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0580/31 Oct/Nov 2023, Question 1: Mixed Numbers and Improper Fractions

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 15 marks

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The question, in short

Various short number questions: write six and a half million in figures, round 37 508, classify numbers from a list, insert brackets, convert and compute fractions, find a reciprocal, and subtract mixed numbers.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 1 mark

Write six and a half million using digits.

  1. 16.5 × 1 000 000 = 6 500 000

Answer6 500 000

Part (b) · 1 mark

Round 37 508 to the nearest thousand.

  1. 137 508 is between 37 000 and 38 000, nearer 38 000
  2. 2= 38 000

Answer38 000

Part (ci) · 1 mark

From the given list, choose a factor of 18.

  1. 118 ÷ 6 = 3, so 6 is a factor of 18

Answer6 or 9

Part (cii) · 1 mark

From the given list, choose a multiple of 12.

  1. 136 = 3 × 12, so 36 is a multiple of 12

Answer36

Part (ciii) · 1 mark

From the given list, choose a square number.

  1. 19 = 3², so 9 is a square number

Answer9 or 36

Part (civ) · 1 mark

From the given list, choose a prime number.

  1. 131 has only factors 1 and 31, so 31 is prime

Answer31

Part (cv) · 1 mark

From the given list, choose an irrational number.

  1. 1√1000 = 31.62… cannot be written as a fraction, so √1000 is irrational

Answer√1000

Part (di) · 1 mark

Insert one pair of brackets in 24 − 4 × 3 + 2 so it equals 62.

  1. 1(24 − 4) × 3 + 2 = 20 × 3 + 2 = 62

Answer(24 − 4) × 3 + 2 = 62

Part (dii) · 1 mark

Insert one pair of brackets in 24 − 4 × 3 + 2 so it equals 4.

  1. 124 − 4 × (3 + 2) = 24 − 20 = 4

Answer24 − 4 × (3 + 2) = 4

Part (e) · 1 mark

Convert 3/4 to a decimal.

  1. 13 ÷ 4 = 0.75

Answer0.75

Part (f) · 1 mark

Calculate 3/7 of 126.

  1. 1126 ÷ 7 = 18
  2. 218 × 3 = 54

Answer54

Part (g) · 1 mark

State the reciprocal of 0.5.

  1. 1Reciprocal = 1 ÷ 0.5 = 2

Answer2

Part (h) · 3 marks

Work out 5 2/3 − 2 1/5 without a calculator, showing working; give a mixed number in simplest form.

  1. 15 2/3 − 2 1/5 = 17/3 − 11/5
  2. 2= 85/15 − 33/15 = 52/15
  3. 3= 3 7/15

Answer3 7/15

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Also searched as: 0580/31/O/N/23 · 0580_w23_qp_31 · 0580 w23 31 · question 1.
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