Standard
Algebra I · High school · Math
Topics typically covered
Typical US high school Algebra I — aligned with Khan Academy Algebra 1 units and Common Core high school Algebra conceptual categories.
Algebraic foundations
- Variables and expressions — Translate between words and algebraic expressions; evaluate expressions for given values.
- Properties of real numbers — Use commutative, associative, and distributive properties to rewrite expressions.
- Order of operations — Simplify numeric and algebraic expressions with exponents, grouping, and absolute value.
Linear equations and inequalities
- One- and multi-step equations — Solve linear equations in one variable, including those with fractions and decimals.
- Literal equations — Rearrange formulas to isolate a chosen variable.
- Linear inequalities — Solve and graph inequalities on a number line; write compound inequalities.
- Absolute value equations and inequalities — Solve equations and inequalities involving absolute value and interpret solutions.
Functions and graphs
- What is a function? — Distinguish functions from relations; use function notation f(x).
- Domain and range — Identify domain and range from graphs, tables, and verbal descriptions.
- Linear functions — Graph and write linear functions in slope-intercept and point-slope form.
- Slope and rate of change — Interpret slope as a constant rate of change in tables, graphs, and contexts.
- Piecewise and absolute-value graphs (intro) — Read and sketch simple piecewise-linear and absolute-value graphs.
Systems of equations and inequalities
- Solve systems by graphing — Estimate solutions of two linear equations from their graphs.
- Substitution — Solve systems algebraically by substitution.
- Elimination — Solve systems by adding or subtracting multiples of equations.
- Systems in context — Write and solve systems that model word problems.
- Systems of linear inequalities — Graph solution regions for systems of inequalities.
Exponents and radicals
- Properties of exponents — Multiply, divide, and raise powers with integer exponents.
- Scientific notation — Convert and compute with numbers in scientific notation.
- Square roots and simple radicals — Simplify square roots and solve equations of the form x² = k.
- Rational exponents (intro) — Connect nth roots with fractional exponents in basic cases.
Polynomials and factoring
- Add, subtract, and multiply polynomials — Combine like terms and expand products of binomials and multinomials.
- Greatest common factor — Factor out the GCF from polynomial expressions.
- Factoring trinomials — Factor quadratic trinomials with leading coefficient 1 and simple a ≠ 1 cases.
- Special products — Recognize difference of squares and perfect-square trinomials.
Quadratic functions and equations
- Features of parabolas — Identify vertex, axis of symmetry, intercepts, and direction of opening.
- Solve by factoring — Solve quadratic equations using factoring when possible.
- Solve by square roots — Solve equations of the form (x − h)² = k.
- Quadratic formula (intro) — Use the quadratic formula and interpret the discriminant at a basic level.
- Quadratic applications — Model simple projectile and area problems with quadratics.
Sequences
- Arithmetic sequences — Identify common differences and write recursive and explicit formulas.
- Geometric sequences (intro) — Identify common ratios and write simple geometric sequence formulas.
Data and linear models
- Scatter plots — Create scatter plots and describe form, direction, and strength of association.
- Line of best fit — Fit a linear model informally or with technology and interpret slope and intercept.
- Residuals and predictions (intro) — Use a linear model to make predictions and discuss limitations.
Related courses
Parallel materials covering overlapping topics — not the same as this course page.
- 9th Grade (Common Core)
Grade-level Common Core standards for the same band
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