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Integrated 2 is the second year of a three year high school mathematics sequence. The program is designed to use patterns, modeling and conjectures to build student understanding and competency in mathematics. The expectation is to develop and maintain a studentâ€™s growth mindset and teach students how to learn math in a collaborative process where multiple methods and representations are celebrated. Students will be expected to learn through collaboration, collection of data, experimentation and conjectures. Technology will also play a key role in learning. This course aligns with the five goals of the UC mathematics requirement. Students will learn mathematical sense making, make and test conjectures, justify conclusions, use mathematical models to represent real-world data, be able to provide clear and concise answers, and have computational and symbolic fluency.

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

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