Common Core State Standards: Precalculus
Skills available for Washington Precalculus standards
Domain
Print skill plan
9-12.HSN
Number and Quantity
9-12.HSN-CN The Complex Number System
9-12.HSN-CN.A Perform arithmetic operations with complex numbers.
9-12.HSN-CN.A Perform arithmetic operations with complex numbers.
9-12.HSN-CN.A.3: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
Complex conjugates
Operations with complex numbers
Absolute value
9-12.HSN-CN.A.3: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
Complex conjugates
Operations with complex numbers
Absolute value
9-12.HSN-CN.B Represent complex numbers and their operations on the complex plane.
9-12.HSN-CN.B Represent complex numbers and their operations on the complex plane.
9-12.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.
Complex numbers
Polar and rectangular forms
9-12.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.
Complex numbers
Polar and rectangular forms
9-12.HSN-CN.B.5: Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.
9-12.HSN-CN.B.5: Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.
9-12.HSN-CN.B.6: Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.
9-12.HSN-CN.B.6: Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.
9-12.HSN-VM Vector and Matrix Quantities
9-12.HSN-VM.A Represent and model with vector quantities.
9-12.HSN-VM.A Represent and model with vector quantities.
9-12.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).
9-12.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).
9-12.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.
9-12.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.
9-12.HSN-VM.A.3: Solve problems involving velocity and other quantities that can be represented by vectors.
9-12.HSN-VM.A.3: Solve problems involving velocity and other quantities that can be represented by vectors.
9-12.HSN-VM.B Perform operations on vectors.
9-12.HSN-VM.B Perform operations on vectors.
9-12.HSN-VM.B.4: Add and subtract vectors.
9-12.HSN-VM.B.4: Add and subtract vectors.
9-12.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.
9-12.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.
9-12.HSN-VM.B.4b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
9-12.HSN-VM.B.4b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
9-12.HSN-VM.B.4c: Understand vector subtraction v – w as v + (–w), where –w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.
9-12.HSN-VM.B.4c: Understand vector subtraction v – w as v + (–w), where –w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.
9-12.HSN-VM.B.5: Multiply a vector by a scalar.
9-12.HSN-VM.B.5: Multiply a vector by a scalar.
9-12.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, vy) = (cvx, cvy).
9-12.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, vy) = (cvx, cvy).
9-12.HSN-VM.B.5b: Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).
9-12.HSN-VM.B.5b: Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).
9-12.HSN-VM.C Perform operations on matrices and use matrices in applications.
9-12.HSN-VM.C Perform operations on matrices and use matrices in applications.
9-12.HSN-VM.C.6: Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.
9-12.HSN-VM.C.6: Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.
9-12.HSN-VM.C.7: Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.
9-12.HSN-VM.C.7: Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.
9-12.HSN-VM.C.8: Add, subtract, and multiply matrices of appropriate dimensions.
Addition and subtraction
Multiplication
Mixed operations
9-12.HSN-VM.C.8: Add, subtract, and multiply matrices of appropriate dimensions.
Addition and subtraction
Multiplication
Mixed operations
9-12.HSN-VM.C.9: Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
9-12.HSN-VM.C.9: Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
9-12.HSN-VM.C.10: Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
Determinant of a matrix
Inverse of a matrix
9-12.HSN-VM.C.10: Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
Determinant of a matrix
Inverse of a matrix
9-12.HSN-VM.C.11: Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.
9-12.HSN-VM.C.11: Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.
9-12.HSN-VM.C.12: Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.
9-12.HSN-VM.C.12: Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.
9-12.HSA
Algebra
9-12.HSA-REI Reasoning with Equations and Inequalities
9-12.HSA-REI.C Solve systems of equations.
9-12.HSA-REI.C Solve systems of equations.
9-12.HSA-REI.C.8: Represent a system of linear equations as a single matrix equation in a vector variable.
9-12.HSA-REI.C.8: Represent a system of linear equations as a single matrix equation in a vector variable.
9-12.HSA-REI.C.9: Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).
9-12.HSA-REI.C.9: Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).
9-12.HSF
Functions
9-12.HSF-IF Interpreting Functions
9-12.HSF-IF.C Analyze functions using different representations.
9-12.HSF-IF.C Analyze functions using different representations.
9-12.HSF-IF.C.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
9-12.HSF-IF.C.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
9-12.HSF-IF.C.7d: Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
9-12.HSF-IF.C.7d: Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
9-12.HSF-BF Building Functions
9-12.HSF-BF.A Build a function that models a relationship between two quantities.
9-12.HSF-BF.A Build a function that models a relationship between two quantities.
9-12.HSF-BF.A.1: Write a function that describes a relationship between two quantities.
9-12.HSF-BF.A.1: Write a function that describes a relationship between two quantities.
9-12.HSF-BF.A.1c: Compose functions.
9-12.HSF-BF.A.1c: Compose functions.
9-12.HSF-BF.B Build new functions from existing functions.
9-12.HSF-BF.B Build new functions from existing functions.
9-12.HSF-BF.B.4: Find inverse functions.
9-12.HSF-BF.B.4: Find inverse functions.
9-12.HSF-BF.B.4b: Verify by composition that one function is the inverse of another.
9-12.HSF-BF.B.4b: Verify by composition that one function is the inverse of another.
9-12.HSF-BF.B.4c: Read values of an inverse function from a graph or a table, given that the function has an inverse.
9-12.HSF-BF.B.4c: Read values of an inverse function from a graph or a table, given that the function has an inverse.
9-12.HSF-BF.B.4d: Produce an invertible function from a non-invertible function by restricting the domain.
9-12.HSF-BF.B.4d: Produce an invertible function from a non-invertible function by restricting the domain.
9-12.HSF-BF.B.5: Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
Convert between forms
Solve exponential equations
Solve logarithmic equations
9-12.HSF-BF.B.5: Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
Convert between forms
Solve exponential equations
Solve logarithmic equations
9-12.HSF-TF Trigonometric Functions
9-12.HSF-TF.A Extend the domain of trigonometric functions using the unit circle.
9-12.HSF-TF.A Extend the domain of trigonometric functions using the unit circle.
9-12.HSF-TF.A.3: Use special triangles to determine geometrically the values of sine, cosine, and tangent for Ï€/3, Ï€/4, and Ï€/6, and use the unit circle to express the values of sine, cosine, and tangent for Ï€ – x, Ï€ + x, and 2Ï€ – x in terms of their values for x, where x is any real number.
9-12.HSF-TF.A.3: Use special triangles to determine geometrically the values of sine, cosine, and tangent for Ï€/3, Ï€/4, and Ï€/6, and use the unit circle to express the values of sine, cosine, and tangent for Ï€ – x, Ï€ + x, and 2Ï€ – x in terms of their values for x, where x is any real number.
9-12.HSF-TF.A.4: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
9-12.HSF-TF.A.4: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
9-12.HSF-TF.B Model periodic phenomena with trigonometric functions.
9-12.HSF-TF.B Model periodic phenomena with trigonometric functions.
9-12.HSF-TF.B.6: Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.
9-12.HSF-TF.B.6: Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.
9-12.HSF-TF.B.7: Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.
9-12.HSF-TF.B.7: Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.
9-12.HSF-TF.C Prove and apply trigonometric identities.
9-12.HSF-TF.C Prove and apply trigonometric identities.
9-12.HSF-TF.C.9: Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
9-12.HSF-TF.C.9: Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
9-12.HSG
Geometry
9-12.HSG-GPE Expressing Geometric Properties with Equations
9-12.HSG-GPE.A Translate between the geometric description and the equation for a conic section.
9-12.HSG-GPE.A Translate between the geometric description and the equation for a conic section.
9-12.HSG-GPE.A.3: Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.
9-12.HSG-GPE.A.3: Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.
9-12.HSG-GMD Geometric Measurement and Dimension
9-12.HSG-GMD.A Explain volume formulas and use them to solve problems.
9-12.HSG-GMD.A Explain volume formulas and use them to solve problems.
9-12.HSG-GMD.A.2: Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.
9-12.HSG-GMD.A.2: Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.
9-12.HSS
Statistics and Probability
9-12.HSS-MD Using Probability to Make Decisions
9-12.HSS-MD.A Calculate expected values and use them to solve problems.
9-12.HSS-MD.A Calculate expected values and use them to solve problems.
9-12.HSS-MD.A.1: Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.
9-12.HSS-MD.A.1: Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.
9-12.HSS-MD.A.2: Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
9-12.HSS-MD.A.2: Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
9-12.HSS-MD.A.3: Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.
9-12.HSS-MD.A.3: Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.
9-12.HSS-MD.A.4: Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.
9-12.HSS-MD.A.4: Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.
9-12.HSS-MD.B Use probability to evaluate outcomes of decisions.
9-12.HSS-MD.B Use probability to evaluate outcomes of decisions.
9-12.HSS-MD.B.5: Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
9-12.HSS-MD.B.5: Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
9-12.HSS-MD.B.5a: Find the expected payoff for a game of chance.
9-12.HSS-MD.B.5a: Find the expected payoff for a game of chance.
9-12.HSS-MD.B.5b: Evaluate and compare strategies on the basis of expected values.
9-12.HSS-MD.B.5b: Evaluate and compare strategies on the basis of expected values.