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0580/32 Feb/Mar 2024, Question 4: Dividing in a Given Ratio

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 15 marks

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The question, in short

Use a bar chart of weekly television sales (58 total) plus price, scatter and probability contexts to find chart values, a fraction, a mode, a reduced price, correlation type, tree probabilities and an expected count.

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

Part (ai) · 1 mark

Read the bar chart to state how many televisions were sold on Monday.

  1. 1Read the height of the Monday bar
  2. 23

Answer3

Part (aii) · 1 mark

Find the fraction of the 58 televisions sold on Sunday, using the Sunday bar.

  1. 1Sunday bar = 11
  2. 2Fraction = 11/58

Answer11/58

Part (aiii) · 4 marks

Using Wednesday:Friday = 2:3 for the remaining sales, work out both days and complete the bar chart.

  1. 1Known days: 3 + 4 + 4 + 16 + 11 = 38
  2. 2Other two days: 58 − 38 = 20
  3. 320 ÷ (2 + 3) = 4, so Wednesday = 2 × 4 = 8, Friday = 3 × 4 = 12
  4. 4Draw a bar of height 8 for Wednesday and height 12 for Friday

AnswerCompletely correct bar chart: Wednesday 8, Friday 12

Part (aiv) · 1 mark

State the mode of the daily television sales from the completed chart.

  1. 1The tallest bar is Saturday
  2. 2Mode = Saturday

AnswerSaturday

Part (b) · 2 marks

A $550 television is reduced by 4%; calculate its new price.

  1. 14% of 550 = 22
  2. 2New price = 550 − 22 = $528

Answer528

Part (c) · 1 mark

From the scatter diagram of price against television size, state the type of correlation.

  1. 1As size increases, price increases
  2. 2Positive correlation

AnswerPositive

Part (di) · 2 marks

Complete the tree diagram for two televisions, using 0.02 as the probability a television is faulty.

  1. 1P(not faulty) = 1 − 0.02 = 0.98
  2. 2Each faulty branch is 0.02, each not faulty branch is 0.98

Answer1st: faulty 0.02, not faulty 0.98; 2nd after faulty: faulty 0.02, not faulty 0.98; 2nd after not faulty: faulty 0.02, not faulty 0.98

Part (dii) · 2 marks

Calculate the probability that both televisions Hemang buys are faulty.

  1. 1P(both faulty) = 0.02 × 0.02
  2. 2= 0.0004

Answer0.0004

Part (diii) · 1 mark

Given 4150 televisions sold in a year, calculate the expected number that are faulty.

  1. 1Expected = 4150 × 0.02
  2. 2= 83

Answer83

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