Questions
ADVANCED MATHEMATICS
Calculus (Adv), C2 Differential Calculus (Adv) 1. Calculus, 2ADV C2 2016 HSC 5 MC
Trig Differentiation (Y12) What is the derivative of
Teacher: Michael Boulus (A)
Exam Equivalent Time: 57 minutes (based on allocation of 1.5 minutes per mark) (B)
(C)
C2 L&E and Trig Differentiation (D)
2. Calculus, 2ADV C4 2018 HSC 5 MC
What is the derivative of where ?
1% 2% 3% 4%
(A)
*Analytics based on the average
L&E Differentiation contribution to the 2ADV HSC
Trig Differentiation exams over the past decade. (B)
(C)
HISTORICAL CONTRIBUTION
(D)
C2 Log/Exponential and Trig Differentiation has contributed a healthy 3.2% to past
Advanced exams, on average over the past decade.
3. Calculus, 2ADV C2 2013 HSC 4 MC
This topic has been split into two sub-topics for analysis purposes: 1-Log and
Exponential Differentiation (1.9%), and 2-Trig Differentiation (1.3%). What is the derivative of ?
This analysis looks at Trig Differentiation.
(A)
HSC ANALYSIS - What to expect and common pitfalls (B)
This topic represents a low difficulty area where students should score highly. Again
we flag that stand alone questions have been notably absent in the first two new (C)
syllabus exams.
(D)
Trig Differentiation when examined prior to 2020 as a stand alone topic, has offered
up very achievable band 3 difficulty marks.
HSC Marker's Comments have noted that students who wrote out the quotient rule 4. Calculus, 2ADV C2 2019 HSC 11b
and all its inputs before substituting in values made less mistakes. Differentiate . (2 marks)
Notwithstanding the omission in the 2020-21 papers, this topic is crucial gateway
knowledge for numerous later Y12 topics and must be a core competency of every 5. Calculus, 2ADV C2 2012 HSC 12aii
student.
Differentiate with respect to .
. (2 marks)
6. Calculus, 2ADV C2 2006 HSC 2aii 16. Calculus, 2ADV C2 2008 HSC 2aiii
Differentiate with respect to :
Differentiate with respect to . (2 marks)
. (2 marks)
7. Calculus, 2ADV C2 2004 HSC 3aii
Differentiate with respect to : 17. Calculus, 2ADV C2 EQ-Bank 2
. (2 marks) Differentiate with respect to :
(2 marks)
8. Calculus, 2ADV C2 2006 HSC 2ai
Differentiate with respect to . (2 marks) 18. Calculus, 2ADV C2 2019 MET1 1b
Let .
9. Calculus, 2ADV C2 2007 HSC 2aii
Find . (2 marks)
Differentiate with respect to :
. (2 marks)
19. Calculus, 2ADV C2 2022 HSC 25
10. Calculus, 2ADV C2 2009 HSC 2ai Let .
Find the value of , for , for which AND . (3 marks)
Differentiate with respect to :
(2 marks)
20. Calculus, 2ADV C2 EQ-Bank 10
11. Calculus, 2ADV C2 2010 HSC 1e The function .
If , find the value of . (2 marks)
Differentiate with respect to . (2 marks)
Copyright © 2004-22 The State of New South Wales (Board of Studies, Teaching and Educational Standards NSW)
12. Calculus, 2ADV C2 2010 HSC 2a
Differentiate with respect to . (2 marks)
13. Calculus, 2ADV C2 2011 HSC 4a
Differentiate with respect to . (2 marks)
14. Calculus, 2ADV C2 2013 HSC 11c
Differentiate . (2 marks)
15. Calculus, 2ADV C2 2017 HSC 11c
Differentiate . (2 marks)
Worked Solutions 5. Calculus, 2ADV C2 2012 HSC 12aii
1. Calculus, 2ADV C2 2016 HSC 5 MC
2. Calculus, 2ADV C4 2018 HSC 5 MC
6. Calculus, 2ADV C2 2006 HSC 2aii
3. Calculus, 2ADV C2 2013 HSC 4 MC
7. Calculus, 2ADV C2 2004 HSC 3aii
4. Calculus, 2ADV C2 2019 HSC 11b
8. Calculus, 2ADV C2 2006 HSC 2ai 12. Calculus, 2ADV C2 2010 HSC 2a
i. MARKER’S COMMENT: A
significant number of students did
not know the quotient rule and
many found assistance by writing
out before going
into calculations.
9. Calculus, 2ADV C2 2007 HSC 2aii
13. Calculus, 2ADV C2 2011 HSC 4a
10. Calculus, 2ADV C2 2009 HSC 2ai
11. Calculus, 2ADV C2 2010 HSC 1e
COMMENT: There is no necessity
to take out the common factor in
this case.
14. Calculus, 2ADV C2 2013 HSC 11c
15. Calculus, 2ADV C2 2017 HSC 11c 19. Calculus, 2ADV C2 2022 HSC 25
Mean mark 53%.
16. Calculus, 2ADV C2 2008 HSC 2aiii
17. Calculus, 2ADV C2 EQ-Bank 2
20. Calculus, 2ADV C2 EQ-Bank 10
18. Calculus, 2ADV C2 2019 MET1 1b
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