PRECALCULUS, PART 2

Price: $95 | Credits: 5 | Dept: Math | Course ID# 225-2

This course is designed to be the second semester of Precalculus. Students will build on previous fundamental concepts from Algebra I, Geometry, and Algebra II or Integrated Math 1, 2, & 3 courses. Students will use the concepts in this course, especially functions to strengthen previous mathematical reasoning and conceptual understanding for mathematical problem solving. Proficiency with these topics is especially important for students who are interested in preparing for college math courses and/or who intend to study Calculus.  Precalculus is approved by the University of California A-G as mathematics (category C).

Upon completion of this course, the student is awarded 5 credits. Each credit corresponds to 15 hours of study. Of course, some students work more quickly than others, and some can devote more hours to study, so some students are able to complete the course in an accelerated rate.

LEARNING OBJECTIVES

In this module, students gain a comprehension of the following:

  • How to graph points using polar coordinates and graph polar equations.
  • How to convert between rectangular and polar coordinates and equations.
  • How complex numbers can be represented in polar form, as well as, performing operations and defining certain characteristics of complex numbers when written in polar form.
  • How to perform operations with matrices, find inverses and determinants of matrices.
  • Understand different methods for solving systems of linear equations using matrices. 
  • What vectors are and what defines them.
  • How to express vectors both algebraically and graphically and perform operations with them.
  • Explore two-dimensional as well as three-dimensional vectors, and apply the knowledge to solve real-world problems.
  • Understand four conic sections – circles, ellipses, parabolas, and hyperbolas. 
  • How to write equations for the four different conic sections, plus how to identify important characteristics about each of them and use those characteristics to graph them accurately.
  • Classify conic sections if they are given in general form, as well as being able to write equations and graph conic sections that have been rotated from the usual x-y plane.
  • Understand parametric equations and their significance in solving real-world problems involving projectile motion.
  • Different kinds of ordered lists of numbers called sequences and their sums, called series – arithmetic and geometric.
  • The Binomial Theorem
  • Probability – counting principles for calculating probabilities of certain events occurring.
  • Preview of Calculus – the three major fundamental concepts taught in a typical Calculus course. 

TOPICS COVERED

This course covers the following topics:

  • Polar coordinates and complex numbers.
  • Matrices.
  • Vectors.
  • Conic sections and parametric equations.
  • Sequences, probability, and introduction to calculus
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