Free Grade 3 Working with Introducing Reverse Differentiation Common Errors Quizzes
Free Grade 3 quizzes for Working with Introducing Reverse Differentiation Common Errors: 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
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain working with introducing reverse differentiation common errors
Explain working with introducing reverse differentiation common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with introducing reverse differentiation common errors
Calculate working with introducing reverse differentiation common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with introducing reverse differentiation common errors
Compare working with introducing reverse differentiation common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with introducing reverse differentiation common errors
Justify working with introducing reverse differentiation common errors 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 Introducing Reverse Differentiation Common Errors 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^2 + 6x.[1]
- 2.Differentiate y = 5x^4 + 8x.[1]
- 3.Differentiate y = 3x^2 + 5x.[1]
- 4.Differentiate y = 4x^2 + 1x.[1]
- 5.Differentiate y = 6x^4 + 6x.[2]
- 6.Differentiate y = 2x^5 + 7x.[2]
- 7.Differentiate y = 1x^3 + 1x.[2]
- 8.Differentiate y = 3x^4 + 1x.[2]
- 9.Find the gradient of y = 3x^5 + 8x at x = 1.[3]
- 10.Find the gradient of y = 1x^4 + 1x at x = 1.[3]
- 11.Find the gradient of y = 6x^3 + 1x at x = 3.[3]
- 12.Find the gradient of y = 6x^5 + 4x at x = 3.[3]
Show answers and working
1. dy/dx = 6x^1 + 6
Multiply by the power, then reduce the power by 1. 3x^2 → 6x^1; 6x → 6.
2. dy/dx = 20x^3 + 8
Multiply by the power, then reduce the power by 1. 5x^4 → 20x^3; 8x → 8.
3. dy/dx = 6x^1 + 5
Multiply by the power, then reduce the power by 1. 3x^2 → 6x^1; 5x → 5.
4. dy/dx = 8x^1 + 1
Multiply by the power, then reduce the power by 1. 4x^2 → 8x^1; 1x → 1.
5. dy/dx = 24x^3 + 6
Multiply by the power, then reduce the power by 1. 6x^4 → 24x^3; 6x → 6.
6. dy/dx = 10x^4 + 7
Multiply by the power, then reduce the power by 1. 2x^5 → 10x^4; 7x → 7.
7. dy/dx = 3x^2 + 1
Multiply by the power, then reduce the power by 1. 1x^3 → 3x^2; 1x → 1.
8. dy/dx = 12x^3 + 1
Multiply by the power, then reduce the power by 1. 3x^4 → 12x^3; 1x → 1.
9. 23
dy/dx = 15x^4 + 8. At x = 1: 15 × 1 + 8 = 23.
10. 5
dy/dx = 4x^3 + 1. At x = 1: 4 × 1 + 1 = 5.
11. 163
dy/dx = 18x^2 + 1. At x = 3: 18 × 9 + 1 = 163.
12. 2434
dy/dx = 30x^4 + 4. At x = 3: 30 × 81 + 4 = 2434.
Worked examples
Differentiate y = 4x^3 + 7x.
- Multiply by the power, then reduce the power by 1.
- 4x^3 → 12x^2; 7x → 7.
- Answer: dy/dx = 12x^2 + 7
Differentiate y = 3x^4 + 7x.
- Multiply by the power, then reduce the power by 1.
- 3x^4 → 12x^3; 7x → 7.
- Answer: dy/dx = 12x^3 + 7
Find the gradient of y = 3x^4 + 4x at x = 3.
- dy/dx = 12x^3 + 4.
- At x = 3: 12 × 27 + 4 = 328.
- Answer: 328
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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- Start with Rules and Methods in Introducing Reverse Differentiation Common Errors, Key Vocabulary of Introducing Reverse Differentiation Common Errors, Introducing Reverse Differentiation Word Problems. Each one has its own free lesson, worksheet and quiz.
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