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AMC · Number Theory & Geometry

Practice Problems
Made Simple

20 carefully crafted problems based on key concepts from digit constraints, perfect squares, prime factorization, and isosceles trapezoids. Pick your answer — instant feedback!

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20 Remaining

Part A · Number Properties

Q 1 – 10
⚡ Quick Memory Points
Master these before you start Part A:
DIGIT POS · ones → tens → hundreds → thousands
PERFECT SQ · n² always ends in 0,1,4,5,6,9
SEMIPRIME · p × q (exactly two primes, can repeat)
1 LESS · n²−1 = (n−1)(n+1)

Part B · Trapezoid Geometry

Q 11 – 20
⚡ Quick Memory Points
Master these before you start Part B:
ISO-TRAP · legs equal → base angles equal
60-60 TRAP · drop heights → equilateral triangles on sides
LEG = HEIGHT · if base angle = 60°, leg length = h
PERIMETER · AD + BC + 2·AB = total