(i) A car travels a distance of 72 km at a certain average speed of x km per hour 31 and then travels a distance of 81 km at an average speed of 6 km per hour more than its original average speed. If it takes 3 hours to complete the total journey then form a quadratic equation and solve it to find its original average speed.

(ii) Given matrix, prove that X² = 4X + 5I

(iii) Use ruler and compasses for the following question taking a scale of 10 m = 1 cm. 4 A park in a city is bounded by straight fences AB, BC, CD and DA. Given that AB = 50 m, BC = 63 m, ∠ABC = 75°. D is a point equidistant from the fences AB and BC. If ∠BAD = 90°, construct the outline of the park ABCD. Also locate a point P on the line BD for the flag post which is equidistant from the corners of the park A and B.

Solution

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