Answers - Pearson Global Schools

​
Mathematics B
7 a k 5 400
​
7 a A 5 100p 5 2 pr 2 1 2prh
c 4 hours d 62.5 m 3
→ 100p 2 2pr 2 5 2prh
m (min) 5 6 7 8 9 10
50
→
___ ​ 2 r 5 h r t (°C) 80 67 57 50 44 40
→ V 5 pr 2 h 5 pr ​(
2 ___ 50
​ 2 r r )​ 5 50pr 2 pr 2
b t
b r 0 1 2 3 4 5
80 t 400
m
V 0 153.9 289.0 386.4 427.3 392.7
V
V 50πr πr 3
0 5
m
c 53 (°C) d 6 min 40 s e 5.3 < m < 8
0
Exercise 156*
r
c V max 5 427.3 cm 3
d d 5 8.16 cm, h 5 8.2 cm
1 y
2
8 b V 5 (10 2 2x)(10 2 2x)x 5 100x 2 40x 2 2 4x 3
y 1 4 x
c x 0 1 2 3 4 5
V 0 64 72 48 16 0
4 0
x
3 y
4 y
y
8
x x 4
5
d V max 5 74 cm 3 , 1.67 3 6.66 3 6.66 3 6.66 cm
1.3 0
x
0 1
x
Exercise 156
y x 2 2 x
1 y
2
5 a
y 4 x (°) 30 35 40 45 50 55 60
x
d (m) 3.3 7.9 10 10.6 10 8.6 6.7
1
d (m)
0 4 x
d 100 x 2000
x
y
3 y
4
y – 8 x
y 10
30
x
b 10.6 m at x 5 45°
60 x
c 37° < x < 54°
1
0
x
6 a
0
x 0 1 2 3 4 5
10 x
R 0 3 4 4.5 4.8 5
x 1 3 5
5 a t (months) 1 2 3 4 5 6
C 2 4 6
R, C (£1000s)
y 2000 1000 667 500 400 333
C x 1
b y
6x
R
2000 y 2000
x 1
t
0
5 x
b P . 0 when 0.27 , x , 3.7 so between 27 and 370 boards per week
0 1
t
c 3.3 months
d 2.7 months approx.
c £1100 when x 5 1.45 so 145 boards hired out
6 a
7 b
t (hours) 1 5 10 15 20
r (m) 1 2 3 4 5
v (m 3 ) 1000 200 100 67 50
A (m 2 ) 106 75 90 126 177
b v
A (m 2 )
A 2πr 2 100
v 1000
r
1000
t
0 1 5 r (m)
0 1
t
c A 5 75 m 2 at r 5 2.0 m
38
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