Grade 11 Math: Advanced Algebra and Precalculus Foundations
A 48-session Term 1 self-learning course for Grade 11 mathematics. The course moves from advanced function reasoning through polynomial, rational, exponential, logarithmic, and trigonometric foundations. Each session uses teacher-style explanations, expanded worked examples, self-checks, independent practice, and APA 7 references.
📚 Course Curriculum
Session Focus. Today you will evaluate functions, interpret function notation, and distinguish an input from an output in symbolic and verbal settings. This session is …
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Session Focus. Today you will identify domain and range from formulas, restrictions, and graphs while using interval notation correctly. This session is written for independent …
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Session Focus. Today you will describe vertical shifts, horizontal shifts, stretches, compressions, and reflections from symbolic function notation. This session is written for independent study, …
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Session Focus. Today you will compose functions, interpret composite expressions, and decide whether an inverse relationship is reasonable. This session is written for independent study, …
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Session Focus. Today you will connect slope, intercepts, vertex form, standard form, and factored form as different views of equations. This session is written for …
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Session Focus. Today you will calculate and interpret average rate of change from tables, graphs, equations, and contexts. This session is written for independent study, …
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Session Focus. Today you will evaluate, graph, and interpret functions whose rules change across intervals. This session is written for independent study, but it should …
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Session Focus. Today you will compare functions represented in different forms and justify which grows faster, starts higher, or reaches a target first. This session …
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Session Focus. Today you will add, subtract, multiply, and classify polynomials while keeping degree and leading term visible. This session is written for independent study, …
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Session Focus. Today you will predict polynomial end behavior using degree and leading coefficient. This session is written for independent study, but it should feel …
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Session Focus. Today you will select efficient factoring methods for polynomials and use factoring to reveal zeros. This session is written for independent study, but …
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Session Focus. Today you will connect factors, roots, x-intercepts, and multiplicity to graph behavior. This session is written for independent study, but it should feel …
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Session Focus. Today you will use evaluation to find remainders and test whether a binomial is a factor. This session is written for independent study, …
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Session Focus. Today you will divide polynomials accurately and interpret quotient, divisor, and remainder. This session is written for independent study, but it should feel …
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Session Focus. Today you will perform basic complex arithmetic and use conjugate root structure in polynomial problems. This session is written for independent study, but …
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Session Focus. Today you will construct polynomial functions from zeros, multiplicities, degree, and a point. This session is written for independent study, but it should …
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Session Focus. Today you will sketch polynomial graphs using zeros, multiplicity, y-intercept, and end behavior. This session is written for independent study, but it should …
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Session Focus. Today you will solve polynomial inequalities using zeros, sign charts, and interval testing. This session is written for independent study, but it should …
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Session Focus. Today you will use polynomial functions to model area, volume, revenue, and constrained geometric situations. This session is written for independent study, but …
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Session Focus. Today you will synthesize function notation, transformations, polynomial structure, graphs, and inequalities under mixed conditions. This session is written for independent study, but …
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Session Focus. Today you will simplify rational expressions while preserving excluded values from the original expression. This session is written for independent study, but it …
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Session Focus. Today you will analyze rational function graphs using asymptotes, intercepts, and sign behavior. This session is written for independent study, but it should …
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Session Focus. Today you will distinguish removable discontinuities from vertical asymptotes and locate intercepts accurately. This session is written for independent study, but it should …
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Session Focus. Today you will solve rational equations by clearing denominators and checking for invalid solutions. This session is written for independent study, but it …
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Session Focus. Today you will solve rational inequalities using sign charts that include zeros and undefined values. This session is written for independent study, but …
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Session Focus. Today you will solve systems where lines, quadratics, and rational functions intersect. This session is written for independent study, but it should feel …
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Session Focus. Today you will choose between linear, quadratic, polynomial, rational, exponential, and logarithmic models based on pattern and context. This session is written for …
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Session Focus. Today you will combine polynomial and rational reasoning in multi-step problems requiring restrictions, graph features, and algebraic justification. This session is written for …
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Session Focus. Today you will represent arithmetic and geometric sequences explicitly and recursively. This session is written for independent study, but it should feel like …
Open trial session →Session Focus. Today you will write and analyze exponential functions using initial value, base, and repeated percent change. This session is written for independent study, …
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Session Focus. Today you will interpret shifts, reflections, and stretches of exponential functions. This session is written for independent study, but it should feel like …
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Session Focus. Today you will interpret every parameter in exponential models and connect symbolic models to real descriptions. This session is written for independent study, …
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Session Focus. Today you will compare model families by first differences, second differences, ratios, and long-run behavior. This session is written for independent study, but …
Open trial session →Session Focus. Today you will find inverses, restrict domains when needed, and verify inverse relationships by composition. This session is written for independent study, but …
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Session Focus. Today you will interpret logarithms as inverse operations for exponential equations. This session is written for independent study, but it should feel like …
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Session Focus. Today you will expand, condense, and evaluate logarithmic expressions using product, quotient, and power properties. This session is written for independent study, but …
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Session Focus. Today you will graph logarithmic functions using inverse relationships, vertical asymptotes, and transformations. This session is written for independent study, but it should …
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Session Focus. Today you will solve exponential and logarithmic equations using common bases, inverse operations, and property-based rewriting. This session is written for independent study, …
Open trial session →Session Focus. Today you will solve logarithmic inequalities while protecting domain restrictions. This session is written for independent study, but it should feel like a …
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Session Focus. Today you will synthesize sequence, exponential, inverse, and logarithmic reasoning in multi-step problems. This session is written for independent study, but it should …
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Session Focus. Today you will convert between degrees and radians and use arc length ideas to interpret circular motion. This session is written for independent …
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Session Focus. Today you will use the unit circle to find exact sine, cosine, and tangent values for special angles. This session is written for …
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Session Focus. Today you will identify amplitude, period, midline, and asymptotes in trigonometric graphs. This session is written for independent study, but it should feel …
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Session Focus. Today you will model shifted and stretched sinusoidal behavior using amplitude, period, midline, and phase shift. This session is written for independent study, …
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Session Focus. Today you will verify and use fundamental trigonometric identities to simplify expressions. This session is written for independent study, but it should feel …
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Session Focus. Today you will solve trigonometric equations on specified intervals using unit-circle values and algebraic structure. This session is written for independent study, but …
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Session Focus. Today you will solve non-right triangles and compute triangle area using trigonometric relationships. This session is written for independent study, but it should …
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Session Focus. Today you will connect advanced algebra, functions, exponential-logarithmic reasoning, and trigonometry in a final mixed review. This session is written for independent study, …
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Course Syllabus
This self-paced Grade 11 Math course follows a 48-lesson sequence. Work through the modules in order so that each skill supports the next.
Course sequence
Module 1 - Lessons 1-8
- Week 1, Session 1: Function Notation, Inputs, and Outputs
- Week 1, Session 2: Domain, Range, and Interval Thinking
- Week 1, Session 3: Transformations of Functions
- Week 1, Session 4: Composition and Inverse Basics
- Week 2, Session 1: Advanced Review of Linear and Quadratic Structure
- Week 2, Session 2: Rate of Change and Average Rate
- Week 2, Session 3: Piecewise and Absolute-Value Functions
- Week 2, Session 4: Function Comparison Checkpoint
Module 2 - Lessons 9-16
- Week 3, Session 1: Polynomial Operations and Structure
- Week 3, Session 2: End Behavior and Leading Terms
- Week 3, Session 3: Factoring Strategy Review
- Week 3, Session 4: Zeros, Roots, and Multiplicity
- Week 4, Session 1: Remainder and Factor Theorems
- Week 4, Session 2: Synthetic and Long Division
- Week 4, Session 3: Complex Numbers and Conjugate Roots
- Week 4, Session 4: Building Polynomials from Conditions
Module 3 - Lessons 17-24
- Week 5, Session 1: Polynomial Graphs from Equations
- Week 5, Session 2: Polynomial Inequalities
- Week 5, Session 3: Polynomial Modeling
- Week 5, Session 4: Unit 1 Mastery Assessment: Polynomial and Function Reasoning
- Week 6, Session 1: Rational Expressions and Restrictions
- Week 6, Session 2: Rational Function Graphs
- Week 6, Session 3: Holes, Asymptotes, and Intercepts
- Week 6, Session 4: Rational Equations and Extraneous Solutions
Module 4 - Lessons 25-32
- Week 7, Session 1: Rational Inequalities
- Week 7, Session 2: Systems Involving Nonlinear Functions
- Week 7, Session 3: Function Model Selection
- Week 7, Session 4: Mixed Polynomial and Rational Challenge Set
- Week 8, Session 1: Arithmetic and Geometric Sequences
- Week 8, Session 2: Exponential Functions
- Week 8, Session 3: Exponential Transformations
- Week 8, Session 4: Growth, Decay, and Parameter Meaning
Module 5 - Lessons 33-40
- Week 9, Session 1: Comparing Linear, Quadratic, and Exponential Models
- Week 9, Session 2: Inverse Functions in Depth
- Week 9, Session 3: Logarithms as Inverses
- Week 9, Session 4: Logarithmic Properties
- Week 10, Session 1: Logarithmic Graphs and Transformations
- Week 10, Session 2: Exponential and Logarithmic Equations
- Week 10, Session 3: Logarithmic Inequalities and Domains
- Week 10, Session 4: Unit 2 Mastery Assessment: Exponential and Logarithmic Thinking
Module 6 - Lessons 41-48
- Week 11, Session 1: Radian Measure and Circular Motion
- Week 11, Session 2: Unit Circle Exact Values
- Week 11, Session 3: Sine, Cosine, and Tangent Graphs
- Week 11, Session 4: Sinusoidal Transformations
- Week 12, Session 1: Trigonometric Identities
- Week 12, Session 2: Trigonometric Equations
- Week 12, Session 3: Law of Sines, Law of Cosines, and Triangle Area
- Week 12, Session 4: Term 1 Synthesis and Final Assessment
Practice and completion
- Use worked examples and lesson practice to check understanding after each module.
- Review incorrect answers, explain the correction, and repeat weak skills.
- Complete the available mixed or final course practice to demonstrate readiness.
Course Outcomes
By the end of this course, learners will be able to:
- Explain and apply the mathematical ideas in Week 1, Session 1: Function Notation, Inputs, and Outputs.
- Solve multi-step problems involving Week 4, Session 1: Remainder and Factor Theorems and show a clear method.
- Interpret representations and check the reasonableness of work involving Week 7, Session 1: Rational Inequalities.
- Choose efficient strategies for unfamiliar questions related to Week 9, Session 4: Logarithmic Properties.
- Combine skills from Week 12, Session 4: Term 1 Synthesis and Final Assessment with earlier topics in mixed practice.
- Use feedback and answer explanations to diagnose and correct mistakes.
- Complete mixed, exam-style practice with clearer reasoning and greater independence.
📝 Practice Questions
512 interactive questions with instant feedback and explanations.
Enroll for free to unlock the full practice bank after the trial sessions.