Question 1 · 1 mark · Difficulty 2/3
Write x² + 6x in completed square form.
- (x + 3)² − 9
- (x + 3)² + 9
- (x + 6)² − 36
- (x + 3)²
Show answer & explanation
✓ Answer: A — (x + 3)² − 9
Halve 6 to get 3: (x + 3)² − 3² = (x + 3)² − 9.
Home › AQA GCSE Mathematics › Solving quadratic equations by completing the square and the quadratic formula
AQA · GCSE · Mathematics
Solving quadratic equations by completing the square and the quadratic formula
Practice Questions
19 AQA GCSE Mathematics questions on Solving quadratic equations by completing the square and the quadratic formula, each with instant feedback and a full examiner-style mark scheme.
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Question 2 · 1 mark · Difficulty 2/3
Write x² + 4x + 1 in completed square form.
- (x + 2)² − 3
- (x + 2)² + 1
- (x + 4)² − 3
- (x + 2)² − 5
Show answer & explanation
✓ Answer: A — (x + 2)² − 3
(x + 2)² = x² + 4x + 4, so x² + 4x + 1 = (x + 2)² − 4 + 1 = (x + 2)² − 3.
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AQA GCSE Mathematics: Solving quadratic equations by completing the square and the quadratic formula FAQ
How many AQA GCSE Mathematics questions on Solving quadratic equations by completing the square and the quadratic formula are there on Kramizo?
Kramizo currently has 19 exam-board-aligned practice questions on Solving quadratic equations by completing the square and the quadratic formula 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 Solving quadratic equations by completing the square and the quadratic formula 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 Solving quadratic equations by completing the square and the quadratic formula 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 Solving quadratic equations by completing the square and the quadratic formula typically tested on AQA GCSE Mathematics papers?
Solving quadratic equations by completing the square and the quadratic formula 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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