CERTC Weekly Exam 1 MathematicsElectrical Engineering Instruction: Select the correct answer for each of the following 16. From a group of 5 boys and 3 girls three children are selected at questions. Mark only one answer for each item by shading the box random. Calculate the probability that the selected group contains corresponding to the letter of your choice on the answer sheet provided. only one girl. A. 15/28* C. 5/28 Strictly no erasures allowed. Use pencil no. 1 only. NOTE: Whenever you come across a caret (^) sign, it means B. 1/5 D. 5/8 exponentiation. 17. A die is rolled. If the outcome is an even number, what is the probability that it is a prime number? 1. Which set is closed under subtraction? A. odd integers C. integers* A. 1/2 C. 2/3 B. counting numbers D. prime numbers B. 1/6 D. 1/3* 18. A die is thrown twice and the sum of the number appearing is 2. Round off 0.0034750 to 3 significant figures. A. 0.003 C. 0.00347 observed to be 6. What is the conditional probability that the B. 0.00348* D. 0.0347 number 4 has appeared at east once. A. 3/5 C. 2/5* 3. Ben exercises every 12 days and Isabel every 8 days. Ben and B. 2/36 D. 5/36 Isabel both exercised today. How many days will it be until they exercise together again? 19. In a certain school, 20% of the students failed in English, 15% of A. 34 C. 14 the students failed in Mathematics, and 10% of the students B. 24* D. 18 failed both in English and Mathematics. A student is selected at random. If he failed in English, what is the probability that he also 4. Two CERTC reviewees while solving a quadratic equation in x failed in Mathematics? with leading coefficient ‘1’, one copied the constant term A. 1/10 C. 1/2* incorrectly and got the roots 3 and 2. The other copied the constant term correctly -6. What are the correct roots of the B. 1/5 D. 2/5 equation? 20. A function f(x) is a(n) ______ function if f(-x)= f(x). A. -2,3 C. -3,2 A. Odd C. even* B. -6,-1 D. -1,6* B. Periodic D. constant 5. If r1 and r2 are the roots of x 2 +18x + 30 = 2 x 2 +18x + 45 21. A function f(x) is a(n) ______ function if f(-x)= -f(x). A. Odd* C. even Find r r where r2 > r1 . 2 1 2 B. Periodic D. constant A. -16.81 C. -1.18 ( ) 2 B. 20.00 D. -23.79 22. If log10 x = 3 - log10 x 2 . Which of the following can be a value of 6. How many digits are there in 999666 ? x? A. 665 C. 1998 A. 10-3 C. x10 B. 2019 D. 203 B. 102 D. 10x 7. The expression 3x 4 + x 2 + 7x +1= 0 contains how many imaginary 23. A tiger is now 50 of her leaps ahead of a lion which is pursuing roots? her. How many more leaps will the tiger take before it is A. 1 or 2 C. 2 or 4 overtaken if she takes 5 leaps while the lion takes 4 leaps, but 2 B. 2 or 0 D. 3 or 0 of the lion’s leaps are equivalent to 3 of the tiger’s leaps? 8. What is the range of the function y=5-√(4-x2)? A. 350 C. 420 B. 325 D. 250 * A. { y | 3 £ y £ 5} C. { y | 3 ³ y ³ 5} 1 x 5x-2 B. { y | -2 £ y £ 2} D. { y | y ³ 0} 24. Simplify: + - x+1 x-6 x 2 -5x-6 A. (x-4)/(x-6)* C. (x-3)/(x+6) 9. If f(x)=x2-1, g(x)=√(2x), h(x)=2-x, what is ? B. (x-2)/(x-6) D. (x-6)/(x-4) A. 2-3x C. 4-3x B. 3-2x D. 3x+4 25. The number o.123123123… is a/an A. irrational number C. surd 10. The number 10.080 has how many significant digits? B. rational number* D. transcendental A. 2 C. 4 B. 3 D. 5 26. Simplify, (3x3 - 4x2y + 5xy2 + 6y3) / (x2 - 2xy + 3y2). A. 3x-5y C. 2x-3y 11. Find the sum of the roots of the equation B. 3x+2y* D. 3x+5y 5x6 + 2x5 + x 4 -8x3 - 2x 2 -8 = 0 27. Find the remainder if 3x3 - 4x2y + 5xy2 + 6y3 is divided by x2 - A. 5 C. 0.80 2xy + 3y2. B. -0.40 D. -2.50 A. 0* C. 2 12. According to the upper and lower bound theorem, which of the B. 1 D. 3 following is the lower bound of the zeros of x 3 - 4x 2 + 2 . 28. If 10x = 4, then the value of 102x + 1 is A. 0 C. -1 A. 26 C. 40 B. 160 * D. 900 B. 3 D. 4 13. Three unbiased dice are thrown simultaneously. Find the ( ) 29. In the equation 3x 2 + m+1 x + 24 = 0 , find m if one of the root is probability of getting a sum of 8. twice the other. A. 5/108 C. 5/54 A. -19,17 C. 19,-17 B. -12,18 D. 12,-18 B. 7/72* D. 2/34 14. A player tosses two fair coins. He wins P5.0 if 2 heads appear, 30. The equation (2k + 2) x 2 + (4 - 4k) x + k - 2 = 0 has roots, which P3.0 if one head appear and P1.0 if no head occur. Determine his are reciprocals of each other. Find the value of k. A. 2 C. -4 * expected value of the amount? B. -2 D. 3 A. P5.2 C. P2.5* B. P4.5 D. P5.4 31. The equation whose roots are equal to twice those of the equation x3-6x2+11x-6=0. 15. A bag contains 10 red and 8 black balls. Two balls are drawn at A. x3-12x2+22x-12=0 C. x3-24x2+12x-12=0 random. Find the probability that the balls drawn are of different B. x3-12x2+44x-48=0 * D. x3-12x2+48x-44=0 colors. 32. Find the value of C in the expression 5x2-2x+C to make it a A. 5/17 C. 80/153* perfect square trinomial. B. 17/153 D. 17/80 A. 1/5* C. 1/4 B. 25 D. 16 CERTC-RF Review Center : MANILA-CEBU-BAGUIO (0932-175-1218) Page 1 CERTC Weekly Exam 1 Mathematics Electrical Engineering 33. If one root of 9x^2-6x+k=0 exceeds the other by 2, find the value 50. Find the sum of the values of x satisfying the equation 5(5x 5 x ) of k. = 26 are: A. 8 C. 5 A. 1 C. 2 B. -8* D. -6 B. 3 D. 0* 34. The set A = Æ is: { } A. Null set C. Singleton* 51. The function f :N ® N , where N is the set of natural numbers, B. Infinite D. Empty defined by f(x)=7x+11 is A. Injective * C. Surjective 35. The number 77 is divided into two parts such that the GCF of the B. Bijective D. nota two parts is 11 and their LCM is 110. The smaller of the two part 52. When two dice are rolled, what are the odds against getting is doubles? A. 11 C. 22* A. 1:5 C. 1:6 B. 44 D. 55 B. 5:1* D. 6:1 36. A father takes his twins and a younger child out to dinner on the 53. What are the odds for a fair game? twins’ birthday. The restaurant charges P495 for the father and A. 0:0 C. 1:1* P45 for each year of a child’s age, where the age is defined as B. 2:1 D. 1:2 the age at the most recent birthday. If the bill is P945, which of the following could be the age of the youngest child? 54. When a die is rolled, what are the odds in favour of getting a 5 or A. 1 C. 2* a 6? B. 3 D. 4 A. 2:3 C. 1:2* B. 3:2 D. 2:1 37. If one root of 9x^2-6x+k=0 exceeds the other by 2, find the value of k. 55. A box contains a penny, a nickel, a dime, and a quarter. If two A. 8 C. -8* coins are selected without replacement, the probability of getting B. 5 D. -6 an amount greater than 11c is A. 5/72 C. 2/3* 38. From the equation 12x3-8x2+kx+18=0, find the value of k if one B. 3/4 D. 5/6 root is the negative of the other. A. -18 C. -27* 56. The probability that a family visits Safari Zoo is 0.65, and the B. -12 D. -31 probability that a family rides on the Mt. Pleasant Tourist Railroad is 0.55. The probability that a family does both is 0.43. Find the 39. Alex was asked to multiply a number by 3/2. Instead he divided the probability that the family visits the zoo or the railroad. number by 3/2 and obtained a number smaller by 2/3. The number was A. 0.77* C. 0.22 A. 4/5* C. 3/5 B. 0.12 D. 0.10 B. 2/3 D. 1/2 57. Three coins are tossed; what is the probability of getting 3 heads 40. Three bells A, B, and C begin ringing at the same time and continue to if it is known that at least two heads were obtained? do so at intervals of 21, 28, and 30, respectively. The bells will ring A. 1/4* C. 2/3 together again after B. ½ D. 3/8 A. 7 seconds C. 7 minutes* 58. In a certain group of people, it is known that 40% of the people B. 630 seconds D. 1 hr take Vitamins C and E on a daily basis. It is known that 75% take 1+ x 2 Vitamin C on a daily basis. If a person is selected at random, 41. Determine the range of the function f(x) = . what is the probability that the person takes Vitamin E given that x2 the person takes Vitamin C? A. [0,1] C. (0,1) A. 5/13 C. 7/12 ( ) B. 1,¥ D. éë1,¥ ) B. 3/11 D. 8/15* 42. If f(x) = x 5 + cos x , then f(x) is 59. The probabilities that a page of a training manual will have 0, 1, 2, or 3 typographical errors are 0.75, 0.15, 0.10, and 0.05 A. an even function C. an odd function respectively. If 6 pages are randomly selected, the probability that B. neither even nor odd D. a constant function 2 will contain no errors, 2 will contain one error, one will contain 2 errors, and one will contain 3 errors is ( ) 43. If f(x)=x2+1, then the value of f f (x) is equal to A. 0.078 C. 0.063 4 2 B. 0.042 D. 0.011 A. x +2x +2 C. x4+2x2+2 * B. x4+2x2+1 D. None of these 60. A man is dealt a poker hand (5 cards) from an ordinary deck x+4 of playing cards. In how many ways can he be dealt with a 44. Solve the inequality <2 . flush? x-3 ( ) A. -3,¥ ( C. -13,-3 ) A. 3,650 B. 5,108* C. 2,457 D. 4,540 B. ( -¥,-13 ) D. None of these 61. The number of boating accidents on a large lake follows a ( ) ( x + 4) < 0 is 2 Poisson distribution. The probability of an accident is 0.01. If 45. The solution to inequality x - 1 there are 500 boats on the lake on a summer day, the probability ( A. -¥,1 ) C. ( -¥,-4 ) that there will be exactly 4 accidents will be A. 0.192 C. 0.263 ( B. -1,4 ) D. (1,4 ) B. 0.175* D. 0.082 46. Solve the absolute value inequality 3x - 2 ³ 1. 62. An eight-sided die is rolled. The average number of tosses that it will take to get a 6 is A. [1/3,1] C. {1/3,1} A. 6 C. 16 æ 1ù B. (1/3,1) D. ç -¥, ú È éë1,¥ è 3û ) B. 8* D. 12 5 3 2 63. Find the sum of the coefficients of x 2 2 x 3 47. Solve: |x-1| > 2. 2 A. [-∞,-1)U[3,+ ∞) C. [-∞,-1) [3,+ ∞) A. 210* C. 230 B. 220 D. 240 B. (-∞,-1)U[3,+ ∞)* D. (-∞,-1] [3,+ ∞) 64. Evaluate 11 4 8 9 729 ... 22500 3375000 48. Ming has 15 quarters, 30 dimes and 48 nickels. He wants to group his money so that each group has the same number of A. 128,384,568 C. 129,391,900* each coin. How much money will each group be worth? B. 124,384,568 D. 129,931,900 A. 2.25$ C. 1.45$ 25 B. 1.65$ D. 3.05$* 65. Find the coefficient of the term involving x 6 of the binomial 10 49. Which of the following is the range of the signum function? 32 2 A. {−1,0,1} C. {0,1} 2x 2x 3 B. {−∞, +∞} D. None of the these CERTC-RF Review Center : MANILA-CEBU-BAGUIO (0932-175-1218) Page 2 CERTC Weekly Exam 1 Mathematics Electrical Engineering A. -258048* C. -122880 B. 215040 D. 46080 66. Find the sum of the first four terms of the sequence ( n starts at 0) an an1 an2 an3 given that a0 1 , a1 1 , a2 2 and stops 77. Three circles of radii 115, 150, and 225 m, respectively, are tangent to each other externally. Find the angles of the triangle at n 5 formed by joining the centres of the circles. A. 4* C. 6 A. 43°10', 61°20', 75°30' * C. 75°30', 27°08', 78°12' B. 5 D. 7 B. 82°21', 43°10', 55°46' D. 55°46', 61°20', 64°03' 78. Three circles with radii 3.0, 5.0, and 9.0 cm are externally and f 1 2 , find f 8 n 67. If f n 1 n f n tangent. What is the area of the triangle formed by joining their centers? A. 48 cm2 * C. 24 cm2 12 13 A. C. B. 32 cm2 D. 52 cm2 7 15 79. Suppose that the angles of ∆𝐴𝐵𝐶 satisfy cos(3𝐴) + cos(3𝐵) + 35 41 B. * D. cos(3𝐶) = 1. Two sides of the triangle have lengths 10 and 13. 32 32 There is a positive integer 𝑚 so that the maximum possible length 68. Determine the range of the following function for the remaining side is √𝑚 . Find 𝑚. x 1 1 x 0 A. 277 C. 399 * f x x 1 0 x 1 B. 344 D. 211 80. Find the sum of the values of 𝑥 such that 𝑐𝑜𝑠 3 3𝑥 + 𝑐𝑜𝑠 3 5𝑥 = A. 1,1 C. 1,0 8 𝑐𝑜𝑠 3 4𝑥 ∗ 𝑐𝑜𝑠 3 𝑥 , where 𝑥 is measured in degrees and 100 < 𝑥 < 200. B. 0,1 * D. undefined A. 603 C. 306 3x3 7 x 4 B. 906 * D. 609 69. Decomposing the given function in such a way that it x 2 2 2 81. An airplane is moving horizontally at 240 mi/h when a bullet is shot with speed 2750 ft/s at right angles to the path of the Ax B Cx D is decomposed into a form , determine, airplane. Find the resultant speed and direction of the bullet. x2 2 f x A. 3210 ft/s, 7.3° with the path of the plane A B C D B. 2770 ft/s, 82.7° with the path of the plane * C. 2770 ft/s, 7.3° with the path of the plane A. 3 C. 5 D. 3210 ft/s, 82.7° with the path of the plane B. 4 D. 6* 1 70. Suppose f x is a function that satisfies f x 5 f 3 x 82. The airspeed of an airplane is 200 kph. There is a wind of 30 kph x from 270°. Find the groundspeed in order to track 0°. x 0 . What is f 4 ? A. 143 kph at 17°33' C. 156 kph at 21°78' B. 198 kph at 8°40' * D. 179 kph at 5°56' A. 5/4 C. 2 83. From a point A on level ground, the angles of elevation of the top B. 37/96* D. 27/83 D and bottom B of a flagpole situated on the top of a hill are measured as 47°54' and 39°45'. Find the height of the hill if the 71. How many ways are there to choose 4 different numbers from the height of the flagpole is 115.5 ft. set x | x 0 x 11 so that no two of the 4 numbers are A. 285.2 ft C. 349.3 ft * consecutive? B. 505.1 ft D. 402.7 ft 84. Find the height of a tree if the angle of elevation of its top A. 10 C. 20 changes from 20° to 40° as the observer advances 75 ft toward B. 35* D. 40 its base. A. 32 ft C. 48 ft * 72. Let n . Suppose a function L is defined as B. 24 ft D. 26 ft 0 if n 1 85. A tower standing on level ground is due north of point A and due west of point B, a distance c ft from A. If the angles of elevation of L n L 2 1 if n 1 the top of the tower as measured from A and B are (α and β, respectively, find the height h of the tower. 𝑐 𝑐 Find L 25 A. ℎ = 2 2 * √(cot α) + (cot β) C. ℎ = 2 2 √(tan 𝛼) + (tan 𝛽) 𝑐 𝑐 A. 2 C. 4* B. ℎ = D. ℎ = √(cot α)2 − (cot β)2 √(tan 𝛼)2 − (tan 𝛽)2 B. 3 D. 5 73. A a, b, c, d and B x, y, z , A B , if aRy, dRy, bRx, cRz , 86. From point A, a pilot flies 125 km in the direction N38°20'W and identify the type of function. turns back. Through an error, the pilot then flies 125 km in the direction S51°40'E. How far and in what direction must the pilot A. Injective and Non-surjective now fly to reach the intended destination A? B. Non-injective and Surjective* A. S45°20'W, 29.0 km * C. N45°20'E, 32.0 km C. Injective and Surjective B. W45°20'S, 29.0 km D. E45°20'N, 32.0 km D. Non-Injective and Non-surjective 87. Two ships have radio equipment with a range of 200 km. One is 74. If f x x 2 and g x 3 x , find f 1 g 1 2 155 km N42°40'E and the other is 165 km N45°10'W of a shore station. Can the two ships communicate directly? A. 8 C. 6* A. Yes, they are 198 km apart. B. 2 D. -2 B. Yes, they are 162 km apart. C. No, they are 222 km apart. * 75. What can you say about the sets A and B if we know that D. No, they are 201 km apart. A B B A ? A. B A C. A B 88. A lighthouse is 10 km northwest of a dock. A ship leaves the dock B. A B D. None of the above* at 9 A.M. and steams west at 12 kmh. At what time will it be 8 km (𝑠𝑖𝑛θ)2 +2(cos θ)2 from the lighthouse for the second time? 76. Simplify . A. 9:17 AM C. 9:20 AM 𝑠𝑖𝑛θ cosθ A. sin θ + 3csc θ C. tan θ + 2cot θ * B. 9:54 AM * D. 10:15 AM B. sin θ - 3csc θ D. tan θ - 2cot θ CERTC-RF Review Center : MANILA-CEBU-BAGUIO (0932-175-1218) Page 3 CERTC Weekly Exam 1 Mathematics Electrical Engineering 89. What time between 2 and 3 o’clock will the angle between the 99. 55. Pen and Apple can do a piece of work in 42 days, Apple and hands of the clock be bisected by the line connecting the center PenApple in 31 days, PenApple and Pen in 20 days. In how many of the clock and the 3 o’clock mark? days can all of them do the work together? A. 2:18:27.6 * C. 2:17:56.3 B. 2:16:00.0 D. 2:19:03.1 A. 20 C.18 B. 19 * D. 22 90. A man has $4.85 in his pocket all in coins. If he has six more 100. 57. Ten liters of 25% love solution and 15 liters of 35% salt solution nickels than dimes and twice as many quarters as dimes, how are poured into a cauldron originally containing 30 liters of 10% love many coins of each type does he have? solution. What is the love percent concentration in the mixture? A. 14 dimes, 7 nickles, and 13 quarters B. 7 dimes, 13 nickles, 14 quarters * A 18.75% C. 22.25% C. 13 dimes, 14 nickles, and 7 quarters B. 19.55% * D. 20.65% D. 14 dimes, 13 nickels, and 7 quarters 101. 58. How many liters of water must be added to 80 liters of a 40% 91. A worker can do a job 1.25 times faster than another worker. bitterness solution to produce a solution that is 25% bitterness? When both do the job together, they can do it in five hours. How long would it take for the slower worker to do the job? A. 32 C. 24 A. 12.5 hrs C. 8.75 hrs B. 36 D. 48 * B. 11.25 hrs * D. 10.33 hrs 102. 59. In how many minutes after 1PM will the hands of the clock be directly opposite to each other the first time? 92. Train A leaves the terminal 2 hours after Train B left the same terminal. Train B is running at 20 mph slower than Train A. Find A. 16.3636 C.21.8181 the speed of Train A if it overtakes Train B in three hours. B. 38.1818 D. 5.4545 * A. 30 mph C. 60 mph* B. 50 mph * D. 40 mph 103. 60. What time between 3PM and 4PM will the hands of the clock make an angle of 30 degrees from each other the first time? 93. There are 5 geese in a gaggle. If working together, the gaggle A. 3:5.4545 C.3:10.9090 * produces 55 eggs in 5555 days, what is the average number of B. 3:16.3636 D.3:21.8181 days it takes a single goose to lay an egg? A. 5 C. 555 104. 61. What time between 7PM and 8PM will the hands of the clock be B. 505 * D. 101 perpendicular to each other the second time? 94. A tree has 10 pounds of apples at dawn. Every afternoon, a bird A. 7:49.0909 C. 7:54.5454 * comes and eats x pounds of apples. Overnight the amount of B. 7:38.1818 D. 7:51.2727 food on the tree increases by 10%. What is the maximum value 105. 62. The resistance of a wire varies directly with its length and of x such that the bird can sustain itself indefinitely on the tree inversely with its area. If a certain piece of wire 10 m long and 0.10 without the tree running out of food? cm in diameter has a resistance of 100 ohms, what will its resistance A. 11/12 C. 11/10 be if its uniformly stretched so that its length becomes 12 m? B. 12/11 D. 10/11 * A. 144 ohms * C. 120 ohms 95. Let x be a three-digit number. The hundreds digit is twice the B. 130 ohms D. 110 ohms units digit and if 396 be subtracted from the number, the order of 106. 63. The force of attraction between two lovers of mass m1 and m2 the digits will be reversed. If the sum of the digits is 17, find x. varies directly as the product of their masses and inversely as the A. 683 C. 854 * square of the distance between them. If the masses of the bodies and B. 386 * D. 458 the distance between them is doubled, the force of attraction will become 96. Ten liters of 25% salt solution and 15 liters of 35% salt solution are poured into a cauldron originally containing 30 liters of 10% A. four times C. two times salt solution. What is the salt percent concentration in the B. half D. will not change * mixture? 107. 64. The quotient of a two-digit number divided by the sum if the digits A. 22.25% C. 19.55% * is 4. If the number be subtracted from the sum of the squares of its B. 18.75% D. 20.65% digits, the difference is 9. Find the number. A. 30 C.54 B. 4 D.36 * 108. 65. A box contains nickels, dimes, and quarters worth a total of $2.10. There are twice as many dimes as quarters, and the number of nickels is two less than the number of dimes. How many dimes are there? A. 8 * C. 6 B. 7 D. 4 109. 66. Ten years from now, the sum of the ages of Vy and Na is equal to 50. Six years ago, the difference of their ages is equal to 6. After 5 years, what is the product of the ages of Vy and Na? A. 216 C. 391 * B. 384 D. 229 -------------------------------------------------------------------------------- 110. 67. The Minister of Magic hosted a party with 316 guests composing of wizards, witches, and squibbs. There were 78 more squibbs than witches and 56 more witches than wizards. How many wizards were in the party? IN CASE WALA NAKAPADALA SI KEVIN KINI ANG SUMPAY A. 44 C. 50 B. 42 * D. 46 97. 51. Given that w varies directly as the product of x and y and inversely as the square of z, and that w = 4 , when x = 2, y = 6, and z 111. 68. Mundungus Fletcher stole a locket at 1PM and rode his = 3. Find the value of w when x = 1, y = 4, and z = 2. broomstick at a speed of 45km/hr. He was seen by a muggle at 2PM A. 4 C.3 * and was chased by an auror in a broomstick at 54km/hr. He will be B. 2 D.1 imprisoned at Azkaban at? 98. 52. The electric power which a transmission line can transmit is A. 8PM C. 6PM proportional to the product of its design voltage and the current B. 7PM * D. 5PM capacity, and inversely to the transmission distance. A 115 kV line rated at 1000 A can transmit 150 MW over 150 km. How much 112. 69. Find two consecutive odd numbers such that thrice the smaller power can a 230 kV line rated at 1500 A transmit over 100 km. number exceeds the larger by 12. A. 567 C. 675 * A. 5,7 C. 11,13 B. 756 D. 576 B. 7,9 * D. 9,11 CERTC-RF Review Center : MANILA-CEBU-BAGUIO (0932-175-1218) Page 4 CERTC Weekly Exam 1 Mathematics Electrical Engineering 113. 70. Hogwarts Express traveling 50 mph left King's Cross Station 40 minutes before a second train traveling 55 mph. How long should it 3x1 x2 x3 x4 10 take for the second train to overtake Hogwarts Express? x1 3x2 x3 x4 20 A. between 6 & 7 hrs * B. between 4 & 5 hrs D. between 5 & 6 hrs x1 x2 3x3 C.x4between 30 7 & 8 hrs 114. 71. Arthur Weasley is 9 times as old as Ron. In 3 years, Arthur will be x1 x2 x3 3x4 40 only 5 times as old as Ron. What is currently the difference of their ages? Solve for x3 A. 30 C. 24 * A. 40/6 C. 4/60 B. 27 D. 21 d. 0 115. 72. There are 5 geese in a gaggle. If working together, the gaggle b. 3/40 produces 55 eggs in 5555 days, what is the average number of days it takes a single goose to lay an egg? 124. Which of the following describes the function as shown below? A. 5 C. 505 * B. 555 D. 101 116. 73. If Hermione gets a 97 in her Ancient Runes exam, her average will be 90. If she gets 73, her average will be 87. How many exams has Hermione already takeA treen? A. 8 C. 7 * B. 6 D. 5 A. Injective and Non-surjective B. Non-injective and Surjective C. Injective and Surjective D. Non-injective and Non-surjective 125. If x : y : z 4 : 3 : 2 and 2 x 4 y 3z 20 , find x, y , z . a. -8,6,-4 c. 7,-5,6 b. -5,4,-6 d. 9,-4,5 126. The mantissa of a logarithm is A. Always positive B. Always negative 117. Which of the following equations has a horizontal asymptote of C. Either positive or negative zero and a vertical asymptote of 2 and -4? D. An integer only 7x 3 7x 3 A. C. x 2x 8 2 x 2x 8 2 17 127. Find the product of the solutions of the equation 7 a 8 7 a 7x 3 B. D. All of the above a. 1.2 c. -2.3 x 2x 8 2 b. 4.5 d. -1.5 19. Given N (x) where D (x) is a cubic equation with real roots, If 118. Which of the following is the solution set of D(x) 5b 10 30 and 7b 2 40 A.x4 C. D (x) has a root with a multiplicity of 3, the partial fraction decomposition of N (x) has how many terms? B. D. x 6 D(x) a. 2 c. 4 119. Which of the following shows the difference of two cubes b. 3 d. 5 property? A. (a b)(a 2 ab b2 ) C. (a b)(a 2 ab b2 ) 20. What is the last digit of 24000 ? a. 4 c. 8 B. b. 6 d. 0 D. (a b)(a b)(a b) 3x 1 x3 (a b)(a 2 ab b2 ) 1 21. Simplify 2 x 1 x 3x 2 x 2 2 120. Quartic equations are solved using A. Quadratic Formula C. Third Method 1 2x Cardan’s Method D. Ferrari’s Method a. c. B. x x 1 121. A method to test a number’s primality. 1 A. Euclidean Algorithm C. Mersenne Prime b. d. x2 2 x 1 B. Cardan’s Method D. Ferrari’s Method x 1 122. Let a and b be positive integers. lcm(a, b) gcd(a, b) 128. Which of the following numbers is both non-terminating and non- would be repeating? a. a b c. ab a. 100/3 c. 3i b. 1 d. e a b. d. 1 129. Determine the 10th term of the sequence whose first three terms 2b are 1/3, 1/7, 1/11. a. 0.0256 c. 0.0286 123. 10. From the system of linear equations b. 0.0233 d. 0.0213 CERTC-RF Review Center : MANILA-CEBU-BAGUIO (0932-175-1218) Page 5 CERTC Weekly Exam 1 Mathematics Electrical Engineering 130. The numbers 28, x+2,112 form a geometric progression. What is 4, 3.6, 3.24,... are needed so that the 10th term? 27. How many terms in the GP a. 28,672 c. 7/256 the sum exceeds 35? b. 7168 d. 14,336 a. 17 c. 19 b. 18 d. 20 131. In group of 120 students labelled 1 to 120, all even numbered students opt for Math, whose numbers are divisible by 5 opt for Physics and those whose numbers are divisible by 7 opt for 28. Find the 7th term of the GP 2, 6,18,... Electronic/Electrical. How many opt for none of the three subjects? a. 1456 c. 1458 a. 19 c. 21 b. 1457 d. 1459 b. 41 d. 57 132. Let A and B be two finite sets such that n(A) = 20, n(B) = 28 and 29. Find n ( A2 ) if A 0,1 n(A ∪ B) = 36, find n(A ∩ B). a. 17 c. 8 a. {(0, 0), (0,1), (1, 0), (1,1)} c. {(0, 0), (1,1)} b. 24 d. 12 b. 4 d. {0,1} 133. In a group of 60 people, 27 like cold drinks and 42 like hot drinks 30. Suppose that A is the set of sophomores at your school and B is and each person likes at least one of the two drinks. How many CC like both coffee and tea? the set of students in discrete mathematics at your school. B would be a. 9 c. 11 b. 10 d. 12 a. the set of sophomores taking discrete mathematics in your school x | x A or x B then which of b. the set of sophomores at your school who are not 134. Given set A and B and if taking discrete mathematics the following is similar to the above statement? Hint: means “is c. the set of students at your school who either are an element of”. sophomores or are taking discrete mathematics d. the set of students at your school who either are not a. A B c. A* B sophomores or are not taking discrete mathematics b. A B d. A B 31. Identify the type of function shown 135. Which of the following laws of the algebra of sets is the Involution law? a. A A A c. ACC A b. A A A d. AU A a. One-to-one, Onto 22. The sum of a geometric series is 3/8 and the second term is 1/12. b. One-to-one, not onto Find the greatest possible common ratio. c. Onto, not one-to-one d. Not a function a. 2/3 c. 1/3 b. 1/2 d. 1/6 136. Let a = 444…444 and b = 999…999 (both have 2010 digits). What is the 2010th digit of the product ab? a. 3 c. 5 b. 4 d. 6 23. What is the cardinality of this set. {Æ} a. 0 c. 2 b. 1 d. 3 32. Identify the function shown 1 if n 1 f (x) u (t) 24. Let f (n) . Find f(5) a. c. f (x) x 2 f (n 1) 3 otherwise b. f (x) x d. f (x) x a. 58 c. 60 b. 59 d. 61 33. A number that can be expressed as a ratio of two integers. a. Divisible number 25. Evaluate 17mod5 b. Integrable numbers c. Pseudoprimes a. 2 c. 4 d. Rational number b. 3 d. 5 34. Find the range the function that assigns to each positive integer thenumber of the digits 0, I, 2, 3, 4, 5, 6, 7, 8, 9 that donot appear 26. Let A, B, and C be non-empty sets. Simplify the expression as decimal digits of the integer A (B C) a. 0 x9 c. 0 x9 a. (C B ) A c. (A B) C b. x 10 d. 1 x 10 (C B) A ( A B) C b. d. 35. Divide x 4 10 x 2 9 x 20 by x 4 . What is the remainder? CERTC-RF Review Center : MANILA-CEBU-BAGUIO (0932-175-1218) Page 6 CERTC Weekly Exam 1 Mathematics Electrical Engineering a. 40 c. 50 A. 144 ohms * C. 120 ohms b. 45 d. 55 B. 130 ohms D. 110 ohms 63. The force of attraction between two lovers of mass m1 and m2 varies 12 directly as the product of their masses and inversely as the square of 36. Let a1 2 and an 1 for n>1. Find an as n the distance between them. If the masses of the bodies and the 2 an 5 distance between them is doubled, the force of attraction will become A. four times C. two times approaches B. half D. will not change * 64. The quotient of a two-digit number divided by the sum if the digits is 4. a. 4/3 c. 2 If the number be subtracted from the sum of the squares of its digits, b. 3/2 d. 0 the difference is 9. Find the number. A. 30 C.54 37. Which of the following numbers satisfy the equation x3 x 1 B. 4 D.36 * a. Plastic Number 65. A box contains nickels, dimes, and quarters worth a total of $2.10. There are twice as many dimes as quarters, and the number of nickels b. Iron Number is two less than the number of dimes. How many dimes are there? c. Fibonacci Number A. 8 * C. 6 d. Lucas Number B. 7 D. 4 38. Who discovered the Fibonacci sequence? 66. Ten years from now, the sum of the ages of Vy and Na is equal to 50. a. Lucas Six years ago, the difference of their ages is equal to 6. After 5 years, b. Fibonacci what is the product of the ages of Vy and Na? c. Leonardo A. 216 C. 391 * B. 384 D. 229 d. Jacobsthal 67. The Minister of Magic hosted a party with 316 guests composing of 51. Given that w varies directly as the product of x and y and inversely as wizards, witches, and squibbs. There were 78 more squibbs than the square of z, and that w = 4 , when x = 2, y = 6, and z = 3. Find the witches and 56 more witches than wizards. How many wizards were in value of w when x = 1, y = 4, and z = 2. the party? C. 4 C.3 * A. 44 C. 50 B. 42 * D. 46 D. 2 D.1 68. Mundungus Fletcher stole a locket at 1PM and rode his broomstick at a 52. The electric power which a transmission line can transmit is speed of 45km/hr. He was seen by a muggle at 2PM and was chased proportional to the product of its design voltage and the current by an auror in a broomstick at 54km/hr. He will be imprisoned at capacity, and inversely to the transmission distance. A 115 kV line Azkaban at? rated at 1000 A can transmit 150 MW over 150 km. How much power A. 8PM C. 6PM can a 230 kV line rated at 1500 A transmit over 100 km. B. 7PM * D. 5PM A. 567 C. 675 * 69. Find two consecutive odd numbers such that thrice the smaller number B. 756 D. 576 exceeds the larger by 12. 53. The sum of Maria and Deborrah's ages is 18. In 3 years, Maria will be A. 5,7 C. 11,13 twice as old as Deborrah. How old is Maria? B. 7,9 * D. 9,11 A. 4 C. 5 70. Hogwarts Express traveling 50 mph left King's Cross Station 40 B. 14 D.13 * minutes before a second train traveling 55 mph. How long should it 54. Eight years ago, the sum of the ages of Jiovanni and Quiseo was 26. take for the second train to overtake Hogwarts Express? In five years, Jiovanni will be 35 less than twice the age of Quiseo. A. between 6 & 7 hrs * How old is Quiseo? B. between 4 & 5 hrs D. between 5 & 6 hrs A. 24 * C. 36 71. Arthur Weasley is 9 times as old as Ron. In 3 years, Arthur will be only B. 39 D. 32 5 times as old as Ron. What is currently the difference of their ages? 55. Pen and Apple can do a piece of work in 42 days, Apple and PenApple A. 30 C. 24 * in 31 days, PenApple and Pen in 20 days. In how many days can all of B. 27 D. 21 them do the work together? 72. There are 5 geese in a gaggle. If working together, the gaggle A. 20 C.18 produces 55 eggs in 5555 days, what is the average number of days it B. 19 * D. 22 takes a single goose to lay an egg? 56. My boyfriend can repair my heart in 6 hrs. My girlfriend can do the A. 5 C. 505 * same job in 10 hours. On a given day, my boyfriend begins to work B. 555 D. 101 and after 2 hrs, he is jointly helped by my girlfriend. In how many hours 73. If Hermione gets a 97 in her Ancient Runes exam, her average will be will they completely repair my heart? 90. If she gets 73, her average will be 87. How many exams has A. 2.5 hrs * C. 4.5 hrs Hermione already takeA treen? B. 5.5 hrs D. 3.5 hrs A. 8 C. 7 * 57. Ten liters of 25% love solution and 15 liters of 35% salt solution are B. 6 D. 5 poured into a cauldron originally containing 30 liters of 10% love 74. A tree has 10 pounds of apples at dawn. Every afternoon, a bird comes solution. What is the love percent concentration in the mixture? and eats x pounds of apples. Overnight the amount of food on the tree A 18.75% C. 22.25% inceases by 10%. What is the maximum value of x such that the bird B. 19.55% * D. 20.65% can sustain itself indefinitely on the tree without the tree running out of 58. How many liters of water must be added to 80 liters of a 40% food. bitterness solution to produce a solution that is 25% bitterness? A. 11/10 C. 11/12 A. 32 C. 24 B. 12/11 D. 10/11 * B. 36 D. 48 * 75. Aliens from Lumix have one head and four legs, while those from 59. In how many minutes after 1PM will the hands of the clock be directly Obscra have two heads and only one leg. If 60 aliens attend a joint opposite to each other the first time? Lumix and Obscra interworld conference, and there are 129 legs A. 16.3636 C.21.8181 present, how many heads are there? B. 38.1818 D. 5.4545 * A. 97 * C. 79 B. 54 D. 45 60. What time between 3PM and 4PM will the hands of the clock make an angle of 30 degrees from each other the first time? 76. The incenter of a triangle lies on the Euler’s line only in the case of A. 3:5.4545 C.3:10.9090 * ______ triangle. B. 3:16.3636 D.3:21.8181 A. Obtuse C. Right B. Isosceles* D. Equilateral 61. What time between 7PM and 8PM will the hands of the clock be perpendicular to each other the second time? 77. Find the area of a triangle with sides 23, 13 and 18. A. 7:49.0909 C. 7:54.5454 * A. 116.65* C. 90.07 B. 7:38.1818 D. 7:51.2727 B. 1571.88 D. 144.91 62. The resistance of a wire varies directly with its length and inversely 78. At a point on level ground, the angle of elevation of the top of the tower with its area. If a certain piece of wire 10 m long and 0.10 cm in is 20⁰30”. Twenty feet nearer, the angle of elevation is now 30⁰23’50”. diameter has a resistance of 100 ohms, what will its resistance be if its How high is the tower to the nearest foot? uniformly stretched so that its length becomes 12 m? A. 18ft C. 19ft* CERTC-RF Review Center : MANILA-CEBU-BAGUIO (0932-175-1218) Page 7 CERTC Weekly Exam 1 Mathematics Electrical Engineering B. 20ft D. 21ft 97 .Three times an angle is a supplement to four times another angle. The first angle is a complement of three times of the second angle. Find 79. A hiker climbs a mountain 1000 ft high which is inclined 35⁰ with the the angles. horizontal. Upon reaching the summit, he looks back downwards and A. 30,20 C. 144,-18 finds that another hiker on level ground, spotted with an angle of B. 36,72 D. 36,18* depression of 15⁰, is approaching the foot of the mountain. How far is 98. A triangle has sides 13 and 20 and an included angle of 34⁰. An angle the second hiker from the foot of the mountain? bisector bisects the given angle dividing the triangle into two parts. Find A. 434 ft C. 1152 ft the ratio of the areas of the larger part to the smaller part. B. 2304 ft* D. 1728 ft A. 1.4 C. 1.5 80. What is the reference angle of -143⁰? B. 1.6* D. 1.7 A. 37⁰* C. -37⁰ 99. Find the exact value of cos(A+B) if sinA=3/5, tanB=-5/12, 0<A<π/2 and B. -53⁰ D. 53⁰ π/2<B<π. A. 33/65 C. -63/65* 81. An artillery is set at an angle of 488 mils. The firing angle was later B. -33/65 D. 63/65 added by 14 gradians. What is the new firing angle in radians? 100. Solve for x: arctan2x + arctanx = π/4. A. 0.2225π* C. 0.11125π A. 0.149 C. 0.281* B. 0.445π D. 1.595π B. 0.421 D. 0.316 82. Which of the following is a possible measurements of the sides of a 39. Identify the type of function shown triangle. A. 2,3,6 C. 2,5,6* a. Tangent B. . Cotangent B. 7,3,4 D. 3,4,9 C. Secant 83. The pair of opposite angles formed when two lines intersects. D. Cosecant A. Adjacent angles C. Complementary angles B. Explementary angles D. Vertical angles* 84. Fifteen degrees less than the complement of an angle is 11/68 of the explement of the angle. Find the angle in radian. A. π/8 C. π/9* B. π/10 D. π/11 85. Find the ratio of the areas of the circumscribing and inscribed circles of the triangle which sides are 6,11 and 13. A. 2.979 C. 8.875* B. 1.726 D. 1.732 86. The angle of inclination of ascend of a road having 8.25% grade is _____ degrees. A. 4.72* C. 4.27 B. 5.12 D. 1.86 9 5 3 7 11 are solutions to the equation 87. A pilot wants to maintain a groundspeed of 130 knots over a course 40. , , , , , of 35⁰ north of east. Wind is blowing from the northeast at 40 knots. At 8 8 8 8 8 8 what course must the pilot direct the aircraft? A. N 57.35⁰ E* C. N 32.65⁰ E a. sin(2 x) cos(2 x) c. 2 cos(x) 3 B. N 55.35⁰ E D. N 48.65⁰ E 88. Which is true to both quadrant 3 and 4? A. Secant positive C. Secant negative B. Cosecant positive D. Cosecant negative* b. 2sin(5 x) 3 d. none of the above 89. Scout rangers A and B are on east-west line, 5 km apart. Ranger A detects a poacher at C, on bearing 60⁰. Ranger B simultaneously detects the same poacher on a bearing of 330⁰. Find the distance from ranger A to C. A. 2.5 km C. 4.3 km* B. 5.8 km D. 8.7 km 𝑐𝑜𝑠 2 0+𝑐𝑜𝑠 2 1+𝑐𝑜𝑠 2 2+⋯.+𝑐𝑜𝑠 2 90 90. Solve: 𝑠𝑖𝑛2 0+𝑠𝑖𝑛2 1+𝑠𝑖𝑛2 2+⋯+𝑠𝑖𝑛2 90 A. 1* C. 0 B. 0.5 D. 0.57 𝑡𝑎𝑛𝑢 91. Simplify +1 𝑠𝑒𝑐𝑢(2𝑐𝑜𝑠 2 𝑢−𝑐𝑜𝑠2𝑢) A. cosu +1 C. tanu +1 B. secu +1 D. sinu+1* 92. Given triangle ABC with sides a=16, b= 13 and c=20. Let the point of intersection of the angle bisectors be point D. Find the area of triangle ABD. A. 42.37* C. 84.75 B. 115 D. 57.5 93. Given triangle ABC with sides 13, 12 and 20, find the area of the escribed circle tangent to the 20-unit side. A. 2820.36* C. 897.75 B. 2432.46 D. 2280.36 94. A hostileship was spotted 50 miles away from a navy ship at a bearing of N35⁰E. It is sailing at 50 mph in N15⁰E. An intercept boat was sent from the navy ship. Find the bearing of the boat if it must intercept the ship in 2.5 hours. A. E 20.67⁰ N C. N 20.67⁰ E* B. E 10.33⁰ N D. N 10.33⁰ E 95.A plane 1000 ft above the air spotted two boats A and B. Boat A is due N20⁰E at an angle of depression of 35⁰ while Boat B is due S53⁰W at angle of depression of 20⁰. Find the distance between the two boats. A. 3900ft C. 4000 ft B. 4100 ft* D. 4200 ft 96. In a triangle with sides 12,16 and 18, find the area of the region inside its circumscribing circle and outside its inscribed circle. A. 67.57 C. 212.26* B. 81.41 D. 317.42 CERTC-RF Review Center : MANILA-CEBU-BAGUIO (0932-175-1218) Page 8