Answers - Pearson Global Schools

Mathematics B
7 a v 5 3t 2 1 8t 2 5 b a 5 6t 1 8 c v 5 6 m/s; a 5 14 m/s 2
8 a v 5 3t 2 2 4t 1 3 b a 5 6t 2 4 c v 5 7 m/s; a 5 8 m/s 2
9 a 2t 1 10 b 14 m/s
10 a 6 2 2t b 2 m/s
Exercise 203*
1 a v 5 8t 1 ​
2__
​
​ ​
t 2 ​ b a 5 8 2
4__
t 3 ​
2 a v 5 6 2
4__
t 2 ​ b a 5
8__
t 3 ​
3 a 20 1 10t b 30 m/s, 40 m/s, 50 m/s c 10 m/s 2
4 a 8t 1 5 b 13 m/s, 21 m/s, 29 m/s c 8 m/s 2
5 a 40 2 10t b 30 m/s, 20 m/s, 10 m/s, 0 m/s c 80 m
6 a 25 2 2t b 12.5 c 156.25 m
​
​
​
​
​
ds
7 a
__ ​ 5 2​ ___ 36 dt t ​ ; __ dv 36
​ 5
___
3 dt t 3 ​
b 3 s
c 28 m
ds
8 a
__ ​ 5 2t 1
8__ dv
dt t 2 ​;
___
dt ​ 5 21 2 ___ 16
t 3 ​
b 7 m/s c 2 s d 44 m
9 a 8 s b 3 s c 170 m
10 a 5 s b 50 m
Exercise 204 (Revision)
dy
1 a ​ ___
dx ​ 5 3 b ​ ___ dy
dx ​ 5 0 c ​ ___ dy
dx ​ 5 3x2 d ​
​
​
​
​
​
​
​
​
​
​
​
​
​
​
___ dy
​5 4x3
dx
dy
e
___
dx ​ 5 dy
5x4 f
___
dx ​ 5 dy
12x5 g
___
dx ​ 5 dy
15x4 h
___
​5 160x7
dx
dy
2 a
___
dx ​ 5 dy
6x2 1 10x b
___
dx ​ 5 14x 2 3 c ___ dy
dx ​ 5 15x2
dy
d
___
dx ​ 5 dy
12x3 2 10x e
___
dx ​ 5 dy
3x2 1 10x f
___
dx ​ 5 2x 1 2 g ___ dy
​5 4x 2 9
dx
dy
h
___
dx ​ 5 2x 1 4
dy
3 a
___
dx ​ 5 4 b ___ dy
dx ​ 5 25 c ___ dy
dx ​ 5 26 d ___ dy
​5 19
dx
dQ
4 a
___
dt ​ 5 3t2 2 16t 1 14
b (i) 14 m 3 /s 2 (ii) 26 m 3 /s 2 (iii) 9 m 3 /s 2
dy
5 a
___
dx ​ 5 3x2 2 3 b (1, 0), (21, 4)
c (21, 4) is max, (1, 0) is min.
dy
6 a
___
dx ​ 5 3x2 1 6x 2 9 b (23, 28), (1, 24)
c (23, 28) is max, (1, 24) is min.
7 a v 5 24t m/s, 48 m/s b a 5 24 m/s 2 , 24 m/s 2
8 a v 5 3t 2 1 8t 2 3 m/s, 377 m/s b a 5 6t 1 8 m/s 2 , 68 m/s 2
Exercise 204* (Revision)
​
​
​
​
​ ​
​
​
​
​
​
​
​
​
​
​
​
dy
1 a
___
dx ​ 5 2x22 5 2
1__
dy
x 2 ​ b
___
dx ​ 5 22x23 5 2
2__
x 3 ​
dy
c
___
dx ​ 5 1__ ​x​ 2 1_
2 ​ 5 ____ 1
2 2​ __
√ x d ___ dy
dx ​ 5 23x24 5 2
3__
x 4 ​
dy
e
___
dx ​ 5 16
216x25 5 2
___
dy
x 5 ​ f
___
dx ​ 5 2x23 5 2
1__
x 3 ​
dy
g
___
dx ​ 5 4x 1 3 2 dy
4x22 h
___
dx ​ 5 2 1 3x22
2 a 22 b 2 c 0 d 22​
1_
8 ​
3 4y 5 3x 1 4
4 y 5 23x, y 5 3x 2 9
5 a y 5 4x 2 7 b x 5 0 is a max, x 5
4_
3​is a min.
6 p 5 1
dC
7 a
___
dt ​ 5 4 2 16
16t22 5 4 2
___
t 2 ​ b t 5 2, C 5 16
c 212 °C/month
dP
8 a
___
dt ​ 5 10t 2 10 10 000
000t22 5 10t 2
______
t 2 ​
b t 5 10, P 5 1500
​
​
9 t 5 5, s 5 125 m
10 a
ds
v 5
__
​5 3t 2 2 300 km/s, a 5
__ dv
​5 6t km/s 2
dt dt
b at t 5 5, v 5 2225 km/s, a 5 30 km/s 2
c t 5 10 s
Exercise 205
1 7.39 cm 2 2 29.7 cm 2 3 36.2 cm 2
4 8.46 cm 2 5 121 cm 2 6 77.0 cm 2
Exercise 205*
1 173 cm 2 2 48.1 cm 3 16.5 cm
4 51.4° 5 53.5 cm 2 6 65.8 cm
Exercise 206
1 a 11.7 cm b 14.2 cm c 34.4°
2 a 18.6 cm b 28.1 cm c 48.6°
3 a 14.1 cm b 17.3 cm c 35.4°
4 a 28.3 cm b 34.6 cm c 35.1° d 19.5°
5 a 4.47 m b 4.58 m c 29.2° d 12.6°
6 a 407 m b 402 m c 8.48° d 13.3°
7 a 43.3 cm b 68.7 cm c 81.2 cm
8 a 28.9 cm b 75.7 cm c 22.4°
Exercise 206*
1 a 16.2 cm b 67.9° c 55.3 cm 2
2 a 26.5 cm b 61.8° c 1530 cm 2
3 a 30.3° b 31.6° c 68.9°
4 a 36.9° b 828 cm 2
5 a 15 m b 47.7° c €91 300
6 a 66.4° b 32.9°
7 46.5 m
8 a OW 5 4290 m, OS 5 2760 m
b 36.0°
c 197 km/h
Exercise 207
1 5.08 cm 2 2 1.85 cm 2 3 24.0 cm 2
4 14.4 cm 2 5 411 cm 2 6 569 cm 2
Exercise 207*
1 6.97 cm 2 2 12.8 cm 3 11.5 cm 2
4 8.68 cm 5 7.96 3 10 21 m 3 6 165 cm
Exercise 208 (Revision)
1 148 cm 2
2 a AC 5 42.4 cm b 33.9 cm c 68.0° d 58.0°
3 a 18.4° b 500 m c 11.3°
4 a 68.9 m 2 b 120 m 2
5 a 22.4 cm b 26.4 cm c 32.1° d 35.0°
6 a 14.1 cm 2 b 67.8 cm 2
Exercise 208* (Revision)
1 Pythagoras proof
2 4.68 m 2
3 a AC 5 70.7 cm b 98.7 cm
c 27.9° d 216 000 cm 2
4 a x is the length of the diagonal of the
square that is the bottom face of the cube.
Using Pythagoras
x 2 5 8 2 1 8 2
​ ​5 128
x 5 √ ____
128 ​5 √ _______
64 3 2 ​5 √ ___
64 ​3 √ __ 2 ​5 8​ √ __ 2 ​
b 50.5°
5 92.1 m
8 x
8
6 a 70.7 m b 60.4 m c 41.4° d 67.5° e 9038 m 2
7 14.3 cm
8 5.2 cm/s
48
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