O-LevelMathematicsAlgebra and graphs4024/22 · May/June 2025 · Q157 Marks
These are the first four patterns in a sequence made from black beads and from white beads. [Figure showing Pattern 1, Pattern 2, Pattern 3, Pattern 4]
- (a)Complete the table for Pattern 5. Pattern number | 1 | 2 | 3 | 4 | 5 Number of white beads | 5 | 7 | 9 | 11 | ? Total number of beads | 6 | 10 | 15 | 21 | ?[1]
- (b)(i)Find an expression for the number of white beads in Pattern n[2]
- (b)(ii)the total number of beads in Pattern n.[2]
- (c)Bill has only 88 white beads but lots of black beads. Pattern p is the largest possible pattern he can make using these beads. Work out the value of p.[2]
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 (May/June 2025). The mark or mark type is shown in brackets.
- [1] 13 28
- [2] B1 for answer 2n + p or qn + 3, q ≠ 0 or for 2n + 3 oe seen
- [2] B1 for quadratic expression in n as answer or for at least two second differences of 1 seen and none incorrect or for correct answer seen
- [2] M1dep for their (2p + 3) = 88 dep on their 2p + 3 of form ap + b (a, b ≠ 0)
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