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4024/12 Oct/Nov 2020, Question 20: Pattern Sequences and Special Sequences

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 5 marks

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The question, in short

Using a dot-pattern sequence where each pattern adds a row and two dots per row, complete a grid drawing, fill a table, and derive expressions in n for rows, dots per row, and total dots.

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

Part (a) · 1 mark

Draw the fourth pattern on the grid, continuing the rule of one extra row and two extra dots per row.

  1. 1Pattern 4 has 5 rows with 7 dots in each row
  2. 2Draw a rectangle of dots 7 wide and 5 high

AnswerRectangle with base 7 dots, height 5 dots

Part (bi) · 1 mark

Fill the missing table entries for patterns 1 to 4, including rows, dots per row, and total dots.

  1. 1Pattern 3: 4 rows of 5 dots, total 4 × 5 = 20
  2. 2Pattern 4: 5 rows of 7 dots, total 5 × 7 = 35

Answer| Pattern number | 3 | 4 | | Number of rows | 4 | 5 | | Number of dots in each row | 5 | 7 | | Total number of dots | 20 | 35 |

Part (bii) · 1 mark

Write a formula in n giving p, the number of rows in pattern n.

  1. 1Rows: 2, 3, 4, 5, … go up by 1, starting at 2
  2. 2p = n + 1

Answern + 1

Part (biii) · 1 mark

Write a formula in n giving q, the number of dots in each row of pattern n.

  1. 1Dots per row: 1, 3, 5, 7, … go up by 2, starting at 1
  2. 2q = 2n − 1

Answer2n − 1

Part (biv) · 1 mark

Write a formula in n for the total dots in pattern n.

  1. 1Total = rows × dots in each row = p × q
  2. 2= (n + 1)(2n − 1) = 2n² + n − 1

Answer(n + 1)(2n − 1) or 2n² + n − 1

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Also searched as: 4024/12/O/N/20 · 4024_w20_qp_12 · 4024 w20 12 · question 20.
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