Illustrate the following on graph paper and shade the region which satisfies all the three inequalities at the same time :

\(- x + 5y \leq 10 ; 3x - 4y \leq 8\) and \(x > -1\).

The table below is for the relation \(y = 2 + x - x^{2}\)

(a) Using a scale of 2cm to 1 unit on each axis, draw the graph of the relation in the interval \(-2 \leq x \leq 3\).

(b) From your graph, find the greatest value of y and the value of x for which this occurs.

(c) Using the same scale and axes, draw the graph of \(y = 1 - x\)

(d) Use your graphs to solve the equation \(1 + 2x - x^{2} = 0\)

Two towns K and Q are on the parallel of latitude 46°N. The longitude of town K is 130°W and that of town Q is 103°W. A third town P also on latitude 46°N is on longitude 23°E, Calculate:

(i) the length of the parallel of latitude 46°N, to the nearest 100km;

(ii) the distance between K and Q, correct to the nearest 100km;

(iii) the distance between Q and P measured along the parallel of latitude, to the nearest 10km.

[Take \(\pi = 3.142\); Radius of the earth = 6400km]

(a) Prove that the sum of the angles in a triangle is two right angles.

(b) In a triangle LMN, the side NM is produced to P and the bisector of < LNP meets ML produced at Q. If < LMN = 46°, and < MLN = 80°, calculate < LQN, stating clearly your reasins.

Using a ruler and a pair of compasses only, 

(a) construct (i) a triangle ABC such that |AB| = 5cm, |AC| = 7.5cm and < CAB = 120° ; (ii) the locus \(L_{1}\) of points equidistant from A and B ; (iii) the locus \(L_{2}\) of points equidistant from Ab and AC, which passes through the triangle ABC.

(b) Label the point P where \(L_{1}\) and \(L_{2}\) intersect; 

(c) Measure |CP|.