Formulas for Math Exam

For Lopuszynski Algebra 1 Class 2024-2025

Arithmetic Sequences

a_n = a₁ + (n - 1)d

Geometric Sequences

a_n = a₁r^n-1

Recursive Formula

a_n = ra_n-1

Direct Variation

y = kx

Slope Formula

m=\frac{y_{_2}-y_1}{x_2-x_1}

Point-Slope Formula

y - y₁ = m(x - x₁)

Slope-Intercept Formula

y = mx + b

Standard Form of Linear Equations

Ax + By = C

*Remember*

• A, B, and C are all integers

• A cannot be negative

Solving Systems of Linear Equations

• Graphing: to find the intersecting point visually

• Substitution: rearrange an equation to insert what the variable equals into the other equation

• Elimination: add/subtract the equations

  • Match the coefficient and variable to eliminate it and solve for each variable

Absolute Value Inequalities

1. If not isolated, isolate the absolute value

2. Rewrite the absolute value inequality as a compound inequality

3. Solve