Pre-Calculus
Mathematics Curriculum
Motion: Functions model dynamic phenomena.
In this course, connections between previous algebra and geometry courses are made and used to model real life situations. This includes a rigorous study of polynomial, exponential, logarithmic and trigonometric functions. The AP course may include mathematical induction, the binomial expansion theorem, series, and limits and also follows the core content provided by College Board. A graphing calculator (TI-83 or TI-84) series is required for this course. Students may not earn credit for both Trigonometry and Pre-Calculus.
Unit 1: Polynomial and Rational Functions
Students develop an understanding of two key function concepts while exploring polynomial and rational functions. The first concept is covariation or how output values change in tandem with changing input values. The second concept is rates of change, including average rates of change, rate of change at a point, and changing rates of change. The central idea of a function as a rule for relating two simultaneously changing sets of values provides students with a vital tool that has many applications in nature, human society, and business.
Common Core State Standards: N.CN.A.3-4, N.CN.A.6, IF.B.4-6, IF.C.7d, SSE.A.2, APR.C.5-7, REI.D.11, N.Q.1-3
Unit 2: Exponential and Logarithmic Functions
Students build an understanding of exponential and logarithmic functions. When an aspect of a phenomenon changes proportionally to the existing amount, exponential and logarithmic models are employed to harness the information. Exponential functions are key to modeling population growth, radioactive decay, interest rates, and the amount of medication in a patient. Logarithmic functions are useful in modeling sound intensity and frequency.
Common Core State Standards: A.REI.11, F.IF.4, F.IF.7e, F.IF.8b, F.IF.1c, F.BF.4 - 5, F.LE.1a, F.LE.1c, F.LE.2-5, N.Q.1-3
Unit 3: Trigonometric and Polar Functions
Students explore trigonometric functions and their relation to the angles and arcs of a circle. Trigonometric functions are ideal for modeling periodic or repeated pattern phenomena. Polar functions are also explored and have deep ties to trigonometric functions as they are both based on the circle. Polare functions are defined on the polar coordinate systems that use the circular concepts of radii and angles to describe location instead of rectangular concepts of left-rights and up-down. Trigonometry serves as a bridge between these two systems.
Common Core State Standards: F.TF.1-9, N.Q.1-3, F.IF.7e
Unit 4: Functions Involving Parameters, Ventors and Matrices
Students explore function types that will expand their understanding of the function concepts. Parametric functions have multiple dependent variables' values paired with a single input variable or parameter. Modeling scenarios with parametric functions allows students to explore change in terms of components. Another major function type involves matrices mapping a set of input vectors to output vectors. The capacity to make large quantities of vectors instantaneously is the basis for vector-based computer graphics. This function type can also be applied to any system that can be expressed in terms of components of vectors, such as electrical systems, network connections, and regional population distribution changes over time. Vectors and matrices are also powerful tools of data science as they can be used to model aspects of complex scientific and social science phenomena.
Common Core State Standards: N.CN.4, A.REI, 8 - 9, N.VM. 1 - 5, N.VM.7 - 12