Practise 28 exam-style questions on Scale factors, scale drawings and maps for Edexcel GCSE Maths (Non-calculator). Write your answer as you would in the exam and get it marked in seconds against the mark scheme, point by point, with an AI tutor on hand if you get stuck.
28 questions
1–5 marks each
Instant marking
No sign-up needed
20 questions, marked as you go
Sample questions with model answers
Here are 4 of the questions in this topic, each with a model answer, an explanation of why it earns the marks and the mark scheme an examiner would use.
Question 1
2 marks
A map has a scale of 1 : 25 000. On the map, two villages are 8 cm apart.
Work out the real distance between the two villages. Give your answer in kilometres.
Model answer
8 × 25 000 = 200 000 cm 200 000 cm = 2000 m = 2 km
Explanation
Multiply the map distance by the scale number to get the real distance in the same units (cm). Then divide by 100 000 to change centimetres to kilometres.
Mark scheme
1 mark
M1 for 8 × 25 000 (= 200 000 cm)
correct answer with no working scores full marks
1 mark
A1 for 2 (km)
cao
Question 2
2 marks
A photo measures 15 cm by 10 cm. The photo is enlarged so that the longer side is 24 cm.
Work out the length of the shorter side of the enlarged photo.
Model answer
Scale factor = 24 ÷ 15 = 1.6 Shorter side = 10 × 1.6 = 16 cm
Explanation
In an enlargement every length is multiplied by the same scale factor. Adding 9 cm to both sides is a common mistake: that changes the shape of the photo.
Mark scheme
1 mark
M1 for the scale factor 24 ÷ 15 (= 1.6)
or 10 × 24 ÷ 15; correct answer with no working scores full marks
1 mark
A1 for 16 (cm)
cao; 19 (adding 9 cm) scores 0
Question 3
3 marks
A rectangle has length \((x + 3)\) cm and width \(x\) cm. The rectangle is enlarged with scale factor 4. The perimeter of the enlarged rectangle is 88 cm.
Work out the value of \(x\).
Model answer
Perimeter of the original \(= 2(x + 3) + 2x = 4x + 6\) Every length is multiplied by 4, so the perimeter is multiplied by 4. \(4(4x + 6) = 88\) \(4x + 6 = 22\) \(4x = 16\) \(x = 4\)
Explanation
An enlargement multiplies every length by the scale factor, so the perimeter is multiplied by 4 too. Dividing 88 by 4 first gives the original perimeter, 22 cm, which leads to a simple equation.
Mark scheme
1 mark
M1 for the perimeter of the original, \(4x + 6\), or the sides of the enlargement, \(4x\) and \(4x + 12\)
or 88 ÷ 4 = 22; correct answer with no working scores full marks
1 mark
M1 for a correct equation, e.g. \(4(4x + 6) = 88\) or \(4x + 6 = 22\)
1 mark
A1 for \(x = 4\)
cao
Question 4
4 marks
A right-angled triangle has sides of length 5 cm, 12 cm and 13 cm. The triangle is enlarged so that the perimeter of the enlarged triangle is 75 cm.
Work out the area of the enlarged triangle.
Model answer
Original perimeter = 5 + 12 + 13 = 30 cm Scale factor = 75 ÷ 30 = 2.5 Shorter sides of the enlarged triangle: 5 × 2.5 = 12.5 cm and 12 × 2.5 = 30 cm Area = \(\dfrac{1}{2} \times 12.5 \times 30 = 187.5\) cm²
Explanation
The perimeter is a length, so it scales by the length scale factor, 2.5. The right angle is between the 5 cm and 12 cm sides, so these give the base and height. Multiplying the original area by 2.5 is wrong: area scales by \(2.5^2 = 6.25\).
Mark scheme
1 mark
P1 for the perimeter of the original, 5 + 12 + 13 = 30 cm
correct answer with no working scores full marks
1 mark
P1 for the scale factor, 75 ÷ 30 = 2.5
1 mark
P1 for the shorter sides of the enlarged triangle, 12.5 cm and 30 cm, or for the original area 30 cm² multiplied by \(2.5^2\)
1 mark
A1 for 187.5 (cm²)
cao; 75 (area × 2.5) scores P1 P1 P0 A0
Ready to try the rest? Every answer you write is marked against the mark scheme, so you can see exactly where the marks are.
Ctrl + Enter to check
AI TutorHints first, answers after you try
Hi! Stuck? Ask me for a hint and I’ll help you work it out. Once you’ve checked your answer I can explain exactly where the marks are.
