AMC Admissions Open: AMC 8, 10 and 12 Eligibility Guide

AMC admissions are open for our AMC 8, AMC 10 and AMC 12 programmes. This page explains which contest your child is eligible for, what each one actually tests, when to start preparing, and how our teaching works — so you can decide before you commit to anything.

Which AMC is my child eligible for?

The American Mathematics Competitions run three levels, and eligibility is decided by grade and age, not by ability. A strong Class 7 student cannot sit the AMC 10 early, and a Class 11 student cannot drop down to the AMC 10 because it is easier. Getting this wrong is the most common mistake parents make, so it is worth being precise.

Contest	Eligibility	Format	Marking
AMC 8	Grade 8 or below, under 14.5 on contest day	25 questions, 40 minutes	1 mark per correct answer, no penalty
AMC 10	Grade 10 or below, under 17.5 on contest day	25 questions, 75 minutes	6 correct, 1.5 for blank, 0 for wrong
AMC 12	Grade 12 or below, under 19.5 on contest day	25 questions, 75 minutes	6 correct, 1.5 for blank, 0 for wrong

A student in Class 9 or 10 is eligible for the AMC 10. A student in Class 11 or 12 must take the AMC 12. Both the AMC 10 and AMC 12 run in two versions, A and B, on separate dates, and a student may attempt both — the better score is the one that counts towards qualification.

The marking scheme is the part most students misunderstand

On the AMC 10 and 12, a blank is worth $1.5$ marks and a wrong answer is worth nothing. That single rule changes how the paper should be attempted. If a student can eliminate no options at all, guessing has an expected value of

$$E_{\text{guess}} = \frac{1}{5} \times 6 + \frac{4}{5} \times 0 = 1.2$$

which is less than the $1.5$ marks a blank guarantees. Guessing blind loses marks. But eliminate just one option and the arithmetic flips:

$$E_{\text{guess}} = \frac{1}{4} \times 6 = 1.5$$

Break the tie with a second elimination and guessing becomes clearly correct at $2.0$ marks. We teach this explicitly, because a student who leaves eight questions blank rather than guessing badly on them will often outscore a stronger mathematician who guessed on all of them.

What each contest actually tests

All three draw on the same four areas — algebra, geometry, number theory and counting — but the demand changes sharply between levels.

AMC 8

Arithmetic, ratio and proportion, basic geometry, simple counting and elementary number theory. No trigonometry, no logarithms, no calculus. The difficulty is not in the content but in the phrasing: a question that a student could answer in a school test becomes hard when it is asked sideways. Roughly the first fifteen questions are approachable for a well-prepared student; the last ten separate the field.

AMC 10

Everything in the AMC 8 plus quadratics, coordinate geometry, similar triangles, the power of a point, modular arithmetic and systematic counting. Trigonometry and logarithms are outside the syllabus, which is the formal difference from the AMC 12.

AMC 12

Adds trigonometry, logarithms, complex numbers, sequences and series, and more demanding polynomial work. A question might ask for the sum of the roots of a polynomial, where recognising that $\sum r_i = -\frac{a_{n-1}}{a_n}$ turns a page of algebra into one line. That habit — finding the structure rather than grinding the computation — is what the AMC 12 rewards and what we spend most of our teaching time on.

What a good score looks like

Both the AMC 10 and AMC 12 are qualifying routes to the American Invitational Mathematics Examination. The cutoff is set as a percentile of that year's cohort, not as a fixed number, so it moves annually and nobody can promise you a target in advance. In broad terms the AMC 10 has historically required roughly the top 2.5% and the AMC 12 the top 5%, but treat those as context rather than as a line to aim at.

The practical consequence for a parent is simple. A student needs to be solving the first fifteen questions reliably and quickly, so that there is time left for the harder ten. Almost nobody qualifies by being brilliant at question 24; they qualify by never losing a mark on questions 1 to 15.

When should we start?

Nine to twelve months before the contest is the honest answer for a student starting from a standard school syllabus. That is not a sales figure — it is how long it takes to build the two things the AMC actually measures.

• Recognition. Seeing that a problem is really about the pigeonhole principle, or similar triangles, or a clever substitution. This only comes from working through a few hundred problems, and it cannot be rushed.
• Speed under pressure. Seventy-five minutes for twenty-five questions is three minutes each. A student who knows the mathematics but has never worked against a clock will run out of time, and that is a training problem, not a mathematics problem.

Starting three months out is still worthwhile. Starting three weeks out is not, and we will tell you so rather than take the fee. That is the main reason we keep AMC admissions open well ahead of the contest window rather than filling seats in the final weeks.

How our programme works

Small live classes, taught by people who have coached students to AIME qualification, not recorded video. Every session is built around problems rather than lectures, because problem-solving is not a spectator activity.

• Diagnosis first. A timed paper before teaching starts, so we know whether the gap is in algebra, geometry, counting or simply in pace.
• Topic teaching against real problems. Each concept is introduced through past AMC questions, so a student sees immediately how it is examined.
• Timed mock papers under contest conditions, with a full worked solution to every question afterwards.
• Strategy. Which questions to attempt, when to skip, when to guess and when to leave blank — the marking-scheme arithmetic above, trained until it is automatic.

Try it before you enrol

While AMC admissions are open, book a trial class. You will see how we teach, and we will tell you honestly which contest your child should be entered for and whether this year or next is the sensible target. Parents can submit the form without paying anything.

You can also work through our free timed mock papers with instant scoring and full solutions, or read the complete AMC 8 syllabus breakdown and our AMC 10 and 12 preparation guide first. There is no obligation to any of it.