algebra
Function — AMC & AIME Problems
67 problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Function — a algebra concept — each with a professionally curated solution, many with a video solution too, from LIVE by Po-Shen Loh. Browse all concepts or the full past-contest archive.
LIVE focuses on challenge. As a social enterprise, we also explain standard school concepts one at a time, for free, on our sister site Expii. For this idea: Evaluating Functions - Examples & Practice, Composing Functions at a Point, What Are Inverse Functions?.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
Filter by difficulty
These problems’ difficulty ratings come from real solve attempts on our platform. Tap a band or a contest to filter the list below, and tap a selected band again to include all difficulties. See the full difficulty guide.
AMC 10
AMC 12
- 1950 AMC 12 Problem 11
- 1950 AMC 12 Problem 17
- 1950 AMC 12 Problem 37
- 1950 AMC 12 Problem 44
- 1951 AMC 12 Problem 33
- 1952 AMC 12 Problem 11
- 1954 AMC 12 Problem 16
- 1954 AMC 12 Problem 17
- 1957 AMC 12 Problem 16
- 1958 AMC 12 Problem 4
- 1959 AMC 12 Problem 17
- 1960 AMC 12 Problem 24
- 1961 AMC 12 Problem 34
- 1963 AMC 12 Problem 1
- 1967 AMC 12 Problem 6
- 1967 AMC 12 Problem 14
- 1968 AMC 12 Problem 5
- 1970 AMC 12 Problem 5
- 1970 AMC 12 Problem 16
- 1970 AMC 12 Problem 25
- 1971 AMC 12 Problem 21
- 1971 AMC 12 Problem 30
- 1972 AMC 12 Problem 29
- 1974 AMC 12 Problem 12
- 1974 AMC 12 Problem 27
- 1976 AMC 12 Problem 10
- 1977 AMC 12 Problem 22
- 1980 AMC 12 Problem 14
- 1980 AMC 12 Problem 22
- 1982 AMC 12 Problem 12
- 1982 AMC 12 Problem 19
- 1983 AMC 12 Problem 8
- 1999 AMC 12 Problem 18
- 2000 AMC 12 Problem 15
- 2002 AMC 12A Problem 19
- 2003 AMC 12A Problem 19
- 2003 AMC 12A Problem 25
- 2004 AMC 12B Problem 13
- 2005 AMC 12A Problem 20
- 2007 AMC 12B Problem 9
- 2008 AMC 12A Problem 12
- 2009 AMC 12A Problem 9
- 2011 AMC 12A Problem 21
- 2015 AMC 12B Problem 18
- 2017 AMC 12B Problem 7
- 2024 AMC 12A Problem 13
- 2024 AMC 12A Problem 25
- 2025 AMC 12A Problem 25
More algebra concepts
- Absolute value
- Ages
- Algebraic manipulation
- AM-GM Inequality
- Arithmetic sequence
- Arithmetico-geometric series
- Binomial theorem
- Calculus
- Cauchy-Schwarz Inequality
- Completing the square
- Complex number
- Custom operation
- De Moivre’s Theorem
- Determinant
- Difference of squares
- Factoring
- Fibonacci
- Floor and ceiling functions
- Functional equation
- Geometric sequence
- Inequality
- Linear equation
- Logarithm
- Matrix
- Mixture
- Newton’s Sums
- Partial fractions
- Polynomial
- Quadratic
- Radical
- Rational equation
- Rationalizing denominator
- Recursion
- Roots of unity
- Simon’s Favorite Factoring Trick
- Slope
- Substitution
- Sum and difference of cubes
- Sum of first n cubes
- Sum of first n odd numbers
- Sum of first n squares
- Summation
- Symmetry (algebra)
- System of equations
- Telescoping
- Vieta’s Formulas
- Zero product property