Download - Algbra Trigo Wkly Exm Solution

MATHEMATICSEXCEL REVIEW CENTER

WEEKLY EXAM 011. How many different numbers of eight digits each

can be formed by using three 4’s, three 6’s and two 8’s? A. 560 * C. 840B. 1250 D. 720

Solution to Problem No. 1

2. What is the 17th term of the sequence 68, 56, 44, 32 …A. – 124 * C. 234B. – 324 D. 421


3. What is the fifty-fifth term of 1, -1, 1, -1 … A. 1 * C. 0B. -1 D. infinity


4. Which of the following is the value of m for the given equation m (raised to negative 2/3) – m (raised to negative 1/3 ) – 2 = 0.A. 1 C. 0 B. – 1 * D. 5


5. Determine the real root of the equation y = x3 – 4x2 – 12 x –6 = f(x) , to the nearest thousand. A. 5.231 C. 6.124 *B. 7.312 D. 3.124


6. If tan A = 1/3 and cot B = 2, tan ( A – B ) is equal to : ______A. 11/7 C. – 11/7B. – 1/7 * D. 1/7


7. Solve the root of the given equation

.A. 5 C. 10B. – 5 D. no solution *


8. Solve for x: 3 (raised to – 2x ) = 27.A. 1/3 C. 3/2 B. 2/3 D. – 3/2 *


9. Suppose a trip from dormitory to the lake at 30 mph takes 12 minutes longer than the return trip at 48 mph. How far are the dormitory and the lake?A. 20 miles C. 15 miles B. 18 miles D. 16 miles *


10. Which of the following quadratic equations whose sum and product of the roots are 4 and 7 respectively.A. x2 – 4x + 7 = 0 * C. x2 – 2x + 8 = 0B. x2 – 5x + 10 = 0 D. x2 – 10x + 15 =

0


11. The first term of geometric sequence is 3 and the fourth term is -24. Find the sum of the first 10 terms ?A. – 1320 C. – 1230B. – 1983 D. – 1023 *


12. If the probability that a player shoots a 3-point range is 2/5, determine the probability of shooting 5 out of 8 attempts.

CEBU: 2nd Fl. LBF Building V. Gullas St., Cebu City Tel/fax (032) 253-8759 or 254-4384 MANILA: 4th Flr. CMMFI Bldg. R. Papa St. Sampaloc, Manila Tel/fax (02) 736-2688 e-mail: [email protected]

310’215’x y

512


A. 28.4 % C. 31.1 %B. 12.4 % * D. 21.3 %


13. The illumination received for a light source varies inversely as the square of the distance from the source and directly as its candle power. At what distance from a 50-cp light would the illumination be one-half that received at 20 ft from a 40-cp light?

A. 10 C. 3

B. 5 D. 5


14. The mean of 10 numbers is x and the mean of another 5 numbers is y. What is the mean of the 15 numbers?

A. * C.

B. D. none of these


15. Five balls numbered 1, 2, 3, 4, and 5 are placed in an urn. If one ball is drawn one at a time at random without replacing the ball after drawing, what is the probability that they are in ascending order?A. 1/24 C. 1/120 *B. 0.20 D. 0.02


16. If x = y and y = x . This illustrates which axiom in Algebra?A. symmetric axiom C. reflexive axiomB. transitive axiom D. inverse axiom


If x = y and y = x then it is symmetric Axiom

17. The time required for two examinees to solve the same problem differs 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. 5 minutes * C. 3 minutesB. 2 minutes D. 4 minutes


18. Solve the inequality : (3x – 2 ) ¿ ( 5x – 12 )A. x ¿ 5 * C. x < 5

B. x > 5 D. x ¿ 5


19. What is the multiplicative inverse of x?A. – x C. 1/x *B. – 1/x D. x2


20. Two ships are observed from a cliff that is 512 ft high. At a certain instant the angles of depression as observed are 215’ and 310’. How far are the ships if they are in line and directly outward the observer?A. 7654 C. 7450 B. 7540 * D. 7456


21. An spherical balloon is inflated. During the each second its radius expands by an amount equal to 0.01 in. less than the radius expanded during the previous second. If the radius R expands at the rate of 0.35 in. per second when R = 18 in., what is R exactly 30 seconds later?A. 30.14 C. 24.15 *B. 20.78 D. 23.14




26 25 24 10 10 10

Any of the 25 letters left (since there is one used in the first) can be used.Any of the 24letters left since the two letters are in the first and second places.

Any of the 10 numbers can be used.

300 x x 300

20% 80%20% 25%

=+-

x = 8

120

A

B

O

x = 6

z

22. The quantity 1 – tanh2x is equal to:A. – sech2 x C. csch2 xB. cosh2x D. sech2 x *


Using trigonometric identities:

1 – tan h2 x = sec h2 x

23. If ( 2log x to the base 4 ) – ( log 9 to the base 4 ) = 2, find x:A.10 C. 12 *B.13 D. 11


24. Terry losses 18 lbs in 6 months, 12 lbs in the next 6 months , 8 in the next 6 months and so on for a long time. What is the maximum total weight lost ?A. 60 lbs C. 54 lbs *B. 45 lbs D. 35 lbs


25. How many automobile license plates of six symbols can be made if each one begins with three letters and the ends with 3 digits.A. 15,600,000 * C. 27B. 9 D. 1,674,000


N = = 15,600,000

26. The unit “gross” meansA. 100 pieces C. 12 dozens *B. 100 dozens D. 120 pieces


“ Gross “ means 12 dozens

27. A chemist has 300 grams of 20% hydrochloric acid solution. He wishes to drain some off and replace it with an 80% solutions so as to obtain a 25% solution. How many grams must he drain and replace with the 80 % solution ?A. 20 C. 12B. 23 D. 25 *


0.20(300) – 0.20x + 0.80x = 0.25(300)

x = 25

28. What is the sum of the coefficient in the expansion of

( 2x – 1 ) 20 ?A. 0 * C. 2B. 1 D. 3


The sum of coefficients can be solved by substituting the value of x equal to 1 and if there is a constant it must be raised to the same exponent as of the binomial and subtract it from original.

Sum of Coef. = [ 2(1) – 1 ] 20 - (1)25 = 0

29. Jones can paint a car in 8 hours. Smith can paint the same car in 6 hours. They start to paint the car together. After 2 hours, Jones leaves for lunch and Smith finishes painting the car alone. How long will it take Smith to do the job alone.A. 2.1 hrs C. 2.5 hrs *B. 3.5 hrs D. 3.0 hrs


x = 2.5 hrs

30. The sum of the digits of a three-digit number is 6. The hundreds digit is twice the units digit, and the tens digit is equals the sum of the two other. Find the number.A. 231 * C. 321B. 123 D. 213


Use reverse engineering:

The sum of the digits of the number 231 is six , the hundred digit is 2 which is twice the unit digit 1. The tens digit is 3, which if the sum of the hundred and unit digits which are 2 and 1 respectively. Answer: 231

31. Two ships A and B are sailing from point O along the routes such that the angle AOB is 120°. Ship A is sailing at 20 kph while ship B at 30 kph. How fast is the distance between them changing if at a certain instant, AO = 8 km and OB = 6 km? A. 42.74 kph * C. 40.22 kph

B. 45.75 kph D. 43.65 kph


32. Engineer Rojas owns a jewelry store. She marks up all merchandise 50 percent of cost. If he sells a ring for Php 1500, what did he pay the wholesale for it?A. Php 1500 C. Php 1000 *B. Php 2000 D. Php 800


x ( 1 + 0.50 ) = 1500

x = 1000

33. Eight men can dig 150 ft of trench in 7 hrs. Three men can backfill 100 ft of trench in 4 hrs. How long


Any of the 26 letters


4524

5.35

CA

B

will it take 10 men to dig and fill the 200 ft of trench?A. 9 hrs and 52 min * C. 8 hrs and 40

minB. 10 hrs and 3 min D. 7 hrs and 34

min


34. A man bought 20 chickens for P 20.00. The cocks cost P 3.00 each, the hens P 1.50 each and the chicks cost P 0.50 each. How many chicks did he buy ?A. 13 * C. 15 B. 10 D. 8


This is 2 equations 3 unknowns : use the solutions for Deophantine equations.

Answer: z = 13

35. The top of the cliff C is observed from A to have a vertical angle of 24. The observer then moves horizontally towards the cliff at point B 1500 m from A and found out that the vertical angle of C is 45. A, B and C lie on the same vertical plane. Find the elevation of the cliff if the height of instrument at A is 5.35 m above the sea level. A. 1209.6 m * C. 1450.7 mB. 1325.4 m D. 1190.4 m


eqn. 1 eqn. 2using eqns 1 and 2 and solve for c :

c = 1209.6 m

36. Sheri’s age in 20 years will be the same as Terry’s age is now. Ten years from now, Terry’s age will be twice Sheri’s. How old is Terry now?

A. 20 * C. 30 B. 10 D. 25


x = Sheri’s age now. y = terries age now.

This is 2 equation s two unknowns. Use calculator: x = 20

37. What is the mean proportional to 3 and 12?A. 4 C. 8B. 6 * D. 5


Mean proportional is =

38. If nine candles are blown out on birthday cake containing seven times as many candles altogether, how many candles are there all in all ?A. 2 C. 63 *B. 16 D. 72


There are seven times as many candles; thus ; 7 x 9 = 63

39. Engr Cuervo passes a farmhouse at 3:14 PM. At 3:56 PM he passes the second farm house. If he was traveling at uniform rate of 12 mph, how far apart are the farmhouses?A. 1.2 miles C. 3.0 milesB. 3.6 miles D. 8.4 miles *


There are 42 minutes from 3:14 at 3:56.

S = V t = 12 mi/hr ( 42 / 60 ) hr = 8.4 miles

40. Engr. Hermo needs to work five-sixth of a year to pay his car loan. If Tony begins working on March 1st, at the end of what month will he first be able to pay off his loan ?A. June C. OctoberB. August D. December *


, so , from march the tenth month is

December.

Answer : December

41. A project can be done by 70 men in 100 days. There were 80 men at the start of the project but after 50 days , 20 of them had to be transferred to another project. How long will it take the remaining workforce to complete the job ?A. 70 C. 80B. 50* D. 100


Use man-hour Analysis :

(70)(100) = 80( 50 ) + 60 ( x )

x = 50

42. What is the value of the square root of – 5 x square root of - 10 ?A. square root of 50 C. negative square root of

50 *B. imaginary D. square root of 50 times i

43. If sin = 3/5 and cos = 5/13 , find the sin ( + ).A.0.97 * C. 0.87B.0.78 D. 0.77

44. If the first and the fourth terms of a harmonic progression are 1/3 and 1/9 respectively, find the 8th term.A. 1/14 C. 1/17 *B. 1/11 D. 1/14

45. How many times will a clock strikes in 24 hours if it strikes only at the hours ?A. 156 times * C. 48 timesB. 78 times D. 24 hours


x1500


46. In a commercial survey involving 1,000 persons on brand preference, 120 were found to prefer brand x only, 200 prefer brand y only, 150 prefer brand z only, 370 prefer either brand x or y but not z, 450 prefer brand y or z but not x, and 420 prefer either brand z or x but not y. How many persons have no brand preference, satisfied with any of the 3 brands.

A. 230 * C. 180 B. 280 D. 130

47. In how many ways can you invite one or more of your five friends in a party ?A. 31 * C. 25B. 36 D. 15

48. The number 5 + 3 is :A. rational number C. surd *B. integer D. radicand

49. Two men do a job for P 250. If the men are to share the sum, in the ratio of 2:3 , find each man’s share .A. 100, 150 * C. 50 , 100B. 75, 100 D. 40, 120

50. Cora once went to town to sell some eggs. To the first customer she sold half her eggs and half an egg. To the second customer she sold half of what she then had left and half and egg. To the third customer, again, she sold half of what she then had left and half and egg. Three eggs remained. How many did she start with, assuming that she did not break any of egg ?A. 31 * C. 30B. 33 D. 34



MATHEMATICSTAKE HOME EXAM

INSTRUCTION: Select the correct answer for each of the following questions. Mark only one answer for each item by shading the box corresponding to the letter of your choice on the answer sheet provided. STRICTLY NO ERASURES ALLOWED. Use pencil No. 1 only.

1. An Engineer saved 25% of his income last month. If his expenses increase by 50%, how much must his income increase if he has no savings?A. 15.75 % C. 25.50 %B. 12.50 % * D. 17.50 %

2. If the superelevation of a 150 m highway curve is 10 degrees, what is the permissible velocity that the car may be given in order to maintain motion along the curve?A. 58 kph * C. 60 kphB. 72 kph D. 65 kph

3. What is the volume of a spherical pyramid whose spherical excess is 200 degrees and the radius of the sphere is 5 units?A. 145.44 * C. 132.89B. 159.21 D. 167.12

4. A metal ball is dropped from a height of 2 meters above a smooth floor. How high will it rebound if the coefficient of restitution between the ball and the floor is 0.80?A. 1.28 m * C. 1.63 mB. 1.42 m D. 1.51 m

5. A hollow spherical shell has a radius of 10 units and a mass of 20. What is its mass moment of inertia?A. 1289.3 C. 1620.0B. 1450.2 D. 1333.3 *

6. Evaluate: .A. 1/3 * C. infinityB. 3 D. 1

7. The unit “gross” meansC. 100 pieces C. 12 dozens *D. 100 dozens D. 120 pieces

8. What is the multiplicative inverse of x?C. – x C. 1/x *D. – 1/x D. x2

9. Two sides of a triangle are 6 m and 9 m respectively. If the included angle is changing at the rate of 2 rad per second, at what rate is the third side when the included angle is 60 ?A. 11.78 m/s * C. 17.82 m/sB. 12.45 m/s D. 10.18 m/s

10. Find the slope of the line having the parametric equation y = 4t + 6 and x = t + 1.A. 2 C. 4 *B. 3 D. 5

11. Solve the inequality : (3x – 2 ) ¿ ( 5x – 12 )A. x ¿ 5 * C. x < 5B. x > 5 D. x ¿ 5

12. The quantity 1 – tanh2x is equal to:C. – sech2 x C. csch2 xD. cosh2x D. sech2 x *

13. A water tank is a horizontal circular cylinder 10 feet long and 10 feet in diameter. If the water inside is 7. 5 feet deep, determine the volume of the water contained.A. 600.26 ft3 C. 568.67 ft3

B. 663.44 ft3 D. 631.85 ft3 *

14. 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, the dimes were quarters and the quarters were nickels, the total amount would be $ 3.75. How many quarters are there ? ( Note: Nickel = 5 cents, Dime = 10 cents, Quarter = 25 cents).A. 12 C. 10B. 16 D. 5 *

15. Find the distance of the directrix from the center of an ellipse if its major axis is 10 and its minor axis is 8.A. 8.5 C. 8.3 *B. 8.1 D. 8.7

B.

16. Find the probability of getting exactly 12 out of 30 questions on a true or false question.A.0.12 C. 0.15B.0.08 * D. 0.04

17. If a regular polygon has 27 diagonals, then it is a :A. Nonagon * C. HexagonB. Pentagon D. Heptagon

18. Each of the faces of a regular hexahedron is a :A. triangle C. rectangleB. square * D. hexagon

19. Determine x, so that; x , 2x + 7 , 10x - 7 will be a geometric progression.A. 7, -7/12 C. 7, -14/5B. 7, -5/6 D. 7, - 7/6 *

20. The BPI Family Bank advertises 9.5% accounts that yield 9.84 % annually. Find how often is the interest compounded ?A. Monthly C. Quarterly *B. Semi-annually D. Continuously

21. In Mathematics examination , a student may select 7 problems from a set of 10 problems . In how many ways can he make his choice ?A.120 * C. 720B.530 D. 320

22. Find the probability that a couple having 3 children will have at least one girl.

A.

78 * C.

34

B.

12 D.

58

23. A car weighing 12 kN including its own cargo is moving down a 30 slope. The driver sees an obstruction way ahead, so he applies the brakes at the instant that his speed is 20 m/s. What



constant force parallel to the road must be provided by the brakes so that the car should stop in a distance of 100 m ?A. 8446.5 N * C. 9775.6 NB. 7384.5 N D. 6385.6 N

24. Determine the radius of the sphere whose equation is : x2 + y2 + z2 – 2x + 8y + 16z + 65 = 0A. 5 units C. 4 units *B. 3 units D. 6 units

25. What is the limit value of y =

( x 3 +x )x2+x as x

approaches to zero?A. 1 * C. indeterminateB. 0 D. 3

26. The sides of a triangle are 8 cm , 10 cm, and 14 cm . Determine the radius of the inscribed and circumscribing circle.A. 3.45, 7.14 C. 2.45, 8.14B. 2.45, 7.14 * D. 3.45, 8.14

27. Each angle of the regular dodecagon is equal to ________ degrees.A. 135 C. 125B. 150 * D. 105

28. If eccentricity e of a conic is equal to one , the conic has :A. 2 vertices C. one vertex *B. greater than 2 vertices D. no vertex

29. The conic is symmetric with respect to its :A. latus rectum C. major axisB. principal axis * D. minor axis

30. The rule stating that the limit of the ratio of two functions of the same variable x as x approaches a value a , is equal to the limit of the ratios of their derivatives with respect to x.A. Newton’s Rule C. L’Hospital’s

Rule *B. De Gias’ Rule D. Leibniz Rule

31. If the general equation of the conic is Ax2 + 2Bxy + Cy2 + Dx + Ey + F = 0., and B2 – 4 AC > 0 , then the conic is :

A. circle C. ellipse B. parabola D. hyperbola *

32. What curve is represented by the equation r = a .A. Spiral of Archimedes * C.

CardioidB. Four - Leaved Rose D. Three-

leaved Rose

33. What is the remainder when 5x6 – 4x4 – 7x3 + 2x – 3 is divided by x + 1 . A. 3 * C 4 B. 2 D. 5

34. Find the smallest positive integer n such that the nth derivative of cos x with respect to x is cos x.

A. 2 C. 4 * B. 3 D. 5

35. The piston of an engine is connected by a 12-inch connecting rod to a point on a crank that rotates on a 4-inch radius about the crankshaft. If the crankshaft has an angular speed of 3000 revolutions per minute, determine the rectilinear speed of the piston per second, when the crank is 90 degrees to the motion of the piston.

A. 1,319 C. 1,257 * B. 1,194 D. 1,131

36. Evaluate the ( - 2x ) tan x A. 2 * C.

B. 0 D. 1

37. Find the probability of getting a prime number thrice by tossing a die 5 times.A. 0.3125 * C. 0.4125B. 0.3250 D. 0.3725

38. It is a sequence of numbers such that successive terms differ by a constant.

A. Arithmetic progression * C. Infinite progression

B. Geometric progression D. Harmonic progression

39. How much money you must invest today in order to withdraw P1000 annually for 10 years if the interest rate is 12%?A. P 5650 * C. P 6145B. P 5808 D. P 6454

40. What is the present worth of a P 500 annuity starting at the end of the third year and continuing to the end of the fourth year, if the annual interest rate is 10%.A. P 717.16 * C. P 720.32B. P 842.21 D. P 652.12

41. What is the coefficient of the 8 th term of the expansion of (2x – 3y)9?A. –314928 * C. –213258B. 314928 D. 213258

42. A 250 kg block rest on a 30° plane. If the coefficient of friction is 0.20, find the horizontal force applied on the block to prevent the block from sliding down the plane.A. 73.89 kg C. 82.23 kgB. 78.89 kg D. 84.57 kg *

43. What is the effective rate of 18% compounded semi-quarterly?A. 19.48% * C. 19.25%B. 19.67% D. 19.18 %

44. Money paid for use of borrowed capital.A. Interest rate C. Net income B. Gross income D. Interest *

45. A man walks across the bridge at a rate of 5 fps as a boat passes directly beneath him at 10 fps. If the bridge is 30 ft above the water, how fast are the man and the boat separating after 3 seconds?A. 7.33 fps C. 10.33 fpsB. 8.33 fps * D. 9.33 fps



46. The capacity to do work.A. Energy * C. PowerB. Potential D. Momentum

47. The natural length of a spring is 10 cm. A force of 10 kN will stretched it to a total length of 16 cm. Find the work done in stretching it to a total length of 17 cm.A. 408.33 J * C. 420.55 JB. 530.54 J D. 582.21 J

48. Two ships A and B are sailing from point O along the routes such that the angle AOB is 120°. Ship A is sailing at 20 kph while ship B at 30 kph. How fast is the distance between them changing if at a certain instant, AO = 8 km and OB = 6 km? A. 42.74 kph * C. 40.22 kphB. 45.75 kph D. 43.65 kph

MATHEMATICSTAKE HOME EXAM

INSTRUCTION: Select the correct answer for each of the following questions. Mark only one answer for each item by shading the box corresponding to the letter of your choice on the answer sheet provided. STRICTLY NO ERASURES ALLOWED. Use pencil No. 1 only.

1. In how many ways can 9 books be arranged on a shelf so that 5 of the books are always together?A. 14,400 * C. 10,800 *B. 16,200 D. 12,500

2. The rate at which yeast multiply is proportional to the number present. If the original number doubles in 2 hours, in how many hours will it triple?A. 3.17 hours * C. 2.16 hoursB. 3.03 hours D. 2.84 hours

3. A piece of paper is 0.05 in thick. Each time the paper is folded into half, the thickness is doubled. If the paper was folded 12 times, how thick in feet the folded paper be?A. 205.4 in C. 204.8 in *B. 202.8 in D. 203.4 in

4. A man planned of building a house. The cost of construction is P 500,000 while annual maintenance costs is estimated at P 10,000. If the interest rate is 6%, what is the capitalized cost of the house?A. P 526,666 C. P 583,222B. P 666,667 * D. P 687,333

5. Determine the average horsepower required to raise a 150 kg drum to a height of 20 m over a period of one

minute.A. 0.56 C. 0.80B. 0.66 * D. 0.75

6. Recorded current value of an asset.A. Book value * C. Scrap valueB. Fair value D. Market value

7. If the ratio of a pair of corresponding altitudes of two similar

triangles is 6/7. If the area of the larger triangle is 98, find the area of the smaller triangle.A. 70 C. 64B. 84 D. 72 *

8. What is the volume of a spherical pyramid whose spherical excess is 100° and the radius of the sphere is 10

units?A. 581.78 * C. 532.23B. 550.23 D. 592.28

9. If the first derivative of a function is a constant, then the function is A. sinusoidal C. logarithmicB. linear * D. quadratic

10. Determine how much water should be evaporated from a 50 kg of 30% salt solution to produce a 60% salt solution. A. 20 kg C. 30 kgB. 25 kg * D. 28 kg

11. The simplest form of business organization.A. Sole proprietorship * C. PartnershipB. Cooperative D. Enterprise

12. A car is driven 200 km at a uniform speed. If its speed If its speed had been 10 km/hr less, the trip would have taken 1 hour and 40 minutes more. Find the speed of the car.A. 40 kph * C. 45 kphB. 42 kph D. 43 kph

13. If 3x=9y and 27 y=81z , find x/z?

A. 5/3 C. 3/5B. 3/8 D. 8/3 *

14. Change in momentum is equal to ____.A. work done C. impulse *B. change in KE D. displacement

15. In a row of 7 seats, 4 men and 3 women are to be seated with the women to occupy the even places. How many

such



arrangements are possible?A. 140 ways C. 142 waysB. 144 ways * D. 146 ways

16. A condition where only few individuals produce a certain product and that any action of one will lead to almost the same action of the others.A. Oligopoly * C. monopolyB. semi-monopoly D. perfect

competition17. All are vectors except,

A. displacement C. mass *B. torque D. momentum

18. A circular piece of cardboard with a diameter of one meter 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 diameter of the cone in cm.A. 40 cm C. 30 cm B. 50 cm D. 60 cm *

19. Find the 9th term of the harmonic progression 3, 2, 3/2….A. 5/3 C. 9/4B. 4/9 D. 3/5 *

20. Reduction in the level of national income and output usually accompanied by the fall in the general price level.A. Deflation * C. InflationB. Devaluation D. Depreciation

21. A regular octagon is inscribed in a circle of radius 10. Find the area of the octagon.A. 282.8 * C. 228.8B. 288.2 D. 882.2

22. If a 9.5% account yields 9.84% annually, what is the mode of compounding?A. semi-annually C. bi-monthlyB. quarterly * D. monthly

23. A man 6 ft tall is walking at 4 fps away from a lamp post 22 ft

high. At what rate is the tip of his shadow receding from the lamp post?A. 6.5 fps C. 5.5 fps *B. 4.5 fps D. 7.5 fps

24. What is the radius of the circle circumscribing an isosceles right triangle having an area of 162 cm2?A. 10.21cm C. 12.73 cm *B. 11.45 cm D. 12.05 cm

25. Find the area of the geometric figure whose vertices are at (3,0,0), (3,3,0), (0,0,4) and (0,3,4).A. 15 * C. 20B. 16 D. 18

26. A fly of mass 0.2 grams is caught in a spider’s web. The web vibrates predominantly with a frequency of 10 Hz. At what frequency would the web vibrates if a mosquito of mass 0.10 grams is trapped?A. 14.14 Hz * C. 12.15 HzB. 10.25 Hz D. 16.42 Hz

27. A ball is dropped into the pavement from a height of 3 m and rebounds to a height of 2 m. The fraction of energy lost in the process of striking the pavement is A. 1/2 C. 1/3 *B. 1/4 D. 1/5

28. The median of a triangle is the line connecting the vertex and the midpoint of the opposite side. For a given triangle, these medians intersects at a point which is called the, A. orthocenter C. centroid *B. circumcenter D. incenter

29. At the point of inflection where x = a.A. f “(a) 0 C. f ”(a) > 0B. f” (a) = 0 * D. f “(a) < 0

30. A wedge is cut from a cylinder of radius 10 cm by two planes, one perpendicular to the axis of the cylinder and the other passing through the diameter of the section made by the first plane and inclined to this plane at an angle of 45°. Find the volume of the wedge in cm3.A. 612.55 C. 666.67 *B. 623.32 D. 694.33

31. If the distance x from the point of departure at time t is defined by the equation

x=−16 t2+5000 t+5000 , what is the initial velocity?A. 0 C. 5000 *B. 10,000 D. 2580

32. What is the curve generated by a point rotating about its axis while travelling at constant speed parallel to its axis.A. Helix * C. spiral of

archimedesB. Cycloid D. hypocyloid

33. The greatest unit pressure the soil can continuously withstand.A. yield point C. ultimate

strengthB. bearing strength * D. point of rupture

34. The differential equation has the initial condition x (0) = 12 . What is value of x (2) ?

A. 3.35 x 10-4 C. 3 B. 6 D. 4.03 x 10-3 *

35. Solve the differential equation d2x/dt2 + 4x = 0 with initial conditions x (0) = 10 , x’(0) = 0.

A. x(t) = 10 cos 2t *B. x(t) = 10 cos 2t + 10 sin tC. x(t) = 10 cos2t + 10 sin 2tD. x(t) = 10sin 2t

36. Determine ( 1 – 1/n )n as n approaches zero, n non-positive.A. 0 C. 1 *B. 0.368 D. infinity

37. Find the smallest positive integer n such that the nth derivative of cos x with respect to x is cos x.

A. 2 C. 4 * B. 3 D. 5

38. Determine the tangent to the curve 3y2 = x3 at ( 3, 3 ) and calculate the area of the triangle bounded by the tangent line , the x-axis , and the line x = 3.

A. 3.50 units2 C. 2.50 units2

B. 3.00 units2 * D. 4.00 units2



39. Two sides of a triangle are 6 m and 9 m respectively. If the included angle is changing at the rate of 2 rad per second, at what rate is the third side when the included angle is 60 ?

A. 11.78 m/s * C. 17.82 m/sB. 12.45 m/s D. 10.18 m/s

40. Compute the rate of change of the area of a square with respect to its side at x = 5 inches. A. 8 C. 10B. 14 D. 12

41. A triangle has a variable sides x, y, z subject to the constraint such that the perimeter P is fixed is 18 cm. What is the maximum possible area for the triangle ?

A. 15.59 cm2 * C. 17.15 cm2

B. 18.71 cm2 D. 15.76 cm2

42. Pedro can paint a fence 50% faster than Juan and 20% faster than Pilar, and together they can paint a given fence in 4 hrs. How long will it take Pedro to paint the same fence if he had to work alone ?A. 12 C. 8B. 10 * D. 6

43. For the following statistical data, determine the standard deviation : 112, 121, 132, 143, 154, 165, 176, 197A. 23.41 C. 21.28B. 25.75 D. 19.35

44. Determine ( 1 + n ) (1/n) as n approaches zero n non-negative.

A. 1 C. infinityB. 0 D. 2.718 *

45. The second derivative of the function f(x) is – f(x) . What is a characteristic of this function ?

A. trigonometric * C. logarithmic B. exponential D. hyperbolic

46. Determine the radius of the sphere whose equation is : x2 + y2 + z2 – 2x + 8y + 16z + 65 = 0A. 5 units C. 4 units *B. 3 units D. 6 units

47. Which of the following polar equation is equivalent to the equation x2 + y2 = ay.A. r = a cos C. r2 = a2 sin

B. r = a sin D. r2 = a2 cos

48. Simplify ( 1 + i )10 A. – 32i C. – 2iB. – 16i D. 32i

49. Express by an equation in polar coordinates that the point (r, ) is at distance 4 from (3, 30o). A. r2 - 6r cos( - 30o) = 7 C. r2 + 6r sin ( -

30o) = 7 B. r2 - 6r cos( - 30o) = 25 D. r2 + 6r sin ( -

30o) = 25

50. Two towns A and B , area situated 8 and 12 km back , respectively from a straight river on the bank of which a pumping station C is to be erected to supply water tot both towns. At what point on the bank of the river should the pumping station be built so that the least amount of piping may be required if the measured if the measured point of the river to A and B , respectively is 25 km ?

A. 10 km * C. 24 km B. 15 km D. 7 km
