Home   >  Worksheets   >  GCSE questions by topic   >  Forming and solving equations

MathsLinks Logo Questions by topic

Last update: 05/11/2026

Give feedback : Buy me a coffee

Forming and solving equations

Free Printable Forming and solving equations PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 4)

Download free forming and solving equations worksheets (PDF), GCSE maths past paper questions and worked solutions for Forming and solving equations (4G). This is a Grade 4 algebra topic from the GCSE questions by topic collection for Foundation and Higher tier crossover 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, Maths4Everyone, Corbett Maths, Naiker Maths, Dr Austin, Dr Frost (B. Blocks), 1st Class Maths, Metatutor, GCSE Maths Rocket, E Classroom and PMT, along with past paper question booklets.

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

Free Forming and solving equations PDF Worksheets & Answers

Grade 4 • Topic 4G
Resource Questions Answers
GCSE past paper questions & solutions
 Qs Ans
Graded exam questions & solutions
 Qs Ans
GCSE 9–1 practice booklet & solutions
 Qs Ans
Practice Questions & answers
 Qs Ans
Textbook Exercise & answers
 Qs Ans
Exam question booklet & solutions
 Qs Ans
Practice grid / worksheet & answers
 Qs Ans
Practice grid / worksheet & answers
 Qs Ans
Practice grid / worksheet & answers
 Qs Ans
Building Blocks skill sheet & answers
 Qs Ans
Building Blocks skill sheet & answers
 Qs Ans
Edexcel exam questions & solutions
 Qs Ans
AQA exam questions & solutions
 Qs Ans
Topic worksheet & worked solutions
 Qs Ans
Practice questions & 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
Online topic notes & examples
 Page
Grade 4 topics
4A - Compound interest4B - Indices (index laws)
4C - Prime factors HCF and LCM4D - Real life graphs
4E - Inequalities on a number line4F - Solving inequalities
4G - Forming and solving equations4H - nth term of a linear sequence
4J - Expanding and factorising4K - Pythagoras theorem
4L - Angles in parallel lines4M - Angles in polygons
4N - Surface area4P - Volume of a cuboid
4Q - Volume of a prism4R - Bearings
4S - Cylinders4T - Plans and elevations
4U - Scatter graphs4V - Probability
4W - Averages from tables4X - Reverse mean
4Y - Area of a trapezium4Z - Loci and construction
GCSE Maths Grade 4 Revision Notes & Method

Guide to Forming and solving equations: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

To form and solve an equation from a word problem or geometry diagram, write an algebraic expression for each part using the given letter, then use a known mathematical fact to set up an equation with an = sign.

Common facts used in exams include: perimeter = sum of all outer sides, opposite sides of a rectangle are equal, angles on a straight line = 180°, angles in a triangle = 180°, and angles in a quadrilateral = 360°. Always read the end of the question to check if you need to substitute x back in!

Example 1: Find the size of the largest angle in the triangle below.

(2x + 15)° (x + 20)° (3x − 5)°
(2x + 15) + (3x − 5) + (x + 20) = 180 → 6x + 30 = 180 → x = 25
Largest angle = 3(25) − 5 = 70°

Example 2: A rectangle has sides (2x + 5) cm and (x + 1) cm, and perimeter 42 cm. Find its length.

(2x + 5) cm (x + 1) cm Perimeter = 42 cm
2(2x + 5) + 2(x + 1) = 42 → 6x + 12 = 42 → x = 5
Length = 2(5) + 5 = 15 cm
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Forming and solving equations Questions & Answers

Past Paper Example 1 GCSE Nov 2021 1F Q16 4 marks
Full Paper (PDF) • Mark Scheme (PDF)
ABCD is a kite.
BCDA(4x – 2) cm
AB = (4x - 2) cm
Jasper says that x could be 0.5
(a) Explain why Jasper cannot be correct. [1 mark]
(b) Find the value of x. [3 marks]
Worked Solution & Mark Scheme (4 marks)
Part (a) Solution:
4(0.5) – 2 = 0 C1
Answer (a): If x = 0.5, AB = 4(0.5) – 2 = 0 cm, and a side length cannot be 0
Part (b) Solution:
Perimeter = 2AB + 2(3AB) = 8AB = 64 ⇒ AB = 8 M2
4x – 2 = 8 ⇒ 4x = 10 ⇒ x = 2.5 A1
Answer (b): x = 2.5
Past Paper Example 2 GCSE Nov 2019 1F Q28 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
The diagram shows triangle AOB.
ABO(2x)°(3x)°10°
Angle AOB is **not** an obtuse angle.
Find the greatest value of x.
You must show all your working.
Worked Solution & Mark Scheme (3 marks)
Not obtuse ⇒ Angle AOB ≤ 90° M2
2x + 3x + 10 ≤ 90 ⇒ 5x ≤ 80 ⇒ x ≤ 16, so greatest value of x is 16. A1
Answer: 16
Past Paper Example 3 GCSE Jun 2017 2F Q9 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
3x°2x°
Angles around a point are 90°, 2x° and 3x°. Find the value of x.
Find the value of x.
Worked Solution & Mark Scheme (3 marks)
2x + 3x + 90 = 360 M1
⇒ 5x = 270 M1
⇒ x = 54 A1
Answer: x = 54

← 4F Solving inequalities

Back to GCSE questions by topic

4H nth term of a linear sequence →