O-LevelMathematicsAlgebra and graphs4024/21 · Oct/Nov 2019 · Q68 Marks

These are the first four patterns in a sequence made using counters. [Figure 6 Patterns 1-4] Pattern 1 (3 counters) Pattern 2 (8 counters) Pattern 3 (15 counters) Pattern 4 (24 counters)

(a)Complete the table for the patterns in this sequence. Pattern number | 1 | 2 | 3 | 4 | 5 ---|---|---|---|---|--- Number of counters | 3 | 8 | 15 |[1]
(b)Find an expression, in terms of n, for the number of counters in Pattern n.[2]
(c)(i)Ken has a bag containing 1358 counters. He makes the largest possible pattern in the sequence, Pattern p, using these counters. Find the value of p.[3]
(c)(ii)He uses all of the remaining counters to make another pattern in the sequence, Pattern q. Find the value of q.[2]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

[1] 24 35
[2] n(n+2) oe B1 for quadratic expression in n
[3] 35 B2 for 35 × 37 or 35.8 to 35.9 OR M1 for their n(n + 2) = 1358 M1 for solution of their quadratic (-2 ± √(2²-4×1×(-1358)))/(2×1)
[2] 7 M1FT for 1358–their (c)(i) × (their (c)(i) + 2)

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