O-LevelMathematicsAlgebra and graphs4024/12 · Oct/Nov 2017 · Q265 Marks
The sequence of diagrams shows patterns made from some black beads and some white beads. Each diagram has two rows more than the previous diagram.
- (a)Complete the table for Diagram 5. Diagram number 1 2 3 4 5 Total number of beads 9 16 25 36 Number of white beads 7 10 13 16 Number of black beads 2 6 12 20[1]
- (b)(i)Write down an expression, in terms of n, for (i) the number of white beads in Diagram n,[1]
- (b)(ii)(ii) the total number of beads in Diagram n.[1]
- (c)Find an expression, in terms of n, for the number of black beads in Diagram n. Give your answer in its simplest form.[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 (Oct/Nov 2017). The mark or mark type is shown in brackets.
- [1] 26(a) 49, 19, 30
- [1] 26(b)(i) 3n + 4 oe and isw
- [1] 26(b)(ii) (n+2)² oe
- [2] 26(c) n² + n; or n(n + 1)
- M1 for attempt at their(bii) – their(bi), provided both parts are different expressions in n, and the answer space also contains an expression in n, or is empty: or for a valid method.
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