**Authors: **Zvezdelina Stankova, Zdravka Paskaleva, Maya Alashka, Raina Alashka**Pages:** 244

**ISBN:** 978-954-779-289-0

**Available**: Paperback & PDF

The fourth year of our math curriculum solidifies and expands the foundation built in the first three years.

Archimath motivates and supports school students to become successful with the help of the most popular mathematical textbook series in Bulgarian public schools.

**Overview**

In 9th grade algebra, students continue their study of functions, master systems of quadratic equations, and learn a crystal clear method for solving inequalities involving polynomials, rational expressions, and/or absolute value. In geometry, students revisit the theorems from prior years and find that they can solve harder problems with less effort.

They move on with a unit on similar triangles, making heavy use of algebra they learned early on and setting the stage for trigonometry, which will be studied in 9B. Finally, students use their combinatorics knowledge from 8th grade part B to develop basic probability results.

**These 9th grade math texbooks cultivate a strong relationship between the students and the material; **

by using helpful color coding, symbols,

and by providing appropriate scaffolding for students throughout.

They have been used with great success in the very popular Math Taught the Right Way program at the world-famous Berkeley Math Circle.

In the textbooks, each lesson fits onto a two-page spread, including the practice problems, making it easier to focus on the topic at hand.

Chapter 1. Initial Review

- Preparation for Entrance Test in Algebra
- Preparation for Entrance Test in Geometry
- Test 1 with Solutions
- Test 2 with Solutions
- How Mathematicians Write Solutions
- How to Study for and How to Take Tests

General Problems from 7B-8B Material

- Entrance Level Tests 1-2

Chapter 2. Functions and Linear Systems:

Review with Extensions

- Functions
- Graph of the Quadratic Function
- Properties of Quadratic Functions: Increase

and Decrease, Minimum and Maximum

- Graphical Representation of the Solutions to Equations
- Systems of Equations and Inequalities
- Solving Systems of Linear Equations by Substitution
- Solving Systems of Linear Equations by Addition
- Solving Systems of Linear Equations

by Introducing New Variables

- Lines in the Plane. Number of Solutions
- Graphical Representation of the Solutions

to Linear Systems

- Modeling with Linear Systems
- Summary of “Functions”

Summary of “Linear Systems”

- Tests 1-2 on “Functions/Linear Systems

Chapter 3. Systems of Equations of Degree 2 with Two Unknowns

- Degree 2 Systems of Two Unknowns.

Systems with a Linear Equation

- Solving Systems with a Linear Equation. Exercises
- Systems with Both Equations of Degree 2
- Systems with Both Equations of Degree 2. Exercises
- Solving Degree 2 Systems. Exercises
- Solving Degree 2 Systems

by Introducing New Variables

- Solving Degree 2 Systems

by Introducing New Variables. Exercises

- Modeling with Systems of Equations

of Degree 2 with Two Unknowns

- Summary of “Systems of Equations

of Degree 2 with Two Unknowns”

- Tests on “Systems of Equations

of Degree 2 with Two Unknowns”

- General Problems on “Degree 2 Systems”

Chapter 4. Review of Geometry

- Foundations of Geometry

Test on “Foundations of Geometry”

- Congruent triangles: Part 1
- Congruent triangles: Part 2

Test on “Congruent Triangles”

- Problem Solving w/ Angles and Triangles

Tests 1-2 on “Angles and Triangles”

- Tests 3-4 on “Angles and Triangles”
- Special quadrilaterals
- Euclidean Constructions

Test 1 On “Euclidean Constructions”

Test 2 On “Quadrilaterals”

- Vectors and Operations
- Midsegments and Centroids
- Tests on “Vectors and Operations”

Tests on “Midsegments and Centroids”

- Circles and angles
- Circumcircles and Incircles
- Tests on “Circles and angles”

Tests on “Circumcircles and Incircles”

- Transformations in the Plane, Part I
- Transformations in the Plane, Part II

Test on “Isometries”

- Logic via Geometry
- General Tests 1-2 in Geometry

Chapter 5. Similar Triangles

- Proportional Segments
- Thales’ Theorem and Its Converse
- Property of Angle Bisectors in a Triangle
- Angle Bisectors in a Triangle. Exercises
- Similar Triangles. Definition
- First Criterion for Similarity of Triangles
- First Criterion for Similarity of Triangles. Exercises
- Second and Third Criteria for Similarity of Triangles
- Properties of Similar Triangles
- Properties of Similar Triangles. Exercises
- Ratio of the Areas of Similar Triangles
- Summary of “Similar Triangles”
- Tests on “Similar Triangles”
- General Problems on “Similar Triangles”

Chapter 6. Rational Inequalities

- Rational Expressions: Review
- Tests on “Rational Expressions”

General Problems on “Expressions”

- Union and Intersection of Intervals
- Inequalities |ax + b| > c, a ≠ 0
- Solving Systems of Linear Inequalities with One Unknown
- Solving Systems of Linear Inequalities with One Unknown. Exercises
- Double Inequalities
- Inequalities
- Quadratic Inequalities
- Quadratic Inequalities. Exercises
- The Method of Intervals
- The Method of Intervals in Higher Degrees
- Fractional Inequalities
- The Method of the Intervals. Exercises
- Summary of “Rational Inequalities”
- Tests on “Rational Inequalities”
- General Problems on “Inequalities”

Chapter 7. Classical Probability

- Combinatorics: Review
- Test on “Combinatorics”

General Problems on “Combinatorics”

- Sets
- Random Events
- Classical Probability
- Probability of the Sum of Disjoint Events
- Probability of the Complement
- Probability of an Event. Exercises
- Probability of the Union, Intersection

and Difference of Events

- Probability of the Sum of Compatible Events. Exercises
- Summary of “Classical Probabilities”
- Tests on “Classical Probabilities”
- General Problems on “Probabilities”

Answers

Summary of Concepts and Statements

- Geometry
- Algebra
- Number Theory
- Combinatorics and Probability
- Applied Mathematics
- Logic and True/False Questions