4024/12 Oct/Nov 2024, Question 9: Pattern Sequences and Special Sequences
Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 6 marks
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The question, in short
Using the grid patterns of crosses and circles, draw the next pattern, fill in counts for patterns 4 and 5, and work out cross and circle totals for pattern n.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 1 mark
Sketch Pattern 4 on the square grid, following how the crosses and circles grow from the earlier patterns.
- 1Draw 4 rows of 5 circles, a column of 4 crosses to the right, and a row of 6 crosses underneath
Answer4 rows of 5 circles with a column of 4 crosses to the right, above a row of 6 crosses
Part (b) · 2 marks
Fill the missing cross and circle counts for patterns 4 and 5 in the table.
- 1Crosses go up by 2: Pattern 4 = 10, Pattern 5 = 12
- 2Circles = rows × (rows + 1): Pattern 4 = 4 × 5 = 20, Pattern 5 = 5 × 6 = 30
Answer| Pattern number (n) | 4 | 5 | | Number of crosses | 10 | 12 | | Number of circles | 20 | 30 |
Part (c) · 1 mark
Using 2n + 2 for crosses, calculate how many crosses Pattern 35 contains.
- 12 × 35 + 2 = 72
Answer72
Part (d) · 2 marks
Write a formula in n giving how many circles Pattern n has.
- 1Pattern n has n rows of (n + 1) circles
- 2Number of circles = n(n + 1)
Answern(n + 1)
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