AMC 10

Harder contest sets and tactics.

AMC 10Divisibility★★★★☆Expert+55 XP

How many ordered pairs of positive integers (x, y) satisfy xy = 144?

AMC 10Polynomials★★★★☆Expert+55 XP

Let f(x) = x² − 6x + 5. For how many integers x is f(x) negative?

AMC 10Counting★★★★☆Expert+55 XP

How many positive integers at most 100 are relatively prime to 12?

AMC 10Divisibility★★★☆☆Hard+40 XP

What is the units digit of 2²⁰²⁶?

AMC 10Polynomials★★★☆☆Hard+40 XP

The roots of x² − 7x + 12 = 0 are r and s. What is 1/r + 1/s? (Fraction.)

AMC 10Counting★★★☆☆Hard+40 XP

How many diagonals does a convex 12-gon have?

AMC 10Polynomials★★★☆☆Hard+40 XP

If log₁₀ x = 2, what is log₁₀(100x³)?

AMC 10Geometry★★★☆☆Hard+40 XP

Two sides of a triangle are 7 and 10. How many integer values are possible for the third side?

AMC 10Sequences★★★★☆Expert+55 XP

What is the sum of all positive multiples of 3 that are at most 100?

AMC 10Polynomials★★★☆☆Hard+40 XP

What is i²⁰²⁶, where i is the imaginary unit? (Answer -1, 1, i or -i.)

Premium problem

How many subsets of a 6-element set have an even number of elements?

Premium problem

The roots of x³ − 6x² + 11x − 6 = 0 are a, b, c. What is a² + b² + c²?

AMC 10Sequences★★★☆☆Hard+40 XP

What is 1 + 2 + 4 + 8 + … + 2¹⁰?

Premium problem

How many integers from 1 to 1000 inclusive are perfect squares or perfect cubes?