ELECTRICIAN – PRE-APPRENTICESHIP
MATH ENTRANCE EXAM
NOTE: Please DO NOT write in exam booklet.
Use the answer sheet for your answers.
Electrician – Pre-Apprenticeship
Math Entrance Exam
NOTE: DO NOT MARK SECTION A. PLACE YOUR ANSWERS ON THE
SHEET PROVIDED IN SECTION B.
SECTION A
ADDITION: Add the following:
1.
89809 + 21318 = ?
a.
b.
c.
d.
2.
2/3 + 2/3 = ?
a.
b.
c.
d.
3.
111127
111271
30298
91940
4/6
4/9
1 1/3
1 2/3
5/16 + 3/8 = ?
a.
b.
c.
d.
8/24
11/16
1/3
5/8
SUBTRACTION: Subtract the following:
4.
14642 - 12321 = ?
a.
b.
c.
d.
13410
2330
2231
2321
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Electrician – Pre-Apprenticeship
Math Entrance Exam
5.
4 1/8-1 2/3 = ?
a.
b.
c.
d.
3 17/24
5 19/24
3 1/8
2 11/24
MULTIPLICATION: Multiply the following:
6.
183 x 152 = ?
a.
b.
c.
d.
7.
9/10 x 5/6 = ?
a.
b.
c.
d.
8.
335
27816
12039
12694
1 44/60
45/60
1¼
3/4
1 1/5 x 2 2/3 = ?
a.
b.
c.
d.
3 1/5
3 3/5
1¾
1 3/5
DIVISION: Divide the following:
9.
3268 ÷ 42 = ?
a.
b.
c.
d.
77.80
78
77
77.81
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Electrician – Pre-Apprenticeship
Math Entrance Exam
10. 3/4 ÷ 1/2 - ?
a.
b.
c.
d.
½
1½
2/3
3/8
CALCULATIONS: Complete the calculations as indicated.
11. 477.075 + 64 + 709.999 + 0.0025 = ?
a.
b.
c.
d.
1251.099
1251
1251.07
1251.0765
12. 37.2 - 36.864 = ?
a.
b.
c.
d.
0.4
0.336
74.064
0.33
13. 0.25 x 0.375 = ?
a.
b.
c.
d.
0.094
0.09375
0.625
.667
DECIMALS:
Convert the following fractions to decimals. Round off to the nearest thousandth.
14. 9/16" = ?
a.
b.
c.
d.
.375”
.536”
144”
.563”
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Electrician – Pre-Apprenticeship
Math Entrance Exam
15. 2 11/64" = ?
a.
b.
c.
d.
2.178”
2.172”
2.17”
2.1719”
16. 15/16" = ?
a.
b.
c.
d.
0.938”
0.94”
0.9375”
0.93”
Convert the following decimals to fractions.
17. 0.0625" = ?
a.
b.
c.
d.
1/8”
3/32”
2/3”
1/16”
18. 0.75" = ?
a.
b.
c.
d.
¾”
2/3”
5/7”
13/16”
19. 0.1875" = ?
a.
b.
c.
d.
¼”
3/16”
5/16”
13/75”
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Electrician – Pre-Apprenticeship
Math Entrance Exam
Solve the following equations.
20. 3.2500 - 0.0125 = ?
a.
b.
c.
d.
3.231
3.262
3.261
3.2375
21. 0.625 x 8.808 = ?
a.
b.
c.
d.
5.5
9.433
5.505
8.183
Divide the following decimals.
22. 0.024)481.92 = ?
a.
b.
c.
d.
4.98
20080
.000498
11.566
DECIMAL FRACTIONS:
23. 75/1000 = ?
a.
b.
c.
d.
.075
¾
.75
7.5
24. three thousandths = ?
a.
b.
c.
d.
.3
.03
.003
30/1000
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Electrician – Pre-Apprenticeship
Math Entrance Exam
25. fifty-seven ten thousandths = ?
a.
b.
c.
d.
57/1000
.0057
.057
.00057
ROUNDING:
26. Round 67.1275 to the nearest tenth = ?
a.
b.
c.
d.
67
67.1
67.13
67.128
27. Round 67.1275 to the nearest hundredth = ?
a.
b.
c.
d.
67
67.1
67.13
67.128
28. Round 67.1275 to the nearest thousandth = ?
a.
b.
c.
d.
67
67.1
67.13
67.128
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Electrician – Pre-Apprenticeship
Math Entrance Exam
AVERAGE:
29. What is the average length of the pieces in the diagram below?
a.
b.
c.
d.
3 3/8”
5.267”
5 ¼”
6 1/8”
NEGATIVE QUANTITIES:
30. (-1) + (2) = ?
a.
b.
c.
d.
3
–3
1
–1
31. (-3) - (-4) = ?
a.
b.
c.
d.
-7
7
–1
1
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Electrician – Pre-Apprenticeship
Math Entrance Exam
SQUARE ROOT:
32.
1O24 = ?
a.
b.
c.
d.
33.
32
512
1024
1048576
0.09 = ?
a.
b.
c.
d.
3
0.09
0.3
8100
EXPONENTS:
34.
The value of 62 is
a.
b.
c.
d.
35.
12
3
36
18
The value of 43 is
a.
b.
c.
d.
12
16
64
7
EXPRESS THE FOLLOWING IN POWERS OF TEN:
36.
103 x104 = ?
a.
b.
c.
d.
107
10,000,000
1012
10-1
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Electrician – Pre-Apprenticeship
Math Entrance Exam
37.
109 – 105 = ?
a.
b.
c.
d.
38.
10,000
104
1014
10-4
10,000 = ?
a.
b.
c.
d.
104
103
102
105
METRIC:
39.
The symbol for a milligram is ?
a.
b.
c.
d.
40.
A milligram is what part of a gram?
a.
b.
c.
d.
41.
MG
MM
mg
mm
1/100
1/1000
10
1000
A kilometer is how many meters?
a.
b.
c.
d.
100
1000
.01
.001
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Electrician – Pre-Apprenticeship
Math Entrance Exam
42.
The symbol for a kilometer is ?
a.
b.
c.
d.
Km
mpg
Kpm
kpm
METRIC CONVERSIONS: Do the following conversions.
43.
0.003 L = mL?
a.
b.
c.
d.
44.
47 mm =
a.
b.
c.
d.
45.
0.3
3
30
3000
m?
.047
.47
4.7
4700
Forty five resistors have a mass of 116.6 g. What is the mass of each
resistor? Express your answer to the nearest tenth of a gram.
a.
b.
c.
d.
2.5
2.59
2.591
2.6
PERCENT:
Convert the following percentages to fractions:
46. 66 2/3 = ?
a.
b.
c.
d.
200/3
66 4/6
1/3
2/3
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Electrician – Pre-Apprenticeship
Math Entrance Exam
47. 45% = ?
a.
b.
c.
d.
4/5
9/20
½
3/8
Convert the following fractions to percentages:
48.
1/3 = ?
a.
b.
c.
d.
49.
.33%
33%
.67%
67%
4/9 = ?
a.
b.
c.
d.
4/9%
40%
48%
44%
Convert the following percentages to decimals:
50.
15% = ?
a.
b.
c.
d.
51.
15/100
3/20
.15
.015
167% = ?
a.
b.
c.
d.
167/100
8/50
1.67
16.7
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Electrician – Pre-Apprenticeship
Math Entrance Exam
Convert the following decimals to percentages:
52.
0.6 = ?
a.
b.
c.
d.
53.
.6%
6%
60%
600%
2.45 = ?
a.
b.
c.
d.
2.45%
24.5%
245%
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.
b.
c.
d.
$15.84
$158.40
$327.27
$32.72
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Electrician – Pre-Apprenticeship
Math Entrance Exam
55. Social security = ?
a.
b.
c.
d.
$50.40
$51.00
$54.00
$54.40
56. Union dues = ?
a.
b.
c.
d.
$14.40
$1.44
$3.60
$36.00
GEOMETRY:
QUESTIONS 57 TO 58 REFER TO THE DIAGRAM BELOW.
π = 3.14
Circumference = πd
or 3.14 x d
Area = πr2
25 in.
57.
The circumference of the circle is
a.
b.
c.
d.
38 1/4"
39 1/4"
78 ½”
79 ½”
58. The area of the circle is
a.
b.
c.
d.
159.00 sq.in.
196.00 sq.in.
490.62 sq. in.
1962.50 sq.in.
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Electrician – Pre-Apprenticeship
Math Entrance Exam
QUESTIONS 59 AND 60 REFER TO THE DIAGRAM BELOW.
9m
17.5 m
59.
For the rectangle above, give the perimeter.
a.
b.
c.
d.
60.
26.5 m
53 m
157.5 m
702.3 m
For the rectangle above, give the area.
a.
b.
c.
d.
26.5 m
53 m
157.5 m
702.3 m
QUESTIONS 61 TO 63 REFER TO THE DIAGRAM BELOW.
61.
For the circle above, give the diameter.
a.
b.
c.
d.
1.5”
2.5”
3”
4.7”
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Electrician – Pre-Apprenticeship
Math Entrance Exam
62.
For the circle above, give the circumference.
a.
b.
c.
d.
63.
4.71 m
7.07 m
9.42 m
28.26 m
For the circle above, give the area.
a.
b.
c.
d.
4.71 m
7.07 m
9.42 m
28.26 m
TRIANGLES AND ANGLES
64.
Calculate c in the following right triangle.
a.
b.
c.
d.
3.74
5
9.42
12.56
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Electrician – Pre-Apprenticeship
Math Entrance Exam
65.
What is the type of angle shown below?
a.
b.
c.
d.
66.
right
acute
obtuse
hypotenuse
What is the type of angle shown below?
a.
b.
c.
d.
right
acute
obtuse
hypotenuse
POWERS: Solve the following:
67.
The square of 12 = ?
a.
b.
c.
d.
3
3.46
4
144
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Electrician – Pre-Apprenticeship
Math Entrance Exam
68.
(2/3)3 = ?
a.
b.
c.
d.
2/27
8/27
16/27
2 2/3
ROOTS: Solve the following:
0.81 = ?
69.
a.
b.
c.
d.
70.
10 = ?
a.
b.
c.
d.
71.
.66
.9
1.62
9
.1
3.16
5
100
169/121 = ?
a.
b.
c.
d.
1.18
1.4
1.95
6.93
RATIO AND PROPORTION:
72.
Express the following ratio in lowest terms: 15 to 20 = ?
a.
b.
c.
d.
¾
3/5
7/10
15/20
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Electrician – Pre-Apprenticeship
Math Entrance Exam
73.
Write the inverse of the following ratio: 5 to 7 = ?
a.
b.
c.
d.
74.
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.
b.
c.
d.
75.
15/240
240/15
1/16
16/1
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.
b.
c.
d.
76.
5/7
7/5
.71
1.4
2 kL
3 kL
6 kL
13.5 kL
Write the following proportion. Do not solve.
Seven hundred metres in 50 seconds is the same as 420 m in 30 seconds.
a.
b.
c.
d.
700:50 = 30:420
50:700 = 420:30
700:420 = 50:30
700:50 = 420.30
ALGEBRA: Solve the following:
77.
4x = 12 + 48
a.
b.
c.
d.
x=?
x = 15
x = 51
x = 60
x = 240
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Electrician – Pre-Apprenticeship
Math Entrance Exam
78.
K
Z= M
a.
b.
c.
d.
79.
K = .52
K = 27
K = ZM
K = Z/M
5r2 + 5 = 130
a.
b.
c.
d.
80.
K=?
r=?
r=5
r = 10
r = 25
r = 52
Given T = 260, N = 808
Solve for P where:
T=
P x 5252
N
a.
b.
c.
d.
P = T/N
P = 40
P = 548
P = 400
EQUATIONS: Solve for N in the following questions:
81.
N + 6 = 24
a.
b.
c.
d.
N=4
N = 18
N = 30
N = 144
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Electrician – Pre-Apprenticeship
Math Entrance Exam
82.
6N = 24
a.
b.
c.
d.
83.
N=4
N = 18
N = 30
N = 144
N = 24
6
a.
b.
c.
d.
N=4
N = 18
N = 30
N = 144
GRAPHS:
84.
In the diagram below, the number of square inches of surface covered by
light from a point six feet from the source is
a.
b.
c.
d.
6
30
35
38
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Electrician – Pre-Apprenticeship
Math Entrance Exam
QUESTIONS 85 TO 87 INCLUSIVE REFER TO THE ILLUSTRATION BELOW.
Circle Radius Against Circle Area
85.
Which kind of graph is this?
a.
b.
c.
d.
86.
pie graph
area graph
linear graph
comparison graph
What is the approximate radius of a circle with an area of 100 cm 2?
a.
b.
c.
d.
5.5 cm.
8.0 cm.
315 cm.
3150 cm.
87. What is the approximate area of a circle with a radius of 9 cm?
a.
b.
c.
d.
0.5 cm2
5.5 cm2
260 cm2
300 cm2
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Electrician – Pre-Apprenticeship
Math Entrance Exam
VOLUME:
88. Find the volume of the diagram below.
a.
b.
c.
d.
200 in3
400 in3
1.16 ft3
13.89 ft3
89. Find the volume of the diagram below.
a.
b.
c.
d.
226.19 cm3
452.39 cm3
1357.17 cm3
5428.67 cm3
90. 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.
b.
Tank A
Tank B
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Electrician – Pre-Apprenticeship
Math Entrance Exam
READING DRAWINGS:
91. Which of the figures below, A, B, C, or D can be made from the pattern at
the left?
a.
b.
c.
d.
92.
A
B
C
D
The front and right side views of an object are
The top view is
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Electrician – Pre-Apprenticeship
Math Entrance Exam
93.
The figure below is an example of a
a.
b.
c.
d.
94.
The figure below is an example of a
a.
b.
c.
d.
95.
pictorial diagram
block diagram
wiring diagram
schematic diagram
A wiring diagram is drawn
a.
b.
c.
d.
96.
pictorial diagram
block diagram
wiring diagram
schematic diagram
with blocks
in several colours
in three dimensional form
in two dimensional form
To identify components, a wiring diagram uses
a.
photographs
b.
symbols
c.
blocks
d.
numbers
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Electrician – Pre-Apprenticeship
Math Entrance Exam
TRADE SCIENCE:
97. Electrical energy is usually sold by the
a.
b.
c.
d.
joule
watt
watt-hour
kilowatt-hour
98. The relationship between watts and horsepower is expressed by
a.
b.
c.
d.
1 hp = 1000 W
7.46 hp = 1 W
1 hp = 746 W
1 hp = 9.81 W
99. The meter reading is
a.
b.
c.
d.
100.
5008 kWh
5018 kWh
5908 kWh
6918 kWh
The north end suspended magnet in the diagram below will spin
a.
b.
towards the held magnet.
away from the held magnet.
101. Magnetic flux lines outside of a magnet extend from
a.
b.
north to south.
south to north.
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Electrician – Pre-Apprenticeship
Math Entrance Exam
102. The drawing below represents a
a.
b.
c.
d.
Light circuit
A/C circuit
Simple cell
Dead short
103. The Law of the Conservation of Energy says energy
a.
b.
c.
d.
is easy to make.
can only be changed in form.
cannot change form.
can be destroyed.
104. A single kilowatt is the same as (that is, 1 kW = ?)
a.
b.
c.
d.
one horsepower (1 hp).
one hundred watts (100 W).
one thousand watts (1000 W).
one newton-metre (1 N-m).
TRIGONOMETRY:
QUESTIONS 104 TO 107 INCLUSIVE REFER TO THE ILLUSTRATION
BELOW.
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Electrician – Pre-Apprenticeship
Math Entrance Exam
105. In the triangle shown above SIN A =
a.
b.
c.
c.
b/c
a/c
c/b
b/a
106. In the triangle shown above SIN B =
a.
b.
c.
d.
b/c
a/c
b/a
c/b
107. In the triangle shown above TAN A =
a.
b.
c.
d.
a/b
c/b
b/a
b/c
QUESTIONS 108 TO 110 REFER TO THE ILLUSTATION BELOW.
108. In the triangle shown above, Angle A =
a.
b.
c.
d.
1.111º
41.99º
48.01º
26.91º
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Electrician – Pre-Apprenticeship
Math Entrance Exam
109. In the triangle above, Side C =
a.
b.
c.
d.
26.91
36.03
38.01
72.00
110. In the triangle shown above, Angle B =
a.
b.
c.
d.
0.9º
41.99º
48.01º
70.61º
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