A MathedUp practice collection, not an exam paper. Every question is original MathedUp material.
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Completing the square
Topic practice
Name
ClassDate
Before you start
Write in black pen. Draw graphs and diagrams in pencil.
Write each answer in the space under its question.
Show your working: a correct method can earn marks even when the answer is wrong.
Questions marked need a calculator.
About this exam
Marks for each part are in brackets, like (3).
Diagrams are NOT accurately drawn, unless otherwise indicated.
Read each question through once before you start writing.
Original MathedUp practice material: a topic collection, not an exam paper and not modelled on the format of one. Not affiliated with, endorsed by or produced by any exam board.
Sitting · www.mathedup.co.uk
Higher papers also test Foundation-level questions, so All is the whole topic.
1mark
1Foundation
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Completing the square exam questions for GCSE maths, with worked solutions
Practise completing the square with exam questions written the way GCSE Higher papers test them: writing a quadratic in the form (x + a)² + b, reading the turning point from the answer, finding unknown numbers in the completed square, solving a quadratic exactly, showing that an expression is always positive, and completing the square when the x² term has a number in front. Several questions go on to ask for a sketch of the curve. Every question comes with a worked solution and an answer, and Remix gives you a fresh version with new numbers whenever you want another go.
21 questions: 21 Higher. Every question has a worked solution and an answer. Type your answers in and the page marks them as you go.
What the questions cover
Writing x² + bx + c in the form (x + a)² + b, with whole numbers a and b
Writing down the coordinates of the turning point from a completed square
Finding the turning point of a quadratic by completing the square, with working shown
Finding an unknown number in the equation of a curve from its turning point
Solving a quadratic exactly by completing the square, leaving surds in simplest form
Completing the square when the x² term has a number in front, including a negative one
Showing that a quadratic is always positive, or that its turning point is where it is claimed to be
Sketching a quadratic curve from its completed square, marking the turning point and the y-intercept
How to use this page
Remix gives you a new version of the question in front of you, with new numbers.
New sitting refreshes every question at once.
Solution shows the full working, and Answer shows just the answer.
All questions lists the whole collection, and Scroll puts every question on one page.
Original MathedUp questions, written to practise the skills GCSE papers test. These are not past exam papers, and MathedUp is not affiliated with any exam board.
