Official Style Practice

AMC 8 Master Test

20 Problems · All Major Topics · Detailed Solutions

⏱ Time: 40 min
📝 Problems: 20
📊 Difficulty: AMC 8 Level
✅ 5 choices each
Elapsed Time
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0 / 20 answered
①
Core Concepts & Key Formulas

🔢 Number Theory

  • LCM × GCF = a × b
  • Divisibility rules: 2,3,4,5,6,9,10
  • Prime factorization
  • Remainder problems (mod arithmetic)
LCM(a,b) = a×b / GCF(a,b) # of divisors: (e₁+1)(e₂+1)···

📐 Geometry

  • Area: triangle = ½bh, circle = πr²
  • Pythagorean triples: 3-4-5, 5-12-13
  • Similar triangles: ratios of sides
  • Angle sum: triangle = 180°
Area of circle = πr² Circumference = 2πr Volume of cube = s³

📊 Statistics & Probability

  • Mean = sum ÷ count
  • Median = middle value
  • P(event) = favorable / total outcomes
  • Counting: permutation & combination
P(A and B) = P(A) × P(B) [indep] P(A or B) = P(A)+P(B)-P(A∩B)

➗ Fractions & Percents

  • Percent change = (new−old)/old × 100
  • Simple interest: I = Prt
  • Ratio and proportion
  • Unit rates and conversions
% increase = (new-old)/old × 100 Part/Whole = Percent/100

🔣 Algebra & Patterns

  • Solve linear equations
  • Arithmetic sequences: aₙ = a₁+(n−1)d
  • Word problems → equations
  • Integer operations & exponents
aₙ = a₁ + (n−1)d Sum = n(a₁+aₙ)/2

🎲 Logic & Combinatorics

  • Venn diagrams: inclusion-exclusion
  • Systematic listing / tree diagrams
  • Pigeonhole principle
  • Work and rate problems
|A∪B| = |A|+|B|−|A∩B| Combined rate = 1/t₁ + 1/t₂
②
Worked Examples
Example 1 — Number Theory
What is the least common multiple of 12 and 18?
Solution: 12 = 2² × 3,   18 = 2 × 3²
LCM = 2² × 3² = 4 × 9 = 36
Check: 36 ÷ 12 = 3 ✓,   36 ÷ 18 = 2 ✓
Example 2 — Geometry
A right triangle has legs 6 and 8. What is the hypotenuse?
Solution: Use Pythagorean theorem:
c² = 6² + 8² = 36 + 64 = 100
c = 10   (recognizing 6-8-10 = 2×(3-4-5))
Example 3 — Probability
A fair die is rolled once. What is the probability of rolling a prime number?
Solution: Primes on a die: {2, 3, 5} → 3 outcomes
P = 3/6 = 1/2
Total outcomes = 6 (equally likely)
③
Practice Problems

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📖 Answer Key & Detailed Solutions