New York
Math
Grade 12 Math Courses - NY Plus (+) Standards Curriculum
Discover advanced math concepts in NY's Grade 12 Plus (+) Standards. Explore complex numbers, vectors, matrices, and trigonometry to prepare for college-level mathematics and STEM fields.
NY Grade 12 Math Curriculum: Plus (+) Standards
ID | Math Standard Description | StudyPug Topic |
|---|---|---|
NY.N-CN.A.3+ | Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. |
NY.N-CN.B.4+ | Represent complex numbers on the complex plane in rectangular and polar form. |
NY.N-CN.B.5+ | Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane. |
NY.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. |
NY.N-CN.C.8+ | Extend polynomial identities to the complex numbers. |
NY.N-CN.C.9+ | Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. |
NY.N-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. |
NY.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. |
NY.N-VM.A.3+ | Solve problems involving velocity and other quantities that can be represented by vectors. |
NY.N-VM.B.4+ | Add and subtract vectors. |
NY.N-VM.B.5+ | Multiply a vector by a scalar. |
NY.N-VM.C.6+ | Use matrices to represent and manipulate data. |
NY.N-VM.C.7+ | Multiply matrices by scalars to produce new matrices. |
NY.N-VM.C.8+ | Add, subtract, and multiply matrices of appropriate dimensions. |
NY.N-VM.C.9+ | Understand that matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. |
NY.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. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. |
NY.N-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. |
NY.N-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. |
NY.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. |
NY.A-APR.D.7+ | Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. |
NY.F-BF.B.5+ | Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. |
NY.F-TF.A.3+ | Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π–x, π+x, and 2π–x in terms of their values for x. |
NY.F-TF.C.8+ | Prove the Pythagorean identity sin^2(θ) + cos^2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle. |
NY.F-TF.C.9+ | Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. |
NY.G-SRT.D.9+ | Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. |
NY.G-SRT.D.10+ | Prove the Laws of Sines and Cosines and use them to solve problems. |
NY.G-SRT.D.11+ | Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles. |
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