Free Grade 3 The Quadratic Formula in Context Flashcards
Free Grade 3 flashcards for The Quadratic Formula 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
Core
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify the quadratic formula in context
Identify the quadratic formula in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain the quadratic formula in context
Explain the quadratic formula in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate the quadratic formula in context
Calculate the quadratic formula in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare the quadratic formula in context
Compare the quadratic formula 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 The Quadratic Formula 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 − 16x + 63.[1]
- 2.Factorise x² − 3x − 10.[1]
- 3.Factorise x² + 8x + 16.[1]
- 4.Factorise x² + 4x − 12.[1]
- 5.Solve x² + 4x − 12 = 0.[2]
- 6.Solve x² + 2x − 15 = 0.[2]
- 7.Solve x² − 6x − 16 = 0.[2]
- 8.Solve x² − 5x − 14 = 0.[2]
- 9.Solve x² − 6x + 8 = 0.[3]
- 10.Solve x² + 15x + 54 = 0.[3]
- 11.Solve x² − 1x − 20 = 0.[3]
- 12.Solve x² − 6x − 27 = 0.[3]
Show answers and working
1. (x − 7)(x − 9)
Find two numbers that multiply to 63 and add to -16: -7 and -9. So x² − 16x + 63 = (x − 7)(x − 9).
2. (x + 2)(x − 5)
Find two numbers that multiply to -10 and add to -3: 2 and -5. So x² − 3x − 10 = (x + 2)(x − 5).
3. (x + 4)(x + 4)
Find two numbers that multiply to 16 and add to 8: 4 and 4. So x² + 8x + 16 = (x + 4)(x + 4).
4. (x − 2)(x + 6)
Find two numbers that multiply to -12 and add to 4: -2 and 6. So x² + 4x − 12 = (x − 2)(x + 6).
5. x = -6 or x = 2
Factorise: (x + 6)(x − 2) = 0. One bracket must be zero: x = -6 or x = 2.
6. x = -5 or x = 3
Factorise: (x + 5)(x − 3) = 0. One bracket must be zero: x = -5 or x = 3.
7. x = 8 or x = -2
Factorise: (x − 8)(x + 2) = 0. One bracket must be zero: x = 8 or x = -2.
8. x = -2 or x = 7
Factorise: (x + 2)(x − 7) = 0. One bracket must be zero: x = -2 or x = 7.
9. x = 2 or x = 4
Factorise: (x − 2)(x − 4) = 0. One bracket must be zero: x = 2 or x = 4.
10. x = -6 or x = -9
Factorise: (x + 6)(x + 9) = 0. One bracket must be zero: x = -6 or x = -9.
11. x = -4 or x = 5
Factorise: (x + 4)(x − 5) = 0. One bracket must be zero: x = -4 or x = 5.
12. x = 9 or x = -3
Factorise: (x − 9)(x + 3) = 0. One bracket must be zero: x = 9 or x = -3.
Worked examples
Factorise x² + 12x + 32.
- Find two numbers that multiply to 32 and add to 12: 4 and 8.
- So x² + 12x + 32 = (x + 4)(x + 8).
- Answer: (x + 4)(x + 8)
Solve x² + 7x + 6 = 0.
- Factorise: (x + 1)(x + 6) = 0.
- One bracket must be zero: x = -1 or x = -6.
- Answer: x = -1 or x = -6
Solve x² − 17x + 72 = 0.
- Factorise: (x − 9)(x − 8) = 0.
- One bracket must be zero: x = 9 or x = 8.
- Answer: x = 9 or x = 8
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
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Frequently asked
- Is this Grade 3 The Quadratic Formula 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 The Quadratic Formula, Introducing The Quadratic Formula, Completing the Square. 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 The Quadratic Formula in Context?
- Move on to Expanding Double Brackets, Factorising Quadratics, Completing the Square, Quadratic Graphs, which build directly on this idea.
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