Free Grade 3 Completing the Square in Context Worksheets
Free Grade 3 worksheets for Completing the Square in Context: 12 real questions with a full answer key and worked solutions. A quadratic has an x² term. Factorise by finding two numbers that multiply to the constant and add to the x-coefficient; each bracket gives a solution.
Free
Foundation
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify completing the square in context
Identify completing the square in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain completing the square in context
Explain completing the square in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate completing the square in context
Calculate completing the square in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare completing the square in context
Compare completing the square in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Completing the Square in Context works
A quadratic has an x² term. Factorise by finding two numbers that multiply to the constant and add to the x-coefficient; each bracket gives a solution.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.Factorise x² + 5x − 24.[1]
- 2.Factorise x² + 14x + 48.[1]
- 3.Factorise x² − 4x + 3.[1]
- 4.Factorise x² − 4x − 5.[1]
- 5.Solve x² + 0x − 49 = 0.[2]
- 6.Solve x² + 8x + 7 = 0.[2]
- 7.Solve x² − 14x + 48 = 0.[2]
- 8.Solve x² − 15x + 54 = 0.[2]
- 9.Solve x² − 17x + 72 = 0.[3]
- 10.Solve x² − 1x − 6 = 0.[3]
- 11.Solve x² + 8x + 15 = 0.[3]
- 12.Solve x² + 1x − 56 = 0.[3]
Show answers and working
1. (x + 8)(x − 3)
Find two numbers that multiply to -24 and add to 5: 8 and -3. So x² + 5x − 24 = (x + 8)(x − 3).
2. (x + 8)(x + 6)
Find two numbers that multiply to 48 and add to 14: 8 and 6. So x² + 14x + 48 = (x + 8)(x + 6).
3. (x − 3)(x − 1)
Find two numbers that multiply to 3 and add to -4: -3 and -1. So x² − 4x + 3 = (x − 3)(x − 1).
4. (x − 5)(x + 1)
Find two numbers that multiply to -5 and add to -4: -5 and 1. So x² − 4x − 5 = (x − 5)(x + 1).
5. x = -7 or x = 7
Factorise: (x + 7)(x − 7) = 0. One bracket must be zero: x = -7 or x = 7.
6. x = -7 or x = -1
Factorise: (x + 7)(x + 1) = 0. One bracket must be zero: x = -7 or x = -1.
7. x = 8 or x = 6
Factorise: (x − 8)(x − 6) = 0. One bracket must be zero: x = 8 or x = 6.
8. x = 9 or x = 6
Factorise: (x − 9)(x − 6) = 0. One bracket must be zero: x = 9 or x = 6.
9. x = 8 or x = 9
Factorise: (x − 8)(x − 9) = 0. One bracket must be zero: x = 8 or x = 9.
10. x = -2 or x = 3
Factorise: (x + 2)(x − 3) = 0. One bracket must be zero: x = -2 or x = 3.
11. x = -3 or x = -5
Factorise: (x + 3)(x + 5) = 0. One bracket must be zero: x = -3 or x = -5.
12. x = -8 or x = 7
Factorise: (x + 8)(x − 7) = 0. One bracket must be zero: x = -8 or x = 7.
Worked examples
Factorise x² − 14x + 48.
- Find two numbers that multiply to 48 and add to -14: -6 and -8.
- So x² − 14x + 48 = (x − 6)(x − 8).
- Answer: (x − 6)(x − 8)
Solve x² + 2x − 63 = 0.
- Factorise: (x + 9)(x − 7) = 0.
- One bracket must be zero: x = -9 or x = 7.
- Answer: x = -9 or x = 7
Solve x² + 16x + 63 = 0.
- Factorise: (x + 7)(x + 9) = 0.
- One bracket must be zero: x = -7 or x = -9.
- Answer: x = -7 or x = -9
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Gives x = 3 from (x + 3) = 0.
Correction: x + 3 = 0 means x = −3.
Gets the signs muddled when factorising.
Correction: Check by expanding the brackets.
Teacher tips
- · Use a product–sum grid for finding the pair.
Parent tips
- · Ask what two numbers multiply to 12 and add to 7.
Real-life applications
- · Projectile paths, maximising area.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
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Frequently asked
- Is this Grade 3 Completing the Square in Context worksheet really free?
- Yes. Every worksheets on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- What should a learner already know before this?
- Start with Working with Completing the Square, Introducing Completing the Square, Factorising Quadratics. Each one has its own free lesson, worksheet and quiz.
- How is the worksheet sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Completing the Square in Context?
- Move on to Expanding Double Brackets, Factorising Quadratics, The Quadratic Formula, Quadratic Graphs, which build directly on this idea.
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