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Substitution

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

Download free substitution worksheets (PDF), GCSE maths past paper questions and worked solutions for Substitution (3N). This is a Grade 3 algebra 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, Maths4EveryOne, Metatutor, Maths DIY, Maths Takeaway, Dr Austin, GCSE Maths Rocket, E Classroom and PMT, along with past paper question booklets.

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

Free Substitution PDF Worksheets & Answers

Grade 3 • Topic 3N
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PMT (Edxl)
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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 Substitution: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

Substitution means replacing letters in an algebraic expression or formula with their given numerical values. Always write brackets around any negative number you substitute — especially when squaring: (−3)² = +9, whereas −3² on a calculator gives −9.

Follow the order of operations (BIDMAS): work out Brackets first, then Indices (powers/roots), then Division and Multiplication, and finally Addition and Subtraction. Remember that 3a means 3 × a.

Example 1: Find the value of 4a − 3b when a = 5 and b = −2.

Solution:

Substitute using brackets: 4(5) − 3(−2)
Multiply: 4 × 5 = 20 and −3 × −2 = +6
= 20 + 6 = 26
Answer: 26

Example 2: Given v = u² + 2as, find v when u = −4, a = 3, and s = 5.

Solution:

Substitute: v = (−4)² + 2(3)(5)
Indices first: (−4)² = −4 × −4 = 16
Multiply: 2 × 3 × 5 = 30
Add: v = 16 + 30 = 46  →  Answer: v = 46
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Substitution Questions & Answers

Past Paper Example 1 GCSE Nov 2020 2F Q15 4 marks
Full Paper (PDF) • Mark Scheme (PDF)
T = 3x + 4y
(a) Work out the value of T when x = 5 and y = -7 [2 marks]
(b) Work out the value of y when T = 38 and x = 6 [2 marks]
Worked Solution & Mark Scheme (4 marks)
Part (a) Solution:
3(5) + 4(–7) = 15 – 28 = –13 M1 A1
Answer (a): –13
Part (b) Solution:
38 = 3(6) + 4y M1
⇒ 38 = 18 + 4y
⇒ 4y = 20
⇒ y = 5 A1
Answer (b): 5
Past Paper Example 2 IGCSE Jun 2018 1FR Q20 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
E = n2 + n + 5
(a) Work out the value of E when n = 3 [1 mark]
(b) Is Ali correct?
You must give a reason for your answer. [2 marks]
Worked Solution & Mark Scheme (3 marks)
Part (a) Solution:
3² + 3 + 5 = 17 B1
Answer (a): E = 17
Part (b) Solution:
When n = 4, E = 16 + 4 + 5 = 25 = 5 × 5, not prime M1 A1
Answer (b): No, when n = 4, E = 4² + 4 + 5 = 25 which is not prime
Past Paper Example 3 AQA Nov 2021 2F Q5 2 marks
Full Paper (PDF) • Mark Scheme (PDF)
Work out the value of a2 - 4a when a = 10
Worked Solution & Mark Scheme (2 marks)
a2 - 4a = 102 - 4(10) = 100 - 40 = 60 M1 A1
Answer: Answer 60

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