Domain 2 • Linear Algebra & Equations
Algebra 1 on ALEKS
Algebra 1 is the primary filter for College Algebra placement (score 46+). Questions test your ability to isolate variables, manipulate graphs, solve linear systems, and factor quadratic expressions.
Core Tested Concepts
Multi-Step Linear EquationsDistributing negatives, clearing denominators with LCD, gathering like terms on one side of the equal sign.
Linear Graphs & SlopesSlope formula m = (y2 - y1) / (x2 - x1), slope-intercept form y = mx + b, point-slope form, parallel and perpendicular slopes.
Systems of Linear EquationsSolving 2-variable systems via substitution or elimination, identifying parallel (no solution) and coincident (infinite solutions) lines.
Factoring & PolynomialsFactoring out GCF, factoring trinomials x² + bx + c, difference of squares a² - b² = (a-b)(a+b).
High-Yield Cheat Sheet
Essential Algebra 1 Formulas
Slope Formula
m = (y₂ - y₁) / (x₂ - x₁)
Slope-Intercept
y = mx + b
Difference of Squares
a² - b² = (a - b)(a + b)
Practice Drills
5 Authentic Algebra 1 Practice Questions
1Practice Problem
Solve the linear equation for x: 5(x - 4) + 3 = 2x - 8
Hint: Distribute 5 across (x - 4), combine constants on the left side, then isolate x.
Formula: Distributive property: a(b - c) = ab - ac
2Practice Problem
Find the slope m of the line passing through the points (3, -2) and (-1, 6).
Hint: Use m = (y2 - y1) / (x2 - x1). Watch the double negative on x1.
Formula: m = (y₂ - y₁) / (x₂ - x₁)
3Practice Problem
Solve the system of equations for x: 3x + 2y = 16 x - 2y = 0
Hint: Add the two equations together to eliminate y: 3x + x = 4x, 2y + (-2y) = 0.
Formula: Elimination method
4Practice Problem
Which of the following is the completely factored form of x² - 9x + 20?
Hint: Look for two numbers that multiply to +20 and add to -9.
Formula: x² + (a+b)x + ab = (x+a)(x+b)
5Practice Problem
Simplify using exponent rules: (2x⁴)³
Hint: Apply the power to both the coefficient 2 and the variable term x⁴: 2³ · (x⁴)³.
Formula: (ab)ⁿ = aⁿbⁿ, (aᵐ)ⁿ = aᵐⁿ