Free Grade 3 Working with Reverse Differentiation Essentials Flashcards
Free Grade 3 flashcards for Working with Reverse Differentiation Essentials: 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.
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Core
20 min
24
Learning objectives
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- RememberIdentify working with reverse differentiation essentials
Identify working with reverse differentiation essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with reverse differentiation essentials
Explain working with reverse differentiation essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with reverse differentiation essentials
Calculate working with reverse differentiation essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with reverse differentiation essentials
Compare working with reverse differentiation essentials 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 Working with Reverse Differentiation Essentials 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 = 6x^2 + 8x.[1]
- 2.Differentiate y = 6x^5 + 3x.[1]
- 3.Differentiate y = 3x^5 + 1x.[1]
- 4.Differentiate y = 2x^5 + 1x.[1]
- 5.Differentiate y = 6x^3 + 4x.[2]
- 6.Differentiate y = 6x^4 + 1x.[2]
- 7.Differentiate y = 5x^5 + 3x.[2]
- 8.Differentiate y = 4x^3 + 3x.[2]
- 9.Find the gradient of y = 5x^4 + 8x at x = 2.[3]
- 10.Find the gradient of y = 2x^2 + 2x at x = 2.[3]
- 11.Find the gradient of y = 3x^2 + 9x at x = 3.[3]
- 12.Find the gradient of y = 5x^5 + 2x at x = 1.[3]
Show answers and working
1. dy/dx = 12x^1 + 8
Multiply by the power, then reduce the power by 1. 6x^2 → 12x^1; 8x → 8.
2. dy/dx = 30x^4 + 3
Multiply by the power, then reduce the power by 1. 6x^5 → 30x^4; 3x → 3.
3. dy/dx = 15x^4 + 1
Multiply by the power, then reduce the power by 1. 3x^5 → 15x^4; 1x → 1.
4. dy/dx = 10x^4 + 1
Multiply by the power, then reduce the power by 1. 2x^5 → 10x^4; 1x → 1.
5. dy/dx = 18x^2 + 4
Multiply by the power, then reduce the power by 1. 6x^3 → 18x^2; 4x → 4.
6. dy/dx = 24x^3 + 1
Multiply by the power, then reduce the power by 1. 6x^4 → 24x^3; 1x → 1.
7. dy/dx = 25x^4 + 3
Multiply by the power, then reduce the power by 1. 5x^5 → 25x^4; 3x → 3.
8. dy/dx = 12x^2 + 3
Multiply by the power, then reduce the power by 1. 4x^3 → 12x^2; 3x → 3.
9. 168
dy/dx = 20x^3 + 8. At x = 2: 20 × 8 + 8 = 168.
10. 10
dy/dx = 4x^1 + 2. At x = 2: 4 × 2 + 2 = 10.
11. 27
dy/dx = 6x^1 + 9. At x = 3: 6 × 3 + 9 = 27.
12. 27
dy/dx = 25x^4 + 2. At x = 1: 25 × 1 + 2 = 27.
Worked examples
Differentiate y = 1x^3 + 5x.
- Multiply by the power, then reduce the power by 1.
- 1x^3 → 3x^2; 5x → 5.
- Answer: dy/dx = 3x^2 + 5
Differentiate y = 2x^4 + 3x.
- Multiply by the power, then reduce the power by 1.
- 2x^4 → 8x^3; 3x → 3.
- Answer: dy/dx = 8x^3 + 3
Find the gradient of y = 6x^5 + 8x at x = 1.
- dy/dx = 30x^4 + 8.
- At x = 1: 30 × 1 + 8 = 38.
- Answer: 38
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.
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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 Introducing Reverse Differentiation. 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 Working with Reverse Differentiation Essentials?
- Move on to Working with Reverse Differentiation Techniques, Working with Reverse Differentiation Word Problems, Working with Reverse Differentiation Common Errors, Introducing Reverse Differentiation, which build directly on this idea.
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