Common Mistakes to Avoid in GCSE Maths

Have you ever left a maths exam feeling confident, only to lose marks for 'silly mistakes'? You’re not alone. These errors aren't a sign that you're bad at maths; they are predictable patterns you can learn to fix. The secret to protecting your score lies in "method marks." Examiners award these as a safety net, giving you partial credit for using the right process even if your final answer has a slip-up. By simply showing your steps, you can turn a zero-mark question into a one or two.

Here are the most common errors across Number, Algebra, and Geometry, along with actionable tips to make sure your work gets the credit it deserves.

Secure Easy Marks by Showing Your Working

Losing marks because of a tiny calculation error is a common frustration, but there’s a safety net: method marks. Examiners award these for using the correct process, allowing you to get most of the credit even if your final answer is wrong. To secure these marks, improve your problem-solving skills before you even write a number. Use this 3-step routine to break down questions:

1. Circle the command word (e.g., 'Calculate', 'Explain').

2. Underline the key values and units (e.g., 5kg, £12.50).

3. Box the final instruction (e.g., give your answer to 2 decimal places).

This habit forces you to slow down and show the examiner your thought process, proving you understood the question and turning messy scribbles into logical, mark-earning steps.

The Two Number Traps That Cost Grades

One of the most frequent traps involves negative numbers. It’s tempting to quickly answer a calculation like 7 – (–4) as 3. To avoid this, think of subtracting a negative as taking away a debt. If someone takes away your £4 debt, you are £4 better off. Therefore, 7 – (–4) becomes 7 + 4, which equals 11. This simple analogy makes the rule stick.

Just as tricky is the order of operations, known as BIDMAS. Many students mistakenly think Division always comes before Multiplication. In reality, they have equal priority, and you work from left to right. For example, in 20 ÷ 5 × 2, you first calculate 20 ÷ 5 = 4, then 4 × 2 = 8. This same danger applies to your calculator. When entering a large fraction, always use the fraction button (the key with two boxes) to ensure the calculator understands the order correctly and secures your marks.

Why You Can’t Add Apples and Oranges: Fixing Common Algebra Mistakes

A classic algebra trap is mixing up x + x and x × x. Think of x as an 'apple'. So, x + x is simply 2x (two apples). But x × x creates something new: x². You cannot add x and x². Focusing on this conceptual difference helps prevent simple mistakes.

Another common error is expanding brackets. For 4(x + 5), many write 4x + 5, forgetting the second term. Use 'the claw' method: draw a line from the 4 to the x and another to the +5. This visual check ensures you multiply everything inside, giving the correct 4x + 20.

Finally, know the difference between an expression and an equation. An expression like 4x + 20 can only be simplified. An equation has an equals sign, like 4x + 20 = 60, which tells you it can be solved. Misinterpreting this notation costs marks.

SOH CAH TOA and Other Geometry Goofs

SOH CAH TOA is a classic source of trigonometry errors, usually from misidentifying the sides of a triangle. To fix this, use a foolproof 3-step process on your diagram before calculating:

1. Find the Hypotenuse (H), the longest side opposite the right angle.

2. From the angle you are using (θ), look across to find the Opposite (O).

3. The last side next to your angle is the Adjacent (A).

Another geometry goof is mixing up perimeter and area. Before you calculate, ask yourself: "Am I walking the rim or filling the space?" Perimeter is the ‘rim’ around a shape (add the side lengths). Area is the ‘space’ inside (multiply lengths, like base times height).

With your triangle correctly labelled, choosing sin, cos, or tan becomes logical. Look at the side length you HAVE and the one you NEED. If you have the Adjacent and need the Opposite, you need the formula with O and A—which is TOA (tan). After calculating, always reread the question to avoid rounding and significant figures errors.

How to Decode Word Problems and Check Your Answers

Often, the hardest part of a question is the words, not the maths. Use this 4-step plan to translate the story into a solvable sum:

1. Read and Reread: Understand what the question is actually asking.

2. Highlight Key Info: Circle the numbers, units, and command words.

3. Choose the Operation: Decide if this is a +, -, ×, or ÷ problem.

4. Calculate & Sense Check: Do the sum, then pause to check your work.

That final pause is vital. Check your answers by working backwards using the opposite calculation (the 'inverse'). If you calculated 56 ÷ 8 = 7, your check is 7 × 8 = 56. This quick reverse-calculation catches errors before they cost marks.

Finally, perform a common-sense check. Does the answer feel right? A person's height won't be 15 metres; a chocolate bar won't cost £50. This step helps you spot huge blunders instantly.

Your Action Plan for Fewer Mistakes and More Marks

You no longer have to be frustrated by losing marks on questions you thought you understood. By spotting these predictable traps, you can secure marks that were previously lost. This comes down to a few powerful habits: showing your steps, checking every sign, and asking if your answer makes sense. These practices represent a shift toward a smarter way of working under pressure.

On your next practice paper, make a conscious effort to apply one of these ideas, like showing all your working for a multi-mark question. Each time you do this, you are not just correcting a potential mistake—you are building the methodical confidence that leads to the grade you deserve.