Mathematics

This section contains some useful mathematics for the 14-16 level Physics section

1. Powers of ten

 tera 1 000 000 000 000 1012 8 000 000 000 000 8x1012 2 500 000 000 000 2.5x1012 giga 1 000 000 000 109 8 000 000 000 8x109 2 500 000 000 2.5x109 mega 1 000 000 106 8 000 000 8x106 2 500 000 2.5x106 10 000 104 80 000 8x104 25 000 2.5x104 kilo 1 000 103 8 000 8x103 2 500 2.5x103 100 102 800 8x102 250 2.5x102 10 101 80 8x101 25 2.5x101 1 100 8 8x100 2.5 2.5x100 0.1 10-1 0.8 8x10-1 0.25 2.5x10-1 centi 0.01 10-2 0.08 8x10-2 0.025 2.5x10-2 milli 0.001 10-3 0.008 8x10-3 0.0025 2.5x10-3 0.0001 10-4 0.0008 8x10-4 0.00025 2.5x10-4 micro 0.000 001 10-6 0.008 8x10-6 0.0025 2.5x10-6 nano 0.000 000 001 10-9 0.0008 8x10-9 0.000 000 0025 2.5x10-9 pico 0.000 000 000 001 10-12 0.000 000 000 008 8x10-12 0.000 000 000 0025 2.5x10-12

2. Division by decimals

8/0.1 = 80 6.7/0.1 = 67 50/0.2 = 250 24/1.2 = 20 4/0.001 = 4000

3. Algebra

Pythagoras' theorem
For a right angled triangle: (HYP)2 = (OPP)2 + (ADJ)2
(see the triangle below).

Solving a quadratic equation: ax2 + bx + c = 0

The roots of this equation are: [-b +/-square root(b2 – 4ac)]/2a

The equation of a straight line is: y = mx + c where m is the gradient and c the intercept on the y axis.

a(b – c) = ab – ac

5. Changing the subject of an equation

We meet lots of equations in Physics. What looks like different equations may sometimes be the same equation written in a number if different ways.

For example: V = IR is the same as I = V/R and R = V/I

This is known as changing the subject of the equation or rearranging the equation.
If we start with V = IR and want to find what I is (in other words we need to make I the subject of the equation) then we must first divide both sides by R.
So V divided by R is V/R, IR divided by R is just I and so I = V/R.

You can also use the so-called "magic triangle".
The same example is shown for you.

The top letter is found by multiplying the two lower letters.
Either of the two lower letters is found by dividing the top letter by the other lower letter.

6.Formulae

A little explanation of what formulae actually mean.

(a) If something is written as IR it means I x R
This means exactly the same as RI

So the formula for electrical energy can be written as VIt or IVt or ItV. They all come to the same thing when numbers are put in.

(b) If something is written as at2 it means a x t x t

So the formula for kinetic energy ( ½ mv2) means ½ x m x v x v.

(c) if something is written as [v – u]/t it means that you subtract u from v and then divide the answer by t.

7. Useful areas and volumes

Area of a circle = πr2

Area of the surface of a sphere? = 4πr2

Volume of a sphere? = 4/3 πr3

Volume of a rectangular solid = length x width x height

Area of a triangle = ½ base x height

A VERSION IN WORD IS AVAILABLE ON THE SCHOOLPHYSICS CD