Rates and variation (direct, inverse, joint) — KCSE Mathematics
KCSE Mathematics · 96 practice questions · 4 syllabus objectives
What You'll Learn
Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.
Solve problems involving rates (speed, density, population density) using rate = quantity/time (or similar)
Distinguish between direct, inverse and joint variation; write and use the proportionality equation (y = kx, y = k/x, y = kxz)
Determine the constant of proportionality from a table of values and use it to find unknown quantities
Rates and variation (direct, inverse, joint)
Sample Questions
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In the study of mathematical relationships, understanding how different variables interact is crucial. The following questions explore various scenarios involving proportional relationships and their implications under specific constraints. (a) y ∝ x. If y=21 when x=4, find: (i) k (ii) y when x=6 (iii) x when y=55. (3 marks) (b) z varies inversely as w. When w=4,z=6. Find z when w=6. (2 marks)
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Given that the distance (d) travelled by a vehicle is directly proportional to the time (t) spent driving, and that d = 120 km when t = 2 hours, determine the constant of proportionality and find the distance travelled when the time is increased to 5 hours. (4 marks)
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Identify the relationship when v varies inversely with t and directly with a. If v = 10 when t = 5 and a = 2, calculate v when t = 10 and a = 4. (4 marks)
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Why Practise Rates and variation (direct, inverse, joint)?
KNEC Aligned
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