# Mathematics Pre Calculus

Scope and Sequence: Mathematics

Course/Grade _Precalculus_

 Quarter 1 Quarter 2 Quarter 3 Quarter 4 Unit Titles Linear Algebra and Matrices  Polynomial and Rational Functions Exponential and Logarithmic Functions  Trig Functions Sequences and Series  Analytica Geometry Limits  Derivatives Learning Outcomes (grade level expectations or standards) Solving Systems Linear (with 3 or more variables) Augmented Matrices Matrices on Calculators Applications – Real world Area of Triangle Test Points to see if Collinear Decoding  Domain and Range Real Value vs. Discrete Functions Graph and model Find maximum and minimum values Find zeros Increasing vs. Decreasing Concavity Inverse and Direct Variation Limits of functions Composition of Functions Composition of Inverse functions Define and Graph Describe the behavior Find Domain and Range Simplify exponential and logarithmic expressions Find the inverse of an exponential equation Properties of the logarithmic expressions Solve exponential and logarithmic equations Change the bases of a logarithmic expression Solve real world problems Base e and the natural logarithm  Analyzing Trig functions Circular functions Identities Graphing Increasing and decreasing Transformations Solving trig equations Trigonometric formulas Sum and difference Multiple angle Product to Sum Laws of Sines and Cosines Solving problems using laws of trigonometry Inverse trig functions Applications of trigonometry to real world situations Series Sequences Define and graph sequences and series Calculate the nth term of a sequence and series Recursive Formulas Explicit Formulas Sum of sequences Limits (lower and upper bound) The Binomial theorem  Analytical Geometry Points and lines in Space Conic sections Parabola Ellipse Hyperbola Vectors: Graphing Addition and Subtraction Dot (Cross) Product Three dimensional coordinates Lines and Planes in space Transformation of Geometric figures in the coordinate plane Limits Continuity Tangent lines and slopes Riemann Sum Area under the curve Significant Task (names only) Solving Systems of Multiple Equations  Linear Programing  Analysis of Parabolas  Asymptotes and End Behavior Financial Planning  Exponential growth and decay  Proving Identities  Analysis of sinusoids Technology and Recursives Sequences and Series in real life Analysis of conic sections I Analysis of conic sections 2 Continuous Functions  Limits of Rational Functions  Max/min problems  Definition of derivative Content Supporting Materials (text, calcs, manips) Student text Supporting software Graphing calculators Web-based applications Student text Supporting software Graphing calculators Web-based applications Student text Supporting software Graphing calculators Web-based applications Student text Supporting software Graphing calculators Web-based applications