Mathematics Past Questions and Answers

(a)
In the diagram, ABCD is a rectangular garden (3n - 1)m long and (2n + 1)m wide. A wire mesh 135m long is used to mark its boundary and to divide it into 8 equal plots. Find the value of n.
(b) A cylinder with base radius 14 cm has the same volume as a cube of side 22 cm. Calculate the ratio of the total surface area of the cylinder to that of the cube. [Take \(\pi = \frac{22}{7}\)]

(a) Copy and complete the table of values for \(y = 1 - 4\cos x\).

x	0°	30°	60°	90°	120°	150°	180°	210°	240°	270°	300°
y	-3.0			1.0				4.5			-1.0

(b) Using a scale of 2cm to 30° on the x- axis and 2cm to 1 unit on the y- axis, draw the graph of \(y = 1 - 4\cos x\) for \(0° \leq x \leq 360°\).
(c) Use the graph to : (i) solve the equation \(1 - 4\cos x = 0\) ; (ii) find the value of y when x = 105° ; (iii) find x when y = 1.5.

Multiply 2.7 x 10^-4 by 6.3 x 10⁶ and leave your answers in standard form

Multiply 2.7 x 10^-4 by 6.3 x 10⁶ and leave your answers in standard form

If 9^{(2 - x)} = 3, find x