(a) Copy and complete the following table of values for the relation \(y = 2x^{2} - 7x - 3\).
| x | -2 | -1 | 0 | 1 | 2 | 3 | 4 | 5 |
| y | 19 | -3 | -9 |
(b) Using 2 cm to 1 unit on the x- axis and 2 cm to 5 units on the y- axis, draw the graph of \(y = 2x^{2} - 7x - 3\) for \(-2 \leq x \leq 5\).
(c) From your graph, find the : (i) minimum value of y ;
(ii) gradient of the curve at x = 1.
(d) By drawing a suitable straight line, find the values of x for which \(2x^{2} - 7x - 5 = x + 4\).
(a) If p varies directly as \(r^{2}\) and p = 3.2 when r = 4, find the value of p when r = 6.5.
(b) Solve the simultaneous equations :
\(\frac{x}{2} + \frac{y}{4} = 1 ; \frac{x}{3} - \frac{y}{4} = \frac{-1}{6}\)
Without using Mathematical tables or a calculator, simplify :
(a) \(\sqrt{50} - 3\sqrt{2}(2\sqrt{2} - 5) - 5\sqrt{32}\)
(b) \(\frac{1}{2} \log_{10} \frac{25}{4} - 2 \log_{10} \frac{4}{5} + \log_{10} \frac{320}{125}\).
(a) Simplify : \(625^{\frac{3}{8}} \times 5^{\frac{1}{2}} \div 25\)
(b) Solve the following equations correct to one decimal place.
(i) \(\tan (\theta + 25)° = 5.145\)
(ii) \(5\cos \theta - 1 = 0\), where \(0° \leq \theta \leq 90°\).
In the diagram, PQRS is a circle with centre O and radius 7cm. SQ and PR intersect at K and < SKR = 90°. If the length of the arc SR is four times that of arc PQ, find the length of the arc SR. [Take \(\pi = \frac{22}{7}\)].
