Course Description

This Pre-Calculus course uses an incremental approach to teach advanced algebra, geometry, trigonometry, discrete mathematics, and mathematical analysis. The course emphasizes problem-solving and critical thinking skills, with word problems developed throughout the problem sets that become progressively more complex. Students will gain practice with challenging problems, including rate and work problems involving abstract quantities.

The course also includes a thorough study of Euclidean geometry, exploring theorems, postulates, and proofs. Students will work with concepts such as geometric constructions, congruence, similarity, and coordinate geometry. The trigonometry component covers topics like the unit circle, trigonometric functions, identities, and applications to real-world problems.

By the end of the course, students will be well-prepared for college entrance exams such as the ACT and SAT, as well as for further studies in mathematics. This course is ideal for high school students aiming to strengthen their mathematical foundation and tackle advanced mathematical concepts in preparation for college-level coursework.

Course Details


Tenth Grade Eleventh Grade
Twelfth Grade

Course Objectives

  • Master advanced algebraic concepts and techniques.
  • Understand key principles of Euclidean geometry and apply them to problem-solving.
  • Learn trigonometry fundamentals, including trigonometric functions, identities, and applications.
  • Develop skills in discrete mathematics and mathematical analysis.
  • Build critical thinking and problem-solving skills through complex word problems.
  • Prepare for college entrance exams and further studies in mathematics.

Course Outline

Unit 1: Advanced Algebra

  • Polynomial Functions
    • Understanding polynomials and their properties.
    • Operations with polynomials and factoring techniques.
  • Rational Expressions and Equations
    • Simplifying rational expressions and solving rational equations.
    • Addressing complex fractions and algebraic operations.
  • Exponential and Logarithmic Functions
    • Exploring exponential functions and their applications.
    • Understanding logarithms and solving logarithmic equations.

Unit 2: Euclidean Geometry

  • Geometry Basics
    • Reviewing basic geometric terms and concepts.
    • Exploring geometric constructions and proofs.
  • Congruence and Similarity
    • Understanding congruence and similarity in triangles and other shapes.
    • Applying theorems to solve geometry problems.
  • Coordinate Geometry
    • Analyzing geometric shapes on the coordinate plane.
    • Finding distances, midpoints, and slopes.

Unit 3: Trigonometry

  • The Unit Circle and Trigonometric Functions
    • Understanding the unit circle and its relationship to trigonometric functions.
    • Exploring sine, cosine, tangent, and their inverses.
  • Trigonometric Identities and Equations
    • Learning key trigonometric identities (e.g., Pythagorean, angle-sum).
    • Solving trigonometric equations and applying identities.
  • Applications of Trigonometry
    • Applying trigonometry to real-world problems.
    • Exploring Law of Sines and Law of Cosines.

Unit 4: Discrete Mathematics

  • Sequences and Series
    • Understanding arithmetic and geometric sequences and series.
    • Finding sums of sequences and applying series to solve problems.
  • Combinations and Permutations
    • Learning the fundamentals of counting, combinations, and permutations.
    • Applying combinations and permutations to complex problems.

Unit 5: Mathematical Analysis

  • Limits and Continuity
    • Introduction to the concept of limits and continuity.
    • Exploring limit-based problems and continuity in functions.
  • Derivatives and Tangent Lines
    • Basics of derivatives and their applications.
    • Finding derivatives and using them to determine tangent lines.

Expected Outcomes

By the end of this course, students will have a comprehensive understanding of advanced algebra, geometry, trigonometry, discrete mathematics, and mathematical analysis. They will have developed critical thinking and problem-solving skills, and be well-prepared for college entrance exams and further studies in mathematics or related fields.

Syllabus for upcoming year coming soon. 

Coming soon.

Mr. Erich Gott

Erich Gott holds a B.S. in Physical Education with a Minor in Mathematics, and a Master of Science in Exercise Physiology from BYU. Erich has taught mathematics for 40 years in Utah, Colorado, Dubai, and India.  His teaching experience spans from the middle school and high school levels through college. Erich has been recognized with a National Board Certification in mathematics and early adolescence. He has developed curriculum for elementary through college level math courses. Erich and his wife have 4 children and 12 grandchildren.