# Number Theory

This course covers the following topics in number theory: prime numbers, composite numbers, multiples and factors, prime factorization, simple Diophantine equations, base numbers, modular arithmetic, divisibility rules, linear congruence, and more. Successful completion of the course will enable students to perform better on math competitions, such as Mathcounts and AMC 8/10/12.

# Counting & Probability

This course covers the following topics: fundamental counting principles, permutations, combinations, Pascal's Triangle, basic combinatorial identities, expected value, fundamentals of probability, geometric probability, the Binomial Theorem, set theory, conditional probability, mutually exclusive and inclusive events, binomial experiments, and more. Successful completion of this course will enable students to perform better in math competitions, such as Mathcounts and AMC 8/10/12.

# AMC 8

The American Mathematics Contest 8 (AMC 8, originally called the AJHSME - American Junior High School Mathematics Examination) is held every November. The AMC 8 is for students in the sixth, seventh or eighth grade and for accelerated fourth and fifth grade students. It is a 25-question, 40-minute multiple-choice contest, given the Tuesday before Thanksgiving week. A student’s score is the number of problems correctly solved, and there is no penalty for guessing. The material covered is the middle school mathematics curriculum. Any student 14.5 years of age or younger on the day of the contest and not enrolled in grades 9, 10, 11 or 12 or equivalent are eligible to participate. Students who score 20 or better on the AMC 8 are invited to take the next set of contests, the AMC 10 and AMC 12.

The AMC 8 course at The Masters Prep is available during the summer program and the fall trimester only. One-on-one private tutoring is available all year round.

# AMC 10

The American Mathematics Contest 10 (AMC 10, added in 2000, when the names of the AMC 8 and AMC 12 were updated) is a 25 question, 75 minute multiple choice examination in secondary school mathematics containing problems that can be understood and solved with pre-calculus concepts. The AMC 10 is designed for students in a program leading to a high school diploma, under 17.5 years of age on the day of the contest, and not enrolled in grades 11 or 12 or equivalent.

## Qualification for the AIME

AMC 10 students who rank in the top 2.5% nationally (or score at least 120 out of 150 points) will qualify for the AIME.

## Test Dates

The AMC 10 and AMC 12 Contests are given on two different dates, (designated by the use of the "A" and "B" suffix on the contest names - AMC 12A, AMC 10A, AMC 12B or AMC 10B) about two weeks apart, in February. A student may choose to take one contest on both dates. In other words, an 11th or 12th grader may take the AMC 12 on both dates. A student in 10th grade or below may choose whether he will take the AMC 10 or the AMC 12 on each date, so a 10th grader can take the AMC 10 A and the AMC 12B, the AMC 12A and the AMC 10B, the AMC 12A and the AMC 12B, or the AMC 10A and the AMC 10B.

The AMC 10 course at The Masters Prep is available during the summer program, fall trimester, and spring trimester. One-on-one private tutoring is available all year round.

# AMC 12

The American Mathematics Contest 12 (AMC 12, originally called the AHSME - Annual High School Mathematics Examination) is a 25 question, 75 minute multiple choice examination in secondary school mathematics containing problems that can be understood and solved with pre-calculus concepts. The AMC 12 is designed for students in a program leading to a high school diploma, and under 19.5 years of age on the day of the contest.

## Qualification for the AIME

AMC 12 students who rank in the top 5% nationally (or score at least 100 out of 150 points) will qualify for the American Invitational Mathematics Exam (AIME).

The AMC 12 course at The Masters Prep is avaialble during the summer program, fall trimester, and spring trimester. One-on-one private tutoring is available all year round.

# AIME

The American Invitational Mathematics Examination (AIME), is a 15 question, 3 hour examination in which each answer is an integer number from 0 to 999. It is given on two different dates, (designated by the use of the "I" and "II" suffix on the contest names - AIME-I and AIME -II) about two weeks apart, in late March. The questions on the AIME are much more difficult than the AMC 10 and the AMC 12 and students are very unlikely to obtain the correct answer by guessing. As with the AMC 10 and AMC 12 (and the USAMO), all problems on the AIME can be solved by pre-calculus methods. Unlike on the AMC 10 and the AMC 12 a student can only take the AIME once.

The AIME course at the Masters Prep is available during the summer program, fall trimester, and spring trimester. One-on-one private tutoring is available all year round.

# Joe Holbrook Memorial Math Competition

# (Bergen County Academies Math Competition)

Formerly the BCAMC, Joe Holbrook Memorial Math Competition is an annual math contest given to 4th to 8th grade students. The late Joe Holbrook was the original coach of the AAST Math Team, and the contest was renamed in 2012. The test is a 50 question, 1 hour 30 minute examination.

The JHMMC course at the Masters Prep is available during the summer program and fall trimester only. One-on-one private tutoring is available all year round.