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Mathematics Workbook 8B Grade

ArchiMath Publishing LLC

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

Pages: 200

ISBN: 978-954-779-269-2

Available: Paperback & PDF

The second part of 8 grade workbooks 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. 


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.

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.

The Workbook for 8th garde will strengthen the basic knowledge and skills needed to master the 8th grade mathematics material. 

To each topic in the 8B Textbook correspond problems in the 8B 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 8B Worksheets highlight the basic knowledge in the 8B 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 8 grade Math Worksheets can be used for independent work by the student;

 to assign homework; 

to conduct tests; 

and for practical work with applications.

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

 94-95. Linear Functions, Eq’ns, Inequalities, I-II

 96-97. The Function y = ax2 , a ≠ 0, I-II

  1. Exercises on “Functions,” I-III
  2. Test Preps 1-2 on “Functions”
  3. Tests 1-3 on “Functions”

Chapter 9. Systems of Linear Equations

102-103. Linear Equations with Two Unknowns, I-II

  1. Systems of Linear Equations
  2. Solving Systems by Substitution
  3. Solving Systems by Addition
  4. Solving Systems of Equations. Exercises
  5. Model with Systems of Equations
  6. Exercises on “Systems of Equations,” I-II

 Test Preps 1-2 on “Systems of Equations,”

  1. Tests 1-2 on “Systems of Equations”

Chapter 10. Systems of Linear Inequalities

  1. Intersection and Union of Intervals
  2. Systems of Two Linear Inequalities
  3. Solving Systems of Inequalities
  4. Inequalities f (x) .g (x) > 0 and f (x) .g (x) < 0

116-117. Modular Inequalities | ax + b | < c or > c

  1. Exercises on “Systems of Inequalities,” I-II

 Test Preps 1-2 on “Systems of Inequalities”

  1. Tests 1-2 on “Systems of Inequalities”

Chapter 11. Part I: Circles and Angles

  1. Circle. Circle and Point. Circle and Line
  2. Tangents to a Circle
  3. 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. Apply Inscribed and Peripheral Angles
  9. Circles and Angles. Exercises
  10. Problems on “Circles and Angles,” I-III
  11. Tests 1-2 on “Circles and Angles”

Chapter 11. Part II: Circles and Polygons

  1. Geometric Constructions (Review)
  2. Construction Problems
  3. Geometric Locus of Points in the Plane
  4. GLP that Oversee a Segment at an Angle

136-137. Circumcircle of a Triangle. Exercises

138-139. Incircle of a Triangle. Exercises

140-141. Famous Points in a Triangle. Exercises

  1. Construct a Triangle. Exercises

143-144. Cyclic Quadrilateral. Exercises

145-146. Circumscribed Quadrilateral. Exercises

147-148. Problems on “Circles and Polygons,” I-III

149-150. Tests 1-2 on “Circles and Polygons”

Chapter 12. Equations and Roots

  1. Factor Quadratic Trinomials
  2. Biquadratic Equations

153-154. Equations Reducing to Quadratics. Exercises

155-156. Vieta’s Formulas and Applications

  1. Modeling with Quadratic Equations

 Exercises on “Equations and Roots,” I-II

 Test Preps 1-2 on “Equations and Roots”

  1. Tests 1-2 on “Equations and Roots”

Chapter 13. Rational Expressions

  1. Rational Expressions. Domain
  2. Reduce and Expand Rational Expressions
  3. Put Rational Expressions under a CD
  4. Add/Subtract Rational Expressions
  5. Operate on Rational Expressions
  6. Transform Rational Expressions

165-166. Rational Equations. Exercises

  1. Model with Rational Equations
  2. Exercises on “Rational Equations,” I-II

 Test Preps 1-2 on “Rational Expressions”

  1. Tests 1-2 on “Rational Expressions”

Chapter 14. Basic Combinatorial Concepts

171-172. Multiply/Add Possibilities. Exercises

  1. Permutations
  2. Variations
  3. Combinations
  4. Exercises on “Combinatorics,” I-II

Chapter 15. Yearly Review

179-180. Rational Numbers, Roots, and Equations

  1. Rational Expressions and Equations
  2. Vectors, Midsegments, and Centroids
  3. Circle Geometry
  4. Exit Test Preps 1-2

 Exit Tests 1-2 on 8th Grade Material