Date | November 2021 | Marks available | 1 | Reference code | 21N.2.AHL.TZ0.5 |
Level | Additional Higher Level | Paper | Paper 2 | Time zone | Time zone 0 |
Command term | Plot | Question number | 5 | Adapted from | N/A |
Question
Let .
Let and , where .
The current, , in an AC circuit can be modelled by the equation where is the frequency and is the phase shift.
Two AC voltage sources of the same frequency are independently connected to the same circuit. If connected to the circuit alone they generate currents and . The maximum value and the phase shift of each current is shown in the following table.
When the two voltage sources are connected to the circuit at the same time, the total current can be expressed as .
Plot the position of on an Argand Diagram.
Express in the form , where , giving the exact value of and the exact value of .
Find in the form .
Hence find in the form , where and .
Find the maximum value of .
Find the phase shift of .
Markscheme
A1
[1 mark]
A1A1
Note: Accept an argument of . Do NOT accept answers that are not exact.
[2 marks]
(M1)
A1
[2 marks]
M1
(A1)
attempt extract real part using cis form (M1)
OR A1
[4 marks]
(M1)
(M1)
max A1
[3 marks]
phase shift A1
[1 mark]
Examiners report
This question produced the weakest set of responses on the paper. There seemed a general lack of confidence when tackling a problem involving complex numbers. Whilst most candidates could represent a complex number on the complex plane, far fewer had the ability to move between the different forms of complex numbers. This is clearly an area of the course that needs more attention when being taught. Part (c) is challenging but it should be noted that a candidate who has answered parts (a) and (b) with confidence should find this both straightforward, and also an example of a type of problem that is mentioned in the syllabus guidance.
This question produced the weakest set of responses on the paper. There seemed a general lack of confidence when tackling a problem involving complex numbers. Whilst most candidates could represent a complex number on the complex plane, far fewer had the ability to move between the different forms of complex numbers. This is clearly an area of the course that needs more attention when being taught. Part (c) is challenging but it should be noted that a candidate who has answered parts (a) and (b) with confidence should find this both straightforward, and also an example of a type of problem that is mentioned in the syllabus guidance.
This question produced the weakest set of responses on the paper. There seemed a general lack of confidence when tackling a problem involving complex numbers. Whilst most candidates could represent a complex number on the complex plane, far fewer had the ability to move between the different forms of complex numbers. This is clearly an area of the course that needs more attention when being taught. Part (c) is challenging but it should be noted that a candidate who has answered parts (a) and (b) with confidence should find this both straightforward, and also an example of a type of problem that is mentioned in the syllabus guidance.
This question produced the weakest set of responses on the paper. There seemed a general lack of confidence when tackling a problem involving complex numbers. Whilst most candidates could represent a complex number on the complex plane, far fewer had the ability to move between the different forms of complex numbers. This is clearly an area of the course that needs more attention when being taught. Part (c) is challenging but it should be noted that a candidate who has answered parts (a) and (b) with confidence should find this both straightforward, and also an example of a type of problem that is mentioned in the syllabus guidance.
This question produced the weakest set of responses on the paper. There seemed a general lack of confidence when tackling a problem involving complex numbers. Whilst most candidates could represent a complex number on the complex plane, far fewer had the ability to move between the different forms of complex numbers. This is clearly an area of the course that needs more attention when being taught. Part (c) is challenging but it should be noted that a candidate who has answered parts (a) and (b) with confidence should find this both straightforward, and also an example of a type of problem that is mentioned in the syllabus guidance.
This question produced the weakest set of responses on the paper. There seemed a general lack of confidence when tackling a problem involving complex numbers. Whilst most candidates could represent a complex number on the complex plane, far fewer had the ability to move between the different forms of complex numbers. This is clearly an area of the course that needs more attention when being taught. Part (c) is challenging but it should be noted that a candidate who has answered parts (a) and (b) with confidence should find this both straightforward, and also an example of a type of problem that is mentioned in the syllabus guidance.