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0580/32 May/Jun 2021, Question 9: Linear Inequalities

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 9 marks

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The question, in short

Using rectangular blocks, a sequence of patterns grows as shown; students draw the next pattern, complete a block-count table, derive a formula in n, and use 84 blocks to find the largest possible pattern and leftover blocks.

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

Part (a) · 1 mark

On the dotted grid, sketch Pattern 4 following the block arrangement shown in the earlier patterns.

  1. 1Draw a row of 7 blocks with 3 blocks on top of the middle (10 blocks in total)

AnswerRow of 7 blocks with 3 blocks on top of the middle

Part (b) · 2 marks

Fill in the missing block totals for pattern numbers 4 and 5 in the given table.

  1. 1The number of blocks goes up by 3 each time
  2. 2Pattern 4: 7 + 3 = 10, Pattern 5: 10 + 3 = 13

Answer| Pattern number | 4 | 5 | | Number of blocks | 10 | 13 |

Part (c) · 2 marks

Write an expression involving n that gives the block count for pattern number n.

  1. 1Difference 3, so 3n + c; for n = 1: 3 + c = 1, c = −2
  2. 2Number of blocks = 3n − 2

Answer3n − 2

Part (d) · 4 marks

With 84 blocks available, determine the highest pattern number Tara can build and how many blocks are left over.

  1. 1Patterns use 1, 4, 7, 10 blocks: add 3 each time, so nth term = 3n − 2
  2. 23n − 2 = 84 gives n = 86 ÷ 3 = 28.6…
  3. 3Largest whole pattern is 28, using 3 × 28 − 2 = 82 blocks
  4. 4Blocks remaining = 84 − 82 = 2, so Pattern number 28, 2 blocks remaining

AnswerPattern number 28, Number of blocks remaining 2

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