Page 42 - Spotlight A+ SPM Additional Mathematics Form 4 & 5

Form
5
Chapter 7 Linear Programming Additional Mathematics

7.1

1. Shade the region which represented by the (c) In a week, Jason makes x cupboard P and y
following linear inequality. C1 cupboard Q. He has a capital of RM2 000.
1
2
(a) y < x + 3 (b) y > x – 1 The cost of making a cupboard P is RM200
2 5 and a cupboard Q is RM100.
y y
4. Represent each of the following linear
6 3 inequalities graphically. C3
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1 4 2 (a) x > 4
y = –x + 3 2 y = –x – 1 1
2
2 5 y , 8
x x (b) x , 7
–6 –4 –2 0 2 –3 –2 –1 0 1
–2 –1 y > 1
(c) x > –2
y > 4
4
8
(c) y , x – 5 (d) y < – x – 3 (d) x + y > 2
3 9
y , 6
y y
(e) x + y < 4
2 x x + y . 1
–8 –6 –4 –2 0 (f) x > y
x –1
–2 0 2 4 6 x . 1
4
–2 y = – –x – 3 –2
8 (g) y < 2x CHAP.
–4 y = –x – 5 9 –3
3
–6 –4 y > x + 2 7
(h) y > 2x
y < 3x
2. Determine the linear inequality which satisfies
each of the following regions. C2 5. Shade the region R which satisfied the
(a) (b) following inequalities. C2
x > 0
y y y > x
y < 2x + 1
4 2 6
y = –x + 2 7 x + y < 8.
2 3 y = –x + 5 4
3
x 2
–4 –2 0 2 4 x = 0
–2 x
–3 –2 –1 0 1
–4 –2 y = 2x + 1
8 y = x
(c) (d)
6
y y
4
4 4
3 8 2 2 x + y = 8
2 y = – –x + 4 x
3
–2 0 2 4 6
1 –2 5 y = 0
x –4 y = –x – 4 0 2 4 6 8
–1 0 1 2 3 2

3. Write a mathematical model for each of the 6. Draw y > 2x + 1 and y , 2x – 3 on the
following situations. C1 same graph. Is there any solution for these
(a) The number of participants for course A inequalities? C2
is at most three times than the number of
participants for course B. 7. Is the point (2, 1) a solution of the inequalities
(b) The number of male workers exceed the x + y . 1 and 2x + y , 8? C2
number of female workers by at most 40.

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C07 Spotlight Add Math F5.indd 383 23/04/2021 3:39 PM