#### The Hyperbola. 1.
The accompanying diagram shows the
graph of xy = 8
1.1
What is the relationship
between x and y? Explain.
1.2
What happens to the value of y
if x becomes bigger?
1.3
How do the values of one variable change
if the other variable becomes smaller?
1.4
What is the value of
1.4.1
y if x = 2?
1.4.2
x if y = 4?
1.4.3
y if x = 1,6?
1.4.4
x if y = 20?
1.4.5
y if x = 0?
1.4.6
x if y = 0?
1.5
1.6
What are the intercepts on the axes?
2.
Cookies are given equally to children. There are 40 cookies that can be given.
2.1
Complete the table below:
 Number of cookies 1 2 4 b 8 10 d 40 Number of children 40 20 a 8 5 c 2 1
2.2
What relationship is there between number of cookies given and number of children? Explain.
2.3
What shape will the graph have? Explain
2.4
Draw the graph with number of cookies on the x-axis and number of children on the y-axis.
2.5
Does the shape of the graph correspond to your prediction in 2.3?
2.6
How many children can get 6 cookies each? Is this an acceptable answer? Explain.
3.
The table below shows the volume of a gas at a certain pressure and at a constant temperature.
 Pressure, p (in kPa) 48 60 80 b 120 160 Volume, V (in cubic cm) 100 80 a 48 40 c
3.1
Calculate the values of a, b and c.
3.2
Write down in words and symbols, the relationship between pressure and volume and give a reason.
3.3
What will the shape of the graph be? Explain.
3.4
Can p or V become equal to 0? Explain.
3.5
Draw the graph with pressure on the x-axis and volume on the y-axis.
3.6
The maximum volume that the container can have is 1 200 cubic cm. What will the pressure in the
container be?
3.7
What is the minimum volume of the container if the maximum pressure is 200 kPa?
4.
The table below shows the time taken to drive a certain distance at different speeds.
 Speed, v (in km/h) 10 15 20 b 60 100 Time, t (in h) 6 4 a 2 1 c
4.1
Complete the table by calculating the values of the unknowns.
4.2
What, do you think, is the relationship between the speed and the time taken?
Explain your reasoning. Also write the relationship using the symbols in the table.
4.3
Use your answer in 4.2 to predict the shape of the graph of time on the x-axis and speed
on the y-axis.
4.4
Draw the graph with time on the x-axis and speed on the y-axis.
4.5