SCool Revision Summary
SCool Revision Summary
The Basics:
Find the distance between two points using Pythagoras' theorem.
The midpoint is the average (mean) of the coordinates.
The gradient =
Parallel lines have the same gradient. The gradients of perpendicular lines have a product of 1.
Straight Lines:
Equation of a straight line is y = mx + c, where m = gradient, c = yintercept.
The equation of a line, if we know one point and the gradient is found using:
(y  y_{1}) = m(x  x_{1})
(If given two points, find the gradient first, then use the formula.)
Two lines meet at the solution to their simultaneous equations.
Note: When a line meets a curve there will be 0,1, or two solutions.

Use substitution to solve the simultaneous equations

Rearrange them to form a quadratic equation

Solve the quadratic by factorising, or by using the quadratic formula.

Find the ycoordinates by substituting these values into the original equations.
Other Graphs (also in Functions):
Sketch the curve by finding:

Where the graph crosses the yaxis.

Where the graph crosses the xaxis.

Where the stationary points are.

Whether there are any discontinuities.

What happens as
Circles:
Cartesian equation for a circle is (x  a)^{2} + (y  b)^{2} = r^{2} , where (a, b) is the centre of the circle and r is the radius.
Parametric Equations:
Sketch the graph by substituting in values and plotting points.
Find the cartesian form by either using substitution (use t = ...), or by using the identity, .
Find the gradient using the chain rule: