**Authors: **Zvezdelina Stankova, Zdravka Paskaleva, Maya Alashka, Raina Alashka

**Pages:** 238

**ISBN: **978-954-779-270-8

**Available**: Paperback & PDF

The 8th grade math textbooks continue the march to higher level mathematics. In algebra, students encounter the basics of algebraic functions and their graphs, learn to solve systems of linear equations and inequalities, solidify their understanding of polynomial equations, and begin working with rational expressions.

**Overview**

Their study of advanced geometry continues with a rigorous development of classic theorems on circles and their inscribed angles and polygons. In the final chapter, students get an introduction to combinatorics, a field often used to provide bridges between other branches of mathematics. Once again, the year’s curriculum ends with a summary of the ideas and techniques students have added to their personal mathematica toolboxes.

Chapter 8. Functions

- Rectangular Coordinate System (Review)
- The Concept of a Function
- Graph of a Function
- Different Ways to Define a Function
- Direct Proportionality. Definition
- Graph of a Direct Proportionality
- Linear Function and Its Graph
- Applications of Linear Functions
- The Function y = | ax + b | and Its Graph
- Inverse Variation
- Graph of an Inverse Variation
- Linear Functions, Equations, and Inequalities, Part I
- Linear Functions, Equations, and Inequalities, Part II
- The Function y = ax2 , a ≠ 0, I
- The Function y = ax2 , a ≠ 0, II
- Summary of “Functions,” I
- Summary of “Functions,” II
- Tests 1-2 on “Functions”
- General Problems on “Functions”

Chapter 9. Systems of Linear Equations

with Two Unknowns

- Linear Equations w/ Two Unknowns, I
- Linear Equations w/ Two Unknowns, II
- Systems of Linear Equations with Two Unknowns
- Solving Systems by Substitution
- Solving Systems by Addition
- Solving Systems of Equations. Exercises
- Modeling with Systems of Equations
- Summary of “Systems of Equations”
- Tests 1-2 on “Systems of Equations”
- General Problems on “Systems of Equations”

Chapter 10. Systems of Linear Inequalities with One Unknown

- Intersection/Union of Intervals
- Systems of Two Linear Inequalities

with One Unknown

- Solving Systems of Inequalities with One Unknown
- Inequalities of the Type

f (x) . g (x) > 0 and f (x) . g (x) < 0

- Modular Inequalities of the Type

| ax + b | < c, a ≠ 0

- Modular Inequalities of the Type

| ax + b | > c, a ≠ 0

- Summary of “Linear Inequalities”
- Tests 1-2 on “Linear Inequalities”
- General Problems on “Linear Inequalities”

Chapter 11. Circle Geometry

Part I: Circles and Angles

- Circle. Circle and Point. Circle and Line
- Tangents to a Circle
- The Relative Position of Two Circles
- Central Angle. Arc of a Circle
- Chords, Arcs, and Angles
- Inscribed Angle
- Peripheral (Tangential) Angle
- Applications of Inscribed and Peripheral Angles
- Circles and Angles. Exercises
- Summary of “Circles and Angles”
- Tests 1-2 on “Circles and Angles”

Part II: Circles and Polygons (Optional)

- Geometric Constructions (Review)
- Construction Problems
- Geometric Locus of Points in the Plane
- GLP that Oversee a Segment at an Angle
- Circle Circumscribed about a Triangle
- Circumcircle of a Triangle. Exercises
- Circle Inscribed in a Triangle
- Incircle of a Triangle. Exercises
- Famous Points in a Triangle
- Famous Points in a Triangle. Exercises
- Constructing a Triangle. Exercises
- Quadrilateral Inscribed in a Circle
- Cyclic Quadrilateral. Exercises
- Circumscribed Quadrilateral
- Circumscribed Quadrilateral. Exercises
- Summary of “Circles and Polygons,” I
- Summary of “Circles and Polygons,” II
- General Problems on “Circles and Polygons”
- Tests 1-2 on “Circles and Polygons” 8th Grade Material

Answers

Chapter 12. Equations and Roots

- Factoring Quadratic Trinomials
- Biquadratic Equations
- Equations Reducing to Quadratic Ones
- Equations Reducing to Quadratic Ones. Exercises
- Vieta’s Formulas
- Applications of Vieta’s Formulas
- Summary of “Equations and Roots”
- Tests 1-2 on “Equations and Roots”

Chapter 13. Rational Expressions

- Rational Expressions. Domain
- Basic Property of Rational Expressions
- Put Rational Expressions over a CD
- Add/Subtract Rational Expressions
- Multiply, Divide, and Take Powers
- Transform Rational Expressions
- Rational Equations
- Rational Equations. Exercises
- Model with Rational Equations
- Summary of “Rational Expressions”
- Tests 1-2 on “Rational Expressions”
- General Problems on “Rational Expressions”

Chapter 14. Basic Combinatorial Concepts

- Multiply/Add Possibilities
- Multiply/Add Possibilities. Exercises
- Permutations
- Variations
- Combinations
- Summary of “Basics in Combinatorics”
- Test on “Basics in Combinatorics”

Chapter 15. Yearly Review

- Algebraic and Geometric Inequalities
- Rational Numbers, Roots, Equations
- Applications of Vieta’s Formulas
- Rational Expressions
- Functions
- Systems of Equations and Inequalities
- Parallelograms and Trapezoids
- Vectors and Operations
- Midsegments and Centroids
- Transformations in the Plane. Isometries
- Circles and Angles
- Circumcircles and Incircles
- Basic Combinatorial Concepts
- Exit Tests 1-2 on 8th Grade Material

Answers