Year 9 maths: finishing KS3 and getting ready for GCSE

What do children learn in Year 9 maths?

In Year 9 maths, children finish the key stage 3 programme of study. The curriculum says that by the end of KS3, children should know, apply and understand everything in it. It doesn't say which topics are taught in Year 9, so your child's school decides what's left for this year and how to bring the strands together. Ask the school for its maths scheme of work or curriculum map if you'd like to see the plan.

The curriculum also says moving on should depend on how secure a child's understanding is. Children who grasp ideas quickly should get richer, harder problems before moving on to new content, and children who need more time should get more practice first. So Year 9 isn't only about new topics: it's also a chance to make the KS3 basics secure.

Year 9 maths topics

The curriculum doesn't say which topics belong in Year 9, so this list gives the topics usually finished by the end of key stage 3, strand by strand, taken from the KS3 programme of study. By the end of Year 9, children should have covered the whole KS3 curriculum. Under each strand is how the GCSE content carries it on in Years 10 and 11.

Number

By the end of KS3: powers and roots, prime factors, standard form for very large and very small numbers, and rounding to decimal places or significant figures. For example, 32,000 in standard form is 3.2 × 10⁴, and 0.00056 is 5.6 × 10⁻⁴.

At GCSE: calculating with standard form, working with fractional indices, and upper and lower bounds for rounded measurements.

Algebra

By the end of KS3: expanding brackets, including two brackets multiplied together, factorising by taking out a common factor, solving equations of every linear kind, rearranging formulae, inequalities, straight-line graphs in the form y = mx + c, and finding approximate solutions to simultaneous equations from a graph.

At GCSE: factorising quadratic expressions, solving quadratic equations, and solving simultaneous equations with algebra as well as graphs.

Worked example: expand (x + 3)(x + 5). Multiply each term in the first bracket by each term in the second: x × x is x², x × 5 is 5x, 3 × x is 3x, and 3 × 5 = 15. Collect the like terms: x² + 8x + 15.

Ratio, proportion and rates of change

By the end of KS3: ratio, direct and inverse proportion, percentage change including finding the original value, simple interest, and compound units like speed and density.

At GCSE: growth and decay problems, including compound interest, and more about how graphs show proportion and rates of change.

Worked example: after a 20% discount, a jacket costs £48. That's 80% of the original price. 1% is 48 ÷ 80 = 0.6, so 100% is £60.

Geometry and measures

By the end of KS3: area and perimeter of circles and composite shapes, volume of prisms and cylinders, angle facts, congruent and similar triangles, Pythagoras' theorem, and trigonometric ratios in right-angled triangles.

At GCSE: surface area and volume of spheres, pyramids and cones, circle theorems, vectors, and trigonometry in triangles that aren't right-angled.

Worked example: a right-angled triangle has shorter sides of 3 cm and 4 cm. By Pythagoras' theorem, the square of the longest side (the hypotenuse) is the sum of the squares of the other two: 9 + 16 = 25. The square root of 25 is 5, so the hypotenuse is 5 cm.

Probability

By the end of KS3: the 0 to 1 scale, probabilities adding up to 1, Venn diagrams, and sample spaces for single and combined events.

At GCSE: tree diagrams, and the probability of two events happening one after the other, including when the first affects the second.

Statistics

By the end of KS3: averages and range, charts for grouped data, and scatter graphs for two sets of data.

At GCSE: histograms, cumulative frequency, box plots and quartiles, and lines of best fit on scatter graphs, along with knowing that a link between two things doesn't prove one causes the other.

Year 9 and GCSE options

Maths isn't one of the GCSE options, because every child carries on with it. GOV.UK lists maths as one of the three core subjects at key stage 4, with English and science, and the core subjects are compulsory. Schools must also offer at least one subject from each of the arts, design and technology, the humanities and modern foreign languages. Your child's school will explain how and when it asks children to choose their other subjects, so it's worth asking early if you're not sure.

Getting ready for GCSE maths

Key stage 4 starts in Year 10. During key stage 4 most children work towards GCSEs, and most take them in Year 11. The GCSE subject content says that GCSE builds on maths typically taught at key stage 3, and that schools don't need to teach it again if children have learned it well. The key stage 4 programme of study says KS3 and KS4 together cover everything in the GCSE. So the KS3 maths your child learns in Year 9 is part of the GCSE course, not a separate stage before it.

Foundation and higher tier

GCSE maths has two tiers: foundation and higher. The GCSE subject content marks some topics as content that only higher-attaining students will be assessed on. Your child's school decides which tier they're entered for, and can explain how it makes that choice. Our guides to GCSE maths foundation and GCSE maths higher explain each tier.

What GCSE maths assesses

The GCSE has three assessment objectives, and each tier weights them differently:

Assessment objective	Foundation tier	Higher tier
AO1: use and apply standard techniques	50%	40%
AO2: reason, interpret and communicate mathematically	25%	30%
AO3: solve problems within maths and in other contexts	25%	30%

So at least half of the marks are for reasoning and problem solving rather than routine methods. That's the same "fluency, reasoning, problem solving" pattern as the KS3 curriculum, which is one reason the ways of working in Year 9 matter as much as the topics.

Formulae to learn

GCSE students are given a formula sheet in the exam, with formulae such as the area of a circle, Pythagoras' theorem and the area of a trapezium. Some formulae aren't on it and still have to be learned, such as the areas of a rectangle, triangle and parallelogram, the volume of a cuboid, and speed, distance and time. Most of these first come up in KS3, so learning them well in Year 9 helps later. Our GCSE maths formulae page has the full lists.

Maths words for Year 9

Standard form

A way of writing very big or very small numbers as a number from 1 to just under 10, times a power of 10, like 3.2 × 10⁴.

Significant figures

The digits in a number that carry meaning about its size, counting from the first digit that isn't zero. 0.04867 to 2 significant figures is 0.049.

Identity

A statement that is true for every value of the letter, like 2(x + 1) ≡ 2x + 2.

Inequality

A statement that one amount is bigger or smaller than another, using signs like <, >, ≤ and ≥.

Error interval

The range of values a rounded number could have come from. A length of 70 cm to the nearest 10 cm could be anything from 65 cm up to, but not including, 75 cm.

Subject of a formula

The letter a formula is written to work out. In speed = distance ÷ time, speed is the subject.

Simultaneous equations

Two equations with the same two unknowns that are both true at once.

Hypotenuse

The longest side of a right-angled triangle, opposite the right angle.

Pythagoras' theorem

In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.

Trigonometric ratios

Sine, cosine and tangent: ratios of the sides of a right-angled triangle that link its angles to its lengths.

Congruent

Exactly the same shape and size.

Similar

The same shape but a different size, where one is an enlargement of the other.

Bivariate data

Data about two things for each item, like height and shoe size, which can be shown on a scatter graph.

Outlier

A value that is far away from the rest of the data.

End of year 9 maths tests

There's no national maths test in Year 9. GOV.UK's guide to the national curriculum lists national assessments for the primary years and GCSEs in key stage 4, but none for Years 7, 8 and 9. If your child's school sets an end-of-year maths test or exam, the school writes it and decides what it covers, so ask your child's maths teacher which topics will come up and how the results are used. The school's curriculum map shows what's been taught so far, which is a good guide to what to revise.

For a bit of practice at home, try the Year 9 maths questions below.

Year 9 maths questions to try

These are our own practice questions, not a test from school. They cover topics from across the KS3 strands above.

1. Write 45,000 in standard form.
2. Round 0.04867 to 2 significant figures.
3. A right-angled triangle has shorter sides of 6 cm and 8 cm. How long is the hypotenuse?
4. Solve 5x − 3 = 2x + 9.
5. Expand and simplify (x + 2)(x + 7).
6. A price falls from £50 to £40. What is the percentage decrease?
7. A number rounded to the nearest 10 is 70. Write its error interval.

Answers

1. 4.5 × 10⁴
2. 0.049
3. 10 cm (36 + 64 = 100, and the square root of 100 is 10)
4. x = 4 (take 2x from both sides to get 3x − 3 = 9, then 3x = 12)
5. x² + 9x + 14
6. 20% (the price fell by £10, and £10 is ¹⁄₅ of £50)
7. 65 ≤ x < 75

How to help with Year 9 maths at home

• Make the basics secure. Fractions, negative numbers, percentages and quick times tables are used all through GCSE maths. Gaps here are worth closing now, and there's no rush or shame in going back to them.
• Start a formula list. A page of the formulae your child meets in KS3, like the area of a circle and Pythagoras' theorem, is a good thing to build up and test each other on.
• Ask for the reasoning. Half or more of the GCSE marks are for reasoning and problem solving, so asking "why does that work?" and "how else could you do it?" is good preparation.
• Practise little and often. A few questions most days, with mistakes fixed straight away, does more than long sessions before a test.
• Talk to the school about GCSE. Ask how the GCSE course is organised from Year 10, and how the school chooses between foundation and higher tier.

Our Year 8 maths guide covers the middle of key stage 3, and the KS3 maths guide has an overview of all three years.