Free Grade 3 Working with Product Rule Quizzes
Free Grade 3 quizzes for Working with Product Rule: 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
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain working with product rule
Explain working with product rule accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with product rule
Calculate working with product rule accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with product rule
Compare working with product rule accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with product rule
Justify working with product rule 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 Product Rule 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 + 8x.[1]
- 2.Differentiate y = 6x^4 + 9x.[1]
- 3.Differentiate y = 6x^3 + 5x.[1]
- 4.Differentiate y = 1x^5 + 8x.[1]
- 5.Differentiate y = 6x^3 + 6x.[2]
- 6.Differentiate y = 4x^3 + 4x.[2]
- 7.Differentiate y = 3x^4 + 9x.[2]
- 8.Differentiate y = 2x^5 + 2x.[2]
- 9.Find the gradient of y = 2x^4 + 1x at x = 3.[3]
- 10.Find the gradient of y = 2x^2 + 4x at x = 2.[3]
- 11.Find the gradient of y = 4x^3 + 1x at x = 2.[3]
- 12.Find the gradient of y = 3x^5 + 9x at x = 1.[3]
Show answers and working
1. dy/dx = 6x^1 + 8
Multiply by the power, then reduce the power by 1. 3x^2 → 6x^1; 8x → 8.
2. dy/dx = 24x^3 + 9
Multiply by the power, then reduce the power by 1. 6x^4 → 24x^3; 9x → 9.
3. dy/dx = 18x^2 + 5
Multiply by the power, then reduce the power by 1. 6x^3 → 18x^2; 5x → 5.
4. dy/dx = 5x^4 + 8
Multiply by the power, then reduce the power by 1. 1x^5 → 5x^4; 8x → 8.
5. dy/dx = 18x^2 + 6
Multiply by the power, then reduce the power by 1. 6x^3 → 18x^2; 6x → 6.
6. dy/dx = 12x^2 + 4
Multiply by the power, then reduce the power by 1. 4x^3 → 12x^2; 4x → 4.
7. dy/dx = 12x^3 + 9
Multiply by the power, then reduce the power by 1. 3x^4 → 12x^3; 9x → 9.
8. dy/dx = 10x^4 + 2
Multiply by the power, then reduce the power by 1. 2x^5 → 10x^4; 2x → 2.
9. 217
dy/dx = 8x^3 + 1. At x = 3: 8 × 27 + 1 = 217.
10. 12
dy/dx = 4x^1 + 4. At x = 2: 4 × 2 + 4 = 12.
11. 49
dy/dx = 12x^2 + 1. At x = 2: 12 × 4 + 1 = 49.
12. 24
dy/dx = 15x^4 + 9. At x = 1: 15 × 1 + 9 = 24.
Worked examples
Differentiate y = 5x^3 + 5x.
- Multiply by the power, then reduce the power by 1.
- 5x^3 → 15x^2; 5x → 5.
- Answer: dy/dx = 15x^2 + 5
Differentiate y = 2x^5 + 3x.
- Multiply by the power, then reduce the power by 1.
- 2x^5 → 10x^4; 3x → 3.
- Answer: dy/dx = 10x^4 + 3
Find the gradient of y = 1x^3 + 3x at x = 2.
- dy/dx = 3x^2 + 3.
- At x = 2: 3 × 4 + 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
How mastery is evidenced, and which standards it maps to.
Every free resource for Working with Product Rule
One concept, one ecosystem — all of it free.
Goes deeper
The entities below this one, each with the same complete free resource set.
Sibling concepts
Related concepts
Lateral links, including across subjects.
Next topics
All free formats for this concept
Every kind below is a real page, generated from this entity.
Learn — Meet the idea.
Practice — Build fluency.
Revise — Keep it in memory.
Assess — Prove mastery.
Apply — Use it in context.
Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 Working with Product Rule quiz really free?
- Yes. Every quizzes 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 Product Rule, Chain Rule. Each one has its own free lesson, worksheet and quiz.
- How is the quiz 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 Product Rule?
- Move on to Product Rule in Context, Rate of Change, Differentiating Powers, Tangents and Normals, which build directly on this idea.
Related resources
Stuck on Working with Product Rule? The AI Tutor already knows this page, its prerequisites and its common mistakes.
Open the free AI Tutor