Category: Similarity And Enlargement

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

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.

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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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).

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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)

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)

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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:

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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

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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

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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.

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

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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

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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

answer

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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

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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

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KCSE MATHEMATICS QUESTIONS AND SOLUTIONS

Topically Analysed

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.

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

​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. (3mks)

ANSWER

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:

Form 2 Mathematics

N.8

Form 2 Mathematics

14

Form 2 Mathematics

16

Form 2 Mathematics

23

Form 1 Mathematics

15

Form 2 Mathematics

16

Form 2 Mathematics

12

Form 2 Mathematics

23

​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

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.

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

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)

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)

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

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.