Mr Palmer's AQA GCSE Physics Notes

Mathematics for Physics






}




Writing Numbers





Units



The unit always goes after the number without any space

Incorrect:


    ☒ m45
    ☒ 78 N


Correct:


    ☑45m
    ☑78N


You may expect to come across the following units:









Scientific Notation



Scientific notation is used when a number is too large or too small to be written in standard form. For example, the distance from the Earth to the edge of the observable universe is 435,000,000,000,000,000,000,000,000m -- rather too large to write comfortably. Scientific notation is given in the form:



We would say this as `Y times ten to the power of Z'. Your calculator shows `times ten to the power of' with the letter E.







A positive exponent on the 10 means you must add that many zeros after the number. (Don't forget the commas). A negative exponent on the 10 means you must move the decimal point that many places to the left.



Prefixes



Prefixes are used to make talking about large or small numbers simpler. The word kilometer, for example, is really two parts, the prefix kilo and the unit meter. The kilo means 1,000, so a kilometer (km) is a thousand (1,000) meters. A terameter (Tm) is a trillion (1,000,000,000) meters and a nanometer (nm) is a billionth of a meter (0.000000001m).

You may come across the following prefixes:









Unit Conversions



In order to convert one unit into another, you multiply by a fraction that equals one and makes the units cancel. For example, if you need to convert 35m into km, this is how you would do it:







The fraction
is equal to 1 because a kilometer is the same thing as a thousand meters. We can flip the fraction and write
if we need to convert the other way. To convert 4,500km into meters we would do the following:







As as last example, we'll convert one week into seconds:







As you can see, each of the fractions above follows the rule that it must be equal to one, and it is arranged to cancel out all of the units and leave only seconds.



Order of Operations



In mathematics, in order to ensure that everyone who is looks at formula will calculate the same results we must agree on the order of operations. You must perform mathematical operations in the following sequence.


  1. Exponents and roots

  2. Multiplication and division

  3. Addition and subtraction



Example:


Given the following values, calculate the value of E:











Plug in the correct values.



First you must calculate the exponents and roots.



The you must calculate all multiplications and divisions.



Lastly, perform any addition and subtraction.





Algebra






 Navigation

Physics P1 Topics
  1. Heat
  2. Energy
  3. Electricity
  4. Power
  5. Electromagnetic Spectrum
  6. Nuclear Radiation
  7. Origins of the Universe


Physics P2 Topics
  1. Motion
  2. Forces
  3. Energy
  4. Static Electricity
  5. Current Electricity
  6. Mains Electricity
  7. Momentum
  8. Nuclear Physics

Other
  1. Mathematics for Physics