Mathematics

This section contains some useful mathematics for the Intermediate level Physics section

1. Powers of ten

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

4. Trigonometry

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 = pr²

Area of the surface of a sphere? = 4pr²

Volume of a sphere? = 4/3 pr³

Volume of a rectangular solid = length x width x height

Area of a triangle = ½ base x height