AMC 10 Practice Test Papers With Full Solutions

There is a specific kind of AMC 10 student who is being failed by their own preparation: the one who understands every solution when they read it, and still scores 90. They do not have a mathematics problem. They have a decision problem - which questions to attempt, which to abandon, and when to stop. An AMC 10 practice test is where those decisions get trained, and it is the part of preparation most students skip entirely.

This guide covers the scoring arithmetic that decides who qualifies for the AIME, how to run a paper so it produces evidence rather than a number, and where our 15-paper series fits. Three papers are free.

The scoring is the strategy

The AMC 10 is 25 questions in 75 minutes. A correct answer scores 6, a wrong answer scores 0, and a blank scores 1.5. That blank is the single most misunderstood rule in the competition, and it changes everything about how the paper should be attempted.

Because a blank pays 1.5, a random guess must beat 1.5 to be worth making. On a five-option question a blind guess pays 6 x 0.2 = 1.2 marks on average, which is less than the 1.5 you already had. Guessing blind on the AMC 10 loses marks. That is the opposite of the AMC 8, and students who carry AMC 8 habits upward bleed points.

The arithmetic of elimination is worth memorising:

• Guess from 5 options: 1.2 expected - worse than leaving it blank
• Eliminate 1, guess from 4: 1.5 expected - exactly break-even
• Eliminate 2, guess from 3: 2.0 expected - worth guessing
• Eliminate 3, guess from 2: 3.0 expected - clearly worth guessing

So the rule is: guess only when you can eliminate at least two options. Otherwise leave it blank and bank the 1.5. Most students have never done this calculation, and it is worth several marks on its own.

What the AIME cutoff means for your target

The AIME qualification threshold for the AMC 10 is a fixed 100 points rather than a moving percentile. That is a target you can plan against directly, and the plan is less demanding than it looks.

Consider 14 correct, 11 blank, 0 wrong: that is 14 x 6 + 11 x 1.5 = 84 + 16.5 = 100.5, which qualifies. You do not need to solve the hard half of the paper. You need to solve the first fourteen or so questions with near-perfect accuracy and then have the discipline to stop.

This reframes preparation completely. The student who chases problems 21 to 25 while making two careless errors in the first ten is working on the wrong thing. Accuracy on the front half is worth far more than reach into the back half.

Why timed papers, and not more problem sets

Everything above is a decision under time pressure, and decisions cannot be rehearsed on an untimed problem set. When there is no clock, you never have to decide whether question 17 is worth four more minutes - you just keep going. The clock is what makes the practice real.

A timed paper also exposes something a problem set hides: where your accuracy breaks down. Most students are near-perfect on the first eight questions when relaxed, and make one or two errors there when hurried. Those errors cost 6 marks each and are entirely avoidable. You cannot find them without a clock.

How to run a paper properly

Sit it in one 75-minute block. No pausing, no lookups. Mark every answer you were unsure of with a dot as you go.

Before marking, do a second pass on paper. Note which questions you attempted, which you left, and roughly how long the hard ones took. This record is more valuable than the score.

Score it two ways. First your actual score. Then recompute what you would have scored if you had left every dotted question blank instead of answering it. If the second number is higher, your guessing threshold is set too low and that is your single biggest fix.

Redo every miss untimed before reading the solution. A question you solve in five quiet minutes was a pacing failure. A question you still cannot solve is a knowledge gap. These need completely different responses, and lumping them together is why students plateau.

What the series contains

Fifteen papers, 425 questions, sat online with instant marking and a full worked solution on every question. The structure mirrors how preparation should actually run.

Ten topic-wise papers across number theory, algebra, geometry, counting and probability, and permutations and combinatorics - two papers each. These are for the build phase, when you want repeated exposure to one family of methods until they are automatic.

Five full mock papers at 25 questions in 75 minutes, matching the real paper exactly in length, timing and difficulty curve. These are for the last stretch, when the thing being trained is judgement rather than technique.

An eight-week schedule

Weeks 1-2. Sit one full mock cold, before revising. Then the two algebra and two number theory papers. Build the error log.

Weeks 3-5. Geometry and counting, all four papers, plus permutations. These topics carry the most marks in questions 8 to 18, which is exactly the band that decides whether you clear 100.

Weeks 6-7. Full mocks, one per week, strictly timed. After each, run the two-way scoring check above.

Week 8. One final mock, then stop. Re-read your error log rather than learning anything new. The last week should lower your error rate, not raise your ceiling.

Free papers to start with

Three papers in the series are free for everyone, with no card and no trial - one number theory, one algebra, and a complete full mock.

• Full Mock - Paper 1, free, 25 questions in 75 minutes
• Algebra - Paper 1, free, topic-wise
• Number Theory - Paper 1, free, topic-wise
• The full 15-paper series - 425 questions with solutions

Sit the full mock cold, apply the blank-versus-guess rule from the start, and see what it does to your score. Most students gain marks from that rule alone on their first attempt.

When you need more than papers

Papers show you what is wrong. They do not always show you why. If your log keeps saying "could not find the setup" on geometry, more papers will keep producing that same line - you need someone to show you the two or three configurations that recur, and then papers become useful again.

Our AMC 10 preparation course runs live small-group sessions two to three times a week and uses these papers as the between-class work, so lessons target what each student's log actually shows. If you are working alone, the series is still complete on its own, and the free mock is the right place to begin.

In short

The blank is worth 1.5 and a blind guess is worth 1.2, so guessing without eliminating two options is a losing move. The AIME threshold of 100 is reachable with fourteen correct answers and the discipline to leave the rest. An AMC 10 practice test, sat under a real clock and reviewed honestly, is what turns that arithmetic into a score.