# SPM Additional Mathematics 2017, Paper 2 (Question 1 – 3)

Question 1 (5 marks):
Solve the following simultaneous equations:
x – 3y = 1,
x2 + 3xy + 9y2 = 7

Solution:

Question 2 (7 marks):
It is given that the equation of a curve is $y=\frac{5}{{x}^{2}}.$
(a) Find the value of $\frac{dy}{dx}$ when x = 3.
(b) Hence, estimate the value of $\frac{5}{{\left(2.98\right)}^{2}}.$

Solution:
(a)

(b)

Question 3 (8 marks):
Diagram 1 shows a circle and a sector of a circle with a common centre O. The radius of the circle is r cm.

It is given that the length of arc PQ and arc RS are 2 cm and 7 cm respectively. QR = 10 cm.
[Use θ = 3.142]
Find
(a) the value of r and of θ,
(b) the area, in cm2, of the shaded region.

Solution
:

(a)

(b)