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KCSE MATHEMATICS QUESTIONS AND SOLUTIONS


Topically Analysed


Form 3
Form 2
Form 4
Form 1

The sum of the interior angles of a regular polygon is 1260°. Find the size of each exterior angle of the polygon. (3 marks)

22/5/2023

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​The sum of the interior angles of a regular polygon is 1260°. Find the size of each exterior angle of the polygon. (3 marks)

​KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 7
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The figure below shows solid frustum of a pyramid with a square top of side 6cm and a square base of side 10cm. The slant edge of the frustum is 8cm.

13/5/2023

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The figure below shows solid frustum of a pyramid with a square top of side 6cm and a square base of side 10cm. The slant edge of the frustum is 8cm. 

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a) Calculate the total surface area of the frustum (4mks) 
b) Calculate the volume of the solid frustum. (3mks) 
c) Calculate the angle between the planes BCHG and the base EFGH. (3mks
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Four interior angles of a hexagon are 100, 140, 125 and 105. The fifth interior angle is four times the sixth. Find, in degrees the fifth interior angle. (3mks)

11/5/2023

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​Four interior angles of a hexagon are 100, 140, 125 and 105. The fifth interior angle is four times the sixth. Find, in degrees the fifth interior angle. (3mks)

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The figure below is a right pyramid of rectangular base of length 12cm and width 9cm.  The slanting edge has a length of 19.5cm.

29/4/2023

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​The figure below is a right pyramid of rectangular base of length 12cm and width 9cm.  
The slanting edge has a length of 19.5cm.

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​ANSWER

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THE FIGURE BELOW SHOWS A RECTANGULAR BASED RIGHT PYRAMID, USE IT TO ANSWERS QUESTIONS THAT FOLLOW:

2/1/2023

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The interior angles of a hexagon are 2x + 5, 4x - 5, 4x + 5, 3x, 4x - 20 and 2x. Find the value of x.

21/11/2021

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The interior angles of a hexagon are 2x + 5, 4x - 5, 4x + 5, 3x, 4x - 20 and 2x. Find the value of x.    (3mks)


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​The exterior angle of regular polygon is an eighth of the interior angle. How many sides does the regular polygon have?

24/10/2021

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​The exterior angle of regular polygon is an eighth of the interior angle. How many sides does the regular polygon have? (3mks)

Worked Answer:

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K.C.S.E Mathematics Q & A - MODEL 2018PP1QN21

20/9/2020

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Form 2 Mathematics


The figure below shows two triangles, ABC and BCD with a common base BC = 3.4 cm. AC = 7.2 cm, CD = 7.5 cm and ABC = 90°.
The area of triangle ABC = Area of triangle ∠BCD.
Picture
Calculate, correct to one decimal place:
(a) the area of triangle ABC;
(b) the size of ∠BCD; 
(c) the length of BD;
(d) the size of ∠BDC.
answers
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K.C.S.E Mathematics Q & A - MODEL 2005.PP1.QN.5

17/9/2020

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Form 1 Mathematics



The size of each interior angle of a regular polygon is five times the size of the exterior angle. Find the number of sides of the polygon.

Answer
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K.C.S.E Mathematics Q & A - MODEL 2004.PP2.QN.24

16/9/2020

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Form 2 Mathematics



The figure below shows a model of a roof with a rectangular base PQRS PQ = 32 cm and QR = 14 cm. The ridge XY = 12 cm and is centrally placed. The faces PSX and QRY are equilateral triangles M is the midpoint of QR.

Picture

Calculate 

(a) 

(i) the length of YM 

(ii) The height of Y above the base PQRS 

(b) The angle between the planes RSXY and PQRS 

(c) The acute angle between the lines XY and QS

Answer
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K.C.S.E Mathematics Q & A - MODEL 2017PP1QN05

15/9/2020

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Form 1 Mathematics


Given that the exterior angle of a regular hexagon is x. find the size of each interior angle of the hexagon.
answer
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K.C.S.E Mathematics Q & A - MODEL 2015PP1QN09

10/9/2020

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Form 2 Mathematics


The sum of interior angles of a regular polygon is 24 times the size of the exterior angle.
(a) Find the number of sides of the polygon. 
(b) Name the polygon
answer
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K.C.S.E Mathematics Q & A - MODEL 2015PP1QN05

9/9/2020

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Form 2 Mathematics


A piece of wire is bent into the shape of an isosceles triangle. The base angles are each 48° and the perpendicular height to the base is 6 cm. Calculate,
correct to one decimal place, the length of the wire.
answer
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K.C.S.E Mathematics Q & A - MODEL 2004.PP1.QN.2

9/9/2020

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Form 1 Mathematics



The size of an interior angle of a regular polygon is 1560.Find the number of sides of the polygon.
Answer
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K.C.S.E Mathematics Q & A - MODEL 2014PP2QN18

8/9/2020

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Form 3 Mathematics


In the figure below OS is the radius of the circle centre O. Chords SQ and TU are extended to meet at P and OR is perpendicular to QS at R. OS = 61cm, PU=50cm, UT=40cm and PQ =30cm.
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a) Calculate the lengths of:
i) QS: 
ii) OR
c) Calculate, correct to 1 decimal place:
i)The size of angle ROS: 
ii) The length of the minor arc QS.
answers
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K.C.S.E Mathematics Q & A - MODEL 2014PP1QN10

7/9/2020

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Form 1 Mathematics


The sum of interior angles of a regular polygon is 18000. Find the size of each exterior angle
answer
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K.C.S.E Mathematics Q & A - MODEL 2014PP1QN07

7/9/2020

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Form 2 Mathematics


The area of a sector of a circle, radius 2.1cm, is 2.31cm^2. The arc of the sector subtends an angle θ, at the centre of the circle. Find the value of θ in radians to
2 correct decimal places
answer
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K.C.S.E Mathematics Q & A - MODEL 2013PP1QN13

2/9/2020

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Form 2 Mathematics


A triangle ABC is such that AB = 5 cm, BC = 6 cm and AC = 7 cm.
a) Calculate the size of angle ACB, correct to 2 decimal places. 
b) A perpendicular drawn from A meets BC at N. calculate the length AN correct to one decimal place.
answer
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K.C.S.E Mathematics Q & A - MODEL 2013PP1QN11

2/9/2020

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Form 1 Mathematics


The interior angles of an octagon are 2x,1/2?, (x + 40)0, 1100, 1350, 1600, (2x + 10)0 and 1850.
Find the value of x.
answer
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K.C.S.E Mathematics Q & A - MODEL 2012PP1QN24

31/8/2020

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Form 2 Mathematics


In the figure below, PQ is parallel to RS. The lines PS and RQ intersect at T. RQ = 10 cm, RT:TQ = 3:2, angle PQT = 40° and angle RTS - 80°.
Picture
(a) Find the length of RT.
(b) Determine, correct to 2 significant figures:
(i) the perpendicular distance between PQ and RS; 
(ii) the length of TS. 
(c) Using the cosine rule, find the length of RS correct to 2 significant figures. 
(d) Calculate, correct to one decimal place, the area of triangle RST.
answers
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K.C.S.E Mathematics Q & A - MODEL 2009PP1QN17

19/8/2020

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Form 2 Mathematics


In the figure below (not drawn to scale), AB = 8cm, AC= 6cm, AD= 7cm, CD= 2.82 cm and angle CAB =500
Picture
Calculate, to 2 decimal places
a) The length BC, 
b) The size of angle ABC, 
c) The size of angle CAD, 
d) The area of triangle ACD
b) Express vector NM in terms of OB
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OP = OM + 2 MN, find the coordinates of P.
answers
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K.C.S.E Mathematics Q & A - MODEL 2009PP1QN10

19/8/2020

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Form 2 Mathematics


The size of an interior angle of a regular polygon is 6 ½ times that of its exterior angle determine the number of sides of the polygon.
answer
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K.C.S.E Mathematics Q & A - MODEL 2009PP1QN06

19/8/2020

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Form 2 Mathematics


The figure below represents a plot of land ABCD such that AB = 85 m, BC =75 m , CD = 60 m DA = 50m and angle ABC = 900
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Determine the area of the plot in hectares correct to two decimal places
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 2007PP1QN10

12/8/2020

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Form 2 Mathematics


In the figure below <A = 620, <B = 410, BC = 8.4 cm and CN is the bisector of < ACB.

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Calculate the length of CN to 1 decimal place.
answer
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