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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 2008PP2QN24

18/8/2020

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Form 3 Mathematics


The table below shows values of x and some values of y for the curvey = x +3+3x2+-4x-12 in the range -4 ≤ x ≤ 2.
a) Complete the table by filling in the missing values of y.
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b) On the grid provided, draw the graph y=x3 + 3x2+ -4x – 12 for -4 ≤ x ≤ 2.Use the scale. Horizontal axis 2cm for I unit and vertical axis 2cm for 5 units.
c) By drawing a suitable straight line on the same grid as the curve, solve the equation x3+3x2-5x-6=0
answers
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K.C.S.E Mathematics Q & A - MODEL 2008PP2QN23

18/8/2020

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Form 1 Mathematics


Halima deposited Ksh. 109375 in a financial institution which paid simple interest at the rate of 8% p.a. At the end of 2 years, she withdrew all the money. She then invested the money in share. The value of the shares depreciated at 4% p.a. during the first year of investment. In the next 3 years, the value of the shares appreciated at the rate of 6% every four months
a) Calculate the amount Halima invested in shares.
b) Calculate the value of Halima's shares.
(i) At the end of the first year; 
(ii) At the end of the fourth year, to the nearest shilling. 
c) Calculate Halima„s gain from the share as a percentage.
(ii) Find the values of x and y. 
(iii) Calculate the time taken before the policemen were unable to
communicate.
answers
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K.C.S.E Mathematics Q & A - MODEL 2008PP2QN22

18/8/2020

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Form 4 Mathematics


The table below shows the distribution of marks scored by 60 pupils in a test.
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a) On the grid provided, draw an ogive that represents the above information
b) Use the graph to estimate the interquartile range of this information.

answers
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K.C.S.E Mathematics Q & A - MODEL 2008PP2QN21

18/8/2020

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Form 2 Mathematics


Two policemen were together at a road junction. Each had a walkie talkie. The maximum distance at which one could communicate with the other was 2.5 km.
One of the policemen walked due East at 3.2 km/h while the other walked due North at 2.4 km/h the policeman who headed East traveled for x km while the one who headed North traveled for y km before they were unable to communicate.
(a) Draw a sketch to represent the relative positions of the policemen. 
(b) (i) From the information above form two simultaneous equations in x
and y.
answers
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K.C.S.E Mathematics Q & A - MODEL 2008PP2QN20

18/8/2020

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Form 2 Mathematics


In the figure below DA is a diameter of the circle ABCD centre O, radius 10cm. TCS is a tangent to the circle at C, AB=BC and angle DAC= 380
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a) Find the size of the angle;
(i) ACS; 
(ii) BCA 
b) Calculate the length of:
(i) AC 
(ii) AB
answers
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K.C.S.E Mathematics Q & A - MODEL 2008PP2QN19

18/8/2020

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Form 4 Mathematics


a) complete the table below, giving the values correct to 2 decimal places.
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b) On the grid provided, draw the graphs of y=sin 2x and y=3cosx-2 for 00 ≤ x ≤3600 on the same axes.
 Use a scale of 1 cm to represent 300 on the x-axis and 2cm to represent 1 unit on the y-axis.
 c) Use the graph in (b) above to solve the equation 3 Cos x – sin 2x = 2.
 d) State the amplitude of y=3cosx-2.
answers
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K.C.S.E Mathematics Q & A - MODEL 2008PP2QN17

18/8/2020

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Form 1 Mathematics


a) A trader deals in two types of rice; type A and with 50 bags of type B. If
he sells the mixture at a profit of 20%, calculate the selling price of one bag of the mixture. 
b) The trader now mixes type A with type B in the ratio x: y respectively. If the cost of the mixture is Ksh 383.50 per bag, find the ratio x: y. 
c) The trader mixes one bag of the mixture in part (a) with one bag of the mixture in part (b).
Calculate the ratio of type A rice to type B rice in this mixture.

answers
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K.C.S.E Mathematics Q & A - MODEL 2008PP2QN16

18/8/2020

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Form 4 Mathematics


Find in radians, the values of x in the interval 00≤ x ≤ 2π0+ for which 2 cos 2x=1.
 (Leave the answers in terms of π )
answer
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K.C.S.E Mathematics Q & A - MODEL 2008PP2QN15

18/8/2020

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Form 4 Mathematics


A particle moves in a straight line from a fixed point. Its velocity Vms-1 after t seconds is given by V=9t2 – 4t +1
Calculate the distance traveled by the particle during the third second.
answer
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K.C.S.E Mathematics Q & A - MODEL 2008PP2QN14

18/8/2020

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Form 4 Mathematics


The figure below represents a triangular prism. The faces ABCD, ADEF and CBFE are rectangles.
AB=8cm, BC=14cm, BF=7cm and AF=7cm.
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Calculate the angle between faces BCEF and ABCD.
answer
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K.C.S.E Mathematics Q & A - MODEL 2008PP2QN13

18/8/2020

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Form 3 Mathematics


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answer
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K.C.S.E Mathematics Q & A - MODEL 2008PP2QN12

18/8/2020

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Form 2 Mathematics


Solve for y in the equation log10 (3y +2)-1-log10 (y-4)
answer
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K.C.S.E Mathematics Q & A - MODEL 2008PP2QN11

18/8/2020

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Form 3 Mathematics


The equation of a circle is given by 4x2 + 4y2+- 8x+ 20y – 7 = 0. Determine the coordinates of the centre of the circle.
ANSWER
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K.C.S.E Mathematics Q & A - MODEL 2008PP2QN10

18/8/2020

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Form 4 Mathematics


Points A(2,2)and B(4,3) are mapped onto A‟(2,8) and b‟ (4,15) respectively by a transformation T.
Find the matrix of T.
answer
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K.C.S.E Mathematics Q & A - MODEL 2008PP2QN09

17/8/2020

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Form 2 Mathematics


In the figure below, angles BAC and ADC are equal. Angle ACD is a right angle. The ratio of the sides.
AC: BC =4: 3
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Given that the area of triangle ABC is 24 cm2+. Find the triangle ACD
answer
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K.C.S.E Mathematics Q & A - MODEL 2008PP2QN08

17/8/2020

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Form 3 Mathematics


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answer
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K.C.S.E Mathematics Q & A - MODEL 2008PP2QN07

17/8/2020

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Form 4 Mathematics


An aero plane flies at an average speed of 500 knots due East from a point p (53.40e) to another point Q. It takes 2 ¼ hours to reach point Q. Calculate:
 (i) The distance in nautical miles it traveled;
 (ii) The longitude of point Q to 2 decimal places
answer
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K.C.S.E Mathematics Q & A - MODEL 2008PP2QN06

17/8/2020

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Form 3 Mathematics


A student at a certain college has a 60% chance of passing an examination at the first attempt. Each time a student fails and repeats the examination his chances of passing are increased by 15%
Calculate the probability that a student in the college passes an examination at the second or at the third attempt.

answer
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K.C.S.E Mathematics Q & A - MODEL 2008PP2QN05

17/8/2020

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Form 3 Mathematics


The top of a table is a regular hexagon. Each side of the hexagon measures 50.0 cm. Find the maximum percentage error in calculating the perimeter of the top of the table.
answer
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K.C.S.E Mathematics Q & A - MODEL 2008PP2QN04

17/8/2020

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Form 3 Mathematics


​The position vectors of points A and B are;
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A point P divides AB in AB it he ratio 2:3. Find the position Vector of point P.
answer
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K.C.S.E Mathematics Q & A - MODEL 2008PP2QN03

17/8/2020

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Form 1 Mathematics


​Line AB given below is one side of triangle ABC. Using a ruler and a pair of compasses only;
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(i) Complete the triangle ABC such that BC=5cm and angle ABC=45
(ii) On the same diagram construct a circle touching sides AC,BA produced and BC produced.

answer
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K.C.S.E Mathematics Q & A - MODEL 2008PP2QN01

17/8/2020

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Form 2 Mathematics


In this question, show all the steps in your calculations, giving the answer each stage. Use logarithms correct to decimal places, to evaluate.
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answer
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K.C.S.E Mathematics Q & A - MODEL 2008PP1QN24

17/8/2020

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Form 4 Mathematics


The distance s metres from a fixed point O, covered by a particle after t seconds is given by the equation;
S =t3 -6t2 + 9t + 5.
 a) Calculate the gradient to the curve at t=0.5 seconds
b) Determine the values of s at the maximum and minimum turning points of the curve.
c) On the space provided, sketch the curve of s= t3-6t2+9t + 5.
answers
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K.C.S.E Mathematics Q & A - MODEL 2008PP1QN23

17/8/2020

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Form 3 Mathematics


A group of people planned to contribute equally towards a water project which needed Ksh 200 000 to complete, However, 40 members of the group without from the project.
As a result, each of the remaining members were to contribute Ksh 2500.
a) Find the original number of members in the group. 
b) Forty five percent of the value of the project was funded by Constituency Development Fund (CDF). Calculate the amount of contribution that would be made by each of the remaining members of the group. 
c) Member‟s contributions were in terms of labour provided and money contributed. If the ratio of the value of labour to the money contributed was 6:19; calculate the total amount of money contributed by the members.
answers
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K.C.S.E Mathematics Q & A - MODEL 2008PP1QN22

17/8/2020

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Form 2 Mathematics


The diagram below represents a conical vessel which stands vertically. The which stands vertically,. The vessels contains water to a depth of 30cm. The radius of the surface in the vessel is 21cm. (Take  π=22/7).
Picture
a) Calculate the volume of the water in the vessels in cm3
b) When a metal sphere is completely submerged in the water, the level of the water in the vessels rises by 6cm. Calculate:
 (i) The radius of the new water surface in the vessel;
 (ii) The volume of the metal sphere in cm3
(iii) The radius of the sphere.
answers
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