Course Description
Prerequisite: Algebra 2, Geometry
Co-requisite: none
Precalculus serves as the foundational course for the study of Calculus. It's subject matter can be split into three main components: Trigonometry, Linear Algebra and Mathematical Analysis. Topics covered include Systems of Equations, Trigonometry, Exponential and Logarithmic Functions, Polar Coordinates, Vectors, Sequences and Induction.
Course Materials
Precalculus, 4e, Blitzer, Robert, 2010, Pearson
Link to Powerschool for grades Link to SuccessNet for online textboox Essential Standards and Resource Links
| Functions and Graphs | Students are able to manipulate functions through transformations, combinations and composition of functions. Students can find the inverse of a function. Students find the roots and poles of a rational function and can graph the function and locate its asymptotes. |
Exponential and Logarithmic Functions
| Students are familiar with and adept at the addition of complex numbers. They can represent a complex number in polar form and know how to multiply complex numbers in their polar form. They can use the trigonometric form of complex numbers. Students understand and use the properties of logarithms and exponents to simplify expressions, solve problems, approximate or graph them. |
Trigonometry Fundamentals | Students can convert between degrees and radians. Students know the definition of sine and cosine as y- and x- coordinates of points on the unit. Students know the six trigonometric functions and can graph them. Students compute, by hand, the values of the trigonometric functions and the inverse trigonometric functions at various standard points. Students know trig identities such as sum, difference, double and half angle formulas, and can use those formulas to prove or simplify other trig identites. |
Applications of Trigonometry
| Students use trigonometry to determine unknown sides or angles in right triangles. Students know the law of sines and the law of cosines and apply those laws to solve problems. Students are adept at using trigonometry in a variety of applications. Students can determine polar coordinates of a point given in rectangular coordinates and vice versa. Students represent equations given in rectangular coordinates in terms of polar coordinates. Students can find the dot product of two vectors. |
Linear Algebra
| Students solve systems of linear equations and inequalities (in two or three variables) by substation, elimination, and graphically. Students solve linear equations in any number of variables by using Gauss-Jordan elimination. Students can compute the inverse of a matrix using row-reduction methods or Cramer’s rule. |
| Fundamentals of Calculus | Students are familiar with conic sections, both analytically and geometrically, can determine what type of conic section the equation represents; and determine its geometric components (foci, asymptotes, and so forth). Students can give proofs of various formulas by using the technique of mathematical induction.Students are familiar with the notion of the limit of sequences and functions and can determine whether certain sequences converge or diverge. |
