16 Plus Entrance Exam Maths | Sixth Form Entry Explained

What is a 16 plus entrance exam?

It is a test some sixth forms use to admit students into Year 12 at age 16. Independent schools set their own 16 plus papers, often in maths among other subjects, and since private schools do not have to follow the national curriculum, each school decides its own content and timing. State school sixth forms work under the School Admissions Code 2021, which lets them select by ability and set academic entry criteria, provided those criteria are the same for their own students and for applicants from outside. In practice that usually means GCSE grades: the DfE calls grade 4 a standard pass and aligns the bottom of grade 7 with the old grade A. Modern Age Coders teaches GCSE Higher maths live online for both routes.

Where to begin

Three courses for 16 plus and sixth form entry

Nearly every 16+ maths requirement rests on GCSE Higher. Choose by where your student is now. Each card opens the syllabus.

16P / 01

GCSE maths, Foundation and Higher

Our main course for Years 10 and 11, covering AQA, Edexcel and OCR, with Higher algebra and problem solving at its core.

Open the syllabus →

16P / 02

IGCSE maths

For students at schools that teach IGCSE, whose 16+ papers may lean on Extended content.

Open the syllabus →

16P / 03

A level maths

For students who want a head start on the pure maths they will meet in Year 12.

Open the syllabus →

Two routes

How do sixth forms decide who gets a Year 12 place?

State sixth forms decide on published admission arrangements, often with GCSE grade requirements. Independent schools decide on their own tests, interviews and references. The table sets the two side by side.

Two ways into Year 12 (state rules from the School Admissions Code 2021; independent practice in general terms)
	State school sixth form, including grammar schools	Independent school sixth form
Rules that apply	The School Admissions Code 2021	The school's own admissions policy
Can it select by ability?	Yes: school sixth forms are one of three kinds of school the Code permits to select	Yes, as the school chooses
Typical entry test	Academic entry criteria, usually GCSE grades in chosen subjects	The school's own 16+ papers, often with an interview
Same rules for insiders?	Required: criteria "must be the same for both external and internal places"	Set by the school
Interviews	A meeting about courses is allowed but "cannot form part of the decision making process"	Often part of the decision
When decided	Confirmed once GCSE results are known	Often before GCSEs, from papers sat in Year 11

The Admissions Code's rule on selection is short. Footnote 20 says there is "a general restriction on selection by ability" and names only three exceptions: "designated grammar schools; schools with partially selective arrangements which already had such arrangements in place during the 1997/98 school year; and school sixth forms." So any state school sixth form may, in principle, set academic requirements, not only grammar schools. GOV.UK's own description of grammar schools adds that they "select their pupils based on academic ability and there is a test to get in", which for Year 12 entry may mean a sixth form test as well as grades; each school publishes its own arrangements.

Sources: Department for Education, School Admissions Code 2021; GOV.UK, grammar schools; GOV.UK, the national curriculum; all read 31 October 2026. Modern Age Coders is not connected with any school or sixth form.

State sixth forms

What GCSE maths grade do sixth forms ask for?

Each sixth form sets its own, course by course, and publishes it. The DfE's grading guidance explains what the numbers mean, and the Admissions Code sets the rules around them.

GCSE 9 to 1 grades, as the DfE factsheet for parents explains them (May 2019)
Grade	What the DfE says
9	"Grade 9 is the highest grade and will be awarded to fewer students than the old A*."
7	"The bottom of grade 7 is aligned with the bottom of grade A"
4	"The bottom of grade 4 is aligned with the bottom of grade C"; the DfE "recognises grade 4 and above as a 'standard pass'"
Below 4 in maths	Grade 4 is the minimum in English and maths; below it, students "need to continue to study these subjects as part of their post-16 education"
Entry requirements	"Employers, universities and colleges will continue to set the GCSE grades they require for entry to employment or further study."

Because each sixth form chooses its own requirements, we do not print a "typical" grade for A level maths here; families should read the sixth form's prospectus for the year of entry. What the Admissions Code does guarantee is fairness in how those requirements are applied. Paragraph 2.6 says sixth form criteria "must be the same for both external and internal places", that arrangements for external applicants "must be consulted upon, determined, and published" on the same timetable as other entry points, and that looked after and previously looked after children who meet the academic criteria get the "highest priority" if a sixth form is oversubscribed.

The meeting is not an interview

The Code allows a sixth form to meet applicants "to discuss options and academic entry requirements for particular courses", but adds that "this meeting cannot form part of the decision making process on whether to offer a place."

For a state sixth form, the grades decide, not a conversation. That makes the GCSE result itself the thing to prepare for.

Where an entrance test fits

By our reading of the Code, if a state sixth form uses a test or a course-specific task, it belongs in the arrangements the school must consult on and publish, so families can see it in advance.

Read the arrangements for the exact year of entry: they are set a year ahead under the same timetable as Year 7.

Sources: DfE, GCSE new grading scale factsheets (parents, May 2019); School Admissions Code 2021, paragraphs 1.9 and 2.6. Read 31 October 2026.

16+ papers

What is on an independent school 16 plus maths paper?

Each school writes or commissions its own, so there is no common syllabus. What every paper sat in Year 11 shares is a ceiling: it can only test what a strong student has been taught before GCSE results.

Independent schools are free to design their own admissions. GOV.UK notes that private schools "do not have to follow the national curriculum", and test providers sell bespoke papers: Quest Admissions, for example, builds entrance tests "For ages 7+ to 16+" that are "Bespoke and branded to your school". By our own reasoning, a maths paper sat in the autumn or winter of Year 11 comes before the GCSE course is finished, so it sits inside GCSE Higher content taught by then. Schools often add an interview and a reference, and some ask for predicted grades.

GCSE Higher topics a 16+ maths paper commonly draws on (our summary; check each school's own guidance)
Area	Topics	Why it matters for a 16+ paper
Number	Indices including fractional, surds, standard form, recurring decimals	Short questions that show fluency without a calculator
Algebra	Factorising quadratics, the quadratic formula, simultaneous equations, rearranging, algebraic proof	The core of most harder questions and of A level maths
Functions and graphs	Gradients, perpendicular lines, transformations of graphs	Links algebra to pictures; common in multi-part questions
Geometry	Pythagoras and trigonometry, circle theorems, similarity	Tests reasoning and written justification
Probability and statistics	Tree diagrams, conditional probability, averages from tables	Careful reading under time pressure
Problem solving	Unfamiliar multi-step questions	Separates a strong grade 7 from a grade 9 mindset

What to ask each school

Which subjects are tested, how long the maths paper is, whether a calculator is allowed, whether there is an interview, and when the papers are sat.

Ask too whether the school expects A level maths applicants to sit a harder or separate paper; some do.

What we will not do

Reproduce any school's 16+ papers, or present our practice as a school's. We have not seen their papers.

Predict a result or promise a place. Each school decides, usually on more than one paper.

Worked examples, written by us

How should a student work a GCSE Higher style question?

Three original problems of the kind a 16+ maths paper or a top GCSE grade needs, each solved with full working. None is from a school paper or an exam board.

1. Factorise, then check

Solve x squared minus 5x minus 14 = 0. Find two numbers that multiply to minus 14 and add to minus 5: minus 7 and 2. So (x minus 7)(x + 2) = 0, giving x = 7 or x = minus 2. Check one root: 49 minus 35 minus 14 is 0. Students who only reach for the formula lose time; students who never check lose marks.

2. Growth, not addition

A town of 8,000 people grows by 5 per cent a year. What is its population after 3 years? The multiplier is 1.05, applied three times: 8,000 times 1.05 cubed. 1.05 squared is 1.1025, times 1.05 is 1.157625, so the answer is 9,261. Adding 15 per cent once gives 9,200, a wrong answer that many papers list on purpose.

3. A tidy proof

Prove that (n + 1) squared minus (n minus 1) squared is always a multiple of 4. Expand: n squared + 2n + 1 minus (n squared minus 2n + 1). The squares and the ones cancel, leaving 4n. Since n is a whole number, 4n is 4 times a whole number, so a multiple of 4. The last sentence is the proof; the algebra only sets it up.

A practice set written by Modern Age Coders at GCSE Higher level
Question (ours)	Answer	The reasoning
Simplify the square root of 72.	6 times the square root of 2	72 is 36 times 2, and the square root of 36 is 6. Look for the largest square factor.
Evaluate 8 to the power two thirds.	4	The cube root of 8 is 2, then square it. Root first keeps the numbers small.
A bag has 3 red and 2 blue counters. Two are taken without replacement. Probability both are red?	3 tenths	3 fifths times 2 quarters. The second fraction changes because one red has gone.
In a right-angled triangle the side opposite angle x is 7 cm and the hypotenuse is 14 cm. Find x.	30 degrees	Sine x is 7 over 14, a half, and sine 30 is a half. Spotting exact values saves a calculator step.
Find the nth term of 2, 6, 12, 20, ...	n squared + n	Second differences are 2, so start with n squared; what is left, 1, 2, 3, 4, is n.
A line has gradient 3. What is the gradient of a line perpendicular to it?	Minus one third	Perpendicular gradients multiply to minus 1.

Each answer here is worth one or two marks on its own, but on a 16+ paper they tend to arrive inside longer questions with no hints. In lessons we set them that way: the final demand only, so the student has to choose the tool, not just use it.

A plan

How should a Year 10 or Year 11 student prepare for sixth form entry maths?

Find out each sixth form's rules first, then secure GCSE Higher algebra early, then practise unfamiliar problems with full working. The steps below are our plan.

List each sixth form and write down its route: GCSE grade criteria (state) or its own 16+ papers (independent), with dates and any interview.
For state sixth forms, read the published arrangements for your year of entry, including the subject grades for A level maths if that is the plan.
For independent schools, ask what the maths paper covers, how long it is and whether calculators are allowed.
Secure GCSE Higher algebra in Year 10: factorising, the quadratic formula, simultaneous equations, rearranging and indices.
Add geometry and probability reasoning, writing every step, through the autumn of Year 11.
Practise unscaffolded questions weekly, then timed papers in the weeks before any 16+ sitting.

For the GCSE itself, our GCSE maths page covers the three boards and both tiers, and our IGCSE maths page covers international specifications. For students heading into Year 12 maths, the A level maths page shows what comes next.

Timeline

From Year 10 to a Year 12 place

Independent 16+ papers often fall in Year 11, and state sixth form places follow GCSE results. Our stages serve both.

Four stages before sixth form entry (our plan)
When	Stage	Secure when
Year 10, autumn	1. Number and algebra basics	Indices, surds, expanding and factorising done accurately without notes
Year 10, spring to summer	2. Higher algebra	Quadratics, simultaneous equations and rearranging solved in any context
Year 11, autumn	3. Reasoning and proof	Geometry and probability answers written as full chains of working
Before any 16+ paper	4. Unfamiliar problems	Timed questions with no hints finished with time to check

If time is short

Stage 2 matters most. Higher algebra underlies the hardest questions on any 16+ paper and on the GCSE.

After one lesson we tell you frankly what is realistic.

Into Year 12

The same algebra is the base of A level maths. Some students also explore maths through coding.

Strong students can try the senior challenges in our UK competitions calendar.

All related courses

Courses for 16 plus and sixth form entry

From GCSE through to Year 12. Each card opens its syllabus.

I

GCSE and IGCSE

Years 10 and 11

UK / PSF / 01

GCSE maths

Foundation and Higher for the three English boards.

Open the syllabus

UK / PSF / 02

IGCSE maths

Core, Extended and Additional Mathematics.

Open the syllabus

UK / PSF / 03

Algebra foundations

For students whose algebra needs rebuilding first.

Open the syllabus

II

Stretch

Aiming high

UK / PSF / 04

Competition maths

Unfamiliar problems and proof.

Open the syllabus

UK / PSF / 05

Statistics and probability

Data and chance, beyond the GCSE basics.

Open the syllabus

III

Year 12

Sixth form

UK / PSF / 06

A level maths

Pure, mechanics and statistics.

Open the syllabus

UK / PSF / 07

A level further maths

Core pure and applied options.

Open the syllabus

UK / PSF / 08

Maths through coding

Python to explore and check maths.

Open the syllabus

How lessons run

Live lessons for Year 10 and Year 11 students

Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays. Teaching happens from India, which never moves its clocks, so the difference from UK time is four and a half hours in summer and five and a half in winter. Your timetable is always written in UK time.

After school

The common slot for Years 10 and 11.

Weekend morning

Long enough for a timed paper.

Holidays

Extra sessions before a 16+ sitting.

Higher algebra first

The topic that unlocks the hardest questions.

Full working

Every answer set out as a marker would want it.

No-hint questions

Final demand only, the method chosen by the student.

Written by us

No school or board paper reproduced.

Class or private

A class of 15 to 20 at one level, or one-to-one lessons.

No promises

Places are decided by sixth forms, not tutors.

Student work

What our older students have built

Work by teenage students at our school. More on student labs.

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Fees

Fees for 16 plus entrance maths lessons

One monthly fee, shown in the currency used for UK families. The first lesson is free, with no joining charge.

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Group batch

USD 100

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A class of 15 to 20 at a similar level
The same teacher through Year 11
Timed, no-hint practice
Quieter weeks around mocks

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One to one

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One teacher, one student
Shaped around one school's paper
Good for a single stubborn topic

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16 plus questions

What families ask about 16 plus and sixth form entry maths

What is a 16 plus entrance exam?

It is a test a sixth form uses to admit students into Year 12. Independent schools usually set their own 16 plus papers, often with an interview; state sixth forms usually rely on GCSE grade criteria instead.

Can a state school sixth form select by ability?

Yes. The School Admissions Code 2021 allows school sixth forms, as well as grammar schools and some partially selective schools, to select by ability and to set academic entry criteria.

Do internal and external applicants face the same criteria?

At state school sixth forms, yes. The Admissions Code says academic entry criteria must be the same for both external and internal places.

Can a state sixth form interview me?

It can hold a meeting to discuss options and course requirements, but the Admissions Code says that meeting cannot form part of the decision on whether to offer a place.

What GCSE maths grade do I need for sixth form?

Each sixth form sets its own and publishes it, often course by course. The DfE calls grade 4 a standard pass and aligns the bottom of grade 7 with the old grade A, so check the prospectus for the exact requirement.

What maths is on an independent 16 plus paper?

Each school decides. Because papers are often sat in Year 11, they draw on GCSE Higher content taught by then, such as algebra, quadratics, geometry and probability. Ask the school for its own guidance.

Are there 16 plus past papers?

Some schools publish samples on their own sites; others do not. We do not copy any school's papers, and our lessons use questions we write at GCSE Higher level.

What happens if I do not get grade 4 in maths?

The DfE says students who do not reach grade 4 in maths need to continue studying it as part of their post-16 education. Sixth forms set their own rules about which courses are then open.

When are lessons?

Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays. Every time is set in UK time.

Can you guarantee a sixth form place?

No. Sixth forms decide places on their own published criteria or tests. We teach the maths and the habits that strong results need.

Related pages

More on GCSE and sixth form maths

What comes before and after Year 12 entry.

GCSE maths tuition

Foundation and Higher, all three English boards.

IGCSE maths tuition

International specifications many independent schools teach.

A level maths tuition

The course most 16+ maths applicants are heading for.

Common Entrance maths

The earlier independent-school entry points, at 11 and 13.

UK competitions calendar

Senior maths challenges for able students.

Coding classes in the UK

All our UK pages in one place.

Related pages in this guide

Part of the guide: UK selective school maths tests: 7+, 11+, 13+ and 16+

Tests by provider and entry point

11+ by area

Northern Ireland transfer test

More guides: UK maths exam boards and specification codes · UK maths year by year, Reception to Year 11 · UK university admissions: maths tests and computing applications · UK maths enrichment, competitions and able pupils

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Tell us the student's year, current maths level and the sixth forms on the list. We check each one's route, teach a real lesson and tell you frankly where things stand.

Want to read first? The GCSE maths course lists every topic, and how we teach explains our approach with teenagers.

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Three courses for 16 plus and sixth form entry

GCSE maths, Foundation and Higher

IGCSE maths

A level maths

How do sixth forms decide who gets a Year 12 place?

What GCSE maths grade do sixth forms ask for?

The meeting is not an interview

Where an entrance test fits

What is on an independent school 16 plus maths paper?

What to ask each school

What we will not do

How should a student work a GCSE Higher style question?

1. Factorise, then check

2. Growth, not addition

3. A tidy proof

How should a Year 10 or Year 11 student prepare for sixth form entry maths?

From Year 10 to a Year 12 place

If time is short

Into Year 12

Courses for 16 plus and sixth form entry

GCSE and IGCSE

GCSE maths

IGCSE maths

Algebra foundations

Stretch

Competition maths

Statistics and probability

Year 12

A level maths

A level further maths

Maths through coding

Live lessons for Year 10 and Year 11 students

Higher algebra first

Full working

No-hint questions

Written by us

Class or private

No promises

What our older students have built

NutriLife

Misti

GuardianX

SkyCast

Fees for 16 plus entrance maths lessons

Rated 4.9 across 547 Google reviews

What families ask about 16 plus and sixth form entry maths

What is a 16 plus entrance exam?

Can a state school sixth form select by ability?

Do internal and external applicants face the same criteria?

Can a state sixth form interview me?

What GCSE maths grade do I need for sixth form?

What maths is on an independent 16 plus paper?

Are there 16 plus past papers?

What happens if I do not get grade 4 in maths?

When are lessons?

Can you guarantee a sixth form place?

More on GCSE and sixth form maths

GCSE maths tuition

IGCSE maths tuition

A level maths tuition

Common Entrance maths

UK competitions calendar

Coding classes in the UK

Related pages in this guide

Tests by provider and entry point

11+ by area

Northern Ireland transfer test

Book a free maths lesson

Want a class sooner? Book a priority demo

Keep exploring Modern Age Coders

More maths tuition

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