How to spend 40 minutes on 25 questions

Two students can know exactly the same math and score six points apart on the AMC 8. The difference is usually what they do with the 40 minutes: where they slow down, where they cut their losses, and whether every bubble gets filled in. Strategy won't replace knowing the material, but it's the cheapest improvement available in the final weeks. Here's how we coach it.

The setup, briefly: 25 multiple-choice questions, 40 minutes, no calculator, one point per correct answer, nothing deducted for a wrong one. The test is given by the Mathematical Association of America once a year, typically in late January, through schools and other registered hosts. If you want the scoring details first, read our guide to AMC 8 scoring and awards.

A time budget by question band

The average is 96 seconds a question, but averages mislead here, because the questions are ordered roughly from easy to hard. If you spend 96 seconds on problem 2 you're wasting time you'll need on problem 22. This is the budget we use. It's a starting point, and you should adjust it after a few timed practice tests.

A few notes on why the budget looks like this. The first band is the cheapest source of points, so protect it from careless errors, and finish it a bit early if you can. Bank that time. The second band is where most students either speed ahead or get stuck, so the checkpoint at 20 minutes matters: if you're at question 16 with 20 minutes left, you're right on schedule. The final band gets less time per question than the one before it, not because those problems are easier but because you won't solve all of them, and you don't want to burn the whole clock on one.

Wear a watch, or check whatever clock the room provides, at two points: after question 8 and after question 16. That's all the clock-watching most students need. Looking every minute makes people anxious and doesn't help.

When to skip

Every question is worth one point, so the goal is to collect the points that are cheapest first. That means skipping on purpose is a real skill, not a failure.

A good rule: if you've spent about two minutes on a problem and you can't say what your next step is, put a mark next to it, circle your best guess, and move on. Not a problem that's taking time but moving, which can be worth finishing. A problem that isn't moving. Students tend to be bad at this in both directions: some abandon problems one step from the answer, and others pour seven minutes into a dead end because they've already invested so much.

Come back to marked problems in the last few minutes, or earlier if you have time. A fresh look often turns up the idea you missed, and sometimes you'll realize you misread the question on the first pass.

A worked example of pacing in action

Picture a student who's solid but not yet an award contender. She breezes through questions 1 to 8 in about seven minutes, so she's a minute ahead. In the second band she gets stuck on question 13, a counting problem, and notices she's spent two and a half minutes without a plan. She circles her best guess, marks the question, and moves on. She reaches question 16 at the 19-minute mark.

In the third band she solves 17, 18 and 20 cleanly, skips 19 after two minutes, and guesses 21 after eliminating two choices. At 30 minutes she goes to the last four problems, solves 22 and 23, and finds no way into 24 and 25. With 3 minutes left she returns to 13, tries listing cases a second way, and finds the miscount. She fills in 19, 24 and 25 with guesses chosen after crossing out what she can. Nothing is blank.

Nobody had to be a genius for that to work. She had a budget, two checkpoints, a two-minute rule and a habit of filling every bubble. Those four things are all trainable, and the way to train them is repeated timed practice followed by honest review, which is why we suggest at least two or three full timed tests in the last month before the real thing.

Guessing, done properly

Since there's no penalty for wrong answers, never leave a bubble empty. But some guesses are better than others.

• Eliminate first. Most problems have at least one choice that's obviously too large, too small, the wrong sign, or not a whole number when the answer must be one. Each choice you rule out raises your odds.
• Use size and units. If a rectangle fits inside a 10 by 10 square, its area isn't 200. Estimate the answer even roughly and throw away the impossible choices.
• Test the choices. On algebra and number problems, plugging the answer choices back into the problem can be faster than solving. Start with the middle value.
• Don't rely on patterns in the letters. A guess is a guess. Pick a letter and move on rather than burning seconds hunting for a pattern.

In the last three minutes, the job is to go down the answer sheet and make sure every question has a mark. Practice this in your timed tests so it becomes automatic.

Checking your work without wasting time

Checking every answer from scratch isn't possible in 40 minutes. Instead, use cheap checks, built into the solution as you go.

• Reread the last line of the question before you bubble. Students lose points on questions like "what is the difference," "which is not," or "in square units," after solving a different problem perfectly.
• Substitute back. For equations and word problems, put your answer into the original statement. It takes ten seconds.
• Ask whether it's reasonable. A probability above 1, a negative length, or a number of people that isn't whole signals an error.
• Check that the bubble matches the work. Circle the answer in the test book, then bubble it right away, and glance at the question number on the answer sheet. A shifted row is a painful way to lose points.

Common traps

• Diagrams not to scale. Never measure or trust the look of a figure. Use the numbers given.
• Answering the wrong quantity. You solved for x, but the question asked for 2x + 1. Underline what's being asked.
• Double counting. In counting problems, check whether the order matters and whether different-looking cases are really the same.
• Forgetting special cases. Zero, one, negative numbers, and a number being its own factor often break an otherwise tidy solution.
• Unit mix-ups. Minutes versus hours, inches versus feet, a percent versus a fraction.
• Arithmetic slips with no calculator. Write steps down. Mental math under pressure is where a 7 times 8 becomes 54.
• Spending your best minutes on a problem you like. Interesting isn't the same as valuable. Every question is one point.

Staying calm

Many students freeze when they hit a problem they don't recognize, typically around the middle of the test. That's normal and it's built into the contest: the last problems are hard enough that most students don't finish everything, and that's true for strong students as well. When you hit a wall, do something concrete: draw a picture, try small numbers, write down what you know, or list the first few cases. Doing something is better than staring. If it still doesn't open up after two minutes, mark it and go.

The week before

The week before the test isn't the time to learn new material. The best thing to do is rehearse.

• Seven to five days out: take one full timed test under real conditions, no calculator, and review it in detail. Use a free full-length mock AMC 8 if you need a fresh one; its report shows your pacing, which is useful for adjusting the budget above.
• Four to three days out: redo a handful of problems from your error log, especially careless ones. Skim your list of formulas and tools: area formulas, divisibility rules, the common Pythagorean triples, the ways to count.
• Two days out: a light session of 30 minutes, a few mixed problems for warm-up. Then stop.
• The night before: pack pencils, erasers, and a watch if allowed. Check your school or host's rules on what you can bring, since calculators aren't allowed, and check the start time and room. Go to bed on time.
• The morning of: eat something, arrive early, and do three or four easy problems to wake up your brain. Don't try to cram.

Our preparation guide covers the longer arc, and the topics guide is a good last read of what each area looks like.

A last note for parents

What helps most on test day is very little: a good night's sleep, a decent breakfast, and a calm message that the goal is to solve what you can and fill in the rest. Afterward, resist the urge to quiz your child on each question. Ask which problem they liked best. The students who stay interested are the ones who keep improving.