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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 2007PP2QN24

13/8/2020

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Form 3 Mathematics


Two bags A and B contain identical balls except for the colours. Bag A contains 4 red balls and 2 yellow balls. Bag B contains 2 red balls and 3 yellow balls.
(a) If a ball is drawn at random from each bag, find the probability that both balls are of the same colour. 
(b) If two balls are drawn at random from each bag, one at a time without replacement, find the probability that:
(i) The two balls drawn from bag A or bag B are red 
(ii) All the four balls drawn are red

answers
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K.C.S.E Mathematics Q & A - MODEL 2007PP2QN23

13/8/2020

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Form 4 Mathematics


The table below shows the values of the length X ( in metres ) of a pendulum and the corresponding values of the period T ( in seconds) of its oscillations obtained in an experiment.
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(a) Construct a table of values of log X and corresponding values of log T,
correcting each value to 2 decimal places 
(b) Given that the relation between the values of log X and log T approximate to a linear law of the form m log X + log a where a and b are constants
(i) Use the axes on the grid provided to draw the line of best fit for the graph of log T against log X.
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(ii) Use the graph to estimate the values of a and b 
(b) Find, to decimal places the length of the pendulum whose period is 1 second
answers
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K.C.S.E Mathematics Q & A - MODEL 2007PP2QN22

13/8/2020

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Form 4 Mathematics


A company is considering installing two types of machines. A and B. The information about each type of machine is given in the table below.
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The company decided to install x machines of types A and y machines of type B(a) Write down the inequalities that express the following conditions
I. The number of operators available is 40
 II. The floor space available is 80m2
 III. The company is to install not less than 3 type of A machine
 IV. The number of type B machines must be more than one third the number of type A machines
 (b) On the grid provided, draw the inequalities in part ( a) above and shade the unwanted region
 (c) Draw a search line and use it to determine the number of machines of each type that should be installed to maximize the daily profit.
answers
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K.C.S.E Mathematics Q & A - MODEL 2007PP2QN21

13/8/2020

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Form 3 Mathematics


In this question use a ruler and a pair of compasses only
In the figure below, AB and PQ are straight lines
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(a) Use the figure to:
(i) Find a point R on AB such that R is equidistant from P and Q 
(ii) Complete a polygon PQRST with AB as its line of symmetry and hence measure the distance of R from TS. 
(b) Shade the region within the polygon in which a variable point X must lie given that X satisfies the following conditions
I: X is nearer to PT than to PQ
II: RX is not more than 4.5 cm
III. angle PXT > 90
answers
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K.C.S.E Mathematics Q & A - MODEL 2007PP2QN20

13/8/2020

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Form 3 Mathematics


The gradient function of a curve is given by the expression 2x + 1. If the curve passes through the point ( -4, 6);
(a) Find:
(i) The equation of the curve 
(ii) The vales of x, at which the curve cuts the x- axis 
(b) Determine the area enclosed by the curve and the x- axis
ANSWERS
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K.C.S.E Mathematics Q & A - MODEL 2007PP2QN18

13/8/2020

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Form 3 Mathematics


Given that y is inversely proportional to xn and k as the constant of proportionality;
(a) (i) Write down a formula connecting y, x, n and k
(ii) If x = 2 when y = 12 and x = 4 when y = 3, write down two expressions for k in terms of n. Hence, find the value of n and k.
(b) Using the value of n obtained in (a) (ii) above, find y when x = 5 1/3
answers
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K.C.S.E Mathematics Q & A - MODEL 2007PP2QN17

13/8/2020

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Form 1 Mathematics


A tank has two inlet taps P and Q and an outlet tap R. when empty, the tank can be filled by tap P alone in 4 ½ hours or by tap Q alone in 3 hours. When full, the tank can be emptied in 2 hours by tap R.
(a) The tank is initially empty. Find how long it would take to fill up the tank
(i) If tap R is closed and taps P and Q are opened at the same time 
(ii) If all the three taps are opened at the same time
(b) The tank is initially empty and the three taps are opened as follows
P at 8.00 a.m
Q at 8.45 a.m
R at 9.00 a.m
(i) Find the fraction of the tank that would be filled by 9.00 a.m
(ii) Find the time the tank would be fully filled up

answers
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K.C.S.E Mathematics Q & A - MODEL 2007PP2QN16

13/8/2020

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Form 3 Mathematics


Find the radius and the coordinate of the centre of the circle whose equation is 2x2 + 2y2 – 3x + 2y + ½ = 0
answer
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K.C.S.E Mathematics Q & A - MODEL 2007PP2QN15

13/8/2020

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Form 3 Mathematics


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answer
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K.C.S.E Mathematics Q & A - MODEL 2007PP2QN14

13/8/2020

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Form 3 Mathematics


The figure below is a sketch of the graph of the quadratic function y = k
( x+1) (x-2)
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Find the value of k
answer
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K.C.S.E Mathematics Q & A - MODEL 2007PP2QN13

13/8/2020

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Form 4 Mathematics


Two places A and B are on the same circle of latitude north of the equator. The longitude of A is 1180W and the longitude of B is 1330E. The shorter distance between A and B measured along the circle of latitude is 5422 nautical miles.Find, to the nearest degree, the latitude on which A and B lie
answer
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K.C.S.E Mathematics Q & A - MODEL 2007PP2QN12

13/8/2020

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Form 2 Mathematics


Vector q has a magnitude of 7 and is parallel to vector p. Given that
p= 3 i –j + 1 ½ k, express vector q in terms of I, j, and k.
answer
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K.C.S.E Mathematics Q & A - MODEL 2007PP2QN11

13/8/2020

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Form 3 Mathematics


In the figure below AB is a diameter of the circle. Chord PQ intersects AB at N. A tangent to the circle at B meets PQ produced at R.
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Given that PN = 14cm, NB = 4 cm and BR = 7.5 cm, calculate the length of:
(a) NR 
(b) AN
answer
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K.C.S.E Mathematics Q & A - MODEL 2007PP2QN10

13/8/2020

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Form 1 Mathematics


A carpenter wishes to make a ladder with 15 cross- pieces. The cross- pieces are to diminish uniformly in length from 67 cm at the bottom to 32 cm at the top.
Calculate the length in cm, of the seventh cross- piece from the bottom
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K.C.S.E Mathematics Q & A - MODEL 2007PP2QN09

13/8/2020

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Form 2 Mathematics


Water and milk are mixed such that the ratio of the volume of water to that of milk is 4: 1. Taking the density of water as 1 g/cm3 and that of milk as 1.2g/cm3, find the mass in grams of 2.5 litres of the mixture.
answer
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K.C.S.E Mathematics Q & A - MODEL 2007PP2QN08

13/8/2020

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Form 3 Mathematics


A rectangular block has a square base whose side is exactly 8 cm. Its height measured to the nearest millimeter is 3.1 cm
Find in cubic centimeters, the greatest possible error in calculating its volume.
answer
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K.C.S.E Mathematics Q & A - MODEL 2007PP2QN07

13/8/2020

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Form 2 Mathematics


Find the equation of a straight line which is equidistant from the points ( 2,3) and ( 6, 1), expressing it in the form ax + by = c where a, b and c are constants
answer
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K.C.S.E Mathematics Q & A - MODEL 2007PP2QN06

13/8/2020

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Form 1 Mathematics


The cash price of a T.V set is Kshs 13, 800. A customer opts to buy the set on Hire purchase terms by paying a deposit of Kshs 2, 280
If simple interest of 20% p.a is charged on the balance and the customer is required to repay by 24 equal monthly installments, calculate the amount of each installment.
answer
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​Related Questions and Answers on Commercial Arithmetic I

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K.C.S.E Mathematics Q & A - MODEL 2007PP2QN05

12/8/2020

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Form 4 Mathematics


A particle moves in a straight line through a point P. Its velocity v m/s is given by v= 2 -1, where t is time in seconds, after passing P. The distance s of the particle from P when t = 2 is 5 metres. Find the expression for s in terms of t.
answer
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K.C.S.E Mathematics Q & A - MODEL 2007PP2QN04

12/8/2020

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Form 3 Mathematics


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answer
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K.C.S.E Mathematics Q & A - MODEL 2007PP2QN03

12/8/2020

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Form 2 Mathematics


Solve the equation 3 cos x = 2 sin2 x, where 00 ≤ x ≤ 3600
answer
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K.C.S.E Mathematics Q & A - MODEL 2007PP2QN02

12/8/2020

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Form 3 Mathematics


Given that;
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​express x in terms of y and z
answer
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K.C.S.E Mathematics Q & A - MODEL 2007PP2QN01

12/8/2020

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Form 2 Mathematics


Using logarithm tables, evaluate
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answer
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K.C.S.E Mathematics Q & A - MODEL 2007PP1QN24

12/8/2020

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Form 4 Mathematics


The diagram on the grid below represents as extract of a survey map showing two adjacent plots belonging to Kazungu and Ndoe.
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The two dispute the common boundary with each claiming boundary along different smooth curves coordinates ( x, y) and (x, y2) in the table below, represents points on the boundaries as claimed by Kazungu Ndoe respectively.
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(a) On the grid provided above draw and label the boundaries as claimed by Kazungu and Ndoe
answers
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K.C.S.E Mathematics Q & A - MODEL 2007PP1QN23

12/8/2020

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Form 4 Mathematics


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(b) In a certain week a businessman bought 36 bicycles and 32 radios for total of Kshs 227 280. In the following week, he bought 28 bicycles and 24 radios for a total of Kshs 174 960
Using matrix method, find the price of each bicycle and each radio that he bought
(c) In the third week, the price of each bicycle was reduced by 10% while the price of each radio was raised by 10%. The businessman bought as many bicycles and as many radios as he had bought in the first two weeks.
Find by matrix method, the total cost of the bicycles and radios that the businessman bought in the third week.

answers
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