Dual Enrollment Program Pre-DE Course: Algebra I
Dual Enrollment Program Pre-DE Course: Algebra I
[Description?]
Topics and Objectives
Chapter and section numbers refer to Algebra I in MyMathLab by Elayn Martin-Gay with contributions from Robert Blitzer.
1.9 Properties of Real Numbers
(45 exercises)
- Vocabulary and Readiness Check
- Use the commutative and associative properties
- Use the distributive property
- Name the properties illustrated by the statements
2.1 Simplifying Algebraic Expressions
(51 exercises)
- Combine like terms
- Use the distributive property to remove parentheses
- Write word phrases as algebraic expressions
- Name the properties illustrated by the statements
2.2 and 2.3 Properties of Equality
(35 exercises)
- Use the addition property of equality to solve linear equations
- Simplify an equation and then use the addition property of equality
- Use the multiplication property of equality to solve linear equations
- Use addition and multiplication properties of equality to solve linear equations
2.4 Solving Linear Equations
(39 exercises)
- Apply a general strategy for solving a linear equation
- Solve equations containing fractions
2.5 Introduction to Problem Solving
(28 exercises)
- Solve problems involving direct translations
- Solve problems involving relationships among unknown quantities
- Solve problems involving consecutive integers
2.6 Formulas and Problem Solving
(35 exercises)
- Substitute values into a formula and solve for the unknown variable
- Solve a formula for one of its variables
- Use formulas to solve problems
2.8 Mixture and Distance Problem Solving
(17 exercises)
- Solve mixture problems
- Solve uniform motion problems
3.1 Reading Graphs and the Rectangular Coordinate System
(34 exercises)
- Define the rectangular coordinate system and plot ordered pairs of numbers
- Graph paired data to create a scatter diagram
- Determine whether an ordered pair is a solution of an equation in two variables
- Find missing coordinate of an ordered pair solution given one coordinate of the pair
- Interpret information given in a scatter plot
3.2 Graphing Linear Equations
(32 exercises)
- Identify linear equations
- Graph an equation by finding and plotting ordered pair solutions
- Solve application problems
3.3 Intercepts
(28 exercises)
- Identify intercepts of a graph
- Graph a linear equation by finding and plotting intercepts
- Identify and graph vertical and horizontal lines
3.4 Slope and Rate of Change
(34 exercises)
- Find the slope of a line given points on the line
- Find the slopes of horizontal and vertical lines
- Find the slope of a line given its equation
- Slope as a rate of change
3.5 Equations of a Line
(34 exercises)
- Use the slope-intercept form to write an equation of a line
- Use the slope-intercept form to graph a linear equation
- Use the point-slope form to find equation of line given slope and a point on the line
- Use the point-slope form to find an equation of a line given two points on the line
- Use the point-slope form to solve problems
- Find equations of vertical and horizontal lines
3.6 Functions
(31 exercises)
- Identify relations, domains, and ranges
- Identify functions
- Use the vertical line test
- Use function notation
3.7 Graphing Linear Functions
(18 exercises)
- Graph linear functions
- Graph linear functions by finding intercepts
- Graph vertical and horizontal lines
- Decide whether a situation describes a linear function
3.8 Graphing Piecewise Defined Functions; Shifting/Reflecting Graphs
(18 exercises)
- Graph piecewise-defined functions
- Use vertical and horizontal shifts to graph a function
- Use function notation
- Graph nonlinear equations
- Vertical and horizontal shifts
4.1 Linear Inequalities and Problem Solving
(33 exercises)
- Graph inequalities on number lines
- Solve inequalities
- Solve inequality applications
4.2 Compound Inequalities
(33 exercises)
- Solve compound inequalities involving or
- Solve compound inequalities involving and
4.3 Absolute Value Equations
(27 exercises)
- Solve absolute value equations
4.4 Absolute Value Inequalities
(26 exercises)
- Solve absolute value inequalities of the form $|x|>a$
- Solve absolute value inequalities of the form $|x|<a$
4.5 Graphing Linear Inequalities in Two Variables
(30 exercises)
- Determine ordered pairs that are solutions to linear inequalities in two variables
- Graph linear inequalities in two variables
5.1 Solving Systems of Linear Equations by Graphing
(23 exercises)
- Determine if an ordered pair is a solution of a system of equations in two variables
- Solve a system of linear equations by graphing
5.2 Solving Systems of Linear Equations by Substitution
(20 exercises)
- Use the substitution method to solve a system of linear equations
5.3 Solving Systems of Linear Equations by Elimination
(23 exercises)
- Use the addition method to solve a system of linear equations
5.4 Systems of Linear Equations and Problem Solving
(22 exercises)
- Choose a solution that satisfies the given conditions
- Write a system of equations to describe a situation
- Use a system of equations to solve problems
5.5 Systems of Linear Inequalities
(16 exercises)
- Solve systems of linear inequalities
- Use mathematical models involving linear inequalities
5.7 Mean, Median, and Mode
(17 exercises)
- Calculate mean, median, and mode
- Determine effects of linear transformations of data
- Work with box plots
- Use box plots to discuss and compare data sets
- Determine the median, first and third quartiles, and interquartile range of a data set
- Work with measures of central tendency
6.1 Exponents
(39 exercises)
- Evaluate exponential expressions
- Use the product rule for exponents
- Use the power rules for products and quotients
- Use the quotient rule for exponents, and define a number raised to the 0 power
- Decide which rule(s exercises) to use to simplify an expression
6.2 Adding and Subtracting Polynomials
(45 exercises)
- Vocabulary and Readiness Check
- Define polynomial, monomial, binomial, trinomial, and degree
- Find the value of a polynomial given replacement values for the variables
- Simplify a polynomial by combining like terms
- Add and subtract polynomials
6.3 Multiplying Polynomials
(41 exercises)
- Use the distributive property to multiply polynomials
6.4 Special Products
(28 exercises)
- Square a binomial
- Multiply the sum and difference of two terms
6.5 Negative Exponents
(32 exercises)
- Simplify expressions containing negative exponents
- Use all the rules and definitions for exponents to simplify exponential expressions
6.6 Graphing Exponential Functions and Using the Compound Interest Formula
(30 exercises)
- Graph exponential functions
- Graph transformations of exponential functions
- Use the compound interest formula
6.7 Exponential Growth and Decay Functions
(10 exercises)
- Model exponential growth
- Model exponential decay
- Model exponential decay with half-life
A.F Arithmetic and Geometric Sequences
(27 exercises)
- Identify arithmetic sequences and their common differences
- Identify geometric sequences and their common ratios
- Determine if a sequence is arithmetic or geometric
7.1 Greatest Common Factor and Factoring by Grouping
(29 exercises)
- Find the greatest common factor of a list of integers
- Factor out the greatest common factor from a polynomial
- Factor a polynomial by grouping
7.2 Factoring Trinomials of the Form $x^2+bx+c$
(40 exercises)
- Factor trinomials of the form $x^2+bx+c$
- Factor out greatest common factor and factor a trinomial of the form $x^2+bx+c$
7.3 Factoring Trinomials of the Form $ax^2+bx+c$ and Perfect Square Trinomials
(47 exercises)
- Factor trinomials of the form $ax^2+bx+c$, where $a$ is not equal to 1
- Factor out a GCF before factoring a trinomial of the form $ax^2+bx+c$
- Use the grouping method to factor trinomials of the form $ax^2+bx+c$
- Factor perfect square trinomials
7.5 Factoring Binomials
(24 exercises)
- Factor the difference of two squares
- Factor other binomials
7.6 Solving Quadratic Equations by Factoring
(25 exercises)
- Use the zero factor theorem
- Solve quadratic equations by factoring
- Solve equations with degree greater than 2 by factoring
7.7 Solving Quadratic Equations and Problem Solving
(26 exercises)
- Solve problems that can be modeled by quadratic equations
9.2 and 9.4 Simplifying Square Roots and Rationalizing Denominators
(21 exercises)
- Use the product rule to simplify square roots
- Use the quotient rule to simplify square roots
- Rationalize denominators
10.1 Solving Quadratic Equations by the Square Root Property
(27 exercises)
- Use the square root property to solve quadratic equations
- Solve problems modeled by quadratic equations
10.2 Solving Quadratic Equations by Completing the Square
(13 exercises)
- Write perfect square trinomials
- Solve quadratic equations of the form $x^2+bx+c=0$ by completing the square
- Solve quadratic equations of the form $ax^2+bx+c=0$ by completing the square
10.3 Solving Quadratic Equations by the Quadratic Formula
(26 exercises)
- Use the quadratic formula to solve quadratic equations
- Approximate solutions to quadratic equations
- Determine the number of solutions of a quadratic equation using the discriminant
- Solve geometric problems modeled by quadratic equations
10.4 Quadratic Functions and Their Graphs
(49 exercises)
- Graph quadratic functions of the form $f(x)=a(x-h)^2+k$
- Write quadratic functions in the form $f(x)=a(x-h)^2+k$
- Use the vertex formula to help graph quadratic functions of the form $f(x)=ax^2+bx+c$
Course Profile
| Name | Last Modified |
|---|---|
| Algebra I COURSE PROFILE with Supplemental Activities 7-13-2022 [docx] | 2022-07-13 |