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4024/21 May/Jun 2022, Question 2: Pattern Sequences and Special Sequences

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 10 marks

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The question, in short

Using the tile patterns shown, fill in missing table values for pattern 5, then derive formulas and use them to find a pattern number and a tile total.

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

Part (a) · 2 marks

Fill the empty cells in the table for pattern 5, giving grey, white and total tile counts.

  1. 1Grey tiles go up by 4: 18, 22
  2. 2White tiles are 2n²: 2 × 16 = 32, 2 × 25 = 50
  3. 3Total = grey + white: 18 + 32 = 50, 22 + 50 = 72

Answer| Pattern number | 4 | 5 | | Number of grey tiles | 18 | 22 | | Number of white tiles | 32 | 50 | | Total number of tiles | 50 | 72 |

Part (b) · 2 marks

Write a formula using n that gives the grey tile count for pattern n.

  1. 1Difference is 4, so 4n + …
  2. 2n = 1: 4 + 2 = 6
  3. 34n + 2

Answer4n + 2

Part (c) · 2 marks

Given a pattern with 98 grey tiles, work out its pattern number k.

  1. 14k + 2 = 98
  2. 24k = 96
  3. 3k = 24

Answer24

Part (d) · 2 marks

Write a formula using n that gives the white tile count for pattern n.

  1. 1White: 2, 8, 18, 32, … second difference = 4, so 2n²
  2. 2Check: n = 3 gives 2 × 9 = 18
  3. 32n²

Answer2n²

Part (e) · 2 marks

Work out how many tiles altogether are in pattern 20.

  1. 1Total = 2n² + 4n + 2
  2. 2= 2 × 20² + 4 × 20 + 2 = 800 + 80 + 2
  3. 3= 882

Answer882

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Also searched as: 4024/21/M/J/22 · 4024_s22_qp_21 · 4024 s22 21 · question 2.
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