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# Algebra 1

Algebra  basically consists of symbols and expressions , equations in variables.

Here is the list of Algebra 1 topics .
Preliminary Topics or Pre-Algebra

1) Number Sense:

(a) Integers, Rational Numbers
(b) Absolute Values
(c) Conversion between Fractions, Decimals and Percentage Values
(d) Factoring Numbers, LCM and GCF
(e) Scientific Notation

2) Exponents:
• Basic Rules

3) Order of Operations:
Example: Simplify $2(3^2\ +$ $\frac{12}{6})$ $-\ 6$

4) Arithmetic Properties:

(a) Associative Property
(b) Distributive Property

5) Simplifying Algebraic Expressions:
Example: Add and simplify $(2x + 4y) + (x - y)$
Algebra 1 Topics:

1) Variables:
(a) Converting the given information to mathematical expressions using variables

Example: A number is $3$ less than double another number $n$ = $2m - 3$

(b) Evaluating Algebraic Expression

Example: Evaluate $2x + 3y$ when $x$ = $3$ and $y$ = $-2$.

(c) Solving Literal Equations EX: Solve $x$ = $\frac{4y}{3t}$ for $x$.

2) Linear Equations:
(a) Solving Simple One-Step Equations
Example: Solve $n + 8$ = $12$
(b) Solving Two-Step Equations
Example: $2x + 3$ = $17$
(c) Equations with Fractions
Example: $\frac{1}{2}$ $x - 4$ = $10$
(d) Equations with Variables on Both Sides

Example: $2x - 3$ = $x + 5$
(e) Real Life Word Problems

3) Ratio and Proportions

• Numeric Problems and Word Problems

4) Writing Equations:
(a) Equation of a Line in Different Forms:
• Slope-intercept Form $y$ = $mx + b$

• Intercepts Form $\frac{x}{b}$ $+$ $\frac{y}{b}$ = $1$

• General Form $Ax + by + c$ = $0$
(b) Given Slope and Point
(c) Given Two Points
(d) Writing Equations from Word Problems
• Age Problems

• Speed-Distance Problems

• Uniform Rate Problems

5) Converting Units

6) Graphing Equations
(a) Plotting Points (numbers as points) on Number Line and $x - y$ Plane.
(b) Graphing Using a Point Chart
(c) Slope  of a Line

• Calculating Slope

• Graphing Slope

• Determining Slope from Equation of Line
(d) Rate of Change as the Slope (for word problems)

(e) Graphing using the $x$ and $y$ intercepts.

7) System of Equations

(a) Graphical Method of Solving the System
(b) Substitution Method
(c) Elimination Method
(d) Word Problems
• Mixture Problems

• Coin Problems

• Work Word Problems.

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 More topics in  Algebra 1 Algebra 1 Problems Solving Equations Solving Equations by Factoring Solving Equations with Two Variables How to Solve Equations with Fractions Solving Equations by Substitution Solving Equations with integers Solving Linear Equations Solving Radical Equations Rational equations Systems of Equations Quadratic Equations Polynomial Solving Equations with Exponents Solving Trigonometric Equations Solving Systems of Equations by Graphing Solving Polynomial Equations Solving Absolute Value Equations Solving Rational Equations Solving Equations with Variables on both sides Solving Quadratic Equations Solving Logarithmic Equations Solving Systems of Equations Solving Inequalities Polynomial Inequalities Systems of Inequalities Rational Inequalities Inequalities with Fractions Quadratic Inequalities Logarithmic Equations Exponential Equations Matrices
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