KCSE MATHEMATICS QUESTIONS AND SOLUTIONS

Given that Cos 2x⁰ = 0.8070, find x when 0⁰ < x < 360⁰ ( 4 marks)

Find, without using Mathematical Tables the values of x which satisfy the equation Log₂ (x² – 9) = 3 log₂ (2 + 1) (4 marks)

Pipe a can fill an empty water tank in 3 hours while, pipe B can fill the same tank in 6 hours, when the tank is full it can be emptied by pipe C in 8 hours. Pipes A and B are opened at the same time when the tank is empty. If one hour later, pipe C is also opened, find the total time taken to fill the tank (4 marks)

The first three consecutive terms of a geometrical progression are 3, x and 5 ¹/₃. Find the value of x. ( 2 marks)

The diagram below is a part of a figure which has rotational symmetry of order 4 about O.

(a) Complete the figure ( 1 mark) 

(b) Draw all the lines of symmetry of the completed figure ( 2 marks)

In a fund- raising committee of 45 people, the ratio of men to women is 7: 2. Find the number of women required to join the existing committee so that the ratio of men to women is changed to 5: 4 ( 3 marks)

Without using mathematical Tables, simplify

Find the value of y in the equation

The diagram below represents a rectangular swimming pool 25m long and 10m wide. The sides of the pool are vertical.

The floor of the pool slants uniformly such that the depth at the shallow end is 1m at the deep end is 2.8 m.

Calculate:

The points P, Q, R and S have position vectors 2p, 3p, r and 3r respectively, relative to an origin O. A point T divides PS internally in the ratio 1:6

(a)

(b) Find the coordinates of two points on the curve other than (0,0) at which x- coordinate and y- coordinate are equal (3 marks)

A boat which travels at 5 km/h in still water is set to cross a river which flows from the north at 6km/h. The boat is set on a course of x⁰ with the north.

(a) Given that cos x⁰ = ³/₅ , calculate

(b) If the boat is to sail on a bearing of 135⁰, calculate the bearing of possible course on which it can be set ( 4 marks)

The data below shows the masses in grams of 50 potatoes

(a) On the grid provide, draw a cumulative frequency curve for the data (4mks)

(b) Use the graph in (a) above to determine

The gradient of a curve at point (x,y) is 4x – 3. the curve has a minimum value of – 1/8

(a) Find

(i) The value of x at the minimum point ( 1 mark)

(ii) The equation of the curve ( 4 marks)

(b) P is a point on the curve in part (a) (ii) above. If the gradient of the curve at P is -7, find the coordinates of P ( 3 marks)