Sketch the graph of , labelling any points where the graph intersects the coordinate axes.
Did this page help you?
Sketch the graph of , labelling any points where the graph intersects the coordinate axes.
How did you do?
Did this page help you?
Sketch the graph of , labelling any points where the graph intersects the coordinate axes.
How did you do?
Did this page help you?
Sketch the graph of , labelling any points where the graph intersects the coordinate axes and stating the equations of any asymptotes.
How did you do?
Did this page help you?
On the axes below, sketch the graphs of both and
.
Using your graph, or otherwise, find the solution to the simultaneous equations
and
.
How did you do?
Did this page help you?
How did you do?
Sketch the graph of , labelling any points where the graph intersects the coordinate axes.
How did you do?
Did this page help you?
Express in the form
, where
are integers to be found.
How did you do?
Hence sketch the graph of labelling any points where the graph intersects the coordinate axes.
How did you do?
Did this page help you?
is proportional to
.
When .
Find the constant of proportionality
Sketch the graph of against
.
How did you do?
Did this page help you?
By sketching the graphs of and
on the same diagram show that there are two real solutions to the equation
.
How did you do?
Did this page help you?
Use the factor theorem to show that is a factor of the function
.
How did you do?
Hence, or otherwise, express as a product of three linear factors.
How did you do?
Sketch the graph of labelling any points where the graph intersects the coordinate axes.
How did you do?
Did this page help you?
The diagram below shows the graph of a circle with equation .
Add straight lines passing through the point to the diagram to show how the circle can have either no, one or two intercepts. All lines must pass through the point .
How did you do?
Did this page help you?
Sketch the graph of labelling any points where the graph intersects the coordinate axes.
How did you do?
Did this page help you?
Sketch the graph of and write down the equations of any asymptotes.
How did you do?
Did this page help you?
On the axes below sketch the graphs of both and
.
How did you do?
Using your graph, or otherwise, find the solution to the simultaneous equations
and
.
How did you do?
Did this page help you?
is inversely proportional to
. When
. Find the constant of proportionality and sketch the graph of
against
.
How did you do?
Did this page help you?
Sketch the graph of labelling any points where the graph intersects the coordinate axes.
How did you do?
Did this page help you?
On the same diagram, sketch the graphs of and
.
How did you do?
Use your graph to determine the number of solutions to the equation
.
How did you do?
Did this page help you?
A machine computes a calculation in time, seconds, that is proportional to the number of processes,
, involved. For a calculation involving 10 processes the machine takes 0.01 seconds.
Show that the constant of proportionality is 0.001.
How did you do?
Hence write down an equation linking the number of processes to the time taken
.
How did you do?
Find the time it takes for the machine to compute a calculation involving 200 processes.
How did you do?
How many processes are involved for a calculation taking 2.3 seconds?
How did you do?
Did this page help you?
The diagram below shows the graph of , where
.
Sketch the graph of , where
.
How did you do?
State which graph the following points must lie on and find the value of in each case.
How did you do?
Did this page help you?
Show that is a factor of
.
How did you do?
Fully factorise .
How did you do?