KCSE MATHEMATICS QUESTIONS AND SOLUTIONS

The diagram below represents a cuboid ABCDEFGH in which FG= 4.5 cm, GH = 8cm and HC = 6 cm

Calculate:

(a) complete the table below, giving your values correct to 2 decimal places ( 2 marks)

(b) On the grid provided, using the same scale and axes, draw the graphs of y = sin x⁰ and y = 1 – cos x⁰ ≤ x ≤ 180⁰

(c) Use the graph in (b) above to

A boat at point x is 200 m to the south of point Y. The boat sails X to another point Z. Point Z is 200m on a bearing of 310⁰ from X, Y and Z are on the same horizontal plane.

(a) Calculate the bearing and the distance of Z from Y ( 3 marks)

(b) W is the point on the path of the boat nearest to Y. Calculate the distance WY ( 2 marks)

(c) A vertical tower stands at point Y. The angle of point X from the top of the tower is 6⁰ calculate the angle of elevation of the top of the tower from W (3 marks)

A curve is represented by the function y = ¹/₃ x³ + x² – 3x + 2

Diet expert makes up a food production for sale by mixing two ingredients N and S. One kilogram of N contains 25 units of protein and 30 units of vitamins. One kilogram of S contains 50 units of protein and 45 units of vitamins. If one bag of the mixture contains x kg of N and y kg of S.

(a) BCD is a rectangle in which AB = 7.6 cm and AD = 5.2 cm. draw the rectangle and construct the lucus of a point P within the rectangle such that P is equidistant from CB and CD ( 3 marks)

(b) Q is a variable point within the rectangle ABCD drawn in (a) above such that 600 ≤ AQB≤ 900 On the same diagram, construct and show the locus of point Q, by leaving unshaded, the region in which point Q lies

Abdi and Amoit were employed at the beginning of the same year. Their annual salaries in shillings progressed as follows:

Triangles ABC and A”B”C” are drawn on the Cartesian plane provided. Triangle ABC is mapped onto A”B”C” by two successive transformations

(a) Find R ( 4 marks)

(b) Using the same scale and axes, draw triangles A’B’C’, the image of triangle ABC under transformation R ( 2 marks)

(c) Describe fully, the transformation represented by matrix R ( 2 marks)

The figure below represents below represents a prism of length 7 cm AB = AE = CD = 2 cm and BC – ED = 1 cm

Draw the net of the prism ( 3 marks)

Expand and simplify (3x – y)⁴.

Hence use the first three terms of the expansion to approximate the value of (6-0.2)⁴ ( 4 marks)

A salesman earns a basic salary of Kshs. 9,000 per month In addition he is also paid a commission of 5% for sales above Kshs 15,000 In a certain month he sold goods worth Kshs. 120,000 at a discount of 2 ½ %

Calculate his total earnings that month ( 3 marks)

Two lines L₁ and L₂ intersect at a point P. L₁ passes through the points (-4,0) and (0,6).

Given that L₂ has the equation: y = 2x – 2, find, by calculation, the coordinates of P. ( 3 marks)

A stone is thrown vertically upwards from a point O After t seconds, the stone is S metres from O Given that S= 29.4t – 4.9t²,

Find the maximum height reached by the stone ( 3 marks)

The density of a solid spherical ball varies directly as its mass and inversely as the cube of its radius.

When the mass of the ball is 500g and the radius is 5 cm, its density is 2 g per cm³ Calculate the radius of a solid spherical ball of mass 540 density of 10g per cm³.

Successive moving averages of order 5 for the numbers 9,8.2, 6.7,5.4, 4.7 and k are A and B. Given that A – B = 0.6 find the value of k.

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: