# Integrated Math 2

## Course Summary

Building on concepts learned in Integrated Math 1, students expand their knowledge around mathematical sense-making, using mathematical models to represent real-world data, making and testing conjectures and justifying conclusions, and computational and symbolic fluency. Students focus on quadratic expressions, equations, and functions, and expand their knowledge of right triangle trigonometry and surface area and volume. Explore probability and data including experimental, theoretical and compound probability. In this course, develop mathematical skills through collaboration, data collection, experimentation, and conjectures.

This course is the second of a three-year Integrated Math series.

**Course Prerequisite(s):**Integrated Math 1

## Curriculum

This is a 2-semester course. We do not recommend taking both semesters simultaneously.

##### Unit 1: Proving Theorems about Lines and Angles

- Lines and Angles
- Proving Angles Congruent
- Properties of Parallel Lines
- Proving Lines Parallel
- Parallel and Perpendicular Lines
- Parallel Lines and Triangles

##### Unit 2: Proving Theorems About Triangles

- Mid-segments of Triangles
- Perpendicular and Angle Bisectors
- Bisectors in Triangles
- Medians and Altitudes
- Indirect Proof
- Inequalities in One Triangle
- Inequalities in Two Triangles

##### Unit 3: Proving Theorems about Quadrilaterals

- The Polygon Angle-Sum Theorems
- Properties of Parallelograms
- Proving That a Quadrilateral is a Parallelogram
- Properties of Rhombuses, Rectangles, and Squares
- Conditions for Rhombuses, Rectangles, and Squares
- Trapezoids and Kites
- Applying Coordinate Geometry
- Proofs Using Coordinate Geometry

##### Unit 4: Similarity

- Similar Polygons
- Proving Triangles Similar
- Similarity in Right Triangles
- Proportions in Triangles
- Dilations
- Similarity Transformations

##### Unit 5: Right Triangles and Trigonometry

- The Pythagorean Theorem and its Converse
- Special Right Triangles
- Trigonometry
- Angles of Elevation and Depression
- Areas of Regular Polygons

##### Unit 6: Circles

- Circles and Arcs
- Areas of Circles and Sectors
- Tangent Lines
- Chords and Arcs
- Inscribed Angles
- Angle Measures and Segment Lengths

##### Unit 7: Surface Area and Volume

- Surface Areas of Prisms and Cylinders
- Surface Areas of Pyramids and Cones
- Volumes of Prisms and Cylinders
- Volumes of Pyramids and Cones
- Surface Areas and Volumes of Spheres
- Areas and Volumes of Similar Solids

##### Unit 8: Properties of Exponents with Rational Exponents

- Multiplying Powers with the Same Base
- More Multiplication Properties of Exponents
- Division Properties of Exponents
- Rational Exponents and Radicals

##### Unit 9: Polynomials and Factoring

- Adding and Subtracting Polynomials
- Multiplying and Factoring
- Multiplying Binomials
- Multiplying Special Cases
- Factoring x^2+bx+c
- Factoring ax^2+bx+c
- Factoring Special Cases

##### Unit 10: Quadratic Functions

- Quadratic Graphs and Their Properties
- Graphing Quadratic Functions
- Solving Quadratic Equations
- Factoring to Solve Quadratic Equations
- Completing the Square
- The Quadratic Formula and the Discriminant
- Complex Numbers
- Linear, Quadratic, and Exponential Models
- Systems of Linear and Quadratic Equations
- A New Look at Parabolas

##### Unit 11: Probability

- Experimental and Theoretical Probability
- Permutations and Combinations
- Compound Probability
- Probability Models
- Conditional Probability Formulas

##### Unit 12: Other Types of Functions

- Properties of Exponential Functions
- Graphing Radical Functions
- Piecewise Functions
- Combining Functions
- Composition and Inverse Functions

##### Unit 13: Sequence and Series

- Mathematical Patterns
- Arithmetic Sequences
- Geometric Sequences
- Arithmetic Series
- Geometric Series