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Math for Grade 10
1 Number Systems
1-1 Introduction to Number Systems
1-2 Types of Numbers
1-2 1 Natural Numbers
1-2 2 Whole Numbers
1-2 3 Integers
1-2 4 Rational Numbers
1-2 5 Irrational Numbers
1-2 6 Real Numbers
1-3 Properties of Numbers
1-3 1 Commutative Property
1-3 2 Associative Property
1-3 3 Distributive Property
1-3 4 Identity Property
1-3 5 Inverse Property
1-4 Operations with Real Numbers
1-4 1 Addition
1-4 2 Subtraction
1-4 3 Multiplication
1-4 4 Division
1-4 5 Order of Operations (PEMDASBODMAS)
1-5 Exponents and Radicals
1-5 1 Exponent Rules
1-5 2 Scientific Notation
1-5 3 Square Roots
1-5 4 Cube Roots
1-5 5 nth Roots
1-6 Rationalizing Denominators
2 Algebra
2-1 Introduction to Algebra
2-2 Expressions and Equations
2-2 1 Simplifying Algebraic Expressions
2-2 2 Linear Equations
2-2 3 Quadratic Equations
2-2 4 Solving Equations with Variables on Both Sides
2-2 5 Solving Literal Equations
2-3 Inequalities
2-3 1 Linear Inequalities
2-3 2 Quadratic Inequalities
2-3 3 Absolute Value Inequalities
2-4 Polynomials
2-4 1 Introduction to Polynomials
2-4 2 Adding and Subtracting Polynomials
2-4 3 Multiplying Polynomials
2-4 4 Factoring Polynomials
2-4 5 Special Products
2-5 Rational Expressions
2-5 1 Simplifying Rational Expressions
2-5 2 Multiplying and Dividing Rational Expressions
2-5 3 Adding and Subtracting Rational Expressions
2-5 4 Solving Rational Equations
2-6 Functions
2-6 1 Introduction to Functions
2-6 2 Function Notation
2-6 3 Graphing Functions
2-6 4 Linear Functions
2-6 5 Quadratic Functions
2-6 6 Polynomial Functions
2-6 7 Rational Functions
3 Geometry
3-1 Introduction to Geometry
3-2 Basic Geometric Figures
3-2 1 Points, Lines, and Planes
3-2 2 Angles
3-2 3 Triangles
3-2 4 Quadrilaterals
3-2 5 Circles
3-3 Geometric Properties and Relationships
3-3 1 Congruence and Similarity
3-3 2 Pythagorean Theorem
3-3 3 Triangle Inequality Theorem
3-4 Perimeter, Area, and Volume
3-4 1 Perimeter of Polygons
3-4 2 Area of Polygons
3-4 3 Area of Circles
3-4 4 Surface Area of Solids
3-4 5 Volume of Solids
3-5 Transformations
3-5 1 Translations
3-5 2 Reflections
3-5 3 Rotations
3-5 4 Dilations
4 Trigonometry
4-1 Introduction to Trigonometry
4-2 Trigonometric Ratios
4-2 1 Sine, Cosine, and Tangent
4-2 2 Reciprocal Trigonometric Functions
4-3 Solving Right Triangles
4-3 1 Using Trigonometric Ratios to Solve Right Triangles
4-3 2 Applications of Right Triangle Trigonometry
4-4 Trigonometric Identities
4-4 1 Pythagorean Identities
4-4 2 Angle Sum and Difference Identities
4-4 3 Double Angle Identities
4-5 Graphing Trigonometric Functions
4-5 1 Graphing Sine and Cosine Functions
4-5 2 Graphing Tangent Functions
4-5 3 Transformations of Trigonometric Graphs
5 Statistics and Probability
5-1 Introduction to Statistics
5-2 Data Collection and Representation
5-2 1 Types of Data
5-2 2 Frequency Distributions
5-2 3 Graphical Representations of Data
5-3 Measures of Central Tendency
5-3 1 Mean
5-3 2 Median
5-3 3 Mode
5-4 Measures of Dispersion
5-4 1 Range
5-4 2 Variance
5-4 3 Standard Deviation
5-5 Probability
5-5 1 Introduction to Probability
5-5 2 Basic Probability Concepts
5-5 3 Probability of Compound Events
5-5 4 Conditional Probability
5-6 Statistical Inference
5-6 1 Sampling and Sampling Distributions
5-6 2 Confidence Intervals
5-6 3 Hypothesis Testing
2-1 Introduction to Algebra

2-1 Introduction to Algebra

Key Concepts of Algebra

Algebra is a branch of mathematics that uses symbols and letters to represent numbers and quantities in equations and formulas. It is a powerful tool for solving problems and understanding relationships between different quantities.

1. Variables and Constants

In algebra, variables are symbols (usually letters) that represent unknown values. Constants are fixed values that do not change. For example, in the equation \( y = 2x + 3 \), \( x \) is a variable, and 2 and 3 are constants.

Example:

In the expression \( 5x + 7 \), \( x \) is the variable, and 5 and 7 are constants.

2. Expressions and Equations

An algebraic expression is a combination of variables, constants, and operators (like addition, subtraction, multiplication, and division). An equation is a statement that two expressions are equal. For example, \( 3x + 4 \) is an expression, and \( 3x + 4 = 10 \) is an equation.

Example:

The expression \( 2x^2 + 5x - 3 \) involves variables and constants combined with operators.

The equation \( 2x + 3 = 9 \) states that the expression \( 2x + 3 \) is equal to 9.

3. Solving Equations

Solving an equation means finding the value of the variable that makes the equation true. This often involves isolating the variable on one side of the equation. For example, to solve \( 2x + 3 = 9 \), you would first subtract 3 from both sides, then divide by 2 to find \( x \).

Example:

Solve \( 2x + 3 = 9 \):

1. Subtract 3 from both sides: \( 2x = 6 \)

2. Divide both sides by 2: \( x = 3 \)

4. Algebraic Properties

Algebraic properties, such as the commutative, associative, and distributive properties, help simplify and solve equations. For example, the distributive property states that \( a(b + c) = ab + ac \).

Example:

Using the distributive property to simplify \( 3(x + 2) \):

\[ 3(x + 2) = 3x + 6 \]

5. Applications of Algebra

Algebra is used in various real-world applications, such as calculating interest rates, determining distances, and solving problems in physics and engineering. Understanding algebra helps in making predictions and decisions based on mathematical models.

Example:

If you invest $1000 at an annual interest rate of 5% compounded annually for 3 years, you can calculate the future value using the formula \( A = P(1 + r)^t \):

\[ A = 1000(1 + 0.05)^3 \approx 1157.63 \]

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