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KCSE MATHEMATICS QUESTIONS AND SOLUTIONS


Topically Analysed


Form 3
Form 2
Form 4
Form 1

K.C.S.E Mathematics Q & A - MODEL 2017PP2QN24

17/9/2020

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Form 2 Mathematics


The length of a room is 3 m shorter than three times its width. The height of the room is a quarter of its length. The area of the floor is 60 m2.
(a) Calculate the dimensions of the room.
 (b) The floor of the room was tiled leaving a border of width y m, all round. If the area of the border was 1.69m2,
 find:
(i) the width of the border;
(ii) the dimensions of the floor area covered by tiles.
answers
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K.C.S.E Mathematics Q & A - MODEL 2017PP2QN23

17/9/2020

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Form 3 Mathematics


(a) The 5th term of an AP is 82 and the 12th term is 103.
Find:
(i) the first term and the common difference; 
(ii) the sum of the first 21 terms. 
(b) A staircase was built such that each subsequent stair has a uniform difference in height. The height of the 6th stair from the horizontal floor was 85 cm and the height of the 10th stair was 145 cm.
Calculate the height of the 1st stair and the uniform difference in height of the stairs.

answers
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K.C.S.E Mathematics Q & A - MODEL 2017PP2QN22

17/9/2020

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Form 4 Mathematics


A trader stocks two brands of rice A and B. The rice is packed in packets of the same size. The trader intends to order fresh supplies but his store can accommodate a maximum of 500 packets. He orders at least twice as many packets of A as of B.
He requires at least 50 packets of B and more than 250 packets of A. If he orders x packets of A and y packets of B,
(a) Write the inequalities in terms of x and y which satisfy the above information. 
(b) On the grid provided represent the inequalities in part (a) above
(c) The trader makes a profit of Ksh 12 on a packet of type A rice and Ksh 8 on a packet of type B rice. Determine the maximum profit the trader can make.
answer
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K.C.S.E Mathematics Q & A - MODEL 2017PP2QN21

17/9/2020

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Form 3 Mathematics


Three quantities X, Y and Z are such that X varies directly as the square root ofY and inversely as the fourth root of Z. When X = 64, Y = 16 and Z = 625.
(a) Determine the equation connecting X, Y and Z.
(b) Find the value of Z when Y = 36 and X = 160.
(c) Find the percentage change in X when Y is increased by 44%.
answers
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K.C.S.E Mathematics Q & A - MODEL 2017PP2QN20

17/9/2020

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Form 4 Mathematics


The figure below represents a cuboid ABCDEFGH in which AB = 16 cm, BC = 12 cm and CF = 6 cm.
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(a) Name the projection of the line BE on the plane ABCD.
Calculate correct to 1 decimal place:
(i) the size of the angle between AD and BF; 
(ii) the angle between line BE and the plane ABCD; 
(iii) the angle between planes HBCE and BCFG. 
(c) Point N is the midpoint of EF. Calculate the length BN, correct to 1 decimal place.

answers
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K.C.S.E Mathematics Q & A - MODEL 2017PP2QN19

17/9/2020

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Form 3 Mathematics


The table below shows values of x and some values of for the curve y = x3 -2x2 -9x + 8 for -3 ≤ x ≤ 5. Complete the table.
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(b) On the grid provided, draw the graph of y = x3- 2x2- 9x + 8 for -3 ≤ x ≤ 5 for Use the scale; 1 cm represents 1 unit on the x-axis 2 cm represents 10 units on the y-axis
(c) (i) Use the graph to solve the equation  x2 - 2x3 -9x + 8 = 0.
 (ii) By drawing a suitable straight line on the graph, solve the equation  x2 - 2x2- 11x + 6 = 0.
answers
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K.C.S.E Mathematics Q & A - MODEL 2017PP2QN18

17/9/2020

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Form 4 Mathematics


The vertices ofa rectangle ABCD are: A(0,2), B(0,4), C(4,4) and D(4,2). The vertices of its image under a transformation T are; A’(0,2) , B’(0,4) , C’(8,4) and D’(8,2).
On the grid provided, draw the rectangle ABCD and its image A’B’C’D’ under T.
(ii) Describe fully the T. 
(iii) Determine the matrix of transformation. 
(b). On the same grid as in (a), draw the image of rectangle ABCD under a shear with line x =-2 invariant and A(0, 2) is mapped onto A”(0,0).
answers
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K.C.S.E Mathematics Q & A - MODEL 2017PP2QN17

17/9/2020

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Form 3 Mathematics


The income tax rates of a certain year were as shown in the table below:
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In that year, Shaka’s monthly earnings were as follows: Basic salary Ksh 28600
House allowance Ksh 15 000
Medical allowance Ksh 3 200
Transport allowance Ksh 540
Shaka was entitled to a monthly tax relief of Ksh 1056.
(a) Calculate the tax charged on Shaka’s monthly earnings. 
(b) Apart from income tax, the following monthly deductions were made; a Health Insurance fund of Ksh 500, Education Insurance of Ksh 1 200 and 2% of his basic salary for widow and children pension scheme. Calculate Shaka’s monthly net income from his employment.
answer
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K.C.S.E Mathematics Q & A - MODEL 2017PP2QN16

17/9/2020

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Form 3 Mathematics


Given that OA = 3i+ 4j+ 7k, OB= 4i + 3j + 9k and OC = i + 6j + 3k. show that points A, B and C are collinear.
answer
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K.C.S.E Mathematics Q & A - MODEL 2017PP2QN15

17/9/2020

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Form 4 Mathematics


The area of a triangle is 24 square units. The triangle is mapped onto image P by the matrix
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K.C.S.E Mathematics Q & A - MODEL 2017PP2QN14

17/9/2020

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Form 3 Mathematics


A committee of 3 people was chosen at random from a group of 5 men and 6 women. Find the probability that the committee consisted of more men than women. 
answer
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K.C.S.E Mathematics Q & A - MODEL 2017PP2QN13

17/9/2020

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Form 4 Mathematics


A basket ball team scored the points in 6 matches: 10, 12, 14, 16, 28 and 30. Using an assumed mean of l5. Determine the standard deviation correct to 2 decimal places.
answer
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K.C.S.E Mathematics Q & A - MODEL 2017PP2QN12

17/9/2020

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Form 4 Mathematics


Determine the amplitude, period and the phase angle of the curve: y = 5/2 sin (4θ + 60°)
answer
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K.C.S.E Mathematics Q & A - MODEL 2017PP2QN11

17/9/2020

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Form 3 Mathematics


The equation of a circle is x2+ y2 - 4x + 6y + 4 = 0. On the grid provided, draw the circle.
answer
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K.C.S.E Mathematics Q & A - MODEL 2017PP2QN10

17/9/2020

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Form 4 Mathematics


An aircraft took off from a point P (65° S, 76° W) and flew due North to a point Q. The distance between P and Q is 5400 nm.
Determine the position of Q.
answer
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K.C.S.E Mathematics Q & A - MODEL 2017PP2QN09

17/9/2020

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Form 4 Mathematics


​The figure below is a triangle ABC.
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(a) On the triangle, locate the locus of points equidistant from AC and AB and 5 cm from B.
(b) Shade the region R, inside the triangle, which is less than 5 cm from B and nearer to AC than AB.
answer
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K.C.S.E Mathematics Q & A - MODEL 2017PP2QN08

17/9/2020

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Form 1 Mathematics


Using a ruler and a pair of compasses only, construct:
(a) a triangle LMN in which LM = 5 cm, LN = 5.6 cm and MLN = 45° 
(b) the circle that touches all the sides of the triangle.

answer
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K.C.S.E Mathematics Q & A - MODEL 2017PP2QN07

17/9/2020

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Form 3 Mathematics


Simplify
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K.C.S.E Mathematics Q & A - MODEL 2017PP2QN06

17/9/2020

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Form 3 Mathematics


Make t  the subject of ;
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answer
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K.C.S.E Mathematics Q & A - MODEL 2017PP2QN05

16/9/2020

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Form 3 Mathematics


In the figure below, PQRS is a cyclic quadrilateral. PQ = QR, PQR =105° and PS is parallel to QR.
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Determine the size of.
(a) ∠ PSR 
(b)∠ PQS.
answer
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K.C.S.E Mathematics Q & A - MODEL 2017PP2QN04

16/9/2020

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Form 2 Mathematics


Without using mathematical tables or a calculator, evaluate
5/6 log10 64 + log10 50 - 41og10 2.
answer
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K.C.S.E Mathematics Q & A - MODEL 2017PP2QN03

16/9/2020

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Form 1 Mathematics


A miller was contracted to make porridge flour to support a feeding program. He mixed millet, sorghum, maize and Omena in the ration 1:2:5:1. The cost per kilogram of millet was Ksh 90, sorghum Ksh 120, maize Ksh 30 and omena Ksh 150.
Calculate:
(a) the cost of one kilogram of the mixture;
(b) the selling price of 1 kg of the mixture if the miller made a 30% profit.
answer
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K.C.S.E Mathematics Q & A - MODEL 2017PP2QN01

16/9/2020

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Form 3 Mathematics


The roots of a quadratic equation are x = -3/5 and x = 1. Form the quadratic equation in the form ax2 + bx + c = 0 where a, b and c are integers.
answers
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K.C.S.E Mathematics Q & A - MODEL 2017PP1QN24

16/9/2020

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Form 4 Mathematics


The equation of a curve is given as y = 2x3 -9/2 x2 -15x + 3.
(a) Find: (i) the value of y when x = 2;
(ii) the equation of the tangent to the curve at x = 2.
 (b) Determine the turning points of the curve.
answers
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K.C.S.E Mathematics Q & A - MODEL 2017PP1QN23

16/9/2020

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Form 3 Mathematics


An institution intended to buy a certain number of chairs for Ksh 16 200. The supplier agreed to offer a discount of Ksh 60 per chair which enabled the institution to get 3 more chairs.
Taking x as the originally intended number of chairs,
(a) Write an expressions in terms of x for:
(i) original price per chair; 
(ii) price per chair after discount. 
(b) Determine:
(i) the number of chairs the institution originally intended to buy; 
(ii) price per chair after discount; 
(iii) the amount of money the institution would have saved per chair if it bought the intended number of chairs at a discount of 15%.
answers
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