Where can I download free the quadratic formula PDF worksheets with answers?

On this MathsLinks page you can download free printable the quadratic formula PDF worksheets (Qs) and full worked solutions or mark schemes (Ans) from Maths Genie, Corbett Practice, Corbett Textbook, Maths Made Easy, 1st Class Maths, plus a printable one-page the quadratic formula revision guide.

What GCSE grade is the quadratic formula (7E)?

The quadratic formula (topic code 7E) is a Grade 7 algebra topic in GCSE Maths for Edexcel, AQA, OCR, Eduqas and IGCSE specifications.

Free The quadratic formula Worksheets (PDF) with Answers — GCSE Maths

Free The quadratic formula PDF Worksheets & Answers

Grade 7 • Topic 7E

Resource	Questions	Answers
Maths Genie Graded exam questions & 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
1st Class Maths (Edxl) Edexcel exam questions & solutions	Qs	Ans
1st Class Maths (AQA) AQA exam questions & solutions	Qs	Ans
Maths4EveryOne Structured worksheet & solutions	Qs	Ans
Metatutor Topic worksheet & worked solutions	Qs	Ans
Maths Takeaway GCSE Maths Takeaway exam questions	Qs	Ans
Maths DIY Exam-style booklet & solutions	Qs	Ans
Dr Austin (1) Practice grid / worksheet & answers	Qs	Ans
Dr Austin (2) 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
Cognito Interactive online lesson & practice	Page
esheets Self-marking online worksheet	Page

Grade 7 topics
7A - Surds	7B - Bounds
7C - Proportion (harder)	7D - Algebraic fractions
7E - The quadratic formula	7F - Factorising harder quadratics
7G - Trigonometric & exp. Graphs	7H - Rearranging (harder)
7J - Functions (harder)	7K - Iteration
7L - Area of any triangle	7M - The sine rule
7N - The cosine rule	7P - Congruent triangles
7Q - 3D pythagoras / trig.	7R - Histograms
7S - Conditional probability	7T - Exact trig. values (harder)
7U - Area of a segment

Explanation:

Use the quadratic formula x = −b ± √(b² − 4ac)2a when a quadratic equation ax² + bx + c = 0 cannot be easily factorised, or when the question asks for solutions to a given number of decimal places or significant figures, or in surd form.

Always rearrange the equation so that the right-hand side equals 0 first, then write down the values of a, b, and c including their signs. Put negative numbers in brackets when substituting into (−b)² − 4(a)(c) so your calculator squares the negative sign properly.

Example 1: Solve 2x² − 7x − 3 = 0 to 2 d.p.

Solution:

Here a = 2, b = −7, c = −3

x = −(−7) ± √((−7)² − 4(2)(−3))2(2)

x = 7 ± √(49 + 24)4 = 7 ± √734

x = 3.8860... or x = −0.3860...

Answer: x = 3.89 or x = −0.39 (2 d.p.)

Example 2: Solve x² + 6x = 4 in the form p ± √q.

Solution:

Rearrange to x² + 6x − 4 = 0 (a = 1, b = 6, c = −4)

x = −6 ± √(6² − 4(1)(−4))2(1) = −6 ± √522

Since √52 = √4 × √13 = 2√13:

x = −6 ± 2√132 = −3 ± √13

Answer: x = −3 ± √13

Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper The quadratic formula Questions & Answers

10-Question Interactive Quiz More Past Paper Questions

Past Paper Example 1 OCR Nov 2020 4H Q15 3 marks

Full Paper (PDF) • Mark Scheme (PDF)

(b) @@TABULAR₀@@
Describe the error and write the correct solution.

(b) @@TABULAR₀@@
Describe the error and write the correct solution. [3 marks]

Worked Solution & Mark Scheme (3 marks)

Part (b) Solution:

Error: −b was not divided by 2a M2
Correct solution: x = (8 ± √(64 − 24)) / 4 = (8 ± √40) / 4 ⇒ x = 0.419 or x = 3.58 (3 s.f.). C1

Answer (b): Error: The −(−8) term should also be divided by 2 × 2 (the fraction line should go under the whole numerator).
Correct solution: x = (8 ± √40) / 4 ⇒ x = 0.419 or x = 3.58.

Past Paper Example 2 OCR Nov 2017 4H Q18 4 marks

Full Paper (PDF) • Mark Scheme (PDF)

Solve this equation algebraically.
Give your solutions correct to 2 decimal places.
3x² + 5x - 1 = 0

Worked Solution & Mark Scheme (4 marks)

Using the quadratic formula with a = 3, b = 5, c = −1: M2
x = (−5 ± √(5² − 4 × 3 × (−1))) / (2 × 3) = (−5 ± √(25 + 12)) / 6 = (−5 ± √37) / 6. M1
x = (−5 + 6.08276) / 6 = 0.1804... ≈ 0.18, or x = (−5 − 6.08276) / 6 = −1.8471... ≈ −1.85. A1

Answer: x = 0.18 or -1.85

Past Paper Example 3 AQA Jun 2025 2H Q15 2 marks

Full Paper (PDF) • Mark Scheme (PDF)

Solve 3x² + 5x - 9 = 0

Give your solutions as decimals.

Worked Solution & Mark Scheme (2 marks)

x = [–5 ± √(5² – 4(3)(–9))] / (2 × 3) = [–5 ± √133] / 6. M1
x ≈ 1.09 and x ≈ –2.76. A1

Answer: 1.09 and –2.76

← 7D Algebraic fractions

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