Free Grade 3 Introducing Quadratic Sequences Common Errors Quizzes
Free Grade 3 quizzes for Introducing Quadratic Sequences Common Errors: 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.
- UnderstandExplain introducing quadratic sequences common errors
Explain introducing quadratic sequences common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing quadratic sequences common errors
Calculate introducing quadratic sequences common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing quadratic sequences common errors
Compare introducing quadratic sequences common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing quadratic sequences common errors
Justify introducing quadratic sequences common errors 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 Introducing Quadratic Sequences Common Errors 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 + 6x + 8.[1]
- 2.Factorise x² + 9x + 14.[1]
- 3.Factorise x² − 12x + 35.[1]
- 4.Factorise x² − 7x + 6.[1]
- 5.Solve x² + 6x − 27 = 0.[2]
- 6.Solve x² + 9x + 14 = 0.[2]
- 7.Solve x² − 12x + 27 = 0.[2]
- 8.Solve x² − 8x − 9 = 0.[2]
- 9.Solve x² + 2x − 48 = 0.[3]
- 10.Solve x² + 0x − 1 = 0.[3]
- 11.Solve x² − 5x − 14 = 0.[3]
- 12.Solve x² + 5x − 6 = 0.[3]
Show answers and working
1. (x + 2)(x + 4)
Find two numbers that multiply to 8 and add to 6: 2 and 4. So x² + 6x + 8 = (x + 2)(x + 4).
2. (x + 2)(x + 7)
Find two numbers that multiply to 14 and add to 9: 2 and 7. So x² + 9x + 14 = (x + 2)(x + 7).
3. (x − 5)(x − 7)
Find two numbers that multiply to 35 and add to -12: -5 and -7. So x² − 12x + 35 = (x − 5)(x − 7).
4. (x − 1)(x − 6)
Find two numbers that multiply to 6 and add to -7: -1 and -6. So x² − 7x + 6 = (x − 1)(x − 6).
5. x = -9 or x = 3
Factorise: (x + 9)(x − 3) = 0. One bracket must be zero: x = -9 or x = 3.
6. x = -2 or x = -7
Factorise: (x + 2)(x + 7) = 0. One bracket must be zero: x = -2 or x = -7.
7. x = 3 or x = 9
Factorise: (x − 3)(x − 9) = 0. One bracket must be zero: x = 3 or x = 9.
8. x = 9 or x = -1
Factorise: (x − 9)(x + 1) = 0. One bracket must be zero: x = 9 or x = -1.
9. x = -8 or x = 6
Factorise: (x + 8)(x − 6) = 0. One bracket must be zero: x = -8 or x = 6.
10. x = 1 or x = -1
Factorise: (x − 1)(x + 1) = 0. One bracket must be zero: x = 1 or x = -1.
11. x = -2 or x = 7
Factorise: (x + 2)(x − 7) = 0. One bracket must be zero: x = -2 or x = 7.
12. x = -6 or x = 1
Factorise: (x + 6)(x − 1) = 0. One bracket must be zero: x = -6 or x = 1.
Worked examples
Factorise x² − 10x + 9.
- Find two numbers that multiply to 9 and add to -10: -9 and -1.
- So x² − 10x + 9 = (x − 9)(x − 1).
- Answer: (x − 9)(x − 1)
Solve x² + 15x + 54 = 0.
- Factorise: (x + 6)(x + 9) = 0.
- One bracket must be zero: x = -6 or x = -9.
- Answer: x = -6 or x = -9
Solve x² − 3x − 4 = 0.
- Factorise: (x + 1)(x − 4) = 0.
- One bracket must be zero: x = -1 or x = 4.
- Answer: x = -1 or x = 4
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
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- What should a learner already know before this?
- Start with Introducing Quadratic Sequences Word Problems, Introducing Quadratic Sequences Techniques, nth Term of a Linear Sequence. Each one has its own free lesson, worksheet and quiz.
- How is the quiz 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 Introducing Quadratic Sequences Common Errors?
- Move on to Working with Quadratic Sequences, Quadratic Sequences in Context, which build directly on this idea.
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