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KCSE MATHEMATICS QUESTIONS AND SOLUTIONS


Topically Analysed


Form 3
Form 2
Form 4
Form 1

2X]2 + 2y]2 - 6X + 10y + 9 = 0 is the equation of a circle.  Find the radius and the centre of the circle.

28/11/2021

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GRAPHICAL METHODS | Determining of the centre and radius of a circle | FORM 3 LEVEL | PAPER 2 QUESTIONS | SECTION A

2X² + 2y² - 6X + 10y + 9 = 0 is the equation of a circle.  Find the radius and the centre of the circle. (4mks)

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Given that P = QX]n make n the subject of the formula and simplify your answer.

28/11/2021

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FORMULAE AND VARIATIONS | Change of the subject | FORM 3 LEVEL | PAPER 2 QUESTIONS | SECTION A

​Given that P = QXⁿ make n the subject of the formula and simplify your answer.                     (3mks)

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Solve for θ in the equation sin (3θ+120) degrees

27/11/2021

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​Solve for θ in the equation sin (3 θ + 120)degrees

Picture

Worked Answer:

Solve for θ in the equation sin (3 θ + 120)degrees



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​The initial salary of Mr. Lutta is sh. 42, 000 per annum. His salary increases by 13% each year. Determine his total earnings after 15 years. Give your answer to the nearest thousands

26/11/2021

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​The initial salary of Mr. Lutta is sh. 42, 000 per annum. His salary increases by 13% each year. Determine his total earnings after 15 years. Give your answer to the nearest thousands.  (3mks)

​​Worked Answer:

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Find the value of a and b where a and b are ​rational numbers

26/11/2021

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Find the value of a and b where a and b are ​rational numbers.   (3mks)

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​Worked Answer:

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Solve the equation below.

26/11/2021

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Solve the equation below.  (3 marks)

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Worked Answer:

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Use logarithms correct to 4 decimal places to evaluate.

26/11/2021

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Use logarithms correct to 4 decimal places to evaluate. (3mks)

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Worked Answer:

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Given that y = 7 + 3x-x sqr, complete the table below

22/11/2021

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(a) Given that y = 7 + 3x-x², complete the table below.(2mks)

Picture

Worked Solution

Picture


Picture

(b) On the grid provided and using a suitable scale draw the graph of y = 7 + 3x-x². (2mks)

(c) On the same grid draw the straight line and use your graph to solve the equation x² - 4x– 3 = 0.    (3mks)

(d) Determine the coordinates of the turning point of the curve. (2mks)

Worked Solution:

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A man invests Ksh.24, 000 in an account which pays 16% interest p.a. the interest is compounded quarterly. Find the amount in the account after 1 and half years.

19/11/2021

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​A man invests Ksh.24, 000 in an account which pays 16% interest p.a. the interest is compounded quarterly. Find the amount in the account after 1½ years.                                              (3mks)

Worked Solution

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Evaluate the Simultaneous equations:

19/11/2021

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​Solve the simultaneous equations

​xy =  4
x + y = 5 

Worked Solution

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An arithmetic progression is such that the first term is -5, the last is 135 and the sum of progression is 975.

25/10/2021

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a) An arithmetic progression is such that the first term is -5, the last is 135 and the sum of progression is 975.

Calculate

i) The number of terms in the series (7mks)

ii) The common difference of the progression (2mks)

b) The sum of the first three terms of a geometric progression is 27 and the first term is 36. determine the common ratio and the value of the fourth term (4mks)



Worked Solution:

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Draw the graph of

25/10/2021

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​Draw the graph of 

Picture

b) Using a suitable line solve

2x2 – 3x – 50 = 0 (5mks)



Worked solution:

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A Kenyan tourist left Germany for Kenya through Switzerland. While in Switzerland he bought a watch worth 52 Deutsche marks. Find the value of the watch in:-

24/10/2021

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A Kenyan tourist left Germany for Kenya through Switzerland. While in Switzerland he bought a watch worth 52 Deutsche marks.

Find the value of the watch in:-

a) Swiss Francs
b) Kenya shillings (3mks)

Use the exchange rates below

1 Swiss Franc = 1.28 Deutsche marks
1 Swiss Franc = 45.21 Kenya shillings

Worked Answer:

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Given that Cos q = 5/13 and that 2700 £ q £ 3600, work out the value of Tan q + Sin q without using a calculator or mathematical tables.  (3mks)

24/10/2021

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Worked Answer

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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN23

24/9/2020

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Form 3 Mathematics


In the figure below, OA = a, OB = b and BX meets OY at C. OX:OA = 1:2 and BY:YA = 1:3.
Picture
(a) Express in terms of a and b: 
(ii) OY; 
(iii) BX. 
(b) Given that OC = hOY and BC = kBX, determine the values of h and k.
answers
Picture
Picture

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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN18

24/9/2020

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Form 3 Mathematics


Mbaka bought some plots at Ksh 400,000 each. The value of each plot appreciated at the rate of 10% per annum. 
(a) Calculate the value of a plot after 2 years. 
(b) After some time t, the value of a plot was Ksh 558,400. Find t, to the nearest month. 
(c) Mbaka sold all the plots he had bought after 4 years for Ksh2,928,200.
Find the percentage profit Mbaka made, correct to 2 decimal places.

answers
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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN16

24/9/2020

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Form 3 Mathematics


The length of a shadow' of a mast was measured at intervals of 1 hour and recorded as shown in the table below.
Picture
(a) On the grid provided, draw the graph of length against time.
Picture
(b) Determine the rate of change of the shadow’ length at = 2 
answers
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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN15

24/9/2020

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Form 3 Mathematics


Solve for x in log(7x—3) + 2 log 5 = 2 + log(x + 3).
answer
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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN13

24/9/2020

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Form 3 Mathematics


Picture
answer
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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN12

24/9/2020

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Form 3 Mathematics


The table below' shows income tax rates in a certain year.
Picture
In that year, mawira earned a salary of 41000 per month. calculate mawira's income tax per month given that a monthly tax relief of ksh 1162 was allowed 
answer
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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN08

24/9/2020

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Form 3 Mathematics


OAB is a Sector of a circle of radius r cm. Angle AOB = 60°.
Find, in its simplest form, an expression in terms of r and π for the perimeter of the sector.

Picture
answer
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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN06

24/9/2020

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Form 3 Mathematics


A bag contains 6 red counters and 4 blue counters. Two counters are picked from the bag at random, without replacement.
(a) Represent the events using a tree diagram. 
(b) Find the probability that the two counters picked are of the same colour.
answers
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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN04

24/9/2020

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Form 2 Mathematics


An arc of a circle subtends an angle of 150° at the circumference of the circle. Calculate the angle subtended by the same arc at the centre of the circle.
ANSWER
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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN03

23/9/2020

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Form 3 Mathematics


A quantity P varies inversely as the square of another quantity L.When P = 0.625, L = 4. Determine P when L= 0.2.
ANSWER
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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN01

23/9/2020

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Form 3 Mathematics


Simplify
Picture
Give the answer in the form a + b √c where a, b and c are integers.
ANSWER
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