#### Grade 11 - More exercises.

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.