y ∝ x: Problem Solving & Reasoning
Mathematics
GCSE Foundation
16 questions
~32 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the concept of direct proportion y ∝ x through problem solving, real-world applications, and reasoning tasks tailored for GCSE Foundation students.
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y ∝ x: Problem Solving & Reasoning
Subject: MathematicsGrade: GCSE Foundation
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Untitled Worksheet
Grade GCSE Foundation
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
If y is directly proportional to x and y = 12 when x = 4, find the constant of proportionality k and write the formula for y in terms of x.
[3 marks]2.
Plot the graph of y = 2x for x from 0 to 5 on the grid provided.
[3 marks]3.
Calculate y when x = 7 if y ∝ x and y = 10 when x = 5.
[2 marks]4.
Construct a straight line on the grid that passes through the points (2, 4) and (4, 8). Is this consistent with y ∝ x? Explain.
[3 marks]B
Problem Solving & Reasoning
Answer all questions. Show detailed reasoning and calculations.
1.
A car consumes fuel at a rate proportional to the distance traveled. If 50 litres are used to travel 200 km, how much fuel is needed to travel 350 km? Assume proportionality.
[4 marks]2.
A recipe uses 300g of sugar for 4 servings. How much sugar is needed for 10 servings? Show your reasoning.
[3 marks]3.
A machine produces 120 units in 6 hours. At the same rate, how many units will it produce in 10 hours? Show your working.
[3 marks]4.
Explain why the graph of y = 4x is a straight line through the origin. What does the slope represent?
[3 marks]C
Real-world Applications
Answer all questions, showing your reasoning and calculations.
1.
A cyclist pedals at a speed proportional to the effort applied. If applying effort level 3 results in a speed of 15 km/h, what effort level is needed to achieve a speed of 20 km/h?
[3 marks]2.
A factory produces 500 units in 8 hours. How many units can it produce in 20 hours, assuming constant rate? Show your work.
[3 marks]D
Challenge & Extension
Attempt these more challenging problems. Show your detailed reasoning.
1.
A tank is filled at a rate proportional to the time. If it takes 4 hours to fill half the tank, how long will it take to fill the entire tank? Explain your reasoning.
[4 marks]2.
A map scale shows that 1 cm represents 5 km. If a route measures 7.5 cm on the map, what is the actual distance? Is this consistent with y ∝ x? Explain.
[3 marks]E
Mixed Review
Try these mixed questions to test your understanding of y ∝ x.
1.
Write the formula for y if y is directly proportional to x and y = 9 when x = 3.
[2 marks]2.
Plot the graph of y = 5x for x from 0 to 4 on the grid provided.
[3 marks]F
Error Analysis
Review the following and identify the mistake. Correct your answer accordingly.
1.
A student claims that y ∝ x but plots the points (1,2), (2,4), and (3,6) and concludes y is proportional to x². What is wrong?
[3 marks]2.
A graph of y = 4x is mistakenly drawn with a slope of 2. What is the error and how can it be fixed?
[3 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet