O-LevelMathematicsAlgebra and graphs4024/21 · May/June 2022 · Q210 Marks
Here are the first four patterns in a sequence made using grey tiles and white tiles. [Figure showing Pattern 1, Pattern 2, Pattern 3, Pattern 4]
- (a)Complete the table for the first five patterns in this sequence. [Table with Pattern number 1-5, Number of grey tiles, Number of white tiles, Total number of tiles][2]
- (b)Find an expression, in terms of n, for the number of grey tiles in Pattern n.[2]
- (c)Pattern k has 98 grey tiles. Find k.[2]
- (d)Find an expression, in terms of n, for the number of white tiles in Pattern n.[2]
- (e)Find the total number of tiles in Pattern 20.[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 2022). The mark or mark type is shown in brackets.
- [2] 18 22 32 50 50 72
- B1 for one row or column correct
- [2] 4n + 2 oe final answer
- B1 for 4n + k oe seen
- [2] 24
- M1 for their (4k + 2) = 98
- [2] 2n² oe final answer
- B1 for answer kn² + ... , k ≠ 0 or second difference = 4 soi
- [2] 882
- M1 for 2×20² + 4×20 + 2 oe or n = 20 substituted into their(b) + their(d) oe
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