The metric system

The metric system uses several symbols to represent different powers of ten. The most common include:

Name	Prefix	Power of 10	Example
mega	M	6	90.9 MHz
kilo	k	3	110 km/hr
centi	c	-2	30 cm
milli	m	-3	10 mg
micro	μ	-6	0.6 μm
nano	n	-9	400 - 700 nm
pico	p	-12	50 pF

MKS units

The MKS (meter-kilogram-second) system of units is part of the SI (Systeme Internationale) that is the standard in much of the world outside of the United States, and in science.

Length

The meter was originally defined as 1/10⁷ of the distance from the equator to the North pole measured along a longitude passing through Paris.
In 1899 it was defined as the length between two marks on a particular platinum-iridium rod kept in Paris.
In 1960 the meter was redefined as 1,650,763.73 wavelengths of a particular orange light emitted by krypton-86.
One meter is about the length of your stride.

Mass

One kilogram is about 2.2 pounds.
The standard kilogram is a particular platinum-iridium cylinder at the International Bureau of Weights and Measures near Paris.
One litre of water has a mass of 1 kg.

Time

The second is defined as the time required for 9,192,631,770 periods of the radiation emitted when an electron in a cesium atom makes a particular transition.
One year = π x 10⁷ s
Average human lifespan = 2 x 10⁹ s
Age of the Universe = 10¹⁸ s

Exercise

Determine your height in meters and your mass in kilograms. Figure out how many seconds it took you to figure this out.

Unit conversion

Example of a unit conversion:
Michael Johnson ran 200 m in 19.32 seconds when he set the world record for that distance. Express his average speed in km per hour.

Average speed =
distance

time
=
200 m

19.32 s
= 10.35 m/s

10.35 m/s x
1 km

1000 m
x
3600 s

1 hr
= 10.35 x 3.6 = 37.27 km/hr

For the non-metric types, this is over 23 mph!

Squaring, cubing, etc.

If 100 cm = 1 m, how many cm² = 1 m²?

How many cubic cm are in 1 cubic meter?

If you filled 1 cubic meter with water, what mass of water would you have?

Basic geometry

Consider a right-angled triangle. You should know the Pythagorean theorem:
Pythagorean theorem: a² + b² = c²

You should also have no trouble remembering SOHCAHTOA:

sin(θ) =
opposite

hypotenuse
cos(θ) =
adjacent

hypotenuse

tan(θ) =
opposite

adjacent

Algebra

You should have no problem rearranging equations to solve for particular variables.

The quadratic equation

If you have an equation that looks like ax² + bx + c = 0, the quadratic equation can be used to solve for x. Generally there are two solutions:

Calculus

You Should know how to work out integrals such as:

Integrals

∫ 3t dt

∫ (1/x) dx

∫ sin(4t) dt

∫ 3t dt = (3/2)t² + c

∫ (1/x) dx = ln(x) + c

∫ sin(4t) dt = (-1/4)cos(4t) + c

You should also be able to differentiate:

Derivatives

d(12t³)/dt

d(e^kx)/dx

d(sin[4t])/dt

d(12t³)/dt = 36t²

d(e^kx)/dx = k e^kx

d(sin[4t])/dt = 4 cos(4t)

Other important concepts from calculus:

the integral is the area under the curve
the derivative is the slope
to maximize or minimize a function take its derivative and set it equal to zero