O-LevelMathematicsAlgebra and graphs4024/22 · May/June 2024 · Q49 Marks

The diagrams show the first four patterns in a sequence. [Figure 4.1] Draw Pattern 5 on the grid below.

(a)(i)The diagrams show the first four patterns in a sequence. [Figure 4.1] Draw Pattern 5 on the grid below.[1]
(a)(ii)Complete the table. Pattern (n) 1 2 3 4 5 6 Total number of triangles 1 4 9 16 Number of grey triangles 0 1 3 Number of white triangles 1 3 6[2]
(a)(iii)Write an expression, in terms of n, for the total number of triangles in Pattern n.[1]
(a)(iv)Write an expression, in terms of n, for the number of white triangles in Pattern n.[2]
(b)(i)The 3rd term of a linear sequence is 34. The 8th term of the same linear sequence is 14. Find the value of the first term of this sequence.[2]
(b)(ii)Find the value of the first negative term of this sequence.[1]

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Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

[1] (Pattern 5 drawn)
[2] (Table values)
B1 for one row correct or column 5 correct or column 6 correct
[1] n² oe final answer
[2] 1/2 n² + 1/2 n oe final answer
B1 for n²/2 + n/2 oe seen or answer kn² [+ ....] oe or second difference = 1
[2] 42
M1 for (34-14)/(8-3) oe or (34-14)/(3-8) oe or a + 2d = 34 and a + 7d = 14 oe or B1 for difference = 4 or difference = -4
[1] -2

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