Free Grade 3 Introduction to Introducing Reverse Differentiation Common Errors Flashcards
Free Grade 3 flashcards for Introduction to 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
Higher
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introduction to introducing reverse differentiation common errors
Explain introduction to introducing reverse differentiation common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introduction to introducing reverse differentiation common errors
Calculate introduction to introducing reverse differentiation common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introduction to introducing reverse differentiation common errors
Compare introduction to introducing reverse differentiation common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introduction to introducing reverse differentiation common errors
Justify introduction to 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 Introduction to 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 = 6x^3 + 9x.[1]
- 2.Differentiate y = 5x^2 + 7x.[1]
- 3.Differentiate y = 1x^2 + 9x.[1]
- 4.Differentiate y = 2x^4 + 7x.[1]
- 5.Differentiate y = 5x^2 + 1x.[2]
- 6.Differentiate y = 5x^4 + 8x.[2]
- 7.Differentiate y = 3x^3 + 4x.[2]
- 8.Differentiate y = 6x^4 + 2x.[2]
- 9.Find the gradient of y = 3x^3 + 7x at x = 2.[3]
- 10.Find the gradient of y = 5x^5 + 1x at x = 1.[3]
- 11.Find the gradient of y = 3x^4 + 3x at x = 3.[3]
- 12.Find the gradient of y = 4x^3 + 8x at x = 2.[3]
Show answers and working
1. dy/dx = 18x^2 + 9
Multiply by the power, then reduce the power by 1. 6x^3 → 18x^2; 9x → 9.
2. dy/dx = 10x^1 + 7
Multiply by the power, then reduce the power by 1. 5x^2 → 10x^1; 7x → 7.
3. dy/dx = 2x^1 + 9
Multiply by the power, then reduce the power by 1. 1x^2 → 2x^1; 9x → 9.
4. dy/dx = 8x^3 + 7
Multiply by the power, then reduce the power by 1. 2x^4 → 8x^3; 7x → 7.
5. dy/dx = 10x^1 + 1
Multiply by the power, then reduce the power by 1. 5x^2 → 10x^1; 1x → 1.
6. dy/dx = 20x^3 + 8
Multiply by the power, then reduce the power by 1. 5x^4 → 20x^3; 8x → 8.
7. dy/dx = 9x^2 + 4
Multiply by the power, then reduce the power by 1. 3x^3 → 9x^2; 4x → 4.
8. dy/dx = 24x^3 + 2
Multiply by the power, then reduce the power by 1. 6x^4 → 24x^3; 2x → 2.
9. 43
dy/dx = 9x^2 + 7. At x = 2: 9 × 4 + 7 = 43.
10. 26
dy/dx = 25x^4 + 1. At x = 1: 25 × 1 + 1 = 26.
11. 327
dy/dx = 12x^3 + 3. At x = 3: 12 × 27 + 3 = 327.
12. 56
dy/dx = 12x^2 + 8. At x = 2: 12 × 4 + 8 = 56.
Worked examples
Differentiate y = 2x^3 + 2x.
- Multiply by the power, then reduce the power by 1.
- 2x^3 → 6x^2; 2x → 2.
- Answer: dy/dx = 6x^2 + 2
Differentiate y = 1x^3 + 9x.
- Multiply by the power, then reduce the power by 1.
- 1x^3 → 3x^2; 9x → 9.
- Answer: dy/dx = 3x^2 + 9
Find the gradient of y = 5x^4 + 6x at x = 2.
- dy/dx = 20x^3 + 6.
- At x = 2: 20 × 8 + 6 = 166.
- Answer: 166
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 Introducing Reverse Differentiation Word Problems. Each one has its own free lesson, worksheet and quiz.
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