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Plus (+) Standards

New York High School Plus Standards Math

Video lessons and practice for every Plus (+) Standards topic. Aligned to NYS Next Generation Mathematics Learning Standards for New York high school students.

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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.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.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-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.

New York High School Plus Standards Math Topics

New York's Plus (+) Standards represent the most advanced content in the NYS Next Generation Mathematics Learning Standards. These topics go beyond the core graduation requirements and are designed for students pursuing higher-level mathematics, college STEM programs, or advanced Regents coursework.

Complex Numbers and the Complex Plane

Students working through Plus Standards begin with a deep study of complex numbers. This includes finding conjugates, computing moduli and quotients, and representing complex numbers in both rectangular and polar form on the complex plane. Students also explore addition, subtraction, multiplication, and conjugation of complex numbers geometrically, calculate distances and midpoints in the complex plane, and extend polynomial identities to complex numbers. The section concludes with the Fundamental Theorem of Algebra and its application to quadratic polynomials.

Vectors and Matrices

A major section of the Plus Standards covers vectors and matrices. Students learn to recognize vector quantities as having both magnitude and direction, represent them as directed line segments, find vector components, and solve real-world problems involving velocity. They practice adding and subtracting vectors and multiplying vectors by scalars.

Matrix work includes using matrices to represent and manipulate data, multiplying matrices by scalars, and performing addition, subtraction, and multiplication of matrices of appropriate dimensions. Students explore key properties: matrix multiplication is not commutative but satisfies associative and distributive properties. They also study zero and identity matrices, determinants, and multiplicative inverses. A key application is working with 2×2 matrices as transformations of the plane and interpreting the absolute value of the determinant in terms of area.

The Binomial Theorem

Students learn to apply the Binomial Theorem to expand expressions of the form (x + y)^n for positive integers n. This powerful algebraic tool connects to combinatorics and prepares students for calculus-level series work.

Rational Expressions and Functions

This section treats rational expressions as a system analogous to rational numbers — closed under addition, subtraction, multiplication, and division by a nonzero rational expression. Students practice operations with rational expressions and move on to graphing rational functions, identifying zeros and asymptotes from factored forms, and analyzing end behavior.

Logarithms and Exponents

Students deepen their understanding of the inverse relationship between exponents and logarithms and use this relationship to solve problems. This reinforces skills from earlier coursework while pushing toward more rigorous problem-solving.

Advanced Trigonometry

The trigonometry portion of the Plus Standards is extensive. Students use special triangles to determine exact values of sine, cosine, and tangent for π/3, π/4, and π/6. They use the unit circle to find values of trigonometric functions for π–x, π+x, and 2π–x, explain symmetry (odd and even) and periodicity of trig functions, and prove the Pythagorean identity sin²(θ) + cos²(θ) = 1.

Students also prove and apply the addition and subtraction formulas for sine, cosine, and tangent. The section closes with triangle applications: deriving the formula A = ½ab sin(C), proving the Laws of Sines and Cosines, and applying these laws to find unknown measurements in both right and non-right triangles.

How StudyPug Supports New York Plus Standards Students

StudyPug provides video lessons and practice problems for every one of these Plus Standards topics. Each lesson is short — typically 5 to 15 minutes — and broken into segments students can pause and replay. After watching, students can test their understanding with practice problems matched to the same standard. Whether preparing for a New York Regents exam or getting ahead for college math, StudyPug keeps every topic accessible on any device.