Free Grade 3 Reverse Differentiation Worksheets
Free Grade 3 worksheets for 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 reverse differentiation
Identify reverse differentiation accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain reverse differentiation
Explain reverse differentiation accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate reverse differentiation
Calculate reverse differentiation accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare reverse differentiation
Compare 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 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 = 1x^4 + 7x.[1]
- 2.Differentiate y = 6x^2 + 2x.[1]
- 3.Differentiate y = 3x^2 + 2x.[1]
- 4.Differentiate y = 5x^4 + 4x.[1]
- 5.Differentiate y = 4x^2 + 7x.[2]
- 6.Differentiate y = 6x^3 + 6x.[2]
- 7.Differentiate y = 1x^2 + 3x.[2]
- 8.Differentiate y = 5x^2 + 6x.[2]
- 9.Find the gradient of y = 3x^3 + 1x at x = 1.[3]
- 10.Find the gradient of y = 2x^5 + 3x at x = 1.[3]
- 11.Find the gradient of y = 6x^3 + 9x at x = 1.[3]
- 12.Find the gradient of y = 2x^4 + 6x at x = 2.[3]
Show answers and working
1. dy/dx = 4x^3 + 7
Multiply by the power, then reduce the power by 1. 1x^4 → 4x^3; 7x → 7.
2. dy/dx = 12x^1 + 2
Multiply by the power, then reduce the power by 1. 6x^2 → 12x^1; 2x → 2.
3. dy/dx = 6x^1 + 2
Multiply by the power, then reduce the power by 1. 3x^2 → 6x^1; 2x → 2.
4. dy/dx = 20x^3 + 4
Multiply by the power, then reduce the power by 1. 5x^4 → 20x^3; 4x → 4.
5. dy/dx = 8x^1 + 7
Multiply by the power, then reduce the power by 1. 4x^2 → 8x^1; 7x → 7.
6. dy/dx = 18x^2 + 6
Multiply by the power, then reduce the power by 1. 6x^3 → 18x^2; 6x → 6.
7. dy/dx = 2x^1 + 3
Multiply by the power, then reduce the power by 1. 1x^2 → 2x^1; 3x → 3.
8. dy/dx = 10x^1 + 6
Multiply by the power, then reduce the power by 1. 5x^2 → 10x^1; 6x → 6.
9. 10
dy/dx = 9x^2 + 1. At x = 1: 9 × 1 + 1 = 10.
10. 13
dy/dx = 10x^4 + 3. At x = 1: 10 × 1 + 3 = 13.
11. 27
dy/dx = 18x^2 + 9. At x = 1: 18 × 1 + 9 = 27.
12. 70
dy/dx = 8x^3 + 6. At x = 2: 8 × 8 + 6 = 70.
Worked examples
Differentiate y = 4x^4 + 5x.
- Multiply by the power, then reduce the power by 1.
- 4x^4 → 16x^3; 5x → 5.
- Answer: dy/dx = 16x^3 + 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 = 3x^3 + 6x at x = 1.
- dy/dx = 9x^2 + 6.
- At x = 1: 9 × 1 + 6 = 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
How mastery is evidenced, and which standards it maps to.
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Frequently asked
- Is this Grade 3 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 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 Reverse Differentiation?
- Move on to Definite Integrals, Area Under a Curve, Differentiation, which build directly on this idea.
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