Free Grade 3 Rules and Methods in Introducing Reverse Differentiation Common Errors: Visual Models Quizzes
Free Grade 3 quizzes for Rules and Methods in Introducing Reverse Differentiation Common Errors: Visual Models: 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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20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify rules and methods in introducing reverse differentiation common errors: visual models
Identify rules and methods in introducing reverse differentiation common errors: visual models accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain rules and methods in introducing reverse differentiation common errors: visual models
Explain rules and methods in introducing reverse differentiation common errors: visual models accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate rules and methods in introducing reverse differentiation common errors: visual models
Calculate rules and methods in introducing reverse differentiation common errors: visual models accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare rules and methods in introducing reverse differentiation common errors: visual models
Compare rules and methods in introducing reverse differentiation common errors: visual models 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 Rules and Methods in Introducing Reverse Differentiation Common Errors: Visual Models 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 = 5x^4 + 5x.[1]
- 2.Differentiate y = 5x^4 + 6x.[1]
- 3.Differentiate y = 4x^5 + 2x.[1]
- 4.Differentiate y = 4x^2 + 6x.[1]
- 5.Differentiate y = 6x^4 + 1x.[2]
- 6.Differentiate y = 6x^4 + 3x.[2]
- 7.Differentiate y = 5x^4 + 2x.[2]
- 8.Differentiate y = 4x^5 + 5x.[2]
- 9.Find the gradient of y = 4x^3 + 1x at x = 3.[3]
- 10.Find the gradient of y = 1x^2 + 7x at x = 3.[3]
- 11.Find the gradient of y = 3x^5 + 4x at x = 1.[3]
- 12.Find the gradient of y = 3x^5 + 2x at x = 3.[3]
Show answers and working
1. dy/dx = 20x^3 + 5
Multiply by the power, then reduce the power by 1. 5x^4 → 20x^3; 5x → 5.
2. dy/dx = 20x^3 + 6
Multiply by the power, then reduce the power by 1. 5x^4 → 20x^3; 6x → 6.
3. dy/dx = 20x^4 + 2
Multiply by the power, then reduce the power by 1. 4x^5 → 20x^4; 2x → 2.
4. dy/dx = 8x^1 + 6
Multiply by the power, then reduce the power by 1. 4x^2 → 8x^1; 6x → 6.
5. dy/dx = 24x^3 + 1
Multiply by the power, then reduce the power by 1. 6x^4 → 24x^3; 1x → 1.
6. dy/dx = 24x^3 + 3
Multiply by the power, then reduce the power by 1. 6x^4 → 24x^3; 3x → 3.
7. dy/dx = 20x^3 + 2
Multiply by the power, then reduce the power by 1. 5x^4 → 20x^3; 2x → 2.
8. dy/dx = 20x^4 + 5
Multiply by the power, then reduce the power by 1. 4x^5 → 20x^4; 5x → 5.
9. 109
dy/dx = 12x^2 + 1. At x = 3: 12 × 9 + 1 = 109.
10. 13
dy/dx = 2x^1 + 7. At x = 3: 2 × 3 + 7 = 13.
11. 19
dy/dx = 15x^4 + 4. At x = 1: 15 × 1 + 4 = 19.
12. 1217
dy/dx = 15x^4 + 2. At x = 3: 15 × 81 + 2 = 1217.
Worked examples
Differentiate y = 4x^4 + 9x.
- Multiply by the power, then reduce the power by 1.
- 4x^4 → 16x^3; 9x → 9.
- Answer: dy/dx = 16x^3 + 9
Differentiate y = 1x^4 + 4x.
- Multiply by the power, then reduce the power by 1.
- 1x^4 → 4x^3; 4x → 4.
- Answer: dy/dx = 4x^3 + 4
Find the gradient of y = 3x^2 + 6x at x = 2.
- dy/dx = 6x^1 + 6.
- At x = 2: 6 × 2 + 6 = 18.
- Answer: 18
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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