Group Study

ENGINEERING MATHEMATICS 1. A sequence of numbers or quantities in which there is always the same relation between each quantity and the one succeeding it. a. Series b. Progression c. Arithmetic Progression d. Geometric Progression 2. Public health records indicate that t weeks after the outbreak of SARS approximately

𝑄=

20

thousands of people had caught the disease. How many people had originally caught the disease? If the trend continues, approximately how many people will have caught the disease? a. 1, 20 b. 20000, 1000 c. zero, infinity d. 1000, 20000 1+19𝑒 −1.2𝑡

3. It takes a boat 4 times to travel upstream against a river current than it takes the same boat to travel downstream. If the speed of the current is 24 kph, what is the speed of the boat in still water? a. 13.33 ms-1 b. 20 ms-1 -1 c. 40 ms d. 11.11 ms-1 4. Ace can finish a job in 10 days. Sabo can finish the job in 15 days. If the two men work together for 3 days, and Luffy came to help, it will take another 2 days to finish the 90% of the job. How long will it take for the three of them working together finish half of the job? a. 2 days b. 2.5 days c. 3 days d. 3.5 days

sum of their children’s ages. How many were children in the family? a. 4 b. 5 c. 6 d. 7 7. Suppose that ab means 3b-a. What is the Page | 1 value of x if 2(5x) = 1. a. 1/10 b. 2 c. 10/3 d. 10 8. Determine the value of ab if log 8 𝑎 + log 4 𝑏 2 = 5 and log 8 𝑏 + log 4 𝑎2 = 7. a. 18 b. 262144 c. 9 d. 512 9. At what time after 3:00 o’clock will the hands of the clock form a 60 degree angle the for the second time? a. 3:05.45 b. 3:27.27 c. 3:05.54 d. 3:27.72 10. An angle between a horizontal line and the line joining the observer’s eye to some object beneath the horizontal line. a. angle of elevation b. angle of depression c. angle of repose d. angle of inclination 11. A paper equilateral triangle ABC has side length 12. The paper triangle is folded so that the vertex A touches a point on side BC a distance of 3 from point C. Determine the length of the fold. a. 6.86 b. 6.96 b. 8.96 d. 9.86

5. What is the last digit of 1! + 3! + 5! + … + 2017! + 2019!? a. 5 b. 6 c. 7 d. 8

12. The point of concurrency of the angle bisector of the triangle is called . a. circumcenter b. incenter c. centroid d. orthocenter

6. The sum of the parent’s ages is twice the sum of their children’s ages. Five years ago, the sum of the parent’s ages is four times the sum of their children’s ages. In fifteen years, the sum of the parent’s ages will be equal to the

13. What do you call to an infinite sided polygon? a. apeirogon b. myriagon c. chilliagon d. enneacontagon

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14. The portion of a sphere included between two planes which intersects in a diameter.

ENGINEERING MATHEMATICS a. Spherical Wedge b. Spherical Segment c. Spherical Lune d. Spherical Zone

a. 12 c. 24

15. A cow is tethered by a 10 m rope to the outside of a hexagonal shed with side 8 m in a grassy field. What area of grass can the goat graze? a. 68 sq. m. b. 68 sq. m. b. 86 sq. m. d. 86 sq. m.

22. The midpoint of the line segment between P1(x,y) and P2(-2,4) is PM(2,-1). Find the coordnates of P1. a. (6,5) b. (6,-6) c. (5,-6) d. (5,-5)

16. A pentagon has sides 20 cm. An inner pentagon with sides of 10 cm is inside and concentric to the larger pentagon. Determine the area inside and concentric to the larger pentagon but outside of the smaller pentagon. a. 430.70 sq. cm b. 573.26 sq. cm c. 473.77 sq. cm d. 516.14 sq. cm 17. The corners of a cubical block touched the closest spherical shell that encloses it. The volume of the box is 2744 cm3. What volume in cm3 inside the shell is not occupied by the block? a. 4713.56 b. 1728.21 c. 9023.23 d. 2903.14 18. The sum of the radii of the bases of a frustrum of a cone is 7 cm. If it has an altitude of 6 cm. and a volume of 232.48 cm3, compute the radius of the smaller base. a. 5 cm b. 4 cm c. 2 cm d. 3 cm 19. A tetrahedron has a surface area of 140 sq. m. Compute for the volume of the tetrahedron. a. 80 cu. m. b. 86 cu. m. c. 92 cu. m. d. 98 cu. m.

b. 18 d. 30

23. The x and y intercepts of the line are 2 and 5 respectively. Determine the equation of this line. a. 5x – 2y – 10 = 0 b. 5x + 2y = 0 c. 5x + 2y +10 = 0 d. 5x – 2y = 0 24. Find the distance between the point A(3,4) and the line 5x + 12y - 10 = 0. a. 33/13 b. 43/13 c. 53/13 d. 63/13 25. Find the distance between the lines 4x – 3y = 12 and 8x – 6y = -16. a. 3 b. 4 c. 5 d. 6 26. A figure formed by the intersection of a plane and a right circular cone. a. Hyperbola b. Ellipse c. Parabola d. Conic Sections 27. The major axis of the elliptical path in which the earth moves around the sun is approximately 186,000,000 miles and the eccentricity of the ellipse is 1/60. Determine the apogee of the earth. a. 93,000,000 miles b. 91,450,000 miles c. 94,335,100 miles d. 94,550,000 miles

20. Find the inclination of the line that passes through the points (4,-3) and (-1,3). a. 129.8 deg b. 151.2 deg c. 162.6 deg d. 124.5 deg

28. Find the radical axis of the circle x2 + y2 + 8x – 6y = 0 and the circle x2 + y2 – 12x – 16y + 20 = 0. a. 2x + y = 2 b. x + 2y = 2 c. 2x – y = 2 d. x – 2y = 2

21. Find the area of a pentagon connecting the points A(3,0), B(2,3), C(-1,2), D(-2,-1) and E(0,-3)

29. The line passing through the focus and perpendicular to the directrix of a parabola.

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ENGINEERING MATHEMATICS a. latus rectum c. transverse axis

b. axis of parabola d. major axis

30. An arch 18 m high has a form of parabola with a vertical axis. The length of the horizontal beam placed across the arch 8 m from the top is 64 m. Find the width of the bottom. a. 76 m b. 86 m c. 96 m d. 106 m 31. How many 3 digit odd numbers can be form from the digits 0, 1, 2, 3, 4 and 5 where no digit may repeated in a given number? a. 36 b. 48 c. 52 d. 76 32. In how many ways can 4 persons be seated in consecutive seats in a row of 8 seats? a. 72 b. 96 c. 120 d. 168 33. My school’s ECE club has 6 boys and 8 girls. I need to select a team to send to the IECEP competition. We want 6 people on the team. In how many ways can I select the team to have more boys than girls? a. 1414 b. 4141 c. 469 d. 694 34. A pair of fair dice is thrown. Find the probability that the sum is 10 or greater if 5 appears on the first die. a. 1/3 b. 3/11 c. 1/4 d. 4/11 35. In a guessing type of exam with 4 choices, what is the probability that you will get at least 7 of the 10 items? a. 0.0031 c. 0.0038 b. 0.03089 d. 0.3089 36. During an acquaintance party, each person shake hands with all other in the party. If there were a total of 91 handshakes, how many persons attend the party?

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a. 11 c. 13

b. 12 d. 14

37. On the first six tests, Ares scores were 95, 91, 92, 78, 92, and 86. If Ares took a seventh test and raised his test’s mean by exactly +1, what was his score on the seventh test? a. 89 b. 95 c. 92 d. 96 38. If P(A) = 0.7; P(B) = 0.6 and P(A ⋂ B) = 0.4, find the value of P(AC ⋂ BC). a. 0.2 b. 0.3 c. 0.4 d. 0.1 39. For all sets A and B, (A ⋂ B) ⋃ (A ⋂ BC) is equal to: a. A b. B C c. A d. BC 40. What is the 2nd derivative of sinh x? a. -sinh x b. –cosh x c. sinh x d. cosh x 41. We are given the values of the differentiable real functions f, g, h, as well as the derivatives of their pairwise products, at x = 0: f(0) = 1; g(0) = 2; h(0) = 3; (gh)’(0) = 4; (hf)’(0) = 5; (fg)’(0) = 6. Find the value of (fgh)’(0). a. 10 b. 12 c. 14 d. 16 42. The charge in coulombs that passes through a wire after t seconds is given by the function: Q(t) = t3 – 2t2 + 5t + 2. Determine the average current during the first two seconds. a. 5 b. 7 c. 9 d. 11 43. Find the slope of the ellipse x2 + 4y2 - 10x + 16y + 5 = 0 at the point where y = -2 + 80.5 and x = 7. a. -0.1654 b. -0.1538 c. -0.1768 d. -0.1463

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ENGINEERING MATHEMATICS 44. A rectangle has side length sin x and cos x for some x. What is the largest possible area of such a rectangle? a. 1/4 b. 3/4 c. 1/2 d. 1

51. A hole of radius 2 is drilled through the axis of a sphere of radius 3. Compute the volume of the remaining solid. a. 46.832 b. 56.235 c. 26.315 d. 18.327 Page | 4

45. A man whose height is 1.8 m is walking directly away from a lamp post at constant rate of 1.2 m/s. If the lamp is 12 m above the ground, find the rate at which the tip of his shadow is moving. a. 5.29 m/s b. 5.01 m/s c. 2.21 m/s d. 1.42 m/s 46. The length of a rectangle of a constant area 800 sq. cm is increasing at a rate of 4 cm per second. What is the rate of change of the width when the width is 10 cm? a. 0.5 cm/s b. -0.5 cm/s c. 32 cm/s d. -32 cm/s 47. Which of the following is NOT an improper integral? +∞ 0 a. ∫−∞ 𝑥 2 𝑑𝑥 b. ∫−∞ 𝑒 𝑥 𝑑𝑥 1

𝑥2

c. ∫−3 𝑥 4 +3𝑥 3 𝑑𝑥

5

d. ∫0

𝑥2

𝑥 3 −8𝑥 2

𝑑𝑥

48. Find the centroid of the area under the curves 5y2 = 16x and y2 = 8x -24 a. (0, -2.2) b. (-2.2, 0) c. (2.2, 0) d. (0, 2.2)

52. A bag containing originally 60 kg of flour is lifted through a vertical distance of 9 m while it is being lifted, the flour is leaking from the bag at such rate that the number of pounds lost is proportional to the square root of the distance traversed. If the total loss of the flour is 12 kg, find the amount of work done in lifting the bag. a. 4591 J b. 5338 J c. 4290 J d. 6212 J 53. Find the volume of the solid formed if we rotate the ellipse 4x2 + 9y2 = 36 about the line 4x + 3y = 20. a. 482 b. 452 c. 48 d. 45 54. The differential equation in the form: (1-x2)y” – xy’ + n2y = 0 is called as: a. Chebyshev Differential Equation b. Hermite Differential Equation c. Laguerre Differential Equation d. Legendre Differential Equation

49. Find the centroid of the area under the curves y2 = 9x and its latus rectum. a. (0, 1.35) b. (1.35, 0) c. (1.53, 0) d. (0, 1.53)

55. The differential equation in the form: y” – 2xy’ + 2ny = 0 is called as: a. Chebyshev Differential Equation b. Hermite Differential Equation c. Laguerre Differential Equation d. Legendre Differential Equation

50. Find the moment of inertia of the area bounded by the curve x2 = 4y, the line y = 1 and the y-axis on the first quadrant with respect to the x-axis. a. 8/15 b. 4/7 c. 16/15 d. 8/7

56. The differential equation in the form: xy” + (1-x)y’ + ny = 0 is called as: a. Chebyshev Differential Equation b. Hermite Differential Equation c. Laguerre Differential Equation d. Legendre Differential Equation 57. The differential equation in the form: (1-x2)y” – 2xy’ + n(n+1)y = 0 is called as:

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ENGINEERING MATHEMATICS a. b. c. d.

Chebyshev Differential Equation Hermite Differential Equation Laguerre Differential Equation Legendre Differential Equation

58. Given a differential equation in the form y’+P(x)y=Q(x)yn. What is the name of this DE if n=0? a. Linear DE b. Variable Separable DE c. Bernoulli DE d. Parabolic DE 59. Obtain a particular solution for the following differential equation, given x = 2 and y = 3. 2xyy’=1+y2 a. y=sqrt(5x-1) b. y=sqrt(2x+1) c. y=sqrt(x-1) d. y=sqrt(3x+2) 60. Solve the following differential equation: yiv+2y”+1=0 a. C1cos(x)+C2sin(x)+C3e-3xcos(x)+C4e-3xsin(x) b. C1cos(x)+C2sin(x)+C3excos(x)+C4exsin(x) c. C1xcos(x)+C2xsin(x) d. C1cos(x)+C2sin(x)+C3xcos(x)+C4xsin(x) 61. A thermometer has 70C reading. It was placed in a room having a 20C ambient temperature. In 4 minutes, the thermometer reading became 30C. What is the thermometer reading after another 11 minutes? a. 20.5C b. 20.1C c. 0.59C d. 0.12C 62. A bacteria culture is known to grow at a rate proportional to the amount present. After four hour, 1000 strands of the bacteria are observed in the culture; and after four hours, 3000 strands. Find the approximate number of strands of the bacteria originally in the culture. a. 496 b. 964 c. 694 d. 946 63. What is s in the Laplace Transform? a. Complex Time b. Complex Frequency c. Complex Variable d. Complex Plane

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64. The series expansion of (sin t)/t is a. 1 – t2/3! + t4/5! – t6/7! + … b. 1/t – t2/2! + t4/4! – t6/6! + … c. 1 + t2/3! + t4/5! + t6/7! + … d. 1 – t3/3! + t5/5! – t7/7! + … Page | 5

65. Find the Laplace Transform of 4 – 3t + 5t a. 4s-1 – 3s-2 + 10s-3 b. 4 – 3s-1 + 10s-2 c. 4s – 3s2 + 10s3 d. 4 – 3s + 10s2

2

66. Determine the Laplace Transform of etcos wt. a. (s-1)/[(s-1)2 + w2] b. (s-1)/[(s+1)2 - w2] c. (s+1)/[(s+1)2 + w2] d. (s-1)/[(s-1)2 - w2] 67. Determine the Wronskian of the set: {ex, e-x} a. -2 b. 1 c. 3 d. 0 68. Determine a0 in the Fourier Series expansion of the function f(x) = x2 in the interval of >x>-. a. 2/3 b. 22/3 c. /3 d. 2/3 69. Solve for a3 in the Fourier Series expansion of f(x). 1, 𝑖𝑓 − 𝜋 < 𝑥 < 0 𝑓(𝑥) = { 2, 𝑖𝑓 0 < 𝑥 < 𝜋 a. 0 b. 3/2 c. 1/2 d. 5/2 70. Given a discrete function: x[n] = (7/8)nu[n]. Determine the z-transform. a. 1/[1-(7/8)z] b. 1/[1-(7/8)z-1] c. z/[1-(7/8)z] d. z-1/[1-(7/8)z-1] 71. Evaluate e1+i a. 1.46+2.29i c. 1.64+2.29i

b. 1.46-2.29i d. 1.64-2.29i