Genius Lab | Courses Detail

Integrated Math 3

High School

As the third part of the integrated pathway, this course deepens fluency with polynomial operations and graphs, connects transformations across families of functions, extends trigonometry beyond right triangles, and introduces rational functions and statistical reasoning. Emphasis is on modeling, structure, and multiple representations (algebraic, graphical, numerical, verbal).

Students will operate on and factor:

Operate on, factor, divide, and graph polynomials; use identities and series.
Use logarithms to solve exponential equations and interpret contexts.
Transform and compare functions (root, exponential, logarithmic).
Solve non-linear equations and systems; analyze extraneous solutions.
Apply trigonometry (laws of sines/cosines, unit circle, sinusoidal models).
Build and critique models; design studies; apply binomial and normal ideas.
Analyze and model with rational functions and expressions.

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Unit 1: Polynomial Arithmetic 6 Lessons | Total 240 min

1. 1: Intro to Polynomials 40 min

2. 2: Average Rate of Change of Polynomials 40 min

3. 3: Adding & Subtracting Polynomials 40 min

4. 4: Multiplying Monomials by Polynomials 40 min

5. 5: Multiplying Binomials by Polynomials 40 min

6. 6: Special Products (squares, cubes, conjugates) 40 min

Unit 2: Polynomial Factorization 7 Lessons | Total 280 min

1. 1: Factoring Monomials 40 min

2. 2: Greatest Common Factor (GCF) 40 min

3. 3: Taking Common Factors (Factor by Grouping) 40 min

4. 4: Factoring Higher-Degree Polynomials 40 min

5. 5: Factoring Using Structure 40 min

6. 6: Polynomial Identities (and Proof/Verification) 40 min

7. 7: Geometric Series (Formulas & Applications) 40 min

Unit 3: Polynomial Division 4 Lessons | Total 160 min

1. 1: Dividing by 𝑥 x (Monomial Divisors) 40 min

2. 2: Dividing Quadratics by Linear Factors 40 min

3. 3: Dividing by Linear Factors (Long/Synthetic Division) 40 min

4. 4: Remainder Theorem & Applications 40 min

Unit 4: Polynomial Graphs 4 Lessons | Total 160 min

1. 1: Zeros & Multiplicity 40 min

2. 2: Positive/Negative Intervals & Sign Charts 40 min

3. 3: End Behavior & Leading Term Analysis 40 min

4. 4: Synthesis: Sketching & Interpreting Polynomial Graphs 40 min

Unit 5: Logarithms 6 Lessons | Total 240 min

1. 1: Introduction to Logarithms 40 min

2. 2: 𝑒 e and the Natural Logarithm 40 min

3. 3: Properties of Logarithms 40 min

4. 4: Change-of-Base Formula 40 min

5. 5: Solving Exponential Equations with Logs 40 min

6. 6: Exponential Models & Interpretation 40 min

Unit 6: Transformations of Functions 7 Lessons | Total 280 min

1. 1: Shifts (Horizontal/Vertical) 40 min

2. 2: Reflections & Symmetry 40 min

3. 3: Scaling (Stretches/Compressions) 40 min

4. 4: Putting It All Together (Composite Transformations) 40 min

5. 5: Graphs of Square- & Cube-Root Functions 40 min

6. 6: Graphs of Exponential Functions 40 min

7. 7: Graphs of Logarithmic Functions 40 min

Unit 7: Equations 6 Lessons | Total 240 min

1. 1: Rational Equations & Restrictions 40 min

2. 2: Square-Root Equations 40 min

3. 3: Extraneous Solutions (Detection & Justification) 40 min

4. 4: Cube-Root Equations 40 min

5. 5: Quadratic Systems (Algebraic & Graphical) 40 min

6. 6: Solving Equations by Graphing (Technology OK) 40 min

Unit 9: Modeling 5 Lessons | Total 200 min

1. 1: Modeling with Function Combinations (Sum, Product, Composition) 40 min

2. 2: Interpreting Key Features (Intercepts, Extrema, Rates) 40 min

3. 3: Manipulating Formulas (Solving for a Variable) 40 min

4. 4: Modeling with Two Variables 40 min

5. 5: Modeling with Multiple Variables 40 min

Unit 10: Study Design 2 Lessons | Total 80 min

1. 1: Samples & Surveys (Bias, Methods) 40 min

2. 2: Observational Studies & Experiments (Controls, Randomization) 40 min

Unit 11: Binomial Probability 1 Lessons | Total 40 min

1. 1: Binomial Settings, Formula, and Interpretation 40 min

Unit 12: Normal Distributions 1 Lessons | Total 40 min

1. 1: Normal Models, z-Scores, and Areas 40 min

Unit 13: Rational Functions 9 Lessons | Total 360 min

1. 1: Canceling Common Factors & Simplified Form 40 min

2. 2: End Behavior (Degrees & Leading Coefficients) 40 min

3. 3: Discontinuities (Holes & Asymptotes) 40 min

4. 4: Graphs of Rational Functions 40 min

5. 5: Modeling with Rational Functions 40 min

6. 6: Multiply & Divide Rational Expressions 40 min

7. 7: Add/Subtract Rational Expressions – Intro 40 min

8. 8: Add/Subtract (Factored Denominators) 40 min

9. 9: Add/Subtract (Non-factored; LCD Strategy) 40 min

Integrated Math 3

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