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1 ELECTRICIAN PRE-APPRENTICESHIP MATH ENTRANCE EXAM NOTE: Please DO NOT write in exam booklet. Use the answer sheet for your answers.
2 NOTE: DO NOT MARK SECTION A. PLACE YOUR ANSWERS ON THE SHEET PROVIDED IN SECTION B. SECTION A ADDITION: Add the following: =? a b c d /3 + 2/3 =? a. 4/6 b. 4/9 c. 1 1/3 d. 1 2/3 3. 5/16 + 3/8 =? a. 8/24 b. 11/16 c. 1/3 d. 5/8 SUBTRACTION: Subtract the following: =? a b c d D:\Users\ \Desktop\Electrician Entrance Exam.doc 2
3 5. 4 1/8-1 2/3 =? a. 3 17/24 b. 5 19/24 c. 3 1/8 d. 2 11/24 MULTIPLICATION: Multiply the following: x 152 =? a. 335 b c d /10 x 5/6 =? a. 1 44/60 b. 45/60 c. 1 ¼ d. 3/ /5 x 2 2/3 =? a. 3 1/5 b. 3 3/5 c. 1 ¾ d. 1 3/5 DIVISION: Divide the following: =? a b. 78 c. 77 d D:\Users\ \Desktop\Electrician Entrance Exam.doc 3
4 10. 3/4 1/2 -? a. ½ b. 1 ½ c. 2/3 d. 3/8 CALCULATIONS: Complete the calculations as indicated =? a b c d =? a. 0.4 b c d x =? a b c d..667 DECIMALS: Convert the following fractions to decimals. Round off to the nearest thousandth /16" =? a..375 b..536 c. 144 d..563 D:\Users\ \Desktop\Electrician Entrance Exam.doc 4
5 /64" =? a b c d /16" =? a b c d Convert the following decimals to fractions " =? a. 1/8 b. 3/32 c. 2/3 d. 1/ " =? a. ¾ b. 2/3 c. 5/7 d. 13/ " =? a. ¼ b. 3/16 c. 5/16 d. 13/75 D:\Users\ \Desktop\Electrician Entrance Exam.doc 5
6 Solve the following equations =? a b c d x =? a. 5.5 b c d Divide the following decimals ) =? a b c d DECIMAL FRACTIONS: /1000 =? a..075 b. ¾ c..75 d three thousandths =? a..3 b..03 c..003 d. 30/1000 D:\Users\ \Desktop\Electrician Entrance Exam.doc 6
7 25. fifty-seven ten thousandths =? a. 57/1000 b c..057 d ROUNDING: 26. Round to the nearest tenth =? a. 67 b c d Round to the nearest hundredth =? a. 67 b c d Round to the nearest thousandth =? a. 67 b c d D:\Users\ \Desktop\Electrician Entrance Exam.doc 7
8 AVERAGE: 29. What is the average length of the pieces in the diagram below? a. 3 3/8 b c. 5 ¼ d. 6 1/8 NEGATIVE QUANTITIES: 30. (-1) + (2) =? a. 3 b. 3 c. 1 d (-3) - (-4) =? a. -7 b. 7 c. 1 d. 1 D:\Users\ \Desktop\Electrician Entrance Exam.doc 8
9 SQUARE ROOT: 32. 1O24 =? a. 32 b. 512 c d =? a. 3 b c. 0.3 d EXPONENTS: 34. The value of 6 2 is a. 12 b. 3 c. 36 d The value of 4 3 is a. 12 b. 16 c. 64 d. 7 EXPRESS THE FOLLOWING IN POWERS OF TEN: x10 4 =? a b. 10,000,000 c d D:\Users\ \Desktop\Electrician Entrance Exam.doc 9
10 =? a. 10,000 b c d ,000 =? a b c d METRIC: 39. The symbol for a milligram is? a. MG b. MM c. mg d. mm 40. A milligram is what part of a gram? a. 1/100 b. 1/1000 c. 10 d A kilometer is how many meters? a. 100 b c..01 d..001 D:\Users\ \Desktop\Electrician Entrance Exam.doc 10
11 42. The symbol for a kilometer is? a. Km b. mpg c. Kpm d. kpm METRIC CONVERSIONS: Do the following conversions L = ml? a. 0.3 b. 3 c. 30 d mm = m? a..047 b..47 c. 4.7 d Forty five resistors have a mass of g. What is the mass of each resistor? Express your answer to the nearest tenth of a gram. a. 2.5 b c d. 2.6 PERCENT: Convert the following percentages to fractions: /3 =? a. 200/3 b. 66 4/6 c. 1/3 d. 2/3 D:\Users\ \Desktop\Electrician Entrance Exam.doc 11
12 47. 45% =? a. 4/5 b. 9/20 c. ½ d. 3/8 Convert the following fractions to percentages: 48. 1/3 =? a..33% b. 33% c..67% d. 67% 49. 4/9 =? a. 4/9% b. 40% c. 48% d. 44% Convert the following percentages to decimals: % =? a. 15/100 b. 3/20 c..15 d % =? a. 167/100 b. 8/50 c d D:\Users\ \Desktop\Electrician Entrance Exam.doc 12
13 Convert the following decimals to percentages: =? a..6% b. 6% c. 60% d. 600% =? a. 2.45% b. 24.5% c. 245% d. 2450% PROBLEM SOLVING: An apprentice electrician works 40 hours and earns $18.00 per hour. The deductions are: income tax 22%; social security - 7%; union dues 5%. Find each amount to the nearest whole cent. 54. Income tax =? a. $15.84 b. $ c. $ d. $32.72 D:\Users\ \Desktop\Electrician Entrance Exam.doc 13
14 55. Social security =? a. $50.40 b. $51.00 c. $54.00 d. $ Union dues =? a. $14.40 b. $1.44 c. $3.60 d. $36.00 GEOMETRY: QUESTIONS 57 TO 58 REFER TO THE DIAGRAM BELOW. 25 in. π = 3.14 Circumference = πd or 3.14 x d Area = πr The circumference of the circle is a. 38 1/4" b. 39 1/4" c. 78 ½ d. 79 ½ 58. The area of the circle is a sq.in. b sq.in. c sq. in. d sq.in. D:\Users\ \Desktop\Electrician Entrance Exam.doc 14
15 9 m Electrician Pre-Apprenticeship QUESTIONS 59 AND 60 REFER TO THE DIAGRAM BELOW m 59. For the rectangle above, give the perimeter. a m b. 53 m c m d m 60. For the rectangle above, give the area. a m b. 53 m c m d m QUESTIONS 61 TO 63 REFER TO THE DIAGRAM BELOW. 61. For the circle above, give the diameter. a. 1.5 b. 2.5 c. 3 d. 4.7 D:\Users\ \Desktop\Electrician Entrance Exam.doc 15
16 62. For the circle above, give the circumference. a m b m c m d m 63. For the circle above, give the area. a m b m c m d m TRIANGLES AND ANGLES 64. Calculate c in the following right triangle. a b. 5 c d D:\Users\ \Desktop\Electrician Entrance Exam.doc 16
17 65. What is the type of angle shown below? a. right b. acute c. obtuse d. hypotenuse 66. What is the type of angle shown below? a. right b. acute c. obtuse d. hypotenuse POWERS: Solve the following: 67. The square of 12 =? a. 3 b c. 4 d. 144 D:\Users\ \Desktop\Electrician Entrance Exam.doc 17
18 68. (2/3) 3 =? a. 2/27 b. 8/27 c. 16/27 d. 2 2/3 ROOTS: Solve the following: =? a..66 b..9 c d =? a..1 b c. 5 d /121 =? a b. 1.4 c d RATIO AND PROPORTION: 72. Express the following ratio in lowest terms: 15 to 20 =? a. ¾ b. 3/5 c. 7/10 d. 15/20 D:\Users\ \Desktop\Electrician Entrance Exam.doc 18
19 73. Write the inverse of the following ratio: 5 to 7 =? a. 5/7 b. 7/5 c..71 d The primary winding of an electric transformer has 240 turns, and the secondary winding has 15 turns. What is the ratio of the primary winding to the secondary? a. 15/240 b. 240/15 c. 1/16 d. 16/1 75. Use proportion to solve the following problem. A cylindrical barrel contains 9 kl of gasoline when filled to a depth of 3 m. How many kl does the barrel contain when the level is 2 m? a. 2 kl b. 3 kl c. 6 kl d kl 76. Write the following proportion. Do not solve. Seven hundred metres in 50 seconds is the same as 420 m in 30 seconds. a. 700:50 = 30:420 b. 50:700 = 420:30 c. 700:420 = 50:30 d. 700:50 = ALGEBRA: Solve the following: 77. 4x = x =? a. x = 15 b. x = 51 c. x = 60 d. x = 240 D:\Users\ \Desktop\Electrician Entrance Exam.doc 19
20 K 78. Z = M K =? a. K =.52 b. K = 27 c. K = ZM d. K = Z/M 79. 5r = 130 r =? a. r = 5 b. r = 10 c. r = 25 d. r = Given T = 260, N = 808 Solve for P where: T= P x 5252 N a. P = T/N b. P = 40 c. P = 548 d. P = 400 EQUATIONS: Solve for N in the following questions: 81. N + 6 = 24 a. N = 4 b. N = 18 c. N = 30 d. N = 144 D:\Users\ \Desktop\Electrician Entrance Exam.doc 20
21 82. 6N = a. N = 4 b. N = 18 c. N = 30 d. N = 144 N = 24 6 GRAPHS: a. N = 4 b. N = 18 c. N = 30 d. N = In the diagram below, the number of square inches of surface covered by light from a point six feet from the source is a. 6 b. 30 c. 35 d. 38 D:\Users\ \Desktop\Electrician Entrance Exam.doc 21
22 QUESTIONS 85 TO 87 INCLUSIVE REFER TO THE ILLUSTRATION BELOW. Circle Radius Against Circle Area 85. Which kind of graph is this? a. pie graph b. area graph c. linear graph d. comparison graph 86. What is the approximate radius of a circle with an area of 100 cm 2? a. 5.5 cm. b. 8.0 cm. c. 315 cm. d cm. 87. What is the approximate area of a circle with a radius of 9 cm? a. 0.5 cm 2 b. 5.5 cm 2 c. 260 cm 2 d. 300 cm 2 D:\Users\ \Desktop\Electrician Entrance Exam.doc 22
23 VOLUME: 88. Find the volume of the diagram below. a. 200 in 3 b. 400 in 3 c ft 3 d ft Find the volume of the diagram below. a cm 3 b cm 3 c cm 3 d cm There are two rectangular tanks. Tank A's dimensions are: 10m x 6m x 5m. Tank B's dimensions are: 7m x 4m x 8m. Which tank holds more? a. Tank A b. Tank B D:\Users\ \Desktop\Electrician Entrance Exam.doc 23
24 READING DRAWINGS: 91. Which of the figures below, A, B, C, or D can be made from the pattern at the left? a. A b. B c. C d. D 92. The front and right side views of an object are The top view is D:\Users\ \Desktop\Electrician Entrance Exam.doc 24
25 93. The figure below is an example of a a. pictorial diagram b. block diagram c. wiring diagram d. schematic diagram 94. The figure below is an example of a a. pictorial diagram b. block diagram c. wiring diagram d. schematic diagram 95. A wiring diagram is drawn a. with blocks b. in several colours c. in three dimensional form d. in two dimensional form 96. To identify components, a wiring diagram uses a. photographs b. symbols c. blocks d. numbers D:\Users\ \Desktop\Electrician Entrance Exam.doc 25
26 TRADE SCIENCE: 97. Electrical energy is usually sold by the a. joule b. watt c. watt-hour d. kilowatt-hour 98. The relationship between watts and horsepower is expressed by a. 1 hp = 1000 W b hp = 1 W c. 1 hp = 746 W d. 1 hp = 9.81 W 99. The meter reading is a kwh b kwh c kwh d kwh 100. The north end suspended magnet in the diagram below will spin a. towards the held magnet. b. away from the held magnet Magnetic flux lines outside of a magnet extend from a. north to south. b. south to north. D:\Users\ \Desktop\Electrician Entrance Exam.doc 26
27 102. The drawing below represents a a. Light circuit b. A/C circuit c. Simple cell d. Dead short 103. The Law of the Conservation of Energy says energy a. is easy to make. b. can only be changed in form. c. cannot change form. d. can be destroyed A single kilowatt is the same as (that is, 1 kw =?) a. one horsepower (1 hp). b. one hundred watts (100 W). c. one thousand watts (1000 W). d. one newton-metre (1 N-m). TRIGONOMETRY: QUESTIONS 104 TO 107 INCLUSIVE REFER TO THE ILLUSTRATION BELOW. D:\Users\ \Desktop\Electrician Entrance Exam.doc 27
28 105. In the triangle shown above SIN A = a. b/c b. a/c c. c/b c. b/a 106. In the triangle shown above SIN B = a. b/c b. a/c c. b/a d. c/b 107. In the triangle shown above TAN A = a. a/b b. c/b c. b/a d. b/c QUESTIONS 108 TO 110 REFER TO THE ILLUSTATION BELOW In the triangle shown above, Angle A = a º b º c º d º D:\Users\ \Desktop\Electrician Entrance Exam.doc 28
29 109. In the triangle above, Side C = a b c d In the triangle shown above, Angle B = a. 0.9º b º c º d º D:\Users\ \Desktop\Electrician Entrance Exam.doc 29
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