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Cambridge IGCSE Maths (0580) · Non-calculator · Timed

0580 non-calculator mini-paper

Twelve questions, two on each of the six written methods the non-calculator papers depend on. Extended: all 12 in 30 minutes. Core: questions 1 to 8 in 20 minutes. Work on paper with no calculator, then mark yourself against the worked answers.

The questions

No calculator. Write down every step: on the real paper, method marks are for working the examiner can see.

Core and Extended

Question 1 Core Long multiplication and division

Work out \(4.7 \times 0.36\).

Show the worked answer
  1. \(47 \times 36 = 47 \times 30 + 47 \times 6 = 1410 + 282 = 1692\)
  2. The two numbers have \(1 + 2 = 3\) decimal places between them, so the answer has \(3\).

Answer: \(1.692\)

Question 2 Core Fractions

Work out \(2\tfrac{2}{5} \times 1\tfrac{7}{8}\). Give your answer as a mixed number.

Show the worked answer
  1. \(\tfrac{12}{5} \times \tfrac{15}{8}\)
  2. Cancel first: \(\tfrac{12}{8} = \tfrac{3}{2}\) and \(\tfrac{15}{5} = 3\), so this is \(\tfrac{3 \times 3}{2} = \tfrac{9}{2}\).
  3. \(\tfrac{9}{2} = 4\tfrac{1}{2}\)

Answer: \(4\tfrac{1}{2}\)

Question 3 Core Estimation

By rounding each number to 1 significant figure, estimate the value of \(812 \times 0.0496\).

Show the worked answer
  1. \(812 \approx 800\) and \(0.0496 \approx 0.05\)
  2. \(800 \times 0.05 = 40\)

Answer: \(40\)

Question 4 Core Standard form

Work out \((9 \times 10^8) \div (3.6 \times 10^3)\). Give your answer in standard form.

Show the worked answer
  1. \(9 \div 3.6 = 90 \div 36 = 2.5\)
  2. \(10^8 \div 10^3 = 10^5\)

Answer: \(2.5 \times 10^5\)

Question 5 Core Long multiplication and division

A school is taking \(1240\) students on a trip. Each coach has \(53\) seats.
Work out the smallest number of coaches needed.

Show the worked answer
  1. \(53 \times 20 = 1060\) and \(1240 - 1060 = 180\).
  2. \(53 \times 3 = 159\), so \(23\) coaches seat \(1219\) students, which is not enough.
  3. \(53 \times 24 = 1272\), which is enough.

Answer: \(24\) coaches

Question 6 Core Fractions

A water tank is \(\tfrac{2}{3}\) full. After \(18\) litres are used, it is \(\tfrac{5}{12}\) full.
Work out how many litres the tank holds when it is full.

Show the worked answer
  1. \(\tfrac{2}{3} - \tfrac{5}{12} = \tfrac{8}{12} - \tfrac{5}{12} = \tfrac{3}{12} = \tfrac{1}{4}\)
  2. So \(\tfrac{1}{4}\) of the tank is \(18\) litres.
  3. \(18 \times 4 = 72\)

Answer: \(72\) litres

Question 7 Core Estimation

Estimate the value of \(\sqrt{3.92 \times 24.6}\). Show the values you use.

Show the worked answer
  1. \(3.92 \approx 4\) and \(24.6 \approx 25\), which keeps the product a square number.
  2. \(\sqrt{4 \times 25} = \sqrt{100} = 10\)

Answer: \(10\)

Question 8 Core Standard form

A grain of sand has a mass of \(7 \times 10^{-4}\) grams.
How many grains of sand have a total mass of \(2.8\) kg? Give your answer in standard form.

Show the worked answer
  1. \(2.8\) kg \(= 2800\) g \(= 2.8 \times 10^3\) g
  2. \(\dfrac{2.8 \times 10^3}{7 \times 10^{-4}} = 0.4 \times 10^7\)
  3. \(0.4 \times 10^7 = 4 \times 10^6\)

Answer: \(4 \times 10^6\)

Extended only

Question 9 Extended Surds

Write \(\dfrac{15}{\sqrt{5}}\) in the form \(a\sqrt{5}\), where \(a\) is an integer.

Show the worked answer
  1. Multiply top and bottom by \(\sqrt{5}\): \(\dfrac{15\sqrt{5}}{5}\)
  2. \(= 3\sqrt{5}\)

Answer: \(3\sqrt{5}\)

Question 10 Extended Exact trig values

In triangle \(ABC\), angle \(B = 90^\circ\), angle \(A = 60^\circ\) and \(AB = 5\) cm.
Find the exact length of \(BC\).

Show the worked answer
  1. \(BC\) is opposite angle \(A\) and \(AB\) is adjacent to it, so \(\tan 60^\circ = \tfrac{BC}{5}\).
  2. \(BC = 5 \tan 60^\circ = 5\sqrt{3}\)

Answer: \(5\sqrt{3}\) cm

Question 11 Extended Surds

Write \(\dfrac{1 + \sqrt{3}}{2 - \sqrt{3}}\) in the form \(a + b\sqrt{3}\), where \(a\) and \(b\) are integers.

Show the worked answer
  1. Multiply top and bottom by \(2 + \sqrt{3}\).
  2. Bottom: \((2 - \sqrt{3})(2 + \sqrt{3}) = 4 - 3 = 1\)
  3. Top: \((1 + \sqrt{3})(2 + \sqrt{3}) = 2 + \sqrt{3} + 2\sqrt{3} + 3 = 5 + 3\sqrt{3}\)

Answer: \(5 + 3\sqrt{3}\)

Question 12 Extended Exact trig values

Solve \(2\cos x = \sqrt{3}\) for \(0^\circ \le x \le 90^\circ\).

Show the worked answer
  1. \(\cos x = \tfrac{\sqrt{3}}{2}\)
  2. From the half-equilateral triangle, \(\cos 30^\circ = \tfrac{\sqrt{3}}{2}\).

Answer: \(x = 30^\circ\)

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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. Paper times are from the official 0580 syllabus for 2025 to 2027.

Questions students ask

How long should the mini-paper take?

Extended: all 12 questions in 30 minutes. Core: questions 1 to 8 in 20 minutes. That is about the pace of the real non-calculator papers (Paper 2 is 100 marks in 2 hours; Paper 1 is 80 marks in 1 hour 30 minutes).

Are these Cambridge questions?

No. Every question was written for IGCSE Math Revision and checked independently before publishing. They are the same questions as on the six method pages, picked so the paper covers every method. For real papers, use the Cambridge copies linked from our 0580 past papers page.

How do I mark it?

Press Finish (or let the timer run out). Every worked answer opens; compare it with yours and press Right or Not yet. Each Not yet links to the method page to practise next.