Preliminary Mathematics – Trigonometry and Real Functions
Outcomes Assessed
P4 - chooses and applies appropriate arithmetic, algebraic, graphical, trigonometric and
geometric techniques.
P5 - understands the concept of a function and the relationship between a function and its graph
Topic areas:
 Trigonometric ratios (5.1–5.5)
 Real functions (4.1–4.4)
Failure to hand this task in by the due date may result in you receiving an N Determination warning letter which clearly indicates
you are at risk of not attaining your Record of School Achievement or Higher School Certificate
Task
Create a set of study questions with worked solutions based directly on the past paper questions attached.
Present two of your questions with their solutions to the class. The questions will be chosen at random, one
from each topic; therefore all questions must be prepared to be presented.
Instructions
1. Create a set of study questions with fully worked solutions for the 2 topics listed above. These
questions should be directly based on the past HSC questions provided to you. There should be one
created question for each past paper question.
2. The questions you create should be exactly the same level of difficulty as the past paper question
they are based on. For example, a trigonometric equation must involve the same number of steps of
the same difficulty as the past paper question it is based on. If you are unsure if your question is
difficult enough you are able to seek guidance from your teacher. Questions that are not at an HSC
standard of difficulty will receive zero marks. Questions that are HSC level, but are only equivalent
to a one mark question will receive only a maximum of one mark for the worked solution, and no
marks for comparable level of difficulty.
3. For the study questions, marks will be awarded to you according to the correctness of your solution
(based on the mark allocation of the corresponding past paper question) and the appropriateness of
the question you have chosen. The study questions must be handed in at the beginning of the lesson
on the due date, before the presentations begin. They will be handed back to you just before your
presentation, so you can refer to them. This is to ensure you do not alter your work after seeing
other students’ presentations.
Outcome
P4
P5
Question
Questions meet the
outcome
1
2
3
4
5
6
7
8
9
10
Yes
1
1
1
1
1
1
1
1
1
1
No
0
0
0
0
0
0
0
0
0
0
Created question is a
comparable level of
difficulty to the past
paper question
Yes
No
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
Worked solution
maximum marks
available (1 mark
lost for each error)
2
2
2
2
2
2
2
2
2
2
4. For the presentation, marks will be awarded according to the clarity of your explanation, and your
appropriate use of mathematical language, (including diagrams if appropriate). A presentation using
the whiteboard is sufficient; however you may use a computer and projector if you choose.
Outcome
P4
P5
Communication of worked solution
Concise use of
appropriate mathematical
language; verbal
explanation effectively
refers to and correlates
with
written/diagrammatic
working. Both the verbal
and written explanation
clearly demonstrates the
correctness of the
solution. Solution
explained in a logical
sequence
Mostly appropriate
mathematical language;
verbal explanation nearly
always effectively refers
to and correlates with
written/diagrammatic
working. Both the verbal
and written explanation
mostly demonstrates the
correctness of the
solution. Solution
explained in a nearly
logical sequence
Some use of appropriate
mathematical language;
verbal explanation has
some correlation with
written/diagrammatic
working. Either the verbal
or written explanation
partially demonstrates
the correctness of the
solution. Explanation has
some logical sequencing.
Limited appropriate
mathematical language;
verbal explanation does
not closely correlate with
written/diagrammatic
working, and the
correctness of the
solution has not been
clearly or logically
demonstrated
10
10
6-9
6-9
3-5
3-5
1-2
1-2
No mathematical
language relevant to the
correct solution used;
verbal explanation does
not correlate with
written/diagrammatic
working, working has no
logic.
0
0
Outcome P4 Marks available: 30
Mark
Grade
25 - 30
A
Outstanding
19 - 24
B
High
13 – 18
C
Sound
7 – 12
D
Basic
1-6
E
Limited
0
N/A
Description
The student has demonstrated extensive knowledge and understanding of the topic of trigonometry and
calculations to do with finding missing angles, sides of triangles and solving trigonometric equations. They
have demonstrated highly developed skills in the explanation of solutions to these problems.
The student has demonstrated thorough knowledge and understanding of the topic of trigonometry and
calculations to do with finding missing angles, sides of triangles and solving trigonometric equations. They
have demonstrated well developed skills in the explanation of solutions to these problems.
The student has demonstrated sound knowledge and understanding of the topic of trigonometry and
calculations to do with finding missing angles, sides of triangles and solving trigonometric equations. They
have demonstrated competent skills in the explanation solutions to these problems.
The student has demonstrated basic knowledge and understanding of the topic of trigonometry and
calculations to do with finding missing angles, sides of triangles and solving trigonometric equations. They
have demonstrated basic skills in the explanation solutions to these problems.
The student has demonstrated limited knowledge and understanding of the topic of trigonometry and
calculations to do with finding missing angles, sides of triangles and solving trigonometric equations. They
have demonstrated limited skills in the explanation solutions to these problems.
No evidence of knowledge and understanding.
Outcome P5 Marks available: 30
Mark
Grade
Description
25 - 30
A
Outstanding
19 - 24
B
High
13 – 18
C
Sound
7 – 12
D
Basic
1-6
E
Limited
0
N/A
The student has demonstrated extensive knowledge and understanding of the topic of functions and
graphs and calculations to do with finding domain, range, regions, and proving information about function.
They have demonstrated highly developed skills in the explanation solutions to these problems.
The student has demonstrated thorough knowledge and understanding of the topic of functions and
graphs and calculations to do with finding domain, range, regions, and proving information about function.
They have demonstrated well developed skills in the explanation solutions to these problems.
The student has demonstrated sound knowledge and understanding of the topic of functions and graphs
and calculations to do with finding domain, range, regions, and proving information about function. They
have demonstrated competent skills in the explanation solutions to these problems.
The student has demonstrated basic knowledge and understanding of the topic of functions and graphs
and calculations to do with finding domain, range, regions, and proving information about function. They
have demonstrated basic skills in the explanation solutions to these problems.
The student has demonstrated limited knowledge and understanding of the topic of functions and graphs
and calculations to do with finding domain, range, regions, and proving information about function. They
have demonstrated limited skills in the explanation solutions to these problems.
No evidence of knowledge and understanding.
Comments: (what the student has done well, areas of weakness, what the student can do to improve)
Past Paper Questions
Trigonometry Topic
1.
2.
3.
4.
5.
Functions Topic
6.
7.
8.
9.
10.