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Mathematics Workbook 8A Grade

ArchiMath Publishing LLC

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

Pages: 150 

ISBN: 978-954-779-260-9

Available: Paperback & PDF

In the third year of the Bulgarian Math curriculum, the 8A books continue to build upon the foundational marriage between algebra and geometry.

The workbooks provide space for students to try the solved examples from the reading on their own, plus additional worksheets to further student understanding. In both books, the exercises contain problems that are extremely similar to the solved examples, as well as variations that require critical thinking skills to transform difficult problems into more manageable ones.


The 8A Workbook will strengthen the basic knowledge and skills needed to master the 8A material. 

To each topic in the 8A Textbook correspond problems in the 8A Workbook that every student should be able to solve. Some problems have a solution and some have the beginning of a solution. After working on such problems, students should be able to complete the remaining problems on their own.

The 8A Worksheets highlight the basic knowledge in the 8A Textbook;

 have a teaching component;

 help students learn to organize and correctly write solutions to problems; 

and save time for the teacher in searching for more problems.

 The 8A Worksheets can be used for independent work by the student; to assign homework; to conduct tests; and for practical work with applications.

After a brief review of polynomials, triangle congruence, and constructions, the textbook opens with a systematic treatment of linear inequalities, moving on to the triangle inequality and other classic inequalities in triangles. Students continue their axiomatic study of geometry with the classification of quadrilaterals and careful study of their properties. In algebra, students learn to work efficiently with square roots and solve quadratic equations, giving a proof of the quadratic formula along the way. 

This semester concludes with vector geometry and isometries in the plane, topics that most students in the US will not encounter in middle school or high school. However, the Bulgarian curriculum leads students to greater mathematical maturity, and they are entirely prepared for these advanced topics after working through the earlier books.

Chapter 1. Initial Review

  1. Test 1 on “Integer Expressions”
  2. Tests 2-3 on “Linear Equations”
  3. Tests 4-5 on “Modeling w/ Linear Equations”
  4. Tests 6-7 on “Algebra on Polynomials”
  5. Test 8 on “Foundations of Geometry”
  6. Test 9 on “Congruent Triangles”
  7. General Tests 10-12 on 6B-7B Material

Chapter 2. Algebraic Inequalities. Part I

10-12. Numerical/Equivalent Inequalities. Properties

  1. Inequalities with One Unknown
  2. Linear Inequalities with One Unknown
  3. Representing Solutions by Intervals and Graphs
  4. Inequalities that Reduce to Linear Ones
  5. Inequalities. Exercises
  6. Applications of Linear Inequalities
  7. Problems/Preps on “Algebraic Inequalities”
  8. Mini-Tests on “Algebraic Inequalities”

Chapter 2. Geometric Inequalities. Part II

  1. Inequalities btw Sides and Angles in Triangle
  2. Inequalities btw Sides and Angles. Exercises

24-25. The Triangle Inequality

  1. Test on “Geometric Inequalities”

Chapter 3. Parallelograms. Trapezoids

  1. Parallelogram. Properties of Its Sides
  2. Properties of the Diagonals in a Parallelogram
  3. Properties of the Angles in a Parallelogram
  4. Parallelogram. Exercises

33-34. Rectangle, Parts I-II

  1. Rhombus
  2. Square
  3. Types of Parallelograms. Exercises
  4. Trapezoid, Part I. Isosceles Trapezoid
  5. Trapezoid, Part II. Right Trapezoid
  6. Problems/Preps on “Quadrilaterals”
  7. Tests on “Parallelograms. Trapezoids”
  8. Mini-Tests on Chapters 2-3

Chapter 4. Square Roots

  1. Irrational Numbers
  2. Square Roots
  3. Properties of Square Roots

45-46. Operations with Square Roots, Parts I-II

  1. Working w/ Expressions w/ Square Root
  2. Rationalizing Expressions w/ Square Roots
  3. Problems/Test Preps on “Square Roots”
  4. Tests on “Square Roots”

Chapter 5. Quadratic Equations

  1. Quadratic Equations. Incomplete Ones
  2. The Roots of a Quadratic Equation
  3. Solving Quadratic Equations
  4. Equations that Reduce to Quadratic Ones
  5. Problems/Test Preps on “Quadratic Equations”
  6. Tests on “Quadratic Equations”

Chapter 6. Vector and Operations. Part I

  1. Vector. Definitions
  2. Sum of Vectors
  3. Sum of Vectors. Exercises
  4. Product of a Vector with a Number
  5. Difference of Vectors
  6. Applications of Vectors
  7. Problems on “Vectors and Operations”
  8. Quizzes on “Vectors and Operations”

Chapter 6. Midsegments and Centroids. Part II

  1. Midsegment of a Triangle
  2. Midsegment of a Triangle. Exercises
  3. Centroid of a Triangle
  4. Centroid of a Triangle. Exercises
  5. Midsegment of a Trapezoid
  6. Midsegment of a Trapezoid. Exercises
  7. Applications of Midsegments and Centroids
  8. Problems on “Midsegments and Centroids”
  9. Tests on “Midsegments and Centroids”

Chapter 7. Isometries

  1. Translation (along a Vector)
  2. Rotation (about a Point)
  3. Central Symmetry (Point Reflection)
  4. Reflection (across a Line)
  5. Isometries. Exercises
  6. Problems/Test Preps on “Isometries”
  7. Tests on “Isometries”