Practise 39 exam-style questions on Calculating with integers, decimals and fractions 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.
39 questions
1–5 marks each
Instant marking
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20 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
At 6 am the temperature was −8 °C. By noon the temperature had risen by 13 degrees. By midnight the temperature had fallen by 17 degrees from its value at noon.
Work out the temperature at midnight.
Model answer
Noon: −8 + 13 = 5 °C Midnight: 5 − 17 = −12 °C
Explanation
A rise means add and a fall means subtract. A number line helps: from −8 up 13 reaches 5, then down 17 goes past zero to −12.
Mark scheme
1 mark
M1 for −8 + 13 (= 5) or −8 + 13 − 17 or 13 − 17 (= −4)
correct answer with no working scores full marks
1 mark
A1 for −12 (°C)
cao
Question 2
2 marks
A piece of ribbon is \(12\frac{3}{5}\) m long. It is cut into pieces that are each \(\frac{7}{10}\) m long.
Change the mixed number to an improper fraction, then divide by multiplying by the reciprocal. You could also use decimals: 12.6 ÷ 0.7 = 126 ÷ 7 = 18.
Mark scheme
1 mark
M1 for \(\dfrac{63}{5} \div \dfrac{7}{10}\) or \(\dfrac{63}{5} \times \dfrac{10}{7}\) or \(\dfrac{126}{10} \div \dfrac{7}{10}\) or 12.6 ÷ 0.7
correct answer with no working scores full marks
1 mark
A1 for 18
cao
Question 3
3 marks
Lily needs to fill 30 glasses with juice. Each glass holds \(\frac{3}{16}\) of a litre. Juice is sold in bottles that each hold \(1\frac{3}{4}\) litres.
What is the smallest number of bottles Lily needs to buy?
Model answer
Juice needed: \(30 \times \dfrac{3}{16} = \dfrac{90}{16} = 5\frac{5}{8}\) litres 3 bottles hold \(3 \times 1\frac{3}{4} = 5\frac{1}{4}\) litres, which is not enough. 4 bottles hold 7 litres, which is enough. Lily needs 4 bottles.
Explanation
Work out the total juice needed, then compare it with the amount in whole bottles. \(5\frac{5}{8} \div 1\frac{3}{4} = 3\frac{3}{14}\), and you cannot buy part of a bottle, so round up to 4.
Mark scheme
1 mark
P1 for \(30 \times \dfrac{3}{16}\) (\(= \dfrac{90}{16} = 5\frac{5}{8}\) litres), or \(1\frac{3}{4} \div \dfrac{3}{16}\) (\(= 9\frac{1}{3}\) glasses per bottle)
correct answer with no working scores full marks
1 mark
P1 for \(5\frac{5}{8} \div 1\frac{3}{4}\) (\(= 3\frac{3}{14}\)), or for showing 3 bottles is not enough, e.g. 3 × \(1\frac{3}{4} = 5\frac{1}{4}\) < \(5\frac{5}{8}\), or 30 ÷ 9 (glasses per full bottle) = 3.33...
1 mark
A1 for 4
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Question 4
4 marks
A theatre sells 1200 tickets for a show. \(\frac{3}{8}\) of the tickets are child tickets and the rest are adult tickets. A child ticket costs £16.75 and an adult ticket costs £24.50
Find the number of each type of ticket first. Split the multiplications to make them easier: 450 × 16.75 = 400 × 16.75 + 50 × 16.75. Give money answers to 2 decimal places (£25 912.50, not £25 912.5).
Mark scheme
1 mark
P1 for 1200 ÷ 8 × 3 (= 450 child tickets) and 750 adult tickets
correct answer with no working scores full marks
1 mark
P1 for 450 × 16.75 (= 7537.50)
ft their number of child tickets
1 mark
P1 for 750 × 24.50 (= 18 375)
ft their number of adult tickets
1 mark
A1 for £25 912.50
cao
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