### Integrated Math IV (3018) WV

Integrated Math IV (3018) WV is a full-year, high school credit course that is intended for the student who has successfully mastered core algebraic and conceptual geometric concepts. The course primarily focuses on the skills and methods of analyticgeometry and trigonometry while investigating further relationships in functions, probability, number theory, limits, and the introduction of derivatives.

#### CURRICULUM CONTENT AND SKILLS FOCUS

UNIT 1: RELATIONS AND FUNCTIONS
Students will examine functions and inverses of functions and combine functions to verify inverses.

UNIT 2: FUNCTIONS
Students will solve polynomials using the quadratic theorem, remainder theorem and factor theorem. They will identify graphs of different polynomial equations and inequalities and understand complex numbers.

UNIT 3: TRIGONOMETRIC FUNCTIONS
Students will identify and solve for missing components of trigonometric functions, calculating trigonometric values for different angles. They will relate degrees to radians and radians to degrees.

UNIT 4: TRIGONOMETRIC FUNCTIONS AND THEIR GRAPHS
Students will use parametric equations with trigonometric operations to model and solve problems. They will calculate amplitude, period, and phase shift for graphed trigonometric functions.

UNIT 5: INVERSE TRIGONOMETRIC FUNCTIONS
Students will solve for unknowns using inverse trigonometric functions and recognize their graphs.

UNIT 6: IDENTITIES AND FUNCTIONS OF MULTIPLE ANGLES
Students will simplify trigonometric expressions utilizing trigonometric identities and double and half-angel formulas.  They will combine the identities and angle formulas learned in this unit to prove trigonometric relationships.

UNIT 8: APPLICATION OF TRIGONOMETRIC FUNCTIONS
Students will solve problems using trigonometric functions, and combine trigonometric functions and vectors to solve incline plane problems and navigation problems.

UNIT 9: VECTORS AND POLAR AND PARAMETRIC FUNCTIONS
Students will study vectors and convert equations from Cartesian to polar coordinates and from polar to Cartesian coordinates.

UNIT 10: CONIC SECTIONS
Students will identify properties and equations of circles, ellipses, parabolas and hyperbolas. They will calculate point rotations and apply them to equations.

UNIT 11: SEQUENCES AND SERIES
Students will use the explicit formula and the recursive formula to find the nth term as well as the general term of an arithmetic sequence or geometric sequence.  They will calculate basic and combined summations and apply mathematical induction.

UNIT 12: INFERENCES AND CONCLUSIONS FROM DATA
Students will find the mean, median, and mode of a given set of data. They will present and interpret data presented in a histogram, dot plot, or box-and-whisker plot, and calculate expected value.

State: National