Pre-AP Pre-Calculus Syllabus

Course Overview:

This course will cover all topics in the Elmore County Pacing Guide.

The objective of this course is to prepare students for Advanced Placement Calculus and the AP Calculus exam. It will give students an understanding of the mathematical concepts needed for AP Calculus and subsequent college level mathematics courses. It will also provide students with a working knowledge of technology necessary to help them succeed at this level.

The textbook for this course is:

Glencoe Advanced Mathematical Concepts, (2001)

Course Outline:

Unit 1: Preparation for Pre-Calculus

Factoring Polynomials

  • (Supplement by teacher) Factor by grouping and GCF
  • (Supplement by teacher) Special polynomials
  • (Supplement by teacher) Completing the Square
  • (4.2) Solving Quadratic Equations: Completing the Square

and Quadratic Formula

Unit 2: Functions

  • (1.2) Composition of Functions
  • (1.4) Writing Linear Equations
  • (1.5) Writing Equations of Parallel And Perpendicular Lines
  • (1.6) Real World Data with Linear Functions
  • (1.7) Piecewise Functions

Unit 3: Matrices

  • (2.1) Solving Systems with 2 Variables
  • (2.2) Solving Systems with 3 Variable
  • (2.3) Matrix Operations
  • (2.5) Determinates and Multiplicative Inverses

Unit 4: Inverse Functions and Rational Functions

  • (3.1) Symmetry and Coordinate Graphs
  • (3.2) Families of Graphs
  • (3.3) Graphs of Nonlinear Inequalities
  • (3.4) Inverse Functions and Relations
  • (3.5) Continuity and End Behavior
  • (3.6) Critical Points and Extrema
  • (3.7) Graphs of Rational Functions
  • (3.8) Direct, Inverse, and Joint Variation

Unit 5: Trigonometry

  • (5.2) Trigonometric Ratios in Right Triangles
  • (5.3) Trigonometric Ratios on the Unit Circle
  • (5.5) Solving Right Triangles
  • (5.6) The Law of Sines
  • (5.8) The Law of Cosines
  • (6.3) Graphing Sine and Cosine Functions
  • (6.4) Amplitude and Period of Sine and Cosine
  • (6.5) Translations of Sine and Cosine Functions
  • (6.7) Graphing other Trigonometric Functions
  • (6.8) Trigonometric Inverses and Their Graphs
  • (7.1) Basic Trigonometric Identities
  • (7.3) Sum and Difference Identities
  • (7.4) Double Angle and Half Angle Identities
  • (7.5) Solving Trigonometric Equations

Unit 6: Vectors

  • (8.1) Geometric Vectors
  • (8.2) Algebraic Vectors
  • (8.4) Perpendicular Vectors
  • (8.5) Applications with Vectors

Unit 7: Complex Numbers

  • (9.5) Simplifying Complex Numbers
  • (9.6) The Complex Plane and Polar Form of Complex Numbers
  • (9.7) Products and Quotients of Complex Numbers in Polar Form
  • (9.8) Powers and Roots of Complex Numbers

Unit 8: Conics

  • (10.3) Ellipses
  • (10.4) Hyperbolas
  • (10.6) Parametric Equations

Unit 9: Logarithms and Exponents

  • (11.1) Real Exponents
  • (11.2) Exponential Functions
  • (11.3) The Number e
  • (11.4) Logarithmic Functions
  • (11.6) Natural Logarithms

Unit 10: Limits

  • (12.2) Geometric Sequence
  • (12.3) Infinite Sequence
  • (12.6) Binomial Theorem
  • (15.1) Limits
  • (15.2) Derivatives and Antiderivatives
  • (15.3) Area Under a Curve

Unit 11: Statistics and Probability

  • (13.1) Permutations and Combinations
  • (13.2) Permutations with Repetitions and Circular Permutations
  • (13.3) Probability and Odds
  • (13.4) Probabilities and Compound Events
  • (13.5) Conditional Probability
  • (13.6) The Binomial Theorem and Probability

Materials:

It is highly recommended that each student purchase a graphing calculator. The one used extensively throughout the course is the TI-84. I may have a limited number to use in the classroom setting, but it will be necessary for the student to use at home as well. This calculator will serve them through this course as well as the AP Calculus course and any subsequent college math courses your student will take.

Testing:

Tests will be given in the AP Exam format which consists of multiple choice and free response questions. Each set of questions will contain both calculator and no calculator groups. The majority of the tests may be given over a two day period with different types of questions each day. The test days are Tuesday, Thursday, and Friday.

Grading:

The grading for the course will consist of tests, quizzes, and homework/classwork. The percentage for each is as follows:

Tests: 60%

Quizzes, Homework, Classwork: 40%

Quizzes will most often consist of selected pre worked homework problems, as well as separate given quizzes.

Students who perform poorly on a test will be allowed to make corrections for additional points.

Percentage / Letter
89.5% to 100% / A
79.5% to 89.49% / B
69.5% to 79.49% / C
59.5% to 69.49% / D
Below 59.5% / F

*Note that an extra point is awarded on the students GPA for taking an AP course.

Tutoring:

Tutoring sessions will be provided every Wednesday beginning immediately after 7th period.