What's on the curriculum for GCSE maths exams? Your complete guide on what to expect

• Mathematics is a required GCSE, meaning all pupils in England have to take it.
• If they fail, they will need to try again until they either pass or turn 18.
• The maths GCSE qualification covers a range of topics that build on one another.
• These will include algebra, geometry, probability, statistics, and more.

Numeracy and a good understanding of basic mathematical concepts is one of the most essential skills young people learn at school.

Secondary school pupils typically get a bit of freedom in choosing which GCSE qualifications they study towards, but there are a few which are required for all students; mathematics, a science subject, and English language or literature - both, in many schools. If they don’t pass these key maths or English exams, they will have to try again.

But what do pupils taking the standard maths GCSE actually have to learn about? It is worth noting that most GCSE candidates in England may have AQA, OCR, Pearson Edexcel or WJEC Eduqas as their exam board, and course content and assessments may differ slightly between each. On top of that, the government is currently conducting a full review of the National Curriculum, what young people learn in school - and how that knowledge is assessed may soon change.

Here’s a breakdown of some of the key areas the course will cover from the government’s official guidance on the curriculum.

Numbers

Numbers are obviously at the heart of maths, which is the art of learning to manipulate them. GCSE students are expected to learn and understand basic calculations, including how to add, subtract, multiply and divide numbers - large and small, positive and negative - as well as integers, decimals, simple fractions, and eventually even surds and multiples of π (plus what all of this vocabulary means), in stages that build on what they’ve learned before.

They’ll learn how these four basic operations interact, and when they cancel each other out. They’ll also learn how to use brackets, powers, and roots to work out what order to do these calculations in, and eventually how to estimate powers and roots of positive numbers too.

Learning to change decimals into fractions and vice versa will also be key, working with them in ratio problems. This will form part of calculating measurements like mass, length, time, money using standard units, and how to round where appropriate.

Algebra

Pupils will learn basic algebraic notation - a way of writing equations using letters and symbols. This will include things like writing ‘ab’ instead of ‘a x b’, or ‘3y’ instead of ‘y+y+y’.

They will then learn key formulas, which can eventually be used to solve maths questions presented in word form. Breaking these problems down into simple formula will allow students to follow them by swapping in the relevant numbers for letters.

The goal is eventually for candidates to be able to simplify and manipulate algebraic expressions, by doing things like collecting like terms and taking out common factors. They should be able to understand the formulas well enough to rearrange them, to best suit what they have to calculate.

Ratio, proportion and rates of change

Students will learn to express one number as a fraction of another. They’ll be able to do the calculations behind this too, breaking down quantities into parts and expressing it as a ration. Eventually, they will also be able to break down ratios into their simplest form.

This builds up to working with percentages, using them to compare proportions of different things, and calculating increases and decreases - some of the building blocks of financial maths.

A key part of this topic will be learning to switch between different units, like time, length, area, volume and mass. Calculating compound units will also come into it - speed, rates of pay, prices, density, pressure, and more. Finally, they will need to be able to understand basic line graphs that demonstrate these how these change, when compared to standard units like time, for example.

Geometry and measures

For this segment, candidates will have to break out the protractor. They will learn about all kinds of different polygons, and the types of lines and angles that make them up (and yes - Pythagoras’ Theorem still gets a mention).

Constructing figures and solving problems by bisecting lines or angles with a ruler and compass, learning to deduce what an angle is likely to be in any given shape from the size of the other angles, calculating a circle’s radius or diameter - geometry’s got it all. Pupils will get to learn about rotating, reflecting and translating shapes too.

Then comes measurement. Here young people will learn how to interpret things like maps and to-scale drawings, while measuring line segments and angles. But there’s a calculation aspect to it too - including learning how to calculate areas of different shapes, using the sine and cosine rules.

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Probability

At its core, GCSE-level probability will be about learning to describe and analyse the frequency of different outcomes in hypothetical experiments - using tools like using tables, frequency trees, and even Venn diagrams.

Using ideas like randomness, fairness, and equally-likely events, students will eventually be able to calculate what the outcome of a future experiment - like, say, flipping a coin repeatedly - would be.

Statistics

Statistics at GCSE level is largely about being able to understand things about broader populations, by looking at a sample, while also understanding the limitations of doing this - correlation not necessarily equalling causation, for example. Displaying or understanding this information using basic graphs (think table, pie, bar, and line) will also come into it.

The end goal is for students to be able to get a data set, analyse and interpret it. This will include calculating averages (mean, median, and mode) and spreads (range, outliers, and quartiles), presenting that data in a clear way, and describing what it tells them about a group more broadly than the sample set.

What do you think about the topics currently covered in the maths GCSE. Are they the same as you went to school, and do they need to change? Have your say and make your voice heard by leaving a comment below.