Practise 18 exam-style questions on Order of operations and inverse operations for Edexcel GCSE Maths (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
Instant marking
No sign-up needed
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
1 mark
Here is a calculation.
\[4 + 2.5 \times 6 - 1.5^2\]
Insert one pair of brackets so that the value of the calculation is 36.75
Without brackets the value is \(4 + 15 - 2.25 = 16.75\). To make it larger you need to multiply a bigger number by 6, so put brackets round 4 + 2.5. Always check by working out the calculation with your brackets.
Mark scheme
1 mark
B1 for \((4 + 2.5) \times 6 - 1.5^2\)
cao
Question 2
2 marks
Lily wants to work out
\[\dfrac{24 + 36}{4 \times 3}\]
She types this into her calculator:
24 + 36 ÷ 4 × 3 =
Her calculator shows 51
Explain why her answer is wrong and work out the correct answer.
Model answer
The calculator follows the order of operations: it works out \(36 \div 4 = 9\), then \(9 \times 3 = 27\), then \(24 + 27 = 51\). Lily needed to type (24 + 36) ÷ (4 × 3). Correct answer: \(60 \div 12 = 5\)
Explanation
A calculator does division and multiplication before addition, working left to right. The fraction line groups the whole numerator and the whole denominator, so both need brackets when typed in one line. Note that ÷ 4 × 3 is not the same as ÷ 12.
Mark scheme
1 mark
C1 for an explanation, e.g. the calculator divides only 36 by 4 and then multiplies by 3 (it works out \(24 + 9 \times 3\)); she needs brackets round 24 + 36 and round 4 × 3
1 mark
B1 for 5
cao
Question 3
3 marks
\[\dfrac{\sqrt{6.2^2 + k}}{1.6} = 4.25\]
Work out the value of \(k\).
Model answer
Multiply both sides by 1.6: \(\sqrt{6.2^2 + k} = 4.25 \times 1.6 = 6.8\) Square both sides: \(6.2^2 + k = 6.8^2 = 46.24\) \(38.44 + k = 46.24\) \(k = 7.8\)
Explanation
Undo the operations one at a time, starting with the last one done to \(k\)'s expression: multiply by 1.6, then square to remove the square root, then subtract \(6.2^2\). Check: \(\sqrt{38.44 + 7.8} = \sqrt{46.24} = 6.8\) and \(6.8 \div 1.6 = 4.25\).
Mark scheme
1 mark
M1 for \(4.25 \times 1.6\) (= 6.8)
correct answer with no working scores full marks
1 mark
M1 for \(6.8^2 - 6.2^2\) or \(46.24 - 38.44\)
ft their 6.8
1 mark
A1 for 7.8
cao
Question 4
4 marks
Here are the steps of a number machine.
Start with \(x\) Square it Subtract 2.25 Multiply by 0.8 Find the reciprocal
The output is 0.125
Work out the possible values of \(x\).
Model answer
Reverse each step: Reciprocal of 0.125: \(\dfrac{1}{0.125} = 8\) Divide by 0.8: \(8 \div 0.8 = 10\) Add 2.25: \(10 + 2.25 = 12.25\) Square root: \(\pm\sqrt{12.25} = \pm 3.5\) \(x = 3.5\) or \(x = -3.5\)
Explanation
Work backwards through the machine using inverse operations in the reverse order. The reciprocal is its own inverse. The inverse of squaring is taking the square root, and both 3.5 and −3.5 square to 12.25, so there are two possible starting values.
Mark scheme
1 mark
M1 for the reciprocal of 0.125 (= 8)
correct answer with no working scores full marks
1 mark
M1 for \(8 \div 0.8\) (= 10)
ft their 8
1 mark
M1 for \(10 + 2.25\) (= 12.25) and taking the square root
ft their 10
1 mark
A1 for 3.5 and −3.5
cao; both values needed
Ready to try the rest? Every answer you write is marked against the mark scheme, so you can see exactly where the marks are.
Ctrl + Enter to check
AI TutorHints first, answers after you try
Hi! Stuck? Ask me for a hint and I’ll help you work it out. Once you’ve checked your answer I can explain exactly where the marks are.
