Differential Calculus

Average gradient

Change in yChange in x

=△y△x

=y2−y1x2−x1

Limits




Limits from first principles



Differentiation
Differentiate from first principles



Rules of differentiation



Notation 




The gradient of a curve




Turning points

Intro to Differential Calculus

Functional notation, average gradient, limits, derivative from first principles and rules

Sketch graphs

Straight line




You can also let y=0 and calculate x to draw the line.

The Circle




The Ellipse




The Parabola




The Hyperbola


Solve simultaneous equations graphically

The Circle and the tangent

The equation of a circle

(x-a)² + (y-b)² = r²



The equation of a tangent

Equations of straight lines

Two point form





One point and a gradient (Point slope form)





The distance between two points

,



The midpoint of a line segment

,

Different forms of the Straight line

The Gradient(Slope)-intercept form

$y=mx+c$

Where m = gradient = difference in y divided by the difference in x





The Intercept form





http://www.vitutor.com/geometry/line/intercept_form.html

The General form

$ax+bx+c=0$
$\mathrm{<br>}$ $$

Angle between points is given

If you are given an angle (Θ) and you must determine the gradient: The tangent of the angle is the gradient of the line: tanΘ = m


The equation is given

$y=mx+c$
m is the gradient.

Two points are given

$m=\frac{y_2-<!--\; -\; -->y_1}{x_2-<!--\; -\; -->x_1}$



Parallel lines
If two lines are parallel, their gradients are the same.




Perpendicular lines
If two lines are perpendicular, their gradients are opposite and inverse of one another.

Manipulation of technical formulee

Rules for manipulating formulas 

1. What you do on the one side of the equal sign you must do on the other side.
2. If you must make an exponent the subject, you use logs.
3. The inverse operation of a 'root' is a 'power'.
   $\text{T}heinverseof\sqrt[3]{}is({)}^3$

Make u the subject of:

$v=u+atv-<!--\; -\; -->at=u\therefore <!--\; \therefore \; -->u=v-<!--\; -\; -->at$