*75 minutes*.

1.If (3x + 1)/3 - (x - 3)/2 = 2 + (2x - 3)/3

find the value of x

(b) Factorize completely:

15 x

^{2 }y - 20 xy

^{2}

^{}

2) f and g are functions defined as follows:

f: x -> 3x - 5

g: x -> ½ x

a) Calculate the value of f(-3)

b) Write expressions for (i) f

^{-1 }(x) and (ii) g

^{-1 }(x)

c) Hence or otherwise, write an expression for: (gf)

^{-1}

^{}

^{}

3) Sketch the graph of the function: x

^{2 }+ x - 6 for: -4

__<__x

__<__3

Given the range of F estimate the interval of the domain for which F(x) < 0

4) Sketch the graph of the curve: y = 2x

^{2 }- 3x - 2

a) Using the graph find the gradient of the curve at the point where x = 2.

b) On the same axes, draw the graph of: 5y = 18x + 36

c) Using your graphs find the solutions to the simultaneous equations:

y + 2 = 2x

^{2 }- 3x

5y = 18x + 36

5) A car starts from rest and accelerates for 5 seconds to a point P, reaching 30 m/s. It maintains this velocity for 10 seconds.

a) Using 1 cm to represent 2 seconds on the time axis and 1 cm to represent 5 meters per second on the vertical (velocity) axis, draw the velocity-time graph for this part of the car's journey.

b) Using your graph calculate:

i) the velocity of the car after 2 seconds

ii) the car's acceleration in the first 5 seconds

iii) The distance traveled in 15 seconds.

iv) the average speed for the 15 seconds

6) a) Given that q varies directly as p, use the values of q and p in the table below to calculate the values of a and b:

p......

**2**........

**8**...........

**a**

--------------------------

q.....

**6.1**.....

**b**..........

**1.2**

b) 7 pencils and 5 erasers cost $11.60, whereas 5 pencils and 3 erasers cost $7.60. Find the cost of 8 erasers.

c) If S varies directly as (r + 1) and S = 8 when r = 3, calculate the value for r when S = 50.

7) The floor of a room is in the shape of a rectangle. The floor is c meters long. The width of the floor is 2 meters less than its length.

a) State, in terms of c:

i) the width of the floor

ii) the area of the floor

b) If the area of the floor is 15 m

^{2}write down an equation in c to show this information.

(c) Use the equation to determine the width of the floor.

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