IGCSE Maths 0580 The Four Operations Past Paper Questions and Worked Solutions

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IGCSE Maths (0580) · Number · 1.6

Every the four operations question from 15 Cambridge IGCSE Mathematics (0580) past papers (May/June 2025 to May/June 2026), syllabus section 1.6. 27 questions covering Core and Extended tiers, ordered from Core to Extended. Each question is labelled with its question paper code (for example 0580/11/M/J/26) and every final answer matches the official Cambridge mark scheme. Try each question first, then click “Show solution” to check your working. This page is part of our IGCSE Maths 0580 Number past paper questions.

0580 The Four Operations past paper questions: Core (Papers 1 and 3)

11 markCore

May/June 2026 · Paper 1 · 0580/11/M/J/26 · Q8

In a town, the lowest temperature one night is −12.6 °C. The highest temperature the next day is 25.7 °C. Calculate the difference between these two temperatures.

Show solution
  1. Difference = highest − lowest = 25.7 − (−12.6).
  2. Subtracting a negative is the same as adding: 25.7 + 12.6.
  3. Difference = 38.3 °C
Answer 38.3 °C
23 marksCore

May/June 2026 · Paper 1 · 0580/11/M/J/26 · Q17

Work out 21⁄6 − 13⁄5. Write your answer as a fraction in its simplest form.

Show solution
  1. Change to improper fractions: 21⁄6 = 13⁄6 and 13⁄5 = 8⁄5.
  2. The lowest common denominator of 6 and 5 is 30: 13⁄6 = 65⁄30 and 8⁄5 = 48⁄30.
  3. Subtract the numerators: 65⁄30 − 48⁄30 = 17⁄30
Answer 17⁄30
31 markCore

May/June 2026 · Paper 1 · 0580/12/M/J/26 · Q2(a)

Add 63 and 28.

Show solution
  1. Add the tens: 60 + 20 = 80. Add the units: 3 + 8 = 11.
  2. 80 + 11 = 91
Answer 91
42 marksCore

May/June 2026 · Paper 1 · 0580/12/M/J/26 · Q6

Put one pair of brackets into each calculation to make it correct. (a) 7 × 3 − 2 × 4 = 28 (b) 9 − 80 ÷ 8 − 6 = 5

Show solution
Part (a)
  1. Without brackets: 21 − 8 = 13, which is wrong. We need 28 = 7 × 4, so the bracket must make 1.
  2. 3 − 2 = 1, so 7 × (3 − 2) × 4 = 7 × 1 × 4 = 28 ✓
  3. 7 × (3 − 2) × 4 = 28
Answer 7 × (3 − 2) × 4 = 28
Part (b)
  1. We need 9 − 4 = 5, so the bracket must make 4.
  2. 80 ÷ 8 − 6 = 10 − 6 = 4 ✓
  3. 9 − (80 ÷ 8 − 6) = 5
Answer 9 − (80 ÷ 8 − 6) = 5
53 marksCore

May/June 2026 · Paper 1 · 0580/12/M/J/26 · Q27

Work out 31⁄3 − 13⁄4. Give your answer as a mixed number in its simplest form.

Show solution
  1. Change to improper fractions: 31⁄3 = 10⁄3 and 13⁄4 = 7⁄4.
  2. The lowest common denominator of 3 and 4 is 12: 10⁄3 = 40⁄12 and 7⁄4 = 21⁄12.
  3. Subtract: 40⁄12 − 21⁄12 = 19⁄12.
  4. 19 ÷ 12 = 1 remainder 7, so the answer is 17⁄12
Answer 17⁄12
65 marksCore

May/June 2026 · Paper 1 · 0580/13/M/J/26 · Q11

2⁄5 of the area of a shape is blue, 3⁄7 is green and the rest is red.

(a) What fraction of the shape is red? (b) 12 cm² of the shape is green. Find the total area of the shape.

Show solution
Part (a)
  1. Add the blue and green fractions using a common denominator of 35.
  2. 2⁄5 = 14⁄35 and 3⁄7 = 15⁄35, so blue + green = 29⁄35.
  3. The whole shape is 1 = 35⁄35, so red = 35⁄35 − 29⁄35 = 6⁄35
Answer 6⁄35
Part (b)
  1. 3⁄7 of the area is 12 cm², so 3 parts = 12 and 1 part (1⁄7) = 12 ÷ 3 = 4 cm².
  2. Whole area = 7 parts = 7 × 4 = 28 cm²
Answer 28 cm²
72 marksCore

May/June 2026 · Paper 3 · 0580/31/M/J/26 · Q13

Put one pair of brackets into each calculation to make it correct. (a) 10 + 12 − 8 × 5 = 30 (b) 10 + 20 × 7 ÷ 5 = 30

Show solution
Part (a)
  1. Without brackets: 10 + 12 − 40 = −18, which is wrong. We need 10 + 20 = 30, so the bracket must make 20.
  2. (12 − 8) × 5 = 4 × 5 = 20 ✓
  3. 10 + (12 − 8) × 5 = 30
Answer 10 + (12 − 8) × 5 = 30
Part (b)
  1. We need something ÷ 5 = 30, so the bracket must make 150.
  2. 10 + 20 × 7 = 10 + 140 = 150 ✓
  3. (10 + 20 × 7) ÷ 5 = 30
Answer (10 + 20 × 7) ÷ 5 = 30
83 marksCore

Feb/Mar 2026 · Paper 1 · 0580/12/F/M/26 · Q1

(a) Subtract 9 from 1321. (b) Divide 814 by 2. (c) Write down the multiple of 6 that is nearest to 20.

Show solution
Part (a)
  1. 1321 − 9: take 10 away and add 1 back. 1321 − 10 = 1311, then 1311 + 1 = 1312
Answer 1312
Part (b)
  1. Halve each part: 800 ÷ 2 = 400 and 14 ÷ 2 = 7, so 814 ÷ 2 = 407
Answer 407
Part (c)
  1. Multiples of 6 near 20: 6 × 3 = 18 and 6 × 4 = 24.
  2. 18 is 2 away from 20 and 24 is 4 away, so the nearest is 18
Answer 18
92 marksCore

Feb/Mar 2026 · Paper 1 · 0580/12/F/M/26 · Q11

Put one pair of brackets into each calculation to make it correct. (a) 6 × 5 − 3 + 5 = 42 (b) 4 − 80 + 20 ÷ 10 = −6

Show solution
Part (a)
  1. We need 6 × 7 = 42, so the bracket must make 7. Try 5 − 3 + 5 = 7.
  2. 6 × (5 − 3 + 5) = 42
Answer 6 × (5 − 3 + 5) = 42
Part (b)
  1. We need 4 − 10 = −6, so the rest must make 10. Try (80 + 20) ÷ 10 = 100 ÷ 10 = 10.
  2. 4 − (80 + 20) ÷ 10 = −6
Answer 4 − (80 + 20) ÷ 10 = −6
103 marksCore

Feb/Mar 2026 · Paper 1 · 0580/12/F/M/26 · Q26

Work out 33⁄5 × 22⁄9. Give your answer in its simplest form.

Show solution
  1. Change to improper fractions: 33⁄5 = 18⁄5 and 22⁄9 = 20⁄9.
  2. Cancel before multiplying: 18 and 9 share 9 (18 ÷ 9 = 2, 9 ÷ 9 = 1), and 20 and 5 share 5 (20 ÷ 5 = 4, 5 ÷ 5 = 1).
  3. 2⁄1 × 4⁄1 = 8
Answer 8
112 marksCore

Oct/Nov 2025 · Paper 1 · 0580/11/O/N/25 · Q11

The temperature at midnight is −2 °C. The temperature at noon is 5 °C.

(a) Find the difference between these temperatures.

(b) The temperature at 9 am is 8 °C higher than the temperature at midnight. Work out the temperature at 9 am.

Show solution
Part (a)
  1. Difference = higher − lower = 5 − (−2).
  2. Subtracting a negative means adding: 5 + 2 = 7 °C
Answer 7 °C
Part (b)
  1. Start at −2 °C and go up 8 degrees: −2 + 8 = 6 °C
Answer 6 °C
122 marksCore

Oct/Nov 2025 · Paper 1 · 0580/11/O/N/25 · Q18

Work out 11⁄18 − 2⁄9. Give your answer as a fraction in its simplest form.

Show solution
  1. The denominators are 18 and 9. 18 is a multiple of 9, so use 18.
  2. 2⁄9 = 4⁄18 (multiply top and bottom by 2).
  3. 11⁄18 − 4⁄18 = 7⁄18
  4. 7 and 18 have no common factor, so this is in its simplest form.
Answer 7⁄18
133 marksCore

Oct/Nov 2025 · Paper 1 · 0580/11/O/N/25 · Q28

Work out 82⁄3 ÷ 15⁄8. Give your answer as a mixed number in its simplest form.

Show solution
  1. Change to improper fractions: 82⁄3 = 26⁄3 and 15⁄8 = 13⁄8.
  2. To divide by a fraction, multiply by its reciprocal: 26⁄3 × 8⁄13.
  3. Cancel 26 and 13 (26 ÷ 13 = 2): 2⁄3 × 8⁄1 = 16⁄3.
  4. 16 ÷ 3 = 5 remainder 1, so the answer is 51⁄3
Answer 51⁄3
142 marksCore

Oct/Nov 2025 · Paper 1 · 0580/12/O/N/25 · Q9

The temperature at midday on Monday is −3 °C. The temperature at 10 pm on Monday is −15 °C.

(a) Calculate the difference between these two temperatures.

(b) The temperature at midday on Tuesday is 23 °C higher than the temperature at 10 pm on Monday. Calculate the temperature at midday on Tuesday.

Show solution
Part (a)
  1. Difference = higher − lower = −3 − (−15).
  2. Subtracting a negative means adding: −3 + 15 = 12 °C
Answer 12 °C
Part (b)
  1. Start at −15 °C and go up 23 degrees: −15 + 23 = 8 °C
Answer 8 °C
153 marksCore

Oct/Nov 2025 · Paper 1 · 0580/12/O/N/25 · Q18

Work out 25⁄6 ÷ 41⁄4. Write your answer as a fraction in its simplest form.

Show solution
  1. Change to improper fractions: 25⁄6 = 17⁄6 and 41⁄4 = 17⁄4.
  2. To divide, multiply by the reciprocal: 17⁄6 × 4⁄17.
  3. The 17s cancel: 4⁄6.
  4. Simplify by dividing top and bottom by 2: 2⁄3
Answer 2⁄3
163 marksCore

Oct/Nov 2025 · Paper 1 · 0580/13/O/N/25 · Q25

Work out 3⁄4 × 12⁄3. Give your answer as a mixed number in its simplest form.

Show solution
  1. Change the mixed number to an improper fraction: 12⁄3 = 5⁄3.
  2. Multiply: 3⁄4 × 5⁄3. The 3s cancel, leaving 5⁄4.
  3. 5 ÷ 4 = 1 remainder 1, so the answer is 11⁄4
Answer 11⁄4
172 marksCore

Oct/Nov 2025 · Paper 3 · 0580/33/O/N/25 · Q14

Carl packs pens into boxes. Each box holds 68 pens. Carl has 980 pens and 14 boxes. Does Carl have enough boxes to pack all the pens? Show how you decide.

Show solution
  1. Work out how many pens 14 boxes can hold: 14 × 68 = 952.
  2. Compare with the number of pens: 952 < 980, so 28 pens are left over.
  3. No, because 14 boxes only hold 952 pens
  4. Tip: He would need 980 ÷ 68 = 14.4…, so 15 boxes.
Answer No, because 14 boxes only hold 952 pens
182 marksCore

May/June 2025 · Paper 1 · 0580/11/M/J/25 · Q3

Two numbers have a sum of −2 and a product of −15. Work out the two numbers.

Show solution
  1. The product is negative, so one number is positive and the other is negative.
  2. List factor pairs of 15: 1 × 15 and 3 × 5.
  3. Try each pair with one negative so the sum is −2: 1 + (−15) = −14 ✗, 3 + (−5) = −2 ✓
  4. The numbers are 3 and −5
  5. Check: 3 × (−5) = −15 ✓
Answer 3 and −5
192 marksCore

May/June 2025 · Paper 1 · 0580/11/M/J/25 · Q6

Put one pair of brackets into each calculation to make it correct.

(a) 7 − 5 × 4 + 8 = 16

(b) 7 − 5 × 4 + 8 = −21

Show solution
Part (a)
  1. Without brackets: 7 − 20 + 8 = −5, which is wrong. Try brackets round 7 − 5.
  2. (7 − 5) × 4 + 8 = 2 × 4 + 8 = 8 + 8 = 16 ✓
  3. (7 − 5) × 4 + 8 = 16
Answer (7 − 5) × 4 + 8 = 16
Part (b)
  1. To get −21 we need to take a large number away from 7. Put brackets round 5 × 4 + 8.
  2. 5 × 4 + 8 = 20 + 8 = 28, and 7 − 28 = −21 ✓
  3. 7 − (5 × 4 + 8) = −21
Answer 7 − (5 × 4 + 8) = −21
202 marksCore

May/June 2025 · Paper 1 · 0580/11/M/J/25 · Q13

Work out. (a) −5 × −4 (b) −8 + (−3)

Show solution
Part (a)
  1. Negative × negative = positive. 5 × 4 = 20.
  2. −5 × −4 = 20
Answer 20
Part (b)
  1. Adding a negative number is the same as subtracting: −8 + (−3) = −8 − 3.
  2. Start at −8 and go down 3 more: −11
Answer −11
212 marksCore

May/June 2025 · Paper 1 · 0580/12/M/J/25 · Q8

Put one pair of brackets into each calculation to make it correct.

(a) −12 + 4 ÷ 2 − 3 = −16

(b) −3 − 4 + 5 − 7 = −5

Show solution
Part (a)
  1. Without brackets: −12 + 2 − 3 = −13, which is wrong. We need −12 − 4 = −16, so the rest must make −4.
  2. 4 ÷ (2 − 3) = 4 ÷ (−1) = −4 ✓
  3. −12 + 4 ÷ (2 − 3) = −16
Answer −12 + 4 ÷ (2 − 3) = −16
Part (b)
  1. We need −3 − 2 = −5, so the bracket must make 2.
  2. 4 + 5 − 7 = 2 ✓
  3. −3 − (4 + 5 − 7) = −5
Answer −3 − (4 + 5 − 7) = −5
222 marksCore

May/June 2025 · Paper 1 · 0580/12/M/J/25 · Q12

Tim has a method for multiplying a number by 99. He shows his method for 53 × 99:

53 × 99 = 53 × 100 − 53 = 5300 − 53 = 5247.

Work out 85 × 99 using Tim’s method.

Show solution
  1. Tim’s method: 99 is 100 − 1, so multiply by 100 and then take away the number once.
  2. 85 × 99 = 85 × 100 − 85
  3. 85 × 100 = 8500
  4. 8500 − 85 = 8415
Answer 8415

0580 The Four Operations past paper questions: Extended (Papers 2 and 4)

232 marksExtended

May/June 2026 · Paper 2 · 0580/22/M/J/26 · Q4

Work out 1⁄6 ÷ 2⁄7.

Show solution
  1. To divide by a fraction, multiply by its reciprocal: 1⁄6 ÷ 2⁄7 = 1⁄6 × 7⁄2.
  2. Multiply the tops and the bottoms: 1 × 7⁄6 × 2 = 7⁄12
Answer 7⁄12
242 marksExtended

Feb/Mar 2026 · Paper 2 · 0580/22/F/M/26 · Q1

Work out. (a) 0.7² (b) 2 ÷ 0.04

Show solution
Part (a)
  1. 0.7² = 0.7 × 0.7. Work out 7 × 7 = 49 first.
  2. There is 1 decimal place in each 0.7, so 2 in the answer: 0.49
Answer 0.49
Part (b)
  1. Multiply both numbers by 100 to make the divisor a whole number: 2 ÷ 0.04 = 200 ÷ 4.
  2. 200 ÷ 4 = 50
Answer 50
251 markExtended

Oct/Nov 2025 · Paper 2 · 0580/22/O/N/25 · Q1

The temperature at 4 am is −12 °C. The temperature at 4 pm is 21 °C. Find the increase in temperature from 4 am to 4 pm.

Show solution
  1. Increase = later temperature − earlier temperature = 21 − (−12).
  2. Subtracting a negative means adding: 21 + 12 = 33 °C
Answer 33 °C
263 marksExtended

Oct/Nov 2025 · Paper 2 · 0580/22/O/N/25 · Q9

Rajid has a full bottle of juice. He drinks 1⁄3 of the full bottle on Monday. He drinks 3⁄7 of the full bottle on Tuesday. Find the fraction of the bottle of juice remaining.

Show solution
  1. Use a common denominator of 21: 1⁄3 = 7⁄21 and 3⁄7 = 9⁄21.
  2. Total drunk = 7⁄21 + 9⁄21 = 16⁄21.
  3. The full bottle is 21⁄21, so the fraction remaining = 21⁄21 − 16⁄21 = 5⁄21
Answer 5⁄21
271 markExtended

Oct/Nov 2025 · Paper 4 · 0580/43/O/N/25 · Q9

Draw a ring around the calculation that is equivalent to n ÷ 23⁄5.

Show solution
  1. Change the mixed number to an improper fraction: 23⁄5 = 2 × 5 + 3⁄5 = 13⁄5.
  2. Dividing by a fraction is the same as multiplying by its reciprocal (the fraction turned upside down).
  3. n ÷ 13⁄5 = n × 5⁄13
Answer n × 5⁄13

Question papers used on this page

All the four operations questions above, listed by 0580 question paper code.

QP codeFile namePaperQuestions
0580/11/M/J/260580_s26_qp_11May/June 2026 · Paper 1 (Core)Q8, Q17
0580/12/M/J/260580_s26_qp_12May/June 2026 · Paper 1 (Core)Q2(a), Q6, Q27
0580/13/M/J/260580_s26_qp_13May/June 2026 · Paper 1 (Core)Q11
0580/22/M/J/260580_s26_qp_22May/June 2026 · Paper 2 (Extended)Q4
0580/31/M/J/260580_s26_qp_31May/June 2026 · Paper 3 (Core)Q13
0580/12/F/M/260580_m26_qp_12Feb/Mar 2026 · Paper 1 (Core)Q1, Q11, Q26
0580/22/F/M/260580_m26_qp_22Feb/Mar 2026 · Paper 2 (Extended)Q1
0580/11/O/N/250580_w25_qp_11Oct/Nov 2025 · Paper 1 (Core)Q11, Q18, Q28
0580/12/O/N/250580_w25_qp_12Oct/Nov 2025 · Paper 1 (Core)Q9, Q18
0580/13/O/N/250580_w25_qp_13Oct/Nov 2025 · Paper 1 (Core)Q25
0580/22/O/N/250580_w25_qp_22Oct/Nov 2025 · Paper 2 (Extended)Q1, Q9
0580/33/O/N/250580_w25_qp_33Oct/Nov 2025 · Paper 3 (Core)Q14
0580/43/O/N/250580_w25_qp_43Oct/Nov 2025 · Paper 4 (Extended)Q9
0580/11/M/J/250580_s25_qp_11May/June 2025 · Paper 1 (Core)Q3, Q6, Q13
0580/12/M/J/250580_s25_qp_12May/June 2025 · Paper 1 (Core)Q8, Q12

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