The number of child births recorded in 50 maternity centres of a local government in August 1993 are as follows :

50 99 81 86 69 85 93 63 92 65 77 74 76 71 90 74 81 94 67 75 95 81 68 105 99 68 75 75 76 73 79 74 80 69 74 62 74 80 79 68 79 75 75 71 83 75 80 85 81 82

(a) Construct a frequency distribution table, using class intervals 45 - 54, 55 - 64, etc.

(b) Draw the histogram for the distribution 

(c) Use your histogram to estimate the mode.

(d) Calculate the mean number of births.

The lengths of the parallel sides of a trapezium are 9cm and 12cm. If the area of the trapezium is 105cm², find the perpendicular distance between the parallel sides.

• A. 5cm
• B. 7cm
• C. 10cm
• D. 15cm

Divide 2x³ + 11x² + 17x + 6 by 2x + 1.

• A. x² + 5x + 6
• B. 2x² + 5x - 6
• C. 2x² + 5x + 6
• D. x² - 5x + 6

P is a point on the same plane with a fixed point A. If P moves such that it is always equidistant from A, the locus of P is

• A. a straight line joining A and P
• B. the perpendicular bisector of AP
• C. a circle with centre A
• D. the triangle with centre P

If cos \(\theta\) = x and sin 60^o = x + 0.5 0^o < \(\theta\) < 90^o, find, correct to the nearest degree, the value of \(\theta\)

• A. 32^o
• B. 40^o
• C. 60^o
• D. 69^o

Differentiate \(x^{2} + xy - 5 = 0\).

• A. \(\frac{-(2x + y)}{x}\)
• B. \(\frac{(2x - y)}{x}\)
• C. \(\frac{-x}{2x + y}\)
• D. \(\frac{(2x + y)}{x}\)

Expression 0.612 in the form \(\frac{x}{y}\), where x and y are integers and y \(\neq\) 0

• A. \(\frac{153}{250}\)
• B. \(\frac{68}{111}\)
• C. \(\frac{61}{100}\)
• D. \(\frac{21}{33}\)

25% of Z = 37.5 Therefore

• A. Z = 1.5
• B. Z = 9.375
• C. Z = 150
• D. Z = 937.5

Evaluate \(\int\limits_0^\frac{\pi}{2}\) sinxdx

• A. 2
• B. -1
• C. 1
• D. -2

Differentiate \(\frac{x}{x + 1}\) with respect to x.

• A. \(\frac{1}{x + 1}\)
• B. \(\frac{1}{(x + 1)^{2}}\)
• C. \(\frac{1 - x}{x + 1}\)
• D. \(\frac{1 - x}{(x + 1)^{2}}\)