Using a ruler and pair of compasses only, construct triangle ABC in which AB = 6cm, BC = 8cm and angle ABC = 45⁰. Drop a perpendicular from A to BC to meet line BC at M. Measure AM and AC.                                                        (4 Marks)

A measuring cylinder of base radius 5cm contains water whose level reads 6cm high. A spherical object is immersed in the water and the new level reads 10cm. Calculate the radius of the spherical object         (3 Marks)

In triangle ABC below, AC = BC, AB is parallel to DE, AB = 15cm, DE = 7.5cm and BE = 6cm.

Calculate

(a) Length CE                                                                     (2 Marks)

(b) Area of quadrilateral ABED.                                                     (2 Marks)

Give sin (90 – a) = ¹/₂ find without using trigonometric tables the value of cos a .           (2 Marks)

A rectangle whose area is 96m² is such that its length is 4metres longer than its width.

Find

(a) It dimensions                                                                  (3 Marks)

(b) Its perimeter                                                                         (1 Mark)

A salesman gets a commission of 2.4% on sales up to Sh. 100,000. He gets additional commission of 1.5% on sales above this. Calculate the commission he gets for sales worth Sh. 280,000.           (3 Marks)

The circle below whose area is 18.05cm² circumscribes triangle ABC where AB = 6.3cm, BC = 5.7cm and AC = 4.2cm. Find the area of the shaded part.                                        (4 Marks)

Find x if     3^2x+3  +  1  =  28                            (2 Marks)

Simplify:                                                      (3mks)

Mr. Owino spends 1/4 of his salary on school fees. He spends 2/3 of the remainder on food and a fifth of what is left on transport. He saves the balance. In certain month he saved Sh. 3400. What was his salary?                             (3 marks)