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Herald Sun VCE Exam Guide
VCE Specialist Mathematics
Elizabeth Burns, MAV Councillor
Look carefully at the results from last year’s examination and workout why so many students gave
an incorrect response, analyses these responses and note the pitfalls. Learn from their mistakes!
For example, in Q6, only 43% answered correctly E, but 21% answered C and 16% D It is worth
analysing why so few students answered correctly.
Question 6
Which one of the following relations has a graph that passes through the point 1 + 2i in the
complex plane?
A
zz = 5
B
Arg(z) =
C
|z – 1 | = |z – 2i|
D
Re(z) = 2Im(z)
E
z+z =2
p
3
The key word here is graph. The best way to tackle this problem is to sketch or draw the graphs of
each option. The point 1 + 2i is on the circle x2 + y2 = 5 not on the circle x2 + y2 = √5 which is the
graph of A; the graph of B is a ray starting from but not including the origin that makes and angle of
𝜋
3
with the positive Re z direction and the point 1 + √3i is on the line, not 1 + 2i ; the graph of C is the
set of points – a line – equidistant from 1 and 2i and includes the point 1+
5
1
i ; 1+ i is a point on
4
2
the graph of D hence by default the answer must be E. The graph of E is the line x = 1 hence it will
contain the required specified point. The high level of responses for C and D suggest a selection
based on the presence of the numbers 1 and 2 rather than a clearly thought out solution to the
problem.
Question 16 was answered correctly (A) by only 23% of student but 53% responded to option D.
Question 16
The diagram above shows a mass suspended in equilibrium by two light strings that make angles of
60⁰ and 30⁰ with a ceiling. The tensions in the strings are
the mass is
and
and the weight force acting on
. The correct statement is
For equilibrium, the resultant force acting on a particle is zero hence the correct statement is A.
Answer D attempts to resolve the forces in the j direction but should read
In this case, the three forces can be rearranged in a triangle because the system is in equilibrium.
So with multiple choice questions do not be distracted and check answers carefully.
The VCAA has prepared a sample examination for the new study and it is available on their website.
Make sure that you have completed this exam and sought solutions. From the new Probability and
statistics area of study, here are a couple of questions.
Question 18
Given that X is a normal random variable with mean 10 and standard deviation 8, and that Y is a
normal random variable with mean 3 and standard deviation 2, and X and Y are independent
random variables, the random variable Z defined by Z = X – 3Y will have mean μ and standard
deviation σ given by
A
μ = 1, σ = 28
B
μ = 19, σ = 2
C
μ= 1, σ = 2 7
D
μ = 19, σ = 14
E
μ = 1, σ = 10
This is a standard application of the rules for the linear combinations of independent random
variables. :
E(aX + bY )= aE(X)+ bE(Y ) and Var(aX + bY )= a2Var(X)+ b2Var(Y ) which
can be found on the sample exam formula sheet.
Note that Var(X) = 64 and Var(Y) = 4
Hence E(X – 3Y) = E(X) – 3E(Y) = 1 and Var(X – 3Y) = Var(X) + 9Var(Y) = 100. Hence σ = 10 so the
answer is E. Again be careful. Answer C is the result of writing Var(X – 3Y) = Var(X) – 9Var(Y)
Question 20
A Type I error would occur in a statistical test where
A
H0 is accepted when H0 is false
B
H1 is accepted when H1 is true
C
H0 is rejected when H0 is true
D
H1 is rejected when H1 is true
E
H0 is accepted when H0 is true
By definition, a Type I error occurs when the null hypothesis, H0 is rejected when it is true hence the
answer is C, again a straight forward question if you know the definitions.
Make sure that you work out a disciplined timetable and stick to it. Do as many questions from past
examinations, text books and other sources as you can. But most of all, work closely with the person
who knows you best – your teacher.