Mathematics Methods Formula Notes

All the formulas for Maths Methods 1+2 (Australia). I got it from the website www.vcehelp.com.au and it's really helpful!

HideShow resource information
  • Created by: Meg
  • Created on: 26-01-11 00:10
Preview of Mathematics Methods Formula Notes

First 505 words of the document:

Downloaded from ­ www.vcehelp.com.au
Created by VCE student Nicholas Buttigieg for Maths Methods Unit 1/2
Here is an article for all of the functions and graphs used in Maths Methods Units 1 & 2. You
can use these as study notes if you like. To look for any diagrams on the shape of graphs,
refer to your textbook.
Linear Graphs
· The form is y = mx + c, where m is the gradient and c is the y-intercept.
· The gradient between two points is equal to m = =
· Two lines with the same gradient are parallel to each other and do not intersect.
· To find the equation of a straight line given two points, use the formula:
m(x - x1) = y - y1, where m is the gradient.
· When given equations of the form ax + by + c = 0, then transpose to y = mx + c
· Vertical lines are of the form x = a, where the x-axis intercept is given as (a, 0).
· Horizontal lines are of the form y = c, where the y-axis intercept is given as (0, c).
· Perpendicular lines can be calculated using the formula: m1 m2 = -1.
· To calculate the tangent of the angle of slope, calculate the gradient, then substitute
it into tan to get the angle.
· The distance between two points is given as
· The midpoint of a line segment is given as
Parabolas
· The form is y = ax2 + bx + c, which is known as polynomial form.
· The form is y = a (x ­ b)2 + c, which is known as turning point form.
· Parabolas of the form y = ax2, in which the axis of symmetry is x = 0, and the turning
point is (0,0). If a is greater than 1, the graph will be narrower than y = x2. If it is
between 0 and 1, the graph will be wider. If a is negative, then the graph is inverted
or reflected in the x-axis.
· Parabolas of the form y = ax2 + c involve a translation up or down the y-axis. The
axis of symmetry is x = 0 and the turning point is (0, c), which correlates to the y-
intercept.
· Parabolas of the form y = a(x ­ b)2 involve a translation left or right along the x-axis.
The axis of symmetry is x = -b and the turning point is (-b, 0), which correlates to the
x-intercept.
· The turning point of a parabola is (-b, c) from the turning point form.
· The turning point of a parabola from polynomial form can be found by completing the
square so it is in turning point form.
· To find x-intercepts, either factorise the equation or use the quadratic formula:
x=
· The axis of symmetry is x = -b from the turning point form.
· The axis of symmetry is x = from the polynomial form.
· The discriminant is equal to = b2 ­ 4ac.
Get more free VCE resources at www.vcehelp.com.au

Other pages in this set

Page 2

Preview of page 2

Here's a taster:

If < 0, then there are no real solutions.
· If = 0, then there is one rational solution.
· If > 0, then there are two solutions. If it results in a perfect square, there are two
rational solutions. If it is not a perfect square, there are two irrational solutions.
Rectangular Hyperbolas
· The form is y = a / (x - h) + k.…read more

Page 3

Preview of page 3

Here's a taster:

When sketching semicircles, draw the graph of the circle. If there is a positive sign in
front of the radical, then draw the top half of the circle. If there is a negative sign,
then draw the bottom half of the circle.
· The x-intercepts can be calculated by substituting y = 0.
· The y-intercepts can be calculated by substituting x = 0.…read more

Page 4

Preview of page 4

Here's a taster:

If the value of a is greater than 1, the graph has a positive gradient. This means that
when x approaches , then y will increase exponentially. If the value of a is between
0 and 1, then this will produce a negative index. Therefore, this is the same as the
graph with the positive index, but is reflected in the y-axis.…read more

Page 5

Preview of page 5

Here's a taster:

In graphs of the form y = a sin n (x ± b) + c and y = a cos n (x ± b) + c, a horizontal
and vertical translation has occurred. The graph is moved b units to the left or right,
then moved c units up or down.
Tangent Function
· The form is y = k tan n (x ± b) + c.
· The basic graph is y = tan x.…read more

Comments

No comments have yet been made

Similar Mathematics resources:

See all Mathematics resources »See all resources »