1
Lesson 1: Transition from arithmetic to algebra
1.1
Lesson 1: Transition from arithmetic to algebra
Constants:
1.2
Lesson 1: Transition from arithmetic to algebra
Constants:
Coefficients:
1.3
Lesson 1: Transition from arithmetic to algebra
Constants:
Coefficients:
Variables:
1.4
2
Constants: are values that do not change within a given mathematical problem or expression. They are fixed numbers or symbols that represent a specific value. For example, in the equation y = 3x + 5, the number 5 is a constant because it remains the same throughout the problem. Common constants in mathematics include numbers like π (pi) and e, which represent specific mathematical values.
2.1
3
Coefficients: are the numerical factors that multiply variables in a mathematical expression or equation. They are constants that indicate the magnitude or strength of the relationship between variables. In the equation y = 3x + 5, the number 3 is a coefficient, as it multiplies the variable 'x' to determine the value of 'y'. Coefficients can be positive, negative, whole numbers, fractions, or decimals, but they do not change within a given problem or expression.
3.1
4
4.1
5
Some Practical Examples
5.1
Some Practical Examples 3x
5.2
Some Practical Examples 3x
5.3
Some Practical Examples
3x Variable
5.4
Some Practical Examples
3x Variable
5.5
Some Practical Examples
3x Variable
Coefficient
5.6
6
Constants are numbers
6.1
Constants are numbers e
6.2
Constants are numbers e 2 5
6.3
Constants are numbers e 2 5 −7
6.4
Constants are numbers π e 2 5 −7
6.5
7
Algebraic Expressions
7.1
Algebraic Expressions
A combination of variables, constants, and mathematical operations (such as addition, subtraction, multiplication, and division).
7.2
Algebraic Expressions
A combination of variables, constants, and mathematical operations (such as addition, subtraction, multiplication, and division).
Example:
7.3
Algebraic Expressions
A combination of variables, constants, and mathematical operations (such as addition, subtraction, multiplication, and division).
Example: 3x −7
7.4
Algebraic Expressions
A combination of variables, constants, and mathematical operations (such as addition, subtraction, multiplication, and division).
Example: 3x −7 3x + 2 3x +1
7.5
8
8.1
8.2
8.3
8.4
Linear Equation
8.5
Linear Equation
8.6
Linear Equation
Quadratic Equation
8.7
Linear Equation
8.8
Quadratic Equation ↙
8.9
Linear Equation Quadratic Equation ↙ Exponent 2
Linear Equation
Exponent 2
↘
8.10
Quadratic Equation ↙
Exponent 1
Exponent 2
Linear Equation
↘
Quadratic Equation ↙
8.11
9
Like Terms
9.1
Like Terms
"Like terms" refer to terms that have the same variables raised to the same power. In other words, terms that only differ by their coefficients are considered like terms.
9.2
10
For example, in the expression
3x + 2y - 5x - 7, the terms 3x and -5x are like terms because they both have the variable x raised to the first power.
10.1