is 6m from

the center of the circle. Compute the area of the bigger segment. A. 354.89 sq. m B. 378.42 sq. m C. 363.56 sq. m D. 383.64 sq. m 48) The distance between the centers of the three circles which are mutually tangent to each other externally are 10,12 and 14 units. The area of the largest circle is A. 72𝜋 C. 64𝝅 B. 23𝜋 D. 16𝜋 49) A trapezoid has an area of 36 m^2 and an altitude of 2 m. Its two bases have ratio of 5:4. What are the lengths of the bases? A. 12, 15 C. 8, 10 B. 7, 11 D. 20, 16 50) A rhombus has diagonals of 32 and 20 inches. Determine its area. A. 360 C. 320 B. 280 D. 400 51) If the sides of a parallelogram and an included angle are 6, 10 and 100°, respectively, find the length of the shorter diagonal. A. 10.63 C. 10.73 B. 10.37 D. 10.23 52) Find the area of a quadrilateral having sides AB=10cm, BC=5cm, CD=14.14cm and DA=15cm. If the sum of the opposite angle is equal to 225 A. 96 sq.cm C. 94 sq.cm B. 100 sq.cm D. 98 sq.cm 53) The area of a regular hexagon inscribed in a circle of radius 1 is A. 1.316 C. 2.598 B. 2.945 D. 3.816 54) Find the area of a regular octagon inscribed in a circle of radius 10cm? A. 283 C. 298 B. 289 D. 238

55) Find the area of a regular pentagon whose side is 30m and apothem is 17.2 m. A. 154842 C. 1080 B. 1085 D. 1095 56) The area of a circle is 89.42 sq. inches. What is the length of the side of a regular hexagon inscribed in a circle? A. 5.533 C. 6.335 B. 5.335 D. 7.335 57) Find each interior angle of a pentagon. A. 90 C. 150 B. 108 D. 180 58) Find the angle in mils subtended by a line 10 yards long at a distance of 1000 yards. A. 1 C. 2.5 B. 10 D. 4 59) A certain angle has a supplement 5 times the complement. What is the angle? A. 67.5 C. 30 B. 58.5 D. 27 60) Find the sum of the interior angles of the vertices of a five pointed star inscribed in a circle. A. 150 C. 170 B. 160 D. 180