Mathematics Past Questions and Answers

(a) If \(\frac{3p + 4q}{3p - 4q} = 2\), find \(p : q\).
(b)
The diagram shows the cross section of a bridge with a semi-circular hollow in the middle. If the perimeter of the cross section is 34 cm, calculate the :
(i) length PQ; (ii) area of the cross section.
[Take \(\pi = \frac{22}{7}\)].

(a) Copy and complete the table of values, correct to one decimal place, for the relation \(y = 3\sin x + 2\cos x\) for \(0° \leq x \leq 360°\).

x

0°

30°

60°

90°

120°

150°

180°

210°

240°

270°

300°

330°

360°

y

3.0

1.6

-2.0

-3.6

-3.0

2.0

(b) Using scales of 2cm to 30°mon the x- axis and 2cm to 1 unit on the y- axis, draw the graph of the relation \(y = 3\sin x + 2\cos x\) for \(0°\leq x \leq 360°\).
(c) Use the graph to solve :
(i) \(3\sin x + 2\cos x = 0\)
(ii) \(2 + 2\cos x + 3\sin x = 0\).

Express 0.0000407, correct to 2 significant figures

Express 0.0000407, correct to 2 significant figures

If x varies inversely as y and y varies directly as z, what is the relationship between x and z?