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KCSE MATHEMATICS QUESTIONS AND SOLUTIONS


Topically Analysed


Form 3
Form 2
Form 4
Form 1

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. 

Picture
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
Picture
Picture

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Draw the quadrilateral with vertices at A (-6,-1) B (-6,-4) C (3,-7) and D (3,2).

11/5/2023

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​Draw the quadrilateral with vertices at A (-6,-1) B (-6,-4) C (3,-7) and D (3,2). 

Picture
Picture

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The volume of two similar cans is 96cm³ and 1.5 litres.  If the total surface area of the smaller canis 144cm², determine the surface area of the larger can

29/4/2023

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​The volume of two similar cans is 96cm³ and 1.5 litres.  If the total surface area of the smaller can
is 144cm², determine the surface area of the larger can.                                                       (3mks)

ANSWER

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If the bucket above has a hole and 1.1 cm3 of water leaks out every 5 seconds and collects in a cylindrical can of base radius and height 10 cm and 25 cm respectively. Calculate how long it takes to fill the cylindrical can.   (4 marks)

27/12/2022

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The diagram below shows a bucket in the shape of a frustum of a cone with diameters 36 cm and 24 cm and a vertical height of 28 cm. The bucket contains water such that the diameter of the water surface is 30cm. Calculate the volume of the bucket.  (6 marks)
Picture
Picture
If the bucket above has a hole and 1.1 cm3 of water leaks out every 5 seconds and collects in a cylindrical can of base radius and height 10 cm and 25 cm respectively. Calculate how long it takes to fill the cylindrical can.   (4 marks)
Picture

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Two similar cans have different heights 8cm and other one 10cm. If the surface area of the larger can is 480cm3, find the surface area of the smaller can (3mks)

24/10/2021

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Two similar cans have different heights 8cm and other one 10cm. If the surface area of the larger can is 480cm3, find the surface area of the smaller can    (3mks)

Worked Answer:

Picture



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K.C.S.E Mathematics Q & A - MODEL 2005.PP2.QN.8

19/9/2020

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Form 2 Mathematics



The volumes of two similar solid cylinders are 4752 cm3 and 1408 cm3. If the area of the curved surface of the smaller cylinder is 352 cm2, find the area of the curved surface of the larger cylinder. ( 4 marks)
aNSWER
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K.C.S.E Mathematics Q & A - MODEL 2016PP1QN14

14/9/2020

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Form 2 Mathematics


A small cone of height 8cm is cut off from a bigger cone to leave a frustum of height 16cm. If. the volume of the smaller cone is 160cm3, find the volume of the frustum.
answer
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K.C.S.E Mathematics Q & A - MODEL 2014PP1QN16

7/9/2020

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Form 2 Mathematics


Points A(-2, 2) and B(-3, 7) are mapped onto Aʹ(4, -10) and Bʹ(0, 10) by an enlargement. Find the scale factor of the enlargement
answer
Picture

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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
Picture
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K.C.S.E Mathematics Q & A - MODEL 2002PP2QN015

29/8/2020

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Form 1 Mathematics



​In the diagram below, ABCD is a trapezium with AB parallel to DC. The diagonals AC and BD intersect at E.
Picture
  • a) Giving reasons show that triangle ABE is similar to triangle CDE.
  • b) Giving that AB = 3DC, find the ratio of DB to EB.
aNSWER
Picture

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K.C.S.E Mathematics Q & A - MODEL 2011PP1QN16

26/8/2020

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Form 2 Mathematics


A small cone of height 8 cm is cut off from a bigger cone to leave a frustum of height 16 cm, if the volume of the smaller cone is 160 cm3, find the
volume of the frustum
answers
Picture
Picture

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K.C.S.E Mathematics Q & A - MODEL 2006PP1QN12

9/8/2020

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Form 2 Mathematics


Two points P and Q have coordinates ( -2 ,3) and (1,3) respectively. A translation map point P to P" ( 10, 10)
(a) Find the coordinates of Q" the image of Q under the translation
Picture
answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 2000PP2QN23

14/7/2020

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Form 2 Mathematics




The diagram on the grid provided below shows a trapezium ABCD on the same grid.
  • (a)
    • (i) Draw the image A’B’C’D of ABCD under a rotation of 900 clockwise about the origin.
    • (ii) Draw the image of A”B”C”D” of A’B’C’D’ under a reflection in line y = x. State coordinates of A”B”C”D”.
  • (b) A”B”C”D” is the image of A”B”C”D under the reflection in the line x = 0. Draw the image A”B” C”D” and state its coordinates.
  • (c) Describe a single transformation that maps A” B”C”D onto ABCD.
Answer
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K.C.S.E Mathematics Q & A - MODEL 1998PP1QN23

7/6/2020

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​Use a ruler and a pair of compasses only for all constructions in this question

(a) On the line BC given below, construct triangle ABC such that ∠ABC = 300 and BA = 12 cm

  • (b) Construct a perpendicular from A to meet BC produced at D. Measure CD
  • (c) Construct  triangle A’B’C’ such that the area of triangle A’B’C is the three quarters of the area  of triangle ABC and on the same side  of BC as triangle ABC.
  • (d) Describe the lucus of A’
K.C.S.E Mathematics Q & A - MODEL 1998PP1QN23

ANSWER
K.C.S.E Mathematics Q & A - MODEL 1998PP1QN23
Picture
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K.C.S.E Mathematics Q & A-MODEL 1995PP1QN7

11/5/2020

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The ratio of the lengths of the corresponding sides of two similar rectangular water tanks is 3:5. The volume of the smaller tank is 8.1 m3. Calculate the volume of the larger tank.

3 MARKS
MARKING SCHEME
Picture
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