1.1

x is inversely
proportional to y because their product, xy, is a constant : xy = 8

1.2

y becomes
smaller but never becomes 0.

1.3

If one
variable becomes smaller, the other variable becomes greater.

1.4.1

y = 4

1.4.2

x = 2

1.4.3

y = 5

1.4.4

x = 0,4

1.4.5

y is not a real number.

1.4.6

x is not a real number.

1.5

Division
by 0 is not allowed. The product of any number and 0 is 0.

But in
this case the product must be 8. x or y can therefore not be equal to 0.

1.6

The graph
does not intersect the axes and therefore there are no intercepts.

x and y
can not be equal to 0. See 1.5.

2.1

a = 10

b = 5

c = 4

d = 20

2.2

Number of
cookies given is inversely

proportional
to the number of children

because their
product is a constant.

2.3

The graph
is a hyperbola because

the number
of cookies is inversely

proportional to the number of children.

2.4

See
accompanying graph.

2.5

Yes.

2.6

6,66667
children can get 6 cookies each.

It is not an acceptable answer because the number of children must be a whole number.

Fractions of
a child do not exist. They are discrete values.

3.1

a = 60; b = 100 and c = 30.

3.2

Pressure
is inversely proportional to

the volume
of the gas because

their product
is a constant.

3.3

The graph
will be a hyperbola because

pressure is
inversely proportional to

the volume
of the gas.

3.4

No.
The product of any number and 0 is 0.

In this case
the product of pressure

and volume equals
4800.

Therefore p or
v can not be equal to 0.

3.5

See the
accompanying graph.

3.6

p = 4 kPa

3.7

minimum volume = 24 cubic cm.

4.1

a = 3;
b = 30 and c = 0,6

4.2

The speed is
inversely proportional to

the time taken
because the product of

speed and time
is a constant,

60. d = vt

4.3

The graph
will be a hyperbola because

speed
is inversely proportional to time

OR, the product
of speed and time

is a constant.

4.4

See the
accompanying graph.

4.5

Yes.

4.6.1

t = 0,75
; t = 0,3

4.6.2

v = 600
and v = 10

4.7

Yes.
Speed and time are real numbers and can have any value. They are not
discrete values.