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Ratio and proportion — KCSE Mathematics

KCSE Mathematics · 109 practice questions · 4 syllabus objectives

36 easy36 medium37 hard

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

Express and simplify ratios; divide a quantity in a given ratio

Solve problems involving direct and inverse proportion using the unitary method and algebraic approach

Apply ratio and proportion to map reading (scales), mixing solutions and sharing resources

Ratio and proportion

Sample Questions

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1
easySHORT ANSWER4 marks

Identify the ratio in which two solutions of salt water are mixed if solution A has a concentration of 15% and solution B has a concentration of 5%. If the final mixture needs to be 10% concentrated, state the ratio of solution A to B required. (4 marks)

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Part (a) — 4 marks
Let the ratio be x:y, where x = amount of solution A and y = amount of solution B (1 mk)
Set up the equation 10 = (15x + 5y) / (x + y) (1 mk)
Solve to find x:y = 1:1 (1 mk)
State that the required ratio is 1:1 (1 mk)
2
easySHORT ANSWER2 marks

Identify the scale of a map that represents a distance of 50 km as 5 cm. If a distance of 20 km is to be represented on the same map, calculate the length in centimetres. (2 marks)

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Part (a) — 2 marks
Scale = 1 cm represents 10 km (1 mk)
Length for 20 km = 2 cm (1 mk)
3
easySHORT ANSWER2 marks

State the new price of a product if its original price was KES 800 and it is increased in the ratio of 3:5. (2 marks)

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Part (b) — 2 marks
Calculate total parts of the ratio = 3 + 5 = 8 (1 mk)
New price = 800 × (5/3) = KES 1333.33 (1 mk)
4

State the amount of money each student receives if KES 600 is shared among 4 students in the ratio 2:3:1:4. (3 marks)

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Why Practise Ratio and proportion?

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