O-LevelMathematicsAlgebra and graphs4024/21 · Oct/Nov 2018 · Q86 Marks
The diagram shows part of a number grid. [Figure 8.1] A vertical rectangle enclosing three numbers, as shown, can be placed anywhere on the grid. The grid is continued downwards.
- (a)If n represents the number in the top of the rectangle, complete the rectangle with expressions, in terms of n, for the other two numbers. [Figure 8.2][1]
- (b)Omar multiplies the top number in the rectangle by the bottom number. He then squares the middle number in the rectangle. He finds the difference between these two results. Using your answers to part (a), show that this difference is always 25.[2]
- (c)Lena places a rectangle on the grid. She adds the three numbers in her rectangle. The sum of the three numbers is 174. Find the largest number in Lena's rectangle.[3]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.
- [1] Both correct
- [2] n^2 + 5n + 5n + 25 – n^2 – 10n = 25
- or n^2 + 10n + 25 – (n^2 + 10n) = 25
- M1 for (n+5)^2 and n(n+10)
- A1
- [3] 63
- M1 for n + n + 5 + n + 10 = 174 oe
- A1 for n = 53
- If 0 scored, SC1 for answer 53
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