Edexcel IGCSE Math A Foundation 4.11 Similarity Questions

Practise using scale factors in similar shapes, from missing lengths and scale drawings to area and volume ratio problems.

Exam points

use linear scale factors from diagrams or maps to find lengths and real distances
convert linear scale factors to area or volume scale factors for similar solids
work backwards from surface area or volume information to find a missing value

Covered syllabus points

4.11.A Geometrical properties of similar figures 4.11.B Maps and scale drawings

[Maximum number: 4]

ABC and DEF are similar triangles.

Figure for Question 1 — Edexcel IGCSE Math A Foundation

(a)

Work out the length of DF.
cm

[ 2 ]

Scale examples:
$\frac{15}{6},\quad \frac{6}{15},\quad \frac{4.2}{6},\quad \frac{6}{4.2}$

Final answer:
10.5

Equivalent answers accepted.

(b)

Work out the length of BC.
cm

[ 2 ]

$19.5 \div 2.5$ or $19.5 \times 0.4$ oe or
$4.2 \times \frac{19.5}{(\mathrm{a})}$

M1; if using DF, follow through their answer from part (a).

Final answer:
7.8

A1 oe.

[Maximum number: 4]

Here is a scale drawing showing the positions of Paris and Bordeaux.

Figure for Question 2 — Edexcel IGCSE Math A Foundation

Alain drives from Paris to Bordeaux.
The distance that he drives is 590 km .
This distance is greater than the actual straight line distance between Paris and Bordeaux.

How much greater?
Show your working clearly.

Scale drawing measurement:
$6\text{ cm to }6.4\text{ cm}$

Straight-line distance:
$6\times80=480$
to
$6.4\times80=512$

Difference from $590\text{ km}$ :
590-512=78
to
590-480=110

Final answer:
$78\text{ to }110\text{ km}$

Working required.

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Covered syllabus points

Question 1

Question (a)

Question (b)

Question 2