Edexcel GCSE Maths (1MA1), Higher tier · Ratio, proportion and rates of change
Practise Direct and inverse proportion. 1 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
Written for this site in the style of Edexcel exam questions. They are not taken from real past papers.
Question 1Easy2 marks
Here are the ingredients needed to make a fruit smoothie for 4 people. 320 g strawberries 240 ml yoghurt 400 ml apple juice
Nadia wants to make a fruit smoothie for 3 people. Work out how much apple juice Nadia needs.[2]
Show the answer and mark scheme
Answer: 300 ml
M1 for \(400 \div 4 \times 3\) oe
A1 for 300 cao
Worked solution: For 1: \(400 \div 4 = 100\) ml. For 3: \(100 \times 3 = 300\) ml.
Question 2Medium3 marks
Here are the ingredients needed to make 10 biscuits. 120 g flour 80 g butter 40 g sugar
Tariq has 300 g of flour, 110 g of butter and 70 g of sugar. Work out the greatest number of biscuits Tariq can make. You must show your working.[3]
Show the answer and mark scheme
Answer: 13
P1 for a correct method for one ingredient, e.g. \(300 \div 12\) (\(= 25\)) or a comparison with the recipe
P1 for a correct method for all three ingredients
A1 for 13 cao
Worked solution: 300 g of flour is enough for \(300 \div 12 = 25\) biscuits 110 g of butter is enough for \(110 \div 8 = 13.75\) biscuits 70 g of sugar is enough for \(70 \div 4 = 17.5\) biscuits The butter will run out first, so the greatest number is 13.
Question 3Hard5 marks
\(y\) is inversely proportional to the square of \(x\). Sara says, 'If \(x\) is doubled, then \(y\) is halved.'
(a) Is Sara correct? Give a reason for your answer.[2]
(b) When \(x = 2\), \(y = 45\). Find the positive value of \(x\) when \(y = 5\).[3]
Show the answer and mark scheme
(a)Answer: No: \(y = \frac{k}{x^2}\), and \(\frac{k}{(2x)^2} = \frac{k}{4x^2}\), so \(y\) is divided by 4.
M1 for \(y = \frac{k}{x^2}\) and \(\frac{k}{(2x)^2}\), or a numerical example with a stated \(k\)
C1 for 'no', \(y\) is divided by 4 (becomes a quarter)
Worked solution: If \(y = \frac{k}{x^2}\) then replacing \(x\) by \(2x\) gives \(\frac{k}{4x^2} = \frac{1}{4} \times \frac{k}{x^2}\). So \(y\) is divided by 4, not 2.
(b)Answer: 6
M1 for \(45 = \frac{k}{2^2}\)
M1 for \(k = 180\) and \(5 = \frac{180}{x^2}\)
A1 for 6
Worked solution: \(k = 45 \times 4 = 180\). \(5 = \frac{180}{x^2}\), so \(x^2 = 36\) and \(x = 6\).