# SPM 2021 Add Maths Trial Paper (Selangor) – Paper 1 (Question 1 & 2)

Question 1:

(a)(i)
Express p in terms of q and find g-1 (x) in term of p.
(a)(ii)   ,
determine the value of n by comparing the g-1 (x) above with the given gn-1 (x).
Next, find the value of k. [5 marks]

(b)
What is the condition on p so that g = g-1 ? [1 mark]

Solution:
(a)(i)

(a)(ii)
$\begin{array}{l}{g}^{n-1}\left(x\right)={g}^{-1}\left(x\right)=\frac{px-5}{3x-2}\\ \therefore n-1=-1\\ n=0\\ \\ 3x-2\ne 0\\ x\ne \frac{2}{3}\\ k=\frac{2}{3}\end{array}$

(b)

Question 2:
Find the range of values of x for 5 < 2x2 + x + 4 and 2x2 + x + 4 ≤ 10.
Hence, solve the inequality 5 < 2x2+ x + 4 ≤ 10.
[4 marks]

Solution:
5 < 2x2 + x + 4
0 < 2x2 + x – 1
2x2 + x – 1 > 0
(2x – 1)(x + 1) > 0
x < -1 or x > ½

2x2 + x + 4 ≤ 10
2x2 + x – 6 ≤ 0
(2x – 3)(x + 2) ≤ 0
-2 ≤ x ≤ 3/2

x < -1, x > ½ or -2 ≤ x ≤ 3/2
-2 ≤ x < -1   or  ½ < x ≤ 3/2