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0580/32 Feb/Mar 2023, Question 8: Quadratic and Cubic Sequences

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 17 marks

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The question, in short

Using a striped rectangle and a growing square-column pattern, work out symmetry, extend the sequence, and derive and apply formulas for grey, white and total squares.

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

Part (ai) · 1 mark

State how many rotational symmetries the striped rectangle has.

  1. 1The diagram looks the same after a half turn and a full turn
  2. 2Order of rotational symmetry = 2

Answer2

Part (aii) · 2 marks

Draw every mirror line on the rectangle.

  1. 1Draw a vertical line through the middle of the rectangle
  2. 2Draw a horizontal line through the middle of the rectangle

Answer2 lines of symmetry drawn

Part (bi) · 1 mark

Draw the fourth diagram on the grid.

  1. 1Diagram 4 is 6 squares wide and 6 squares high
  2. 2Columns: grey, white, white, white, white, grey

AnswerCorrect diagram drawn

Part (biia) · 1 mark

State how many grey columns Diagram n contains.

  1. 1Every diagram has one grey column on each side
  2. 2Diagram n has 2 grey columns

Answer2

Part (biib) · 2 marks

Give an expression in n for how many columns Diagram n has in total.

  1. 1Diagrams 1, 2, 3 have 3, 4, 5 columns: always 2 more than n
  2. 2Total columns = n + 2

Answern + 2

Part (biic) · 1 mark

Give an expression in n for the share of columns in Diagram n that are grey.

  1. 1Fraction grey = grey columns ÷ total columns
  2. 2= 2/(n + 2)

Answer2/(n+2)

Part (biiia) · 3 marks

Fill the missing entries for Diagrams 4 and 5 in the table.

  1. 1Diagram 4 is 6 × 6: total = 36, grey = 2 × 6 = 12, white = 36 − 12 = 24
  2. 2Diagram 5 is 7 × 7: total = 49, grey = 2 × 7 = 14, white = 49 − 14 = 35
  3. 3Grey: 12, 14; White: 24, 35; Total: 36, 49

Answer| Number of grey squares | 12 | 14 | | Number of white squares | 24 | 35 | | Total number of squares | 36 | 49 |

Part (biiib) · 2 marks

Give an expression in n for the grey square count in Diagram n.

  1. 1Grey squares go up by 2 each time: 6, 8, 10, …
  2. 22 grey columns each n + 2 high: 2(n + 2)
  3. 3= 2n + 4

Answer2n + 4

Part (biiic) · 2 marks

Using n(n + 2) for white squares, calculate the white square count when n = 30.

  1. 1n(n + 2) with n = 30: 30 × (30 + 2)
  2. 2= 30 × 32 = 960

Answer960

Part (biiid) · 2 marks

Given Diagram k has 1296 squares altogether, determine k.

  1. 1Total squares = (k + 2)² = 1296
  2. 2k + 2 = √1296 = 36
  3. 3k = 34

Answer34

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Also searched as: 0580/32/F/M/23 · 0580_m23_qp_32 · 0580 m23 32 · question 8.
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