# SPM Additional Mathematics 2018, Paper 1 (Question 5 – 7)

Question 5 (3 marks):
Find the value of

Solution:
(a)
$\begin{array}{l}\underset{x\to 1}{\mathrm{lim}}\left(7-{x}^{2}\right)\\ =7-{\left(1\right)}^{2}\\ =6\end{array}$

(b)

Question 6 (4 marks):
It is given that L = 4t t2 and x = 3 + 6t.
(a) Express $\frac{dL}{dx}$ in terms of t.
(b) Find the small change in x, when L changes from 3 to 3.4 at the instant t = 1.

Solution:
(a)

(b)

Question 7 (4 marks):
Diagram 2 shows the curve y = g(x). The straight line is a tangent to the curve.
Diagram 2

Given g’(x) = –4x + 8, find the equation of the curve.

Solution: