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0580/33 Oct/Nov 2022, Question 10: Solving Linear Equations

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 10 marks

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The question, in short

Using dot-and-line patterns shown in a diagram, students extend the sequence, tabulate dot and line counts, derive a rule and formula for dots, and use a given line formula to find dots for 129 lines.

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

Part (a) · 1 mark

Draw the fourth pattern in the sequence, continuing the dot-and-line arrangement shown.

  1. 1Continue the zigzag: 4 top dots and 5 bottom dots joined alternately (9 dots)
  2. 2Add a vertical line up from each top dot and down from each bottom dot (17 lines)

AnswerPattern 4 drawn correctly

Part (b) · 2 marks

Fill in the missing dot and line counts for Pattern 4 in the table.

  1. 1Dots go up by 2: 7 + 2 = 9
  2. 2Lines go up by 4: 13 + 4 = 17

AnswerNumber of dots 9, Number of lines 17

Part (ci) · 1 mark

State how the dot count changes from one pattern to the next.

  1. 13, 5, 7, … : add 2

AnswerAdd 2

Part (cii) · 2 marks

Give an expression using n for how many dots Pattern n contains.

  1. 1Difference 2, so 2n + c; 2 × 1 + c = 3 gives c = 1
  2. 22n + 1

Answer2n + 1

Part (d) · 4 marks

Given lines in Pattern n equal 4n + 1, determine the dot count when 129 lines are used.

  1. 14n + 1 = 129
  2. 24n = 128, n = 32
  3. 3Dots = 2 × 32 + 1 = 65

Answer65

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