Quiz 2
Quiz 2 Multiple-choice questions on further revisionary mathematics
All questions have only one correct answer. 1. Differentiating y = 4x5 gives: (a) dy 2 6 (b) dy = 20 x 4 = x dx dx 3 2.
∫ (5 − 3t 2 ) dt is equal to:
(a) 5 − t3 + c (b) − 3t3 + c
(c) dy (d) dy = 5x 4 = 4 x6 dx dx
(c) − 6t + c (d) 5t − t3 + c
3. A graph of resistance against voltage for an electrical circuit is shown in Figure M2.1. The equation relating resistance R and v oltage 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
160 145 140 Resistance R
120 100 80 70 60 40 20 0
20 40 60 80 100 120 Voltage V
Figure M2.1
4. The gradient of the curve y = − 2x3 + 3x + 5 at
x = 2 is:
(a) − 21 (b) 27 (c) − 16 (d) − 5 5. The value of
1
∫ 0 (3sin 2θ − 4cosθ ) dθ , correct to 4 significant figures, is:
(a) − 0.06890 (b) − 1.242 (c) − 2.742 (d) − 1.569
6. A graph of y against x, two engineering quantities, produces a straight line.
A table of values is shown below:
x 2
y 9 3 5
− 1
p
Mechanics of Solids, Second Edition © 2016 C. Ross, J. Bird and A. Little. Published by Taylor & Francis. All rights reserved.
The value of p is:
1 (a) − (b) − 2 (c) 3 (d) 0 2 dy 7. If y = 5 x 3 − 2 , is equal to: dx (a) 8.
5 15 x − 2 x (b) 2 x5 − 2 x + c (c) 2 2
(d) 5 x − 2 x
2
∫ 9 t 3 dt is equal to:
(a)
t4 2 + c (b) t 2 + c 18 3
(c)
2 4 t + c 9
(d)
2 3 t +c 9
9. 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 litre (b) 2.7 litre (c) 2700 litre (d) 270 litre
10. Evaluating
π /3
∫0
3sin 3x dx gives:
(a) 1.503 (b) − 18 (c) 2 (d) 6
11. Here are four equations in x and y. When x is plotted against y, in each case a straight line results. y 3 2 y (i) y + 3 = 3x (ii) y + 3x = 3 (iii) − = x (iv) = x + 2 2 3 3 Which of these equations are parallel to each o ther?
(a) (i) and (ii) (b) (i) and (iv)
(c) (ii) and (iii)
(d) (ii) and (iv)
12. Differentiating i = 3 sin 2t − 2 cos 3t with respect to t gives:
(a) 3 cos 2t + 2 sin 3t
(b) 6(sin 2t − cos 3t)
13.
∫ (5sin 3t − 3cos5t ) dt is equal to:
(a) −5 cos 3t + 3 sin 5t + c 5 3 (c) − cos3t − sin5t + c 3 5
(c)
3 3 cos 2t + sin 3t 2 2
(b) 15(cos 3t + sin 3t) + c (d)
3 5 cos3t − sin5t + c 5 3
Mechanics of Solids, Second Edition © 2016 C. Ross, J. Bird and A. Little. Published by Taylor & Francis. All rights reserved.
(d) 6(cos 2t + sin 3t)
14. Which of the straight lines shown in Figure M2.2 has the equation y + 4 = 2x?
(a) (iv) (b) (ii) (c) (iii) (d) (i) y 6
y 6
4 x
0
4
6
6 (i)
(ii)
y 6
y
6 6 x
0
6
6 x
0
6
0
6
2
6 x
6
6 (iii)
(iv)
Figure M2.2
15. Given y = 3e x + 2 ln 3x , (a) 6e x +
dy is equal to: dx
2 2 (b) 3e x + 3x x
(c) 6e x +
2 2 (d) 3e x + 3 x
16. Given f (t) = 3t4 − 2, f ′(t) is equal to: −
(a) 12t 3 − 2 (b)
17.
∫
(a)
1+ 8 e2 x
4 e2 x
3 5 t − 2t + c 4
(c) 12t3 (d) 3t5 − 2
dx is equal to:
+ c (b) x +
4 e2 x
(c) x −
2 e2 x
+ c (d) x −
8 e2 x
+c
18. 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 c opper, which is given by the gradient of the graph, is:
(a) 96000 Pa (b) 1.04 × 10−11 Pa (c) 96 Pa (d) 96 × 109 Pa
Mechanics of Solids, Second Edition © 2016 C. Ross, J. Bird and A. Little. Published by Taylor & Francis. All rights reserved.
19. The gradient of the curve y = 4x2− 7x + 3 at the point (1, 0) is
(a) 3 (b) 0 (c) 1 (d) −7 2
20. Evaluating ∫ 2e3t dt , correct to 4 significant figures, gives: 1
(a) 2300 (b) 255.6 (c) 766.7 (d) 282.3
1. (b) 6. (d) 11. (b) 16. (c)
2. (d) 7. (a) 12. (d) 17. (c)
3. (d) 8. (a) 13. (c) 18. (a)
4. (a) 9. (d) 14. (a) 19. (c)
5. (b) 10. (c) 15. (b) 20. (b)
Answers Mechanics of Solids, Second Edition © 2016 C. Ross, J. Bird and A. Little. Published by Taylor & Francis. All rights reserved.
All questions have only one correct answer. 1. Differentiating y = 4x5 gives: (a) dy 2 6 (b) dy = 20 x 4 = x dx dx 3 2.
∫ (5 − 3t 2 ) dt is equal to:
(a) 5 − t3 + c (b) − 3t3 + c
(c) dy (d) dy = 5x 4 = 4 x6 dx dx
(c) − 6t + c (d) 5t − t3 + c
3. A graph of resistance against voltage for an electrical circuit is shown in Figure M2.1. The equation relating resistance R and v oltage 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
160 145 140 Resistance R
120 100 80 70 60 40 20 0
20 40 60 80 100 120 Voltage V
Figure M2.1
4. The gradient of the curve y = − 2x3 + 3x + 5 at
x = 2 is:
(a) − 21 (b) 27 (c) − 16 (d) − 5 5. The value of
1
∫ 0 (3sin 2θ − 4cosθ ) dθ , correct to 4 significant figures, is:
(a) − 0.06890 (b) − 1.242 (c) − 2.742 (d) − 1.569
6. A graph of y against x, two engineering quantities, produces a straight line.
A table of values is shown below:
x 2
y 9 3 5
− 1
p
Mechanics of Solids, Second Edition © 2016 C. Ross, J. Bird and A. Little. Published by Taylor & Francis. All rights reserved.
The value of p is:
1 (a) − (b) − 2 (c) 3 (d) 0 2 dy 7. If y = 5 x 3 − 2 , is equal to: dx (a) 8.
5 15 x − 2 x (b) 2 x5 − 2 x + c (c) 2 2
(d) 5 x − 2 x
2
∫ 9 t 3 dt is equal to:
(a)
t4 2 + c (b) t 2 + c 18 3
(c)
2 4 t + c 9
(d)
2 3 t +c 9
9. 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 litre (b) 2.7 litre (c) 2700 litre (d) 270 litre
10. Evaluating
π /3
∫0
3sin 3x dx gives:
(a) 1.503 (b) − 18 (c) 2 (d) 6
11. Here are four equations in x and y. When x is plotted against y, in each case a straight line results. y 3 2 y (i) y + 3 = 3x (ii) y + 3x = 3 (iii) − = x (iv) = x + 2 2 3 3 Which of these equations are parallel to each o ther?
(a) (i) and (ii) (b) (i) and (iv)
(c) (ii) and (iii)
(d) (ii) and (iv)
12. Differentiating i = 3 sin 2t − 2 cos 3t with respect to t gives:
(a) 3 cos 2t + 2 sin 3t
(b) 6(sin 2t − cos 3t)
13.
∫ (5sin 3t − 3cos5t ) dt is equal to:
(a) −5 cos 3t + 3 sin 5t + c 5 3 (c) − cos3t − sin5t + c 3 5
(c)
3 3 cos 2t + sin 3t 2 2
(b) 15(cos 3t + sin 3t) + c (d)
3 5 cos3t − sin5t + c 5 3
Mechanics of Solids, Second Edition © 2016 C. Ross, J. Bird and A. Little. Published by Taylor & Francis. All rights reserved.
(d) 6(cos 2t + sin 3t)
14. Which of the straight lines shown in Figure M2.2 has the equation y + 4 = 2x?
(a) (iv) (b) (ii) (c) (iii) (d) (i) y 6
y 6
4 x
0
4
6
6 (i)
(ii)
y 6
y
6 6 x
0
6
6 x
0
6
0
6
2
6 x
6
6 (iii)
(iv)
Figure M2.2
15. Given y = 3e x + 2 ln 3x , (a) 6e x +
dy is equal to: dx
2 2 (b) 3e x + 3x x
(c) 6e x +
2 2 (d) 3e x + 3 x
16. Given f (t) = 3t4 − 2, f ′(t) is equal to: −
(a) 12t 3 − 2 (b)
17.
∫
(a)
1+ 8 e2 x
4 e2 x
3 5 t − 2t + c 4
(c) 12t3 (d) 3t5 − 2
dx is equal to:
+ c (b) x +
4 e2 x
(c) x −
2 e2 x
+ c (d) x −
8 e2 x
+c
18. 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 c opper, which is given by the gradient of the graph, is:
(a) 96000 Pa (b) 1.04 × 10−11 Pa (c) 96 Pa (d) 96 × 109 Pa
Mechanics of Solids, Second Edition © 2016 C. Ross, J. Bird and A. Little. Published by Taylor & Francis. All rights reserved.
19. The gradient of the curve y = 4x2− 7x + 3 at the point (1, 0) is
(a) 3 (b) 0 (c) 1 (d) −7 2
20. Evaluating ∫ 2e3t dt , correct to 4 significant figures, gives: 1
(a) 2300 (b) 255.6 (c) 766.7 (d) 282.3
1. (b) 6. (d) 11. (b) 16. (c)
2. (d) 7. (a) 12. (d) 17. (c)
3. (d) 8. (a) 13. (c) 18. (a)
4. (a) 9. (d) 14. (a) 19. (c)
5. (b) 10. (c) 15. (b) 20. (b)
Answers Mechanics of Solids, Second Edition © 2016 C. Ross, J. Bird and A. Little. Published by Taylor & Francis. All rights reserved.
