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At the conclusion of this course, the student should be able to:
1. Apply effective learning strategies for transfer level mathematics.
2. Assess and improve their mathematical competency.
3. Solve and graph linear equations in one and two variables, and inequalities in one variable.
4. Evaluate and solve literal equations.
5. Find an equation for a line given information about the line.
6. Perform the operations of addition, subtraction, multiplication, division, and factoring of polynomials.
7. Use the laws of exponents to simplify expressions.
8. Solve application and modeling problems that use a system of equations.
9. Define function, domain, and range, and use function notation.
10. Identify basic features of the graphs of linear, polynomial, radical, rational, exponential, logarithmic, trigonometric, and absolute value functions.
11. Use graphing technology to construct graphs and use to solve nonlinear equations and inequalities in one variable, as well as to locate roots, intersection points, and extrema.
12. Use algebraic methods to solve equations that involve polynomial and radical expressions.
13. Apply algebraic and graphical methods to solve application problems.
14. Simplify and operate on radical, rational, exponential, logarithmic, and absolute value expressions in preparation to succeed in precalculus algebra.
15. Solve equations involving rational, exponential, logarithmic, and absolute value functions.
16. Perform advanced operations with functions (using symbolic, graphical, and numerical representations) and apply knowledge to application and modeling problems.
17. Define and graph inverse functions.
18. Define and apply the trigonometric functions, using right triangle and unit circle approaches, and using degree and radian measures.
19. Identify and interpret characteristics of functions (including intercepts, turning points, extreme values, intervals of positive/negative/increasing/decreasing value, transformations, symmetry, asymptotes, and holes).
20. Graph polynomial, rational, absolute value, radical, exponential, logarithmic, trigonometric, and inverse trigonometric functions.
21. Verify and apply trigonometric identities.
22. Solve equations symbolically and graphically (involving polynomial, rational, absolute value, radical, exponential, logarithmic, and trigonometric functions) over the real numbers; and, as appropriate, the complex numbers.
23. Solve application and modeling problems using the trigonometric functions, identities, and the Laws of Sines and Cosines.
24. Graph piecewise-defined functions.
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I. Topics Related to Developing Effective Learning Strategies
A. Study skills: organization and time management
B. Test preparation and test-taking skills
C. Self-assessment: using performance criteria to judge and improve one's own work, analyzing and correcting errors on one's test
D. Use of strategies identifying, utilizing, and evaluating the effectiveness of resources in improving one's own learning, which may include:
1. Peer study groups
2. Computer resources
3. Lab resources
4. Tutoring resources
5. Growth mindset lessons
II. Concurrent Support for Calculus 1 Topics That May Include:
A. Linear equations and inequalities in one variable
1. Linear equations
2. Applications of linear equations
3. Linear inequalities
4. Formulas
B. Linear equations in two variables
1. Cartesian coordinate system
2. Graphing linear equations, including the slope-intercept method
3. Finding the equation of a line
4. Systems of equations in two variables
C. Functions
1. Definition of relation, function, domain, and range
2. Function notation and evaluation
3. Interval notation, intersection, and union
4. Operations, including difference quotients and composition of functions
5. Catalog of functions
6. Analyze graphs of linear, polynomial, and radical functions with and without graphing technology
7. Symmetry (even and odd functions)
8. Analysis of Functions and Their Graphs
9. Transformations of graphs (shifts, scaling, and reflections)
10. Modeling
D. Polynomial and rational functions
1. Definition
2. Operations
3. Factoring
4. Solving polynomial equations by factoring
5. Graphs of Quadratic and polynomial functions of higher degree
6. Quadratic Functions
a. Vertex and general forms
b. Discriminant
c. Solutions to quadratic equations using factoring, quadratic formula, and completing the square
7. Long division of polynomials
8. Graphs of rational functions
9. Domain and range of Rational Functions
10. Asymptotes and holes
11. Introduction to limit concepts and notation
12. Solutions of polynomial and rational equations, using real numbers and complex numbers as appropriate
E. Integer exponents and laws of exponents
F. Radicals
1. Square roots
2. Simplification
3. Sums and products of radicals
4. Rationalizing denominators of square roots
5. Higher-index radicals
6. Pythagorean Theorem
7. Radical equations
8. Rational exponents
G. Use of technology
1. Evaluate and graph functions
2. Solve equations and inequalities graphically
H. Equations and inequalities
1. Equations
a. Solutions of literal equations
b. Algebraic and graphical solutions of linear, quadratic, and radical equations
2. Inequalities
a. Algebraic solutions to linear inequalities
b Graphical solutions of linear and nonlinear (radical, quadratic, rational, etc.) inequalities using graphing technology
I. Absolute value functions
1. Domain and range
2. Introduction to graphs
3. Equations
J. Exponential functions
1. Domain and range
2. Graphs
3. Properties
4. Equations
K. Logarithmic functions
1. Domain and range
2. Graphs
3. Properties
4. Expand and condense
5. Equations
L. Introduction to applications and modeling
M. Inverse, exponential, and logarithmic functions
1. Definitions
2. Properties
3. Graphs
4. Equations
5. Applications
N. Trigonometric functions
1. Radian and degree measures of angles
a. Arc length
b. Area of a sector
c. Linear and angular velocity
2. Right triangle and unit circle definitions
3. Characteristics of trigonometric functions
O. Identities and conditional equations
1. Fundamental identities
2. Sum and difference identities
3. Related identities and their derivations
4. Conditional trigonometric equations and applications
P. Graphical representation of trigonometric functions
1. Amplitude
2. Reflections
3. Period
4. Phase (horizontal) shift
5. Vertical shifts
Q. Inverse trigonometric functions
1. Definitions
2. Properties
3. Graphs
R. Solutions of triangles
1. Right triangles
2. Oblique triangles
3. Laws of Sines and Cosines
4. Applications