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Additional Mathematics SPM Answers
ANSWERS

Form 4

Chapter 1 Functions (b) y
5
Try This! 1.1
2 Range: 0 ≤ f(x) ≤ 5
1. (a) 3 (b) 3 (c) 7 1
2. (a) Function. Each object has only one image, even 0 x
though the element 6 does not have an object. –3 –2 3
(b) Not a function. Object 2 has three images, which are
2, 4, and 6. (c) y
(c) Not a function. Element s does not have an image.
3. (a) This graph is not a graph of y as a function of x. There
are vertical lines which intersect the graph at two 5 Range: 0 ≤ f(x) ≤ 5
different points.
(b) This graph is a graph of y as a function of x. Each 3
vertical line intersects the graph at one point only.
(c) This graph is a graph of y as a function of x. Each
vertical line intersects the graph at one point only.
(d) This graph is not a graph of y as a function of x. All x
vertical lines intersect the graph at two different points, 0 5 8
except at the y-axis where the vertical line intersects
at one point only.
(d)
4. (a) (i) f : x → x or f(x) = x 3 y
3
(ii) h : x → x + 1 or h(x) = x + 1
(b) A : r → πr or A(r) = πr 2 7
2
2
(c) (i) f : x → 2x + 3x – 1 or f(x) = 2x + 3x – 1
2
(ii) g : x → sin x or g(x) = sin x
5
1 2
5. (a) 0 (b) –3 (c) — (d) – —
4 3
3
6. (a) False (b) True (c) True
7. (a) Domain = {x, y, z}, range = {p, q}
(b) Domain = {–2, –1, 1, 2}, range = {1, 4}
(c) Domain = {1, 2, 3, 4, 5}, range = {12, 24, 36, 48, 60} –4 3 0 2 x
(d) Domain is x ∈ , range is y ∈ . – – 2
(e) Domain is x ∈ , range is y > 3.
(f) Domain is x ∈ , x ≠ –5, range is y ∈ , y ≠ 0.
(g) Domain is x ∈ , range is y > 0. 11. (a) –1 (b) 5 – t (c) 3 – 2t
(h) Domain is x . 0, range is L . 0. 12. (a) 1 (b) 9x + 1 (c) 6z – 2
8. (a) Domain 0 < x < 8, range 3 < y < 15. 13. (a) 2 (b) 4.5 (c) 5 – 2x
(b) Domain –6 < x < 1, range 0 < y < 9.
14. (a) 10 (b) –5, 3 (c) 5
9. (a) When the domain is , all values of y are possible. 15. 5
The range is y ∈ . 3 3
(b) When x is limited to negative values, all values of y will 16. (a) 7, 5 (b) – —, 3 (c) 1, —
5
2
be at least 2. The range is y > 2. 17. (a) 3
(c) The range is {2, 3, 4, 5, 6}. (b) 1, 6
10. (a) y 18. (a) h = 3, k = 1
(b) 0 < f(x) < 9
19. (a) RM77 000
Range: 0 ≤ f(x) ≤ 2 (b) RM10 500
x (c) 3
–2 0 2 (d) V(n) is a function. Each input n will give rise to one
and only one output value of V(n).

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