1.
(7 marks)
Given g(x)  3x3  16x2  23x  6  (x  2)(ax2  bx  c ) ;
(a)
Find the values of a, b, and c.
[3]
(b)
Hence, fully factorise g(x).
[2]
(c)
Solve the equation 3x3  16x2  23x  6  0 .
[2]
2.
(6 marks)
(a)
Describe the transformation(s) when y  cos(x) transforms to y  3 cos(2x) .
[2]
(b)
Describe the transformation/s when y  sin(x) transforms to y  4 sin(x  30) .
[2]
(c)
A trigonometric function has equation y  4 sin(x  30) for 0  x  360 .
Find the maximum value for y and the corresponding value(s) for x.
[2]
3.
(5 marks)
The function below represents y = f(x).
y
6
4
2
– 6
– 4
– 2
2
4
6
x
– 2
– 4
– 6
Draw the following on the axes provided:
(a)
y = f(2x).
[1]
–6
–4
–2
–2
–4
–6
3.
Continued
(b)
y = f(1 - x).
[2]
y
6
4
2
– 6
– 4
– 2
2
4
6
x
– 2
– 4
– 6
(c)
y = 2f(x) - 3.
[2]
y
6
4
2
– 6
– 4
– 2
2
– 2
– 4
– 6
4
6
x
4.
(6 marks)
The graphs of 5 functions are shown below.
y
y
5
4
3
2
1
x
-2
-5
-4
-3
-2
-1
1
2
3
4
5
x
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
Graph A
Graph B
y
-5
-4
-3
-2
y
x
-1
-5
-1
-4
-3
-2
x
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
Graph C
Graph D
y
-3
-2
-1
1
2
3
-1
-2
-3
-4
-5
Graph E
4
5
6
7
8
x
4.
Continued
(a)
Equation
Match each graph above to its corresponding equation below.
y
1
xa
ybx
y  (x  c)2  d
y  x3  e
y  fx  g
Graph
[2]
(b)
Find the value of each of the constants a, b,c,d,e,f and g in the equations above.
[4]
5.
(8 marks)
(a)
Graph the equation, y  x2  4x  7 on the axes below, labelling and stating the:
(i)
(ii)
(iii)
line of symmetry,
turning point,
y-intercept.
[4]
5.
Continued
(b)
Use the discriminant to show this equation ( y  x 2  4x  7 ) has two roots.
[2]
(c)
If the graph is to have only one root, the graph will need to be translated upwards d units.
Use the discriminant to show how you would find the value of d, and give the value of d.
[2]
6.
(4 marks)
(a)

Give the exact value for sin( ) ,
6
[1]
(b)
If tan( )  
1
, determine all values of  , given the domain 2    0 .
.
[3]
Section Two:
CAS Calculator and Scientific
Calculator allowed
[2]
8.
(2 marks)
Under certain circumstances, the volume V (mL) of a given quantity of gas is inversely proportional
to its pressure P (kPa).
In a particular experiment, when the pressure was 90kPa, the volume of gas was 40mL.
What will the volume be when the pressure is increased to 120kPa?
9.
(3 marks)
The equation of a circle is 16  x2  y 2  8x  6y  0 .
Give the coordinate of this circle’s centre and its radius.
10.
(2 marks)
Sketch the graph of y 2  x on the axes below:
11.
(4 marks)
A rectangular piece of cardboard is 4 cm longer than wide. A box of 840 cm³ is constructed by
using this piece of cardboard. A square of 6 cm is cut out in every corner and the resulting flaps
are folded upwards to create the box. Find the dimensions of the box.