AQA•GCSE•Mathematics•Ratio, Proportion & Rates of Change
Scale factors
AQA GCSE Mathematics practice questions with step-by-step solutions
Start Practicing Now
Generate unlimited Scale factors questions. Choose your difficulty level, get instant feedback, and master this topic.
Unlimited questionsDetailed solutionsAQA exam style
Sample Questions
Try before you startPreview AQA GCSE style questions on Scale factors. Click "Show Solution" to see the step-by-step answer.
EasyQuestion 1
[2 marks]A shape is enlarged by scale factor 3. If the original length is 4 cm, what is the new length?
Solution for Question 1
MediumQuestion 2
[3 marks]Two similar triangles have corresponding sides 5 cm and 8 cm. The area of the smaller triangle is 15 cm². Find the area of the larger triangle.
Solution for Question 2
HardQuestion 3
[4 marks]Two similar cylinders have volumes in the ratio 8:27. The height of the smaller cylinder is 4 cm. Find the height of the larger cylinder.
Solution for Question 3
Want more questions like these?
Generate Unlimited QuestionsAbout Scale factors in AQA GCSE
A scale factor describes how many times larger (or smaller) one shape is compared to another. It is the ratio of corresponding lengths in similar shapes.
Scale factor = new length ÷ original length. A scale factor greater than 1 means enlargement; less than 1 means reduction; equal to 1 means same size.
For similar shapes, all corresponding lengths have the same scale factor. If the scale factor of lengths is k, then: the scale factor of areas is k², the scale factor of volumes is k³.
Map scales can be written as ratios like 1:50000, meaning 1 cm on the map represents 50000 cm (500 m) in real life. Or as "1 cm represents 2 km".
To find actual distance from a map: measure the map distance and multiply by the scale. To find map distance from actual: divide the actual distance by the scale.
What you'll practice
Exam-style questions matching the AQA specification, from basic to challenging
How it works
AI generates unique questions each time, with full worked solutions and mark schemes