Number Theory
Divisibility, primes, factors, remainders, and units-digit patterns.
Mathematics
AMC 8 Class
Prepare for the AMC 8 competition: build the core concepts, then practice the problem-solving that contest math rewards.
- 25 multiple-choice questions
- 40 minutes
- Grade 8 and below
- No calculators
What you'll learn
Skills that matter most.
Counting & Probability
Organized lists, the multiplication principle, and avoiding double-counting.
Geometry
Area, perimeter, angles, the Pythagorean theorem, and clever cutting.
Algebra & Arithmetic
Equations, ratios, rates, percents, and fast mental math.
Patterns & Logic
Sequences, working backwards, and reasoning through cases.
Our strategy
How we learn math here.
Different subjects, different strategies. This is the one built for AMC 8 Class.
- Learn the conceptA short lesson on one idea, with a worked example.
- Practice on purposeProblems chosen to use that idea in new ways.
- Race the clockTimed sets build speed and smart answer-choice strategy.
- Review mistakesFind the idea you missed so it sticks next time.
Practice
Try a few problems.
Stuck? Open a hint, or ask the AMC 8 Coach. It will guide you without just giving away the answer.
Problem 1 · Counting
How many positive integers less than 100 are divisible by 3 or 5?
Count multiples of 3, then multiples of 5. Which numbers did you count twice?
There are 33 multiples of 3 and 19 multiples of 5 below 100. Multiples of 15 (6 of them) were counted twice, so 33 + 19 − 6 = 46. This is inclusion–exclusion.
Problem 2 · Number Theory
What is the units digit of 72026?
Write out the units digits of 7¹, 7², 7³, 7⁴, 7⁵. Do you see a cycle?
Units digits of powers of 7 repeat every 4: 7, 9, 3, 1. Since 2026 leaves remainder 2 when divided by 4, the units digit matches 7², which is 9.
Problem 3 · Geometry
A square has the same perimeter as a 6 × 10 rectangle. What is the area of the square?
Find the rectangle's perimeter first, then the side of the square.
The rectangle's perimeter is 2(6 + 10) = 32, so each side of the square is 8 and its area is 8 × 8 = 64.
Meet your AMC 8 Coach
An AI tutor set up to teach the way AMC 8 Class is best learned. Ask questions, get hints, and practice any time.
Ready to join AMC 8 Class?
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