Bsece Licensure Examination In Mathematics - November 1999

BSECE Licensure Examination in Mathematics - November 1999 1.The times required for the examinees to solve the same problem differ by two minutes. Together they can solve 32 problems in one hour. How long will it take for the slower problem solver to solve a problem? a) 3 minutes b) 2 minutes c) 4 minutes d) 5 minutes 2.If y – x ln x, find (d^2 y)(dx^2) a) 1/x^2 b) -1/x c) 1/x d) -1/x^2 3.What nominal rate compounded semi-annually, yields the same amount as 16% compounded quarterly? a) 16.64% b) 16.32% c) 16.00% d) 16.16% 4.A 40-gm rifle with a speed of 300m/s strikes into a ballistic pendulum of mass 5 kg suspended from a cord 1 m long. Compute the vertical height through which the pendulum rises. a) 28.45 cm b) 29.88 cm c) 28.87 cm d) 29.42 cm 5.A regular octagon is inscribed in a circle of a radius 10. Find the area of the octagon. a) 228.2 b) 282.8 c) 238.2 d) 288.2 6.What is the area of the largest rectangle that can be inscribed in a semi-circle of radius 10? a) Sqrt(50) units^2 b) 100 units^2 c) 2(sqrt(50)0 units^2 d) 1000 units^2 7.Given the points (3, 7) and (-4, -7). Solve for the distance between them. a) 16.56 b) 17.65 c) 14.65 d) 15.65

8.Determine the vertical pressure due to column of water 85-m high. a) 8.33 x 10^3 N/m^2 b) 8.33 x 10^5 N/m^2 c) 8.33 x 10^5 N/m^2 d) 8.33 x 10^4 N/m^2 9.The integral of any quotient whose numerator is the differential of the denominator is the _____. a) product b) derivative c) cologarithm d) logarithm 10.You loan from a loan firm an amount of P 100, 000 with a rate of simple interest of 20% but the interest was deducted from the loan at the time the money was borrowed. If at the end of one year, you have to pay the full amount of P 100, 000 what is the actual rate of interest? a) 30.0% b) 18.8% c) 25.0% d) 27.5% 11.Find the distance of the directrix from the center f the ellipse if its major axis is 10 and its minor axis is 8. a) 8.3 b) 8.7 c) 8.1 d) 8.5 12.Evaluate the expression (1 + i^2)^10 where i is the imaginary number. a) 1 b) -1 c) zero d) 10 13.The point of intersection of the planes x + 5y – 2z = 9, 3x – 2y + z = 3 and x + y + z = 2 is at a) (1, -1, 2) b) (2, 1, -1) c) (1, 2, 1) d) (-1, -1, 2) 14.If arctan x + arctan (1/3) = π/4, then the value of x is a) 1/5 b) 1/4 c) 1/2 d) 1/3

15.A 200-gram apple is thrown from the edge of a tall building with an initial speed of 20m/s. What is the change in kinetic energy of the apple if it strikes the ground at 50m/s? a) 210 Joules b) 81 Joules c) 130 Joules d) 100 Joules 16.Find the probability of getting exactly 12 out of 30 questions on a true or false. a) 0.15 b) 0.08 c) 0.04 d) 0.12 17.The sum of the digits of a two-digit number is 11. If the digits are reversed, the resulting number is seven more then twice the original number. What is the original number? a) 44 b) 38 c) 53 d) 83 18.If a regular polygon has 27 diagonals, then it is a, a) heptagon b) pentagon c) hexagon d) nonagon 19.A point moves so that its distance from the point (2, -1) is equal to the distance from the x –axis. The equation of the locus is a) X^2 - 4x -2y + 5 =0 b) X^2 + 4x – 2y – 5 =0 c) X^2 + 4x +2y + 5 = 0 d) X^2 - 4x + 2y + 5 = 0 20.What rate of interest compounded annually is the same as the rate of interest of 8% compounded quarterly?? a) 8.48% b) 8.42% c) 8.86% d) 8.24% 21.The amount of heat needed to change solid to liquid is a) condensation b) solid fusion c) latent heat of fusion d) cold fusion

© Copyright BSECE Online Board Examination Reviewer 2009.

BSECE Licensure Examination in Mathematics - November 1999 22.If a = b, then b = a. This illustrates which axiom in Algebra? a) Transitive axiom b) Symmetric axiom c) Reflexive axiom d) Replacement axiom

23.Find the sum of the roots of 5x^2 - 10x + 2 = 0. a) -1/2 b) 2 c) 1/2 d) -2 24.It is a measure of relationship between two variables. a) Function b) Relation c) Equation d) Correlation 25.A VOM has a selling price of P 400. If it’s selling price is expected to decline at the rate of 10% per annum due to obsolesce, what will be its selling price after 5 years? a) P 200.00 b) P 236.20 c) P 213.10 d) P 249.50 26.Find the area bounded by the curve y = 9 – x^2 and the x axis. a) 30 units^2 b) 18 units^2 c) 25 units^2 d) 36 units^2 27.To compute the value of n factorial, in symbolic form (n!); where n is large number, we use the formula called a) Matheson’s Formula b) Richardson-duchman Formula c) Diophantine Formula d) Stirling’s Formula 28.Find the nominal rate, which if converted quarterly could be used instead of 12% compounded semi-annually. a) 11.83% b) 11.29% c) 21.34% d) 14.02%

29.What is the distance in cm between two vertices of a cube which are farthest from each other, if an edge measures 8 cm? a) 12.32 b) 13.86 c) 16.93 d) 14.33 30.The distance between the points AB defined by A (cos A, sin A) an B (sin A, cosA) is equal to a) Sqrt(2) b) 1 c) 2 tan A d) Cos A 31.Find the length of the vector (2, 4, 4).. a) 5.16 b) 7.00 c) 6.00 d) 8.50

35.According to this law, “The force between two charges varies directly as the magnitude of each charge and inversely as the square of the distance between them..” a) Inverse square Law b) Law of Universal Gravitation c) Newton’s Law d) Coulomb's Law 36.A loan of P 5, 000 is made for a period of 15 months, at a simple interest rate of 15%, what future amount is due at the end of the loan period? a) P 5, 937.50 b) P 5, 842.54 c) P 5, 637.50 d) P 5, 900.90 37.If tan 4A = cot 6A, then what is the value of angle A? a) 14° b) 10° c) 12° d) 9°

32.Mr. J. Reyes borrowed money from the bank. He received from the bank P 1, 842 and promise to repay P 2,000 at the end of 10 months. Determine the simple interest. a) 15.70% b) 19.45% c) 16.10% d) 10.29%

38.At the surface of the earth 9 = 9.806m/s^2. Assuming the earth to be a sphere of radius 6.371 x 10^6 m, compute the mass of the earth. a) 5.12 x 10^24 kg b) 5.97 x 10^23 kg c) 5.62 x 10^24 kg d) 5.97 x 10^24 kg

33.It is a polyhedron of which two faces are equal polygons in parallel planes and the other faces are parallelograms. a) Prismatoid b) Frustum c) Prism d) Tetrahedron

39.Find the approximate change in the volume of a cube of side “x” inches caused by increasing its side by 1%.. a) 0.02 x^2 in^3 b) 0.03 x^2 in^3 c) 0.1 x^2 in^3 d) 0.30 x^2 in^3

34.A regular hexagonal pyramid has a slant height of 4 cm and the length of each side of the base is 6 cm. Find the lateral area. a) 72 cm^2 b) 62 cm^2 c) 52 cm^2 d) 82 cm^2

40.The energy stored in a stretched elastic material such as spring is a) internal energy b) mechanical energy c) kinetic energy d) elastic potential energy 41.A boat can travel 8 miles per hour in still water. What is its velocity with respect to the shore if it heads 35° East of North? a) 8.963 b) 6.743 c) 4.588 d) 5.400

© Copyright BSECE Online Board Examination Reviewer 2009.

BSECE Licensure Examination in Mathematics - November 1999

42.A railroad is to be laid-off in a circular path. What should be the radius if the track is to change direction by 30° at a distance of 157.08 m? a) 300m b) 250 m c) 150 m d) 200 m 43.A central angle of 45 degrees subtends an arc of 12 cm. what is the radius of the circle? a) 15.82 cm b) 15.28 cm c) 12.82 cm d) 12.58 cm 44.A metal washer 1-inch in diameter is pierced by 1/2-inch hole. What is the volume of the washer if it is 1/8 inch thick? a) 0.028 b) 0.074 c) 0.082 d) 0.047

49.Two post, one 8 m and other 12 m high are 15 cm apart. If the posts are supported by a cable running from the top of the first post to a stake on the ground and then back to the top of the second post, find the distance from the lower post to the stake to use minimum amount of wire? a) 8 m b) 4 m c) 9 m d) 6 m 50.In a box there are 25 coins consisting of quarters, nickels and dimes with a total amount of $ 2.75. If the nickels were dimes, and dimes were quarters and the quarters were nickels, the total amount would be $ 3.75. How many quarters are there? a) 5 b) 10 c) 16 d) 12

45.A machine cost P 8,000 and an estimated life of 10 years with a salvage value of P 500. What is its book value after 8 years using straight-line method? a) P 4, 000 b) P 2, 000 c) P 2, 000 d) P 3, 000 46.The volume of the two spheres is the ratio 27:343 and the sum of their radii is 10. Find the radius of the smaller sphere. a) 3 b) 5 c) 4 d) 6 47.The perimeter of an isosceles right triangle is 6.6824. Its area is a) 4 b) 1/2 c) 1 d) 2 48.If (2 log x to the base 4) – (log 9 to the base 4) = 2, find x a) 10 b) 11 c) 13 d) 12

© Copyright BSECE Online Board Examination Reviewer 2009.