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Scale drawings

Free Printable Scale drawings PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 3)

Download free scale drawings worksheets (PDF), GCSE maths past paper questions and worked solutions for Scale drawings (3L). This is a Grade 3 geometry topic from the GCSE questions by topic collection for Foundation and Higher tier GCSE Maths (Edexcel, AQA, OCR and IGCSE).

The free PDF worksheets table below brings together printable question booklets (Qs) and worked answers or mark schemes (Ans) from Maths Genie, Corbett Maths, Maths DIY, Maths Takeaway, Dr Austin, E Classroom and PMT, along with past paper question booklets.

Below the worksheet links you can read our scale drawings revision notes and worked examples with diagrams, try real GCSE past paper scale drawings questions with step-by-step solutions, or download a PDF of all scale drawings worksheet links.

Free Scale drawings PDF Worksheets & Answers

Grade 3 • Topic 3L
Resource Questions Answers
GCSE past paper questions & solutions
 Qs Ans
Graded exam questions & solutions
 Qs Ans
Practice Questions & answers
 Qs Ans
Exam-style booklet & solutions
 Qs Ans
GCSE Maths Takeaway exam questions
 Qs Ans
Practice grid / worksheet & answers
 Qs Ans
GCSE topic booklet & answers
 Qs Ans
PMT (Edxl)
Edexcel GCSE topic questions & solutions
 Qs Ans
PMT (AQA)
AQA GCSE topic questions & solutions
 Qs Ans
PMT (IGCSE)
Edexcel IGCSE topic questions & solutions
 Qs Ans
Interactive online lesson & practice
 Page
Grade 3 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
GCSE Maths Grade 3 Revision Notes & Method

Guide to Scale drawings: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

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
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Scale drawings Questions & Answers

Past Paper Example 1 AQA Jun 2022 2F Q15 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
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.
Worked Solution & Mark Scheme (3 marks)
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
Past Paper Example 2 AQA Nov 2022 3F Q17 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
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.
Worked Solution & Mark Scheme (3 marks)
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
Past Paper Example 3 AQA Nov 2020 2F Q19 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
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.
Worked Solution & Mark Scheme (3 marks)
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

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