AMC Foundations Course

The AMC includes AMC 8, AMC 10, and AMC 12, with multiple-choice questions that reward careful reasoning. AMC 8 has 25 questions in 40 minutes, while AMC 10 and AMC 12 have 25 questions in 75 minutes. Scores on AMC 10 and AMC 12 can qualify students for AIME. A strong strategy starts with understanding the problem, trying smaller cases, drawing diagrams, and looking for patterns. Manage time by skipping hard questions and returning later. Check answers by substituting values back into the problem. Review every mistake to improve reasoning, not just memorization. This course covers the main AMC topics and links to a practice bank with 60 original questions.

Algebra is the most common topic on AMC contests. Practice solving linear equations, simplifying expressions, and working with exponents. Slope-intercept form y = mx + b gives the slope m and y-intercept b. Quadratic equations can be factored or solved with the quadratic formula. The sum of the roots of ax^2 + bx + c = 0 is -b/a. When multiplying powers with the same base, add exponents; when raising a power to a power, multiply exponents. Word problems require translating sentences into equations, then checking the answer in the original context. Build speed by recognizing common forms and practicing mental arithmetic.

Geometry questions on AMC test area, perimeter, volume, angle sums, and the Pythagorean theorem. Know the formulas: rectangle area is length times width, triangle area is half base times height, circle circumference is 2πr, and circle area is πr^2. A square with side s has perimeter 4s and area s^2. A cube with edge s has volume s^3 and surface area 6s^2. The interior angles of a triangle sum to 180°, and a quadrilateral sums to 360°. A trapezoid area is the average of the bases times the height. For right triangles, a^2 + b^2 = c^2. Draw diagrams and label known values before solving.

Number theory and combinatorics appear frequently on AMC. Know divisibility rules, primes, greatest common divisor, least common multiple, factorials, and units digits. Prime numbers have exactly two divisors, and 1 is not prime. The GCD of 12 and 18 is 6, and the LCM of 4 and 6 is 12. Factorials count arrangements: 3 distinct books can be arranged in 3! = 6 ways. The number of ways to choose 2 items from 4 is 4 choose 2 = 6. A coin flipped 3 times has 8 outcomes, and rolling two dice has 36 outcomes. Probability is favorable outcomes divided by total outcomes. Practice recognizing patterns and simplifying fractions.

Strong AMC performance comes from practice and reflection. Start each problem by identifying what is given and what is asked. Try smaller cases, draw diagrams, look for symmetry, and test answer choices. Eliminate clearly wrong choices to improve guessing when needed. Manage time by moving past hard questions and returning later. After each practice set, review every mistake and write the correct reasoning. Track which topics cost the most points and review those first. Use official-style timing and avoid calculators when possible because AMC 8, 10, and 12 do not allow calculators. Build endurance with timed sets and spaced review.