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Cambridge IGCSE Maths (0580) · Topic 1: Number · 1.10

Cambridge IGCSE Maths 0580 Limits of Accuracy Questions

Limits of Accuracy questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.

Practise limits of accuracy →Limits of Accuracy notes

What the syllabus asks

Summarised in our own words: check the exact wording in the official 0580 syllabus.

Limits of Accuracy questions: Core

For everyone: Core students (Papers 1 and 3) and Extended students (Papers 2 and 4).

Question 1 Core non-calculator · easy

A length is \(23\) cm, correct to the nearest centimetre.
Write down the lower bound and the upper bound of the length.

Show the worked answer
  1. Half of the accuracy is \(0.5\) cm.
  2. Lower bound \(23 - 0.5 = 22.5\) cm, upper bound \(23 + 0.5 = 23.5\) cm.

Answer: Lower bound \(22.5\) cm, upper bound \(23.5\) cm

Question 2 Core non-calculator · easy

A mass \(m\) is \(4.7\) kg, correct to 1 decimal place.
Complete the statement: \(\ldots \le m \lt \ldots\)

Show the worked answer
  1. Correct to 1 decimal place means to the nearest \(0.1\), so add and subtract \(0.05\).
  2. \(4.65 \le m \lt 4.75\)

Answer: \(4.65 \le m \lt 4.75\)

Question 3 Core calculator · easy · 2 marks

The number of people at a match is 24 000, correct to the nearest thousand.

(a) Write down the least possible number of people.

(b) Write down the greatest possible number of people.

Show the answer and mark scheme
  • B1 (a) 23 500
  • B1 (b) 24 499

Answer: (a) \(23\,500\) (b) \(24\,499\)

Question 4 Core non-calculator · medium

The number of people at a match is \(3800\), correct to 2 significant figures.
Write down the smallest and largest possible numbers of people.

Show the worked answer
  1. To 2 significant figures, \(3800\) is correct to the nearest \(100\), so the bounds are \(3750\) and \(3850\).
  2. People come in whole numbers: the smallest is \(3750\); \(3850\) would round to \(3900\), so the largest is \(3849\).

Answer: Smallest \(3750\), largest \(3849\)

Question 5 Core non-calculator · medium · 2 marks

The length of a rope is \(l\) metres. \(l = 7.6\), correct to 1 decimal place. Complete the statement: \(\ldots \le l \lt \ldots\)

Show the answer and mark scheme
  • B1 7.55
  • B1 7.65

Answer: \(7.55 \le l \lt 7.65\)

Question 6 Core calculator · medium · 2 marks

A distance, \(d\) metres, is 250 m correct to the nearest 10 m. Write down the error interval for \(d\).

Show the answer and mark scheme
  • B1 245
  • B1 255, in the form \(245 \le d \lt 255\)

Answer: \(245 \le d \lt 255\)

Limits of Accuracy questions: Extended

Extended content, for Papers 2 and 4. Core students can skip these.

Question 7 Extended non-calculator · medium

A rectangle measures \(8\) cm by \(5\) cm, each correct to the nearest centimetre.
Work out the upper bound of the area of the rectangle.

Show the worked answer
  1. Upper bounds: \(8.5\) cm and \(5.5\) cm.
  2. Upper bound of area \(= 8.5 \times 5.5 = 46.75\) cm².

Answer: \(46.75\) cm²

Question 8 Extended calculator · hard

A runner covers \(120\) m, correct to the nearest \(10\) m, in \(15.2\) seconds, correct to 1 decimal place.
Work out the lower bound of the runner's average speed. Give your answer correct to 3 significant figures.

Show the worked answer
  1. Distance bounds: \(115\) m to \(125\) m. Time bounds: \(15.15\) s to \(15.25\) s.
  2. The lowest speed uses the smallest distance and the largest time: \(\frac{115}{15.25} = 7.5409\ldots\) m/s.

Answer: \(7.54\) m/s

Question 9 Extended non-calculator · hard

\(a = 9\) and \(b = 4\), both correct to the nearest whole number.
Work out the upper bound of \(a - b\).

Show the worked answer
  1. \(a\) is between \(8.5\) and \(9.5\); \(b\) is between \(3.5\) and \(4.5\).
  2. The biggest difference uses the largest \(a\) and the smallest \(b\): \(9.5 - 3.5 = 6\).

Answer: \(6\)

Examiner Insights: common mistakes in IGCSE Maths 0580, with fixes (our analysis of public sources) →

Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).

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Questions students ask

Which Cambridge 0580 papers can test limits of accuracy?

Limits of Accuracy is on both tiers (syllabus 1.10), so it can come up on Core Papers 1 (non-calculator) and 3 (calculator), and Extended Papers 2 (non-calculator) and 4 (calculator). Extended candidates also need the Extended parts listed on this page. Half of each tier's marks are on a non-calculator paper, so practise the non-calculator questions without one.

Are these Cambridge past-paper questions?

No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.

Where can I practise more limits of accuracy questions?

In the 0580 practice for topic 1 (Number), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.

More number questions