Download GCSE Session 30 – Further Graphs and

Session 30 - Further Graphs and Transformation of
Functions

Understand that the form y = mx + c
represents a straight line and that m is
the gradient of the line and c is the value
of the y- intercept.

Understand the gradients of parallel and
perpendicular lines.

Parallel gradients are the same,
Perpendicular gradients are minus the
reciprocal.
 Eg a line with gradient ¾ is
perpendicular to a line with….

The gradients of these lines are 2 and -1/2.
The product of the gradients is 2 x -1/2= -1.
You can work out whether 2 lines are perpendicular by
multiplying their gradients. The product of the gradient of
perpendicular lines will always be -1.
 If lines are perpendicular, M1× M2 = − 1




Find the intersection points of the graphs of
a linear and quadratic function, knowing that
these are the approximate solutions of the
corresponding quadratic equation
representing the linear and quadratic
functions.

Questions requiring the approximate solution
of a quadratic equation by drawing a straight
line to intersect with another (given)
simultaneous equations may be set.

Revise Ex 17.2
Reciprocal graphs
 1/x
 2/x
= blue
= red
 3/x = green
The reciprocal will never
cross the axis.
 You need to recognise the shape, working
out a few corresponding points can help you
to plot them. Remember it the negative
values also.
Y=K to the power of x
Y=Kx will never drop below the x
axis
It always crosses the y axis at 1.
Negative values are always
between 0 and 1, where as
positive values increase very
quickly (exponentially)

Congruent triangles

To prove a pair of triangles are congruent
(identical) , you need:
SSS – All three sides
 ASA – two angles and a side
 SAS – two sides and an angle
 RHS – a right-angle, the hypotenuse and
another side


If you can show any of the above are the same
in both triangles then you can say they they
are congruent
Area of a triangle

For any triangle

A = ½ ab Sin C

To use this you need 2 sides and the
angle between them
Special Triangles

A triangle with sides in ration 3:4:5 will
always have a right angle (opposite the
longest side)

A triangle with angles 30,60, 90, will have
sides 1:√3: 2
http://www.themathpage.com/aTrig/30-6090-triangle.htm
 (Search: the maths page, trigonometry,
topic 4)

sin, cos and tan graphs
Transforming Functions
Chapter 34

See Sine wave presentation for
construction of the wave.

For transforming functions see example on
page 367

Generate a few points using a table then
plot them, use 0, 45, 90, 180…and so on

That is everything!

All the criteria in the syllabus has been
covered, It’s now important that you can
remember it all in your exams.

Use past papers to revise. If you struggle
with some questions work in groups to
figure them out.

Look things up in the book if you can’t
remember, but then revise those topics in
more detail.

When practicing exams, try and work at 1
mark per minute, you have just a bit longer
than this in the exam.