 SPM Additional Mathematics (Model Test Paper) – Q&A 1-2

SPM Additional Mathematics (Model Test Paper)

Section A
[40 marks]

Question 1
Solve the simultaneous equations:
2 (xy) = x + y – 1 = 2x2 – 11y2  [5 marks]

2 (xy) = x + y – 1
2x – 2y = x + y – 1
= 3y – 1 —- (1)

x + y – 1 = 2x2 – 11y2
2x2– 11y2 x y+ 1 = 0 —- (2)

Substitute (1) into (2):
2 (3y – 1)2– 11y2 – (3y – 1) y + 1 = 0
2 (9y2– 6y + 1) – 11y2 – 3y + 1 y+ 1 = 0
18y2– 12y + 2 – 11y2 – 4y + 2 = 0
7y2– 16y + 4 = 0
(7y – 2)(y – 2) = 0
$y=\frac{2}{7}\text{or}y=2$

From (1):

When y = 2,
= 3(2) – 1 = 5

Question 2
(a) the value of m, [2 marks]
(b)   gf-1(–2), [3 marks]
(c) function h if hg (x) = 12x + 5 [3 marks]

$\begin{array}{l}mx-3=0\\ m\left(\frac{3}{2}\right)-3=0\\ m=3×\frac{2}{3}=2\end{array}$
$\begin{array}{l}g{f}^{-1}\left(-2\right)=g\left(\frac{2}{3}\right)\\ \text{}=3-4\left(\frac{2}{3}\right)\\ \text{}=\frac{1}{3}\end{array}$
$\begin{array}{l}x=\frac{3-u}{4}\\ h\left(u\right)=12\left(\frac{3-u}{4}\right)+5\\ h\left(u\right)=9-3u+5\\ h\left(u\right)=14-3u\\ h\left(x\right)=14-3x\end{array}$