2012
TRIAL HSC
EXAMINATION
Student Name: _______________________
Teacher:
_______________________
Mathematics
Examiners
Mrs P. Biczo, Mr S. Faulds, Ms S. Cupac, Mr S. Gee and Mr J. Dillon
General Instructions
Reading time - 5 minutes.
Working time - 3 hours.
Write using black or blue pen.
Diagrams may be drawn in pencil.
Board-approved calculators and
mathematical templates may be
used.
A table of standard integrals is
provided at the back of this paper.
Show all necessary working in
Questions 11-16.
Start each question in a separate
answer booklet.
Put your student number on each
booklet.
Total marks - 100
Section I
10 marks
Attempt Questions 1-10
Allow about 15 minutes for this section
Section II
90 marks
Attempt Questions 11-16. Each of these six
questions are worth 15 marks
Allow about 2 hour 45 minutes for this
section

HAHS Mathematics Trial HSC 2012
2
Section I
10 marks
Attempt Questions 1
–
10
Allow about 15 minutes for this section
Use the multiple-choice answer sheet for Questions 1
–
10
1
Which of the following correctly shows the numeral 0.000 015 in scientific notation:
A
5
15 10
B
6
15 10
C
6
1.5 10
D
5
1.5 10
2
When the denominator is rationalised,
1
5
3
A
5
3
2
B
5
3
16
C
5
3
2
D
5
3
3
1
2
x
A
2
1
x
B
2
x
C
1
x
D
x
4
The
solution to
1
3
x
is:
A
4
2
x
B
2
2
x
C
2
4
x
D
4
x
and
2
x
5
The solutions of
2
7
3
0
x
x
are
A
7
37
2
x
B
7
37
2
x
C
7
61
2
x
D
7
61
2
x
6
The solution of
2
5
x
is
A
3
x
B
3
x
C
3
x
D
3
x

HAHS Mathematics Trial HSC 2012
3
7
The number 0.07086 rounded to 3 significant figures is:
A
0.070
B
0.071
C
0.0708
D
0.0709
8
Which of the following parabolas could have the equation
(
5)(
1)
y
x
x
?
A
B
C
D
9
The angle of inclination of the line
l
with the
x
axis, to the nearest degree, is
A
34
B
56
C
124
D
146
10
The solution for
x
which satisfies the pair of
simultaneous equations:
2
3
6
x
y
x
y
is:
A
3
x
B
1
x
C
5
x
D
9
x
x
y
0
x
y
0
x
y
0
3
2
x
0
l
y
y
x
0

HAHS Mathematics Trial HSC 2012
4
Section II
90 marks
Attempt Questions 11
–
16
Allow about 2 hours and 45 minutes for this section
Answer each question in a new answer booklet
.
All necessary working should be shown in every question.
Question 11
(15 marks)
Start a new answer booklet
Marks
(a)
Solve
2
2
6
0.
x
x
2
(b)
In the diagram
A
,
B
and
C
are the points
1, 3 , 13,7
and
7,9
respectively. The
points
3,3
P
and
6,2
Q
are the midpoints of
AC
and
AB
respectively.
(i)
Find the gradient of
PQ
.
1
(ii)
Prove that
ABC
is similar to
.
AQP
3
(iii)
Show that the equation of the line
PQ
is
3
12
0.
x
y
1
(iv)
Find the exact length of
PQ
.
1
(v)
Find the perpendicular distance of the point
A
to the line
PQ
.
2
(vi)
Hence, find the area of
.
APQ
1
Question 11 continued over the page
1, 3
A
x
NOT TO SCALE
y
O
6,2
Q
3,3
P
13,7
B
7,9
C

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