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C1 Tangents - Math Revision for Year 11 Maths Adv; Topic Specific
Math Revision for Year 11 Maths Adv; Topic Specific
Subject
math advanced
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ADV: Calculus (Adv), C1 Introduction to Differentiation (Adv)
Tangents (Y11)
Teacher: Helen Tolhurst
Exam Equivalent Time: 45 minutes (based on HSC allocation of 1 minutes approx. per
mark)
HISTORICAL CONTRIBUTION
C1 Introduction to Differentiation is Y11 content but nonetheless has contributed
meaningfully to past Mathematics exams, accounting for an average of 3% per
year.
This topic has been split into three sub-topics for analysis purposes: 1-The Derivative
Function (0%), 2-Tangents (1%), and 3-Rates of Change (1%).
This analysis looks at the sub-topic Tangents.
HSC ANALYSIS - What to expect and common pitfalls
Tangents in this sub-topic only include examples that require standard differentiation
and importantly excludes log, exponential and trig underlyings which are covered in
later year 12 sub-topics.
Tangent questions that require standard differentiation have been asked an
impressive 5 times in the last decade, most recently in 2019 in a 3-mark question
that caused problems (see 2019 Adv 14d).
While regular question types offer a great opportunity for high scoring, take note of
some more applied examples that created problems for many students (2009 HSC
6c, 2010 HSC 7b).
1. Calculus, 2ADV C1 2009 HSC 1d
2. Calculus, 2ADV C1 2012 HSC 11c
3. Calculus, 2ADV C1 EQ-Bank 1
4. Calculus, 2ADV C1 2011 HSC 2c
5. Calculus, 2ADV C1 2017 HSC 12a
6. Calculus, 2ADV C1 SM-Bank 2
Questions
Find the gradient of the tangent to the curve at the point. (2 marks)
Find the equation of the tangent to the curve at the point where. (2 marks)
i. Use differentiation by first principles to find , given. (2 marks)
ii. Find the equation of the tangent to the curve when. (1 mark)
Find the equation of the tangent to the curve at the point where. (
marks)
Find the equation of the tangent to the curve at the point. (2 marks)
i. Find the equations of the tangents to the curve at the points where the curve cuts
the -axis. (2 marks)
ii. Where do the tangents intersect? (2 marks)
7. Calculus, 2ADV C1 2010 HSC 7b
8. Calculus, 2ADV C1 2019 HSC 14d
The parabola shown in the diagram is the graph. The points and are
on the parabola.
i. Find the equation of the tangent to the parabola at. (2 marks)
ii. Let be the midpoint of.
There is a point on the parabola such that the tangent at is parallel to.
Show that the line is vertical. (2 marks)
iii. The tangent at meets the line at.
Show that the line is a tangent to the parabola. (2 marks)
The equation of the tangent to the curve at the point where is
.
Find the values of and. (3 marks)
9. Calculus, 2ADV C1 2009 HSC 6c
The diagram illustrates the design for part of a roller-coaster track. The section is a straight line
with slope 1, and the section is a straight line with slope – 1. The section is a
parabola. The horizontal distance from the -axis to is 30 m.
In order that the ride is smooth, the straight line sections must be tangent to the parabola at and
at.
i. Find the values of and so that the ride is smooth. (3 marks)
ii. Find the distance , from the vertex of the parabola to the horizontal line through , as shown on
the diagram. (2 marks)
Copyright © 2004-20 The State of New South Wales (Board of Studies, Teaching and Educational Standards NSW)
MARKER'S COMMENT: The best
setting out clearly showed the
derivative function, the gradient,
the point and then finally,
calculations for the equation of the
tangent, as per the Worked
Solution.
4. Calculus, 2ADV C1 2011 HSC 2c
5. Calculus, 2ADV C1 2017 HSC 12a
6. Calculus, 2ADV C1 SM-Bank 2
i.
ii.
♦ Mean mark 37%.
IMPORTANT: The critical
understanding required for this
question is that the gradient of
needs to be equated to the
gradient function (i. ).
7. Calculus, 2ADV C1 2010 HSC 7b
i.
ii.
♦♦♦ Exact data unavailable.
MARKER'S COMMENT: Successful
students equated the curve
gradient to the straight section as
a requirement for a smooth ride.
9. Calculus, 2ADV C1 2009 HSC 6c
i.
ii.
Copyright © 2016-2021 M2 Mathematics Pty Ltd (SmarterMaths.com)
Was this document helpful?
C1 Tangents - Math Revision for Year 11 Maths Adv; Topic Specific
Subject: math advanced
513 Documents
Students shared 513 documents in this course
Was this document helpful?
ADV: Calculus (Adv), C1 Introduction to Differentiation (Adv)
Tangents (Y11)
Teacher: Helen Tolhurst
Exam Equivalent Time: 45 minutes (based on HSC allocation of 1.5 minutes approx. per
mark)
HISTORICAL CONTRIBUTION
C1 Introduction to Differentiation is Y11 content but nonetheless has contributed
meaningfully to past Mathematics exams, accounting for an average of 3.0% per
year.
This topic has been split into three sub-topics for analysis purposes: 1-The Derivative
Function (0.9%), 2-Tangents (1.0%), and 3-Rates of Change (1.1%).
This analysis looks at the sub-topic Tangents.
HSC ANALYSIS - What toexpect and commonpitfalls
Tangents in this sub-topic only include examples that require standard differentiation
and importantly excludes log, exponential and trig underlyings which are covered in
later year 12 sub-topics.
Tangent questions that require standard differentiation have been asked an
impressive 5 times in the last decade, most recently in 2019 in a 3-mark question
that caused problems (see 2019 Adv 14d).
While regular question types offer a great opportunity for high scoring, take note of
some more applied examples that created problems for many students (2009 HSC
6c, 2010 HSC 7b).
1.Calculus, 2ADV C1 2009 HSC 1d
2.Calculus, 2ADV C1 2012 HSC 11c
3.Calculus, 2ADV C1 EQ-Bank 1
4.Calculus, 2ADV C1 2011 HSC 2c
5.Calculus, 2ADV C1 2017 HSC 12a
6.Calculus, 2ADV C1 SM-Bank 2
Questions
Find the gradient of the tangent to the curve at the point . (2 marks)
Find the equation of the tangent to the curve at the point where . (2 marks)
i. Use differentiation by first principles to find , given . (2 marks)
ii. Find the equation of the tangent to the curve when . (1 mark)
Find the equation of the tangent to the curve at the pointwhere . (3
marks)
Find the equation of the tangent to the curve at the point . (2 marks)
i. Find the equations of the tangents to the curve at the points where the curve cuts
the -axis. (2 marks)
ii. Where do the tangents intersect? (2 marks)
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