### Mathematics Past Questions

3731

The marks scored by 50 students in a Geography examination are as follows :

60 54 40 67 53 73 37 55 62 43 44 69 39 32 45 58 48 67 39 51 46 59 40 52 61 48 23 60 59 47 65 58 74 47 40 59 68 51 50 50 71 51 26 36 38 70 46 40 51 42.

(a) Using class intervals 21 - 30, 31 - 40, ..., prepare a frequency distribution table.

(b) Calculate the mean mark of the distribution.

(c) What percentage of the students scored more than 60%?

3732

(a) Simplify $$\frac{x + 2}{x - 2} - \frac{x + 3}{x - 1}$$

(b) The graph of the equation $$y = Ax^{2} + Bx + C$$ passes through the point (0, 0), (1, 4) and (2, 10). Find the :

(i) value of C ; (ii) values of A and B ; (iii) co-ordinates of the other point where the graph cuts the x- axis.

3733

(a) Using ruler and a pair of compasses only, construct : (i) quadrilateral PQRS such that /PQ/ = 10 cm, /QR/ = 8 cm, /PS/ = 6 cm, < PQR = 60° and < QPS = 75° ;

(ii) the locus $$l_{1}$$ of points equidistant from QR and RS ; (iii) locus $$l_{2}$$ of points equidistant from R and S ;

(b) Measure /RS/.

3734

(a) A circle is inscribed in a square. If the sum of the perimeter of the square and the circumference of the circle is 100 cm, calculate the radius of the circle. [Take $$\pi = \frac{22}{7}$$].

(b) A rope 60cm long is made to form a rectangle. If the length is 4 times its breadth, calculate, correct to one decimal place, the :

(i) length ; (ii) diagonal of the rectangle.

3735

(a) Copy and complete the table of values for $$y = \sin x + 2 \cos x$$, correct to one decimal place.

 x 0° 30° 60° 90° 120° 150° 180° 210° 240° y 2.2 -1.2 -2.0 -1.9

(b) Using a scale of 2 cm to 30° on the x- axis and 2 cm to 0.5 units on the y- axis, draw the graph of $$y = \sin x + 2\cos x$$ for $$0° \leq x \leq 240°$$.

(c) Use your graph to solve the equation : (i) $$\sin x + 2 \cos x = 0$$ ; (ii) $$\sin x = 2.1 - 2\cos x$$.

(d) From the graph, find y when x = 171°.