Free Grade 3 Working with Reverse Differentiation Worksheets
Free Grade 3 worksheets for Working with Reverse Differentiation: 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
Foundation
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with reverse differentiation
Identify working with reverse differentiation accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with reverse differentiation
Explain working with reverse differentiation accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with reverse differentiation
Calculate working with reverse differentiation accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with reverse differentiation
Compare working with reverse differentiation 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 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^3 + 2x.[1]
- 2.Differentiate y = 1x^5 + 1x.[1]
- 3.Differentiate y = 1x^2 + 6x.[1]
- 4.Differentiate y = 1x^3 + 4x.[1]
- 5.Differentiate y = 5x^2 + 4x.[2]
- 6.Differentiate y = 2x^3 + 4x.[2]
- 7.Differentiate y = 5x^3 + 4x.[2]
- 8.Differentiate y = 1x^4 + 8x.[2]
- 9.Find the gradient of y = 2x^4 + 7x at x = 3.[3]
- 10.Find the gradient of y = 6x^3 + 8x at x = 3.[3]
- 11.Find the gradient of y = 3x^4 + 3x at x = 2.[3]
- 12.Find the gradient of y = 1x^5 + 1x at x = 2.[3]
Show answers and working
1. dy/dx = 18x^2 + 2
Multiply by the power, then reduce the power by 1. 6x^3 → 18x^2; 2x → 2.
2. dy/dx = 5x^4 + 1
Multiply by the power, then reduce the power by 1. 1x^5 → 5x^4; 1x → 1.
3. dy/dx = 2x^1 + 6
Multiply by the power, then reduce the power by 1. 1x^2 → 2x^1; 6x → 6.
4. dy/dx = 3x^2 + 4
Multiply by the power, then reduce the power by 1. 1x^3 → 3x^2; 4x → 4.
5. dy/dx = 10x^1 + 4
Multiply by the power, then reduce the power by 1. 5x^2 → 10x^1; 4x → 4.
6. dy/dx = 6x^2 + 4
Multiply by the power, then reduce the power by 1. 2x^3 → 6x^2; 4x → 4.
7. dy/dx = 15x^2 + 4
Multiply by the power, then reduce the power by 1. 5x^3 → 15x^2; 4x → 4.
8. dy/dx = 4x^3 + 8
Multiply by the power, then reduce the power by 1. 1x^4 → 4x^3; 8x → 8.
9. 223
dy/dx = 8x^3 + 7. At x = 3: 8 × 27 + 7 = 223.
10. 170
dy/dx = 18x^2 + 8. At x = 3: 18 × 9 + 8 = 170.
11. 99
dy/dx = 12x^3 + 3. At x = 2: 12 × 8 + 3 = 99.
12. 81
dy/dx = 5x^4 + 1. At x = 2: 5 × 16 + 1 = 81.
Worked examples
Differentiate y = 6x^5 + 1x.
- Multiply by the power, then reduce the power by 1.
- 6x^5 → 30x^4; 1x → 1.
- Answer: dy/dx = 30x^4 + 1
Differentiate y = 2x^3 + 7x.
- Multiply by the power, then reduce the power by 1.
- 2x^3 → 6x^2; 7x → 7.
- Answer: dy/dx = 6x^2 + 7
Find the gradient of y = 3x^4 + 3x at x = 1.
- dy/dx = 12x^3 + 3.
- At x = 1: 12 × 1 + 3 = 15.
- Answer: 15
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
- Is this Grade 3 Working with Reverse Differentiation worksheet really free?
- Yes. Every worksheets 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, Differentiation. Each one has its own free lesson, worksheet and quiz.
- How is the worksheet 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?
- Move on to Reverse Differentiation in Context, Definite Integrals, Area Under a Curve, which build directly on this idea.
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