**1. a)** Consider the equation y = -½x+3

What is the gradient of the line described by this equation?

What is the y-intercept of this equation?

**b)** Find the equation of the line that has a gradient of 5 and passes through the point (-5,-2).

**c)** Find the equation of the line that is perpendicular to the line in part b) and passes through the point (2, 1)

Your answer should be left in fractional form.

**2. a)** Solve the equations below simultaneously using the graphical method:

(Hint: Draw up a table of coordinates for each equation and plot on the same set of axes. Use x values between -4 and 4)

y=-x²+1

y=x-5

Indicate the location of the solution(s) on your graph and clearly state the solution(s) in the space below:

**3.** The following graph shows the World Record Times for the 200 m race for flying start machines (a kind of bicycle).

**a)** How would you describe the correlation between Year and World Record Times

**b)** Estimate the correlation coefficient.

**c)** Draw a line of best fit by sight on the graph above.

**d)** Find the equation of the line of best fit.

**e)** Use your equation to predict the World Record Time in 1970.

**f)** Comment on the reliability of your answer in part d).

**4. a)** Factorise the following:

**i)** y=x²-x-42

**ii) **y=6x²+11x-10

**b)** Solve the quadratic equation in part a) (ii) using a method of your choice.

**5.** Some chickens are kept in a square enclosure with sides measuring x metres.

If the number of chickens is increased, the enclosure will have to be made bigger. The enclosure will have 1 metre added to one side and 2 metres added to the adjacent side.

**a) (i)** Draw a labelled diagram of the original enclosure in the space below.

** (ii)** Add to the diagram to show the new enclosure. Mark the lengths of each side on your diagram.

**b)** Find a simplified expression (i.e. no brackets) for the area of the new enclosure

**c)** If the new enclosure has an area of 42 square metres, what were the dimensions of the original enclosure?

**6.** The profit per car, $P, made when a particular model is manufactured in* t* hours is given by the equation:

P=-4*t²+*200*t-*1500

**a)** Sketch a graph showing the relationship between profit (y-axis) and time of manufacture (x-axis).

Show the coordinates of the y-intercept only.

**b)** How long does the manufacturing process need to take in order for the company to make the maximum profit?

**c)** What is the maximum profit that can be made by the car company?

**d)** Indicate the position of the turning point on the sketch graph in part (a) and write down the coordinates of this point in the space below.

**7.** The size of a colony of rare termites is related to the size of the colony’s mound. The relationship can be modelled using the equation below:

h = −*N*²+ 25*N* − 5

Where *N* is thousands of termites and h is the height of the mound in centimetres.

**a)** Sketch the graph showing the relationship between the number of termites (x- axis) and the height of the mound (y-axis).

Show the coordinates of the y-intercept only.

**b)** How many thousands of termites are required to build a mound of maximum height?

**c)** What is the maximum height of a mound predicted by the model?

**d)** Indicate the position of the turning point on the sketch graph in part (a) and write down the coordinates of this point in the space below.

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