Free Grade 3 Quadratic Sequences in Context Flashcards
Free Grade 3 flashcards for Quadratic Sequences 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
Higher
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain quadratic sequences in context
Explain quadratic sequences in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate quadratic sequences in context
Calculate quadratic sequences in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare quadratic sequences in context
Compare quadratic sequences in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify quadratic sequences in context
Justify quadratic sequences 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 Quadratic Sequences 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 + 3x − 28.[1]
- 2.Factorise x² + 1x − 56.[1]
- 3.Factorise x² − 13x + 42.[1]
- 4.Factorise x² − 1x − 6.[1]
- 5.Solve x² − 1x − 30 = 0.[2]
- 6.Solve x² − 2x − 24 = 0.[2]
- 7.Solve x² + 0x − 64 = 0.[2]
- 8.Solve x² − 5x − 14 = 0.[2]
- 9.Solve x² − 8x − 9 = 0.[3]
- 10.Solve x² − 11x + 18 = 0.[3]
- 11.Solve x² − 1x − 6 = 0.[3]
- 12.Solve x² − 9x + 20 = 0.[3]
Show answers and working
1. (x − 4)(x + 7)
Find two numbers that multiply to -28 and add to 3: -4 and 7. So x² + 3x − 28 = (x − 4)(x + 7).
2. (x + 8)(x − 7)
Find two numbers that multiply to -56 and add to 1: 8 and -7. So x² + 1x − 56 = (x + 8)(x − 7).
3. (x − 6)(x − 7)
Find two numbers that multiply to 42 and add to -13: -6 and -7. So x² − 13x + 42 = (x − 6)(x − 7).
4. (x + 2)(x − 3)
Find two numbers that multiply to -6 and add to -1: 2 and -3. So x² − 1x − 6 = (x + 2)(x − 3).
5. x = 6 or x = -5
Factorise: (x − 6)(x + 5) = 0. One bracket must be zero: x = 6 or x = -5.
6. x = 6 or x = -4
Factorise: (x − 6)(x + 4) = 0. One bracket must be zero: x = 6 or x = -4.
7. x = -8 or x = 8
Factorise: (x + 8)(x − 8) = 0. One bracket must be zero: x = -8 or x = 8.
8. x = -2 or x = 7
Factorise: (x + 2)(x − 7) = 0. One bracket must be zero: x = -2 or x = 7.
9. x = -1 or x = 9
Factorise: (x + 1)(x − 9) = 0. One bracket must be zero: x = -1 or x = 9.
10. x = 9 or x = 2
Factorise: (x − 9)(x − 2) = 0. One bracket must be zero: x = 9 or x = 2.
11. x = -2 or x = 3
Factorise: (x + 2)(x − 3) = 0. One bracket must be zero: x = -2 or x = 3.
12. x = 5 or x = 4
Factorise: (x − 5)(x − 4) = 0. One bracket must be zero: x = 5 or x = 4.
Worked examples
Factorise x² + 11x + 18.
- Find two numbers that multiply to 18 and add to 11: 2 and 9.
- So x² + 11x + 18 = (x + 2)(x + 9).
- Answer: (x + 2)(x + 9)
Solve x² − 6x + 8 = 0.
- Factorise: (x − 4)(x − 2) = 0.
- One bracket must be zero: x = 4 or x = 2.
- Answer: x = 4 or x = 2
Solve x² + 5x + 6 = 0.
- Factorise: (x + 2)(x + 3) = 0.
- One bracket must be zero: x = -2 or x = -3.
- Answer: x = -2 or x = -3
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 Quadratic Sequences in Context flashcards really free?
- Yes. Every flashcards 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 Quadratic Sequences, Introducing Quadratic Sequences, nth Term of a Linear Sequence. Each one has its own free lesson, worksheet and quiz.
- How is the flashcards 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 Quadratic Sequences in Context?
- Move on to Term-to-term Rules, nth Term of a Linear Sequence, Geometric Sequences, which build directly on this idea.
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