Mastering Direct & Inverse Proportion
Mathematics
GCSE Higher
1 questions
~2 mins
0 views0 downloads
About This Worksheet
A worksheet covering Direct & Inverse Proportion for GCSE Higher students, focusing on ratios, proportions, and rates of change.
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Mastering Direct & Inverse Proportion
Subject: MathematicsGrade: GCSE Higher
Name:
Date:
Untitled Worksheet
Grade GCSE Higher
A
Introduction
Read the brief explanation below before attempting the questions.
1.
In direct proportion, as one quantity increases, the other increases at a constant rate. In inverse proportion, as one quantity increases, the other decreases at a rate such that their product remains constant.
[2 marks]B
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
If y is directly proportional to x and y = 12 when x = 3, find the constant of proportionality k and write the general formula for y in terms of x.
[3 marks]2.
Inversely proportional, if y = 6 when x = 4, find the constant k such that xy = k. Then, find y when x = 8.
[3 marks]3.
A recipe uses 2 cups of sugar for 5 cups of flour. If the amount of sugar varies directly with the flour, how much sugar is needed for 8 cups of flour?
[3 marks]4.
A car travels 150 miles in 3 hours. Assuming the speed is constant, how long will it take to travel 250 miles?
[3 marks]5.
If the amount of paint needed (A) is inversely proportional to the number of coats (n), and 4 liters are enough for 2 coats, how much paint is needed for 5 coats?
[3 marks]6.
A worker's time (T) to complete a task is inversely proportional to the number of workers (w) involved. If 5 workers take 8 hours, how long will 10 workers take?
[3 marks]7.
A map scale shows 1 cm representing 5 km. If the distance between two cities on the map is 8 cm, what is the actual distance?
[2 marks]8.
The speed of a boat (v) varies directly with the power (p) supplied. If 50 units of power produce a speed of 20 km/h, what power is needed for a speed of 30 km/h?
[3 marks]9.
A quantity of medicine (Q) decreases inversely with time (t). If 100 mg of medicine lasts 4 hours, how long will 60 mg last?
[3 marks]10.
A factory produces 120 units in 6 hours. If production rate is directly proportional to the number of workers, how many units will 10 workers produce in 6 hours if 8 workers produce 120 units?
[3 marks]11.
Challenge: A machine's efficiency (E) varies directly with the number of hours (h) it operates. If 4 hours of operation yields an efficiency of 80, how many hours are needed to achieve an efficiency of 150?
[4 marks]12.
Real-world Application: A car's fuel consumption rate is inversely proportional to its speed. If at 60 km/h, the car consumes 8 liters per 100 km, estimate the fuel consumption at 90 km/h.
[4 marks]Quick Actions
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Details
- Created
- 12/30/2025
- Updated
- 12/30/2025
- Type
- worksheet