Rounding and error intervals - Edexcel GCSE Maths (Non-calculator) Exam Questions

Practise 28 exam-style questions on Rounding and error intervals 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.

28 questions
1–5 marks each
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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

The length, \(L\) cm, of a pencil is 14 cm, correct to the nearest centimetre.

Write down the error interval for \(L\).

Model answer

\(13.5 \le L < 14.5\)

Explanation

Rounding to the nearest centimetre means the true length is within half a centimetre either side of 14. 13.5 rounds up to 14, so it is included (≤), but 14.5 rounds up to 15, so it is not included (<).

Mark scheme

1 mark
B1 for 13.5 and 14.5 as the ends of the interval
correct answer with no working scores full marks
1 mark
B1 for \(13.5 \le L < 14.5\)
cao; do not accept \(13.5 \le L \le 14.5\) or \(L < 14.49\)

Question 2

2 marks

£100 is shared equally between 3 people.

How much money does each person get? Give your answer to an appropriate degree of accuracy.

Model answer

\(100 \div 3 = 33.333\ldots\)
Money is given to the nearest penny (2 decimal places), so each person gets £33.33.

Explanation

An appropriate degree of accuracy depends on the context. Amounts of money in pounds are given to 2 decimal places, because the smallest coin is 1p. £33.3 would mean £33.30, which is not the nearest penny.

Mark scheme

1 mark
M1 for \(100 \div 3 = 33.33\ldots\)
correct answer with no working scores full marks
1 mark
A1 for £33.33
money must be given to the nearest penny; do not accept £33.3 or £33.333

Question 3

3 marks

\(n\) is a positive integer.
When \(\sqrt{n}\) is rounded to 1 decimal place, the result is 4.2

Find all the possible values of \(n\).

Model answer

\(4.15 \le \sqrt{n} < 4.25\)
Square each part: \(4.15^{2} \le n < 4.25^{2}\)
\(17.2225 \le n < 18.0625\)
The only integer in this interval is 18.

Explanation

Squaring keeps the inequalities in the same direction because all the values are positive. 17 is not possible because \(\sqrt{17} \approx 4.12\), which rounds to 4.1. To square 4.15 by hand, use \(415^{2} = 172\,225\).

Mark scheme

1 mark
M1 for \(4.15 \le \sqrt{n} < 4.25\)
correct answer with no working scores full marks
1 mark
M1 for squaring the bounds, \(4.15^{2} = 17.2225\) and \(4.25^{2} = 18.0625\)
or \(17.2225 \le n < 18.0625\)
1 mark
A1 for 18 only
cao

Question 4

4 marks

The length of a rectangle is 8.3 cm, truncated to 1 decimal place.
The width of the rectangle is 4 cm, correct to the nearest centimetre.

Find the error interval for the perimeter, \(P\) cm, of the rectangle.

Model answer

Length (truncated): \(8.3 \le l < 8.4\)
Width (rounded): \(3.5 \le w < 4.5\)
Least perimeter: \(2 \times (8.3 + 3.5) = 2 \times 11.8 = 23.6\)
Greatest perimeter: \(2 \times (8.4 + 4.5) = 2 \times 12.9 = 25.8\)
\(23.6 \le P < 25.8\)

Explanation

The two measurements have different kinds of error interval: truncation starts at 8.3, while rounding to the nearest centimetre goes 0.5 either side of 4. The perimeter is smallest when both are smallest and largest when both are largest.

Mark scheme

1 mark
B1 for the length interval, \(8.3 \le l < 8.4\)
correct answer with no working scores full marks
1 mark
B1 for the width interval, \(3.5 \le w < 4.5\)
1 mark
M1 for \(2 \times (8.3 + 3.5)\) or \(2 \times (8.4 + 4.5)\)
ft their bounds
1 mark
A1 for \(23.6 \le P < 25.8\)
cao

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