Algbra Trigo Wkly Exm Solution

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EXCEL REVIEW CENTER
MATHEMATICSUse ReverseEngineering : m2/3  m1/3 ! 2 (1)2/3 (1)2/ 3 ! 2 p thus; answer is negative 1
WEEKLY EXAM 011. How many different numbers of eight digits each can be formed by using three 4s, three 6s and two 8s? A. 560 * C. 840 B. 1250 D. 720Use PERMUTATION of n things with r, s, and t alike: n! N= where : n = 8 , r = 3 , s = 3 and t = 2 r! s! t! r = 3 ( there are three 4's) s = 3 ( there are three 6's) t = 2 ( there are three 8's ) 8! N= = 560 3! 3! 2!
3
2x
= 27
5.
Determine the real root of the equation y = x 4x2 12 x 6 = f(x) , to the nearest thousand. A. 5.231 C. 6.124 * B. 7.312 D. 3.124Use ReverseEngineering or Used Shift Solve of your 991MS Calculator : y = x 3  4x 2  12 x  6 = f(x) solve f(x) when x = 6.124 f (6.124) = (6.124)3  4(6.124)2 12(6.124) 6 ! 0.169 The above given equation can be written as: x 3  4x 2  12 x  6 = 0.169 x 3  4x 2  12 x  6.169 = 0 p use calculator to solve the roots x = 6.123996 $ 6.124
3
2x ln 3 = ln 27 3 x =2
9.
Solution to Problem No. 1
Solution to Problem No. 5
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 *Distance travelled in both directions are equal : This is a uniform motion problem. Use: Distance = Veloctiy x time 12 30 t + = 48 ( t ) 60 t = 0.125 hr Distance = 48 (0.125 ) = 6 miles
Solution to Problem No. 9
2.
What is the 17 term of the sequence 68, 56, 44, 32 A. 124 * C. 234 B. 324 D. 421
th
6.
Solution to Problem No. 2
If tan A = 1/3 and cot B = 2, tan ( A B ) is equal to : ______ A. 11/7 C. 11/7 B. 1/7 * D. 1/7tan A = 1 3 A ! 18.43 cot B = 2 B = 26.56 1 7
Solution to Problem No. 6 The terms 68, 56, 44, 32 ... are forming AP of common difference equal to 112. d = 32  44 = 44  56 = 56  68 = 12 The 17th term a17 : an = a1 +( n 1 )(d ) a17 = 68 +(171)(12) =  124
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 = 0 2 B. x 5x + 10 = 0 D. x2 10x + 15 = 0Solution to Problem No. 10 The sum of Roots is: B = 4 then B = 4A A The quadratic equation is : Ax 2 + Bx + C = 0 Ax 2 4Ax + 7A = 0 x 2 4x 7 ! 0 The Product of Roots is :: C = 7 then C = 7A A
tan ( A  B ) = tan ( 18.43  26.56 ) = 0.142857 $ 
7.
3.
What is the fiftyfifth term of 1, 1, 1, 1 A. 1 * C. 0 B. 1 D. infinity
Solve the root of the given equation 2x  6 + 9  x = 0 . A. 5 C. 10 B. 5 D. no solution *2x  6 + 9  x = 0
Solution to Problem No. 3
Solution to Problem No. 7
Evaluating the pattern of the given numbers then it is abvious that it is alternating postive and negative 1. Positive 1 for odd's place and negative 1 for even's place; like 2 By Inspection therefore ; 55 th term =  1nd
2x  6 =  9  x p eqn. 1 Square both sides of the equation : 4 ,6th th
and so on..
2x  6
2
=

9x
2
2x  6 = 9  x x=5 If this value is to be substituted to the above equation 1, the left side plus/minus 2 is always equal to negative 2. and 5 is called extraneous root. Therefore, the answer is NO SOLUTION.
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. 1230 B. 1983 D. 1023 *Solution to Problem No. 11 a 4 = a1 r 3 a1 1  r2 1r then 24 = 3 r 3 r=2
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
8.
Solve for x: 3 (raised to 2x ) = 27. A. 1/3 C. 3/2 B. 2/3 D. 3/2 *
S=
= 3 1 (2) ! 102310
1  (2)
Solution to Problem No. 3
Solution to Problem No. 8
12. If the probability that a player shoots a 3point range is 2/5, determine the probability of shooting 5 out of 8 attempts.
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EXCEL REVIEW CENTERA. B. 28.4 % 12.4 % * C. 31.1 % D. 21.3 % B.3x y 4
MATHEMATICSD. none of these A. x u 5 * B. x > 5Solution to Problem No. 18 3 x 2 e 5 x 12 10 e 2x 5 e x or x u 5
C. x < 5 D. x e 5
Solution to Problem No. 12 Use Repeated Trials: 2 3 P = nCr pr qnr ! 8C5 5 55 85
Solution to Problem No. 14 7x110 then 110 ! 10x 10 7x15 y= then 15 ! 5y 5 the sum of 15 numbers is : 110 15 10 x 5 y 2x + y = ! 15 15 3 x=
! 0.124 = 12.4%
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. 0.02Solution to Problem No. 14
19. What is the multiplicative inverse of x? A. x C. 1/x * B. 1/x D. x2Solution to Problem No. 19
The the multiplicative inverse of x is
1 . x
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 50cp light would the illumination be onehalf that received at 20 ft from a 40cp light? C. 3 5 A. 10 10 B. 5 2 D. 5 2Solution to Problem No. 13 IE P d2 then I = k P d2 and I2 = k 40 (20)2 p equation 2
There is only one way of getting it in order and 5 ! ways of getting 5 distinct balls. Thus; the probability is : 1 1 P = ! 5! 120
20. Two ships are observed from a cliff that is 512 ft high. At a certain instant the angles of depression as observed are 2r15 and 3r10. How far are the ships if they are in line and directly outward the observer? A. 7654 C. 7450 B. 7540 * D. 7456Solution to Problem No. 19
512
x 16. If x = y and y = x . This illustrates which axiom in Algebra? A. symmetric axiom C. reflexive axiom B. transitive axiom D. inverse axiomSolution to Problem No. 16 If x = y and y = x then it is symmetric Axiom tan 2o 15'= 512 x+y 512
2r15
3r10
ytan 3 o10'= 512 y 512
1/2 I1 = k
50 p equation 1 (d )2 Divide equation 2 by 1 : I1 ! 1/2 I1 k k 40 (20)2 50 (d )2
x+y= eqn. 1 y= eqn. 2 tan2 15' tan 3o 10' Use equation 2 : 512 512 x + = tan2 15' tan 3o 10' x = 3,776.88 ( bonus )
1 d2 2= 10 50 d = 1000 ! 10 10
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 minutes B. 2 minutes D. 4 minutesSolution to Problem No. 17
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? 2x y xy A. * C. 3 2
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. 23.14Solution to Problem No. 21
1 1 32 = x x2 60 x=5
18. Solve the inequality : (3x 2 ) e ( 5x 12 )
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EXCEL REVIEW CENTERThe sequence of the increase in radius is 0.35, 0.34, 0.33... then; an = a1+ (n 1)(d) a30 = 0.35+ (30 1)(0.01) = 0.06 The sum : n 30 S = a 1+ a n ! 0.35 0.06 ! 6.15 2 2 thus; the radius after 30 seconds is 18 + 6.15 = 24.15 in.
MATHEMATICSB. 9N= Any of the 26 letters in the alphabet can be used.
D. 1,674,000= 15,600,000
Solution to Problem No. 25
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 hrsSolution to Problem No. 29 1 1 1 2 + (x) = 1 8 6 6 x = 2.5 hrs
22. The quantity 1 tanh x is equal to: 2 2 A. sech x C. csch x 2 2 B. cosh x D. sech x *Solution to Problem No. 22 Using trigonometric identities: 1 tan h x = sec h x2 2
2
26. The unit gross means A. 100 pieces B. 100 dozensSolution to Problem No. 25 Gross means 12 dozens
C. 12 dozens * D. 120 pieces
23. If ( 2log x to the base 4 ) ( log 9 to the base 4 ) = 2, find x: A. 10 C. 12 * B. 13 D. 11Solution to Problem No. 23 2log 4 x  log 4 9=2 x2 log 4 = 2 9 4log4 x 2 / 9
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. 12 B. 23 D. 25 *Solution to Problem No. 27
30. The sum of the digits of a threedigit 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. 321 B. 123 D. 213Solution to Problem No. 30 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.
= 42
20% 300 
x2 = 16 9 x = s 12
20% x +
80% x =
25% 300Answer: 231
0.20(300) 0.20x + 0.80x = 0.25(300) x = 25
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 lbsSolution to Problem No. 24 the terms 18, 12, 8... form GP of common ratio 2/3. maximum total weight loss will be attained infinity: a 18 S= 1 = ! 54 1r 1  2/3
28. What is the sum of the coefficient in the expansion of 20 ( 2x 1 ) ? A. 0 * C. 2 B. 1 D. 3Solution to Problem No. 28 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
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 kphSolution to Problem No. 31 Cosine Law z 2 = x 2 + y 2  2 x y cos120 o x dx/dt +y dy/dt cos120o ?x(dy / dt ) y ( dx / dt )A dz = dt z 8 20 +6 30 cos120o ?8(30) 6(20)A dz = dt (8)2 (6)2 2(8)(60)cos120 dz = 42.74 dt
B x=6 O 120r z
 (1)
25
=0
x=8
A
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. 27nd
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Any of the 10 numbers can be used.
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 800Solution to Problem No. 32
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EXCEL REVIEW CENTERx ( 1 + 0.50 ) = 1500 x = 1000
MATHEMATICSS = V t = 12 mi/hr ( 42 / 60 ) hr = 8.4 miles
1500
x
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 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 min B. 10 hrs and 3 min D. 7 hrs and 34 minSolution to Problem No. 33 Rate of Excavation : (8 men)(7 hrs) manhours = 0.3733 150 ft ft Rate of Backfilling : R dig = (3 men)( 4 hrs) manhours = 0.12 100 ft ft The total time : when there are 10 men and t dig + t backfill = t total R bfill = 0.3733 (200) 0.12 (200) = t 10 10 t = 9.86 hrs or 9 hrs and 52 minutes
tan 24 =
c  5.35 x + 1500
p eqn. 1
tan 45 =
c  5.35 1500
p eqn. 2
using eqns 1 and 2 and solve for c : c = 1209.6 m
40. Engr. Hermo needs to work fivesixth 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. October B. August D. December *Solution to Problem No. 40
5 5 (1 year) = 12 ! 10 months 6 6
, so , from march the tenth month is
36. Sheris age in 20 years will be the same as Terrys age is now. Ten years from now, Terrys age will be twice Sheris. How old is Terry now? A. 20 * C. 30 B. 10 D. 25Solution to Problem No. 35 x = Sheris age now. y = terries age now. x + 20 = y y + 10 = 2 ( x + 10 ) This is 2 equation s two unknowns. Use calculator: x = 20
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. 80 B. 50* D. 100Solution to Problem No. 41 Use manhour Analysis : (70)(100) = 80( 50 ) + 60 ( x ) x = 50
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. 8Solution to Problem No. 34 x + y + z = 20 p eqn. 1 3x + 1.4y + 0.5z = 20 p eqn. 2 This is 2 equations 3 unknowns : use the solutions for Deophantine equations. Answer: z = 13
37. What is the mean proportional to 3 and 12? A. 4 C. 8 B. 6 * D. 5Solution to Problem No. 37
Mean proportional is =
x1x 2 ! 3(12) ! 6
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. 72Solution to Problem No. 38 There are seven times as many candles; thus ; 7 x 9 = 63
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 U = 3/5 and cos F = 5/13 , find the sin ( U + F ). A. 0.97 * C. 0.87 B. 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 th 8 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 times B. 78 times D. 24 hours
35. The top of the cliff C is observed from A to have a vertical angle of 24r. 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 45r. 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 m B. 1325.4 m D. 1190.4 mSolution to Problem No. 35
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 miles B. 3.6 miles D. 8.4 miles *Solution to Problem No. 39 There are 42 minutes from 3:14 at 3:56.
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EXCEL REVIEW CENTER46. 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. 25 B. 36 D. 15 48. The number 5 + 3 A. rational number B. integer3 is :
MATHEMATICS
C. surd * D. radicand the men are to find each mans 50 , 100 40, 120
49. Two men do a job for P 250. If share the sum, in the ratio of 2:3 , share . A. 100, 150 * C. B. 75, 100 D.
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. 30 B. 33 D. 34
)RH
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EXCEL REVIEW CENTER
MATHEMATICS7. The unit gross means C. 100 pieces D. 100 dozens B. 8.1 C. 12 dozens * D. 120 pieces B. D. 8.7
MATHEMATICS TAKE HOME EXAMINSTRUCTION: 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 % 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 kph B. 72 kph D. 65 kph 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. 132.89 B. 159.21 D. 167.12 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 m B. 1.42 m D. 1.51 m 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. 1620.0 B. 1450.2 D. 1333.3 * Evaluate: lim A. B. 1/3 * 3 2x 2 3x 1 . 6x 2 C. infinity D. 1
8.
What is the multiplicative inverse of x? C. x C. 1/x * 2 D. 1/x D. x 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 60r ? A. 11.78 m/s * C. 17.82 m/s B. 12.45 m/s D. 10.18 m/s 16. Find the probability of getting exactly 12 out of 30 questions on a true or false question. A. 0.12 C. 0.15 B. 0.08 * D. 0.04 17. If a regular polygon has 27 diagonals, then it is a: A. Nonagon * C. Hexagon B. Pentagon D. Heptagon 18. Each of the faces of a regular hexahedron is a : A. triangle C. rectangle B. square * D. hexagon
9.
2.
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 ) e ( 5x 12 ) A. x u 5 * C. x < 5 B. x > 5 D. x e 5
3.
12. The quantity 1 tanh2x is equal to: C. sech2 x C. csch2 x D. 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. 3 3 A. 600.26 ft C. 568.67 ft B. 663.44 ft3 D. 631.85 ft3 *
19. Determine x, so that; x , 2x + 7 , 10x  7 will be a geometric progression. A. 7, 7/12 C. 7, 14/5 B. 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. Semiannually 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. 720 B. 530 D. 320 Find the probability that a couple children will have at least one girl. 7 3 A. * C. 8 4 1 5 D. B. 2 8 having 3
4.
5.
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. 10 B. 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 *
22.
6.
x pg
23. A car weighing 12 kN including its own cargo is moving down a 30r slope. The driver sees an obstruction way ahead, so he applies the brakes
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EXCEL REVIEW CENTERat 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 N B. 7384.5 N D. 6385.6 N
MATHEMATICS31. If the general equation of the conic is Ax + 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 U. A. Spiral of Archimedes * C. Cardioid B. Four  Leaved Rose D. Threeleaved Rose 33. What is the remainder when 5x 4x 7x + 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. 56 4 3 2
A. Arithmetic progression * progression B. Geometric progression progression
C. Infinite D. Harmonic
24. Determine the radius of the sphere whose equation is : x2 + y2 + z2 2x + 8y + 16z + 65 = 0 A. 5 units C. 4 units * B. 3 units D. 6 units 25. What is the limit value of y = approaches to zero? A. 1 * B. 0
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 6145 B. 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 720.32 B. P 842.21 D. P 652.12 41. What is the coefficient of the 8 term of the expansion of 9 (2x 3y) ? A. 314928 * C. 213258 B. 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 kg B. 78.89 kg D. 84.57 kg * 43. What is the effective rate of 18% compounded semiquarterly? 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 fps B. 8.33 fps * D. 9.33 fpsth
(x x ) x x2
3
as x
C. indeterminate 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, 8.14 B. 2.45, 7.14 * D. 3.45, 8.14 27. Each angle of the regular dodecagon is equal to ________ degrees. A. 135 C. 125 B. 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 axis B. 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. Newtons Rule C. LHospitals Rule * B. De Gias Rule D. Leibniz Rule
35. The piston of an engine is connected by a 12inch connecting rod to a point on a crank that rotates on a 4inch 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 A. 2 * B. 0x pT / 2
Lim ( T  2x ) tan x
C. g D. 1
37. Find the probability of getting a prime number thrice by tossing a die 5 times. A. 0.3125 * C. 0.4125 B. 0.3250 D. 0.3725 38. It is a sequence of numbers such that successive terms differ by a constant.
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EXCEL REVIEW CENTER46. The capacity to do work. A. Energy * B. Potential
MATHEMATICSINSTRUCTION: 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. 8. 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 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 hours B. 3.03 hours D. 2.84 hours 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 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 583,222 B. P 666,667 * D. P 687,333 triangles is 6/7. If the area of the larger triangle is 98, find the area of the smaller triangle. A. 70 C. 64 B. 84 D. 72 * 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. 532.23 B. 550.23 D. 592.28 9. If the first derivative of a function is a constant, then the function is A. sinusoidal C. logarithmic B. linear * D. quadratic
C. Power 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 J B. 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 kph B. 45.75 kph D. 43.65 kph
2.
3.
)RH
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 kg B. 25 kg * D. 28 kg 11. The simplest form of business organization. A. Sole proprietorship * C. Partnership B. 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 kph B. 42 kph D. 43 kph 13. If 3 x ! 9 y and 27 y ! 81 z , find x/z? A. 5/3 C. 3/5 B. 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
4.
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. 0.80 B. 0.66 * D. 0.75 6. Recorded current value of an asset. A. Book value * C. Scrap value B. Fair value D. Market value If the ratio of a pair of corresponding altitudes of two similar
MATHEMATICS TAKE HOME EXAM
7.
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EXCEL REVIEW CENTERthe women to occupy the even places. How many such arrangements are possible? A. 140 ways C. 142 ways B. 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. monopoly B. semimonopoly D. perfect competition 17. All are vectors except, A. displacement C. mass * B. torque D. momentum
MATHEMATICS23. 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. 20 B. 16 D. 18 26. A fly of mass 0.2 grams is caught in a spiders 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 Hz B. 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) > 0 B. 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 t 2 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 archimedes B. Cycloid D. hypocyloid 33. The greatest unit pressure the soil can continuously withstand. A. yield point C. ultimate strength B. bearing strength * D. point of rupture 34. The differentialdx +4x=0 has the dt initial condition x (0) = 12 . What is value of x (2) ? 4 A. 3.35 x 10 C. 3 3 * B. 6 D. 4.03 x 10
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 9 term of the harmonic progression 3, 2, 3/2. A. 5/3 C. 9/4 B. 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. Inflation B. 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. 228.8 B. 288.2 D. 882.2 22. If a 9.5% account yields 9.84% annually, what is the mode of compounding? A. semiannually C. bimonthly B. quarterly * D. monthlyth
equation
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 t C. x(t) = 10 cos2t + 10 sin 2t D. x(t) = 10sin 2t 36. Determine ( 1 1/n ) nonpositive. A. 0 B. 0.368n
as n approaches zero, n C. 1 * 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
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EXCEL REVIEW CENTER38. Determine the tangent to the curve 3y = x at ( 3, 3 ) and calculate the area of the triangle bounded by the tangent line , the xaxis , and the line x = 3. 2 2 A. 3.50 units C. 2.50 units 2 2 B. 3.00 units * D. 4.00 units 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 60r ? A. 11.78 m/s * C. 17.82 m/s B. 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. 10 B. 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 ? 2 2 A. 15.59 cm * C. 17.15 cm 2 2 B. 18.71 cm D. 15.76 cm 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. 8 B. 10 * D. 6 43. For the following statistical data, determine the standard deviation : 112, 121, 132, 143, 154, 165, 176, 197 A. 23.41 C. 21.28 B. 25.75 D. 19.35 44. Determine ( 1 + n ) nonnegative. A. 1 B. 0(1/n) 2 3
MATHEMATICSA. B. 5 units 3 units C. 4 units * D. 6 units
47. Which of the following polar equation is equivalent to the equation x2 + y2 = ay. 2 2 A. r = a cos U C. r = a sin U 2 2 B. r = a sin U D. r = a cos U 48. Simplify ( 1 + i ) A. 32i B. 16i10
C. 2i D. 32i
49. Express by an equation in polar coordinates that o the point (r, U) is at distance 4 from (3, 30 ). 2 o 2 A. r  6r cos(U  30 ) = 7 C. r + 6r sin (U o 30 ) = 7 2 o 2 B. r  6r cos(U  30 ) = 25 D. r + 6r sin (U o 30 ) = 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
)RH
as n approaches zero n C. infinity 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 = 0
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