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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
Properties of Numbers in Grade 10 Math

Properties of Numbers in Grade 10 Math

1. Closure Property

The Closure Property states that the result of an operation on any two numbers of a set is also a number in the same set. For example, in the set of whole numbers, the sum and product of any two whole numbers are always whole numbers.

Example:

If we take two whole numbers, say 3 and 5, their sum is 3 + 5 = 8, which is also a whole number. Similarly, their product is 3 × 5 = 15, which is also a whole number.

2. Associative Property

The Associative Property states that the way in which numbers are grouped in an operation does not change the result. This property applies to both addition and multiplication.

Example:

For addition, (2 + 3) + 4 = 2 + (3 + 4). Here, both sides equal 9.

For multiplication, (2 × 3) × 4 = 2 × (3 × 4). Here, both sides equal 24.

3. Commutative Property

The Commutative Property states that the order in which numbers are added or multiplied does not change the result. This property applies to both addition and multiplication.

Example:

For addition, 2 + 3 = 3 + 2. Both sides equal 5.

For multiplication, 2 × 3 = 3 × 2. Both sides equal 6.

4. Distributive Property

The Distributive Property states that multiplying a number by the sum of two or more addends is the same as multiplying each addend separately and then adding the products. This property is crucial for simplifying expressions.

Example:

For the expression 2 × (3 + 4), we can distribute the 2 to both 3 and 4:

2 × (3 + 4) = 2 × 3 + 2 × 4 = 6 + 8 = 14.

5. Identity Property

The Identity Property states that there exists a unique number for addition (0) and multiplication (1) such that when this number is added to or multiplied by any number, the result is the original number.

Example:

For addition, 5 + 0 = 5.

For multiplication, 5 × 1 = 5.

6. Inverse Property

The Inverse Property states that for every number, there exists another number such that when the two numbers are added or multiplied, the result is the identity element (0 for addition and 1 for multiplication).

Example:

For addition, the inverse of 5 is -5 because 5 + (-5) = 0.

For multiplication, the inverse of 5 is 1/5 because 5 × 1/5 = 1.

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