How to prepare for the AMC 10

• 25 multiple-choice questions, each with five options, in 75 minutes.

• For students in grade 10 and below who are under 17½ on the day of the contest.

• 6 points for a correct answer, 1.5 for a question left blank and 0 for a wrong one, out of 150.

• No calculators.

• It is sat in two versions, the 10A and the 10B, on two dates, usually in November. Strong scores lead to an invitation to the AIME.

• Sitting dates and registration change every year: check the MAA’s AMC page (maa.org) for this year’s.

A blank is worth $1.5$ points. A blind guess among five options is worth $\frac{1}{5}\times 6=1.2$ on average, so a blind guess loses points.

Rule out one option and the guess is worth $\frac{1}{4}\times 6=1.5$, the same as a blank. Rule out two and it is worth $\frac{1}{3}\times 6=2$, more than a blank.

So: guess only when you can eliminate at least two options. Otherwise leave it blank and spend the time on a question you can finish.

• Algebra: equations, inequalities, functions, sequences and series, and polynomials.

• Counting and probability: arrangements, choosing, complementary counting and expected value.

• Number theory: divisibility, primes, gcd and lcm, remainders and digits.

• Geometry: triangles, circles, polygons, similarity, areas and coordinates. Usually the largest share.

There is no calculus or trigonometry beyond the basics. The difficulty is in combining ideas, not in advanced topics.

• Start with a full practice test under time, to find your level and your weak topics.

• Aim first at questions 1 to 15 answered quickly and correctly. For most students that alone is a big step up.

• Then one topic a week, with the formulas on our topics page learnt until they are automatic.

• Keep a notebook of every mistake: what went wrong, and the idea that would have fixed it. Reread it before each test.

• Sit a full practice test every two or three weeks, under time, and watch the blanks and wrong answers change.

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.