Integrated Math 3 / Integrated Math III - 11th Grade Math

This resource includes:

-One Presentation for each section

-One Worksheet set with solutions for each section

-Reference Sheet for each unit

-Unit Test with solutions for each unit

Unit 1: Function Review & Advanced Function Concepts

1.1 Review of key function types
1.2 Function notation and evaluation (including composite expressions)
1.3 Domain and range (with emphasis on restrictions from denominators & radicals)
1.4 Finding composite functions and domains
1.5 Inverse functions
1.6 Testing for invertibility (horizontal line test, restricting domains)
1.7 Modeling with multiple function types in context (choosing the function family)

Unit 2: Higher Degree Polynomial Functions

2.1 Recognizing polynomial functions and their graphs
2.2 End behavior of polynomial functions
2.3 Zeros of polynomials and x-intercepts
2.4 Sketching polynomial graphs from factored form
2.5 Turning points and number of real zeros vs degree
2.6 Adding, subtracting, and multiplying polynomials

2.7 Factoring higher-degree polynomials (grouping, simple patterns)
2.8 Using polynomial division
2.9 Using synthetic division 

2.10 Remainder theorem and using it to test possible zeros
2.11 Using your TI-84 calculator to explore and confirm polynomial graphs & zeros
2.12 Modeling real contexts with polynomial functions (volume, profit, etc.)

Unit 3: Rational Functions

3.1 Rational expressions and simplified form (review of simplifying)
3.2 Graphing basic rational functions with asymptotes
3.3 Identifying asymptotes and holes from equations
3.4 Sketching graphs of simple rational functions using intercepts and asymptotes
3.5 Adding and subtracting rational expressions (general case)
3.6 Multiplying and dividing rational expressions (general case)
3.7 Solving rational equations (including extraneous solutions)
3.8 Applications of rational equations (work problems, rates, proportions)
3.9 Comparing rational models to other function types in context
3.10 Using technology to explore family of rational functions (parameter changes)

Unit 4: Radical & Power Functions

4.1 Radical functions: square root and cube root graphs
4.2 Domain and range of radical functions
4.3 Transformations of radical functions (shifts, stretches, reflections)
4.4 Solving radical equations and checking for extraneous solutions
4.5 Rational exponents and equivalence with radicals
4.6 Power functions
4.7 Graphing power functions and comparing with polynomial & rational graphs
4.8 Modeling contexts with radical and power functions (gravity, area/volume scaling, etc.)

Unit 5: Exponential & Logarithmic Functions

5.1 Review of exponential growth & decay
5.2 Introduction to logarithms as inverses of exponentials
5.3 Converting between exponential and logarithmic forms
5.4 Evaluating logarithms (common bases, using calculator for basic values)
5.5 Graphs of exponential vs logarithmic functions; inverse relationships
5.6 Transformations of exponential functions (shifts and stretches)
5.7 Transformations of logarithmic functions (shifts and stretches)
5.8 Laws of exponents review and extension (including negative & rational exponents)
5.9 Properties of logarithms (product, quotient, power rules)
5.10 Solving exponential equations using logarithms
5.11 Solving logarithmic equations (domain restrictions and extraneous issues)
5.12 Modeling real-world growth/decay with exponential & logarithmic functions (finance, population, pH, Richter scale)

Unit 6: Trigonometric Functions

6.1 Review of trig ratios in right triangles (sin, cos, tan)
6.2 The unit circle: coordinates of key angles
6.3 Sine and cosine as coordinates of points on the unit circle
6.4 Graphs of y=sinx and y=cosx
6.5 Graph of y=tan⁡x (basic shape, asymptotes, period)
6.6 Transformations of trig functions: amplitude, period, phase shift, vertical shift
6.7 Modeling periodic phenomena with trig functions (tides, seasons, sound, etc.)
6.8 Inverse trig functions (arcsin, arccos, arctan) and their restricted domains
6.9 Solving trig equations in a given interval (simple cases)

Unit 7: Trigonometry in Triangles & Geometry Extensions

7.1 Law of Sines
7.2 Law of Cosines
7.3 Choosing Law of Sines vs Law of Cosines in applied problems
7.4 Area of oblique triangles
7.5 Solving real-world and geometric problems using triangle trig

Unit 8: Advanced Geometry & Modeling

8.1 Review: circles in the coordinate plane
8.2 Transformations of conics: translations of circle equations
8.3 Introduction to ellipses and parabolas as conic sections
8.4 Parabolas in vertex form as conic sections
8.5 Using conics to model or approximate real-world shapes (satellite dishes, orbits, etc.)
8.6 3D geometry: surface area & volume review (prisms, cylinders, pyramids, cones, spheres)
8.7 Density and other derived measures (mass, population density, etc.)
8.8 Modeling with geometry and algebra together

Unit 9: Statistics – Inference with Samples & Data

9.1 Sampling methods (random, stratified, cluster, convenience) and bias
9.2 Designing and describing random samples and simulations

9.3 Using sample statistics to estimate population parameters (mean, proportion)
9.4 Understanding margin of error
9.5 Observational studies vs experiments (including randomized experiments)
9.6 Designing experiments: treatment, control, random assignment, lurking variables
9.7 Comparing two treatments or groups using data (difference in means/proportions)
9.8 Informal inference using simulated sampling distributions (what is “unlikely”?)
9.9 Drawing conclusions and communicating results (context, limitations, sources of error)

Unit 10: Conditional Probability & Rules

10.1 Review: simple and compound events, sample spaces
10.2 Conditional probability P(A∣B)P(A|B)P(A∣B) (formal notation and meaning)
10.3 Two-way tables and conditional probabilities
10.4 Independence: definition and tests 

10.5 Interpreting independence and dependence in context (real-world meaning)

10.6 General addition rule

10.7 Using probability rules to model and make decisions (risk, expected value, fairness)