PreAlgebra 1 Syllabus | Counting To Calculus

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Counting to Calculus & Beyond

Textbooks and Syllabi for the Full Course

Tools for Mastering Mathematics Book (For All Students)
PreAlgebra 1 Syllabus
PreAlgebra Textbook
Algebra 1/Algebra 2 Concepts (TW Textbook)
PreCalculus Textbook
Geometry Textbook
Euler - Elements of Algebra (Textbook from the 1700s/1880s)

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Assessment

1. The Whole Numbers

Why Counting To Calculus? (17:29)
1.1. An Introduction to the Whole Numbers (22:30)
1.2. Adding and Subtracting Whole Numbers (29:47)
1.3. Multiplication and Division of Whole Numbers (21:49)
1.4. Prime Factorization (10:57)
1.5. Order of Operations (19:16)
1.6. Solving Equations by Addition and Subtraction (11:20)
1.7. Solving Equations by Multiplication and Division (11:19)

2. The Integers

2.1. An Introduction to the Integers
2.2. Adding Integers
2.3. Subtracting Integers
2.4. Multiplication and Division of Integers
2.5. Order of Operations with Integers
2.6. Solving Equations Involving Integers

3. The Fundamentals of Algebra

3.1. Mathematical Expressions
3.2. Evaluating Algebraic Expressions
3.3. Simplifying Algebraic Expressions
3.4. Combining Like Terms
3.5. Solving Equations Involving Integers II
3.6. Applications

4. Fractions

4.1. Equivalent Fractions
4.2. Multiplying Fractions
4.3. Dividing Fractions
4.4. Adding and Subtracting Fractions
4.5. Multiplying and Dividing Mixed Fractions
4.6. Adding and Subtracting Mixed Fractions
4.7. Order of Operations with Fractions
4.8. Solving Equations with Fractions

5. Decimals

5.1. Introduction to Decimals
5.2. Adding and Subtracting Decimals
5.3. Multiplying Decimals
5.4. Dividing Decimals
5.5. Fractions and Decimals
5.6. Equations with Decimals
5.7. Introduction to Square Roots
5.8. The Pythagorean Theorem

6. Ratio and Proportion

6.1. Introduction to Ratios and Rates (18:01)
6.2. Introduction to Proportion (14:04)
6.3. Unit Conversion: American System (10:45)
6.4. Unit Conversion: Metric System
6.5. American Unit to Metric Unit and Vice-Versa

7. Percents

7.1. Percent, Decimals, Fractions
7.2. Solving Basic Percent Problems
7.3. General Applications of Percent
7.4. Percent Increase or Decrease
7.5. Interest
7.6. Pie Charts

Fundamentals of Algebra

Properties of Algebra

8. Solving Linear Equations (Algebra Tyler Wallace Textbook)

8.1. One-Step Equations
8.2. Two-Step Equations
8.3. General Linear Equations
8.4. Solving with Fractions
8.5. Formulas
8.6. Absolute Value Equations
8.7. Variation
8.8. Application: Number/Geometry
8.9. Application: Age
8.10. Application: Distance

9. Graphing

9.1. The Cartesian Coordinate System
9.2. Graphing Linear Equations
9.3. Points and Lines
9.4. Slope
9.5. Slope-Intercept Form
9.6. Point-Slope Form
9.7. Parallel and Perpendicular Lines

10. Inequalities

10.1. Solve and Graph Inequalities
10.2. Compound Inequalities
10.3 Absolute Value Inequalities

11. Systems of Equations

11.1. Graphing
11.2. Substitution
11.3. Addition/Elimination
11.4. Three Variables
11.5. Application: Value Problems
11.6. Application: Mixture Problems

12. Polynomials

12.1. Exponent Properties
12.2. Negative Exponents
12.3. Scientific Notation
12.4. Introduction to Polynomials
12.5. Multiply Polynomials
12.6. Multiply Special Products
12.7. Divide Polynomials

13. Factoring

Factoring Strategies and Overview
13.1. Greatest Common Factor
13.2. Grouping
13.3. Trinomials where a=1
13.4. Trinomials where a≠1
13.5. Factoring Special Products
13.6. Factoring Strategy
13.7. Solve by Factoring

14. Rational Expressions

14.1. Reduce Rational Expressions
14.2. Multiply and Divide
14.3. Least Common Denominator
14.4. Add and Subtract
14.5. Complex Fractions
14.6. Proportions
14.7. Solving Rational Equations
14.8. Application: Dimensional Analysis

15. Radicals

15.1. Square Roots
15.2. Higher Roots
15.3. Adding Radicals
15.4. Multiply and Divide Radicals
15.5. Rationalize Denominators
15.6. Rational Exponents
15.7. Radicals of Mixed Index
15.8. Complex Numbers

16. Quadratics

16.1. Solving with Radicals
16.2. Solving with Exponents
16.3. Complete the Square
16.4. Quadratic Formula
16.5. Build Quadratics from Roots
16.6. Quadratic in Form
16.7. Application: Rectangles
16.8. Application: Teamwork
16.9 Simultaneous Products
16.10. Application: Revenue and Distance
16.11. Graphs of Quadratics

17. Functions

17.1. Function Notation
17.2. Operations on Functions
17.3. Inverse Functions
17.4. Exponential Functions
17.5. Logarithmic Functions
17.6. Application: Compound Interest
17.7. Trigonometric Functions
17.8. Inverse Trigonometric Functions

Surfaces and Solid

Prisms, Area, and Volume (5:51)
Pyramids, Area and Volume (3:28)
Cylinders and Cones (3:33)
Polyhedrons and Spheres (4:51)

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PreAlgebra 1 Syllabus

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