GCSE Maths Topics Most Students Get Wrong

Most GCSE Maths students don’t fail because they haven’t revised. They lose marks on a small set of topics that trip up students year after year. Knowing which topics those are, and understanding exactly why students drop marks on them, is one of the most efficient ways to improve your grade before the real exams.

This guide covers the most commonly mishandled topics in GCSE Maths across both Foundation and Higher tiers. For each one, we explain the typical mistakes students make and what to do instead. Whether you’re preparing for AQA, Edexcel, OCR, or WJEC, these topics appear across all boards and are worth getting right.

1 Fractions, Decimals and Percentages

Questions involving fractions, decimals, and percentages are some of the most reliable on any GCSE Maths paper, yet they account for a disproportionate number of dropped marks. The reason is almost always one of two things: rushing through what feels like an easy topic, or shaky foundations that were never fully addressed.

Common mistakes

• Adding fractions by adding numerators and denominators separately (for example, writing 1/2 + 1/3 = 2/5)
• Confusing percentage increase and decrease with finding a percentage of a number
• Errors when multiplying or dividing by decimals, particularly values between 0 and 1
• Forgetting to convert fractions to a common denominator before comparing them

What to do

Practise converting fluently between all three forms. Make sure you can find a percentage of an amount, apply a percentage increase or decrease, and work backwards from a percentage to find the original value. These reverse percentage questions appear regularly and catch students who only learnt the forward method.

2 Ratio and Proportion

Ratio and proportion questions are consistently among the most poorly answered on GCSE papers. They often appear in context, requiring students to apply the concept rather than just recognise it, which is where many students come unstuck.

Common mistakes

• Dividing a quantity in the wrong order when sharing in a given ratio
• Not simplifying ratios before working with them
• Confusing direct and inverse proportion
• Errors in unit conversions when ratio questions involve different units

What to do

Always write out the total number of parts first, then divide. For proportion questions, identify whether an increase in one variable causes an increase or decrease in the other before deciding which method to use. Practise both direct and inverse proportion in worded contexts, as these are the formats most likely to appear in the exam.

3 Algebra: Expanding, Factorising and Solving

Algebra underpins a large portion of the GCSE Maths paper, particularly at Higher tier. Errors in basic algebraic manipulation cause knock-on mistakes throughout multi-step questions, multiplying the marks lost from a single misunderstanding.

Common mistakes

• Incorrectly expanding double brackets, particularly when negative terms are involved
• Failing to factorise fully, stopping at a partial factorisation
• Sign errors when solving equations, especially with negative values
• Confusing expanding brackets with factorising (doing the reverse operation to what the question asks)
• Errors when rearranging formulae, particularly when the subject appears more than once

What to do

Practise expanding brackets systematically using FOIL or the grid method. When factorising, always check your answer by expanding it back out. For equations, write each step on a separate line and apply the same operation to both sides explicitly. Slow, methodical working catches far more marks than rushed mental arithmetic.

4 Graphs and Coordinates

Graph questions span a wide range of the GCSE Maths specification, from plotting straight lines to interpreting real-world graphs and sketching quadratics. Students frequently lose marks through careless plotting, misreading scales, or not knowing what a question is actually asking for.

Common mistakes

• Plotting points inaccurately due to misreading the scale on one or both axes
• Not extending lines far enough when drawing a linear graph from an equation
• Confusing gradient and y-intercept when reading from or writing the equation of a line
• Drawing curves as a series of straight line segments rather than smooth curves
• Misidentifying the gradient from a real-life graph such as a distance-time or velocity-time graph

What to do

Before plotting anything, check the scale on both axes carefully. Use a ruler for straight line graphs and draw through at least three points to verify accuracy. For y = mx + c, be clear on which value is the gradient and which is the intercept. Practise reading gradients from real-life graphs and interpreting what they represent in context.

5 Geometry: Angles, Area and Perimeter

Geometry questions are accessible to most students but drop marks consistently because of formula confusion, incorrect rounding, and missing angle rules.

Common mistakes

• Using the wrong area formula, particularly confusing the area of a trapezium with that of a parallelogram
• Forgetting that the formula for the area of a circle uses the radius, not the diameter
• Not applying angle rules correctly in multi-step angle problems
• Rounding intermediate answers in multi-step calculations, causing the final answer to be inaccurate
• Failing to include units, or including the wrong units, in area and perimeter answers

What to do

Learn all area formulae and be able to apply them without a formula sheet. When solving multi-step angle problems, write down the rule you are using alongside each step. Do not round until the final answer. Always check whether a question asks for area or perimeter, as confusing the two is a common and entirely avoidable error.

6 Pythagoras and Trigonometry

Both Pythagoras’ theorem and trigonometry appear regularly across Foundation and Higher papers, yet they generate a high volume of incorrect answers each year. The errors are usually procedural rather than conceptual.

Common mistakes

• Using Pythagoras to find a shorter side but adding rather than subtracting the squares
• Selecting the wrong trigonometric ratio (confusing which sides are opposite, adjacent, and hypotenuse)
• Forgetting to use the inverse function when finding a missing angle
• Applying trigonometry to non-right-angled triangles without using the sine or cosine rule (Higher tier)
• Working in degrees when the calculator is set to radians, or vice versa

What to do

Memorise SOH CAH TOA and practise labelling sides before setting up any equation. For Pythagoras, always identify whether you are finding the hypotenuse or a shorter side and write out the formula before substituting values. Check your calculator is in degree mode before every trigonometry question.

7 Probability

Probability questions are worth a meaningful number of marks across both tiers and involve a broad range of sub-topics: single events, combined events, tree diagrams, Venn diagrams, and frequency tables. Each one has its own set of common errors.

Common mistakes

• Writing probability as a ratio (e.g. 3:7) rather than as a fraction, decimal, or percentage
• Adding probabilities when they should be multiplied (for independent combined events)
• Errors in conditional probability, particularly when events are not replaced
• Misreading frequency tables or two-way tables due to rushing
• Forgetting that probabilities in a tree diagram on a single branch must sum to 1

What to do

Always express probability as a fraction, decimal, or percentage unless the question specifies otherwise. For combined events, draw a tree diagram and label every branch. For conditional probability without replacement, update the denominator on the second set of branches. Check that all branches from each node sum to 1 before calculating.

8 Number: Powers, Roots and Standard Form

Questions involving indices, surds, and standard form appear on nearly every GCSE Maths paper and are reliable mark-droppers, particularly for students who rush through what they assume will be straightforward.

Common mistakes

• Confusing the rules of indices, particularly when multiplying or dividing powers with different bases
• Incorrect handling of negative or fractional indices
• Errors when adding or subtracting numbers in standard form without converting to the same power of ten first
• Misinterpreting very small numbers in standard form (for example, confusing 3 × 10^-4 with 0.0003 or 0.00003)
• Not simplifying surds fully or making errors when rationalising the denominator (Higher tier)

What to do

Write out the laws of indices and make sure you can apply each one fluently. For standard form calculations, convert both numbers to the same power of ten before adding or subtracting. Practise converting between standard form and ordinary numbers in both directions until it is automatic.

9 Statistics: Mean, Median, Mode and Range

Statistics questions are accessible but frequently lose marks through carelessness or misunderstanding of what each measure actually represents.

Common mistakes

• Calculating the mean from a frequency table by dividing by the number of rows rather than the total frequency
• Not ordering a data set before finding the median
• Confusing median and mean, particularly in context questions asking which average is most appropriate
• Finding the range incorrectly by subtracting a middle value rather than the maximum minus the minimum
• Errors in estimated mean calculations when working with grouped data

What to do

For frequency table questions, always multiply each value by its frequency and divide by the total frequency, not the number of groups. For grouped data, use the midpoint of each class interval. Practise identifying which average is most suitable for a given data set and being able to explain your reasoning in writing, as this comes up in context questions.

10 Problem Solving and Multi-Step Questions

The final section of most GCSE Maths papers consists of multi-step problem solving questions worth three to five marks each. These are the questions students most often leave blank or abandon partway through, and they are where the difference between a grade 4 and a grade 6 is frequently decided.

Common mistakes

• Not attempting the question at all when the route to the answer is not immediately obvious
• Failing to show working, meaning method marks are lost even when the final answer is wrong
• Missing a step in the chain of reasoning and arriving at an incomplete answer
• Not reading the question carefully and answering a different question to the one being asked

What to do

Always write something. Even a partial attempt with clear working earns method marks. Break the question into steps: what do I know, what do I need to find, and what is the link between them? Most multi-step questions require two or three techniques applied in sequence, and identifying which techniques are needed is itself a skill that improves with practice on past papers.

Quick Reference: Topics and the Most Common Mistakes

Topic	Most Common Mistake
Fractions, Decimals, Percentages	Adding fractions incorrectly; forgetting reverse percentage method
Ratio and Proportion	Dividing in the wrong order; confusing direct and inverse proportion
Algebra	Sign errors when expanding or solving; incomplete factorisation
Graphs and Coordinates	Misreading scales; confusing gradient and intercept
Geometry	Wrong area formula; rounding too early in multi-step questions
Pythagoras and Trigonometry	Wrong trig ratio selected; forgetting inverse function for angles
Probability	Adding instead of multiplying for combined events; errors on tree diagrams
Powers, Roots, Standard Form	Index law errors; mistakes converting standard form
Statistics	Dividing by number of rows instead of total frequency
Multi-Step Problems	Not showing working; not attempting the question