Free Grade 3 Introducing Quadratic Sequences Techniques Flashcards
Free Grade 3 flashcards for Introducing Quadratic Sequences Techniques: 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
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing quadratic sequences techniques
Explain introducing quadratic sequences techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing quadratic sequences techniques
Calculate introducing quadratic sequences techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing quadratic sequences techniques
Compare introducing quadratic sequences techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing quadratic sequences techniques
Justify introducing quadratic sequences techniques 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 Techniques 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 + 1x − 30.[1]
- 2.Factorise x² + 11x + 18.[1]
- 3.Factorise x² − 9x + 18.[1]
- 4.Factorise x² − 16x + 63.[1]
- 5.Solve x² + 12x + 35 = 0.[2]
- 6.Solve x² + 6x + 8 = 0.[2]
- 7.Solve x² + 0x − 81 = 0.[2]
- 8.Solve x² − 4x − 12 = 0.[2]
- 9.Solve x² + 3x − 4 = 0.[3]
- 10.Solve x² + 2x − 8 = 0.[3]
- 11.Solve x² − 1x − 12 = 0.[3]
- 12.Solve x² − 1x − 6 = 0.[3]
Show answers and working
1. (x + 6)(x − 5)
Find two numbers that multiply to -30 and add to 1: 6 and -5. So x² + 1x − 30 = (x + 6)(x − 5).
2. (x + 2)(x + 9)
Find two numbers that multiply to 18 and add to 11: 2 and 9. So x² + 11x + 18 = (x + 2)(x + 9).
3. (x − 3)(x − 6)
Find two numbers that multiply to 18 and add to -9: -3 and -6. So x² − 9x + 18 = (x − 3)(x − 6).
4. (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).
5. x = -5 or x = -7
Factorise: (x + 5)(x + 7) = 0. One bracket must be zero: x = -5 or x = -7.
6. x = -2 or x = -4
Factorise: (x + 2)(x + 4) = 0. One bracket must be zero: x = -2 or x = -4.
7. x = -9 or x = 9
Factorise: (x + 9)(x − 9) = 0. One bracket must be zero: x = -9 or x = 9.
8. x = -2 or x = 6
Factorise: (x + 2)(x − 6) = 0. One bracket must be zero: x = -2 or x = 6.
9. x = 1 or x = -4
Factorise: (x − 1)(x + 4) = 0. One bracket must be zero: x = 1 or x = -4.
10. x = -4 or x = 2
Factorise: (x + 4)(x − 2) = 0. One bracket must be zero: x = -4 or x = 2.
11. x = -3 or x = 4
Factorise: (x + 3)(x − 4) = 0. One bracket must be zero: x = -3 or x = 4.
12. x = 3 or x = -2
Factorise: (x − 3)(x + 2) = 0. One bracket must be zero: x = 3 or x = -2.
Worked examples
Factorise x² − 15x + 56.
- Find two numbers that multiply to 56 and add to -15: -7 and -8.
- So x² − 15x + 56 = (x − 7)(x − 8).
- Answer: (x − 7)(x − 8)
Solve x² + 15x + 56 = 0.
- Factorise: (x + 7)(x + 8) = 0.
- One bracket must be zero: x = -7 or x = -8.
- Answer: x = -7 or x = -8
Solve x² − 1x − 2 = 0.
- Factorise: (x − 2)(x + 1) = 0.
- One bracket must be zero: x = 2 or x = -1.
- Answer: x = 2 or x = -1
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.
Every free resource for Introducing Quadratic Sequences Techniques
One concept, one ecosystem — all of it free.
Goes deeper
The entities below this one, each with the same complete free resource set.
Sibling concepts
Related concepts
Lateral links, including across subjects.
Next topics
All free formats for this concept
Every kind below is a real page, generated from this entity.
Learn — Meet the idea.
Practice — Build fluency.
Revise — Keep it in memory.
Assess — Prove mastery.
Apply — Use it in context.
Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 Introducing Quadratic Sequences Techniques 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 Introducing Quadratic Sequences Essentials, 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 Introducing Quadratic Sequences Techniques?
- Move on to Introducing Quadratic Sequences Word Problems, Introducing Quadratic Sequences Common Errors, Working with Quadratic Sequences, Quadratic Sequences in Context, which build directly on this idea.
Related resources
- Free Introducing Quadratic Sequences Techniques worksheets
- Free Introducing Quadratic Sequences Techniques quizzes
- Free Introducing Quadratic Sequences Techniques lessons
- Free Introducing Quadratic Sequences Techniques lesson plans
- Introducing Quadratic Sequences Techniques in the knowledge graph
- Free AI Tutor
Stuck on Introducing Quadratic Sequences Techniques? The AI Tutor already knows this page, its prerequisites and its common mistakes.
Open the free AI Tutor