# SPM Additional Mathematics 2017, Paper 1 (Question 8 – 10)

Question 8 (3 marks):
It is given that the sum of the first n terms of an arithmetic progression is ${S}_{n}=\frac{n}{2}\left[13-3n\right]$
Find the nth term.

Solution:

Question 9 (3 marks):
Diagram 5 shows the graph of the function f : x → |1 – 2x| for the domain –2 ≤ x ≤ 4.

Diagram 5

State
(a) the object of 7,
(b) the image of 3,
(c) the domain of 0 ≤ f(x) ≤ 5.

Solution:
(a)
The object of 7 is 4.

(b)
f (x) = |1 – 2x|
f (3) = |1 – 2(3)|
= |1 – 6|
= |–5|
= 5

The image of 3 is 5.

(c)
|1 – 2x| = 5
1 – 2x = ±5
Given when f(x) = 5, x = –2.

When f(x) = –5
1 – 2x = –5
2x = 6
x = 3

Domain: –2 ≤ x ≤ 3.

Question 10 (4 marks):
Given the function g : x → 2x – 8, find

Solution:
(a)

(b)