Free Grade 3 Tangents and Normals in Context Flashcards
Free Grade 3 flashcards for Tangents and Normals in Context: 12 real questions with a full answer key and worked solutions. Differentiation finds the rate of change (the gradient) of a curve. For axⁿ, the derivative is naxⁿ⁻¹.
Free
Core
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify tangents and normals in context
Identify tangents and normals in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain tangents and normals in context
Explain tangents and normals in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate tangents and normals in context
Calculate tangents and normals in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare tangents and normals in context
Compare tangents and normals 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 Tangents and Normals in Context works
Differentiation finds the rate of change (the gradient) of a curve. For axⁿ, the derivative is naxⁿ⁻¹.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.Differentiate y = 3x^3 + 2x.[1]
- 2.Differentiate y = 4x^3 + 5x.[1]
- 3.Differentiate y = 6x^5 + 3x.[1]
- 4.Differentiate y = 2x^2 + 1x.[1]
- 5.Differentiate y = 3x^4 + 5x.[2]
- 6.Differentiate y = 4x^4 + 7x.[2]
- 7.Differentiate y = 5x^4 + 6x.[2]
- 8.Differentiate y = 4x^3 + 3x.[2]
- 9.Find the gradient of y = 4x^3 + 6x at x = 3.[3]
- 10.Find the gradient of y = 6x^5 + 7x at x = 1.[3]
- 11.Find the gradient of y = 4x^2 + 8x at x = 3.[3]
- 12.Find the gradient of y = 6x^4 + 2x at x = 2.[3]
Show answers and working
1. dy/dx = 9x^2 + 2
Multiply by the power, then reduce the power by 1. 3x^3 → 9x^2; 2x → 2.
2. dy/dx = 12x^2 + 5
Multiply by the power, then reduce the power by 1. 4x^3 → 12x^2; 5x → 5.
3. dy/dx = 30x^4 + 3
Multiply by the power, then reduce the power by 1. 6x^5 → 30x^4; 3x → 3.
4. dy/dx = 4x^1 + 1
Multiply by the power, then reduce the power by 1. 2x^2 → 4x^1; 1x → 1.
5. dy/dx = 12x^3 + 5
Multiply by the power, then reduce the power by 1. 3x^4 → 12x^3; 5x → 5.
6. dy/dx = 16x^3 + 7
Multiply by the power, then reduce the power by 1. 4x^4 → 16x^3; 7x → 7.
7. dy/dx = 20x^3 + 6
Multiply by the power, then reduce the power by 1. 5x^4 → 20x^3; 6x → 6.
8. dy/dx = 12x^2 + 3
Multiply by the power, then reduce the power by 1. 4x^3 → 12x^2; 3x → 3.
9. 114
dy/dx = 12x^2 + 6. At x = 3: 12 × 9 + 6 = 114.
10. 37
dy/dx = 30x^4 + 7. At x = 1: 30 × 1 + 7 = 37.
11. 32
dy/dx = 8x^1 + 8. At x = 3: 8 × 3 + 8 = 32.
12. 194
dy/dx = 24x^3 + 2. At x = 2: 24 × 8 + 2 = 194.
Worked examples
Differentiate y = 5x^4 + 8x.
- Multiply by the power, then reduce the power by 1.
- 5x^4 → 20x^3; 8x → 8.
- Answer: dy/dx = 20x^3 + 8
Differentiate y = 3x^5 + 5x.
- Multiply by the power, then reduce the power by 1.
- 3x^5 → 15x^4; 5x → 5.
- Answer: dy/dx = 15x^4 + 5
Find the gradient of y = 5x^2 + 6x at x = 3.
- dy/dx = 10x^1 + 6.
- At x = 3: 10 × 3 + 6 = 36.
- Answer: 36
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Forgets that a constant differentiates to 0.
Correction: Constants have zero gradient.
Reduces the power but forgets to multiply by it.
Correction: Multiply by the power, then reduce it by 1.
Teacher tips
- · Link to gradients of straight lines first.
Parent tips
- · Ask how speed relates to distance over time.
Real-life applications
- · Speed from distance, maximising profit.
Assessment objectives
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Frequently asked
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- 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 Tangents and Normals, Introducing Tangents and Normals, Differentiating Powers. 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 Tangents and Normals in Context?
- Move on to Rate of Change, Differentiating Powers, Stationary Points, Chain Rule, which build directly on this idea.
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