Practise 18 exam-style questions on Ratios, fractions and linear functions for Edexcel GCSE Maths (Non-calculator). Write your answer as you would in the exam and get it marked in seconds against the mark scheme, point by point, with an AI tutor on hand if you get stuck.
18 questions
1–5 marks each
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18 questions, marked as you go
Sample questions with model answers
Here are 4 of the questions in this topic, each with a model answer, an explanation of why it earns the marks and the mark scheme an examiner would use.
Question 1
2 marks
In a club, \(\dfrac{2}{7}\) of the members are boys. The rest of the members are girls.
Write the ratio of girls to boys in the form \(n : 1\).
Model answer
Girls = \(1 - \dfrac{2}{7} = \dfrac{5}{7}\) of the members girls : boys = 5 : 2 Divide both parts by 2: 2.5 : 1
Explanation
A fraction of the whole tells you the parts: \(\dfrac{2}{7}\) boys means 2 parts boys out of 7, so 5 parts are girls. Then divide both parts by the second part to get the form \(n : 1\).
Mark scheme
1 mark
M1 for girls \(= \dfrac{5}{7}\) of the members, or girls : boys = 5 : 2
correct answer with no working scores full marks
1 mark
A1 for 2.5 : 1
oe, e.g. \(\dfrac{5}{2} : 1\)
Question 2
2 marks
A bag contains red counters and green counters in the ratio 5 : 3.
Tom says, "\(\dfrac{5}{3}\) of the counters are red."
Explain the mistake Tom has made and write down the correct fraction.
Model answer
Tom has divided red by green. To find the fraction of all the counters, divide by the total number of parts, 5 + 3 = 8. Fraction red = \(\dfrac{5}{8}\)
Explanation
\(\dfrac{5}{3}\) is greater than 1, which is impossible for a fraction of the counters. The number of red counters is \(\dfrac{5}{3}\) of the number of green counters, but \(\dfrac{5}{8}\) of all the counters.
Mark scheme
1 mark
C1 for a correct explanation, e.g. he has compared red with green instead of with the total; the total is 5 + 3 = 8 parts
accept 'a fraction of the counters cannot be more than 1'
1 mark
B1 for \(\dfrac{5}{8}\)
cao
Question 3
3 marks
A straight ramp rises 30 cm over a horizontal distance of 3.6 m.
Write the ratio of the rise to the horizontal distance in the form 1 : \(n\). The ramp starts at the origin. Taking \(x\) as the horizontal distance and \(y\) as the height, both in metres, write down an equation for the line of the ramp.
Model answer
3.6 m = 360 cm rise : horizontal = 30 : 360 = 1 : 12 The gradient is \(\dfrac{1}{12}\), so the line is \(y = \dfrac{1}{12}x\).
Explanation
The ratio rise : horizontal distance = 1 : 12 is the same as a gradient of \(\dfrac{1}{12}\). A line through the origin with this gradient has equation \(y = \dfrac{1}{12}x\). The units must match before writing the ratio.
Mark scheme
1 mark
M1 for both lengths in the same units, e.g. 30 : 360 or 0.3 : 3.6
correct answer with no working scores full marks
1 mark
A1 for 1 : 12
cao
1 mark
B1 for \(y = \dfrac{1}{12}x\)
oe, e.g. \(12y = x\); ft their ratio
Question 4
4 marks
Company A hires out vans for £0.40 per mile. Company B charges a fixed fee of £30 plus £0.25 per mile.
For one of the companies, the total cost is in direct proportion to the number of miles. Which company is this? Give a reason. Find the number of miles for which both companies charge the same.
Model answer
Company A: \(C = 0.4m\). Company B: \(C = 30 + 0.25m\). Company A's cost is in direct proportion to the miles: cost : miles is always 0.4 : 1 = 2 : 5, and 0 miles costs £0 (the graph goes through the origin). Company B has a fixed fee, so its ratio changes. \(0.4m = 30 + 0.25m\) \(0.15m = 30\) \(m = 30 \div 0.15 = 200\) Both charge £80 for 200 miles.
Explanation
Both costs are linear functions, but only a function of the form \(C = km\) (a line through the origin) keeps a constant ratio between cost and miles. Setting the two costs equal and solving gives where their graphs cross.
Mark scheme
1 mark
P1 for the costs as functions of the number of miles \(m\), \(C = 0.4m\) and \(C = 30 + 0.25m\)
oe
1 mark
P1 for \(0.4m = 30 + 0.25m\), or \(0.15m = 30\)
or a correct trial, e.g. 200 miles gives £80 for both
1 mark
A1 for 200 (miles)
cao
1 mark
C1 for company A, with a correct reason, e.g. cost : miles is always 2 : 5 (£0.40 : 1), or 0 miles costs £0, or its graph is a straight line through the origin
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