1: Graphing Functions
1.1: Use paper and pencil methods and graphing technology to graph polynomial, absolute value, rational, algebraic, exponential, logarithmic, trigonometric and inverse trigonometric functions. Identify domain, range, intercepts, zeros, asymptotes and points of discontinuity of functions. Use graphs to solve problems.
Exponential Functions
Graphs of Polynomial Functions
Logarithmic Functions
Rational Functions
2: Conic Sections
2.1: Derive equations for conic sections. Graph conic sections by hand by completing the square and find foci, centers, asymptotes, eccentricity, axes and vertices (as appropriate).
Addition and Subtraction of Functions
Circles
Ellipses
Hyperbolas
Parabolas
3: Logarithmic and Exponential Functions
3.1: Define and find inverse functions. Verify whether two given functions are inverses of each other. Solve problems involving logarithmic and exponential functions using the laws of logarithms and understand why those properties are true.
Logarithmic Functions
4: Unit Circle
4.1: Define sine and cosine using the unit circle, converting between degree and radian measures. Use the values of the sine, cosine and tangent functions at 0, pi/6, pi/4, pi/3 and pi/2 radians and their multiples.
Cosine Function
Sine Function
Tangent Function
5: Trigonometric Functions
5.1: Define and analyze trigonometric functions, including inverse functions. Solve problems involving trigonometric functions and prove trigonometric identities.
Simplifying Trigonometric Expressions
Translating and Scaling Functions
6: Polar Coordinates and Complex Numbers
6.1: Define and use polar coordinates and complex numbers. Graph equations in the polar coordinate plane. Use their relation to trigonometric functions to solve problems.
Points in the Complex Plane
Roots of a Quadratic
7: Sequences and Series
7.1: Define arithmetic and geometric sequences and series. Prove and use the sum formulas for arithmetic series and for finite and infinite geometric series. Understand and use the concept of a limit of a sequence or function as the independent variable approaches infinity or a number, and recognize an infinite series as the limit of a sequence of partial sums. Use series to solve problems. Derive the binomial theorem by combinatorics.
Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences
Correlation last revised: 5/11/2018