Best fit
Students enrolled in a standard Precalculus course
Precalculus
Precalculus Tutoring
Develop the function, trigonometry, polar, sequence, and graphing fluency that makes later calculus and quantitative coursework manageable.
Precalculus brings earlier algebra together around functions and change. Students deepen their understanding of polynomial, rational, exponential, logarithmic, and trigonometric functions, then extend that work to analytic trigonometry, polar coordinates, sequences, series, and mathematical modeling.
Starting point
Comfort with linear and quadratic functions, equations, and graphs
Session style
One-on-one or small-group tutoring
Student outcome
Analyze polynomial, rational, exponential, logarithmic, and trigonometric functions
Student Menu
Study guide and practice links
Course Overview
A focused precalculus path from functions to advanced representations
This focused standard Precalculus course is distinct from the broader existing Precalculus Honors course and from AP Precalculus, which follows a national College Board framework.
Core function families
Study polynomial, rational, exponential, logarithmic, and trigonometric functions in algebraic and graphical form.
Analytic trigonometry
Use identities and equations to reason beyond right-triangle calculations.
Polar coordinates
Describe points and relationships using distance and angle as an alternative to rectangular coordinates.
Sequences, series, and modeling
Represent patterns, accumulate terms, and use graphs and technology to analyze real situations.
Student Fit
Who this course is for
- Students enrolled in a standard Precalculus course
- Students preparing for calculus or college-level quantitative coursework
- Students who need to connect algebraic techniques with graphs and models
- Students choosing among standard, honors, and AP precalculus pathways
Prerequisites
What students should know before starting
- Comfort with linear and quadratic functions, equations, and graphs
- Working knowledge of polynomial, rational, radical, exponential, and logarithmic expressions
- Basic function notation and graph transformations
Questions
Frequently asked questions
How is this different from Precalculus Honors?
This course follows a focused standard sequence. The existing Honors course has a broader six-unit sequence that also includes complex numbers, vectors, matrices, conic sections, limits, and continuity.
How is this different from AP Precalculus?
AP Precalculus follows the College Board framework and prepares students for a standardized AP Exam. A school Precalculus course follows its local sequence, so its content and emphasis can differ.
Will tutoring follow my school’s sequence?
Yes. This curriculum is a coverage map; sessions can begin with the student’s current unit and adapt to the school’s order, notation, calculator expectations, and assessments.
Curriculum
Precalculus curriculum
A topic-based sequence whose order and emphasis can be adapted to the student’s school curriculum.
1
Polynomial and Rational Functions
Students use structure and graph behavior to analyze equations, zeros, discontinuities, and long-run behavior.
- Polynomial graphs
- Zeros and multiplicity
- End behavior
- Rational functions
- Asymptotes and holes
- Equations and applications
2
Exponential and Logarithmic Functions
Students analyze multiplicative change and use inverse relationships to solve and interpret models.
- Exponential models
- Growth and decay
- Logarithm properties
- Inverse relationships
- Equations
- Applications
3
Trigonometric Functions
The unit circle supports exact values, function graphs, and periodic models.
- Radian and degree measure
- Unit circle
- Six trigonometric functions
- Trigonometric graphs
- Graph transformations
- Periodic modeling
4
Analytic and Applied Trigonometry
Students use identities and equations to transform relationships and solve mathematical or contextual problems.
- Fundamental identities
- Identity verification
- Trigonometric equations
- Inverse trigonometric functions
- Triangle applications
- Multi-step problem solving
5
Polar Coordinates
Students translate between rectangular and polar viewpoints and interpret graphs in a new coordinate system.
- Plotting polar points
- Equivalent polar representations
- Rectangular-polar conversion
- Polar equations
- Polar graphs
- Symmetry and interpretation
6
Sequences, Series, and Integrated Modeling
Patterns, sums, graphing, and technology come together in cumulative problem solving.
- Arithmetic sequences
- Geometric sequences
- Recursive and explicit rules
- Finite series
- Graphing-calculator analysis
- Model selection and interpretation
Practice
Practice for fluency, interpretation, and course readiness
Students work with equations, graphs, tables, and contexts, using technology when it clarifies behavior and by-hand reasoning when it exposes structure.
Function-family comparisons
Graph analysis
Equation solving
Unit-circle retrieval
Identity reasoning
Polar conversions
Sequence modeling
Cumulative mixed review
Outcomes
By the end of this course, students will be able to
- Analyze polynomial, rational, exponential, logarithmic, and trigonometric functions
- Move among algebraic, graphical, numerical, and verbal representations
- Use identities and equations in analytic trigonometry
- Convert between rectangular and polar representations
- Represent and analyze arithmetic and geometric sequences and series
- Use a graphing calculator strategically and interpret its output
Learning Format
How sessions are structured
- One-on-one or small-group tutoring
- Lessons matched to the student’s current school unit
- Worked examples followed by guided and independent practice
- Homework, quiz, and test review
- Error analysis and progress checks
- Graphing and technology support when appropriate
Why Code Scholars
Support that builds real understanding
School-Aligned Support
Sessions can follow the order and pace of the student’s class while still repairing earlier gaps.
Reasoning Before Routines
Students learn why a method works, how to select it, and how to check the result.
Connected Representations
Equations, tables, graphs, diagrams, and verbal descriptions are treated as different views of the same idea.
Targeted Practice
Practice is adjusted to the student’s current misconceptions instead of repeating work they already understand.
Clear Mathematical Communication
Students practice showing work and explaining conclusions with accurate notation.
Stronger Independence
The goal is for students to recognize patterns, choose tools, and recover from mistakes without relying on prompts.
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