Pearson Edexcel International GCSE in Mathematics (Specification A) · 4MA1 · Free · no account needed
Quadratic Equations — exam questions
10 original Incandio exam-style questions on Quadratic Equations, 26 marks, about 33 minutes of writing. Each one carries the command word, the tariff and the specification statement it assesses, exactly as a paper presents them. This is an original Incandio practice question, written to reflect the structure and demands of the qualification. It is not an official Pearson Edexcel past-paper question.
This is the practice set for Quadratic Equations — the module that teaches it. Read the module first if the idea is new; come here when you want to find out whether you can turn it into marks. Completely free, no account needed to read.
What these questions ask of you
5 command words run through this set, and on Pearson Edexcel International GCSE Mathematics A each one means something precise. Answering the wrong command is the commonest way a candidate who understands the module still loses the mark.
- Solve (1–4 marks)
- the value(s) of the unknown that satisfy the equation
- Explain why (1–2 marks)
- one short justification — mathematics almost never asks for extended explanation
- Show that (2–5 marks)
- every step of a derivation to a value that is already printed in the question Misread as: stating the printed answer again instead of deriving it
- Find (1–5 marks)
- a value or expression obtained by a method the learner chooses
- Work out (1–5 marks)
- a calculated result, with the working that produced it
Assessed on Paper 1 and Paper 2.
Where these sit in the specification
Pearson Edexcel International GCSE Mathematics A (4MA1) — statement 2.7. Incandio is aligned to this specification; it is not published by, endorsed by or affiliated with Pearson, and it reproduces none of Pearson's wording.
The 10 questions
Answer them on paper, then open the module's exam practice to have them marked. The mark scheme, the accepted and rejected answers and the annotated model answer are in Incandio and are not printed here — an answer beside its question is not practice.
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(1)Solve
Solve x(x − 5) = 0.
(Total for Question 1 = 1 mark)
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(2)Solve
Solve x² = 49.
(Total for Question 2 = 2 marks)
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(3)Solve
Solve x² + 7x + 12 = 0.
(Total for Question 3 = 3 marks)
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(3)Solve
Solve 2x² − 5x − 3 = 0.
(Total for Question 4 = 3 marks)
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(1)Explain why
Explain why the equation x² + 4 = 0 has no real solutions.
(Total for Question 5 = 1 mark)
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(3)Solve
Solve 3x² + 5x − 4 = 0, giving your answers correct to 2 decimal places.
(Total for Question 6 = 3 marks)
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(3)Show that
Show that x² − 10x + 21 can be written as (x − 5)² − 4.
(Total for Question 7 = 3 marks)
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(3)Find
Find the values of x for which (x + 2)(x − 6) = 20.
(Total for Question 8 = 3 marks)
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(3)Solve
Solve x² + 6x − 3 = 0 by completing the square, leaving your answers in surd form.
(Total for Question 9 = 3 marks)
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(4)Work out
A rectangle has an area of 40 cm². Its length is 3 cm greater than its width. Work out the width of the rectangle.
(Total for Question 10 = 4 marks)
Have them marked, then defend the answer
Practice tells you the mark; teaching it back tells you whether you understand it. On Incandio a topic counts as mastered only once you have taught it and defended it.
- Mark these questions — 10 questions, marked on Incandio against the authored scheme, with the mistake you actually made named.
- Teach it — explain Quadratic Equations to Ember, an AI pupil who does not have it yet and asks the awkward question.
- Defend it — argue it against Muhammad al-Khwarizmi over three rounds, marked against descriptors you can read first.
Completely free. No subscriptions, no paywalls, no account needed to start.
Back to the module
- Quadratic Equations — Four ways to solve a quadratic — factorising, the formula, completing the square, and reading a graph — why each one works, how to choose between them, and how to reason about how many solutions there are.
- All of Incandio Mathematics · Incandio Exam Practice