Page 7 - 1202 Question Bank Additional Mathematics Form 4

PAPER 2

Section A

3 1 5. The diagram shows the graph f : x → 2x + 3 for
1. Given two functions defined by f : x → x + and –1 < x < 3.
4
2
5 2
g : x → – x. f(x)
4 3
(a) Is f (2) + f (3) = f (2 + 3)? Explain your answer. 10
[2 marks] 8 f(x) = 2x + 3

(b) Is g(4) − g(2) = g(4 − 2)? Show your working. 6
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[2 marks]
(c) Find the value of k if f(2k) = 6g(k). [2 marks] 4
(d) Find the value of k if f(k) + g(k) = 5. [2 marks] 2
x
0
2
6
8
10
–2
4
2. (a) The function g is defined by g : x → x + 1 , –2
x – 2
x ≠ 2, find –1
(i) g , [2 marks] (a) Find f (x). [1 mark]
2
(ii) g . [2 marks] (b) Based on (a), find the corresponding coordinates
−1
ax + 1 for the coordinates (1, 5).
(b) The function h as defined by h : x → x , [1 mark]
–1
x ≠ 0 is given by hg (4) = 6, find the value of a. (c) On the same axes, sketch the graph f (x) and
–1
[2 marks] state its domain.
[3 marks]
(d) Hence, draw a line of symmetry for f and f .
–1
3. Given g : x → x + 5, find [2 marks]
2
(a) an expression for each of the following.
(i) g(a + 1), [1 mark]
(ii) g(a ), [2 marks] 6. (a) The functions f and g are defined by f : x → 3x – a
2
b
(iii) g(2b – 1) – g(b). [2 marks] and g : x → , x ≠ 0 where a and b are constants.
x
(b) the possible values of x if g(x) = 5x – 1. Given that f (2) = 0 and fg(2) = 16, find the
2
[2 marks] values of a and b.
[4 marks]
2
4. The diagram shows a part of the mapping for the (b) Hence, find the value of g f (x).
function f : x → ax + b where a and b are constants. [3 marks]
2
f
x ax + b 7. (a) The function g is defined by g : x → 8 – 3x.
2
Find
10 (i) the expression for g and g ,
–1
2
3
(ii) the value of x if g (x) = g (x).
–1
2
[4 marks]
–2 –10
(b) The function h is defined by h : x → ax + b,
a ≠ –1 for the domain 0 < x < 5 . Given that the
(a) Find the value of a and of b. [2 marks] graph y = h(x) passes through the point (8, 5) and
1
(b) Given the mapping starts with x = , where will the graph y = h(x) and y = h (x) intersects at the
−1
2
be the end of the arrow point? [2 marks] point whose x-coordinate is 3. Find the value of a
(c) Find another value of x so that the function f will and of b.
map to −10. [2 marks] [3 marks]
HOTS Analysing
8 Question 2(a)(ii) : 9
SOS TIP 88 To find g (x), let y = x + 1 –1 9 SOS TIP
–1
x – 2
Question 7(b) :
Find h (x) and then solve h (x) = h(x) to find the value of x which is given to be 3.
–1
01_1202 QB AMath F4.indd 9 09/05/2022 11:30 AM