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0580/31 Oct/Nov 2024, Question 5: Dividing in a Given Ratio

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 13 marks

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The question, in short

Use a scatter graph of cost against distance for 12 taxi rides, then handle equal and distance-based cost sharing and compound interest on $18 600.

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

Part (ai) · 1 mark

Decide whether the graph shows positive correlation and justify your choice.

  1. 1True
  2. 2As the distance increases, the cost increases

AnswerTrue and correct description of correlation e.g. as the distance increases the cost increases

Part (aii) · 1 mark

Ring the point representing the ride with an unusually high cost per kilometre.

  1. 1The point (1, 15): $15 for 1 km, far more per km than any other journey
  2. 2Ring the point (1, 15)

Answer(1, 15) circled

Part (aiii) · 1 mark

Add a line of best fit to the scatter graph.

  1. 1Ignore the outlier (1, 15)
  2. 2Rule a straight line following the trend, through about the mean point (4.9, 12.3), with points evenly either side

AnswerAcceptable ruled line of best fit drawn

Part (aiv) · 1 mark

Using your line, estimate the cost of an 8 km ride.

  1. 1Go up from 8 km to the line of best fit, then across to the Cost axis
  2. 2Cost ≈ $18

Answer16 to 19

Part (bi) · 1 mark

Work out Arit's share of $26.40 when split equally three ways.

  1. 126.40 ÷ 3 = $8.80

Answer8.80

Part (biia) · 2 marks

Express 12 : 3 : 7.5 as a ratio in simplest form.

  1. 1× 2: 24 : 6 : 15
  2. 2÷ 3: 8 : 2 : 5

Answer8 : 2 : 5

Part (biib) · 3 marks

Find how much extra Arit pays under distance-based sharing compared with equal sharing.

  1. 1Ratio of distances 12 : 3 : 7.5 = 8 : 2 : 5 (divide by 1.5)
  2. 2Total parts = 8 + 2 + 5 = 15
  3. 3Arit pays 26.40 × 8/15 = $14.08
  4. 4Equal share = 26.40 ÷ 3 = $8.80
  5. 514.08 − 8.80 = 5.28

Answer5.28

Part (c) · 3 marks

Find the value after 6 years of $18 600 invested at 1.7% yearly compound interest, to the nearest dollar.

  1. 118 600 × (1 + 1.7/100)⁶
  2. 2= 18 600 × 1.017⁶ = 20 579.68…
  3. 3= $20 580 to the nearest dollar

Answer20 580

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Also searched as: 0580/31/O/N/24 · 0580_w24_qp_31 · 0580 w24 31 · question 5.
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