Drawing & Using Graphs: WJEC GCSE Higher November 2018 Unit 2 Q16

Higher November 2018 Unit 2 Q16

WJECHigherCurrent spec3 marksDrawing & Using Graphs

16. The graph of \(y = 18 + 3x - x^2\), for values of \(x\) from \(x\) = 0 to \(x\) = 6, is drawn below.

Graph of y = 18 + 3x - x squared from x = 0 to 6 on a grid with y from 0 to 24: it starts at (0, 18), peaks just above 20 near x = 1.5 and meets the x-axis at (6, 0)

Use the trapezium rule, with the ordinates \(x\) = 0, \(x\) = 1, \(x\) = 2, \(x\) = 3, \(x\) = 4, \(x\) = 5 and \(x\) = 6, to estimate the area of the region bounded by the curve, the positive \(x\)-axis and the positive \(y\)-axis. [3]

From the formula list: Area of trapezium \(= \dfrac{1}{2}(a+b)h\)

Mark scheme

Scheme	Marks	Comments
(Area=) ½×[18+0+2(20+20+18+14+8)]	M2	Award M1 for 5 or more values correct and up to 1 incorrect OR all values correct but \(h\) incorrect.
= 89	A1	FT from M1. Condone 89² if offered as the final answer.

Alternative method:

Scheme	Marks	Comments
\(\tfrac{(18+20)}{2} + \tfrac{(20+20)}{2} + \tfrac{(20+18)}{2} + \tfrac{(18+14)}{2} + \tfrac{(14+8)}{2} + \tfrac{(8+0)}{2}\) (Individual areas are: 19, 20, 19, 16, 11, 4.) = 89	M2 A1	Each area may be seen as the sum of the area of a rectangle and a triangle. M1 for the correct calculation for any 4 trapezia (not necessarily added together) OR if an incorrect \(h\) is used throughout. FT from M1. Condone 89² if offered as the final answer. Treat splitting area into 12 parts as MR-1.