WEEKLY RF REVIEW CENTER EXAM 1 Mathematics

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.NOTE: Whenever you come across a caret (^) sign, it means exponentiation.

1. Which set is closed under subtraction?A. odd integers C. integers*B. counting numbers D. prime numbers

2. Round off 0.0034750 to 3 significant figures.A. 0.003 C. 0.00347B. 0.00348* D. 0.0347

3. Solve for x if log x^2=(logx)^2.A. e^2 C. 1*B. 2 D. 3

4. Which of the following is a factor of x4-4x3-7x2+22x+24.A. (x+3) C. (x-1) B. (x-2) D. (x-3)*

5. Solve for x: 3x 5x+1=6x+2.A. 2.1455 C. 2.1544*B. 2.1445 D. 2.4154

6. Simplify:

A. (x-4)/(x-6)* C. (x-3)/(x+6)B. (x-2)/(x-6) D. (x-6)/(x-4)

7. Ming has 15 quarters, 30 dimes and 48 nickels.  He wants to group his money so that each group has the same number of each coin.   How much money will each group be worth?A. 2.25$ C. 1.45$B. 1.65$ D. 3.05$*

8. The number 77 is divided into two parts such that the GCF of the two parts is 11 and their LCM is 110. The smaller of the two part isA. 11 C. 22*B. 44 D. 55

9. Alex was asked to multiply a number by 3/2. Instead he divided the number by 3/2 and obtained a number smaller by 2/3. The number wasA. 4/5* C. 3/5B. 2/3 D. 1/2

10. Three bells A, B, and C begin ringing at the same time and continue to do so at intervals of 21, 28, and 30, respectively. The bells will ring together again afterA. 7 seconds C. 7 minutes*B. 630 seconds D. 1 hr

11. What is the sum of a geometric progression if there are 4 geometric means between 3 and 729?A. 1112 C. 908B. 1092* D. 1290

12. If one root of 9x^2-6x+k=0 exceeds the other by 2, find the value of k.A. 8 C. -8*B. 5 D. -6

13. The ratio of three numbers is 2:5:7. If 7 is subtracted from the second, the resulting numbers form an arithmetic progression. Determine the smallest of the three numbers. A. 28* C. 21B. 15 D. 18

14. Find the coefficient of the term involving x8 in the expansion of

A. 180* C. 210B. 310 D. 120

15. Find the value of x from the series of numbers shown. x + 3x + 9x + 27x…+729x=3279. A. 3* C. 5 B. 6 D. 8

16. From the equation 12x3-8x2+kx+18=0, find the value of k if one root is the negative of the other.

A. -18 C. -27*B. -12 D. -31

17. Find the 16th term of the progression 1/4,1/7, 1/10,... A. 1/43 C. 1/46 B. 1/56 D. 1/49*

18. The number 20,540.00 has how many significant digits?A. 3 C. 5B. 4 D. 7 *

19. In a racing contest, there are 240 cars which will have provisions that will last for 15 hours. Assuming constant hourly consumption for each car, how long will the fuel provisions last if 8 cars withdraw from the race every hour after the first?

A. 16 C. 20B. 18 D. 25*

20. What follows logically in these series of numbers 2,3,4,5,9,17…..A. 33* C. 21B. 37 D. 43

21. Spheres of the same radius are piled in the form of a pyramid with a square base until there is just one sphere at the top layer. If there are 4 spheres on each side of the square, find the total number of spheres in the pile. A. 32 spheres C. 30 spheres* B. 25 spheres D. 28 spheres

22. In a certain city in the Philippines, the car number plate is formed by 4 digits from the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9 followed by 3 letters from the alphabet. How many number plates can be formed?A. 47,174,400* C. 327,600B. 36,723,456 D. 560,377

23. A storage battery discharges at a rate which is proportional to the charge. If the charge is reduce by 50% of its original value at the end of 2 days, how long will it take to reduce the charge to 25% of its original charge?A. 3* C. 5 B. 4 D. 6

24. The second hand of a clock is 4 inches long. Find the speed of the tip of the second hand.A. 0.42 in/sec.* C. 0.55 in/sec.B. 0.34 in/sec. D. 0.48 in/sec

25. To compute the value of n!, where n is a large number, we use A. Stirling’s approximation* C. Diophantine Equation

B. Fermat’s Last Theorem D. Cardan’s Approximation

26. If 19 kilos of gold losses 1 kilo, and 10 kilos of silver losses 1kilo when weighed in water, find the weight of gold in a bar of gold and silver weighing 106 kilos in air and 99 kilos in water.

A. 76* C. 82B. 30 D. 58

27. Three fiends A, B, and C can do a piece of work in t hours working together. Working alone, A can do the work in 6 hours more, B in 1 hour more, and C in twice the time if all working together. How long would it take to finish the work if all working together?A. 20 mins. C. 40 mins.*B. 30 mins. D. 50 mins

28. Two cars A and B run a 10 km straight stretched. It took A 40 min. to reach the finish line with B 2 km. behind A. How long would it take B to reach the finish line?A. 20 mins. C. 40 mins.B. 30 mins. D. 50 mins*

29. A is as old as the combined age of his two brothers B and C. But C is two years older than B. The combined age of the three last year was 3/4 their combined ages at present. How old is B now?A. 2* C. 4B. 4 D. 5

30. Five couples are to eat at a round table with the men and women alternating. If the hostess reserves a place for herself, in how many ways can she assign seats to the others?A. 2,880* C. 576B. 14,400 D. 1288

31. Find the sum of the first five terms of the geometric progression if the third term is 144 and the sixth term is 486.A. 844* C. 749B. 978 D. 540

32. When you use any base other than the decimal system, the division between whole numbers and fractional numbers is referred to asA. radix point* C. indexB. vinculum D. decimal point

33.  A substance goes into solution at the rate of 25% of the undissolved portion each minute. If the initial amount was 64/27 lb, what amount is undissolved after 6 min?A. 16/27 lb C. 64/27 lbB. 27/16 lb D.27/64 lb

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WEEKLY RF REVIEW CENTER EXAM 1 Mathematics

34. In algebra, the operation of root extraction is called a A. evolution* B. involution C. revolution D. indexing

35. Solve for x if 8^x = 2^(y + 2) and 16^(3x - y) = 4^y.A. 2* C.1B 4 D.3

36. How many ounces of pure nickel must be added to 150 ounces of alloy 70% to make an alloy 85% pure.A. 225 C. 175B. 125 D. 150*

37. Spheres of the same size are piled in the form of a pyramid with an equilateral triangle as its base. Determine the total number of spheres in the pile if each side contains 4 spheres?A. 26 C. 24B. 20* D. 30

38. A boy has 8 differently colored beads. In how many ways can he select 2 or more beads to form a bracelet?A. 128 C. 110B. 247* D. 219

39. At what price will you mark a flash drive for sale the cost P600 in order that you may offer 20% discount on the marked price and still makes a profit of 25 % on the selling price? A. P800 C. P1000*B. P1,100 D. P850

40. Which of the following is a prime number?A. 437 C. 487*B. 417 D. 483

41. The sum of the ages of Maria and Anna is 35. When Maria was two thirds her present age and Anna was 3/4 of her present age, the sum of their ages was 25. How old is Maria now?A. 15* C. 21B. 18 D. 23

42. Find the value of “x” in the following series of number 12,13,17,26, x.A. 32 C. 43B. 42* D. 46

43. In how many ways can 9 different books be arranged on a shelf so that 3 of the books are never all 3 together? A. 130,240 C. 332,640*C. 160,480 D. 260,354

44. The terms of a sum may be grouped in any manner without affecting the result. This is known as:A. Commutative Law C. Associative Law*B. Distributive Law D. Reflexive Law

45. A sequence 1, 4, 10, 20, 35, 56… is known as A. Pyramidal numbers C. Tetrahedral numbers*B. Cubic numbers D. Square numbers

46. Nestor has nickels, dimes, and quarters amounting to $1.85. If he has twice as many dimes as quarters, and the number of nickels is two less than twice the number of dimes, how many quarters does he have?A. 3 * C. 8B. 6 D. 10

47. In how many ways can 10 different books be divided among A, B, and C so that A gets 5 books, B 3 books, and C 2 books?A. 2,520 * C. 1,250B. 2,250 D. 2,052

48. From the equation 12x3-8x2+kx+18=0, find the value of k if one root is the negative of the other.A. -18 C. -12B. -27* D. -31

49. Ben exercises every 12 days and Isabel every 8 days. Ben and Isabel both exercised today. How many days will it be until they exercise together again?A. 34 C. 14B. 24* D. 18

50. Find the sum of the coefficients of the expansion of (x+2)4.A. 65* C. 81B. 72 D. 102

51. A number system of base 20A. vigesimal* C. figurateB. icosagonal D. duodecimal

52. Find the 15th term of the progression 1/4,1/7, 1/10,...A. 46 C. 1/46*

B. 1/56 D. 56

53. Find the term containing x2 in the expansion of [x3+(a/x)]10.A. 128a7x2 C. 120a7x2 * B. 210a6x2 D. 320a5x2

54. One microsecond is equal to how many second?A. 10^-3 C. 10^-12 B. 10^-6 * D. 10^-9

55. The distance passed over by a certain pendulum bob in succeeding swings form the geometric progression 16,12,9,... feet respectively. Calculate the total distance traversed by the bob before coming to rest. A. 64 ft * C. 54 ft B. 75 ft D. 96 ft

56. Find the value of A for which the equation A(2x+3)-(x-4) = 3x+10 is an identity.A. -1 C. 2*B. 3 D. -3

57. The equation whose roots equal twice those of the equation x3-6x2+11x-6=0. A. x3-12x2+22x-12=0 C. x3-24x2+12x-12=0B. x3-12x2+44x-48=0 * D. x3-12x2+48x-44=0

58. Find the equation whose roots are numerically equal but opposite in sign to the roots of the equation x3+7x2+11x+5=0. A. x3-7x2+11x-5=0 * C. x3+7x2+11x-5=0 B. x3+7x2-11x+5=0 D. x3-7x2-11x+5=0

59. The arithmetic mean of two numbers is 4, and their harmonic mean is 15/4. Find the numbers.

A. 3 & 5* C. 2 & 6B. 1 & 7 D. 4 & 4

60. Find the real values of x and y satisfying the given equation:(2x+3y)+ i(3x-5y) = 8-i7 .A. x=1, y=-2 C. x=2, y=1B. x=-2, y=-1 D. x=2, y=-1*

61. From the equation 12x3-8x2+kx+18=0, find the value of k if one root is the negative of the other.A. -18 C. -27* B. -12 D. -31

62. In how many ways can a party of 6 people be seated on a row of 6 seats if a certain 2 refuse to sit next to each other?A. 240 ways C. 180 waysB. 480 ways * D. 320 ways

63. How many different 8-digit numbers can be formed from the digits 2, 2, 2, 5, 5, 7, 7,7?

A. 120 C. 520B. 560* D. 410

64. What is the sum of a geometric progression if there are 4 geometric means between 3 and 729?A. 1112 C. 908B. 1092* D. 1290

65. Compute the sum of the 4-digit numbers which can be formed with the four digits 2,3,5,8 if each digit is used only once in each arrangement. A. 119,988 * C. 108,000B. 188,996 D. 128,456

66. In how many minutes after 2 o’clock will the hands of the clock extend in opposite directions for the first time?A. 2: 43min & 0.636 sec C. 2: 43 min & 38 sec *B. 2: 48.636 sec D. 2: 46 min & 30 sec

67. The number 28, x+2, 112 form a geometric progression. What is the 10th term?A. 14336 * C. 16636 B. 31466 D. 13466

68. In the series 1, 1, 1/2, 1/6, 1/24,,..., determine the 6th term. A. 1/28 C. 1/32B. 1/64 D. 1/120 *ƒ

69. Find the harmonic mean between 3/8 and 4.A. 25/34 C. 32/35 B. 24/35* D. 35/24

70. Solve for x in the following equation:

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

Good Luck!

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