Subject
Algebra I
Inequalities, functions, exponents, polynomials, and your first quadratics.
Begin at I if you’re new to Algebra I.
Solving Multi-Step Inequalities
Distribute, combine like terms, then isolate x — flipping the symbol when multiplying or dividing by a negative.
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Compound Inequalities
Solve 'between' inequalities like -3 < x + 2 < 5 by doing the same operation to all three parts at once.
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Absolute Value Equations and Inequalities
|A| = k splits into two cases. The same idea drives absolute value inequalities — a sandwich (<) or two separate pieces (>).
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Functions: Evaluating
Substitute a value for x in a function's rule and simplify. The foundation of function notation.
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Domain and Range
Domain is the set of valid inputs; range is the set of outputs. Watch for denominators that can't be zero and roots that can't be negative.
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Exponent Rules
Three rules for same-base exponents: add when multiplying, subtract when dividing, multiply when raising a power.
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Negative and Zero Exponents
Two more rules: anything to the 0 power is 1, and a negative exponent means take the reciprocal.
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Scientific Notation
Write numbers in the form a × 10^n with 1 ≤ |a| < 10. Used everywhere in science.
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Square Roots and Radicals
Find square roots of perfect squares and simplify radicals by pulling out the largest perfect-square factor.
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Slope from Two Points
Use m = (y₂ − y₁) / (x₂ − x₁) to find the slope between two points.
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Writing Equations: Slope-Intercept Form
Given two points on a line, write the equation in y = mx + b form.
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Point-Slope and Standard Form
The three forms of a line and how to switch between them. Pull slope and intercepts from any of them.
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Parallel and Perpendicular Lines
Parallel lines share slopes; perpendicular slopes are negative reciprocals. Spot both from any form of a line.
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Direct and Inverse Variation
Two patterns where quantities move together: direct (y = kx) and inverse (xy = k). Find k from a known pair and apply it.
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Systems of Linear Equations
Solve systems in two and three variables using substitution and elimination. The solution makes every equation true at once.
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Systems of Linear Inequalities
Find the feasible region's corner points by solving the boundary lines as a system of equations.
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Word Problems with Linear Equations
Translate a real-life situation into an equation, then solve. Practice the find-unknown → write → solve → check loop.
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Adding and Subtracting Polynomials
Combine like terms across polynomials. For subtraction, distribute the negative sign across every term first.
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Multiplying Polynomials (FOIL)
Use FOIL to multiply two binomials. Distribute carefully — sign matters — and combine like terms in the result.
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Factoring
Three methods: GCF, trinomial factoring (find p and q), and difference of squares. Recognize the form first.
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Solving Quadratic Equations
Solve by square roots when the equation is x² = k, or by factoring + the zero-product property for full trinomials.
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Graphing Quadratics
Find the vertex, axis of symmetry, y-intercept, and direction of a parabola from vertex or standard form.
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Pythagorean Theorem
In a right triangle, a² + b² = c². Use it to find a missing side.
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