Date | May 2022 | Marks available | 6 | Reference code | 22M.1.AHL.TZ2.6 |
Level | Additional Higher Level | Paper | Paper 1 (without calculator) | Time zone | Time zone 2 |
Command term | Find | Question number | 6 | Adapted from | N/A |
Question
A function f is defined by f(x)=x√1-x2 where -1≤x≤1.
The graph of y=f(x) is shown below.
Show that f is an odd function.
The range of f is a≤y≤b, where a, b∈ℝ.
Find the value of a and the value of b.
Markscheme
attempts to replace x with -x M1
f(-x)=-x√1-(-x)2
=-x√1-(-x)2(=-f(x)) A1
Note: Award M1A1 for an attempt to calculate both f(-x) and -f(-x) independently, showing that they are equal.
Note: Award M1A0 for a graphical approach including evidence that either the graph is invariant after rotation by 180° about the origin or the graph is invariant after a reflection in the y-axis and then in the x-axis (or vice versa).
so f is an odd function AG
[2 marks]
attempts both product rule and chain rule differentiation to find f' M1
A1
sets their M1
A1
attempts to find at least one of (M1)
Note: Award M1 for an attempt to evaluate at least at one of their roots.
and A1
Note: Award A1 for .
[6 marks]