O-LevelMathematicsAlgebra and graphs4024/21 · May/June 2017 · Q812 Marks
[Figure: Pattern 1, Pattern 2, Pattern 3, Pattern 4 (partially complete)]
- (a)Complete the diagram for pattern 4.[1]
- (b)Complete the table. Pattern n 1 2 3 4 5 Number of grey tiles 10 14 18 Number of white tiles 10 28 54 Total number of tiles 20 42 72 110 156[2]
- (c)Find an expression, in terms of n, for the number of grey tiles in pattern n.[2]
- (d)Pattern x has 110 grey tiles. Find x.[1]
- (e)By considering the number of tiles along the outer edges of each pattern, show that the total number of tiles in pattern n is 4n² + 10n + 6 .[2]
- (f)Hence find an expression, in terms of n, for the number of white tiles in pattern n.[1]
- (g)In pattern p, the total number of tiles is equal to 8 times the number of grey tiles. Find p.[3]
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 2017). The mark or mark type is shown in brackets.
- [1] Correct diagram
- [2] 22 26 \ 88 130
- [1] B1 for 2 or 3 correct
- [2] 4n + 6 oe isw
- [1] B1 for 4n ± k
- [1] 26
- [2] (2n + 3)(2n + 2) leading to 4n² + 10n + 6 with no errors
- [1] B1 for either (2n + 3) or (2n + 2) used
- After 0, SC1 for 4n² + 10n + 6 shown using alternative method
- [1] 4n² + 6n oe
- [3] 7 cao
- [1] M1 for 4p² + 10p + 6 = 8× their (4p + 6)
- [1] A1 for 4p² - 22p – 42[ = 0] oe
- [1] B2 for [p = 7] total 272 grey 272 or B1 for [p = 6] total 240 grey 240
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