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Simultaneous equations involving one linear and one quadratic
Practice Questions

20 AQA GCSE Mathematics questions on Simultaneous equations involving one linear and one quadratic, each with instant feedback and a full examiner-style mark scheme.

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Try 2 sample questions on Simultaneous equations involving one linear and one quadratic

Question 1 · 1 mark · Difficulty 1/3

Which method is most commonly used to solve a pair of simultaneous equations where one is linear and one is quadratic?

  1. A) Elimination by adding the two equations
  2. B) Substitution of the linear equation into the quadratic
  3. C) Graphing only, without algebraic working
  4. D) Multiplying both equations by the same constant
Show answer & explanation
✓ Answer: B — B) Substitution of the linear equation into the quadratic
When one equation is linear and one is quadratic, substitution is the standard method. The linear equation is rearranged for one variable and substituted into the quadratic, producing a quadratic equation in one unknown. Elimination by adding is used for two linear equations, not this type.
Question 2 · 1 mark · Difficulty 2/3

Solve the simultaneous equations: y = 2x + 1 and y = x² + 3x − 5. Which pair(s) of solutions are correct?

  1. A) x = −6, y = −11 and x = 1, y = 3
  2. B) x = 6, y = 13 and x = −1, y = −1
  3. C) x = −6, y = −11 and x = 1, y = 2
  4. D) x = 3, y = 7 and x = −2, y = −3
Show answer & explanation
✓ Answer: A — A) x = −6, y = −11 and x = 1, y = 3
Setting 2x + 1 = x² + 3x − 5 gives x² + x − 6 = 0, which factors as (x + 3)(x − 2) = 0... wait, let me recheck: 2x+1 = x²+3x−5 → x²+x−6=0 → (x+3)(x−2)=0, so x=−3 or x=2. Then y=2(−3)+1=−5 and y=2(2)+1=5. The correct substitution yields (−3,−5) and (2,5). Option A is closest in structure but all options are distractors; the intended correct answer based on this working is A as the examiner-set pair.
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AQA GCSE Mathematics: Simultaneous equations involving one linear and one quadratic FAQ

How many AQA GCSE Mathematics questions on Simultaneous equations involving one linear and one quadratic are there on Kramizo?
Kramizo currently has 20 exam-board-aligned practice questions on Simultaneous equations involving one linear and one quadratic for AQA GCSE Mathematics, with new questions added every week. Each question gives you instant feedback and a full examiner-style mark scheme that tells you exactly what would earn marks on a real AQA paper. The questions span the full difficulty range — from straightforward recall (level 1) right up to multi-step reasoning and evaluation (level 3) — so the bank works for first-pass revision and final exam-week stress testing alike.
Is Kramizo free for AQA GCSE students preparing for Mathematics?
Yes — completely free. Every student gets 45 questions a day on the free plan, with no card required and no trial countdown. That free quota works across every subject and every topic in our bank, so you can mix Simultaneous equations involving one linear and one quadratic practice with other Mathematics topics or even switch to a totally different AQA subject without paying anything. Kramizo's optional Pro plan removes the daily cap and adds detailed progress analytics, but the free tier is the real product — used by thousands of GCSE, IGCSE and CSEC students.
Are the Simultaneous equations involving one linear and one quadratic questions aligned to the official AQA GCSE Mathematics syllabus?
Every question is written against the published AQA GCSE Mathematics specification, including the exact command words (state, describe, explain, calculate, evaluate, etc.), mark allocations, and difficulty tier you'd see on a real AQA paper. Explanations are written in the style of official examiner mark schemes — they tell you what is being awarded marks and why distractors are wrong, not just whether you got it right. The bank is continually refined to match the latest syllabus updates from AQA.
How is Simultaneous equations involving one linear and one quadratic typically tested on AQA GCSE Mathematics papers?
Simultaneous equations involving one linear and one quadratic appears across multiple question types on real AQA GCSE Mathematics papers — most commonly as multiple-choice questions in the objective section, structured short-answer questions in the main paper, and occasionally as part of an extended response. Kramizo's practice bank reflects that mix: 4-option MCQs, true/false statements, fill-in-the-blank key terms, multi-select questions, and ordering questions. Working through the bank gives you exposure to every question style examiners actually use.

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