| Date | November 2016 | Marks available | 3 | Reference code | 16N.2.sl.TZ0.4 |
| Level | SL only | Paper | 2 | Time zone | TZ0 |
| Command term | Find | Question number | 4 | Adapted from | N/A |
Question
Let f(x)=xe−xf(x)=xe−x and g(x)=−3f(x)+1g(x)=−3f(x)+1.
The graphs of ff and gg intersect at x=px=p and x=qx=q, where p<qp<q.
Find the value of pp and of qq.
[3]
a.
Hence, find the area of the region enclosed by the graphs of ff and gg.
[3]
b.
Markscheme
valid attempt to find the intersection (M1)
egf=gf=g, sketch, one correct answer
p=0.357402, q=2.15329p=0.357402, q=2.15329
p=0.357, q=2.15p=0.357, q=2.15 A1A1 N3
[3 marks]
a.
attempt to set up an integral involving subtraction (in any order) (M1)
eg∫qp[f(x)−g(x)]dx, ∫qpf(x)dx−∫qpg(x)dx∫qp[f(x)−g(x)]dx, ∫qpf(x)dx−∫qpg(x)dx
0.537667
area=0.538area=0.538 A2 N3
[3 marks]
b.
Examiners report
[N/A]
a.
[N/A]
b.
