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Mathematics Textbook 8B Grade

ArchiMath Publishing LLC

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. 


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.

What is the added value in our 8 grade textbooks❓
Our math book series promotes at all times:
☑ Simplicity and Elegance: In anything we do, especially in mathematics.
☑ Courage: Not being afraid to make mistakes and to learn from them.
☑ Diversity of Ideas: Via multiple solutions to the same problem.
☑ Learning to Think Deeply: Make connections with previously learned material.


Chapter 8. Functions

  1. Rectangular Coordinate System (Review)
  2. The Concept of a Function
  3. Graph of a Function
  4. Different Ways to Define a Function
  5. Direct Proportionality. Definition
  6. Graph of a Direct Proportionality
  7. Linear Function and Its Graph
  8. Applications of Linear Functions
  9. The Function y = | ax + b | and Its Graph
  10. Inverse Variation
  11. Graph of an Inverse Variation
  12. Linear Functions, Equations, and  Inequalities, Part I
  13. Linear Functions, Equations, and  Inequalities, Part II
  14. The Function y = ax2 , a ≠ 0, I
  15. The Function y = ax2 , a ≠ 0, II
  16. Summary of “Functions,” I
  17. Summary of “Functions,” II
  18. Tests 1-2 on “Functions”
  19. General Problems on “Functions”

Chapter 9. Systems of Linear Equations

 with Two Unknowns

  1. Linear Equations w/ Two Unknowns, I
  2. Linear Equations w/ Two Unknowns, II
  3. Systems of Linear Equations with Two Unknowns
  4. Solving Systems by Substitution
  5. Solving Systems by Addition
  6. Solving Systems of Equations. Exercises
  7. Modeling with Systems of Equations
  8. Summary of “Systems of Equations”
  9. Tests 1-2 on “Systems of Equations”
  10. General Problems on “Systems of Equations”

Chapter 10. Systems of Linear Inequalities  with One Unknown

  1. Intersection/Union of Intervals
  2. Systems of Two Linear Inequalities

 with One Unknown

  1. Solving Systems of Inequalities with One Unknown
  2. Inequalities of the Type

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

  1. Modular Inequalities of the Type

 | ax + b | < c, a ≠ 0

  1. Modular Inequalities of the Type

 | ax + b | > c, a ≠ 0

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

Chapter 11. Circle Geometry

Part I: Circles and Angles

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

Part II: Circles and Polygons (Optional)

  1. Geometric Constructions (Review)
  2. Construction Problems
  3. Geometric Locus of Points in the Plane
  4. GLP that Oversee a Segment at an Angle
  5. Circle Circumscribed about a Triangle
  6. Circumcircle of a Triangle. Exercises
  7. Circle Inscribed in a Triangle
  8. Incircle of a Triangle. Exercises
  9. Famous Points in a Triangle
  10. Famous Points in a Triangle. Exercises
  11. Constructing a Triangle. Exercises
  12. Quadrilateral Inscribed in a Circle
  13. Cyclic Quadrilateral. Exercises
  14. Circumscribed Quadrilateral
  15. Circumscribed Quadrilateral. Exercises
  16. Summary of “Circles and Polygons,” I
  17. Summary of “Circles and Polygons,” II
  18. General Problems on “Circles and Polygons”
  19. Tests 1-2 on “Circles and Polygons” 8th Grade Material


Chapter 12. Equations and Roots

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

Chapter 13. Rational Expressions

  1. Rational Expressions. Domain
  2. Basic Property of Rational Expressions
  3. Put Rational Expressions over a CD
  4. Add/Subtract Rational Expressions
  5. Multiply, Divide, and Take Powers
  6. Transform Rational Expressions
  7. Rational Equations
  8. Rational Equations. Exercises
  9. Model with Rational Equations
  10. Summary of “Rational Expressions”
  11. Tests 1-2 on “Rational Expressions”
  12. General Problems on “Rational Expressions”

Chapter 14. Basic Combinatorial Concepts

  1. Multiply/Add Possibilities
  2. Multiply/Add Possibilities. Exercises
  3. Permutations
  4. Variations
  5. Combinations
  6. Summary of “Basics in Combinatorics”
  7. Test on “Basics in Combinatorics”

Chapter 15. Yearly Review

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