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Scale drawings Quiz

Grade 3 • 3L • 10 Questions (30 Marks)

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Score: 0 / 10
Scale drawings — Notes & Worked Examples Show / Hide

Explanation:

A scale drawing shows a real object reduced in size using a fixed ratio. A scale may be given with units (e.g. 1 cm represents 5 m) or as a unitless ratio (e.g. 1 : 500, which means 1 cm on the drawing = 500 cm in real life).

To find a real-life length, measure the drawing length in cm and multiply by the scale. To find a drawing length, divide the real-life length by the scale (converting to matching units first if needed).

Example 1: A map has a scale of 1 : 25,000. Two villages are 6 cm apart on the map. Find the real distance in km.

N Scale 1 : 25,000 Village A Village B 6 cm
Real distance = 6 × 25,000 = 150,000 cm
150,000 ÷ 100 = 1500 m = 1.5 km

Example 2: A plan uses a scale of 2 cm to 5 m. A rectangular garden is 17.5 m long by 10 m wide. Find its length on the plan.

Garden Plan 4 cm (10 m) ? cm (17.5 m) 2 cm = 5 m
Scale for 1 cm: 5 m ÷ 2 = 2.5 m per 1 cm
Plan length = 17.5 ÷ 2.5 = 7 cm
Question 1
[1 mark]
Scale: 1 cm = 50 m
How many metres is 5 cm?
m
Worked Solution & Answer
5 × 50 = 250 m B1
Answer: 250 m m
Question 2
[1 mark]
A map has a scale of 1 : 100,000
Two towns are 8cm apart on the map
Find the real distance in km
km
Worked Solution & Answer
Multiply the map/diagram measurement by the scale factor to find the real-life distance, then convert units if needed (1 m = 100 cm, 1 km = 1000 m).
8 km
Answer: 8 km km
Question 3 AQA Jun 2022 2F Q15
[3 marks]
The scale drawing shows a tree and a student.
The tree has drawn height 7 cm.
The student has drawn height 2.5 cm.
7 cm2.5 cm
The actual height of the tree is 4.2 metres.
Work out the actual height of the student.
Answer m
Worked Solution & Answer
Scale factor: 7 cm = 4.2 m ⇒ 1 cm = 4.2 ÷ 7 = 0.6 m M2
Actual height of student = 2.5 × 0.6 = 1.5 m. A1
7 cm2.5 cmScale: 7 cm = 4.2 m (0.6 m/cm) → Student = 1.5 m
Answer: Answer 1.5 m
Question Paper (PDF) • Mark Scheme (PDF)
Question 4 AQA Nov 2022 3F Q17
[3 marks]
This scale drawing of a bus has length 8 cm
Scale: 1 cm represents 1.65 m
8 cmScale: 1 cm represents 1.65 m
Work out the actual length of the car.
Give your answer in metres, to the nearest centimetre.
The actual length of the bus is 3.8 times the actual length of a car.
Answer metres
Worked Solution & Answer
Actual length of bus = 8 × 1.65 = 13.2 m M1
Actual length of car = 13.23.8 ≈ 3.47368 m M1
To the nearest centimetre (2 d.p.): 3.47 metres A1
8 cmScale: 1 cm represents 1.65 mBus = 8 × 1.65 = 13.2 m; Car = 13.2 / 3.8 = 3.47 m
Answer: Answer 3.47 metres
Question Paper (PDF) • Mark Scheme (PDF)
Question 5 AQA Nov 2020 2F Q19
[3 marks]
A scale drawing shows the positions of P, Q and R.
Not drawnaccuratelyP×Q×R×
Work out the scale.
On the scale drawing
PQ = 4 cm   QR = 6.5 cm
The actual distance PQ is 50 metres less than the actual distance QR.
1 cm represents metres
Worked Solution & Answer
Difference on drawing = 6.5 - 4 = 2.5 cm M1
Difference in actual distance = 50 metres M1
2.5 cm = 50 m ⇒ 1 cm = 50 ÷ 2.5 = 20 m A1
Not drawnaccuratelyP×Q×R×6.5 - 4 = 2.5 cm = 50 m → 1 cm = 20 m
Answer: 1 cm represents 20 metres
Question Paper (PDF) • Mark Scheme (PDF)
Question 6 AQA Nov 2018 3F Q6
[3 marks]
Here is a plan of a flat with four rectangular rooms.
Not drawnaccuratelyBathroomBedroomKitchenLiving room8 feet12 feet6 feet10 feet8 feet14 feet
On the grid on the opposite page, make an accurate scale drawing of the plan.
Label each room.
Use a scale of 1 cm represents 2 feet
Worked Solution & Answer
Divide each dimension by 2: M1
Bathroom: 8 ft ÷ 2 = 4 cm, 6 ft ÷ 2 = 3 cm
Bedroom: 8 ft ÷ 2 = 4 cm, 10 ft ÷ 2 = 5 cm M1
Kitchen: 12 ft ÷ 2 = 6 cm, 8 ft ÷ 2 = 4 cm
Living room: 12 ft ÷ 2 = 6 cm, 14 ft ÷ 2 = 7 cm A1
Not drawnaccuratelyBathroomBedroomKitchenLiving room8 feet12 feet6 feet10 feet8 feet14 feetScale: 1 cm represents 2 feet (Bath: 4×3 cm, Bed: 4×5 cm, Kit: 6×4 cm, Living: 6×7 cm)
Answer: Bathroom 4×3 cm, Bedroom 4×5 cm, Kitchen 6×4 cm, Living room 6×7 cm
Question Paper (PDF) • Mark Scheme (PDF)
Question 7 AQA Jun 2025 2F Q3
[3 marks]
A path joins points A, B, and C.
The scale drawing shows the path on a centimetre grid.
Scale: 1 centimetre represents 10 metres
NorthABC
(a) Write down the direction of B from A. [1 mark]
Answer
(b) Work out the actual distance along the path from A to C. [2 marks]
Answer metres
Worked Solution & Answer
(a)
From A to B is directly to the right, which is East B1
Answer (a): Answer East
(b)
Distance A to B = 4 cm = 40 m M1
Distance B to C = 3 cm = 30 m
Total distance along path = 40 + 30 = 70 m A1
Answer (b): Answer 70 metres
Question Paper (PDF) • Mark Scheme (PDF)
Question 8 IGCSE Jan 2023 1F Q8
[4 marks]
Here is a scale drawing showing the positions of Paris and Bordeaux.
Scale: 1 cm represents 80 kmParisBordeaux(6.2 cm)
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.
km
Worked Solution & Answer
Map distance between Paris and Bordeaux = 6.2 cm (or 6.0–6.4 cm) M2
Actual straight line distance = 6.2 × 80 = 496 km (or 480–512 km) M1
Difference = 590 − 496 = 94 km (or 78–110 km). A1
Answer: 94 km
Question Paper (PDF) • Mark Scheme (PDF)
Question 9 AQA Nov 2021 2F Q20
[4 marks]
(a) Point B is 400 metres north east of point A.
Mark point B on the centimetre grid.
Use a scale of 1 centimetre represents 100 metres.
20 (b) Points C and D are shown on a different centimetre grid.
Scale: 1 : 1000
Work out the bearing of D from C.
20 (c) Work out the actual distance, in metres, of D from C.
Use the scale 1 : 1000
(a) Point B is 400 metres north east of point A.
Mark point B on the centimetre grid.
Use a scale of 1 centimetre represents 100 metres. [2 marks]
NA
(b) Points C and D are shown on a different centimetre grid.
Scale: 1 : 1000
Work out the bearing of D from C. [1 mark]
Scale: 1 : 1000NCD
Answer °
(c) Work out the actual distance, in metres, of D from C.
Use the scale 1 : 1000 [1 mark]
Answer metres
Worked Solution & Answer
(a)
Scale: 1 cm = 100 m, so 400 m = 4 cm M1
North-East is at bearing 045°. A1
NAB
Answer (a): Point B marked 4 cm from A on bearing 045°
(b)
Point D is directly south of point C, so the bearing is 180°. B1
Answer (b): Answer 180 °
(c)
Grid distance CD = 4 cm
Actual distance = 4 × 1000 cm = 4000 cm = 40 metres. B1
Answer (c): Answer 40 metres
Question Paper (PDF) • Mark Scheme (PDF)
Question 10
[5 marks]
The diagram shows a scale drawing of a tennis court.
The scale of the drawing is 1 : 200
Work out the perimeter of the real tennis court.
Give your answer in metres.
metres
Worked Solution & Answer
Drawing dimensions: length = 11.5 cm, width = 5.8 cm M2
Real length = 11.5 × 200 = 2300 cm = 23 m M1
Real width = 5.8 × 200 = 1160 cm = 11.6 m M1
Perimeter = 2 × (23 + 11.6) = 69.2 m A1
Answer: 69.2 metres
Question Paper (PDF) • Mark Scheme (PDF)
Score: 0 / 10 (0 / 30 marks)
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Grade 3 Quizzes

24 Topics
3A - Error intervals3B - Operations with fractions
3C - Estimation3D - Writing and simplifying ratio
3E - Ratio3F - Proportion recipes
3G - Percentages3H - Percentage change
3J - Exchange rates3K - Conversions and units
3L - Scale drawings3M - Best buy questions
3N - Substitution3P - Solving linear equations
3Q - Straight line graphs3R - Area and circumference
3S - Rotations3T - Reflections
3U - Enlargements3V - Translations
3W - Mixed transformations3X - Area of compound shapes
3Y - Frequency trees3Z - Two way tables