(a) Two positive whole numbers p and q are such that p is greater than q and their sum is equal to three times their difference;
(i) Express p in terms of q ; (ii) Hence, evaluate \(\frac{p^{2} + q^{2}}{pq}\).
(b) A man sold 100 articles at 25 for N66.00 and made a gain of 32%. Calculate his gain or loss percent if he sold them at 20 for N50.00.
(a) Copy and complete the table of values for the relation \(y = 3x^{2} - 5x - 7\).
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
| y | 35 | -7 | -9 | 5 |
(b) Using scales of 2 cm to 1 unit on the x- axis and 2 cm to 5 units on the y- axis, draw the graph of \(y = 3x^{2} - 5x - 7, -3 \leq x \leq 4\).
(c) From the graph : (i) find the roots of the equation \(3x^{2} - 5x - 7 = 0\) ; (ii) estimate the minimum value of y ; (iii) calculate the gradient of the curve at the point x = 2.
(a) If (3 - x), 6, (7 - 5x) are consecutive terms of a geometric progression (GP) with constant ratio r > 0, find the :
(i) values of x ; (ii) constant ratio.
(b) In the diagram above, |AB| = 3 cm, |BC| = 4 cm, |CD| = 6 cm and |DA| = 7 cm. Calculate
(a) Using ruler and a pair of compasses only, construct : (i) a trapezium WXYZ such that |WX| = 10.2 cm, |XY| = 5.6 cm, |YZ| = 5.8 cm, < WXY = 60° and WX is parallel to YZ (ii) a perpendicular from Z to meet \(\overline{WX}\) at N.
(b) Measure : (i) |WZ| ; (ii) |ZN| .
(a)
A segment of a circle is cut off from a rectangular board as shown in the diagram. If the radius of the circle is \(1\frac{1}{2}\) times the length of the chord; calculate, correct to 2 decimal places, the perimeter of the remaining portion. [Take \(\pi = \frac{22}{7}\)]
(b) Evaluate without using calculators or tables, \(\frac{3}{\sqrt{3}}(\frac{2}{\sqrt{3}} - \frac{\sqrt{12}}{6})\).
