O-LevelMathematicsAlgebra and graphs4024/12 · Oct/Nov 2020 · Q205 Marks
The diagram shows a sequence of patterns. Each pattern has one more row, and two more dots in each row, than the pattern before it.
- (a)On the diagram, draw Pattern 4.[1]
- (b)(i)Complete the table for the first four patterns in this sequence. Pattern number | 1 | 2 | 3 | 4 | n Number of rows | 2 | 3 | 4 | p Number of dots in each row | 1 | 3 | q Total number of dots | 2 | 9[1]
- (b)(ii)Find an expression, in terms of n, for p.[1]
- (b)(iii)Find an expression, in terms of n, for q.[1]
- (b)(iv)Find an expression, in terms of n, for the total number of dots in Pattern n.[1]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- [1] 20(a) Rectangle with base 7 dots, height 5 dots
- [1] 20(b)(i) [table values: 3: 4, 5, 20; 4: 5, 7, 35]
- [1] 20(b)(ii) n+1 oe final answer
- [1] 20(b)(iii) 2n-1 oe final answer
- [1] 20(b)(iv) (n+1)(2n-1) or 2n²+n-1 oe
- FT their(b)(ii) × their(b)(iii) provided both in terms of n only
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