Precalculus – 12 (hrs)
Nov 06, 2020 20201124 12:43Precalculus – 12 (hrs)
Precalculus – 12 (hrs)
This leads to a return to the study of complex numbers and a study of linear transformations in the complex plane. Students develop an understanding that when complex numbers are considered points in the Cartesian plane, complex number multiplication has the geometric effect of a rotation followed by a dilation in the complex plane.
Students viewed matrices as representing transformations in the plane and developed an understanding of multiplication of a matrix by a vector as a transformation acting on a point in the plane.
Students look at incidence relationships in networks and encode information about them via highdimensional matrices. Questions on counting routes, the results of combining networks, payoffs, and other applications, provide context and use for matrix manipulations: matrix addition and subtraction, matrix product, and multiplication of matrices by scalars.
Students back to the study of complex roots of polynomial functions. Students first briefly review quadratic and cubic functions and then extend familiar polynomial identities to both complex numbers and to general polynomial functions. Students use polynomial identities to find square roots of complex numbers. The binomial theorem and its relationship to Pascal’s triangle are explored using roots of unity. Revisits, unites, and further expands those ideas and introduces new tools for solving geometric and modeling problems through the power of trigonometry. Helps students recall how to use special triangles positioned within the unit circle to determine geometrically the values of sine, cosine, and tangent at special angles.
The multiplication rule for independent events introduced in Algebra II is generalized to a rule that can be used to calculate the probability of the intersection of two events in situations where the two events are not independent. In this topic, students are also introduced to three techniques for counting outcomes—the fundamental counting principle, permutations, and combinations. These techniques are then used to calculate probabilities, and these probabilities are interpreted in context.

Complex Numbers and Transformations
 Complex Numbers as Vectors Copy
 Complex Number Division Copy
 The Geometric Effect of Some Complex Arithmetic Copy
 Distance and Complex Numbers Copy
 Trigonometry and Complex Numbers Copy
 Discovering the Geometric Effect of Complex Multiplication Copy
 Justifying the Geometric Effect of Complex Multiplication Copy
 Representing Reflections with Transformations Copy
 The Geometric Effect of Multiplying by a Reciprocal Copy
 The Power of the Right Notation Copy
 Exploiting the Connection to Trigonometry Copy
 Exploiting the Connection to Cartesian Coordinates Copy
 Modeling Video Game Motion with Matrices Copy
 Matrix Notation Encompasses New Transformations Copy

Vectors and Matrices
 Networks and Matrix Arithmetic Copy
 Coordinates of Points in Space Copy
 Linear Transformations as Matrices Copy
 Linear Transformations Applied to Cubes Copy
 Composition of Linear Transformations Copy
 Matrix Addition Is Commutative Copy
 Matrix Multiplication Is Distributive and Associative Copy
 Using Matrix Operations for Encryption Copy
 Solving Equations Involving Linear Transformations of the Coordinate Plane Copy
 Solving General Systems of Linear Equations Copy
 Vectors in the Coordinate Plane Copy

Rational and Exponential Functions
 Solutions to Polynomial Equations Copy
 Roots of Unity Copy
 The Binomial Theorem Copy
 Curves in the Complex Plane Copy
 Curves from Geometry Copy
 Volume and Cavalieri’s Principle Copy
 The Structure of Rational Expressions Copy
 Rational Functions Copy
 End Behavior of Rational Functions Copy
 Horizontal and Vertical Asymptotes of Graphs of Rational Functions Copy
 Graphing Rational Functions Copy
 Transforming Rational Functions Copy
 Function Composition Copy
 Solving Problems by Function Composition Copy
 Inverse Functions Copy
 Inverses of Logarithmic and Exponential Functions Copy
 An Area Formula for Triangles Copy
 Law of Sines Copy
 Law of Cosines Copy

Trigonometry
 Special Triangles and the Unit Circle Copy
 Properties of Trigonometric Functions Copy
 Addition and Subtraction Formulas Copy
 Tangent Lines and the Tangent Function Copy
 Waves, Sinusoids, and Identities Copy
 Revisiting the Graphs of the Trigonometric Functions Copy
 Inverse Trigonometric Functions Copy
 Modeling with Inverse Trigonometric Functions Copy

Probability and Statistics
 The General Multiplication Rule Copy
 Counting Rules—The Fundamental Counting Principle and Permutations Copy
 Counting Rules―Combinations Copy
 Using Permutations and Combinations to Compute Probabilities Copy
 Discrete Random Variables Copy
 Probability Distribution of a Discrete Random Variable Copy
 Expected Value of a Discrete Random Variable Copy
 Interpreting Expected Value Copy
 Determining Discrete Probability Distributions Copy
 Estimating Probability Distributions Empirically Copy
 Games of Chance and Expected Value Copy
 Using Expected Values to Compare Strategies Copy
 Making Fair Decisions Copy
 Analyzing Decisions and Strategies Using Probability Copy