FB 18 - Math.pdf

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Excel Review Center Intensive Final Coaching (IFC) FB 18 - Math

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& 4th

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1. For the function, f(x) = x4

+ 5x3

+ 2x2- 20x -

24 which of the following zeroes of f(x) hasa multiplicity of 2?

A. 3 C. -2 *B. -3 D. 2

2. Find the 15thterm if 8k + 4, 6k - 2, and 2k -

7 are the first 3 terms of an arithmeticprogression.

A. 84 C. 72B. -68 D. -90 *

3. Find the volume of a spherical segment ifthe radius of the sphere is 10 cm andaltitude 8 cm.

A. 1747.54 cm3 C. 1372.62 cm3B. 1474.45 cm3 * D. 1440.47 cm3

4. Find the term involving a7in the expansionof (1/2 + a)

12.

A. 24.75 a7 * C. 30.94 a7B. 14.44 a

7D. 15.57 a

7

5. Given: log by = 2x + log bx. Which of thefollowing is true?

A. y = b2x

C. y = xB. y = 2xb D. y = xb2x*

6. Find the number which is 7/4 t imes theexcess of number over 3.

A. 8 C.6B. 7 * D.5

7. A man sold half an egg more than half hiseggs. He then sold half an egg more thanhalf his remaining eggs. He did the samefor the third time. If he had 7 eggs left, howmany eggs does he originally have?

A. 67 C.63 *B. 65 D.61

8. At what time between 4 and 5 oclock

willthe hands of the clock be at right angle forthe first time?

A. 4:6.42 C. 4:5.23B. 4:5.45 * D. 4:7.62

9. The difference of the squares of the digit ofa 2-digit positive numbers is 27. If thedigits are reversed in order and theresulting number is subtracted from theoriginal number, the difference is also 27.What is the original number?

A. 72 C. 63 *B. 56 D. 81

10. How many liters of water must be addedto 35 liters of 89% hydrochloric acidsolution to reduce its strength to 75%?

A. 7.33 C. 6.53 *B. 5.34 D. 4.83

11. A boy is one-third as old as his brotherand 8 years younger than his sister. Thesum of their ages is 38 years. How old isthe boy?

A. 4 C. 6 *B. 5 D. 7

12. The excess of the sum of the fourth andfifth parts over the difference of the halfand third parts of a number is 119. Findthe number.

A. 620 C.220B. 420 * D.110

13. An equilateral triangle is inscribed withina circle whose diameter is 16 cm. In thistriangle, a circle is inscribed, and in thiscircle another equilateral triangle isinscribed, and so on indefinitely. Find thesum of the perimeters of all the triangles?

A. 48 2 C. 46 3

B. 47 3 D. 48 3 *

14. A tank is filled with 240 gallons of acid.Sixty gallons are drawn off and replacedwith water. Then another 60 gallons ofthe mixture are again removed andreplaced with water. This removal is done

5 times. How many gallons of acid remainin the tank after 5 drawing of 60 gallonseach?

A. 52.34 gal C. 55.49 galB. 53.34 gal D. 56.95 gal *

15. The probability that both stages of a two-stage rocket will function correctly is 0.95.The reliability of the first stage is 0.98.What is the reliability of the secondstage?

A. 0.97 * C. 0.93B. 0.95 D. 0.03

16. Given a right spherical tr iangle: C = 90;B = 80; c = 110. Solve for b.

A. 68 * C.54B. 87 D. 64

17. A and B submitted separate proposals forthe construction of a bridge, A offeringthe lower price for the winning bid. Had Aand B reduced their bid prices by 5% and10%, respectively, A would still have wonthe bid, but the difference in their bidswould have been reduced by P3000. Ifthe sum total of the bids is P90000, whatis the bid of A?

A. P50000 C.P40000 *B. P60000 D.P70000

18. A parcel of land in the form of a rectanglehas length 6m longer than its width. If itwas 3m shorter and 2m wider its areawould be decreased by 14 sq. m. Find itsdimensions.

A. 24m x 26m C. 20m x 26m*B. 25m x 23m D. 12m x 40m

19. During the last election, the total numberof voters recorded in a certain

municipality was 8600. Had one-third ofRFs supporters stayed away from thepolls and one-half of EQs behavedlikewise, RFs majority would have beenreduced by 200. How many votes did RFactually received?

A.5500 C.5400*B.4500 D.5600

20. What theorem states that the area oflattice polygon (polygons that havevertices located at the integral nodes of asquare grid or lattice that are spaced aunit distance from their immediateneighbors) can be found simply bycounting the lattice points on the interiorand boundary of the polygon?

A. Pell theoremB. Picks theorem *C. Planck theoremD. Poncelet theorem

21. A box contains 5 radio tubes of which 2are defective. The tubes are tested oneafter the other until 2 defective tubes arediscovered. What is the probability thatthe process stopped on the third test?

A. 0.3 C. 0.2 *B. 0.4 D. 0.1

22. Two planes fly from the same airport. The

first plane leaves at 8:00am flying N 43oW at 240 km/hr while the second leavesat 8:30 am flying N 27oE at 300 km/hr.How far apart the planes at 11:00am?

A. 755.31km C. 946.65kmB. 843.52km * D. 999.12km

23. How many numbers of four different digitscan be formed from 1, 2, 3, 4, 5, 6, 7each containing 2 odd and 2 even digits?

A. 312 C. 524B. 248 D. 432 *

24. A boy counted 73 posts while riding atrain for a time of 8 minutes. He startedcounting as the train passes the first postand stopped with the last one. If the postswere 100 meters apart, how manykilometers an hour was the traintraveling?

A. 54.75 kph C. 54 kph *B. 54.50 kph D. 55 kph

25. Find n: 21C(n,3) = 10C(n,5)

A. 10 * C. 11B. 12 D.13

26. A ring was formed by two concentriccircles. A chord 20cm long is drawntangent to the inner circle. Determine thearea of the ring.

A. 324.17 sq. cm. C. 1256 sq.cmB. 314.16 sq. cm * D. 212.34 sq.cm

27. Find the radius of the circle escribed in atriangle which is tangent to the 17m sideif the triangle has sides equal to 17m,10m and 21m respectively.

A. 7 m C. 8 mB. 12 m * D. 10 m

28. To measure distance AC, a man walks400 ft from A to B, then turns 30

0to face

C, and walks 600ft to C. What is thedistance AC?

A. 967.312 ft * C. 892.153 ftB. 831.463 ft D. 793.134 ft

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29. A regular triangular pyramid has analtitude of 9 m and a volume of 187.06cu. m. What is the base edge in meters?

A. 10m C. 11mB. 12m * D. 13m

30. If the edge of a cube is increased by

99%, by how much is the surface areaincreased?

A. 99% C. 198%B. 400% D. 290%*

31. A goat is tethered to a corner of a 4m by5m water tank by a 6m pole. What areaof the ground outside the water tank canthe goat graze?

A. 83.53 sq.m C. 64.51 sq.mB. 88.75 sq.m * D. 67.39 sq.m

32. A merchant paid P 360 for some crates ofbananas. Four crates were spoiled and

had to be thrown away, but he sold therest at an increase in price of P 2 percrate, gaining P 88.00. How many cratesdid he buy?

A. 60 * C. 50B. 40 D. 39

33. Find the centroid of the triangle formed byjoining the points A (3, 2), B (-1, 4), and C(5, -3).

A. (3, 3) C. (7/3, -1)B. (2, 1) D. (7/3, 1) *

34. A line through (5, -3) and (-1, 4) isperpendicular to a line through (4, 2) and(-3, Y). Find Y.

A. -1 C. 2B. -4 * D. 3

35. A light hangs 15 feet directly above astraight walk on which a man 6 feet

tall iswalking. How fast is the end of the mansshadow traveling when he is walkingaway from the light at a rate of 3 milesper hour?

A. 5 mph * C. 4.7 mphB. 6 mph D. 5.5 mph

36. A particle travels along the parabolay=ax

2+ x + b. At what point do its

abscissa and ordinate change at thesame rate?

A. (0,a) C. (1, 2)B. (-2, 1) D. (0, b) *

37. A clock has hands 1 and 1 3/5 incheslong respectively. At what rate are theends of the hands approaching eachother when the time is 2 oclock? 0.095in/min

A.1 in/min C. 0.03 in/minB. 1.5 in/min D. 0.095 in/min*

38. A triangle has a base 12 feet long and analtitude 8 feet high. Find the area of thelargest rectangle that can be inscribed inthe triangle so that the base of therectangle falls on the base of the triangle.

A.76 sq. ft C. 38 sq. ftB. 24 sq. ft * D. 12 sq. ft

39. Evaluate:0

limtan

x x

x

e e

x

A. -1 C. 0B. infinity D. 2 *

40. Find the area bounded by y = 2x + x2x3, the x axis, and the lines x = -1 and x =1.

A. 2/3 C. 3/2 *B. 1/4 D.1/3

41. Find the volume of the solid generated byrevolving the area bounded by y = x2andy

2= x about x = -1.

A. 3 * C. 4B. 3.5 D. 4.5

42. A right circular tank of depth 12 feet andradius 4 feet is half full of oil weighing 60pounds per cubic foot. Find the work

done in pumping the oil to a height 6 feetabove the tank.

A. 149 ft-tons C. 120 ft-tonsB. B. 136 ft-tons * D. 100 ft-tons

43. Find the length of the curve x2 + y2= 36at the first quadrant from x = 1 to x = 5.

A. 4 units C. 9.5 unitsB. 5.62 units D. 4.91 units *

44. How soon after noon are the hands of aclock together again?

A. 1.091 hr * C. 1.0833 hr

B. 1.5 hr D. 1.05

45. Find the probability that a single toss ofa die will result in a number less than 4if it is given that the toss resulted in anodd number.

A. 1/3 C. 2/3 *B. D. 1/6

46. The interior of a cubical box is lined withinsulating material 4 cm thick. Find theoriginal interior dimensions if the volumeis thereby decreased by 271 cm

3.

A. 9 cm C. 11 cmB. 10 cm * D. 12 cm

47. From 7 consonants and 5 vowels, howmany words can be formed consisting of4 different consonants and 3 differentvowels? The words need not havemeaning.

A. 1,764,000 * C. 50400B. 350 D. 254016000

48. Find the area of each segment formedby an inscribed equilateral triangle if theradius of the circle is 8 cm.

A. 39.3 cm2

* C.78.2 cm2

B. 42.1 cm2 C.47.2 cm2

49. A 6-foot man is running away from thebase of a streetlight that is 15 feet high.If he moves at the rate of 18 feet persecond, how fast is the length of hisshadow changing?

A. 10 fps C. 9 fpsB. 11 fps D. 12 fps *

50. Two of the roots of 2x311x

2+ = 0

are 2, 3.Find the complete equation.

A. 2x311x2+ 17x6 = 0 *

B. 2x311x

2+ 15x2 = 0

C. 2x311x

2- 17x6 = 0

D. 2x311x2- 15x + 2 = 0

51. A circus tent is shaped like a right circularcone. Its diameter is 50meters and theheight at the center is 20meters. Howmuch canvas is in the tent?

A. 2515 m3* C. 1571 m

3

B. 39270 m3 D. 3142 m3

52. The fourth term of an A.P. is 14 and theninth term is 34. Find the thirteenth term.

A. 70 C. 50 *B. 85 D. 35

53. A card is drawn at random from anordinary deck of 52 playing cards. Find

the probability that it is neither a four nora club.

A. 4/13 C. 1/3B. 9/13 * D. 1/5

54. A mold grows at a rate proportional to itspresent size. Initially there is 2 oz of thismold, and two days later there is 3 oz.How much mold will be present in tendays?

A. 17.31 oz C. 15.19 oz *B. 12 oz D. 20 oz

55. A and B are 30 km apart. If they leave atthe same time and travel in the samedirection A overtakes B in 60 hours. Ifthey walk toward each other they meet in5 hours. What is the speed of A?

A. 3.25 kph* C. 4.75 kphB. 2.75 kph D. 1.5 kph

56. A railroad track makes an angle of 4.8owith the horizontal. How far must the traingo up the track for it to gain 30 m inaltitude?

A. 359 m* C. 360 mB. 400 m D. 250m

57. A lighthouse is 10 km northwest of adock. A ship leaves the dock at 9 A.M.and steams west at 12 km/h. At what timewill it be 8 km from the lighthouse?

A. 9:16 A.M. and 9:43 A.M.B. 9:17 A.M. and 9:54 A.M. *C. 9:37 A.M. and 9:32 A.M.D. 9:27 A.M. and 9:56 A.M.

58. A woman hikes 503 m, turns and jogs415 m, turns again, and runs 365 mreturning to her starting point. What is thearea of the triangle formed by her path?

A. 74,600 m2 * C. 64,500 m2B. 53,600 m

2 D. 34,400 m

2

59. Find the number of degrees in the angleformed by a tangent and a chord drawnto the point of tangency if the interceptedarc has measure 38

o.

A. 17o C. 19o*B. 40o D. 10o

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60. If the medians of triangleABC meet in D.Find the length of the median whoseshorter segment is 7.

A. 12 C. 21 *B. 14 D. 10

61. A party costing $30 is planned. It is found

that by adding three more to the group,the cost per person would be reduced by50cents. For how many was the partyoriginally planned?

A. 11 C. 15B. 8 D. 12 *

62. Find the area of the quadrilateral formedby the lines: y = 0, y = 4, y =x, and y =x+4.

A.20 C. 18B.16 * D. 22

63. As a gasoline tank is being emptied, thenumber G of gallons left after t seconds isgiven by G = 3(15 - t)

2. What was the

average rate at which the gasoline wasbeing drained from the tank over the first12 seconds?

A. 32 gal/sec C. 54 gal/sec *B. 64 gal/sec D. 27 gal/sec

64. Four different mathematics books, sixdifferent physics books, and two differentchemistry books are to be arranged on ashelf. How many different arrangementsare possible if the books in eachparticular subject must all stand together?

A. 207,360 * C. 4.8 x 108

B. 8,709,120 D. 34560

65. Four groups of students, consisting of 15,20, 10, and 18 individuals, reported meanweights of 162, 148, 153, and 140 lb,respectively. Find the mean weight o

f allthe students.

A. 142 lb C. 156 lbB. 150 lb * D. 170 lb

66. A hole of radius 1 unit is bored through asphere of radius 3 units, the axis of thehole being a diameter of the sphere. Find

the volume of the remaining part of thesphere.

A.64

3

3 C.

64

3

2*

B.64

4

2 D.

64

3

2

67. A particle moves along the curve y = x3/3with vx= 2 at all times. Find themagnitude of the velocity.

A. 15 C. 12B. 19 D. 18 *

68. Find the length of the indicated arc of thegiven curve: y3= 8x2from x = 1 to x = 8.

A. 7.31 units C. 1.24 unitsB. 9.26 units* D. 5.32 units

69. Suppose a geometric object in themathematicians polar coordinate plane isrepresented by the equation = /4. Theobject is

A. a hyperbola C. a parabolaB. a straight line * D. a spiral

70. The cost C, in pesos per day, ofproducing x TV sets per day is given bythe formula: C = 7000 + 50x0.05x

2.

Find the rate of change of C with respectto x (called the marginal cost) when 200

sets are being produced each day.

A. P40/set C. 50/setB. P30/set * D. 60/set

71. What do you call a prime number with atleast two distinct digits, which remainsprime on every rearrangement of thedigits?

A. Permutable prime *B. Mersene primeC. Combinational primeD. Periodic prime

72. What is another term for a permutable

prime?

A. Indefinite primeB. Variable primeC. Fixed primeD. Absolute prime *

73. A prime number is an integer greater than1 which has:

A. 1 as its only positive divisorB. itself as its only positive divisorC. 1 and itself as its only positive

divisors *D. 1 and its additive inverse as its only

positive divisor

74. What is the smallest composite number?

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

75. A number that is greater than zero yetsmaller than any positive real number iscalled:

A. InfinityB. ZeroC. Negligible

D. Infinitesimal *

76. Which of the following statements abouteven numbers is NOT true?

A. The sum of even numbers is even.B. The difference of even numbers is

even.C. The product of even numbers is

even.D. The quotient of even numbers is

even. *

77. Every positive integer greater than 1 is aprime or can be expressed as a uniqueproduct of primes and powers of primes.

What is this statement commonly called?

A. Rule of PrimesB. Fundamental Theorem of

Arithmetic *C. Fundamental Law of PrimesD. Fundamental Theorem of Numbers

78. The decimal number system is the mostcommonly used number system. What isanother term for this number system?

A. Dyadic number systemB. Decadic number systemC. Denary number system *D. Decanary number system

79. The base of the number system is called:

A. IndexB. Radix *C. CologarithmD. Logarithm

80. What refers to a number system in whichaddition, subtraction, and multiplicationare always defined and the associat iveand distributive laws are valid?

A. FieldB. RangeC. Ring *

D. Domain

81. What refers to the approximation of a realnumber by a rational number?

A. Diocles approximationB. Diophantine approximation *C. Appolonius approximationD. Pythagorean approximation

82. A number is said to be in _____ when it iswritten as the product of a number havingthe decimal point just after the leadingdigit, and a power of 10.

A. scientific notation *B. exponentialC. irrationalD. logarithm

83. What is the multiplicative identityelement?

A. 0B. 1 *C. 1D. infinity

84. Any number divided by infinity equals

A. 0 *

B. 1C. infinityD. indeterminate

85. What system of numeration was theusually used by many ancient culturesbecause humans have ten fingers andten toes on which to count?

A. Sexagesimal numerationB. Mayan numerationC. Vigesimal numeration *D. Aztec numeration

86. The number 0.0320 has how manysignificant digits?

A. 1B. 2C. 3D. 4 *

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87. What theorem links complex numbersand trigonometry?

A. de Malvess theoremB. de Morgan theoremC. dAlemberts theoremD. de Moivres theorem *

88. What is a statement of truth of whichfollows with little or no proof from atheorem?

A. AxiomB. HypothesisC. Corollary *D. Conclusion

89. A proved proposition which is usefulmainly as a preliminary to the proof of atheorem is called:

A. lemma *B. hypothesisC. postulate

D. corollary

90. In mathematics and other fields of logicalreasoning, axioms are used as basis forthe formulation of statements called:

A. lemmaB. hypotheses *C. postulateD. theorem

91. What refers to a sequence of statementsin which each subsequent statement isderivable from one of the previousstatements or from an axiom of a formal

statement?

A. HypothesisB. CorollaryC. ParadoxD. Proof *

92. What is a null hypothesis?

A. A hypothesis that is being teste

d in ahypothesis-testing situation. *

B. A hypothesis that has nothing totest.

C. A hypothesis that need not betested.

D. A hypothesis that has no basis.

93. If a = b then b = a. This illustrates whataxiom in algebra?

A. Symmetric axiom*B. Reflexive axiomC. Transitive axiomD. Replacement axiom

94. If a = b and b = c, then a = c. Thisillustrates:

A. reflexive lawB. law of symmetryC. transitive law*D. substitution law

95. The product of two or more numbers isthe same in whatever order they aremultiplied. This refers to:

A. Associative law of additionB. Commutative law of multiplication *C. Associative law of multiplicationD. Distributive law of multiplication

96. The result that any polynomial with realor complex coefficient has a root in thecomplex plane. What is this theoremcalled?

A. Fundamental theorem of Algebra*B. Fundamental theorem of GeometryC. Fundamental theorem of Arithmetic

D. Fundamental theorem of NumberTheory

97. Every even integer greater than 2 can bewritten as the sum of two primes. This isknown as

A. Fermats last theoremB. Goldbach conjecture *C. Prime number thoeremD. Mersenne primes

98. What is the least proved theorem inMathematics?

A. Goldbach conjecture

B. Fermats last theorem *C. Mersennes propositionD. Pappus propositions

99. What is the most proved theorem inMathematics?

A. Gauss lemmaB. Fermats theoremC. Ptolemys theoremD. Pythagorean theorem *

100. What theorem is considered as the

fundamental theorem of calculus and isused today in almost all computer codesthat solve partial differential equations?

A. Greens theorem *B. Hams theoremC. Gauss theoremD. Guys theorem

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FB 18 - Math.pdf