Dual Enrollment Program Pre-DE Course: Algebra II
[Description?]
Topics and Objectives
Chapter and section numbers refer to Algebra 2 in MyMathLab.
4.1 Solving Systems of Equations in Two Variables
(30 exercises)
- Determine whether an ordered pair is solution of a system of two linear equations
- Solve a system by graphing
- Solve a system by substitution
- Solve a system by elimination
- Solve applications
4.2 Solving Systems of Equations in Three Variables
(13 exercises)
- Determine whether an ordered triple is a solution of system of three linear equations
- Solve a system of three linear equations in three variables
4.3 Systems of Linear Equations and Problem Solving
(18 exercises)
- Solve problems that can be modeled by a system of two linear equations
- Solve problems with cost and revenue functions
- Solve problems that can be modeled by a system of three linear equations
6.5 The Greatest Common Factor and Factoring by Grouping
(17 exercises)
- Factor out the GCF of a polynomial’s terms
- Factor polynomials by grouping
6.6 Factoring Trinomials
(31 exercises)
- Factor trinomials of the form $x^2 + b x + c$
- Factor trinomials of the form $a x^2 + b x + c$ by trial and check or by grouping
- Factor by substitution
6.7 Factoring by Special Products
(30 exercises)
- Factor a perfect square trinomial
- Factor the difference of two squares
- Factor the sum or difference of two cubes
6.8 Solving Equations by Factoring and Problem Solving
(22 exercises)
- Solve polynomial equations by factoring
- Solve problems that can be modeled by polynomial equations
- Find the $x$-intercepts of a polynomial function
7.1 Rational Expressions
(20 exercises)
- Find the domains of rational expressions
- Simplify rational expressions
7.4a Dividing Polynomials
(23 exercises)
- Divide a polynomial by a monomial
- Divide by a polynomial
- Use synthetic division to divide a polynomial by a binomial
7.4b Dividing Polynomials
(11 exercises)
- Use the remainder theorem to evaluate polynomials
- Use the factor theorem
7.5 Solving Equations Containing Rational Expressions
(28 exercises)
- Solve equations containing rational expressions
7.6 Rational Equations and Problem Solving
(23 exercises)
- Solve equations that contain radical expressions
- Use the Pythagorean Theorem to model problems
- Solve application problems
8.1 Radicals and Radical Functions
(31 exercises)
- Find square roots
- Approximate roots
- Find cube roots
- Find $n$th roots
- Find the $n$th root of $a^n$, where $a$ is a real number
- Graph square root and cube root functions
8.2 Rational Exponents
(41 exercises)
- Understand the meaning of $a^{1 \over n}$
- Understand the meaning of $a^{m \over n}$
- Understand the meaning of $a^{-{m \over n}}$
- Use rules for exponents to simplify expressions that contain rational exponents
- Use rational exponents to simplify radical expressions
8.3 Simplifying Radical Expressions
(27 exercises)
- Use the product rule for radicals
- Use the quotient rule for radicals
- Simplify radicals
8.4 Adding, Subtracting, and Multiplying Radical Expressions
(34 exercises)
- Add or subtract radical expressions
- Multiply radical expressions
8.5 Rationalizing Denominators and Numerators of Radical Expressions
(23 exercises)
- Rationalize denominators
- Rationalize denominators having two terms
- Rationalize numerators
8.6 Solving Radical Equations
(28 exercises)
- Solve equations that contain radical expressions
- Use the Pythagorean Theorem to model problems
- Solve application problems
8.7 Complex Numbers
(46 exercises)
- Write square roots of negative numbers in the form $b i$
- Add or subtract complex numbers
- Multiply complex numbers
- Raise $i$ to powers
9.1 Solving Quadratic Equations by Completing the Square
(32 exercises)
- Use the square root property to solve quadratic equations
- Complete and factor a perfect square trinomial
- Solve quadratic equations by completing the square
- Use quadratic equations to solve problems
9.2 Solving Quadratic Equations by the Quadratic Formula
(23 exercises)
- Solve quadratic equations by using the quadratic formula
- Determine number and type of solutions of quadratic equations using discriminant
- Solve geometric problems modeled by quadratic equations
11.7 Solving Nonlinear Systems of Equations
(14 exercises)
- Solve a nonlinear system by substitution
- Solve a nonlinear system by elimination
- Verify solutions to nonlinear systems found using graphs
9.3 Solving Equations by Using Quadratic Methods
(24 exercises)
- Solve quadratic equations by squaring both sides
- Solve quadratic equations by multiplying by the lowest common denominator
- Solve higher degree equations in quadratic form
- Solve equations by converting to a quadratic with substitution
- Solve various equations that are quadratic in form
- Solve problems that lead to quadratic equations
9.4 Zeros of Polynomial Functions
(19 exercises)
- Find zeros of a polynomial function and their multiplicities
- Use the factor theorem and synthetic division
- Find polynomials with given zeros
9.5 Graphs of Polynomial Functions
(33 exercises)
- Graph even and odd power functions
- Describe the end behavior of a polynomial function
- Find the $x$-intercepts of a polynomial function
- Find the maximum number of real zeros, $x$-intercepts, and turning points of a polynomial equation
- Graph polynomial functions
10.2 Inverse Functions
(22 exercises)
- Determine whether a function is a one-to-one function
- Find the inverse of a function
- Use the horizontal line test to decide whether a function is a one-to-one function
- Find the equation of the inverse of a function
- Graph functions and their inverses
10.3 Exponential Functions
(47 exercises)
- Evaluate exponential expressions
- Graph exponential functions
- Graph exponential functions using transformations
- Solve equations of the form $b^x = b^y$
- Solve problems modeled by exponential equations
- Use compound interest formulas to find investment values
10.4 Logarithmic Functions
(46 exercises)
- Convert between logarithmic and exponential notation
- Find the value of logarithmic expressions
- Solve logarithmic equations by using exponential notation
- Simplify using the properties of logarithms
- Identify and graph logarithmic functions
10.5 Properties of Logarithms
(38 exercises)
- Use the product property of logarithms
- Use the quotient property of logarithms
- Use the power property of logarithms
- Use the properties of logarithms together
10.6 Common Logarithms, Natural Logarithms, and Change of Base
(33 exercises)
- Identify and approximate common logarithms
- Identify and approximate natural logarithms
- Evaluate common logarithms of powers of 10
- Evaluate natural logarithms of powers of $e$
- Solve logarithmic equations
- Use the change of base formula
- Solve applications
10.7 Exponential and Logarithmic Equations and Applications
(34 exercises)
- Solve exponential equations
- Solve logarithmic equations
- Solve problems that can be modeled by exponential and logarithmic equations
12.2 Arithmetic and Geometric Sequences
(22 exercises)
- Identify arithmetic sequences and their common differences
- Identify geometric sequences and their common ratios
- Determine if a sequence is arithmetic or geometric
- Find the $n$th term of a geometric sequence
- Solve applications
12.3 Finite Geometric Sequences
(9 exercises)
- Find the sum of a geometric series
- Solve applications
14.1 Angles and Radian Measure
(42 exercises)
- Use radian measure
- Convert between degrees and radians
- Draw angles in standard position
- Find coterminal angles
- Find the length of a circular arc.
14.2 Right Triangle Trigonometry
(20 exercises)
- Use right triangles to evaluate trigonometric functions
- Find trigonometric function values for 30° $( {\pi \over 6} )$, 45° $( {\pi \over 4} )$, and 60° $( {\pi \over 3} )$
- Recognize and use fundamental identities
- Evaluate trigonometric functions with a calculator
14.3 Trigonometric Functions of Any Angle
(51 exercises)
- Use the definitions of trigonometric functions of any angle
- Use the signs of the trigonometric functions
- Find reference angles
- Use reference angles to evaluate trigonometric functions
14.4 Trig Functions of Real Numbers; Periodic Functions
(25 exercises)
- Use a unit circle to define trigonometric functions of real numbers
- Use even and odd trigonometric functions
- Use periodic properties
- Solve application problems
14.5 Graphs of Sine and Cosine Functions
(39 exercises)
- Understand the graph of $y = \sin x$
- Graph variations of $y = \sin x$
- Understand the graph of $y = \cos x$
- Graph variations of $y = \cos x$
- Use vertical shifts of sine and cosine curves
- Solve Application problems
X.1 Observational Studies, Designed Experiments, and Sample Surveys
(14 exercises)
- Identify characteristics of the design of an experimental study
- Describe effects of an experimental study design on its outcome
- Define terms relating to experiments and studies
- Explain the sources of bias in sampling
X.2 Standard Deviation
(19 exercises)
- Determine the standard deviation for a data set
- Compare two data sets using measures of dispersion
X.3 Normal Distribution
(22 exercises)
- Use and interpret margins of error
- Find scores at a specified standard deviation from the mean
- Use the 68–95–99.7 Rule
- Solve applied problems involving normal distributions
- Understand percentiles and quartiles
- Convert a data item to a $z$-score
Course Profile
| Name | Last Modified |
|---|---|
| Algebra II COURSE PROFILE with Supplemental Activities 7-13-2022 [docx] | 2022-07-13 |