Date | May 2019 | Marks available | 3 | Reference code | 19M.2.SL.TZ1.S_4 |
Level | Standard Level | Paper | Paper 2 | Time zone | Time zone 1 |
Command term | Sketch | Question number | S_4 | Adapted from | N/A |
Question
Let f″(x)=(cos2x)(sin6x), for 0 ≤ x ≤ 1.
Sketch the graph of f″ on the grid below:
Find the x-coordinates of the points of inflexion of the graph of f.
Hence find the values of x for which the graph of f is concave-down.
Markscheme
* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.
A1A1A1 N3
Note: Only if the shape is approximately correct with exactly 2 maximums and 1 minimum on the interval 0 ≤ x ≤ 0, award the following:
A1 for correct domain with both endpoints within circle and oval.
A1 for passing through the other x-intercepts within the circles.
A1 for passing through the three turning points within circles (ignore x-intercepts and extrema outside of the domain).
[3 marks]
evidence of reasoning (may be seen on graph) (M1)
eg f″=0, (0.524, 0), (0.785, 0)
0.523598, 0.785398
x=0.524(=π6), x=0.785(=π4) A1A1 N3
Note: Award M1A1A0 if any solution outside domain (eg x=0) is also included.
[3 marks]
0.524<x<0.785(π6<x<π4) A2 N2
Note: Award A1 if any correct interval outside domain also included, unless additional solutions already penalized in (b).
Award A0 if any incorrect intervals are also included.
[2 marks]