MULTIPLE CHOICE QUESTIONS FOR CHAPTERS 1 and 2
All questions have only one correct answer
1. The relationship between the temperature in degrees Fahrenheit (F) and the temperature in degrees
Celsius (C) is given by: F = C + 32
135F is equivalent to:
[a] 43C
[b] 57.2C
[c] 185.4C
[d] 184C
2. Transposing I = for resistance R gives:
[a] I - V
[b]
[c]
[d] VI
3. 11 mm expressed as a percentage of 41 mm is:
[a] 2.68, correct to 3 significant figures
[b] 2.6, correct to 2 significant figures
[c] 26.83, correct to 2 decimal places
[d] 0.2682, correct to 4 decimal places
4. When two resistors Rand Rare connected in parallel the formula is used to
determine the total resistance R. If R= 470 and R= 2.7 k, R(correct to 3 significant
figures) is equal to:
[a] 2.68
[b] 400
[c] 473
[d] 3170
5. 1 + 1 2 - is equal to:
[a] 1
[b]
[c] 2
[d] 1
6. Transposing v = f to make wavelength the subject gives:
[a]
[b] v + f
[c] f - v
[d]
7. The value of is equal to:
[a] 1
[b] 2
[c] -
[d]
8. Four engineers can complete a task in 5 hours. Assuming the rate of work remains constant, six
engineers will complete the task in:
[a] 126 h
[b] 4 h 48 min
[c] 3 h 20 min
[d] 7 h 30 min
9. In an engineering equation . The value of r is:
[a] –6
[b] 2
[c] 6
[d] -2
10. Transposing the formula R = R(1 + t) for t gives:
[a]
[b]
[c]
[d]
11. If the circumference of a circle is 100 mm, its area is:
[a] 314.2 cm
[b] 7.96 cm
[c] 31.83 mm
[d] 78.54 cm
12. 2x - (x – xy) – x(2y – x) simplifies to:
[a] x(3x – 1 – y)
[b] x - 3xy – xy
[c] x(xy – y – 1)
[d] 3x - x + xy
13. The current I in an a.c. circuit is given by: I = .
When R = 4.8, X = 10.5 and I = 15, the value of voltage V is:
[a] 0.98
[b] 1.30
[c] 173.18
[d] 229.50
14. The height s of a mass projected vertically upwards at time t is given by:
s = ut - . When g = 10, t = 1.5 and s = 3.75, the value of u is:
[a] 10
[b] –5
[c] + 5
[d] -10
15. When p = 3, q = - and r = -2, the engineering expression 2pqr is equal to:
[a] 1296
[b] - 36
[c] 36
[d] 18
16. The quantity of heat Q is given by the formula Q = mc(t- t). When m = 5, t= 20, c = 8 and
Q = 1200, the value of t is:
[a] 10
[b] 1.5
[c] 21.5
[d] 50
17. Electrical resistance, R = ; transposing this equation for gives:
[a]
[b]
[c]
[d]
18. 1 is equal to:
[a]
[b] 1
[c] 1
[d] 2
19. (2e – 3f)(e + f) is equal to:
[a] 2e - 3f
[b] 2e - 5ef – 3f
[c] 2e + 3f
[d] 2e - ef – 3f
20. The solution of the simultaneous equations 3x - 2y = 13 and 2x + 5y = -4 is:
[a] x = -2, y = 3
[b] x = 1, y = -5
[c] x = 3, y = -2
[d] x = -7, y = 2
21. 16is equal to:
[a] 8
[b] -
[c] 4
[d]
22. The area of the path shown shaded in Figure M1 is:
[a] 300 m
[b] 234 m
[c] 124 m
[d] 66 m
23. A formula for the focal length f of a convex lens is:. When f = 4 and u = 6, v is:
[a] -2
[b]
[c] 12
[d] -
24. If x = cm, which of the following statements is correct?
[a] x = 16 cm, correct to 2 significant figures
[b] x = 16.09 cm, correct to 4 significant figures
[c] x = 1.61 10 cm, correct to 3 decimal places
[d] x = 16.099 cm, correct to 3 decimal places
25. Volume =. The density (in kg/m) when the mass is 2.532 kg and the volume is 162 cm
is:
[a] 0.01563 kg/m
[b] 410.2 kg/m
[c] 15630 kg/m
[d] 64.0 kg/m
26. The area A of a triangular piece of land of sides a, b and c may be calculated using
A = where s =
When a = 15 m, b = 11 m and c = 8 m, the area, correct to the nearest square metre, is:
[a] 1836 m
[b] 648 m
[c] 445 m
[d] 43 m
27. In triangle ABC in Figure M2, the length AC is:
[a] 18.79 cm
[b] 70.89 cm
[c] 22.89 cm
[d] 16.10 cm
28. PV = mRT is the characteristic gas equation. When P = 100 , V = 4.0, R = 288 and T = 300,
the value of m is:
[a] 4.630
[b] 313600
[c] 0.216
[d] 100592
29. Which of the straight lines shown in Figure M3 has the equation y + 4 = 2x?
[a] (i)
[b] (ii)
[c] (iii)
[d] (iv)
30. The engineering expression is equal to:
[a] 4
[b] 2
[c]
[d] 1
31. In a system of pulleys, the effort P required to raise a load W is given by P = aW + b, where a and
b are constants. If W = 40 when P = 12 and W = 90 when P = 22, the values of a and b are:
[a] a = 5, b =
[b] a = 1, b = - 28
[c] a = , b = - 8
[d] a = , b = 4
32. (16 - 27) is equal to:
[a]
[b] -7
[c] 1
[d] -8
33. Resistance R ohms varies with temperature t according to the formula R = R(1 + t).
Given R = 21 , = 0.004 and t = 100, Rhas a value of:
[a] 21.4
[b] 29.4
[c] 15
[d] 0.067
34. The value of of (4) + 5 - is:
[a] 17
[b] 80
[c] 16
[d] 88
35. The value of , correct to 3 significant figures, is:
[a] 0.0588
[b] 0.312
[c] 17.0
[d] 3.209
36. The pressure p Pascals at height h metres above ground level is given by p =, where p is
the pressure at ground level and k is a constant. Whenp is 1.01×10Pa and the pressure at a
height of 1500 m is 9.9010Pa, the value of k, correct to 3 significant figures is:
[a] 1.33 10
[b] 75000
[c] 173000
[d] 197
37. (2x – y) is equal to:
[a] 4x + y
[b] 2x - 2xy + y
[c] 4x - y
[d] 4x - 4xy + y
38. The final length l of a piece of wire heated through C is given by the formula l = l(1 + ).
Transposing, the coefficient of expansion is given by:
[a]
[b]
[c]
[d]
39. A graph of y against x, two engineering quantities, produces a straight line. A table of values is
shown below:
x 2 -1 p
y 9 3 5
The value of p is:
[a] -
[b] –2
[c] 3
[d] 0
40. The current i amperes flowing in a capacitor at time t seconds is given by: i = 10(1 - e),
where resistance R is 2510ohms and capacitance C is 1610farads. When current ireaches 7
amperes, the time t is:
[a] - 0.48 s
[b] 0.14 s
[c] 0.21 s
[d] 0.48 s
41. A pendulum of length 1.2 m swings through an angle of 12 in a single swing. The length of arc
traced by the pendulum bob is:
[a] 14.40 cm
[b] 25.13 cm
[c] 10.00 cm
[d] 45.24 cm
42. The value of , correct to 4 significant figures, is:
[a] 9.289
[b] 13.56
[c] 13.5566
[d] –3.84410
43. The volume V of a material when the temperature is increased is given by:
V=. The value of t when V = 61.5 cm, V = 60 cm, = 54 and
t = 250 is:
[a] 213
[b] 463
[c] 713
[d] 28028
44. A formula used for calculating the resistance of a cable is R = . A cable’sresistance,
R = 0.50 , its length l is 5000 m and its cross-sectional area a is 4. The resistivity of
the material is:
[a] 6.2510m
[b] 410m
[c] 2.510m
[d] 3.2 10m
45. In the equation 5.0 = 3.0 ln, x has a value correct to 3 significant figures of:
[a] 1.59
[b] 0.392
[c] 0.548
[d] 0.0625
46. Current I in an electrical circuit is given by I = . Transposing for R gives:
[a]
[b]
[c] (E – e)(I + r)
[d]
47. In triangle ABC in Figure M4, length AC is:
[a] 14.04 cm
[b] 18.15 cm
[c] 13.16 cm
[d] 14.90 cm
48. is equal to:
[a]
[b]
[c]
[d]
49. Transposing t = 2 for g gives:
[a]
[b]
[c]
[d]
50. A graph of resistance against voltage for an electrical circuit is shown in Figure M5. The equation
relating resistance R and voltage V is:
[a] R = 1.45 V + 40
[b] R = 0.8 V + 20
[c] R = 1.45 V + 20
[d] R = 1.25 V + 20
51. A graph relating effort E (plotted vertically) against load L (plotted horizontally) for a set of
pulleys is given by L + 30 = 6E. The gradientof the graph is:
[a] 5
[b]
[c] 6
[d]
52. In the right-angled triangle ABC shown in Figure M6, sine A is given by:
[a] b/a
[b] c/b
[c] b/c
[d] a/b
53. In the right-angled triangle ABC shown in Figure M6, cosine C is given by:
[a] a/b
[b] c/b
[c] a/c
[d] b/a
54. In the right-angled triangle shown in Figure M6, tangent A is given by:
[a] b/c
[b] a/c
[c] a/b
[d] c/a
55. In an experiment demonstrating Hooke’s law, the strain in a copper wire was measured for
various stresses. The results included
Stress (megapascals) 18.24 24.00 39.36
Strain 0.00019 0.00025 0.00041
When stress is plotted vertically against strain horizontally a straight line graph results. Young’s
modulus of elasticity for copper, which is given by the gradient of the graph, is:
[a] 96 10 Pa
[b] 1.04 10 Pa
[c] 96 Pa
[d] 96000 Pa
56. radians is equivalent to:
[a] 135
[b] 270
[c] 45
[d] 67.5
57. In the triangular template ABC shown in Figure M7, the length AC is:
[a] 6.17 cm
[b] 11.17 cm
[c] 9.22 cm
[d] 12.40 cm
58. Correct to 3 decimal places, sin(-2.6 rad) is:
[a] 0.516
[b] -0.045
[c] -0.516
[d] 0.045
59. For the right-angled triangle PQR shown in Figure M8, angle R is equal to:
[a] 41.41
[b] 48.59
[c] 36.87
[d] 53.13
60. A hollow shaft has an outside diameter of 6.0 cm and an inside diameter of 4.0 cm. The cross-
sectional area of the shaft is:
[a] 6283 mm
[b] 1257 mm
[c] 1571 mm
[d] 628 mm
61. If cos A = , then sin A is equal to:
[a]
[b]
[c]
[d]
62. The area of triangle XYZ in Figure M9 is:
[a] 24.22 cm
[b] 19.35 cm
[c] 38.72 cm
[d] 32.16 cm
63. Here are four equations in x and y. When x is plotted against y, in each case a straight line results.
(i) y + 3 = 3x (ii) y + 3x = 3 (iii) (iv)
Which of these equations are parallel to each other ?
[a] (i) and (ii)
[b] (i) and (iv)
[c] (ii) and (iii)
[d] (ii) and (iv)
64. The value, correct to 3 decimal places, of cos is:
[a] 0.999
[b] 0.707
[c] -0.999
[d] -0.707
65. A triangle has sides a = 9.0 cm, b = 8.0 cm and c = 6.0 cm. Angle A is equal to:
[a] 82.42
[b] 56.49
[c] 78.58
[d] 79.87
66. An arc of a circle of length 5.0 cm subtends an angle of 2 radians. The circumference of the circle
is:
[a] 2.5 cm
[b] 10.0 cm
[c] 5.0 cm
[d] 15.7 cm
67. In the triangular template DEF shown in Figure M10, angle F is equal to:
[a] 43.5
[b] 28.6
[c] 116.4
[d] 101.5
68. The area of the triangular template DEF shown in Figure M10 is:
[a] 529.2 mm
[b] 258.5 mm
[c] 483.7 mm
[d] 371.7 mm
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