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Skills available for Louisiana high school math standards

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Louisiana Student Standards (adopted in 2025): Advanced Math Functions and Statistics Louisiana Student Standards (adopted in 2025): Advanced Math Functions and Statistics
Louisiana Student Standards (adopted in 2025): Advanced Math Precalculus Louisiana Student Standards (adopted in 2025): Advanced Math Precalculus
Louisiana Student Standards (adopted in 2025): Algebra I Louisiana Student Standards (adopted in 2025): Algebra I
Louisiana Student Standards (adopted in 2025): Algebra II Louisiana Student Standards (adopted in 2025): Algebra II
Louisiana Student Standards (adopted in 2025): Algebra III Louisiana Student Standards (adopted in 2025): Algebra III
Louisiana Student Standards (adopted in 2025): Geometry Louisiana Student Standards (adopted in 2025): Geometry
Louisiana Student Standards (adopted in 2025): Integrated Math I Louisiana Student Standards (adopted in 2025): Integrated Math I
Louisiana Student Standards (adopted in 2025): Integrated Math II Louisiana Student Standards (adopted in 2025): Integrated Math II
Louisiana Student Standards (adopted in 2025): Integrated Math III Louisiana Student Standards (adopted in 2025): Integrated Math III
Louisiana Student Standards (adopted in 2025): Probability and Statistics Louisiana Student Standards (adopted in 2025): Probability and Statistics
Louisiana Student Standards: Algebra I Louisiana Student Standards: Algebra I
Louisiana Student Standards: Algebra II Louisiana Student Standards: Algebra II
Louisiana Student Standards: Geometry Louisiana Student Standards: Geometry
Louisiana Student Standards: Mathematical Practices Louisiana Student Standards: Mathematical Practices

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A3:N Number & Quantity

A3:N-CN The Complex Number System
- A3:N-CN.A Perform arithmetic operations with complex numbers.
  - A3:N-CN.A.2 Use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
  - A3:N-CN.A.3 Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
- A3:N-CN.B Represent complex numbers and their operations on the complex plane.
  - A3:N-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.
  - A3:N-CN.B.5 Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.
  - A3:N-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.
    - Midpoints in the complex plane (PC-W.7)
    - Distance in the complex plane (PC-W.8)
- A3:N-CN.C Use complex numbers in polynomial identities and equations.
  - A3:N-CN.C.7 Solve quadratic equations with real coefficients that have complex solutions.
  - A3:N-CN.C.8 Extend polynomial identities to the complex numbers.
  - A3:N-CN.C.9 Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
    - Fundamental Theorem of Algebra (PC-F.9)
A3:N-VM Vector and Matrix Quantities
- A3:N-VM.A Represent and model with vector quantities.
  - A3:N-VM.A.1 Understand vector attributes.
    - A3:N-VM.A.1a Represent vector quantities as having both magnitude and direction by directed line segments.
    - A3:N-VM.A.1b Use appropriate symbols for vectors and their magnitudes.
  - A3:N-VM.A.2 Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
    - Find the component form of a vector (PC-Y.2)
    - Find the component form of a three-dimensional vector (PC-Z.2)
  - A3:N-VM.A.3 Solve problems involving velocity and other quantities that can be represented by vectors.
- A3:N-VM.B Perform operations on vectors.
  - A3:N-VM.B.4 Add and subtract vectors.
    - A3:N-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.
    - A3:N-VM.B.4b Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
      - Find the magnitude and direction of a vector sum (PC-Y.9)
    - A3:N-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.
      - Subtract vectors (PC-Y.8)
      - Add and subtract three-dimensional vectors (PC-Z.3)
  - A3:N-VM.B.5 Multiply a vector by a scalar.
    - A3:N-VM.B.5a Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise.
      - Multiply a vector by a scalar (PC-Y.10)
      - Scalar multiples of three-dimensional vectors (PC-Z.4)
    - A3:N-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).
      - Find the magnitude of a vector scalar multiple (PC-Y.11)
      - Determine the direction of a vector scalar multiple (PC-Y.12)
- A3:N-VM.C Perform operations on matrices and use matrices in applications.
  - A3:N-VM.C.6 Use matrices to represent and manipulate data.
  - A3:N-VM.C.7 Multiply matrices by scalars to produce new matrices.
    - A3:N-VM.C.7a Multiply with and without technology.
      - Multiply a matrix by a scalar (PC-Q.4)
    - A3:N-VM.C.7b Multiply with and without context.
      - Multiply a matrix by a scalar (PC-Q.4)
  - A3:N-VM.C.8 Add, subtract, and multiply matrices of appropriate dimensions.
  - A3:N-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.
    - Properties of matrices (PC-Q.9)
  - A3:N-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.
    - A3:N-VM.C.10a The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
  - A3:N-VM.C.11 Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector.

A3:A Algebra

A3:A-APR Arithmetic with Polynomials and Rational Expressions
- A3:A-APR.B Understand the relationship between zeros and factors of polynomials.
  - A3:A-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).
- A3:A-APR.C Use polynomial identities to solve problems.
  - A3:A-APR.C.4 Prove polynomial identities and use them to describe numerical relationships.
    - Factor sums and differences of cubes (PC-E.5)
  - A3:A-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. (The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.)
- A3:A-APR.D Rewrite rational expressions.
  - A3:A-APR.D.6 Rewrite simple rational expressions in different forms: Write ^a(x)/_b(x) in the form q(x) + ^r(x)/_b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, synthetic division, or, for the more complicated examples, a computer algebra system.
    - Simplify rational expressions (PC)
    - Divide polynomials using long division (PC-E.2)
  - A3:A-APR.D.7 Perform operations on rational expressions, building from previous knowledge that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression.
A3:A-REI Reasoning with Equations and Inequalities
- A3:A-REI.C Solve System of Equations.
  - A3:A-REI.C.8 Represent a system of linear equations as a single matrix equation in a vector variable.
  - A3:A-REI.C.9 Find the inverse of a matrix if it exists and use it to solve systems of linear equations: Use technology for matrices of dimension 3 × 3 or greater.

A3:F Functions

A3:F-BF Building Functions
- A3:F-BF.A Build a function that models a relationship between two quantities.
  - A3:F-BF.A.1 Write a function that describes a relationship between two quantities.
    - A3:F-BF.A.1c Compose functions.
      - Composition of functions (PC-A.8)
- A3:F-BF.B Build new functions from existing functions.
  - A3:F-BF.B.4 Find inverse functions.
    - A3:F-BF.B.4a Solve an equation of the from f(x) = c for a simple function f that has an inverse and write an expression for the inverse.
    - A3:F-BF.B.4b Verify by composition that one function is the inverse of another.
      - Identify inverse functions (PC-B.1)
      - Check whether two rational functions are inverses (PC-G.4)
    - A3:F-BF.B.4c Read values of an inverse function from a graph or a table, given that the function has an inverse.
    - A3:F-BF.B.4d Produce an invertible function from a non-invertible function by restricting the domain.
  - A3:F-BF.B.5 Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
A3:F-IF Interpreting Functions
- A3:F-IF.C Analyze functions using different representations.
  - A3:F-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.
    - A3:F-IF.C.7d Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
      - Rational functions: asymptotes and excluded values (PC-G.1)
  - A3:F-IF.C.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

A3:G Geometric Reasoning & Logic

A3:G-GPE Expressing Geometric Properties with Equations
- A3:G-GPE.A Translate between the geometric description and the equation for a conic section.
  - A3:G-GPE.A.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
  - A3:G-GPE.A.2 Derive the equation of a parabola given a focus and directrix.
  - A3:G-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.
    - Write equations of ellipses in standard form (PC-U.9)
    - Write equations of hyperbolas in standard form (PC-U.12)

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A3:N Number & Quantity

A3:N-CN The Complex Number System

A3:N-CN.A Perform arithmetic operations with complex numbers.

A3:N-CN.A.2 Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

A3:N-CN.A.3 Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

A3:N-CN.B Represent complex numbers and their operations on the complex plane.

A3:N-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.

A3:N-CN.B.5 Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.

A3:N-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.

A3:N-CN.C Use complex numbers in polynomial identities and equations.

A3:N-CN.C.7 Solve quadratic equations with real coefficients that have complex solutions.

A3:N-CN.C.8 Extend polynomial identities to the complex numbers.

A3:N-CN.C.9 Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

A3:N-VM Vector and Matrix Quantities

A3:N-VM.A Represent and model with vector quantities.

A3:N-VM.A.1 Understand vector attributes.

A3:N-VM.A.1a Represent vector quantities as having both magnitude and direction by directed line segments.

A3:N-VM.A.1b Use appropriate symbols for vectors and their magnitudes.

A3:N-VM.A.2 Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

A3:N-VM.A.3 Solve problems involving velocity and other quantities that can be represented by vectors.

A3:N-VM.B Perform operations on vectors.

A3:N-VM.B.4 Add and subtract vectors.

A3:N-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.

A3:N-VM.B.4b Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

A3:N-VM.B.5 Multiply a vector by a scalar.

A3:N-VM.B.5a Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise.

A3:N-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).

A3:N-VM.C Perform operations on matrices and use matrices in applications.

A3:N-VM.C.6 Use matrices to represent and manipulate data.

A3:N-VM.C.7 Multiply matrices by scalars to produce new matrices.

A3:N-VM.C.7a Multiply with and without technology.

A3:N-VM.C.7b Multiply with and without context.

A3:N-VM.C.8 Add, subtract, and multiply matrices of appropriate dimensions.

A3:N-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.

A3:N-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.

A3:N-VM.C.10a The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.

A3:N-VM.C.11 Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector.

A3:A Algebra

A3:A-APR Arithmetic with Polynomials and Rational Expressions

A3:A-APR.B Understand the relationship between zeros and factors of polynomials.

A3:A-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).

A3:A-APR.C Use polynomial identities to solve problems.

A3:A-APR.C.4 Prove polynomial identities and use them to describe numerical relationships.

A3:A-APR.D Rewrite rational expressions.

A3:A-APR.D.7 Perform operations on rational expressions, building from previous knowledge that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression.

A3:A-REI Reasoning with Equations and Inequalities

A3:A-REI.C Solve System of Equations.

A3:A-REI.C.8 Represent a system of linear equations as a single matrix equation in a vector variable.

A3:A-REI.C.9 Find the inverse of a matrix if it exists and use it to solve systems of linear equations: Use technology for matrices of dimension 3 × 3 or greater.

A3:F Functions

A3:F-BF Building Functions

A3:F-BF.A Build a function that models a relationship between two quantities.

A3:F-BF.A.1 Write a function that describes a relationship between two quantities.

A3:F-BF.A.1c Compose functions.

A3:F-BF.B Build new functions from existing functions.

A3:F-BF.B.4 Find inverse functions.

A3:F-BF.B.4a Solve an equation of the from f(x) = c for a simple function f that has an inverse and write an expression for the inverse.

A3:F-BF.B.4b Verify by composition that one function is the inverse of another.

A3:F-BF.B.4c Read values of an inverse function from a graph or a table, given that the function has an inverse.

A3:F-BF.B.4d Produce an invertible function from a non-invertible function by restricting the domain.

A3:F-BF.B.5 Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

A3:F-IF Interpreting Functions

A3:F-IF.C Analyze functions using different representations.

A3:F-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.

A3:F-IF.C.7d Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

A3:F-IF.C.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

A3:G Geometric Reasoning & Logic

A3:G-GPE Expressing Geometric Properties with Equations

A3:G-GPE.A Translate between the geometric description and the equation for a conic section.

A3:G-GPE.A.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

A3:G-GPE.A.2 Derive the equation of a parabola given a focus and directrix.

A3:G-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.

A3:N-CN.A.2 Use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.