Honors Pre-Calculus

Scope and SequenceEdit


The goals in this Pre-Calculus class will consist of first helping students develop a proficiency in advanced algebra and secondly demonstrating to students how algebra, when studied at an indepth level, naturally extends to more powerful mathematical concepts. Since Honors Pre-Calculus is an advanced high school math course, its study will require and build critical thinking skills by approaching problems in various ways. The methods used in problem-solving will involve the “rule of four” which consists of a numerical, graphical, analytical, and verbal approach. It is important that students develop rote skills but in a broader context that includes understanding topics conceptually.

Scope and SequenceEdit

The following is an outline of the topics covered in Honors Pre-Calculus. An approximate number of days are allotted to the topics since the actual time varies depending upon the richness of class discussions that are generated. Furthermore, the textbook will be utilized as a resource but students will be held responsible for learning all material extensively taught in class. Tests are not generated based solely on problems found in the textbook but on the concepts discussed and developed in class. A minimum of two tests are given within a 6 week grading period.

Unit One (Approximate time 1 weeks)Edit

  • Real Number System
  • Properties of Algebra
  • Evaluating/Simplifying Expressions
  • Interval/Inequality/Set Notation
  • Radical Expressions
  • Factoring

Unit Two ( Approximate time 10 days)Edit

  • More Factoring
  • Simplifying Rational Expressions
  • Solving Equations

Unit Three (Approximate time 9 days)Edit

  • More Solving Equations
  • Solving Inequalities
  • Complex Numbers

Unit Four (Approximate time 7 days)Edit

  • Graphing Linear Equations
  • Slope of a Line
  • Finding x and y intercepts
  • Writing Linear Equations
  • Writing Equations of Parallel and Perpendicular Lines
  • Graphing Linear Inequalities

Unit Five (Approximate 17 days)Edit

  • Identifying Functions
  • Domain/Range
  • Evaluating Functions
  • Inverse Functions
  • Piece-Wise Functions
  • Continuity/Discontinuity
  • Parent Functions
  • Transformation of Parent Functions

Unit Six (Approximate 10 days)Edit

  • Long Division/ Synthetic Division
  • Graphing Rational Functions
  • Polynomial Functions
  • Critical Points and Extrema

Unit Seven (Approximate 4 days)Edit

  • Remainder and Factor Theorem
  • Rational Root Theorem
  • Locating Zeros of a Polynomial
  • Conics (only if time allows)

Unit Eight (Approximate 12 days)Edit

  • Exponential Functions
  • Logarithmic Functions
  • Logarithmic Expressions
  • Logarithmic Equations
    • Applications

Unit NineEdit

  • Right Triangles and Pythagorean Theorem
  • Pythagorean Theorem and Special Right Triangles
  • Applications of Pythagorean Theorem
  • Solving Right Triangles using Trig Ratios
  • Applications of Trig Ratios

Unit Ten- Circular Trig.Edit

  • Angle measure in degree/radian
  • Unit Circle
  • Unwrapping the unit circle- 3 basic trig graphs

Unit Eleven-Graphs of circular trig. functionsEdit

  • Amplitude, period, phase shift, domain/range
  • Transformations of sine, cosine, tangent, cosecant, secant, and cotangent functions

Unit Twelve-inverse trig. functionsEdit

  • Restricting domain/range to get inverse trig functions
  • Finding the value of inverse trig functions
  • Graphing inverse trig functions

Unit Thirteen- Fundamental trig. identitiesEdit

  • Reciprocal Identities
  • Quotient identities
  • Pythagorean identities
  • Proving trig identities

Unit Fourteen- Identities and solve trig. equationsEdit

  • Sum/difference identities
  • Double angle identities
  • Half-angle identities
  • Finding trig values using identities
  • Solving trig equations using identities

Unit Fifteen-Law of cosine/sineEdit

  • Solving Triangles
  • Deriving Law of Sines
  • The ambigous case for law of sines
  • Law of cosines

Unit Sixteen-VectorsEdit

  • Geometric Vectors
  • Algebraic Vectors
  • Vectors in 3-dimensional space
  • Perpendicular vectors
  • Applications of vectors

Unit Seventeen-Polar Coordinate SystemEdit

  • Comparison of real plane, complex plane, and polar plane
  • Polar coordinates
  • Graphs of polar coordinates
  • Polar and rectangular coordinates
  • Polar form of complex numbers
  • Products/Quotients of Complex Numbers
  • Powers and Roots of Complex Numbers

Unit Eighteen-Parametric EquationsEdit

  • Parameters, independent variables, dependent variables and functions
  • Writing Parametric Equations
  • Exploring Parametric Equations with graphing calculator

Unit Nineteen-Systems and MatricesEdit

  • Circles
  • Ellipses
  • Hyperbolas
  • Parabolas
  • Transformations of Conics
  • Systems of Equations
  • Solving with Matrices

Unit Twenty- Sequences and SeriesEdit

  • Arithmetic Sequences and Series
  • Geometric Sequences and Series
  • Infinite Sequences and Series
  • Convergent and Divergent Series
  • Sigma Notation and the nth term
  • Binomial Theorem

  • This outline is subject to change at the discretion of the instructor.

Trigonometry SyllabusEdit

Classroom ExpectationsEdit

  • Be prompt
  • Be prepared
  • Be positive
  • Be polite

Materials NeededEdit

  • Graphing Calculator TI-83+, TI-84
  • Notebook (3-ring binder with pockets)
  • Paper
  • Pen/Pencil

Grading PolicyEdit

  • Tests 55%
  • Daily Grade 30%
  • Final Exam 15%

A minimum of two tests will be given during a 6 –week period. Tests are not generated based solely on problems found in a math textbook and are given in various formats. Daily grades consist of homework, quizzes and so forth. Occasionally a project may be assigned and will count as a major test grade. Students are held responsible for learning extensively all material that is discussed and discovered in class. The math textbook is a resource to be utilized but examples and questions will be given at an indepth level.

  • This syllabus is subject to change at the discretion of the instructor.

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