Date | May 2019 | Marks available | 6 | Reference code | 19M.1.AHL.TZ2.H_9 |
Level | Additional Higher Level | Paper | Paper 1 (without calculator) | Time zone | Time zone 2 |
Command term | Determine | Question number | H_9 | Adapted from | N/A |
Question
Consider the functions and defined on the domain by and .
The following diagram shows the graphs of and
Find the -coordinates of the points of intersection of the two graphs.
Find the exact area of the shaded region, giving your answer in the form , where , .
At the points A and B on the diagram, the gradients of the two graphs are equal.
Determine the -coordinate of A on the graph of .
Markscheme
* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.
attempt to form a quadratic in M1
A1
valid attempt to solve their quadratic M1
A1
A1A1
Note: Ignore any “extra” solutions.
[6 marks]
consider (±) M1
A1
Note: Ignore lack of or incorrect limits at this stage.
attempt to substitute their limits into their integral M1
A1A1
[5 marks]
attempt to differentiate both functions and equate M1
A1
attempt to solve for M1
A1
M1
A1
[6 marks]