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0580/32 May/Jun 2022, Question 7: Venn Diagrams

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 11 marks

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The question, in short

Shade a grid so the shaded fraction matches a partly shaded 12-sector shape, continue a repeating shape pattern, and complete Venn diagrams for shapes classified by colour, size and type.

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

Part (a) · 2 marks

Shade squares in the 9 by 4 rectangle so the same fraction is shaded as in the 12-sector shape with 5 shaded sectors.

  1. 1Fraction shaded = 5/12
  2. 25/12 = 15/36, so shade 15 of the 36 squares

Answer15 squares shaded

Part (bi) · 1 mark

Draw the next two shapes that follow in the repeating sequence of four shapes.

  1. 1The pattern repeats every 4: circle, triangle, rectangle, small rectangle
  2. 2Positions 10 and 11: black triangle, white rectangle

AnswerBlack triangle, white rectangle

Part (bii) · 1 mark

State what is common to the position numbers where the small black rectangle appears.

  1. 1Small black rectangle is at positions 4, 8, 12, …
  2. 2They are all multiples of 4 (divisible by 4)

AnswerDivisible by 4

Part (biii) · 2 marks

Explain why the shape at position 99 is a white rectangle, using the repeating pattern.

  1. 1100 = 4 × 25, so position 100 is a small black rectangle
  2. 2Position 99 is just before it, and the white rectangle always comes just before the small black rectangle
  3. 3So position 99 is a white rectangle and Pierre is correct

Answere.g. 4 × 25 = 100 so the 100th term is a small black rectangle; the 99th term is the term before, and the white rectangle is always before the small black rectangle, so Pierre is correct.

Part (cia) · 1 mark

Draw the four circle shapes into the Venn diagram so it is complete.

  1. 1Black circles are in both B and C: large black circle, small black circle in B ∩ C
  2. 2White circles are in C only: large white circle, small white circle

AnswerLarge black circle and small black circle in B ∩ C; large white circle and small white circle in C only

Part (cib) · 1 mark

Find n(B ∪ C), the number of elements in the union of sets B and C.

  1. 1B ∪ C = 4 black non-circles + 2 black circles + 2 white circles
  2. 2= 8

Answer8

Part (cii) · 3 marks

Label the two sets and draw the six named shapes in the correct regions of the Venn diagram.

  1. 1Left set has large shapes (white and black); right set has black shapes (large and small): label left L, right B
  2. 2L only: large white rectangle; L ∩ B: large black circle
  3. 3B only: small black triangle, small black rectangle
  4. 4Outside: small white circle, small white rectangle

AnswerLeft set L, right set B L only: large white rectangle L ∩ B: large black circle B only: small black triangle, small black rectangle Outside: small white circle, small white rectangle

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Also searched as: 0580/32/M/J/22 · 0580_s22_qp_32 · 0580 s22 32 · question 7.
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