How to prepare for the AMC 8

• 25 multiple-choice questions, each with five options, in 40 minutes.

• For students in grade 8 and below (Year 9 and below in the UK).

• One point for each correct answer and nothing taken off for a wrong one, so every question should be answered.

• No calculators. Scrap paper, a pencil, a ruler and a compass are fine.

• It is usually sat in January. Sitting dates and registration change every year: check the MAA’s AMC page (maa.org) for this year’s.

The questions use middle-school mathematics, but ask for it to be used cleverly. The ones that come up again and again:

• Number sense: fractions, percentages, ratios, averages and working backwards.

• Counting and probability: listing carefully, multiplying choices, and counting what you do not want.

• Geometry: angles, areas of triangles and composite shapes, the Pythagorean theorem, and circles.

• Number theory: factors, primes, divisibility and remainders.

• Algebra and patterns: simple equations, sequences and rates (distance, speed and time).

The first questions take a minute each; the last ones are real puzzles. Most of the score is won in the middle third.

• Week 1: sit a full practice test under time, with no help. Mark it, and write down every topic you missed.

• Weeks 2 to 6: one topic a week, from your list. Twenty minutes a day is enough: a few easier questions to warm up, then two or three hard ones, slowly.

• Every week: redo the questions you got wrong a week ago, without looking at the solution first.

• Week 7: a second full practice test under time. Compare it with the first.

• Week 8: short timed sets of the first fifteen questions, to make the easy points fast and safe. Sleep well before the day.

• Go through once, answering what you can, and mark the ones to come back to. Do not stay stuck.

• Leave a few minutes at the end: with no penalty for a wrong answer, a blank is the only certain zero.

• Check the question asked for what you found: the length, not the area; the number of ways, not the probability.

Original practice tests written by Math Webb in the style of the contest, free to read, each question with its answer and a full worked solution.