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

**Pages:** 196

**ISBN: **978-954-779-210-4

**Available**: Paperback & PDF

To start the second year of this series, the 7 grade textbooks give the students a quick recap of the 6A and 6B material before delving into new topics.

Many students who expand their understanding using Archimath see growth in areas of algebra, geometry, and creative problem solving. It is the best preparation for middle and high school students to tackle college mathematics and beyond. Materials that should be in school, but are often not!

**Overview**

The geometry journey moves on to more complicated polyhedral and round solids, making good use of the algebraic skills built up in 6 grade . In algebra, students also see a step up in sophistication. They encounter ratios and proportions and a few of their many applications, including more experience with representing and analyzing data and practical problems such as recipe and map scaling.

They wrap up the year with an intense study of polynomials and familiar factoring formulas, building skills that will prove invaluable for years to come.

Chapter 1. Initial Review

- Fractions, Parts, and Percents (Review)
- Rational Numbers and Powers (Review)
- Circles and Polygons (Review)
- Graphing and Data (Review)
- How Mathematicians Write Solutions
- Entrance Level: General Test
- How to Study for and How to Take Tests

“Algebra on Polynomials, Part II”

Chapter 2. Polyhedral Solids

- Prism. Regular Prism
- Right prism. Exercises
- Surface area of a Right Prism
- Surface area of a Right Prism. Exercises
- Volume of a Right Prism
- Volume and Surface Area of a Right Prism.
- Pyramid. Regular Pyramid
- Regular Pyramid. Exercises
- Surface Area of a Regular Pyramid
- Surface Area of a Regular Pyramid.
- Constructing Models of Polyhedral Solids.

Practical Exercises

- Volume of a Regular Pyramid
- Volume and Surface Area of a Regular

Pyramid. Exercises

- Summary of the Topic “Polyhedral Solids”
- Tests on the Topic “Polyhedral Solids”

Polynomials, Part II”

Chapter 3. Round Solids

- Right Circular Cylinder
- Surface Area of a Cylinder
- Volume of a Cylinder
- Right Circular Cone
- Surface Area of a Cone
- Surface Area of a Cone. Exercises
- Volume of a Cone
- Sphere. Surface Area of a Sphere
- Ball. Volume of a Ball
- Surface Area/Volume of a Ball. Exercises
- Round Solids. Practical Exercises
- Summary of the Topic: “Round Solids”
- Test on the Topic: “Round Solids”

Chapter 4. Proportions

- Ratio. Proportion
- Proportionality. Constant of Variation
- Basic Property of Proportions
- Properties of Proportions
- Applications of Proportions. Exercises
- The Ratio a : b : c.
- Presenting Data via a Circular Diagram
- Interpreting Data in a Circular Diagram
- Summary of the Topic “Proportions”
- Test on the Topic “Proportions”.

Polynomials, Part II”

Chapter 5. Integer Expressions. Polynomials

- Rational Expressions. Introduction
- Integer Expressions. Numerical Value
- Monomial. Standard Form of a Monomial
- Adding and Subtracting Monomials.

Similar Monomials

- Adding and Subtracting

Similar Monomials. Exercises

- Multiplying, Taking Powers of, and Dividing Monomials
- Polynomials. Standard Form
- Adding and Subtracting Polynomials
- Multiplying a Monomial w/ a Polynomial
- Multiplying a Polynomial w/ a Polynomial
- Multiplying Polynomials. Exercises
- Summary of the Topic “Integer Expressions”
- Test on the Topic “Integer Expressions”

Chapter 6. Algebra on Polynomials. Part I

Degree 2 Formulas

- Equivalent Expressions
- Formulas (a ± b)

2 = a2 ± 2ab + b2

- Formulas (a ± b)

2 = a2 ± 2ab + b2

Exercises

- Formula (a + b)(a − b) = a2 − b2
- Formulas for Quick Multiplication. Exercises
- Quick Multiplication. Applications
- Factoring Polynomials w/ a Common Factor
- Factoring by Using

the Formulas for Quick Multiplication

- Factoring by Grouping
- Factoring by Combining Various Methods
- Factoring by Various Methods. Continuation
- Equivalence Transformation. Applications
- Summary of the Topic

“Algebra on Polynomials, Part I”

- Test on the Topic “Algebra on Polynomials I”

Chapter 6. Algebra on Polynomials. Part II

Degree 3 Formulas (Optional)

- The Formulas (a ± b)

3 = a3 ± 3a2

b + 3ab2 ± b3

- The Formulas a3 ± b3 = (a ± b)(a2 ± ab + b2)
- Formulas for Quick Multiplication.

Exercises with Degrees 2 and 3

- Factoring by Using

the Formulas for Quick Multiplication

- Short Summary of the Topic ; Algebra on Polynomials, Part II