AMC 12
Fifty problems. Ten minutes. Every unit, easiest first.
Toolkit: formulas to know first
- Pythagoras a² + b² = c². Area of triangle ½bh. Heron: √(s(s−a)(s−b)(s−c)).
- Vieta, x² + bx + c: sum of roots −b, product c. (x + y)² = x² + 2xy + y².
- Powers: aᵐ·aⁿ = aᵐ⁺ⁿ. Logs: log(ab) = log a + log b, and arguments must be positive.
- Counting: n!, C(n,k) = n!/(k!(n−k)!). At least one = 1 − none.
- Mod cycles: find when powers first return to 1. Divisors: add 1 to each prime exponent.
- Trig: sin²θ + cos²θ = 1, sin 2θ = 2 sin θ cos θ. Complex: zⁿ = rⁿ(cos nθ + i sin nθ).