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0580/33 May/Jun 2023, Question 1: Pie Charts

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 12 marks

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The question, in short

From a pie chart of favourite sciences and a Venn diagram of geography and history students, work out percentages, fractions, ratios, counts and a probability, and update the diagram.

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

Part (ai) · 1 mark

Using the pie chart angles, work out what percentage picked chemistry.

  1. 1Chemistry angle = 360 − 45 − 225 = 90°
  2. 290/360 × 100 = 25%

Answer25

Part (aii) · 2 marks

Express the share picking physics as a fraction reduced to its lowest terms.

  1. 1Physics = 225/360
  2. 2= 5/8

Answer5/8

Part (aiii) · 2 marks

Give the ratio of biology to chemistry to physics in simplest form.

  1. 1Chemistry has a right-angle mark, so its angle is 90°.
  2. 2Angles give the ratio 45 : 90 : 225.
  3. 3Divide each by 45: 1 : 2 : 5

Answer1:2:5

Part (aiv) · 1 mark

Explain why the chemistry count must be even, using the sector angle.

  1. 1Biology : chemistry = 1 : 2, so chemistry = 2 × biology
  2. 2Biology must be a whole number, so chemistry is a multiple of 2, an even number

AnswerCorrect explanation eg if chemistry has an odd number then biology would not be a whole number of students

Part (av) · 2 marks

Given that 26 students picked chemistry, work out how many picked physics.

  1. 1Chemistry : physics = 2 : 5
  2. 21 part = 26 ÷ 2 = 13
  3. 3Physics = 5 × 13 = 65

Answer65

Part (bi) · 1 mark

Add up all the numbers in the Venn diagram to get the class total.

  1. 15 + 9 + 10 + 4 = 28

Answer28

Part (bii) · 1 mark

State the value of n(G) from the diagram.

  1. 1n(G) = 5 + 9 = 14

Answer14

Part (biii) · 1 mark

For a randomly chosen student, find the probability of studying both subjects.

  1. 1Students in G and H = 9
  2. 2P = 9/28

Answer9/28

Part (biv) · 1 mark

Move one student who studied both so the diagram shows them studying geography only.

  1. 1One student moves from G ∩ H to G only
  2. 2G only: 5 + 1 = 6, G ∩ H: 9 − 1 = 8
  3. 3H only: 10, outside G and H: 4

AnswerG only: 6, G ∩ H: 8, H only: 10, outside G and H: 4

Stuck on a step? Read the free lesson: Pie Charts

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Also searched as: 0580/33/M/J/23 · 0580_s23_qp_33 · 0580 s23 33 · question 1.
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