Prepare for the AMC 8 in a few focused months

Most students who do well on the AMC 8 didn't cram. They did a little real problem solving most weeks for a few months, they got honest about which mistakes were costing them points, and they took at least a couple of full tests under timed conditions before the real one. That's the whole secret, and the rest of this guide is the detail: what to do, in what order, depending on where you start.

A quick note on what the contest is. The AMC 8 is run by the Mathematical Association of America (MAA). It's 25 multiple-choice questions in 40 minutes, it's open to students in grade 8 and below who are under 15.5 on contest day, and it's given once a year, typically in late January. Students usually register through their school or another registered host, so check with your math teacher or the competition manager early. Calculators aren't allowed. For the scoring details, see our guide to AMC 8 scoring and awards.

Start by finding out where you actually are

Before you make a plan, get a baseline. Sit down for one full 25-question test in 40 minutes, with no calculator, no phone and no pausing. Use a released AMC 8 from a past year, or a full-length mock like our free timed mock AMC 8. Score it honestly, then do something most students skip: give yourself another 40 minutes to work the problems you missed or guessed on, untimed, and see how many you can solve.

Those two numbers tell you different things. The first is your current score. The second is roughly your ceiling with the math you already know. A student who scores 9 timed and 17 untimed has a speed and nerves problem. A student who scores 9 timed and 11 untimed has a content problem. The plans are different, and mixing them up wastes months.

The plan, by months out

Four to six months out: build the foundation

This is the time for content, not for tests. Work through the four main areas of the contest: number theory, counting and probability, geometry, and algebra with logic. We break those down in our guide to AMC 8 topics. For each area, learn the core tools and then do 8 to 10 problems on that one idea in a row, so the idea sticks.

• Number theory: factors and multiples, primes, divisibility rules, remainders, GCD and LCM.
• Counting and probability: the multiplication principle, simple arrangements and selections, careful casework, and probability as favorable over total.
• Geometry: area and perimeter, the Pythagorean theorem, similar triangles, angle chasing, and basic circles.
• Algebra and logic: linear equations, ratios and rates, averages, word problems, and reasoning through constraints.

Aim for three or four sessions a week of 30 to 45 minutes. That's enough. A student who does 40 focused minutes four times a week beats one who does a four-hour Sunday marathon, because the brain needs sleep between sessions to hold on to new methods.

Two to three months out: start mixing and timing

Now stop sorting problems by topic. The real test puts a counting problem next to a geometry problem, and part of the skill is recognizing what you're looking at. Use mixed sets of 10 to 12 problems with a loose timer, about 20 minutes. Past AMC 8 problems are ideal for this because they show you the actual style: the wording, the way answer choices are built, and what an "easy" problem 7 looks like compared with a hard one.

Add one full-length timed test every two weeks. Not more. A full test is only useful if you review it properly, and a real review takes longer than the test itself.

The last month: simulate and polish

Take two or three full tests under real conditions: a quiet room, 40 minutes, no calculator, answer sheet filled in. Practice the end-of-test routine too, which means leaving a minute to bubble in a guess on anything blank. Spend the days in between on your weakest area and on the small mistakes you keep repeating. Pacing gets its own treatment in our test-day strategy guide.

The final week

Don't learn new topics. Review your error log, redo a few problems you missed earlier, sleep well and take one light timed set early in the week. The last two days should feel boring.

The plan, by current score

Months out matters, but so does where you start. These are rough bands, not promises. Scores on a single practice test bounce around by a few points, so use the average of two or three tests when you can.

Scoring under 8: fix fundamentals first

At this level the first ten problems aren't reliable yet. That's the best place to put your effort, because those problems are the most winnable. Spend your first weeks making sure fractions, percents, ratios, order of operations, area and perimeter and basic divisibility are automatic. If school math feels easy but the AMC 8 doesn't, the gap is usually problem-solving habits: reading carefully, drawing a picture, and trying small cases. Work only problems 1 to 12 from past tests until you miss two or fewer on them, then move up.

Scoring 8 to 14: tighten the middle

This is where many serious students sit after a first test. You usually get the early problems and miss some of the middle ones to careless errors and a few to missing techniques. Your biggest gain comes from two places. One is accuracy on problems 1 to 15, where every point should be nearly guaranteed. The other is learning the standard counting and number theory tools, because those show up in the middle of every test and are teachable. A student here who stops missing early problems and adds four or five middle problems moves well past the 14 mark.

Scoring 15 to 20: learn the second layer

You have the basics. What's missing now is usually the harder half of the test, problems 16 to 25. Practice multi-step geometry (similar triangles, areas by subtraction, 3D shapes), tougher casework in counting, and algebra that needs a clever substitution rather than brute force. Also start timing individual problems. If a problem has taken you four minutes without progress, cutting your losses is a skill you need.

Scoring 21 or higher: chase the last few points

At this level you're usually missing two to four problems, and they're often among the last few on the test, or a careless slip. Work problems 20 to 25 from many past tests, plus problems from the easier end of the AMC 10. Equally important, find the one or two silly errors you make under time pressure, such as dropping a negative sign or misreading "not," and build a habit that catches them.

How to use past tests and mocks

Released AMC 8 tests are available to the public, and a typical student has many years of them to work with. The mistake is burning them all in the first month. Treat them like a limited supply. A good split is to use the older tests for untimed and topic-based practice early, and to save the most recent several years for timed simulations close to the test, since the style drifts a little over time.

A full-length mock matters because it recreates the part books can't: the pressure of 25 questions against a clock. A good mock comes with a score report that breaks your result down by topic, shows your pacing, and walks through each missed question with a faster method. That last part is where most of the learning happens. Whichever tests you use, never take one without time to review it afterward.

How to review mistakes so they don't come back

Reviewing is what separates students who improve from students who just practice. After each test, go through every missed or guessed problem and sort it into one of five buckets.

• Careless: you knew it and slipped. Misread the question, made an arithmetic error, bubbled the wrong letter.
• Missing tool: you didn't know the idea, such as a divisibility trick or how to count by complement.
• Missing insight: you knew all the tools but didn't see which one applied.
• Time: you could have solved it but ran out of clock.
• Lucky guess: you got it right but couldn't explain why. Count these as misses.

Keep a simple error log, a notebook or a spreadsheet with the date, problem, bucket, and the one-sentence lesson. Every couple of weeks, count the buckets. If half your misses are careless, more content practice won't help; you need slower reading and a checking habit. If most are missing tools, go back to the topic lists above.

For every missed problem, do two more things. First, redo it cold two or three days later without looking at the solution. Second, look for a faster method. AMC problems are written so there's usually a short path, and learning to see it is the main thing that makes students faster. A student who solves a counting problem by listing 20 cases will take two minutes. One who spots a complement (count what you don't want and subtract) takes thirty seconds.

What a good week looks like

For a student starting from scratch four months out, a sample week is four sessions of 35 minutes each. Monday and Wednesday: learn one topic and do ten problems on it. Friday: a mixed set of eight problems from a past test. Sunday: review that set and update the error log. Every other Sunday, swap the review for a full timed test and a longer review the next day. Parents help most by asking one question after a session, "What did you miss and why?", rather than checking answers.

Common mistakes in AMC 8 prep

• Only doing hard problems. Most points come from problems 1 to 15. Don't skip them for the exciting ones.
• Reading solutions instead of attempting problems. If you haven't struggled with a problem for at least ten minutes, you won't remember its solution.
• Practicing with a calculator and then taking the test without one.
• Taking many full tests and reviewing none of them.
• Starting too late and compensating with long sessions the week before.

The bottom line

Take a baseline test, learn the four topic areas, practice mixed and timed sets, and review every mistake in writing. A student who does that for three or four months is prepared, whatever the final number turns out to be. If you want a baseline right away, you can take a free full-length mock AMC 8 and see where you stand.