Mr. Chala SCHOOL OF THE ARTS

Syllabus: Integrated Mathematics 3&4

 

 

Unit 1: Sampling and Reasoning

(Optional)

 

Unit 2 Models of Variation and Growth

2-1 Functions and Graphs

2-2 Linear Models and Direct Variation

2-3 Inverse Variation

      1. Surface Area and Volume of Spheres

      2. Direct Variation with Powers

      3. Using Powers

      4. Doubling and Halving

Unit 3 Linear Systems and Matrices

3-1 Systems and Graphs

      1. Solving Systems by Substitution

      2. Slopes and Systems

      3. Solving Systems by Addition-or-Subtraction

      4. Matrix Operations (The power of mathematics)

      5. Matrices and Transformations

      6. Matrix Multiplication

      7. Using Technology and Matrices with Sytems

Unit 4 Quadratic Functions and Graphs

4-1 Graphing Quadratic Functions

      1. Translating Parabolas

      2. Solving Equations Using Square Roots

      3. Solving Equations Using Factoring

      4. The Quadratic Formula

      5. The Discriminant and Complex Numbers

      6. Quadratic Systems

Unit 5 Coordinate Geometry and Quadrilaterals

5-1 Quadrilaterals

      1. The Distance Formula and Quadrilaterals

      2. Midpoints

      3. Coordinates and Transformations

      4. Coordinates for Triangles and Quadrilaterals

      5. Exploring Properties

 

 

 

 

Unit 6 Counting Strategies, Probability, Binomials

6-1 Exploring Counting Problems

      1. Counting and Permutations

      2. Probability and Odds

      3. Compound Events

      4. Combinations

      5. Pascal’s Triangle

6-7&6-8 (optional)

      1. The Binomial Theorem

Unit 7 Logic and Proof

7-1 to 7-4 Quick Review

      1. Introduction to Proof

      2. Postulates and Proofs in Algebra

      3. Proofs for Angles

      4. Proofs about Parallel Lines

Unit 8 Similar and Congruent Triangles

      1. Converses and Parallel Lines

      2. The Triangle Sum Theorem

      3. Similar Triangles

      4. Congruent Triangles: ASA and AAS

      5. Congruence Triangles: SAS and SSS

      6. Congruence and Isosceles Triangles

      7. Similarity in Right Triangles

      8. Special Right Triangles and Trigonometry

Unit 9 Polynomial and Rational Functions

9-1 Polynomial and Rational Models

      1. Power and Quotient Rules

      2. Solving Rational Equations

      3. Graphing Cubic Functions

      4. Solving Cubic Equations

      5. Parametric Equations

Unit 10 Coordinates and Figures in Space

10-1 Figures in Space

      1. Axis of Rotation

      2. Points That Fit Conditions

      1. Coordinates in Three Dimensions

      2. Distance Formula

      3. Circles and Spheres

Learning By Doing.