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 Topics
ID | Math Standard Description | StudyPug Topic |
|---|---|---|
N-CN.A.3+ | NY.N-CN.A.3+: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. |
N-CN.B.4+ | NY.N-CN.B.4+: Represent complex numbers on the complex plane in rectangular and polar form. |
N-CN.B.5+ | NY.N-CN.B.5+: Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane. |
N-CN.B.6+ | 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. |
N-CN.C.8+ | NY.N-CN.C.8+: Extend polynomial identities to the complex numbers. |
N-CN.C.9+ | NY.N-CN.C.9+: Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. |
N-VM.A.1+ | 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. |
N-VM.A.2+ | 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. |
N-VM.A.3+ | NY.N-VM.A.3+: Solve problems involving velocity and other quantities that can be represented by vectors. |
N-VM.B.4+ | NY.N-VM.B.4+: Add and subtract vectors. |
N-VM.B.5+ | NY.N-VM.B.5+: Multiply a vector by a scalar. |
N-VM.C.6+ | NY.N-VM.C.6+: Use matrices to represent and manipulate data. |
N-VM.C.7+ | NY.N-VM.C.7+: Multiply matrices by scalars to produce new matrices. |
N-VM.C.8+ | NY.N-VM.C.8+: Add, subtract, and multiply matrices of appropriate dimensions. |
N-VM.C.9+ | 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. |
N-VM.C.10+ | 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. |
N-VM.C.11+ | 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. |
N-VM.C.12+ | 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. |
A-APR.C.5+ | 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. |
A-APR.D.7+ | 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. |
F-BF.B.5+ | NY.F-BF.B.5+: Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. |
F-TF.A.3+ | 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. |
F-TF.C.8+ | 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. |
F-TF.C.9+ | NY.F-TF.C.9+: Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. |
G-SRT.D.9+ | 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. |
G-SRT.D.10+ | NY.G-SRT.D.10+: Prove the Laws of Sines and Cosines and use them to solve problems. |
G-SRT.D.11+ | 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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