Math 101.00 - Final Review

Module 1: Interval notation, absolute value expressions, graphing equations, solving linear equations, and applications. Examples are provided for each topic to illustrate the concepts.

Expressing intervals in set-builder notation and graphing on number lines (interval (-3, 4])
Evaluating expressions with absolute values (Example: -|-32|)
Completing tables of values and graphing on coordinate axes (Example equation: y = (x − 1)² + 2, using x-values -2, -1, 0, 1, 2)
Solving linear equations (Example: -x + 1/4 = 2x – 1/2)
Solving application problems using linear equations (Example: finding a final exam score needed to maintain an average score)

Simplifying expressions using exponent rules (Example: simplifying an expression with negative exponents)
Converting between scientific and decimal notation (Example: converting 7,000,000 × 0.0034 to scientific notation)
Converting to decimal notation(Example:Converting 5.2 × 10^5/2.6 × 10^3)

Determining if a relation is a function; identifying domain and range
Evaluating functions (Example: Evaluating f(x) = -x³ - 3x² + 1 at a given value of x; Example: Evaluate f(-2))
Identifying function values, domain and range from a graph

Combining functions using addition, subtraction, multiplication or division (Example; find (f-g)(x) for given f(x) and g(x))

Solving systems of linear equations (using graphing, substitution, or addition)
Solving application problems using systems of equations (Example: Mixing two types of flour with given percentages of whole wheat to create a mixture)

Solving linear inequalities in one variable, and graphing solutions
Solving compound inequalities and graphing solutions on a number line
Solving equations/inequalities with absolute values
Solving linear inequalities in two variables
Solving systems of linear inequalities
Adding, subtracting, multiplying or dividing polynomials (details include long and short division)
Factoring polynomials, solving quadratic equations by factoring
Solving application problems using quadratic equations
Finding the domain of a rational function
Solving rational equations
Solving a formula for a specified variable (e.g., solving I = E / (R+r) for r)
Adding, subtracting, multiplying, and dividing rational expressions
Simplifying complex rational expressions
Dividing polynomials
Simplifying exponential expressions
Converting between exponential and logarithmic form
Evaluating logarithmic expressions
Graphing logarithmic functions
Finding the distance between two points
Finding the midpoint between two points
Finding the equation of a circle

Graphing quadratic functions
Identifying vertex, axis of symmetry, x-intercepts, and y-intercepts
Solving application problems using quadratic functions
Solving quadratic equations using the square root property, completing the square, and the quadratic formula

Graphing exponential functions
Finding the accumulated value of an investment (using compound interest formulas)
Finding the composition of two functions (fog)
Verifying that two functions are inverses
Converting between exponential and logarithmic forms of an expression
Evaluating logarithmic expressions
Graphing logarithmic functions