Free Grade 3 Definite Integrals Quizzes
Free Grade 3 quizzes for Definite Integrals: 12 real questions with a full answer key and worked solutions. A ratio compares parts of a whole. To share in a ratio, add the parts, find one part, then multiply.
Free
Core
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify definite integrals
Identify definite integrals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain definite integrals
Explain definite integrals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate definite integrals
Calculate definite integrals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare definite integrals
Compare definite integrals 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 Definite Integrals works
A ratio compares parts of a whole. To share in a ratio, add the parts, find one part, then multiply.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.Simplify the ratio 6:6.[1]
- 2.Simplify the ratio 18:24.[1]
- 3.Simplify the ratio 16:32.[1]
- 4.Simplify the ratio 24:6.[1]
- 5.Share 54 in the ratio 1:5.[2]
- 6.Share 81 in the ratio 5:4.[2]
- 7.Share 12 in the ratio 3:1.[2]
- 8.Share 60 in the ratio 1:4.[2]
- 9.Share 110 in the ratio 5:6.[3]
- 10.Share 110 in the ratio 3:7.[3]
- 11.Share 36 in the ratio 3:1.[3]
- 12.Share 24 in the ratio 4:2.[3]
Show answers and working
1. 1:1
HCF of 6 and 6 is 6. Divide both parts by it: 1:1.
2. 3:4
HCF of 18 and 24 is 6. Divide both parts by it: 3:4.
3. 1:2
HCF of 16 and 32 is 16. Divide both parts by it: 1:2.
4. 4:1
HCF of 24 and 6 is 6. Divide both parts by it: 4:1.
5. 9 and 45
Total parts: 1 + 5 = 6. One part: 54 ÷ 6 = 9. 1 × 9 = 9, 5 × 9 = 45.
6. 45 and 36
Total parts: 5 + 4 = 9. One part: 81 ÷ 9 = 9. 5 × 9 = 45, 4 × 9 = 36.
7. 9 and 3
Total parts: 3 + 1 = 4. One part: 12 ÷ 4 = 3. 3 × 3 = 9, 1 × 3 = 3.
8. 12 and 48
Total parts: 1 + 4 = 5. One part: 60 ÷ 5 = 12. 1 × 12 = 12, 4 × 12 = 48.
9. 50 and 60
Total parts: 5 + 6 = 11. One part: 110 ÷ 11 = 10. 5 × 10 = 50, 6 × 10 = 60.
10. 33 and 77
Total parts: 3 + 7 = 10. One part: 110 ÷ 10 = 11. 3 × 11 = 33, 7 × 11 = 77.
11. 27 and 9
Total parts: 3 + 1 = 4. One part: 36 ÷ 4 = 9. 3 × 9 = 27, 1 × 9 = 9.
12. 16 and 8
Total parts: 4 + 2 = 6. One part: 24 ÷ 6 = 4. 4 × 4 = 16, 2 × 4 = 8.
Worked examples
Simplify the ratio 30:30.
- HCF of 30 and 30 is 30.
- Divide both parts by it: 1:1.
- Answer: 1:1
Share 54 in the ratio 4:2.
- Total parts: 4 + 2 = 6.
- One part: 54 ÷ 6 = 9.
- 4 × 9 = 36, 2 × 9 = 18.
- Answer: 36 and 18
Share 48 in the ratio 2:6.
- Total parts: 2 + 6 = 8.
- One part: 48 ÷ 8 = 6.
- 2 × 6 = 12, 6 × 6 = 36.
- Answer: 12 and 36
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Divides the total by the ratio numbers directly.
Correction: Add the parts first to find what one part is worth.
Writes the ratio in the wrong order.
Correction: Keep the order the question uses.
Teacher tips
- · Use bar models with equal-sized boxes for each part.
Parent tips
- · Make squash in a 1:4 ratio.
Real-life applications
- · Mixing paint or squash, scaling recipes.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
Every free resource for Definite Integrals
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Frequently asked
- Is this Grade 3 Definite Integrals 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 Reverse Differentiation, Differentiation. 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 Definite Integrals?
- Move on to Area Under a Curve, Differentiation, which build directly on this idea.
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