Free Grade 3 Working with Quadratic Sequences Worksheets
Free Grade 3 worksheets for Working with Quadratic Sequences: 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
Higher
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with quadratic sequences
Identify working with quadratic sequences accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with quadratic sequences
Explain working with quadratic sequences accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with quadratic sequences
Calculate working with quadratic sequences accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with quadratic sequences
Compare working with quadratic sequences 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 Working with Quadratic Sequences 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 − 3x + 2.[1]
- 2.Factorise x² − 5x − 6.[1]
- 3.Factorise x² − 11x + 24.[1]
- 4.Factorise x² + 11x + 28.[1]
- 5.Solve x² + 13x + 42 = 0.[2]
- 6.Solve x² − 4x − 32 = 0.[2]
- 7.Solve x² − 5x − 36 = 0.[2]
- 8.Solve x² + 9x + 18 = 0.[2]
- 9.Solve x² − 7x + 10 = 0.[3]
- 10.Solve x² + 0x − 9 = 0.[3]
- 11.Solve x² − 5x − 14 = 0.[3]
- 12.Solve x² − 9x + 8 = 0.[3]
Show answers and working
1. (x − 2)(x − 1)
Find two numbers that multiply to 2 and add to -3: -2 and -1. So x² − 3x + 2 = (x − 2)(x − 1).
2. (x + 1)(x − 6)
Find two numbers that multiply to -6 and add to -5: 1 and -6. So x² − 5x − 6 = (x + 1)(x − 6).
3. (x − 3)(x − 8)
Find two numbers that multiply to 24 and add to -11: -3 and -8. So x² − 11x + 24 = (x − 3)(x − 8).
4. (x + 7)(x + 4)
Find two numbers that multiply to 28 and add to 11: 7 and 4. So x² + 11x + 28 = (x + 7)(x + 4).
5. x = -7 or x = -6
Factorise: (x + 7)(x + 6) = 0. One bracket must be zero: x = -7 or x = -6.
6. x = -4 or x = 8
Factorise: (x + 4)(x − 8) = 0. One bracket must be zero: x = -4 or x = 8.
7. x = -4 or x = 9
Factorise: (x + 4)(x − 9) = 0. One bracket must be zero: x = -4 or x = 9.
8. x = -3 or x = -6
Factorise: (x + 3)(x + 6) = 0. One bracket must be zero: x = -3 or x = -6.
9. x = 2 or x = 5
Factorise: (x − 2)(x − 5) = 0. One bracket must be zero: x = 2 or x = 5.
10. x = -3 or x = 3
Factorise: (x + 3)(x − 3) = 0. One bracket must be zero: x = -3 or x = 3.
11. x = -2 or x = 7
Factorise: (x + 2)(x − 7) = 0. One bracket must be zero: x = -2 or x = 7.
12. x = 1 or x = 8
Factorise: (x − 1)(x − 8) = 0. One bracket must be zero: x = 1 or x = 8.
Worked examples
Factorise x² + 0x − 25.
- Find two numbers that multiply to -25 and add to 0: -5 and 5.
- So x² + 0x − 25 = (x − 5)(x + 5).
- Answer: (x − 5)(x + 5)
Solve x² + 5x − 14 = 0.
- Factorise: (x − 2)(x + 7) = 0.
- One bracket must be zero: x = 2 or x = -7.
- Answer: x = 2 or x = -7
Solve x² + 2x − 48 = 0.
- Factorise: (x + 8)(x − 6) = 0.
- One bracket must be zero: x = -8 or x = 6.
- Answer: x = -8 or x = 6
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 Working with Quadratic Sequences 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 Introducing Quadratic Sequences, nth Term of a Linear Sequence. 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 Working with Quadratic Sequences?
- Move on to Quadratic Sequences in Context, Term-to-term Rules, nth Term of a Linear Sequence, Geometric Sequences, which build directly on this idea.
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