Edexcel IGCSE Maths
Topic questions Ratio, proportion and rates of change Similarity, lengths, areas and volumes
35 questions · 145 marks · about 3 hours
Also involves Percentages
R, S and T are three similar vases.
The volume of vase S is 72.8% more than the volume of vase R
The height of vase R is h cm The height of vase T is 6 h cm
The surface area of vase S is A cm2 The surface area of vase T is kA cm2
Work out the value of k
The diagram shows two similar quadrilaterals, ABCD and EFGH
AB = 5 cm BC = 4 cm CD = y cm
EF = x cm FG = 10 cm GH = 24 cm
Work out the value of x
Work out the value of y
ABD and ABC are right‑angled triangles.
AB = 16 cm BC = 12 cm AD = 1.5
AC
Find the length of CD Give your answer correct to 3 significant figures.
The diagram shows two triangles, ADE and CDB
ABD is a straight line.
AE = 28 cm ED = 45 cm AB = 21 cm CD = 35 cm
angle AED = angle CBD = 90°
Work out the area of triangle CDB Give your answer correct to 3 significant figures.
Also involves Ratio
The diagram shows two similar quadrilaterals, ABCD and EFGH
| AB = 5 cm | BC = 4 cm | CD = ycm |
| EF = xcm | FG = 10 cm | GH = 24 cm |
Work out the value of x
Work out the value of y
ABD and ABC are right‑angled triangles.
AB = 16 cm BC = 12 cm AD = 1.5
AC
Find the length of CD Give your answer correct to 3 significant figures.
Also involves Forming and solving equations
A and B are two similar solids.
The height of solid A is 31 cm The height of solid B is 18.6 cm
Given that
volume of solid A – volume of solid B = 735 cm³
find the volume of solid A
Here are two similar triangles.
Work out the value of x Show your working clearly.
Also involves Forming and solving equations
The diagram shows two similar vases, A and B
The height of vase A is 30 cm The height of vase B is 12 cm
Given that
surface area of vase A ‒ surface area of vase B = 178.5 cm²
find the surface area of vase A
Also involves Forming and solving equations
Solid A is similar to solid B
Here is some information about solid A and solid B
| solid A | solid B | |
| Height (cm) | 3x | |
| Area (cm2) | 7776 | 486 |
| Volume (cm3) | 8x | 2x+4 |
Work out the height of solid B Give your answer as a decimal.
The diagram shows triangle ABC and triangle ECD
ACD and EBC are straight lines.
AB = 10 cm AC = 8 cm EB = 5 cm CD = 14 cm ED = w cm
Work out the value of w Give your answer correct to one decimal place.
The diagram shows triangle ABC and triangle ECD
ACD and EBC are straight lines.
AB = 10 cm AC = 8 cm EB = 5 cm CD = 14 cm ED = w cm
Work out the value of w Give your answer correct to one decimal place.
Also involves Quadratic equations
Here is a frustum of a cone. The frustum is made by removing a small cone from a similar large cone.
The height of the large cone is 15 cm.
The radius of the base of the large cone is 6 cm. The radius of the base of the small cone is x cm. Given that the volume of the frustum is 
cm3 work out the value of x Show clear algebraic working.
ABCD and EFGH are similar quadrilaterals.
Work out the length of GH
Work out the length of BC
ABCD and EFGH are similar quadrilaterals.
Work out the length of GH
Work out the length of BC
A frustum is made by removing a small square-based pyramid from a similar large squared‑based pyramid as shown in the diagram.
The height of the small pyramid is 15 cm. The height of the large pyramid is 45 cm. The square base of the large pyramid has side length 39 cm.
Work out the total surface area of the frustum. Give your answer correct to the nearest whole number.
A statue and a model of the statue are mathematically similar.
The statue has a total surface area of 3600 cm2 The model has a total surface area of 625 cm2
The volume of the model is 750 cm3
Work out the volume of the statue.
Also involves Forming and solving equations
A and B are two similar vases.
The vases are such that
surface area of vase = B 
surface area of vase A
and that
volume of vase A – volume of vase B = 541.8 cm3
Calculate the volume of vase B
Also involves Percentages · Rounding
The diagram shows two similar metal statues.
The volume of statue B is 20% less than the volume of statue A
The surface area of statue B is k% less than the surface area of statue A
Work out the value of k Give your answer correct to 3 significant figures.
Also involves Algebraic notation and vocabulary · Forming and solving equations
The diagram shows a frustum of a cone, and a sphere.
The frustum, shown shaded in the diagram, is made by removing the small cone from the large cone. The small cone and the large cone are similar.
The height of the small cone is hcm and the radius of the base of the small cone is rcm. The height of the large cone is kh cm and the radius of the base of the large cone is kr cm. The radius of the sphere is r cm.
The sphere is divided into two hemispheres, each of radius rcm.
Solid A is formed by joining one of the hemispheres to the frustum. The plane face of the hemisphere coincides with the upper plane face of the frustum, as shown in the diagram below.
Solid B is formed by joining the other hemisphere to the small cone that was removed from the large cone. The plane face of the hemisphere coincides with the plane face of the base of the small cone, as shown in the diagram below.
The volume of solid A is 6 times the volume of solid B.
find an expression for h in terms of k and r
Also involves Forming and solving equations
A and B are two similar vases.
Vase A has height 10 cm. Vase B has height 15 cm.
The difference between the volume of vase A and the volume of vase B is 1197 cm3
Calculate the volume of vase A
Also involves Scale factors, scale diagrams and maps
Triangle ABC is similar to triangle PQR
AB = 4 cm PQ = 12 cm RQ = 16.5 cm AC = xcm PR = ycm
Calculate the length of BC
Write down an expression for y in terms of x
A and B are two similar solids.
A has a volume of 1836 cm3 B has a volume of 4352 cm3
B has a total surface area of 1120 cm2
Work out the total surface area of A.
The diagram shows five shaded shapes on a grid of squares.
Two of the shapes are congruent.
Write down the letters of these shapes.
On the square grid below, draw a shape that is similar to but is not congruent to shape B.
All of the shapes on the grid have 6 sides.
Write down the mathematical name for a shape that has 6 sides.
Here is a polygon with five sides.
Write down the mathematical name of a polygon with five sides.
Measure the size of the angle marked x.
Two sides of the polygon are parallel.
On the polygon, mark with arrows (>>) this pair of parallel lines.
Here are two triangles.
Triangle A
Triangle B
Are triangle A and triangle B similar triangles? You must give a reason for your answer.
R and S are two similar solid shapes.
Shape R has surface area 108 cm2 and volume 135 cm3 Shape S has surface area 300 cm2
Work out the volume of shape S.
Also involves Simplifying and manipulating expressions · Rearranging formulae
The diagram shows a frustum of a cone and a sphere.
The frustum is made by removing a small cone from a large cone. The cones are similar.
The height of the small cone is hcm. The height of the large cone is 2hcm. The radius of the base of the large cone is rcm.
The radius of the sphere is rcm.
Given that the volume of the frustum is equal to the volume of the sphere,
find an expression for r in terms of h. Give your expression in its simplest form.
Also involves Forming and solving equations · Ratio
The diagram shows two similar vases, A and B.
The height of vase A is 9 cm and the height of vase B is 13 cm.
Given that surface area of vase A + surface area of vase B = 1800 cm2
calculate the surface area of vase A.
A and B are two similar vases.
Vase A has height 24 cm. Vase B has height 36 cm.
Vase A has a surface area of 960 cm2
Work out the surface area of vase B.
Vase B has a volume of V cm3
Find in terms of V, an expression for the volume, in cm3, of vase A.
Also involves Converting between units
ABC and DEF are similar triangles.
Work out the length of DE.
The area of triangle DEF is 525 cm2
Find the area of triangle DEF in m2
ABC and DEF are similar triangles.
Work out the length of DF.
Work out the length of BC.
The diagram shows two similar bottles, A and B.
Bottle A has surface area 240 cm2 Bottle B has surface area 540 cm2 and volume 2025 cm3
Work out the volume of bottle A.
Also involves Algebraic notation and vocabulary
A frustum is made by removing a small cone from a large cone. The cones are mathematically similar.
The large cone has base radius U cm and height h cm.
Given that
find an expression, in terms of h, for the height of the frustum.
The diagram shows two cylinders, A and B.
Cylinder A has height 1.6 m and radius 0.56 m.
Work out the curved surface area of cylinder A. Give your answer in m2 correct to 3 significant figures.
Cylinder B is mathematically similar to cylinder A. The height of cylinder B is 0.6 m.
Work out the radius of cylinder B.
The diagram shows two cylinders, A and B.
Cylinder A has height 1.6 m and radius 0.56 m.
Work out the curved surface area of cylinder A. Give your answer in m2 correct to 3 significant figures.
Cylinder B is mathematically similar to cylinder A. The height of cylinder B is 0.6 m.
Work out the radius of cylinder B.
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