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0580/33 Oct/Nov 2022, Question 1: Factors and Multiples

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 15 marks

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The question, in short

Answer a set of short number questions covering factors, brackets, reciprocals, indices, surds, ordering values, estimation, standard form and primes.

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

Part (a) · 2 marks

List every factor of 68.

  1. 168 = 1 × 68 = 2 × 34 = 4 × 17
  2. 2Factors: 1, 2, 4, 17, 34, 68

Answer1, 2, 4, 17, 34, 68

Part (bi) · 1 mark

Insert one pair of brackets in 7 + 3 × 5 − 1 so it equals 19.

  1. 13 × (5 − 1) = 3 × 4 = 12
  2. 27 + 12 = 19
  3. 37 + 3 × (5 − 1) = 19

Answer7 + 3 × (5 − 1) = 19

Part (bii) · 1 mark

Insert one pair of brackets in 12 + 16 ÷ 2 + 5 so it equals 19.

  1. 1(12 + 16) ÷ 2 = 28 ÷ 2 = 14
  2. 214 + 5 = 19
  3. 3(12 + 16) ÷ 2 + 5 = 19

Answer(12 + 16) ÷ 2 + 5 = 19

Part (ci) · 1 mark

Find the reciprocal of 2/7.

  1. 1Reciprocal of 2/7 = 1 ÷ 2/7
  2. 2= 7/2

Answer7/2 or 3.5 or 3 1/2

Part (cii) · 1 mark

State the value of 10⁰.

  1. 1Any non-zero number to the power 0 is 1
  2. 210⁰ = 1

Answer1

Part (di) · 1 mark

Calculate 3² + 3⁴.

  1. 13² = 9, 3⁴ = 81
  2. 29 + 81 = 90

Answer90

Part (dii) · 1 mark

Calculate √3 × √12.

  1. 1√3 × √12 = √36
  2. 2= 6

Answer6

Part (diii) · 1 mark

Calculate 5⁻³.

  1. 15⁻³ = 1/5³
  2. 2= 1/125

Answer1/125 or 0.008

Part (e) · 2 marks

Order √10, 3.142, 1.8², π and 22/7 from smallest to largest.

  1. 1√10 = 3.162…, 3.142, 1.8² = 3.24, π = 3.14159…, 22/7 = 3.1428…
  2. 2Order: 3.14159… < 3.142 < 3.1428… < 3.162… < 3.24
  3. 3π, 3.142, 22/7, √10, 1.8²

Answerπ, 3.142, 22/7, √10, 1.8²

Part (f) · 2 marks

Estimate (136 + 47.2)/(62.9 ÷ 18.1) by rounding each number to 1 significant figure, showing working.

  1. 1136 ≈ 100, 47.2 ≈ 50, 62.9 ≈ 60, 18.1 ≈ 20
  2. 2(100 + 50)/(60 ÷ 20) = 150/3
  3. 3= 50

Answer50

Part (g) · 1 mark

Write 4.73 × 10⁶ as an ordinary number.

  1. 14.73 × 10⁶ = 4.73 × 1 000 000
  2. 2= 4 730 000

Answer4 730 000

Part (h) · 1 mark

Give a prime number between 30 and 40.

  1. 1Numbers 31 to 39: 31 has no factors other than 1 and 31
  2. 231 (or 37)

Answer31 or 37

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