Introduction to Physics Formulae

In Physics, we use formulae (mathematical equations) to describe how the world works. Think of a formula as a "recipe": if you have the right ingredients (measurements), the formula tells you exactly how to combine them to find the answer. In this chapter, we will master how to use these recipes, how to change them to find different ingredients, and how to present your final "dish" (the answer) perfectly for the examiner.

1. Understanding Formulae

A formula is a statement showing the relationship between different physical quantities. For example, to find out how fast something is moving, we use the relationship between distance and time.

Most formulae in your IGCSE course look like this: \(A = B \times C\).
Example: Weight = mass \(\times\) gravitational field strength, or \(W = m \times g\).

Did you know? You don't always have to memorize every single formula! For the 2025–2027 exams, you are provided with an equation sheet. However, knowing how to use and rearrange them is still the most important skill you can have.

2. The Art of Rearranging (Changing the Subject)

Often, an exam question won't ask for the "main" part of the formula. It might give you the Weight and the mass and ask you to find \(g\). To do this, you need to rearrange the formula.

The Balance Method

The golden rule is: Whatever you do to one side of the equals sign, you must do to the other.

Think of the equals sign (\(=\)) as a balance scale. To keep it level, you must treat both sides fairly.

Example: Find \(m\) in the formula \(W = m \times g\)

  1. We want \(m\) on its own. Currently, it is being multiplied by \(g\).
  2. The opposite of multiplication is division.
  3. Divide both sides by \(g\):
    \(\frac{W}{g} = \frac{m \times g}{g}\)
  4. The \(g\) on the right cancels out, leaving:
    \(m = \frac{W}{g}\)

The "Triangle" Trick

For formulae with three variables (like \(Speed = \frac{Distance}{Time}\)), you can use a formula triangle. This is great if you find algebra a bit scary!

  • Put the quantity that is the "top" of a fraction at the top of the triangle.
  • Put the other two at the bottom.
  • To use it: Cover the one you want to find with your finger. What is left tells you the calculation.

Note: Triangles are helpful, but try to learn the balance method as well, as it works for more complex formulae like \(v^2 = u^2 + 2as\).

Quick Review: The Opposites

To move something to the other side, use its inverse (opposite) operation:

  • \(+\) becomes \(-\)
  • \(\times\) becomes \(\div\)
  • \(x^2\) (squared) becomes \(\sqrt{x}\) (square root)

3. Step-by-Step Calculations: The FIFA Method

To ensure you get full marks (even if you make a tiny calculator error), follow the FIFA steps for every calculation:

  1. F – Formula: Write down the blank formula you are going to use. \(P = I \times V\)
  2. I – Insert: Put the numbers from the question into the formula. \(10 = 2 \times V\)
  3. F – Fine-tune: Rearrange the numbers to find the unknown variable. \(V = \frac{10}{2}\)
  4. A – Answer: Write the final number with its units. \(V = 5\text{ V}\)

Common Mistake: Forgetting to convert units! If the mass is in grams (\(\text{g}\)), you usually need to convert it to kilograms (\(\text{kg}\)) before putting it into the formula. (See the chapter on "Units, quantities and prefixes" for more on this).

4. Working with Big and Small Numbers

In Physics, we deal with massive things (like the mass of a planet) and tiny things (like the charge of an electron). We use Standard Form and Significant Figures to keep things tidy.

Standard Form

Standard form looks like this: \(A \times 10^n\).

  • \(300,000,000\) is written as \(3.0 \times 10^8\)
  • \(0.0005\) is written as \(5.0 \times 10^{-4}\)

Trick: For positive powers, the number tells you how many places the decimal point moved to the right. For negative powers, it moved to the left!

Significant Figures (sig figs)

In your exam, a good rule of thumb is to give your answer to the same number of significant figures as the values given in the question (usually 2 or 3).

Example: If the question gives you \(4.5\text{ m}\) and \(2.1\text{ s}\), your answer should be to 2 sig figs. If you get \(2.14285...\) on your calculator, write \(2.1\).

5. Important Skills for the Exam

The syllabus requires you to be comfortable with several mathematical tools:

  • Using Sine (\(\sin\)): Used in Waves and Light (e.g., \(n = \frac{\sin i}{\sin r}\)). Ensure your calculator is in DEGREES mode!
  • Ratios and Percentages: Often used in Efficiency calculations:
    \(Efficiency = \frac{\text{useful energy output}}{\text{total energy output}} \times 100\%\)
  • Solving Equations: Being able to find \(x\) when it is part of a larger sum.
Key Takeaway Summary

1. Show your work: Examiners give "method marks" even if the final answer is wrong.
2. Units are vital: A number without a unit (like \(\text{kg}\), \(\text{m/s}\), or \(\text{J}\)) usually loses a mark.
3. Practice rearranging: Start with the simple three-part formulae before moving to the ones with squares or brackets.
4. Check your answer: Does it make sense? If you calculate the speed of a person walking and get \(500\text{ m/s}\), you’ve probably made a mistake!

For more information on the specific units used in these formulae, please refer to the "Units, quantities and prefixes" chapter. To see how these calculations are used in experiments, check "Practical investigations and experimental method".