College Algebra: study guide and practice
Also known as: math 101, math 1314, math 1111, math 110, mat 140, intermediate algebra, precalculus i, algebra for college students, math 1010, college algebra and trigonometry
What you will be able to do
- Use function notation, find domains and compose functions
- Solve linear equations and inequalities, including absolute value
- Solve quadratic equations by factoring, completing the square and the formula
- Analyse polynomial and rational functions: zeros, end behaviour, asymptotes
- Model growth and decay with exponential functions and solve with logarithms
- Solve systems of linear equations by substitution and elimination
Topics
- Functions, notation and domainA function assigns exactly one output to each input. Learn to evaluate, find domain and range, compose and invert functions.
- Linear equations and inequalitiesSolve one-variable equations and inequalities, work with slope and lines, and handle absolute value.
- Quadratic equationsSolve ax² + bx + c = 0 by factoring, square roots, completing the square and the quadratic formula, and read a parabola's vertex.
- Polynomial functionsFind zeros, factors and end behaviour of polynomials using the remainder and factor theorems.
- Rational expressions and equationsSimplify, combine and solve fractions with variables, and find asymptotes and holes of rational functions.
- Exponential functions and growthModel repeated percentage growth and decay with f(x) = a·bˣ, including compound interest and half-life.
- LogarithmsUnderstand logarithms as inverses of exponentials, use the log rules and solve equations with unknown exponents.
- Systems of linear equationsSolve two equations in two unknowns by graphing, substitution or elimination, and recognise no-solution and infinite-solution cases.