Chapter 1
Learning Goals
[1.1] Real
Numbers
q Know the types of numbers: Whole, Integer, Rational, Irrational, Real
q Be able to graph any type of number on a number line, including square roots and fractions, without having to use a calculator
q Know the commutative, associative, inverse, and distributive properties. Know when they do or do not apply to operations. For example, does the commutative property work with both multiplication and division?
q Be able to convert units and know what units an answer will have after canceling
q Practice reading word problems slowly and carefully, drawing pictures to help you understand, and solving small parts of the problems as you read through them.
[1.2] Algebraic Expressions and Models
q Be able to simplify expressions (distributing and combining like terms)
q Be able to evaluate expressions using the correct order of operations (PEMDAS)
q
Know the difference between 
and 
, where n is a whole number
q Be able to solve applied problems, such as problems 53-67
q Know the area and perimeter formulas for squares, rectangles, triangles, and circles. You need them to do problems like 53-55.
[1.3] Solving Linear Equations
q Be able to solve all types of equations from basic to fraction busters
q Be able solve equations by graphing them on a calculator and finding their intersection.
q When you solve an equation, know the two special cases for: No answer and All Real Numbers. Graphically, it has to do with parallel lines and lines that are the same exact line. Algebraically, you get either an untrue statement like 2 = 5 when trying to solve or you get a statement that is always true such as 4 = 4.
q Be able to solve applied problems, such as 41-50
[1.4] Rewriting Equations and Formulas
q Be able to solve formulas for any variable in the formula
[1.5] Problem Solving Using Algebraic Models
q Given a word problem, be able to write a verbal model
q Given a word problem, be able to write an algebraic model
q Given a word problem, be able to solve it using algebra or any other strategy that helps you.
q
Be familiar with 
problems. They come up a lot.
[1.6] Solving Linear Inequalities
q Know how to solve and graph simple inequalities.
q Know how to solve and graph compound (double-sided) inequalities.
q Know when you need to “turn around” an inequality when solving.
q Know the difference between open and closed circles.
[1.7] Solving Absolute Value Equations and Inequalities
q Know how to solve absolute value equations. There are usually two answers.
q Know how to solve and graph absolute value inequalities with < or £
q Know how to solve and graph absolute value inequalities with > or ³
q Know how to write an absolute value inequality from a verbal description (word problem)
Chapter 2
Learning Goals
[Notes]Graphing
Calculators
q
Know
how to enter absolute value on your calculator. Ex: y = | x + 2 |
q
Know
how to use the TblSet and Table features to generate an xy-table for you.
q
Know
how to enter equations correctly using parentheses. Ex: 
[2.1] Functions and Their Graphs
q
Know
what a relation is and be familiar with how to represent them using a graph, a
mapping,
an xy-table, or an equation.
q
Know
what a function is. It’s a relation
where …
q
Given
a graph, be able to tell whether the graph is a function or non-function.
(vertical line test)
q
Given
a table of values, be able to tell whether the graph is a function or
non-function.
q
Given
an equation, be able to tell whether the graph is a function or non-function.
q
Be
able to evaluate functions written in f(x) notation.
q
Be
able to graph functions by hand and by calculator.
q
Identify
the domain and range of a graph.
q
Identify
the domain and range of an equation.
[2.2] Slope
q
Given
a graph (or only two points), know how to find slope.
q
Know
the difference between positive slope and negative slope on a graph.
q
Know
how the slopes of parallel lines are related.
q
Know
how the slopes of perpendicular lines are related.
q
Know
the special slopes for vertical and horizontal lines.
[2.3] Linear Equations
q
Be
able to use the slope-intercept form for lines: y = mx + b
q
Know
the equations for vertical and horizontal lines.
[2.4] Linear Equations
q
Be
able to use the point-slope form for lines:
y – y1 = m(x – x1)
q
Given
either two points or a slope and a point, be able to write an equation for the
line.
q
Find
linear equations parallel or perpendicular to a given line or pair of points
(ex: [2.4] 25-28)
q
Given
any graph of a line, be able to write an equation for the line.
q
Given
a linear equation in any form, be able to graph it.
q
Given
a linear equation in any form, be able to find the x and y intercepts.
[2.5] Lines of Best Fit
q
Know
the difference between strong, weak, and no correlation.
q
Know
the difference between positive and negative correlation.
q
Know
how to enter a data table into the Stat Lists in a graphing calculator.
q
Know
how to plot the same data (as above) by hand.
q
Know
how to use the Linear Regression tool to find a line of best fit on a graphing
calculator.
q
Know
how to find a line of best fit by hand.
(Draw a line, pick two points, find the equation.)
q
Know
how to use your equation to make predictions beyond the data table.
[2.6] Linear Inequalities
q
Given
a point and a linear inequality, determine whether the point is a solution.
q
Given
a linear inequality equation, be able to graph solid or dotted and use a test
point to find out which side to shade.
[2.7] Piecewise Functions
q
Given
a piecewise equation, be able to evaluate f(x) points and graph
it.
q
Given
a piecewise graph, be able to write its equation.
q
Be
familiar with the ceiling function, rounding function, and greatest integer
function
q
Given
a description of a piecewise function (word problem) be able to write an
equation for it and graph it.
[2.8] Absolute Value Functions
q
Given
any function in the form
know what the values a, h, and k do to the graph.
q
Given
an absolute value equation, be able to graph it quickly without using tables.
q
Given
the graph of an absolute value function, be able to write its equation.
Chapter 3
Learning Goals
[3.1] Solving Linear Systems by Graphing
q
Determine
whether a given point is a solution to a system.
q
Know
the cases of infinite solutions, no solution, and one solution.
q
Know
how to solve a system of two equations by graphing the equations by hand.
q
Know
how to solve a system of two equations by using the intersection tool on a
graphing calculator.
[3.2] Solving Linear Systems Algebraically
q
Know
how to solve a system of two equations by substitution.
q
Know
how to solve a system of two equations by the linear combination method
(addition method).
[3.3] Graphing and Solving Systems of Linear
Inequalities
q
Know
how to graph a system of inequalities.
q
Know
what a “solution” of a system of inequalities means. It’s ONE of the shaded (“true”) areas.
q
Know
when to use a dotted vs solid line.
q
Know
how to use test points to determine which side of each line to shade.
[3.4] Linear Programming
q
Skip
[3.5] Graphing in 3D
q
Know
how to draw a set of 3D axes and plot a 3D point.
q
Know
how to make a 3D point into a box (with one corner at the point and the other
at the origin).
q
Know
how to find the intercepts of a plane and graph a triangular cross section of
it.
q
Know
how to find the volume and surface area for rectangular solids.
[3.6] Solving Linear Systems in Three Variables
q
Determine
whether a given point is a solution to a system.
q
Know
the cases of infinite solutions, no solution, and one solution.
q
Know
how to solve a system of three equations by substitution.
q
Know
how to solve a system of three equations by the linear combination method
(addition method).
Chapter 4
Learning Goals
[4.1] Matrix Operations
q
Know
how to write the size of a matrix
q
Know
how to add and subtract matrices
q
Know
when you can or can’t add/subtract matrices
q
Know
how to multiply a matrix by a scalar
q
Know
when two matrices are equal (same).
[4.2] Multiplying Matrices
q
Know
how to multiply matrices by hand
q
Know
when you can or can’t multiply matrices
q
Know
that the order of multiplication matters.
A*B isn’t the same as B*A.
[4.3] Determinants and Cramer’s Rule
q
Know
how to find the determinant of a 2x2 matrix by hand
q
You
can ignore everything else in this section
[4.4] Identity and Inverse Matrices
q
Know
what the Identity matrix is and show examples of different sizes.
q
Know
how to find the inverse of a 2x2 matrix by hand.
q
Know
when an inverse doesn’t exist
q
Solve
2x2 matrix equations by hand
[4.5] Solving Systems Using Inverse Matrices
q
Know
how to write a system of equations in matrix form
q
Know
how to solve a system of equations using matrix inverses
Graphing
Calculator Skills
q
Know
how to enter/edit a matrix
q
Know
how to add, subtract, and multiply matrices
q
Know
how to find the determinant of a matrix
q
Know
how to find the inverse of a matrix
q
Know
how to solve 3x3 or 4x4 systems of equations using matrices
Chapter 5
Learning Goals
[5.1] Graphing Quadratic Functions
q
Be
able to find the line of symmetry and vertex of a parabola written in standard
form
q
Know
how to graph a parabola written in standard form by finding/plotting the vertex
and several points on each side.
q
Know
how to graph a parabola written in vertex form.
[5.2] Solving Quadratic Equations by Factoring
q
Know
how to factor these trinomials
o
Difference
of two squares
o
Perfect
square trinomials
o
Any
trinomial written in standard form
o
Trinomials
that have a common factor to take out first.
q
Solve
quadratic equations by factoring and using the zero-product property
q
Use
factoring to solve geometric applications, like problems 92-95
[5.3] Solving Quadratic Equations by Finding Square
Roots
q
Know
how to simplify square roots
q
Know
how to “rationalize the denominator”
q
Know
how to solve quadratic equations by square-rooting.
[5.4] Complex Numbers
q
Know
how to add, subtract, and multiply complex numbers
q
Know
how to plot and find the absolute value of complex numbers
q
Know
how to use the complex conjugate to simplify complex number fractions.
q
Know
how to solve quadratic equations that involve square rooting negative numbers.
[5.5] Completing the Square
q
Know
how to complete the square of a trinomial
q
Know
how to solve quadratic equations by completing the square