Unit 1
Unit 1 will cover Chapters 1 and 2.
1.1 Reduce fractions to lowest terms
1.2
Add and subtract fractions
Use the distributive property
Combine like terms to simplify
Multiplication with fractions
1.3
Addition and subtraction with positive and negative numbers
Multiplication and division with positive and negative numbers
Order of Operations
Division with fractions
1.4 Properties of exponents; simplify expressions involving exponents
2.1 Solve linear equations, including equations involving fractions or decimals
2.2
Given a formula, find the value of a variable given the value of another variable
Solve a given formula for a specified variable (in terms of the other variables)
2.3 Application problems; especially questions involving geometry (rectangles and triangles) and rate/time/distance (RTD problems)
2.4 Solve linear inequalities; be able to graph your solution set and write it in interval notation (pay attention to "square brackets" versus "round brackets")
2.5 Solve compound inequalities ("ands" and "ors"); be able to graph your solution set and write it in interval notation (pay attention to "square brackets" versus "round brackets")
2.6 Solve equations involving absolute value; the equation typically splits into two "cases" leading to two answers
2.7 Solve inequalities involving absolute value; be able to graph the solution set and write it in interval notation (pay attention to "square brackets" versus "round brackets")
Unit 2
Unit 2 will cover Chapters 3 and 4.
3.1
Graph a line by plotting points (using an “input-output” table)
Find the x- and y-intercepts of a line
Graph vertical and horizontal lines
3.2
Find the slope of a line given a graph
Find the slope of a line given two points
3.3
Use slope and y-intercept to graph a line from its equation
Given the equation of a line, identify the slope and y-intercept
Find the equation of a line given…
…the slope and a point
…two points
…a point and parallel/perpendicular to another line
3.4 Graph the solution set of an inequality in two variables
4.4 Graph the solution set of a system of inequalities
3.5
Given a graph, determine whether the graph represents a function
Given a graph, determine the domain and range of the function/relation
3.6
Be able to read and write using function notation
Given a graph, evaluate the function at a specified input value
Given an equation, evaluate the function for a specified input value
3.7
Given a graph, evaluate a composition of functions
Given equations, evaluate a composition of functions
9.2
Given a function, find the equation of its inverse
Know the relationship between the graph of a function and the graph of its inverse
4.1
Solve 2x2 systems of equations using either the substitution or addition (elimination) methods
Be able to identify inconsistent and dependent systems
4.2
Solve 3x3 systems of equations
Be able to identify inconsistent and dependent systems
4.3
Application problems involving systems of equations, especially problems about tickets, interest rates, RTD, and mixtures
Be able to clearly show the appropriate steps in the solving process
Unit 3
Unit 3 will cover Chapter 5.
5.1 Know how to add and subtract polynomials
5.2 Know how to multiply polynomials, including the rules for "special products" (Diff of Squares, and Squaring a Binomial)
5.3 Division of polynomials, including dividing by a monomial (easy kind) and long division (harder kind)
5.4-5.7 Factoring, including factoring by grouping, factoring trinomials, perfect square trinomials, differences of squares, and sums and differences of cubes
5.8 Solving equations by factoring. Also, application questions.
Unit 4
Unit 4 will cover Chapter 6.
6.1 Reduce a rational expression to lowest terms (simplify)
6.2 Multiply and divide rational expressions
6.3 Add and subtract rational expressions
6.4 Simplify complex fractions
6.5 Solve equations with rational expressions in them
6.6 Application questions, specifically "RTD" problems and "combined work" problems
Unit 5
Unit 5 will cover Chapters 7 and 8
7.2 Rewrite rational exponents as radical expressions and vice versa. Evaluate/simplify expressions with rational exponents
7.3 Simplify radicals.
7.4 Simplify radical expressions involving addition and subtraction.
7.5 Simplify radical expressions involving multiplication and division. Rationalize the denominator.
7.6 Solve equations that have radicals in them.
7.7 Do addition, subtraction, multiplication, and division of imaginary numbers.
8.1/8.2 Solve quadratic equations using (1) The Square Root Property, (2) By factoring, or (3) The Quadratic Formula. Know when to use which method.
8.6 Graph quadratic functions that are given in Standard Form. Know how to find the vertex of the parabola.
8.7 Applications, specifically problems involving projectile motion, revenue/cost/profit, and optimization
Unit 6
Unit 6 will cover Sections 9.1, 9.3, 9.5, and 9.6.
9.1
Evaluate exponential expressions, including approximating with a calculator
Draw the graph of exponential functions, or at least match graphs to equations
Application problems involving exponential growth/decay--especially compound interest and population growth
9.3
Rewrite expressions from exponential form to logarithmic form, and vice versa
Evaluate (simplify) logarithms
Draw the graph of a logarithmic function, or at least match graphs to equations
9.5
Approximate common log (log) and natural log (ln) expressions using a calculator
Use the Change-of-Base formula and a calculator to approximate other kinds of logs
9.6
Solving exponential equations
Application problems involving compound interest and population growth