# Algebra 1 Help & Practice

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##### 1Numbers

##### 2Ratios and Proportions

##### 3Percents

##### 4Measurement

##### 5Geometry

##### 6Coordinate Graphs

##### 7Solve Equations

##### 8Single-Variable Inequalities

##### 9Absolute Value Equations and Inequalities

##### 10Data and Graphs

##### 11Number Sequences

##### 12Relations and Functions

##### 13Direct and Inverse Variation

##### 14Linear Functions

- 14.1Slope equation: $m = \frac{y_2-y_1}{x_2- x_1}$
- 14.2Slope-Y-intercept form: y = mx + b
- 14.3General form: Ax + By + C = 0
- 14.4Point-slope form: $y - y_1 = m (x - x_1)$
- 14.5Applications of linear relations
- 14.6Special case of linear equations: Horizontal lines
- 14.7Special case of linear equations: Vertical lines
- 14.8Parallel line equation
- 14.9Perpendicular line equation

- 14.1Slope equation: $m = \frac{y_2-y_1}{x_2- x_1}$
##### 15Linear Inequalities

##### 16Systems of Linear Equations

- 16.1Determining number of solutions to linear equations
- 16.2Solving systems of linear equations by graphing
- 16.3Using elimination method to solve systems of equations
- 16.4Using substitution method to solve systems of equations
- 16.5Money related questions in linear equations
- 16.6Unknown number related questions in linear equations
- 16.7Distance and time related questions in linear equations
- 16.8Rectangular shape related questions in linear equations

- 16.1Determining number of solutions to linear equations
##### 17Exponents

##### 18Scientific Notation

##### 19Exponential Functions

- 19.1Exponents: Power rule
*(a^x)^y = a^(x * y)* - 19.2Exponents: Zero exponent:
*a^0 = 1* - 19.3Exponents: Rational exponents
- 19.4Graphing exponential functions
- 19.5Graphing transformations of exponential functions
- 19.6Finding an exponential function given its graph
- 19.7Continuous growth and decay in exponential and logarithmic functions

- 19.1Exponents: Power rule
##### 20Monomials

##### 21Polynomials

##### 22Factoring

- 22.1Common factors of polynomials
- 22.2Factoring polynomials by grouping
- 22.3Factoring polynomials:
*x^2 + bx + c* - 22.4Factoring polynomials: $ax^2 + bx + c$
- 22.5Factoring perfect square trinomials:
*(a + b)^2 = a^2 + 2ab + b^2*or*(a - b)^2 = a^2 - 2ab + b^2* - 22.6Find the difference of squares:
*(a - b)(a + b) = (a^2 - b^2)* - 22.7Factor theorem

- 22.1Common factors of polynomials
##### 23Quadratic Equations

- 23.1Characteristics of quadratic functions
- 23.2Transformations of quadratic functions
- 23.3Converting from general form to vertex form by completing the square
- 23.4Solving quadratic equations by factoring
- 23.5Solving quadratic equations by completing the square
- 23.6Using quadratic formula to solve quadratic equations
- 23.7Nature of roots of quadratic equations: the discriminant
- 23.8System of linear equations
- 23.9System of linear-quadratic equations

- 23.1Characteristics of quadratic functions
##### 24Functions: Linear, Quadratic, Exponential

##### 25Absolute Value Functions

##### 26Radical Expressions

##### 27Radical Functions and Equations

##### 28Rational Functions and Expressions

- 28.1Long division in polynomial functions
- 28.2Vertical asymptote
- 28.3Horizontal asymptote
- 28.4Slant asymptote
- 28.5Adding and subtracting rational expressions
- 28.6Multiplying rational expressions
- 28.7Dividing rational expressions
- 28.8Solving rational equations
- 28.9Simplifying complex fractions
- 28.10Partial fraction decomposition

- 28.1Long division in polynomial functions
##### 29Piecewise Functions

##### 30Trigonometry

- 30.1Using sine ratio to calculate angles and sides (Sin = $\frac{o}{h})$
- 30.2Using cosine ratio to calculate angles and sides (Cos = $\frac{a}{h}$)
- 30.3 Using tangent ratio to calculate angles and side (Tan = $\frac{o}{a} )$
- 30.4Combination of SohCahToa questions
- 30.5Word problems relating ladder in trigonometry
- 30.6Word problems relating guy wire in trigonometry
- 30.7Other word problems relating angles in trigonometry

- 30.1Using sine ratio to calculate angles and sides (Sin = $\frac{o}{h})$
##### 31Set Theory

##### 32Probability

##### 33Statistics

##### 34Introduction to Matrices