Date | November 2020 | Marks available | 1 | Reference code | 20N.1.AHL.TZ0.H_12 |
Level | Additional Higher Level | Paper | Paper 1 (without calculator) | Time zone | Time zone 0 |
Command term | State | Question number | H_12 | Adapted from | N/A |
Question
Consider the function defined by f(x)=kx-5x-k, where x ∈ ℝ \ {k} and k2≠5.
Consider the case where k=3.
State the equation of the vertical asymptote on the graph of y=f(x).
State the equation of the horizontal asymptote on the graph of y=f(x).
Use an algebraic method to determine whether f is a self-inverse function.
Sketch the graph of y=f(x), stating clearly the equations of any asymptotes and the coordinates of any points of intersections with the coordinate axes.
The region bounded by the x-axis, the curve y=f(x), and the lines x=5 and x=7 is rotated through 2π about the x-axis. Find the volume of the solid generated, giving your answer in the form π(a+b , where .
Markscheme
* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.
A1
[1 mark]
A1
[1 mark]
METHOD 1
M1
A1
A1
, (hence is self-inverse) R1
Note: The statement could be seen anywhere in the candidate’s working to award R1.
METHOD 2
M1
Note: Interchanging and can be done at any stage.
A1
A1
(hence is self-inverse) R1
[4 marks]
attempt to draw both branches of a rectangular hyperbola M1
and A1
and A1
[3 marks]
METHOD 1
(M1)
EITHER
attempt to express in the form M1
A1
OR
attempt to expand or and divide out M1
A1
THEN
A1
A1
A1
METHOD 2
(M1)
substituting A1
M1
A1
A1
Note: Ignore absence of or incorrect limits seen up to this point.
A1
[6 marks]