A-level Maths Revision: Cheeky Revision Shortcuts

1

Coordinate Geometry

The Basics:

Find the distance between two points using Pythagoras’ theorem.

The midpoint is the average (mean) of the coordinates.

The gradient =  grad1

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.

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

Other Graphs (also in Functions):

Sketch the curve by finding:

Where the graph crosses the y-axis.

Where the graph crosses the x-axis.

Where the stationary points are.

Whether there are any discontinuities.

What happens as  m2

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,  m3

Find the gradient using the chain rule:  m4

2

Trigonometry

The Basics from GCSE

Use Pythagoras and Trigonometry in right-angled triangles

Use Sine and Cosine rules in non-right-angled triangles

Radians

2p radians = 360 degrees, arc length s = rq, area of a sector A =  m5

Angles on a coordinate grid are measured anticlockwise from the +ve x-axis.

The trig. functions are positive in these zones:

Use these zones to find the extra solutions