England · Key Stage 4 · Ages 14–15

Year 10 maths:
the year the GCSE
is actually taught

A parent's guide to Year 10 maths in England — what the GCSE course covers, how the three papers and two tiers work, where students quietly fall behind, and the topics that decide how Year 11 feels.

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The short answer

What does a student learn in Year 10 maths?

Year 10 is where the GCSE course is taught. In schools that started the specification in Year 9 it is the middle year of three; in schools that begin in Year 10 it is the first of two. Either way, this is the year the content is met, not revised — and that distinction matters more than anything else on this page.

The subject is the same six areas as key stage 3, taken considerably further: number, algebra, ratio, proportion and rates of change, geometry and measures, probability and statistics — the last two reported together in the boards' weighting tables, which is why they are often quoted as five. What is new is depth. Quadratics get factorised and solved. Simultaneous equations arrive. Trigonometry stops being right-angled triangles only. Percentages become compound interest and reverse problems. Circle theorems, surds and algebraic proof appear on higher tier.

The national curriculum is explicit that key stage 3 and key stage 4 together cover the whole of GCSE mathematics, so a good deal of Year 10 is key stage 3 content being finished properly rather than replaced.

There is almost never an external exam in Year 10 — a small minority of schools enter some students early, but the norm is that nothing is sat until Year 11. Schools run their own mocks and assessments instead, and those are usually what tier conversations are based on.

Sources: the national curriculum programmes of study, and the published specifications for AQA 8300, Pearson Edexcel 1MA1 and OCR J560.

The course, area by area

What GCSE maths covers, and what is new in Year 10

The assessed areas. Which of these your child meets in Year 10 rather than Year 9 or Year 11 depends on the school's scheme.

Number

One of the largest areas at foundation and one of the smallest at higher, which is why the same topic can feel very different depending on the tier.

  • Fractions, decimals and percentages used interchangeably, including as multipliers
  • Percentage change, reverse percentages, simple and compound interest, growth and decay
  • Indices and roots, including negative and fractional indices at higher tier
  • Standard form, in calculations as well as in notation
  • Rounding, estimation, and error intervals; upper and lower bounds at higher tier
  • Exact calculations with π on both tiers; surds at higher tier
Example

A price rises 20% and then falls 20%. Is it back where it started?

No — 1.2 × 0.8 = 0.96, so it is 4% lower. Multipliers make that obvious; adding and subtracting percentages hides it.

Where it usually goes wrong Reverse percentages. "A coat costs £68 after 15% off, what was the original price?" is not £68 plus 15%. It is £68 ÷ 0.85, and it appears on every paper.

Algebra

Around a fifth of the marks at foundation and closer to a third at higher, and the area that most often decides a grade.

  • Expanding and factorising, including quadratics
  • Solving linear, simultaneous and quadratic equations; the quadratic formula and completing the square at higher tier
  • Rearranging formulae; inequalities and their graphs
  • Straight-line graphs, gradients and intercepts; quadratic, cubic and reciprocal graphs
  • Sequences, including nth term and quadratic sequences at higher tier
  • Functions, iteration and algebraic proof at higher tier
Example

x² + 7x + 12 = 0

Two numbers that add to 7 and multiply to 12: 3 and 4. So (x + 3)(x + 4) = 0, and x = −3 or −4.

Where it usually goes wrong Factorising practised only where it works neatly. When the coefficient of x² is not 1, students who learned a pattern rather than a method stop.

Ratio, proportion and rates of change

Worth roughly a quarter of the marks at foundation. Underrated, and often where a foundation-tier grade is made up.

  • Ratio in all its forms, including combining ratios and ratio as a fraction
  • Direct and inverse proportion, algebraically and graphically
  • Compound measures: speed, density, pressure, rates of pay
  • Growth and decay problems, including compound interest
  • Similar shapes, and area and volume scale factors at higher tier
  • Gradient as a rate of change, and the area under a graph at higher tier
Example

Two ratios: A:B = 2:3 and B:C = 4:5. Find A:C.

Match the Bs: A:B = 8:12 and B:C = 12:15, so A:C = 8:15. Combining ratios is a standard question and a standard blank space.

Where it usually goes wrong Compound measures with mismatched units. A speed in km/h and a time in minutes is the trap, and it is deliberate.

Geometry and measures

Angle reasoning becomes proof, and higher tier adds trigonometry beyond right-angled triangles.

  • Angle rules stated as reasons; interior and exterior angles of polygons
  • Pythagoras' theorem and right-angled trigonometry in two and three dimensions
  • Area and volume of prisms, cylinders, cones, spheres and frustums
  • Transformations, including enlargement with fractional scale factors, and negative scale factors at higher tier
  • Constructions and loci
  • Vectors on both tiers; circle theorems, the sine and cosine rules and vector proof at higher tier
Example

Give a reason: angles in the same segment are equal.

Circle theorem questions award marks for naming the theorem, not just for the number.

Where it usually goes wrong Answers with no reasoning. In geometry the mark scheme frequently wants the rule written down, and students who "just see it" lose those marks.

Probability and statistics

Among the smallest areas at both tiers, and the one most often left until last — which is a mistake, because the marks are gettable.

  • Probability of independent and dependent combined events, with tree diagrams, on both tiers; conditional probability notation at higher tier
  • Venn diagrams and set notation
  • Relative frequency and expected outcomes
  • Averages from frequency tables, including grouped data and estimated means
  • Scatter graphs, correlation and lines of best fit
  • Cumulative frequency, box plots and histograms at higher tier
Example

Two counters drawn without replacement from a bag.

The second branch of the tree changes — both the numerator and the denominator. Foundation students meet this too; higher tier adds the notation for it.

Where it usually goes wrong Histograms. They look like bar charts and are not: the frequency is the area, not the height. It is a reliable higher-tier mark for anyone who learns that one line.

Content as set out in the key stage 4 programme of study and the exam boards' published GCSE mathematics specifications. Topic weightings quoted here are Pearson Edexcel's published approximate ranges for 1MA1; AQA publishes assessment-objective weightings only, and OCR publishes its content weightings separately in its question-paper guidance.

The exam

How the GCSE maths papers work

Three papers, all sat in the same series, all at the same tier. The detail differs slightly by board, and the board is the school's choice, not yours.

AQA (8300)Pearson Edexcel (1MA1)OCR (J560)
Papers3, each 1 hour 30 minutes3, each 1 hour 30 minutes3, each 1 hour 30 minutes
Marks80 per paper, 240 total80 per paper, 240 total100 per paper, 300 total
Non-calculatorPaper 1Paper 1Paper 2 (foundation) or Paper 5 (higher)
TiersFoundation 1–5; higher 4–9, with an allowed grade 3Foundation 1–5; higher 4–9, with an allowed grade 3Foundation 1–5; higher 4–9, with an allowed grade 3
FormulaeA formulae sheet is provided in every paperA formulae sheet is provided in every paperA formulae sheet is provided in every paper
WhenMain series in May and June, results in AugustSameSame

Paper structure from each board's published specification. All three boards use the term "allowed grade 3" for a higher-tier candidate who falls just below the grade 4 boundary. Ofqual has confirmed that formulae sheets continue to be provided for the remaining lifetime of the current specifications. There is also a November series, restricted to candidates who were at least 16 on the preceding 31 August — in practice a resit route rather than a Year 10 or Year 11 first entry.

Tiers

Foundation or higher: how the tier decision is made

Foundation tier awards grades 1 to 5. Higher tier awards 4 to 9, with an allowed grade 3 for a candidate who falls just below the grade 4 boundary. All three papers must be at the same tier.

The decision is the school's, usually made in Year 11 from its own assessments, and it can change. Year 10 mocks feed into it but rarely settle it.

The trade-off is real and worth understanding. Foundation covers less content and the questions are more accessible, but the ceiling is grade 5. Higher additionally opens grades 6 to 9 and includes harder material — surds, circle theorems, algebraic proof — that a student who is not secure will spend time on and gain nothing from. A confident grade 5 at foundation is a better outcome than a grade 3 at higher.

Grade 4 is the threshold that removes the requirement to keep studying maths after 16, and the Department for Education's grading factsheets call it a standard pass. Grade 5, which the same factsheets call a strong pass, is the threshold used in the headline school performance measure — which is why it gets talked about more than its practical effect deserves.

What actually keeps both routes open is not a decision in Year 10. It is fluency with fractions, ratio and algebraic manipulation, which every question on either tier assumes.

Where students fall behind

The Year 10 maths difficulties we see most

Four, and the first is the reason most of the others go unnoticed until the mock.

Treating Year 10 as a year off

The exams are more than a year away, and no external result depends on this year. Both facts are true, and together they are how a student arrives in Year 11 with two terms of content they never learned.

Try this at home

Ask what the current topic is, then ask what last half-term's was and whether they could still do it.

The second question is the useful one. GCSE maths is cumulative and nothing gets retaught from scratch.

Where it usually goes wrong Content met and understood in Year 10 costs nothing to revise in Year 11. Content never understood has to be taught from scratch while everything else is being revised, and that is what makes Year 11 feel short.

Algebra that was never secure

Expanding, factorising and rearranging come from Year 9. Year 10 assumes them and immediately builds quadratics, simultaneous equations and rearranged formulae on top.

Try this at home

Ask them to expand (2x + 3)(x − 5) and to make r the subject of A = πr².

2x² − 7x − 15, and r = √(A ÷ π). Hesitation on either is worth more attention than this week's topic.

Where it usually goes wrong Algebra is around a fifth of the marks at foundation and closer to a third at higher, and it is inside geometry and ratio questions too. It is the gap we look for first.

Method marks left on the table

A multi-mark question is designed to be part-credited. A single line with a final answer in it is either fully right or worth nothing, and Year 10 is where that habit sets.

Try this at home

Open a marked mock at a question worth three or four marks and ask how the working earned them.

If your child cannot say, the working is being written for you rather than for the examiner — which is a different thing to fix.

Where it usually goes wrong This is a habit rather than a maths problem. Fixed in Year 10 it costs a few weeks of insistence; left alone it is still costing marks in the exam.

The non-calculator paper

One paper in three is non-calculator. Students who have been using a calculator since Year 7 are often much weaker there than their overall grade suggests.

Try this at home

Ask for 0.4 × 0.3, ¾ ÷ ½, and 15% of 240, with no calculator.

0.12, 1½ and 36. Slowness here puts one paper in three at risk.

Where it usually goes wrong Easy to spot in a mock breakdown: compare the non-calculator paper mark with the other two. A clear gap is a specific, fixable problem rather than a general weakness in maths.

At home

How to help in Year 10

Most of this is about noticing early. Year 10 is the year with room to act.

How we help

How ClassArc supports a Year 10 student

Weekly one-to-one classes on your child's own specification and tier, with the same teacher throughout.

Your child's board, not a generic one

AQA, Edexcel or OCR, foundation or higher, taught alongside the school's own scheme of work rather than as a parallel course.

The algebra checked first

Expanding, factorising and rearranging get tested in the first classes. Almost everything in Year 10 is built on them, and a gap there is why new topics will not stick.

Working written down, every time

Part marks can only be earned on paper. In class nothing is answered in one line, until writing the method is what your child does without being asked.

The non-calculator paper taught deliberately

One paper in three, and the one most easily left to look after itself. It gets its own time in the plan.

Honest about tiers

The tier is the school's decision, and we would not second-guess it. What we add is a clear termly account of what your child can and cannot yet do.

Straight through to the exams

The same teacher can carry on into Year 11, so revision starts from a known picture rather than a fresh assessment.

Inside a class

What a Year 10 ClassArc class looks like

Fifty-five minutes, one teacher, one student, built around the school's current unit.

“

Nothing in Year 11 is taught for the first time twice. Whatever Year 10 skips, Year 11 pays for.

Why the first GCSE year matters most
i
🔍

This week, and last term

The current topic, plus a short check on something from earlier in the year. Retention is the thing Year 10 has to build.

ii
✏️

Taught, then written

The method built on the shared worksheet, with every step written the way a mark scheme expects to see it.

iii
🧩

Exam-style questions

Board-specific questions at the right tier, including the multi-step ones where the marks actually sit.

iv
📌

Set the next step

What held, what did not, and homework aimed at the second — marked before the next class.

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Next

Where to go from here

The year before, the year after, and the qualification itself.

Year 9 maths

The end of key stage 3, three-year GCSE courses, and the algebra Year 10 assumes is already there.

The year before

Year 11 maths

Mocks, past papers, what is on the formulae sheet, results day, and what happens if a resit is needed.

The exam year

GCSE maths tutor

How we teach GCSE across the three boards and both tiers, including past papers and exam technique.

GCSE tutoring

Year 10 maths questions

What topics are covered in Year 10 maths?
The GCSE course: number, algebra, ratio, proportion and rates of change, geometry and measures, and probability and statistics. Which of them fall in Year 10 rather than Year 9 or Year 11 depends on the school's scheme, but Year 10 typically brings quadratics, simultaneous equations, trigonometry, compound percentages and the harder geometry and data work.
How is GCSE maths examined?
By three written papers taken at the end of Year 11, one of which is sat without a calculator. Every paper runs for an hour and a half, and all three must be at the same tier and in the same series. The marks and the non-calculator paper number vary by board — the table above sets out AQA, Edexcel and OCR side by side.
What is the difference between foundation and higher tier?
The grade range and the content. Foundation goes up to grade 5 with more accessible questions; higher reaches grade 9 and adds material such as surds, circle theorems and algebraic proof. A higher-tier candidate who falls just below grade 4 can be given an allowed grade 3. The school decides the tier, and all three papers must match it.
When is the tier decided?
Usually in Year 11, from the school's own assessments, and it can change before entries are made. Year 10 mocks contribute to the picture but rarely settle it. What keeps both routes open is secure fractions, ratio and algebra rather than anything decided this year.
Is a formulae sheet given in the GCSE maths exam?
Yes. A formulae sheet is provided in every GCSE maths paper, and Ofqual has confirmed this continues for the remaining lifetime of the current specifications. It does not remove the need to know which formula to use or how to apply it — boards are required not to set questions that can be answered simply by copying from the sheet.
Does Year 10 have exams?
Almost never external ones — a small minority of schools enter some students early, but for most the first GCSE paper is sat in Year 11. Schools run their own mocks and assessments during the year, which is normal and useful. Those results usually feed into set changes and eventually into the tier decision, so it is worth asking for the breakdown by paper and topic rather than just the grade.
My child's Year 10 mock grade was low. Should I worry?
Not on the grade alone. A Year 10 mock is taken part-way through the course, so it covers content that has not all been taught and revision that has not happened. What is worth looking at is the pattern: which paper, which topics, and whether marks were lost through method or through not knowing the maths.
Should we start revision in Year 10?
Not in the buy-a-revision-guide sense. The content is still being taught, and understanding it as it arrives is worth more than skimming everything early. What does help all year is retention — going back over earlier topics regularly so they are still there in Year 11.
How can a tutor help in Year 10?
By teaching to the school's own board, tier and scheme rather than a parallel course; by finding and fixing the key stage 3 algebra that GCSE assumes; by building the habit of written method, which is worth marks on every paper; and by giving the non-calculator paper the attention it rarely gets.
What does ClassArc cost for a Year 10 student?
Year 10 sits in our Years 9–11 band, from £14 per 55-minute one-to-one class on the largest plan, including past-paper work and exam technique. The first class is free and no card is needed. Full details are on the UK pricing page.
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