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Solving one step equations

Free Printable Solving one step equations PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 2)

Download free solving one step equations worksheets (PDF), GCSE maths past paper questions and worked solutions for Solving one step equations (2J). This is a Grade 2 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, Maths Made Easy, 1st Class Maths, Dr Austin, E Classroom and PMT, along with past paper question booklets.

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

Free Solving one step equations PDF Worksheets & Answers

Grade 2 • Topic 2J
Resource Questions Answers
Practice worksheet & worked solutions
 Qs Ans
Graded exam questions & solutions
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Practice Questions & answers
 Qs Ans
Textbook Exercise & answers
 Qs Ans
MME worksheet & model answers
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Edexcel exam questions & solutions
 Qs Ans
AQA exam questions & solutions
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Practice grid / worksheet & answers
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GCSE topic booklet & answers
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PMT (Edxl)
Edexcel GCSE topic questions & solutions
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PMT (AQA)
AQA GCSE topic questions & solutions
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PMT (IGCSE)
Edexcel IGCSE topic questions & solutions
 Qs Ans
Online topic notes & examples
 Page
Interactive online lesson & practice
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Self-marking online worksheet
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Grade 2 topics
2A - Calculation problems2B - Using a calculator
2C - Systematic listing2D - Fraction of an amount
2E - FDP2F - Simplifying algebra
2G - Writing an expression2H - Function machines
2J - Solving one step equations2K - Angles
2L - Area and perimeter2M - Reading scales
2N - Probability & Probability Scale2P - Frequency polygons
2Q - Unitary method2R - Bar charts
2S - Pie charts2T - Averages
2U - Stem and leaf diagrams
GCSE Maths Grade 2 Revision Notes & Method

Guide to Solving one step equations: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

Solving an equation means finding the value of the unknown letter that makes both sides equal. Think of the equation as a balanced scale: whatever operation you do to one side, you must do the exact same operation to the other side.

To isolate the letter in a one-step equation, apply the inverse (opposite) operation: undo + a by subtracting a, undo − a by adding a, undo × a by dividing by a, and undo ÷ a (a fraction xa) by multiplying by a.

Example 1: Solve:
(a) x + 9 = 23     (b) y − 7 = −3

Solution:

(a) Inverse of + 9 is − 9 on both sides:
• x = 23 − 9 → x = 14
(b) Inverse of − 7 is + 7 on both sides:
• y = −3 + 7 → y = 4

Example 2: Solve:
(a) 6m = 42     (b) w5 = 8

Solution:

(a) 6m means 6 × m, so divide both sides by 6:
• m = 42 ÷ 6 → m = 7
(b) w5 means w ÷ 5, so multiply both sides by 5:
• w = 8 × 5 → w = 40
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Solving one step equations Questions & Answers

Past Paper Example 1 AQA Jun 2023 3F Q1 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
(a) Solve 5x = 15
1 (b) Solve y + 7 = 50
1 (c) Solve c4 = 8
(a) Solve 5x = 15 [1 mark]
(b) Solve y + 7 = 50 [1 mark]
(c) Solve c4 = 8 [1 mark]
Worked Solution & Mark Scheme (3 marks)
Part (a) Solution:
x = 15 ÷ 5 = 3 B1
Answer (a): x = 3
Part (b) Solution:
y = 50 - 7 = 43 B1
Answer (b): y = 43
Part (c) Solution:
c = 8 × 4 = 32 B1
Answer (c): c = 32
Past Paper Example 2 AQA Nov 2022 3F Q7 2 marks
Full Paper (PDF) • Mark Scheme (PDF)
Solve the following linear equations.
(a) Solve 12 - e = 0 [1 mark]
(b) Solve 7f = 0 [1 mark]
Worked Solution & Mark Scheme (2 marks)
Part (a) Solution:
12 - e = 0 ⇒ e = 12 B1
Answer (a): e = 12
Part (b) Solution:
7f = 0 ⇒ f = 0 B1
Answer (b): f = 0
Past Paper Example 3 AQA Nov 2020 2F Q5 2 marks
Full Paper (PDF) • Mark Scheme (PDF)
(a) Solve 7x = 56
5 (b) Solve 25 - y = 18
(a) Solve 7x = 56 [1 mark]
(b) Solve 25 - y = 18 [1 mark]
Worked Solution & Mark Scheme (2 marks)
Part (a) Solution:
x = 56 ÷ 7 = 8 B1
Answer (a): x = 8
Part (b) Solution:
y = 25 - 18 = 7 B1
Answer (b): y = 7

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