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.