S-Cool Revision Summary

S-Cool 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 = y-intercept.

The equation of a line, if we know one point and the gradient is found using:

(y - y1) = m(x - x1)

(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.

  1. Use substitution to solve the simultaneous equations

  2. Rearrange them to form a quadratic equation

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

  4. Find the y-coordinates by substituting these values into the original equations.

Other Graphs (also in Functions):

Sketch the curve by finding:

  1. Where the graph crosses the y-axis.

  2. Where the graph crosses the x-axis.

  3. Where the stationary points are.

  4. Whether there are any discontinuities.

  5. What happens as

Circles:

Cartesian equation for a circle is (x - a)2 + (y - b)2 = r2 , 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: