Licensure Examination in Mathematics - November 1997

BSECE Licensure Examination in Mathematics - November 1997 1.A man wishes his son to receive P 500,000 ten years from now. What amount should he invest today if it will earn interest of 12% compounded annually during the first 5 years and 15% compounded quarterly during the next 5 years? a) P 123,433.23 b) P 145,345.34 c) P 134,678.90 d) P 135,868.19 2.A plane headed due east with airspeed of 240 mph. If a wind at 40 mph is blowing from the north, find the ground speed of the plane. a) 274 mph b) 200 mph c) 243 mph d) 281 mph 3.Given an ellipse ( x^2/36 ) + ( y^2/32 ) = 1. Determine the distance between foci. a) 4 b) 3 c) 18 d) 2 4.What is the accumulated amount after three years of P 6500 invested at the rate of 12% per year compounded semiannually? a) P 9500 b) P 9248 c) P 9321 d) P 9221 5.Find the 100th term of the sequence 1.01, 1.00, 0.99…. a) 0.04 b) 0.02 c) 0.05 d) 0.03 6.Find the value of x in the equation csc x + cot x = 3. a) π/5 b) π/3 c) π/2 d) π/4

7.Convergent series is a sequence of decreasing numbers or when the succeeding term is _______ then the preceding term. a) equal b) ten times more c) lesser d) greater 8.What interest rate compounded monthly is equivalent to 10% effective rate? a) 9.47% b) 9.68% c) 9.57% d) 9.75% 9.The population of the Philippines doubled in the last 30 years from 1967 to 1997.  Assuming the rate of population increase will remain the same, in what year will the population triple? a) 2027 b) 2030 c) 2015 d) 2021 10.Evaluate the limit ln x/x as x approaches infinity. a) infinity b) 1 c) zero d) e 11.A piece of wire is shaped to enclose a square whose area is 169 sq. cm. It is then reshaped to enclose a rectangle whose length is 15 cm. The area of the rectangle is __________. a) 156 sq. cm b) 175 sq. cm c) 165 sq. cm d) 170 sq. cm 12.A line, which is perpendicular to the x-axis, has a slope equal to ________. a) e b) infinity c) 1 d) 2

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13.Find the coordinates of the point P(2, 4) with respect to the translated axis with origin at (1,3). a) ( –1,  –1, –  –1) 1) b) (1, 1) c) (1, – (1, –1) 1) d) ( –1,  –1, 1) 14.The midpoint of the line segment between P1(x1, y1) and P2( –2,  –2, 4) is P(2,  –1).  –1). Find the coordinates of P1. a) (5, – (5, –6) 6) b) ( –6,  –6, 6) c) (6, – (6, –6) 6) d) (6, – (6, –5) 5) 15.If ( x + 3) : 10 = ( 3x  – 2)  – 2) : 8, find ( 2x – 2x – 1).  1). a) 3 b) 4 c) 2 d) 1 16.A market situation whereby there is only one buyer of an item for which there are no goods substitute. a) Monopsony b) Oligopoly c) Oligopsony d) Monopoly 17.If y = x ln x, find d^y/dx^2. a) 1/x^2 b) – b) – 1/x  1/x c) – c) – 1/x^2  1/x^2 d) 1/x 18.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) Law of Universal Gravitation b) Newton’s Law c) Coulomb’s Law d) Inverse Square Law 19.If a regular polygon has 27 diagonals, then it is a ________. a) pentagon b) heptagon c) hexagon d) nonagon

BSECE Licensure Examination in Mathematics - November 1997 20.Of what quadrant is A, if sec  A is positive and csc A is negative? a) II b) III c) I d) IV 21.A machine costs 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 4000 b) P 2500 c) P 3000 d) P 2000 22.The wheel of a car revolves “n” times, while the car travels “x” km. The radius of the wheel in meters is _________. a) 500000x/(pi)n b) 10000x/(pi)n c) 500x/(pi)n d) 5000x/(pi)n 23.The measure of 2.25 revolutions counterclockwise is  _________. a) 805 degrees b) – 810 degrees c) – 835 degrees d) 810 degrees 24.The volume of a sphere is 36π cu. m. The surface area of this sphere in sq. m is _______. a) 24π b) 18π c) 36π d) 12π 25.Find the approximate change in the volume of a cube of side “x” inches caused by increasing its side by 1%. a) 0.03 x^3 cu. in b) 0.1 x^3 cu. in c) 0.02 x^3 cu. in d) 0.3 x^3 cu. in 26.The roots of a quadratic equation are 1/3 and 1/4. What is the equation? a) 12x^2 – 7x – 1 = 0 b) 12x^2 + 7x –1 = 0 c) 12x^2 – 7x + 1 = 0 d) 12x^2 + 7x + 1 = 0

27.If the second derivative of the equation of a curve is equal to the negative of the equation of that same curve, the curve is  _________. a) A paraboloid b) An exponential c) A cissoid d) A sinusoid 28.Three sides of a trapezoid are each 8-cm long. How long is the fourth side when the area of the trapezoid has the greatest value? a) 15 b) 16 c) 10 d) 12 29.A regular octagon is inscribed in a circle of radius 10. Find the area of the octagon. a) 288.2 b) 282.8 c) 238.2 d) 228.2 30.In complex algebra, we use a diagram to present a complex plane commonly called _______. a) Argand diagram b) Funicular diagram c) Venn diagram d) De Moivre’s diagram 31.A 50 kg block of wood rest on top of the smooth plane whose length is 3 m and whose altitude is 0.8 m. How long will it take for the block to slide to the bottom of the plane when released? a) 1.52 s b) 2.14 s c) 2.41 s d) 2.51 s 32.What is the moment of inertia of a cylinder of radius 5 m and a mass of 5 kg? a) 72.5 kg-m^2 b) 120 kg-m^2 c) 380 kg-m^2 d) 62.5 kg-m^2

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33.In an ellipse, a chord which contains a focus and is in a line perpendicular to the major axis is a _________. a) Conjugate axis b) Focal width c) Minor axis d) Latus rectum 34.Which of the following cannot be an operation of matrices? a) Subtraction b) Addition c) Multiplication d) Division 35.If sec^2 A is 5/ 2, the quantity 1  –  sin^2 A is equivalent to  _________. a) 2.5 b) 0.6 c) 1.5 d) 0.4 36.Two triangles have equal bases. The altitude of one triangle is 3 units more than its base while the altitude of the other is 3 units less than its base. Find the altitudes if the areas of the triangle differ by 21 square units. a) 6 and 12 b) 5 and 11 c) 4 and 10 d) 3 and 9 37.A comfortable room temperature is 72°F. What is this temperature expressed in degrees Kelvin? a) 290 b) 275 c) 263 d) 295 38.How long will it take the money to triple itself if invested at 10% compounded semiannually? a) 11.9 yrs b) 13.3 yrs c) 11.3 yrs d) 12.5 yrs 39.Find the 30th term of the arithmetic progression 4, 7, 10…. a) 91 b) 71 c) 81 d) 61

BSECE Licensure Examination in Mathematics - November 1997 40.A car accelerates at a constant rate from 15 mi/hr to 45 mi/hr in 15 seconds, while travelling in a straight line. What is the average acceleration? a) 2.00 ft/sec^2 b) 2.12 ft/sec^2 c) 2.39 ft/sec^2 d) 2.93 ft/sec^2 41.The quartile deviation is a measure of ________. a) certainty b) central tendency c) division d) dispersion 42.15% compounded semiannually will have an effective rate of _________. a) 15.93% b) 16.02% c) 18.78% d) 15.56% 43.The volume of a gas under standard atmospheric pressure 76-cm of Hg is 200 cu. inches. What is the volume when the pressure is 80 cm Hg if the temperature is unchanged? a) 190 cu. in b) 90 cu. in c) 110 cu. in d) 30.4 cu. in

47.The denominator of a certain fraction is three more than twice the numerator. If 7 is added to both terms of the fraction, the resulting fraction is 3/5. Find the original fraction a) 5/13 b) 8/ 3 c) 5/3 d) 13/5 48.Find the length of the vector (2, 4, 4). a) 8.50 b) 6.00 c) 7.00 d) 5.18 49.One side of a regular octagon is 2. Find the area of the region inside the octagon. a) 31 b) 19.3 c) 13.9 d) 21.4 50.The velocity of an automobile starting from rest is given by ds/dt = (90t) ⁄ (t+10) feet/sec. Determine the acceleration after the time interval of 10 sec. a) 2.10 ft/s^2 b) 2.25 ft/s^2 c) 1.71 ft/s^2 d) 2.75 ft/s^2

44.What rate of interest compounded annually is the same as the rate of interest of 8% compounded quarterly? a) 8.42% b) 6.88% c) 8.24% d) 7.90% 45.It is the characteristic of a population which is measurable. a) Distribution b) Parameter c) Sample d) Frequency 46.Convert the θ = π/3 to Cartesian equation. a) x = 3^(1/2) b) y = x c) y = 3^(1/2)x d) 3y = 3^(1/2)x

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