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KCSE MATHEMATICS QUESTIONS AND SOLUTIONS


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Form 3
Form 2
Form 4
Form 1

K.C.S.E Mathematics Q & A - MODEL 2005.PP2.QN.23

23/9/2020

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Form 3 Mathematics



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

Picture

Calculate:

(a) The length of FC ( 2 marks)

(b)

(i) the size of the angle between the lines FC and FH ( 2 marks)

(ii) The size of the angle between the lines AB and FH ( 2 marks)

(c) The size of the angle between the planes ABHE and the plane FGHE (2mks)

Answer
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K.C.S.E Mathematics Q & A - MODEL 2005.PP2.QN.21

23/9/2020

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Form 3 Mathematics



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

Picture

(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

Take the scale: 2 cm for 300 on the x- axis 2 cm for I unit on the y- axis

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

(i) Solve equation 2 sin xo + cos x0 = 1 ( 1 mark)

(ii) Determine the range of values x for which 2 sin xo > 1 – cos x0 ( 1 mark)

Answer
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K.C.S.E Mathematics Q & A - MODEL 2005.PP2.QN.22

23/9/2020

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Form 1 Mathematics



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)

Answer
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K.C.S.E Mathematics Q & A - MODEL 2005.PP2.QN.17

23/9/2020

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Form 4 Mathematics



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

(a) Find dy/dx         (1 mark)

(b) Determine the values of y at the turning points of the curve y = 1/3 x3 + x2 – 3x + 2     ( 4 marks)

Answer
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K.C.S.E Mathematics Q & A - MODEL 2005.PP2.QN.24

23/9/2020

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Form 4 Mathematics



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) Write down all the inequalities, in terms of x and representing the information above ( 2 marks)
(b) On the grid provided draw the inequalities by shading the unwanted regions ( 2 marks)
(c) If one kilogram of N costs Kshs 20 and one kilogram of S costs Kshs 50, use the graph to determine the lowest cost of one bag of the mixture ( 3 marks)

Answer
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K.C.S.E Mathematics Q & A - MODEL 2005.PP2.QN.20

22/9/2020

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Form 4 Mathematics



(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

Answer
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K.C.S.E Mathematics Q & A - MODEL 2005.PP2.QN.19

22/9/2020

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Form 3 Mathematics



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

Abdi: 60,000, 64 800, 69, 600
Amoit 60,000, 64 800, 69 984

(a) Calculate Abdi’s annual salary increment and hence write down an expression for his annual salary in his nth year of employment( 2 marks)

(b) Calculate Amoit’s annual percentage rate of salary increment and hence write down an expression for her salary in her nth year of employment. ( 2 marks)

(c) Calculate the differences in the annual salaries for Abdi and Amoit in their 7th year of employment ( 4 marks)

Answer
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K.C.S.E Mathematics Q & A - MODEL 2005.PP2.QN.18

22/9/2020

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Form 4 Mathematics



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

Picture

(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)

Answer
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Picture

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K.C.S.E Mathematics Q & A - MODEL 2005.PP2.QN.15

22/9/2020

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Form 1 Mathematics



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)

Picture
Answers
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K.C.S.E Mathematics Q & A - MODEL 2005.PP2.QN.13

22/9/2020

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Form 3 Mathematics



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)

Answer
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K.C.S.E Mathematics Q & A - MODEL 2005.PP2.QN.10

22/9/2020

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Form 1 Mathematics



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)

Answer
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K.C.S.E Mathematics Q & A - MODEL 2005.PP2.QN.12

22/9/2020

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Form 4 Mathematics



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)

Answer
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K.C.S.E Mathematics Q & A - MODEL 2005.PP2.QN.16

19/9/2020

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Form 4 Mathematics



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)

Answers
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K.C.S.E Mathematics Q & A - MODEL 2005.PP2.QN.14

19/9/2020

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Form 1 Mathematics



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.

Answer
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K.C.S.E Mathematics Q & A - MODEL 2005.PP2.QN.11

19/9/2020

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Form 1 Mathematics



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.

Answer
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K.C.S.E Mathematics Q & A - MODEL 2005.PP2.QN.9

19/9/2020

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Form 3 Mathematics



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

Answer
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K.C.S.E Mathematics Q & A - MODEL 2005.PP2.QN.8

19/9/2020

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Form 2 Mathematics



The volumes of two similar solid cylinders are 4752 cm3 and 1408 cm3. If the area of the curved surface of the smaller cylinder is 352 cm2, find the area of the curved surface of the larger cylinder. ( 4 marks)
aNSWER
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K.C.S.E Mathematics Q & A - MODEL 2005.PP2.QN.7

19/9/2020

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Form 3 Mathematics



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

Answer
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K.C.S.E Mathematics Q & A - MODEL 2005.PP2.QN.6

19/9/2020

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Form 1 Mathematics



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)

Answers
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K.C.S.E Mathematics Q & A - MODEL 2005.PP2.QN.5

19/9/2020

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Form 3 Mathematics



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

Answer
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K.C.S.E Mathematics Q & A - MODEL 2005.PP2.QN.4

19/9/2020

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Form 2 Mathematics



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

Picture

(a) Complete the figure ( 1 mark) 

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

Answer
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K.C.S.E Mathematics Q & A - MODEL 2005.PP2.QN.3

19/9/2020

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Form 1 Mathematics



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)

Answer
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K.C.S.E Mathematics Q & A - MODEL 2005.PP2.QN.2

19/9/2020

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Form 3 Mathematics



Without using mathematical Tables, simplify

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Answer
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K.C.S.E Mathematics Q & A - MODEL 2005.PP2.QN.1

19/9/2020

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Form 2 Mathematics



Find the value of y in the equation

Picture
Answer
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K.C.S.E Mathematics Q & A - MODEL 2005.PP1.QN.19

19/9/2020

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Form 2 Mathematics



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

Picture

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.

(a) Calculate the volume of water required to completely fill the pool.

(b) Water is allowed into the empty pool at a constant rate through an inlet pipe. It takes 9 hours for the water to just cover the entire floor of the pool.

Calculate:

(i) The volume of the water that just covers the floor of the pool ( 2 marks)

(ii) The time needed to completely fill the remaining of the pool ( 3 marks)

Answer
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