Free Grade 3 Working with Cosine Ratio Quizzes
Free Grade 3 quizzes for Working with Cosine Ratio: 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
Foundation
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain working with cosine ratio
Explain working with cosine ratio accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with cosine ratio
Calculate working with cosine ratio accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with cosine ratio
Compare working with cosine ratio accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with cosine ratio
Justify working with cosine ratio 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 Cosine Ratio 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 12:20.[1]
- 2.Simplify the ratio 4:4.[1]
- 3.Simplify the ratio 36:12.[1]
- 4.Simplify the ratio 12:24.[1]
- 5.Share 50 in the ratio 5:5.[2]
- 6.Share 81 in the ratio 3:6.[2]
- 7.Share 54 in the ratio 3:3.[2]
- 8.Share 20 in the ratio 1:4.[2]
- 9.Share 56 in the ratio 4:3.[3]
- 10.Share 28 in the ratio 1:6.[3]
- 11.Share 56 in the ratio 3:5.[3]
- 12.Share 56 in the ratio 3:4.[3]
Show answers and working
1. 3:5
HCF of 12 and 20 is 4. Divide both parts by it: 3:5.
2. 1:1
HCF of 4 and 4 is 4. Divide both parts by it: 1:1.
3. 3:1
HCF of 36 and 12 is 12. Divide both parts by it: 3:1.
4. 1:2
HCF of 12 and 24 is 12. Divide both parts by it: 1:2.
5. 25 and 25
Total parts: 5 + 5 = 10. One part: 50 ÷ 10 = 5. 5 × 5 = 25, 5 × 5 = 25.
6. 27 and 54
Total parts: 3 + 6 = 9. One part: 81 ÷ 9 = 9. 3 × 9 = 27, 6 × 9 = 54.
7. 27 and 27
Total parts: 3 + 3 = 6. One part: 54 ÷ 6 = 9. 3 × 9 = 27, 3 × 9 = 27.
8. 4 and 16
Total parts: 1 + 4 = 5. One part: 20 ÷ 5 = 4. 1 × 4 = 4, 4 × 4 = 16.
9. 32 and 24
Total parts: 4 + 3 = 7. One part: 56 ÷ 7 = 8. 4 × 8 = 32, 3 × 8 = 24.
10. 4 and 24
Total parts: 1 + 6 = 7. One part: 28 ÷ 7 = 4. 1 × 4 = 4, 6 × 4 = 24.
11. 21 and 35
Total parts: 3 + 5 = 8. One part: 56 ÷ 8 = 7. 3 × 7 = 21, 5 × 7 = 35.
12. 24 and 32
Total parts: 3 + 4 = 7. One part: 56 ÷ 7 = 8. 3 × 8 = 24, 4 × 8 = 32.
Worked examples
Simplify the ratio 30:20.
- HCF of 30 and 20 is 10.
- Divide both parts by it: 3:2.
- Answer: 3:2
Share 63 in the ratio 4:3.
- Total parts: 4 + 3 = 7.
- One part: 63 ÷ 7 = 9.
- 4 × 9 = 36, 3 × 9 = 27.
- Answer: 36 and 27
Share 66 in the ratio 4:7.
- Total parts: 4 + 7 = 11.
- One part: 66 ÷ 11 = 6.
- 4 × 6 = 24, 7 × 6 = 42.
- Answer: 24 and 42
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 Working with Cosine Ratio
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Frequently asked
- Is this Grade 3 Working with Cosine Ratio 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 Cosine Ratio, Sine Ratio. 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 Cosine Ratio?
- Move on to Cosine Ratio in Context, Sine Ratio, Tangent Ratio, Pythagoras' Theorem, which build directly on this idea.
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