Where can I download free solving quadratic equations PDF worksheets with answers?

On this MathsLinks page you can download free printable solving quadratic equations PDF worksheets (Qs) and full worked solutions or mark schemes (Ans) from Maths Genie, Maths4Everyone, Corbett Practice, Corbett Textbook, Maths Made Easy, plus a printable one-page solving quadratic equations revision guide.

What GCSE grade is solving quadratic equations (5H)?

Solving quadratic equations (topic code 5H) is a Grade 5 algebra topic in GCSE Maths for Edexcel, AQA, OCR, Eduqas and IGCSE specifications.

Free Solving quadratic equations Worksheets (PDF) with Answers — GCSE Maths

Free Solving quadratic equations PDF Worksheets & Answers

Grade 5 • Topic 5H

Resource	Questions	Answers
Maths Genie Graded exam questions & solutions	Qs	Ans
Maths4Everyone GCSE 9–1 practice booklet & solutions	Qs	Ans
Corbett Practice Practice Questions & answers	Qs	Ans
Corbett Textbook Textbook Exercise & answers	Qs	Ans
Maths Made Easy MME worksheet & model answers	Qs	Ans
Dr Frost GCSE worksheet & solutions	Qs	Ans
Naiker Maths Exam question booklet & solutions	Qs	Ans
Dr Austin Practice grid / worksheet & answers	Qs	Ans
E Classroom 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
The Maths Room Online topic notes & examples	Page
esheets Self-marking online worksheet	Page

Grade 5 topics
5A - Combining ratios	5B - Direct and inverse proportion
5C - Reverse percentages	5D - Standard form
5E - Speed	5F - Changing the subject
5G - Quadratic expressions	5H - Solving quadratic equations
5J - Drawing quadratic graphs	5K - Cubic/reciprocal graphs
5L - Simultaneous equations	5M - Sector areas and arc lengths
5N - Sim. equ. graphically	5P - Midpoint of a line segment
5Q - Gradient of a line	5R - Equation of a line
5S - Spheres and cones	5T - Similar shapes (lengths)
5U - Trigonometry (SOHCAHTOA)	5V - Exact trig. values
5W - Probability trees	5X - Vectors
5Y - Venn diagrams	5Z - Density
5AA - Pressure

Explanation:

To solve a quadratic equation by factorising, first rearrange the equation so that one side equals zero (ax² + bx + c = 0). Never factorise while there is a non-zero number on the right-hand side.

Factorise the quadratic expression into two brackets, then set each bracket equal to 0 and solve for x (because if two brackets multiply to give 0, at least one bracket must equal 0). Notice that the signs of the roots are opposite to the signs in the brackets.

Example 1: Solve x² − 8x + 15 = 0.

Solution:

Multiply to +15 and add to −8 → −3 and −5

Factorise: (x − 3)(x − 5) = 0

Either x − 3 = 0 or x − 5 = 0

Answer: x = 3 or x = 5

Example 2: Solve x² + 3x = 18.

Solution:

Rearrange to equal 0: x² + 3x − 18 = 0

Multiply to −18, add to +3 → +6 and −3

Factorise: (x + 6)(x − 3) = 0

x + 6 = 0 → x = −6; x − 3 = 0 → x = 3

Answer: x = −6 or x = 3

Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Solving quadratic equations Questions & Answers

10-Question Interactive Quiz More Past Paper Questions

Past Paper Example 1 AQA Jun 2025 1F Q26 / 1H Q10 4 marks

Full Paper (PDF) • Mark Scheme (PDF)

Rectangle with sides (x + 2) cm and (x – 5) cm has area 120 cm². Work out x. [4 marks]

The area of the rectangle is 120 cm²
Work out the value of x.

Worked Solution & Mark Scheme (4 marks)

(The area of a rectangle is length × width)
(x + 2)(x – 5) = 120 ⇒ x² – 3x – 10 = 120 ⇒ x² – 3x – 130 = 0. M3
Factorise: (x – 13)(x + 10) = 0 ⇒ x = 13 (length > 0). A1

Answer: x = 13

Past Paper Example 2 GCSE Nov 2021 1H Q8 3 marks

Full Paper (PDF) • Mark Scheme (PDF)

Solve x² = 5x + 24

Worked Solution & Mark Scheme (3 marks)

x² – 5x – 24 = 0 M1
⇒ (x – 8)(x + 3) = 0 M1
⇒ x = 8 or x = –3 A1

Answer: x = 8 and x = -3

Past Paper Example 3 GCSE Nov 2024 1F Q26 3 marks

Full Paper (PDF) • Mark Scheme (PDF)

Solve x² - 2x - 15 = 0

Worked Solution & Mark Scheme (3 marks)

(x – 5)(x + 3) = 0 M2
⇒ x = 5 or x = –3 A1