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KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~Topically Analyzed

K.C.S.E Mathematics Q & A - MODEL 2013PP2QN24

4/9/2020

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Form 4 Mathematics


The table below shows marks scored by 42 students in a test.
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a) Starting with the mark of 25 and using equal class intervals of 10, make a frequency distribution table. 
b) On the grid provided , draw the ogive for the data 
c) Using the graph in (b) above , estimate:
(i) The median mark 
(ii) The upper quartile mark
answers
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K.C.S.E Mathematics Q & A - MODEL 2013PP2QN23

4/9/2020

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Form 4 Mathematics


The equation of a curve is given by y = 5x − 1/2 x2
 (a) On the grid provided, draw the curve of y = 5x − 1/2 x2 for 0 ≤ x ≤ 6
(b) By integration, find the area bounded by the curve, the line x =6 and the x-axis.
(c) (i) On the same grid as in,(a).draw the line y = 2x.
(ii) Determine the area bounded by the curve and the line y = 2 x.
answers
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K.C.S.E Mathematics Q & A - MODEL 2013PP2QN21

3/9/2020

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Form 4 Mathematics


(a) Complete the table below, giving the values correct to 1 decimal place.
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b) On the grid provided, using the same scale and axes, draw the graphs of y = 2 sin (χ+20)0 and y = √3 cos χ for 00 ≤ χ ≤ 2400.
c) Use the graphs drawn in (b) above to determine:
 i) the value of χ for which 2sin (χ + 20) = √3 cos χ;
 ii)the difference in the amplitudes of y =2sin(χ + 20) and y =√3 cos χ.
answers
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K.C.S.E Mathematics Q & A - MODEL 2013PP2QN20

3/9/2020

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Form 4 Mathematics


The figure ABCDEF below represents a roof of a house. AB=DC=12 m, BC = AD = 6m, AE = BF = CF= DE = 5m and EF = 8m
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(a) Calculate, correct to 2 decimal places, the perpendicular distance of EF from the plane ABCD. 
(b) calculate the angle between :
(I) the planes ADE and ABCD 
(II) The line AE and the plane ABCD, correct to 1 decimal place; 
(III) The planes ABFE and DEFE, correct to 1 decimal place.
ANSWERS
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K.C.S.E Mathematics Q & A - MODEL 2013PP2QN19

3/9/2020

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Form 3 Mathematics


(a) Complete the table below for y = x3+4x2-5x-5
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(b) On the grid provided, draw the graphs of y = x3 +4x2-5x-5 for -5 ≤ x ≤ 2
(c) (i) Use the graph to solve the equation x3 +4x2 – 5x – 5 = 0
(ii) By drawing a suitable straight line on the graph, solve the equation x3 + 4x2 – 5x -5 = - 4x – 1
answers
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K.C.S.E Mathematics Q & A - MODEL 2013PP2QN18

3/9/2020

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Form 3 Mathematics


In the figure below, PR is a diameter of the circle center O. Points P, Q, R and S are on the circumference of the circle. Angle PRQ = 72, QS = QP and line USV
is tangent to the circle at S.
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Giving reasons, Calculate the size of
(a) ˂ QPR 
(b) ˂ PQS 
(c) ˂ OQS 
(d) ˂ RTS 
(e) ˂ RSV
answers
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K.C.S.E Mathematics Q & A - MODEL 2013PP2QN17

3/9/2020

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Form 1 Mathematics


The hire purchase (H.P) price of a public address system was Kshs 276000. A deposit of Kshs 60000 was paid followed by 18 equal monthly installments.
The cash price of the public address system was 10% less than the H.P price.
(a) Calculate
(i) The monthly installments 
(ii) The cash price 
(b) A customer decided to buy the system in cash and was allowed a 5% discount on the cash price. He took a bank loan to buy the system in cash.
The bank charged compound interest on the loan at the rate of 20% p.a. The loan was repaid in 2 years.
Calculate the amount repaid to the bank by the end of the second year 
(c) Express as a percentage of the Hire Purchase price, the difference between the amount repaid to the bank and the Hire Purchase price
answers
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K.C.S.E Mathematics Q & A - MODEL 2013PP2QN16

3/9/2020

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Form 4 Mathematics


The vertices of triangle T are A(1, 2), B(4, 2) and C(3, 4). The vertices of triangle Tʹ, the image of T are Aʹ(1/2 ,1) , Bʹ(2,1) and Cʹ(3/2. 2).
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answer
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K.C.S.E Mathematics Q & A - MODEL 2013PP2QN15

3/9/2020

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Form 4 Mathematics


The position of two towns are (20 S,300 E) and 20S, 37.4 0E) calculate , to the nearest km, the shortest distance between the two towns.(take the radius ofthe earth to be 6370 km)
answer
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K.C.S.E Mathematics Q & A - MODEL 2013PP2QN14

3/9/2020

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Form 3 Mathematics


Solve the equation; 6 cos2 x +7 sin x – 8 = 0 for 00 ≤ x ≤ 900
answer
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K.C.S.E Mathematics Q & A - MODEL 2013PP2QN13

3/9/2020

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Form 3 Mathematics


The table below shows income tax rates in a certain year
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In that year, a monthly personal tax relief of kshs 1056 was allowed .calculate the monthly income tax paid by an employee who earned salary of Ksh 32 500.
answers
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K.C.S.E Mathematics Q & A - MODEL 2013PP2QN12

3/9/2020

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Form 4 Mathematics


A point P moves inside a sector of a circle, centre O, and chord AB such that 2cm < OP ≤ 3cm and angle APB = 65 Draw the locus of P
answer
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K.C.S.E Mathematics Q & A - MODEL 2013PP2QN11

3/9/2020

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Form 3 Mathematics


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answer
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K.C.S.E Mathematics Q & A - MODEL 2013PP2QN10

3/9/2020

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Form 1 Mathematics


Two taps A and B can each fill an empty tank in 3 hours and 2 hours respectively. A drainage tap R can empty the full tank in 6 hours; taps A and R are opened for 5 hours then closed.
(a) Determine the fraction of the tank is still empty 
(b) Find how long it would take to fill the remaining fraction of the tank if all the three taps are opened
answer
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K.C.S.E Mathematics Q & A - MODEL 2013PP2QN09

3/9/2020

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Form 3 Mathematics


Two machines, M and N produce 60% and 40% respectively of the total number of items manufactured in a factory. It is observed that 5% of the items produces
by machine M are defective while 3% of the items produced by machine N are defective.
If an item is selected at random from the factory, find the probability that it is defective

answer
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K.C.S.E Mathematics Q & A - MODEL 2013PP2QN08

3/9/2020

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Form 2 Mathematics


The position vectors of points F, G, and H are f, g, and h respectively. Point H divides FG in the ratio 4:-1. Express h in terms of f and g
answer
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K.C.S.E Mathematics Q & A - MODEL 2013PP2QN07

3/9/2020

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Form 3 Mathematics


(a) expand (1 − ?)5
(b) Use the expansion in (a) up to the term in x3 to approximate the value of (0.98)5
answer
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K.C.S.E Mathematics Q & A - MODEL 2013PP2QN06

3/9/2020

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Form 3 Mathematics


The equation of a circle is given by x2 +4x +y2 -2y – 4 = 0. Determine the centre and radius of the circle
answer
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K.C.S.E Mathematics Q & A - MODEL 2013PP2QN05

3/9/2020

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Form 1 Mathematics


(a) Using a pair of compasses and ruler only, construct an escribed circle to touch side XZ of triangle XYZ drawn below
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(b) Measure the radius of the circle
answer
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K.C.S.E Mathematics Q & A - MODEL 2013PP2QN04

3/9/2020

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Form 3 Mathematics


Solve the equation ; 2 log x – log (x-2) = 2 log3.
answer
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K.C.S.E Mathematics Q & A - MODEL 2013PP2QN02

3/9/2020

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Form 3 Mathematics


A quadratic curve passes through the points (-2, 0) and (1, 0). Find the equation of the curve in the form y = ax2 +bx +c, where a, b and c are constants
answer
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K.C.S.E Mathematics Q & A - MODEL 2013PP2QN01

3/9/2020

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Form 3 Mathematics


The sum of n terms of the sequence; 3, 9, 15, 21, … is 7500. Determine the value of n
answer
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K.C.S.E Mathematics Q & A - MODEL 2013PP1QN24

2/9/2020

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Form 2 Mathematics


​The figure below represents a cone of height 12 cm and base radius of 9 cm from which a similar smaller cone is removed, leaving a conical hole of height 4 cm.
Picture
a) Calculate:
i. The base radius of the conical hole; 
ii. The volume, in terms of π, of the smaller cone that was removed. 
b) (i) Determine the slant height of the original cone.
(ii) Calculate, in terms of it, the surface area of the remaining solid after the smaller cone is removed. 
answers
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K.C.S.E Mathematics Q & A - MODEL 2013PP1QN23

2/9/2020

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Form 2 Mathematics


(a) On the grid provided, draw the square whose verticals are A (6, -2), B (7, -2), C (7, -1) and D (6, -1). 
(b) On the same grid, draw:
i. AʹBʹCʹDʹ, the image of ABCD, under an enlargement scale factor 3, centre (9, -4); 
ii. AʹʹBʹʹCʹʹDʹʹ, the image of AʹBʹCʹDʹ, under a reflection in the line x = 0; 
iii. AʹʹʹBʹʹʹCʹʹʹDʹʹʹ, the the image of AʹʹBʹʹCʹʹDʹʹ under a rotation of + 90 about (0,0)
(c) Describe a single transformation that maps AʹBʹCʹDʹ onto AʹʹʹBʹʹʹCʹʹʹDʹʹʹ
answers
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K.C.S.E Mathematics Q & A - MODEL 2013PP1QN22

2/9/2020

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Form 3 Mathematics


In the figure below, OABC is a trapezium. AB parallel to OC and OC = 5AB. D is a point on OC such that OD: DC = 3:2
Picture
a) Given that OA = p and AB = q, express in terms of p and q:
i. OB; 
ii. AD; 
iii. CB;
b) Lines OB and AD intersect at point X such that AX = kAD and OX = rOB, where
k and r are scalars. Determine the values k and r.
answers
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