Common Core State Standards
CCSS.Math.Content.HSN.RN: The Real Number System
CCSS.Math.Content.HSN.RN.A: Extend the properties of exponents to rational exponents.
CCSS.Math.Content.HSN.RN.A.1: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.
CCSS.Math.Content.HSN.CN: The Complex Number System
CCSS.Math.Content.HSN.CN.A: Perform arithmetic operations with complex numbers.
CCSS.Math.Content.HSN.CN.A.1: Know there is a complex number 𝘪 such that 𝘪² = –1, and every complex number has the form 𝘢 + 𝘣𝘪 with 𝘢 and 𝘣 real.
CCSS.Math.Content.HSN.CN.A.2: Use the relation 𝘪² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
CCSS.Math.Content.HSN.CN.A.3: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
CCSS.Math.Content.HSN.CN.B: Represent complex numbers and their operations on the complex plane.
CCSS.Math.Content.HSN.CN.B.4: Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.
CCSS.Math.Content.HSN.CN.C: Use complex numbers in polynomial identities and equations.
CCSS.Math.Content.HSN.CN.C.7: Solve quadratic equations with real coefficients that have complex solutions.
CCSS.Math.Content.HSN.VM: Vector and Matrix Quantities
CCSS.Math.Content.HSN.VM.A: Represent and model with vector quantities.
CCSS.Math.Content.HSN.VM.A.1: Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., 𝙫, |𝙫|, ||𝙫||, 𝘷).
CCSS.Math.Content.HSN.VM.A.2: Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
CCSS.Math.Content.HSN.VM.A.3: Solve problems involving velocity and other quantities that can be represented by vectors.
CCSS.Math.Content.HSN.VM.B: Perform operations on vectors.
CCSS.Math.Content.HSN.VM.B.4a: Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.
CCSS.Math.Content.HSN.VM.B.4b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
CCSS.Math.Content.HSN.VM.B.5a: Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as 𝘤(𝘷ₓ, 𝘷 subscript 𝘺) = (𝘤𝘷ₓ, 𝘤𝘷 subscript 𝘺).
CCSS.Math.Content.HSA.SSE: Seeing Structure in Expressions
CCSS.Math.Content.HSA.SSE.A: Interpret the structure of expressions
CCSS.Math.Content.HSA.SSE.A.1a: Interpret parts of an expression, such as terms, factors, and coefficients.
CCSS.Math.Content.HSA.SSE.A.1b: Interpret complicated expressions by viewing one or more of their parts as a single entity.
CCSS.Math.Content.HSA.SSE.A.2: Use the structure of an expression to identify ways to rewrite it.
CCSS.Math.Content.HSA.SSE.B: Write expressions in equivalent forms to solve problems
CCSS.Math.Content.HSA.SSE.B.3a: Factor a quadratic expression to reveal the zeros of the function it defines.
CCSS.Math.Content.HSA.SSE.B.3c: Use the properties of exponents to transform expressions for exponential functions.
CCSS.Math.Content.HSA.APR: Arithmetic with Polynomials and Rational Expressions
CCSS.Math.Content.HSA.APR.A: Perform arithmetic operations on polynomials
CCSS.Math.Content.HSA.APR.A.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
CCSS.Math.Content.HSA.APR.B: Understand the relationship between zeros and factors of polynomials
CCSS.Math.Content.HSA.APR.B.2: Know and apply the Remainder Theorem: For a polynomial 𝘱(𝘹) and a number 𝘢, the remainder on division by 𝘹 – 𝘢 is 𝘱(𝘢), so 𝘱(𝘢) = 0 if and only if (𝘹 – 𝘢) is a factor of 𝘱(𝘹).
CCSS.Math.Content.HSA.APR.B.3: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
CCSS.Math.Content.HSA.APR.C: Use polynomial identities to solve problems
CCSS.Math.Content.HSA.APR.C.5: Know and apply the Binomial Theorem for the expansion of (𝘹 + 𝘺)ⁿ in powers of 𝘹 and y for a positive integer 𝘯, where 𝘹 and 𝘺 are any numbers, with coefficients determined for example by Pascal’s Triangle.
CCSS.Math.Content.HSA.CED: Creating Equations
CCSS.Math.Content.HSA.CED.A: Create equations that describe numbers or relationships
CCSS.Math.Content.HSA.CED.A.1: Create equations and inequalities in one variable and use them to solve problems.
CCSS.Math.Content.HSA.CED.A.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
CCSS.Math.Content.HSA.CED.A.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.
CCSS.Math.Content.HSA.CED.A.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
CCSS.Math.Content.HSA.REI: Reasoning with Equations and Inequalities
CCSS.Math.Content.HSA.REI.A: Understand solving equations as a process of reasoning and explain the reasoning
CCSS.Math.Content.HSA.REI.A.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
CCSS.Math.Content.HSA.REI.A.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
CCSS.Math.Content.HSA.REI.B: Solve equations and inequalities in one variable
CCSS.Math.Content.HSA.REI.B.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
CCSS.Math.Content.HSA.REI.B.4b: Solve quadratic equations by inspection (e.g., for 𝘹² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as 𝘢 ± 𝘣𝘪 for real numbers 𝘢 and 𝘣.
CCSS.Math.Content.HSA.REI.C: Solve systems of equations
CCSS.Math.Content.HSA.REI.C.5: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
CCSS.Math.Content.HSA.REI.C.6: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
CCSS.Math.Content.HSA.REI.C.8: Represent a system of linear equations as a single matrix equation in a vector variable.
CCSS.Math.Content.HSA.REI.D: Represent and solve equations and inequalities graphically
CCSS.Math.Content.HSA.REI.D.10: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
CCSS.Math.Content.HSA.REI.D.11: Explain why the 𝘹-coordinates of the points where the graphs of the equations 𝘺 = 𝘧(𝘹) and 𝘺 = 𝑔(𝘹) intersect are the solutions of the equation 𝘧(𝘹) = 𝑔(𝘹); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where 𝘧(𝘹) and/or 𝑔(𝘹) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
CCSS.Math.Content.HSA.REI.D.12: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
CCSS.Math.Content.HSF.IF: Interpreting Functions
CCSS.Math.Content.HSF.IF.A: Understand the concept of a function and use function notation
CCSS.Math.Content.HSF.IF.A.1: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If 𝘧 is a function and 𝘹 is an element of its domain, then 𝘧(𝘹) denotes the output of 𝘧 corresponding to the input 𝘹. The graph of 𝘧 is the graph of the equation 𝘺 = 𝘧(𝘹).
CCSS.Math.Content.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
CCSS.Math.Content.HSF.IF.B: Interpret functions that arise in applications in terms of the context
CCSS.Math.Content.HSF.IF.B.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
CCSS.Math.Content.HSF.IF.B.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
CCSS.Math.Content.HSF.IF.B.6: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
CCSS.Math.Content.HSF.IF.C: Analyze functions using different representations
CCSS.Math.Content.HSF.IF.C.7a: Graph linear and quadratic functions and show intercepts, maxima, and minima.
CCSS.Math.Content.HSF.IF.C.7b: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
CCSS.Math.Content.HSF.IF.C.7c: Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.