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0580/31 May/Jun 2021, Question 7: HCF and LCM

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 19 marks

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The question, in short

Work with expressions for clock production by Martin, Suki and Pierre, a clock-face diagram, time conversions, a faulty clock, and two clocks checked on overlapping days in 2021.

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

Part (ai) · 3 marks

Form a simplified expression for the combined weekly output of the three clockmakers, using x for Martin's count.

  1. 1Martin: x, Suki: x − 3, Pierre: 2(x − 3)
  2. 2Total = x + (x − 3) + 2(x − 3)
  3. 3= x + x − 3 + 2x − 6
  4. 4= 4x − 9

Answer4x − 9

Part (aiia) · 3 marks

Given the weekly total is 35, determine the value of x.

  1. 14x − 9 = 35
  2. 24x = 44
  3. 3x = 11

Answer11

Part (aiib) · 2 marks

Using the clocks made, calculate how many more Pierre produces than Martin.

  1. 1Pierre makes 2 × (11 − 3) = 16 clocks
  2. 216 − 11 = 5

Answer5

Part (bi) · 1 mark

On the clock face diagram, draw hands to display 2.30 pm.

  1. 1Draw the minute hand pointing to 6.
  2. 2Draw the shorter hour hand halfway between 2 and 3.

AnswerHalf-past two shown correctly on clock face

Part (bii) · 2 marks

Find the obtuse angle formed by the clock hands at 2.30 pm.

  1. 1The hands are 3.5 hour-marks apart (from 2.5 to 6)
  2. 2Angle = 3.5/12 × 360
  3. 3= 105°

Answer105

Part (c) · 2 marks

Convert 10 days into seconds, presenting the result in standard form.

  1. 1Seconds = 60 × 60 × 24 × 10
  2. 2= 864000
  3. 3= 8.64 × 10⁵

Answer8.64 × 10⁵

Part (d) · 2 marks

A clock starting at 15 00 runs slow, losing 8 minutes each hour; find its displayed time after 3 1/2 hours.

  1. 1Time lost = 3 1/2 × 8 = 28 minutes
  2. 215 00 + 3 h 30 min = 18 30
  3. 318 30 − 28 min = 18 02

Answer18 02

Part (e) · 4 marks

Two clocks are checked every 6 and every 8 days from 1st January 2021; count the days in 2021 when both are checked.

  1. 1LCM of 6 and 8 = 24, so both are checked every 24 days
  2. 2After 1st January there are 364 more days: 364 ÷ 24 = 15.16…, so 15 more checks together
  3. 3Total = 1 + 15 = 16

Answer16

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Also searched as: 0580/31/M/J/21 · 0580_s21_qp_31 · 0580 s21 31 · question 7.
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