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0580/33 Oct/Nov 2024, Question 2: HCF and LCM

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

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The question, in short

Answer a set of short number and algebra questions: writing a large number in words, ordering values, powers and roots, solving an equation, estimating a calculation, index laws, and a timetable problem.

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

Part (a) · 1 mark

Write 845024 in words.

  1. 1845 thousand and 24
  2. 2Eight hundred and forty five thousand and twenty four

AnswerEight hundred and forty five thousand and twenty four

Part (b) · 2 marks

Arrange 7/18, 39%, 15/40 and 0.388 in ascending order, smallest first.

  1. 17/18 = 0.3888…
  2. 239% = 0.39
  3. 315/40 = 0.375
  4. 40.375 < 0.388 < 0.3888… < 0.39
  5. 515/40, 0.388, 7/18, 39%

Answer15/40, 0.388, 7/18, 39%

Part (ci) · 1 mark

Work out the value of 4 to the power 5.

  1. 14⁵ = 4 × 4 × 4 × 4 × 4 = 1024

Answer1024

Part (cii) · 1 mark

Work out the value of 6 to the power 0.

  1. 1Any non-zero number to the power 0 is 1
  2. 26⁰ = 1

Answer1

Part (ciii) · 1 mark

Work out the value of √16 multiplied by √49.

  1. 1√16 = 4, √49 = 7
  2. 24 × 7 = 28

Answer28

Part (d) · 2 marks

Solve the equation 6x + 5 = 29 for x.

  1. 16x = 29 − 5
  2. 26x = 24
  3. 3x = 4

Answer4

Part (e) · 2 marks

Round each number in (2.7 × 42.4)/(8.6 − 4.3) to 1 significant figure, then estimate the result, showing working.

  1. 12.7 ≈ 3, 42.4 ≈ 40, 8.6 ≈ 9, 4.3 ≈ 4
  2. 2(3 × 40)/(9 − 4)
  3. 3= 120/5
  4. 4= 24

Answer24

Part (f) · 1 mark

Given 3⁵ × 3ˣ = 3²⁰, find x.

  1. 15 + x = 20
  2. 2x = 15

Answer15

Part (g) · 1 mark

Simplify (x⁴)³.

  1. 1(x⁴)³ = x^(4 × 3)
  2. 2= x¹²

Answerx¹²

Part (h) · 3 marks

Boats to A leave every 16 minutes and to B every 34 minutes, both at 07 30; find the next time both leave together.

  1. 116 = 2⁴, 34 = 2 × 17
  2. 2LCM = 2⁴ × 17 = 272 minutes
  3. 3272 minutes = 4 h 32 min
  4. 407 30 + 4 h 32 min = 12 02

Answer12 02

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Also searched as: 0580/33/O/N/24 · 0580_w24_qp_33 · 0580 w24 33 · question 2.
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