Equations & inequalities
Multi-step and compound inequalities, absolute value equations and solving formulas for a letter.
Multi-step inequalitiesHSA.REI.B.3Solve inequalities that need the distributive property or have x on both sides, flipping the sign when dividing by a negative.Absolute value equationsHSA.CED.A.1Solve equations with an absolute value by isolating it and splitting into a positive and a negative case.Literal equationsHSA.CED.A.4Rearrange formulas such as d = rt and P = 2l + 2w to solve for a different letter.Compound inequalitiesHSA.REI.B.3Solve three-part (and) inequalities, or-inequalities, and absolute value inequalities.
Linear functions & sequences
Slope-intercept form, parallel and perpendicular lines, function notation, and arithmetic and geometric sequences.
Slope-intercept formHSF.LE.A.2Write y = mx + b from a slope and a point, or from two points.Parallel and perpendicular linesHSG.GPE.B.5Write the equation of a line parallel or perpendicular to a given line through a given point.Evaluating functionsHSF.IF.A.2Use function notation: substitute the input into f(x) and evaluate, including negative inputs and squares.Arithmetic and geometric sequencesHSF.BF.A.2Find any term of an arithmetic sequence (add d each time) or a geometric sequence (multiply by r each time).
Polynomials & factoring
Adding, subtracting and multiplying polynomials, factoring trinomials, and factoring out common factors and special products.
Adding and subtracting polynomialsHSA.APR.A.1Add and subtract polynomials by combining like terms, distributing the minus sign when subtracting.Multiplying polynomialsHSA.APR.A.1Multiply a monomial by a binomial and two binomials together, then combine like terms.Factoring trinomialsHSA.SSE.A.2Factor x² + bx + c and ax² + bx + c into two binomials.Factoring: GCF and special productsHSA.SSE.A.2Factor out the greatest common factor, and factor differences of squares and perfect-square trinomials.
Quadratic functions & equations
The vertex of a parabola, completing the square, and solving by square roots, factoring or the quadratic formula.
Solving quadratics by factoringHSA.REI.B.4bSolve quadratic equations with the zero product property: get 0 on one side, factor, and set each factor equal to 0.Vertex of a parabolaHSF.IF.C.7aFind the vertex of a parabola from vertex form, or from standard form with x = −b/(2a).Completing the squareHSA.SSE.B.3bRewrite ax² + bx + c in vertex form by completing the square, including odd b and a ≠ 1.The quadratic formulaHSA.REI.B.4bSolve ax² + bx + c = 0 with x = (−b ± √(b² − 4ac)) / (2a), giving exact or rounded solutions.Solving quadratics with square rootsHSA.REI.B.4bSolve x² = k, ax² + c = d and (x − h)² = k by isolating the square and taking square roots.
Radicals & exponential functions
Simplifying square roots, radical equations, rational exponents, and exponential growth and decay.
Simplifying radicalsHSN.RN.A.2Simplify square roots by taking out the largest perfect-square factor, including roots with a number in front and products of roots.Exponential growth and decayHSF.LE.A.2Evaluate exponential functions and use y = a(1 + r)ᵗ and y = a(1 − r)ᵗ for percent growth and decay.Radical equationsHSA.REI.A.2Solve equations with a square root by isolating the root and squaring both sides.Rational exponentsHSN.RN.A.1Evaluate powers with fractional and negative exponents, such as 8^(2/3) and 16^(−3/4).