| Date | None Specimen | Marks available | 3 | Reference code | SPNone.2.sl.TZ0.2 |
| Level | SL only | Paper | 2 | Time zone | TZ0 |
| Command term | Find | Question number | 2 | Adapted from | N/A |
Question
Let \(f(x) = 4x - {{\rm{e}}^{x - 2}} - 3\) , for \(0 \le x \le 5\) .
Find the x-intercepts of the graph of f .
[3]
a.
On the grid below, sketch the graph of f .
[3]
b.
Write down the gradient of the graph of f at \(x = 3\) .
[1]
c.
Markscheme
intercepts when \(f(x) = 0\) M1
(0.827, 0) (4.78, 0) (accept \(x = 0.827\), \(x = 4.78\) ) A1A1 N3
[3 marks]
a.
A1A1A1 N3
Note: Award A1 for maximum point in circle, A1 for x-intercepts in circles, A1 for correct shape (y approximately greater than \( - 3.14\)).
[3 marks]
b.
gradient is 1.28 A1 N1
[1 mark]
c.
Examiners report
[N/A]
a.
[N/A]
b.
[N/A]
c.
Syllabus sections
Topic 2 - Functions and equations » 2.2 » Investigation of key features of graphs, such as maximum and minimum values, intercepts, horizontal and vertical asymptotes, symmetry, and consideration of domain and range.
Show 86 related questions
