Dual Enrollment Program Support Course: Advanced Math Pre-Calculus
This full-year support course (high school credit only) is designed to be ... in support of ... ?
Course Details
- Course Offered
- Fall and Spring (full-year course)
Topics and Objectives
Chapter and section numbers refer to Algebra & Trigonometry, 4e (Kirk Trigsted).
1.1 Linear and Rational Equations
(51 exercises)
- Recognize linear equations
- Solve linear equations with integer coefficients
- Solve linear equations involving fractions
- Solve linear equations involving decimals
- Recognize rational equations
- Solve rational equations that lead to linear equations
1.4 Quadratic Equations
(44 exercises)
- Solve quadratic equations by factoring
- Solve quadratic equations using the square root property
- Solve quadratic equations using the quadratic formula
- Use the discriminant to determine the type of solutions of a quadratic equation
1.6 Other Types of Equations
(40 exercises)
- Solve higher-order polynomial equations
- Solve equations that are quadratic in form
- Solve equations involving single radicals
1.7 Linear Inequalities
(26 exercises)
- Solve linear inequalities in one variable
- Solve three-part inequalities in one variable
1.8 Absolute Value Equations and Inequalities
(34 exercises)
- Solve absolute value equations
- Solve absolute value “less than” inequalities
- Solve absolute value “greater than” inequalities
2.1 The Rectangular Coordinate System
(28 exercises)
- Plot ordered pairs
- Find intercepts of graphs from equations
- Find the midpoint of a line segment using the midpoint formula
- Find the distance between two points using the distance formula
2.2 Circles
(36 exercises)
- Write the standard form of an equation of a circle
- Find the center, radius, intercepts, and sketch the graph of circles given equations in standard form
- Find the center, radius, intercepts, and sketch the graph of circles given equations in general form
2.3 Lines
(54 exercises)
- Determine the slopes of lines through two given points
- Sketch lines given a point and the slope
- Find the equation of a line using the point-slope form
- Find the equation of a line using the slope-intercept form
- Find the equation of a horizontal line and a vertical line
- Write the equation of a line in standard form
- Find the slope and the y-intercept of a line in standard form
- Sketch lines by plotting intercepts
- Sketch a line given its equation in standard form
2.4 Parallel and Perpendicular Lines
(32 exercises)
- Determine whether two lines are parallel, perpendicular, or neither
- Find the equations of lines parallel to given lines
- Find the equations of lines perpendicular to given lines
3.1 Relations and Functions
(56 exercises)
- Find the domain and range of relations, and determine if relations represent functions
- Determine whether equations represent functions
- Use function notation and evaluate functions at given values
- Determine difference quotients
- Use the vertical line test to determine if graphs represent functions
- Classify functions as polynomials, rational functions, or root functions, and find their domains
3.2 Properties of a Function’s Graph
(42 exercises)
- Determine the intercepts of a function
- Determine the domain and range of a function from its graph
- Determine where functions are increasing, decreasing, or constant
- Determine relative maximum and relative minimum values of a function
- Determine whether a function if even, odd, or neither
- Identify function properties from graphs
3.3 Graphs of Basic Functions; Piecewise Functions
(26 exercises)
- Sketch the graphs of the basic functions
- Sketch graphs of basic functions with restricted domains
- Determine functions and their domains from graphs of piecewise-defined functions
- Graph and determine properties of piecewise-defined functions
3.4 Transformations of Functions
(43 exercises)
- Use vertical shifts to graph functions
- Use horizontal shifts to graph functions
- Use vertical stretches and compressions to graph functions
- Use combinations of transformations to graph functions
- Use transformations to sketch the graphs of piecewise-defined functions
3.5 Composite Functions
(19 exercises)
- Find composite functions
- Evaluate composite functions at a given point
3.6 One-to-One Functions; Inverse Functions
(44 exercises)
- Determine if functions are one-to-one
- Determine whether a function is one-to-one using the horizontal line test
- Verify functions are inverses of one another
- Find inverses of one-to-one functions
- Sketch the graphs of inverse functions
- Use the graphs of functions to determine properties about its inverse
4.1 Quadratic Functions
(36 exercises)
- Determine whether the graph of a quadratic function opens up or down
- Determine properties of quadratic function in vertex form and graph the function
- Determine properties of quadratic function using the vertex formula and graph the function
- Determine the equation of a quadratic function given its graph
4.2 Applications of Quadratic Functions
(10 exercises)
- Solve applications involving the maximum of projectile motion functions
- Solve applications involving the maximum of functions in economics
4.3 Graphs of Polynomial Functions
(36 exercises)
- Identify polynomial functions and their degree, leading coefficient, and constant coefficient
- Sketch the graphs of power functions using transformations
- Use the end behavior of polynomial functions to describe the equation of the function
- Determine the intercepts of a polynomial function
- Determine the real zeros of polynomial functions and their multiplicities
- Sketch the graph of a polynomial function using the four-step process
- Determine a possible equation of a polynomial function given its graph
4.6 Rational Functions and Their Graphs
(36 exercises)
- Find the domain and intercepts of rational functions
- Identify vertical asymptotes
- Identify horizontal asymptotes
- Use transformations to sketch the graphs of rational functions
- Find removable discontinuities, intercepts, and asymptotes and sketch graphs of rational functions
5.1 Exponential Functions
(46 exercises)
- Evaluate exponential expressions
- Sketch the graphs of exponential functions
- Determine possible equations of exponential functions given their graphs
- Sketch the graphs of exponential functions using transformations
- Solve exponential equations by relating the bases
- Solve applications involving exponential functions
5.2 Logarithmic Functions
(56 exercises)
- Change equations between exponential form and logarithmic form
- Evaluate logarithmic expressions
- Use properties of logarithms to evaluate expressions
- Use common and natural logarithms
- Sketch the graphs of logarithmic functions
- Find the domain of logarithmic functions
5.3 Properties of Logarithms
(44 exercises)
- Expand and evaluate logarithmic expressions using properties of logarithms
- Condense and evaluate logarithmic expressions using properties of logarithms
- Solve logarithmic equations using the logarithm property of equality
- Use the change of base formula to approximate logarithmic expressions
5.4 Exponential and Logarithmic Equations
(40 exercises)
- Solve exponential equations
- Solve logarithmic equations
5.5 Applications of Exponential and Logarithmic Functions
(16 exercises)
- Solve applications involving compound interest
- Solve exponential growth and decay applications
12.1 Systems of Linear Equations in Two Variables
(13 exercises)
- Verify solutions to a system of linear equations in two variables
- Solve systems of linear equations using the substitution method
- Solve systems of linear equations using the elimination method
- Solve systems of linear equations in two variables using either method
- Solve applied problems using a system of linear equation
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6.1 An Introduction to Angles: Degree and Radian Measure
(58 exercises)
- Understand degree measure
- Understand radian measure
- Convert between degree measure and radian measure
- Find coterminal angles using degree measure
- Find coterminal angles using radian measure
6.3 Triangles
(17 exercises)
- Classify triangles
- Use the Pythagorean Theorem
- Understand similar triangles
- Understand the special right triangles
6.4 Right Triangle Trigonometry
(55 exercises)
- Understand the right triangle definitions of the trigonometric functions
- Use the special right triangles
- Understand the fundamental trigonometric identities
- Understand cofunctions
- Evaluate trigonometric functions using a calculator
6.5 Trigonometric Functions of General Angles
(77 exercises)
- Understand the four families of special angles
- Understand the definitions of the trigonometric functions of general angles
- Find the values of the trigonometric functions of quadrantal angles
- Understand the signs of the trigonometric functions
- Determine reference angles
- Evaluate trigonometric functions of angles belonging to the $\tfrac\pi6$, $\tfrac\pi4$, and $\tfrac\pi3$ families
6.6 The Unit Circle
(9 exercises)
- Understand the definition of the unit circle
- Understand the unit circle definitions of the trigonometric functions
7.1 Graphs of Sine and Cosine Functions
(46 exercises)
- Understand the graph of the sine function and its properties
- Understand the graph of the cosine function and its properties
- Determine properties and sketch graphs of the form $y=A\sin x$ and $y=A\cos x$
- Determine properties and sketch graphs of the form $y=\sin(Bx)$ and $y=\cos(Bx)$
- Determine properties and sketch graphs of the form $y=A\sin(Bx)$ and $y=A\cos(Bx)$
- Determine the equation of a function of the form $y=A\sin(Bx)$ and $y=A\cos(Bx)$ given its graph
7.2 Graphs of Sine and Cosine: Phase Shift & Vertical Shift
(20 exercises)
- Determine properties and sketch graphs of the form and
- Determine properties and sketch graphs of the form and
- Determine properties and sketch graphs of the form and
- Determine the equation of a function of the form and given its graph
7.3 Graphs of Secant, Cosecant, Tangent, and Cotangent
(10 exercises)
- Understand the graph of the tangent function and its properties
- Understand the graph of the cotangent function and its properties
- Understand the graphs of the cosecant and secant functions and their properties
7.4 Inverse Trigonometric Functions Part I
(34 exercises)
- Understand and find the exact and approximate values of the inverse sine function
- Understand and find the exact and approximate values of the inverse cosine function
- Understand and find the exact and approximate values of the inverse tangent function
8.1 Trigonometric Identities
(35 exercises)
- Review and use the fundamental identities
- Verify trigonometric identities
8.2 The Sum and Difference Formulas
(48 exercises)
- Use the sum and difference formulas for the cosine function
- Use the sum and difference formulas for the sine function
- Use the sum and difference formulas for the tangent function
- Use the sum and difference formulas to verify identities
- Use sum and difference formulas to evaluate expressions involving inverse trig functions
8.5 Trigonometric Equations
(32 exercises)
- Solve trigonometric equations that are quadratic in form
- Solve trigonometric equations using identities
- Solve trigonometric equations using a calculator
9.1 Right Triangle Applications
(16 exercises)
- Solve right triangles
- Solve applied problems using right triangles
9.2 The Law of Sines
(31 exercises)
- Determine if the Law of Sines can be used to solve an oblique triangle
- Use the Law of Sines to solve the SAA case or the ASA case
- Use the Law of Sines to solve the SSA (ambiguous) case
- Use the Law of Sines to solve applied problems involving oblique triangles
9.3 The Law of Cosines
(26 exercises)
- Determine whether Law of Sines or Cosines should be used to solve an oblique triangle
- Use the Law of Cosines to solve the SAS case
- Use the Law of Cosines to solve the SSS case
- Use the Law of Cosines to solve applied problems involving oblique triangles
9.4 Area of Triangles
(17 exercises)
- Determine the area of oblique triangles
- Use Heron’s Formula to determine the area of an SSS triangle
- Solve applied problems involving the area of triangles
10.1 Polar Coordinates and Equations
(63 exercises)
- Plot points using polar coordinates
- Determine different representations of a point $(r,\theta)$
- Convert from polar to rectangular coordinates
- Convert from rectangular to polar coordinates
- Convert equations from rectangular to polar form
- Convert equations from polar to rectangular form
10.2 Graphing Polar Equations
(35 exercises)
- Sketch equations of the form $r\cos\theta=a$, $r\sin\theta=a$, $ar\cos\theta+br\sin\theta=c$, and $\theta=a$
- Sketch equations of the form $r=a$, $r=a\sin\theta$, and $r=a\cos\theta$
- Sketch equations of the form $r=a+b\sin\theta$ and $r=a+b\cos\theta$
Course Profile
| Name | Last Modified |
|---|---|
| Advanced Math Precalculus COURSE PROFILE 11-14-2025 [docx] | 2025-12-10 |