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7 Manipulating 2x 3 + 7x 2 – 6 = 0 gives
6 – 2x 3 = 7x 2 .
Dividing by 3x 2 gives
2 2x 7
–– – –– = – .
x
2 3 3
Manipulating this gives
2
– 1 1
–– – x = –– x + 2 – .
x
2 3 3
Model answers
2
y = – x
x 2
y
4
3
2
1
y = – 1
x + 2 1 3 3
– 4 – 3 – 2
– 1 O 1 2 3 4
– 1
2
y = – x
x 2
x
The solution is x = – 3·2, – 1·1 or 0·8.
Graphs – gradient and area (pages 51–52)
4
1 (a) ––– = 1.6 ms
2·5
–2
1
(b) Area under graph = 4 × 3.5 + – × 2.5 × 4 = 14 + 5 = 19 m.
2
2 (a)
Time (t hours) 0 1 2 3 4 5
Number of bacteria (n) 20 60 180 540 1620 4860
(b) Each hour the number of bacteria multiplies by 3 so n = 20 × 3 t .
(c) n
5000
4000
3000
2000
1000
0
1 2 3 4 5
t
2600 – 450
(d) (i) Gradient = –––––––––– = 1075
5 – 3
(ii) The rate of increase in bacteria per hour.
3 t = 0, d = 1 2 48
+ –– – 20 = 29; p = 29
1
t = 5, d = 6 2 48
+ –– – 20 = 24; q = 24
6
t = 7, d = 8 2 48
+ ––8 – 20 = 50; r = 50
14
IGCSE Revision Guide for Mathematics Model Answers © 2004, Hodder & Stoughton Educational