Quiz 1
Quiz 1 Multiple-choice questions on applied mathematics
1.
The relationship between the temperature in degrees Fahrenheit (F) and the temperature in degrees Celsius 9 (C) is given by: F = C + 32. 5 135◦ F is equivalent to: (a) 43◦ C (b) 57.2◦ C ◦ (c) 185.4 C (d) 184◦ C
2.
When a = 2, b = 1 and c = −3, the engineering expression 2ab − bc + abc is equal to: (a) 13 (b) −5 (c) 7 (d) 1
3.
11 mm expressed as a percentage of 41 mm is: (a) 2.68, correct to 3 significant figures (b) 26.83, correct to 2 decimal places (c) 2.6, correct to 2 significant figures (d) 0.2682, correct to 4 decimal places
4.
1 1 1 = + is used to determine RT R1 R2 the total resistance RT . If R1 = 470 and R2 = 2.7k, RT (correct to 3 significant figures) is equal to:
When two resistors R1 and R2 are connected in parallel the formula (a) 2.68 (c) 473
(b) 400 (d) 3170
1 2 2 1 1 + 1 ÷ 2 − is equal to: 3 3 3 3 5 19 1 2 (a) 1 (b) (c) 2 (d) 1 8 24 21 7 6. 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
5.
(c) 3 h 20 min 7.
(d) 7 h 30 min
In an engineering equation
34 1 = . The value of r is: 3r 9
(a) −6
(d) −2
(b) 2
(c) 6
8. A graph of resistance against voltage for an electrical circuit is shown in Figure M1. The equation relating resistance R and voltage V is:
Science for Engineering. 978-1-138-82688-5, © John Bird. Published by Taylor & Francis. All rights reserved.
160 145 140
Resistance R
120
100
80 70 60
40
20
0
20
40
60
80
100
120
Voltage (V )
Figure M1
(a) R = 1.45 V + 40 (c) R = 1.45 V + 20 9.
(b) R = 0.8 V + 20 (d) R = 1.25 V + 20
1 1 − is equal to: 9.83 16.91 (a) 0.0425, correct to 4 significant figures (b) 4.26 × 10−2 , correct to 2 decimal places (c) −0.141, correct to 3 decimal places (d) 0.042, correct to 2 significant figures
10.
A formula for the focal length f of a convex lens is (a) −2
11.
1 12
(c) 12
(d) −
1 2
The expression engineering p + 2p × 3p − 2p simplifies to: p (a) 7p
12.
(b)
1 1 1 = + . When f = 4 and u = 6, v is: f u v
(b) 6p
(c) 9p2 − 2p
(d) 3p
(9.2 × 102 + 1.1 × 103 ) cm in standard form is equal to: (a) 10.3 × 102 cm (c) 10.3 × 103 cm
(b) 20.2 × 102 cm (d) 2.02 × 103 cm
13.
V The current I in an a.c. circuit is given by: I = √ When R = 4.8, X = 10.5 and I = 15, the value 2 R + X2 of voltage V is: (a) 173.18 (c) 0.98
14.
In the engineering equation: 24 × 2t = 64, the value of t is: (a) 1
15.
(b) 2
(c) 3
(d) 4
1 The height s of a mass projected vertically upwards at time t is given by: s = ut − g t 2 . When g = 10, 2 t = 1.5 and s = 3.75, the value of u is: (b) −5
(a) 10 16.
(b) 1.30 (d) 229.50
(c) +5
(d) −10
In the right-angled triangle ABC shown in Figure M2, sine A is given by: (a) b/a
(b) c/b
(c) b/c
(d) a/b A
b c
C
a
B
Figure M2
17.
In the right-angled triangle ABC shown in Figure M2, cosine C is given by: (a) a/b
18.
(c) a/c
(b) a/c
(c) a/b
(d) c/a
Which of the straight lines shown in Figure M3 has the equation y + 4 = 2x ? y 6
y 6
−4
(d) b/a
In the right-angled triangle shown in Figure M2, tangent A is given by: (a) b/c
19.
(b) c/b
0
−6
(a)
Figure M3
4
x
−6
0
−6
(b)
y 6
6
x
−6
0
−6
(c)
y 6
6 x
−6
0
−6
(d)
6
x
20.
The quantity of heat Q is given by the formula Q = mc(t2 − t1 ). When m = 5, t1 = 20, c = 8 and Q = 1200, the value of t2 is: (a) 10
21.
(b) 1.5
(b) 1296
v f
(b) v + f
25.
(b) 1155
(b)
30.
(d) 1695
(d) 2
1 2
5 2
(c) −4
(d) 5
(b) 2
(c) 3
(d) 1
V for resistance R gives: R V I (b) (c) (d) VI I V
Transposing I =
23 mm expressed as a percentage of 3.25 cm is: (a) (b) (c) (d)
29.
(c) 15
If (4x )2 = 16, the value of x is:
(a) I − V 28.
f v
(d)
The equation of a straight line graph is 2y = 5 − 4x. The gradient of the straight line is:
(a) 4 27.
(c) f − v
3 3 ÷ 1 is equal to: 4 4 3 9 5 (a) (b) 1 (c) 1 7 16 16
(a) −2 26.
(d) 18
The lowest common multiple (LCM) of the numbers 15, 105, 420 and 1155 is: (a) 4620
24.
(c) 36
Transposing v = f λ to make wavelength λ the subject gives: (a)
23.
(d) 50
1 When p = 3, q = − and r = −2, the engineering expression 2p2 q3 r 4 is equal to: 2 (a) −36
22.
(c) 21.5
0.708, correct to 3 decimal places 7.08, correct to 2 decimal places 70.77, correct to 4 significant figures 14.13, correct to 2 decimal places 3
16− 4 is equal to: 1 (a) 8 (b) − 3 2
(c) 4
In the engineering equation (a) 0
(b)
1 2
(c) 1
1 8 3 32
(d)
(3) (9)2
(d) 1
1 2
= 32x , the value of x is:
31.
57.06 × 0.0711 cm, which of the following statements is correct? √ 0.0635 x = 16 cm, correct to 2 significant figures
If x = (a)
(b) x = 16.09 cm, correct to 4 significant figures (c) x = 1.61 × 101 cm, correct to 3 decimal places (d) x = 16.099 cm, correct to 3 decimal places mass 32. Volume = . The density (in kg/m3 ) when the mass is 2.532 kg and the volume is 162 cm3 is: density
33.
34.
(a) 0.01563 kg/m3
(b) 410.2 kg/m3
(c) 15630 kg/m3
(d) 64.0 kg/m3
(5.5 × 102 )(2 × 103 ) cm in standard form is equal to: (a) 11 × 106 cm
(b) 1.1 × 106 cm
(c) 11 × 105 cm
(d) 1.1 × 105 cm
In the triangular template ABC shown in Figure M4, the length AC is: (a) 6.17 cm (c) 9.22 cm
(b) 11.17 cm (d) 12.40 cm
A
42°
B
C
8.30 cm
Figure M4
35.
3k + 2k × 4k + k ÷ (6k − 2k) simplifies to: 25k 4 1 (c) + k(3 + 8k) 4
(a)
36.
(b) 1 + 2k (d) 20k 2 +
1 4
Correct to 3 decimal places, sin(−2.6 rad) is: (a) 0.516 (c) −0.516
(b) −0.045 (d) 0.045
37.
38.
The engineering expression a3 b2 c × ab−4 c3 ÷ a2 bc−2 is equivalent to: (b)
(c) a6 bc2
(d) a 2 b−7 c− 2
3
(b) 12
(c) 420
(b) 29.4 (d) 0.067
The solution of the simultaneous equations 3x − 2y = 13 and 2x + 5y = −4 is: (a) x = −2, y = 3 (c) x = 3, y = −2
41.
(b) −12
(c) 16
Electrical resistance R = (a)
43.
(b) x = 1, y = −5 (d) x = −7, y = 2
1 An engineering equation is y = 2a2 b3 c4 . When a = 2, b = − and c = 2, the value of y is: 2 (a) −16
42.
(d) 6
Resistance R ohms varies with temperature t according to the formula R = R0 (1 + αt). Given R = 21 , α = 0.004 and t = 100, R0 has a value of: (a) 21.4 (c) 15
40.
3
The highest common factor (HCF) of the numbers 12, 30 and 42 is: (a) 42
39.
a2 c 6 b3
(a) a2 b5 c2
Ra ρ
(b)
R aρ
(c)
(d) 12
ρL ; transposing this equation for L gives: a a Rρ
(d)
ρa R
For the right-angled triangle PQR shown in Figure M5, angle R is equal to: (a) 41.41◦
(b) 48.59◦
(c) 36.87◦
(d) 53.13◦
P
3 cm
Q
Figure M5
4 cm
R
44.
The value of
0.01372 m is equal to: 7.5
(a) 1.829 m, correct to 4 significant figures (b) 0.001829 m, correct to 6 decimal places (c) 0.0182 m, correct to 4 significant figures (d) 1.829 × 10−2 m, correct to 3 decimal places 45.
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) −
46.
1 2
(b) −2
(c) 3
The engineering expression
(d) 0 (16 × 4)2 is equal to: (8 × 2)4
1 (d) 1 22 47. The area A of a triangular piece of land of sides a, b and c may be calculated using: (a) 4
(b) 2−4
(c)
A=
[s (s − a) (s − b) (s − c)]
a+b+c . When a = 15 m, b = 11 m and c = 8 m, the area, correct to the nearest square where s = 2 metre, is: (a) 1836 m2 (b) 648 m2 (c) 445 m2 48.
(d) 43 m2
0.001010 cm expressed in standard form is: (a) 1010 × 10−6 cm (c) 0.101 × 10−2 cm
49.
(b) 1.010 × 10−3 cm (d) 1.010 × 103 cm
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 = (c) a =
1 4
1 , b = −8 3
(b) a = 1, b = −28 (d) a =
1 ,b=4 5
50.
(a)
51.
53.
2
7 18
(b) −7
If cos A = (a)
52.
1
(16− 4 − 27− 3 ) is equal to:
5 13
(c) 1
8 9
(d) −8
1 2
12 , then sin A is equal to: 13
(b)
13 12
(c)
5 12
(d)
12 5
The area of triangle XYZ in Figure M6 is: (a) 24.22 cm2
(b) 19.35 cm2
(c) 38.72 cm2
(d) 32.16 cm2
3.810 × 10−3 is equal to: (a) 0.003810 (c) 3810
(b) 0.0381 (d) 0.3810
X
37°
Z
Y
5.4 cm
Figure M6
54.
A graph relating effort E (plotted vertically) against load L (plotted horizontally) for a set of pulleys is given by L + 30 = 6E. The gradient of the graph is:
1 1 (b) 5 (c) 6 (d) 6 5 55. The value of 42 ÷ 3 − 2 × 3 + 15 ÷ (1 + 4) is: (a)
(a) 39
(b) 131
(c) 43
1 5
(d) 11
−3π 56. The value, correct to 3 decimal places, of cos 4 (a) 0.999 (c) −0.999
(b) 0.707 (d) −0.707
is:
57.
52 × 5−3 is equivalent to: 5−4 (a) 5−5
58.
The value of 24 ÷ (a) −311
59.
(b) 524
(c) 53
(d) 5
8 − 16[2 + (−3 × 4) − 10] is: 3
(b) 329
(c) −256
(d) 384
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◦ 2 1 1 5 1 60. The value of of 4 − 3 +5÷ − is: 5 2 4 16 4 (a) 17 61.
7 20
(b) 80
1 2
(c) 16
1 4
(d) 88
In Figure M7, AB is called: (a) (b) (c) (d)
the circumference of the circle a sector of the circle a tangent to the circle a major arc of the circle
A
B
Figure M7
62.
The surface area of a sphere of diameter 40 mm is: (a) 201.06 cm2 (b) 33.51 cm2 (c) 268.08 cm2
63.
64.
(d) 50.27 cm2
A vehicle has a mass of 2000 kg. A model of the vehicle is made to a scale of 1 to 100. If the vehicle and model are made of the same material, the mass of the model is: (a) 2 g (b) 20 kg (c) 200 g (d) 20 g 3π radians is equivalent to: 4 (a) 135◦ (b) 270◦ (c) 45◦
(d) 67.5◦
65.
The area of the path shown shaded in Figure M8 is: (a) 300 m2
(b) 234 m2
(c) 124 m2
(d) 66 m2
20 m
2m
15 m 2m
Figure M8
If the circumference of a circle is 100 mm, its area is: (a) 314.2 cm2
(c) 0.06 m2
(d) 1800 m2
(b) 2.7 litres
(c) 2700 litres
(d) 270 litres
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
The total surface area of a cylinder of length 20 cm and diameter 6 cm is: (d) 226.19 cm2
Answers
(b) (c) (a) (a) (a) (d) (d) (b) (c) (b)
4. 11. 18. 25. 32. 39. 46. 53. 60. 67.
(b) (a) (b) (a) (c) (c) (b) (a) (c) (b)
5. 12. 19. 26. 33. 40. 47. 54. 61. 68.
(a) (d) (d) (d) (b) (c) (d) (a) (c) (d)
6. 13. 20. 27. 34. 41. 48. 55. 62. 69.
(c) 980.18 cm2
3. 10. 17. 24. 31. 38. 45. 52. 59. 66.
(c) (a) (d) (b) (b) (a) (b) (d) (d) (d)
7. 14. 21. 28. 35. 42. 49. 56. 63. 70.
(c) (b) (a) (c) (c) (a) (d) (d) (a) (a)
(b) 56.55 cm2
(d) (b) (d) (a) (b) (b) (b) (a) (b) (c)
(a) 433.54 cm2
2. 9. 16. 23. 30. 37. 44. 51. 58. 65.
70.
(b) 18 m2
A water tank is in the shape of a rectangular prism having length 1.5 m, breadth 60 cm and height 300 mm. If 1 litre = 1000 cm3 , the capacity of the tank is: (a) 27 litres
69.
(d) 78.54 cm2
A rectangular building is shown on a building plan having dimensions 20 mm by 10 mm. If the plan is drawn to a scale of 1 to 300, the true area of the building in m2 is: (a) 60,000 m2
68.
(c) 31.83 mm2
(b) (d) (a) (a) (d) (c) (c) (a) (c) (a)
67.
(b) 7.96 cm2
1. 8. 15. 22. 29. 36. 43. 50. 57. 64.
66.
1.
The relationship between the temperature in degrees Fahrenheit (F) and the temperature in degrees Celsius 9 (C) is given by: F = C + 32. 5 135◦ F is equivalent to: (a) 43◦ C (b) 57.2◦ C ◦ (c) 185.4 C (d) 184◦ C
2.
When a = 2, b = 1 and c = −3, the engineering expression 2ab − bc + abc is equal to: (a) 13 (b) −5 (c) 7 (d) 1
3.
11 mm expressed as a percentage of 41 mm is: (a) 2.68, correct to 3 significant figures (b) 26.83, correct to 2 decimal places (c) 2.6, correct to 2 significant figures (d) 0.2682, correct to 4 decimal places
4.
1 1 1 = + is used to determine RT R1 R2 the total resistance RT . If R1 = 470 and R2 = 2.7k, RT (correct to 3 significant figures) is equal to:
When two resistors R1 and R2 are connected in parallel the formula (a) 2.68 (c) 473
(b) 400 (d) 3170
1 2 2 1 1 + 1 ÷ 2 − is equal to: 3 3 3 3 5 19 1 2 (a) 1 (b) (c) 2 (d) 1 8 24 21 7 6. 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
5.
(c) 3 h 20 min 7.
(d) 7 h 30 min
In an engineering equation
34 1 = . The value of r is: 3r 9
(a) −6
(d) −2
(b) 2
(c) 6
8. A graph of resistance against voltage for an electrical circuit is shown in Figure M1. The equation relating resistance R and voltage V is:
Science for Engineering. 978-1-138-82688-5, © John Bird. Published by Taylor & Francis. All rights reserved.
160 145 140
Resistance R
120
100
80 70 60
40
20
0
20
40
60
80
100
120
Voltage (V )
Figure M1
(a) R = 1.45 V + 40 (c) R = 1.45 V + 20 9.
(b) R = 0.8 V + 20 (d) R = 1.25 V + 20
1 1 − is equal to: 9.83 16.91 (a) 0.0425, correct to 4 significant figures (b) 4.26 × 10−2 , correct to 2 decimal places (c) −0.141, correct to 3 decimal places (d) 0.042, correct to 2 significant figures
10.
A formula for the focal length f of a convex lens is (a) −2
11.
1 12
(c) 12
(d) −
1 2
The expression engineering p + 2p × 3p − 2p simplifies to: p (a) 7p
12.
(b)
1 1 1 = + . When f = 4 and u = 6, v is: f u v
(b) 6p
(c) 9p2 − 2p
(d) 3p
(9.2 × 102 + 1.1 × 103 ) cm in standard form is equal to: (a) 10.3 × 102 cm (c) 10.3 × 103 cm
(b) 20.2 × 102 cm (d) 2.02 × 103 cm
13.
V The current I in an a.c. circuit is given by: I = √ When R = 4.8, X = 10.5 and I = 15, the value 2 R + X2 of voltage V is: (a) 173.18 (c) 0.98
14.
In the engineering equation: 24 × 2t = 64, the value of t is: (a) 1
15.
(b) 2
(c) 3
(d) 4
1 The height s of a mass projected vertically upwards at time t is given by: s = ut − g t 2 . When g = 10, 2 t = 1.5 and s = 3.75, the value of u is: (b) −5
(a) 10 16.
(b) 1.30 (d) 229.50
(c) +5
(d) −10
In the right-angled triangle ABC shown in Figure M2, sine A is given by: (a) b/a
(b) c/b
(c) b/c
(d) a/b A
b c
C
a
B
Figure M2
17.
In the right-angled triangle ABC shown in Figure M2, cosine C is given by: (a) a/b
18.
(c) a/c
(b) a/c
(c) a/b
(d) c/a
Which of the straight lines shown in Figure M3 has the equation y + 4 = 2x ? y 6
y 6
−4
(d) b/a
In the right-angled triangle shown in Figure M2, tangent A is given by: (a) b/c
19.
(b) c/b
0
−6
(a)
Figure M3
4
x
−6
0
−6
(b)
y 6
6
x
−6
0
−6
(c)
y 6
6 x
−6
0
−6
(d)
6
x
20.
The quantity of heat Q is given by the formula Q = mc(t2 − t1 ). When m = 5, t1 = 20, c = 8 and Q = 1200, the value of t2 is: (a) 10
21.
(b) 1.5
(b) 1296
v f
(b) v + f
25.
(b) 1155
(b)
30.
(d) 1695
(d) 2
1 2
5 2
(c) −4
(d) 5
(b) 2
(c) 3
(d) 1
V for resistance R gives: R V I (b) (c) (d) VI I V
Transposing I =
23 mm expressed as a percentage of 3.25 cm is: (a) (b) (c) (d)
29.
(c) 15
If (4x )2 = 16, the value of x is:
(a) I − V 28.
f v
(d)
The equation of a straight line graph is 2y = 5 − 4x. The gradient of the straight line is:
(a) 4 27.
(c) f − v
3 3 ÷ 1 is equal to: 4 4 3 9 5 (a) (b) 1 (c) 1 7 16 16
(a) −2 26.
(d) 18
The lowest common multiple (LCM) of the numbers 15, 105, 420 and 1155 is: (a) 4620
24.
(c) 36
Transposing v = f λ to make wavelength λ the subject gives: (a)
23.
(d) 50
1 When p = 3, q = − and r = −2, the engineering expression 2p2 q3 r 4 is equal to: 2 (a) −36
22.
(c) 21.5
0.708, correct to 3 decimal places 7.08, correct to 2 decimal places 70.77, correct to 4 significant figures 14.13, correct to 2 decimal places 3
16− 4 is equal to: 1 (a) 8 (b) − 3 2
(c) 4
In the engineering equation (a) 0
(b)
1 2
(c) 1
1 8 3 32
(d)
(3) (9)2
(d) 1
1 2
= 32x , the value of x is:
31.
57.06 × 0.0711 cm, which of the following statements is correct? √ 0.0635 x = 16 cm, correct to 2 significant figures
If x = (a)
(b) x = 16.09 cm, correct to 4 significant figures (c) x = 1.61 × 101 cm, correct to 3 decimal places (d) x = 16.099 cm, correct to 3 decimal places mass 32. Volume = . The density (in kg/m3 ) when the mass is 2.532 kg and the volume is 162 cm3 is: density
33.
34.
(a) 0.01563 kg/m3
(b) 410.2 kg/m3
(c) 15630 kg/m3
(d) 64.0 kg/m3
(5.5 × 102 )(2 × 103 ) cm in standard form is equal to: (a) 11 × 106 cm
(b) 1.1 × 106 cm
(c) 11 × 105 cm
(d) 1.1 × 105 cm
In the triangular template ABC shown in Figure M4, the length AC is: (a) 6.17 cm (c) 9.22 cm
(b) 11.17 cm (d) 12.40 cm
A
42°
B
C
8.30 cm
Figure M4
35.
3k + 2k × 4k + k ÷ (6k − 2k) simplifies to: 25k 4 1 (c) + k(3 + 8k) 4
(a)
36.
(b) 1 + 2k (d) 20k 2 +
1 4
Correct to 3 decimal places, sin(−2.6 rad) is: (a) 0.516 (c) −0.516
(b) −0.045 (d) 0.045
37.
38.
The engineering expression a3 b2 c × ab−4 c3 ÷ a2 bc−2 is equivalent to: (b)
(c) a6 bc2
(d) a 2 b−7 c− 2
3
(b) 12
(c) 420
(b) 29.4 (d) 0.067
The solution of the simultaneous equations 3x − 2y = 13 and 2x + 5y = −4 is: (a) x = −2, y = 3 (c) x = 3, y = −2
41.
(b) −12
(c) 16
Electrical resistance R = (a)
43.
(b) x = 1, y = −5 (d) x = −7, y = 2
1 An engineering equation is y = 2a2 b3 c4 . When a = 2, b = − and c = 2, the value of y is: 2 (a) −16
42.
(d) 6
Resistance R ohms varies with temperature t according to the formula R = R0 (1 + αt). Given R = 21 , α = 0.004 and t = 100, R0 has a value of: (a) 21.4 (c) 15
40.
3
The highest common factor (HCF) of the numbers 12, 30 and 42 is: (a) 42
39.
a2 c 6 b3
(a) a2 b5 c2
Ra ρ
(b)
R aρ
(c)
(d) 12
ρL ; transposing this equation for L gives: a a Rρ
(d)
ρa R
For the right-angled triangle PQR shown in Figure M5, angle R is equal to: (a) 41.41◦
(b) 48.59◦
(c) 36.87◦
(d) 53.13◦
P
3 cm
Q
Figure M5
4 cm
R
44.
The value of
0.01372 m is equal to: 7.5
(a) 1.829 m, correct to 4 significant figures (b) 0.001829 m, correct to 6 decimal places (c) 0.0182 m, correct to 4 significant figures (d) 1.829 × 10−2 m, correct to 3 decimal places 45.
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) −
46.
1 2
(b) −2
(c) 3
The engineering expression
(d) 0 (16 × 4)2 is equal to: (8 × 2)4
1 (d) 1 22 47. The area A of a triangular piece of land of sides a, b and c may be calculated using: (a) 4
(b) 2−4
(c)
A=
[s (s − a) (s − b) (s − c)]
a+b+c . When a = 15 m, b = 11 m and c = 8 m, the area, correct to the nearest square where s = 2 metre, is: (a) 1836 m2 (b) 648 m2 (c) 445 m2 48.
(d) 43 m2
0.001010 cm expressed in standard form is: (a) 1010 × 10−6 cm (c) 0.101 × 10−2 cm
49.
(b) 1.010 × 10−3 cm (d) 1.010 × 103 cm
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 = (c) a =
1 4
1 , b = −8 3
(b) a = 1, b = −28 (d) a =
1 ,b=4 5
50.
(a)
51.
53.
2
7 18
(b) −7
If cos A = (a)
52.
1
(16− 4 − 27− 3 ) is equal to:
5 13
(c) 1
8 9
(d) −8
1 2
12 , then sin A is equal to: 13
(b)
13 12
(c)
5 12
(d)
12 5
The area of triangle XYZ in Figure M6 is: (a) 24.22 cm2
(b) 19.35 cm2
(c) 38.72 cm2
(d) 32.16 cm2
3.810 × 10−3 is equal to: (a) 0.003810 (c) 3810
(b) 0.0381 (d) 0.3810
X
37°
Z
Y
5.4 cm
Figure M6
54.
A graph relating effort E (plotted vertically) against load L (plotted horizontally) for a set of pulleys is given by L + 30 = 6E. The gradient of the graph is:
1 1 (b) 5 (c) 6 (d) 6 5 55. The value of 42 ÷ 3 − 2 × 3 + 15 ÷ (1 + 4) is: (a)
(a) 39
(b) 131
(c) 43
1 5
(d) 11
−3π 56. The value, correct to 3 decimal places, of cos 4 (a) 0.999 (c) −0.999
(b) 0.707 (d) −0.707
is:
57.
52 × 5−3 is equivalent to: 5−4 (a) 5−5
58.
The value of 24 ÷ (a) −311
59.
(b) 524
(c) 53
(d) 5
8 − 16[2 + (−3 × 4) − 10] is: 3
(b) 329
(c) −256
(d) 384
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◦ 2 1 1 5 1 60. The value of of 4 − 3 +5÷ − is: 5 2 4 16 4 (a) 17 61.
7 20
(b) 80
1 2
(c) 16
1 4
(d) 88
In Figure M7, AB is called: (a) (b) (c) (d)
the circumference of the circle a sector of the circle a tangent to the circle a major arc of the circle
A
B
Figure M7
62.
The surface area of a sphere of diameter 40 mm is: (a) 201.06 cm2 (b) 33.51 cm2 (c) 268.08 cm2
63.
64.
(d) 50.27 cm2
A vehicle has a mass of 2000 kg. A model of the vehicle is made to a scale of 1 to 100. If the vehicle and model are made of the same material, the mass of the model is: (a) 2 g (b) 20 kg (c) 200 g (d) 20 g 3π radians is equivalent to: 4 (a) 135◦ (b) 270◦ (c) 45◦
(d) 67.5◦
65.
The area of the path shown shaded in Figure M8 is: (a) 300 m2
(b) 234 m2
(c) 124 m2
(d) 66 m2
20 m
2m
15 m 2m
Figure M8
If the circumference of a circle is 100 mm, its area is: (a) 314.2 cm2
(c) 0.06 m2
(d) 1800 m2
(b) 2.7 litres
(c) 2700 litres
(d) 270 litres
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
The total surface area of a cylinder of length 20 cm and diameter 6 cm is: (d) 226.19 cm2
Answers
(b) (c) (a) (a) (a) (d) (d) (b) (c) (b)
4. 11. 18. 25. 32. 39. 46. 53. 60. 67.
(b) (a) (b) (a) (c) (c) (b) (a) (c) (b)
5. 12. 19. 26. 33. 40. 47. 54. 61. 68.
(a) (d) (d) (d) (b) (c) (d) (a) (c) (d)
6. 13. 20. 27. 34. 41. 48. 55. 62. 69.
(c) 980.18 cm2
3. 10. 17. 24. 31. 38. 45. 52. 59. 66.
(c) (a) (d) (b) (b) (a) (b) (d) (d) (d)
7. 14. 21. 28. 35. 42. 49. 56. 63. 70.
(c) (b) (a) (c) (c) (a) (d) (d) (a) (a)
(b) 56.55 cm2
(d) (b) (d) (a) (b) (b) (b) (a) (b) (c)
(a) 433.54 cm2
2. 9. 16. 23. 30. 37. 44. 51. 58. 65.
70.
(b) 18 m2
A water tank is in the shape of a rectangular prism having length 1.5 m, breadth 60 cm and height 300 mm. If 1 litre = 1000 cm3 , the capacity of the tank is: (a) 27 litres
69.
(d) 78.54 cm2
A rectangular building is shown on a building plan having dimensions 20 mm by 10 mm. If the plan is drawn to a scale of 1 to 300, the true area of the building in m2 is: (a) 60,000 m2
68.
(c) 31.83 mm2
(b) (d) (a) (a) (d) (c) (c) (a) (c) (a)
67.
(b) 7.96 cm2
1. 8. 15. 22. 29. 36. 43. 50. 57. 64.
66.
