NY High School Plus Standards Math Curriculum

NY High School Plus Standards Math Curriculum

• NY.N-CN.A.3+Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
  • Complex conjugates
  • Distance and midpoint of complex numbers
  • Angle and absolute value of complex numbers
• NY.N-CN.B.4+Represent complex numbers on the complex plane in rectangular and polar form.
  • Polar form of complex numbers
• NY.N-CN.B.5+Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane.
  • Operations on complex numbers in polar form
• 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.
  • Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$
• NY.N-CN.C.8+Extend polynomial identities to the complex numbers.
  • Solving polynomials with unknown coefficients
  • Factoring polynomials: x^2 + bx + c
  • Applications of polynomials: x^2 + bx + c
  • Solving polynomials with the unknown "b" from ax^2 + bx + c
  • Factoring polynomials: ax^2 + bx + c
  • Factoring perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2
  • Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)
• NY.N-CN.C.9+Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
  • Word problems of polynomials
  • Fundamental theorem of algebra
• 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.
  • Use sine ratio to calculate angles and sides (Sin = o / h)
  • Introduction to vectors
  • Magnitude of a vector
  • Direction angle of a vector
• 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.
  • Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
  • Scalar multiplication of vectors
  • Equivalent vectors
• NY.N-VM.A.3+Solve problems involving velocity and other quantities that can be represented by vectors.
  • Word problems relating guy wire in trigonometry
  • Word problems on vectors
• NY.N-VM.B.4+Add and subtract vectors.
  • Slope equation: $m = \frac{y_2-y_1}{x_2- x_1}$
  • Adding and subtracting vectors in component form
  • Operations on vectors in magnitude and direction form
• NY.N-VM.B.5+Multiply a vector by a scalar.
  • Slope intercept form: y = mx + b
  • Unit vector
• NY.N-VM.C.6+Use matrices to represent and manipulate data.
  • Notation of matrices
  • Adding and subtracting matrices
• NY.N-VM.C.7+Multiply matrices by scalars to produce new matrices.
  • Scalar multiplication of matrices
• NY.N-VM.C.8+Add, subtract, and multiply matrices of appropriate dimensions.
  • Matrix multiplication
  • The three types of matrix row operations
• 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.
  • Properties of matrix multiplication
• 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.
  • Zero matrix
  • Identity matrix
  • The determinant of a 2 x 2 matrix
  • The determinant of a 3 x 3 matrix (General & Shortcut Method)
  • The Inverse of a 2 x 2 matrix
• 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.
  • Transforming vectors with matrices
  • Transforming shapes with matrices
• 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.
  • Finding the transformation matrix
• 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.
  • Pascal's triangle
  • Binomial theorem
  • Determining the equation of a polynomial function
• 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.
  • Negative exponent rule
  • Multiplying rational expressions
  • Dividing rational expressions
  • Descartes' rule of signs
• NY.F-BF.B.5+Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
  • Product rule of logarithms
  • Solving exponential equations with logarithms
  • What is a logarithm?
  • Converting from logarithmic form to exponential form
  • Evaluating logarithms without a calculator
  • Common logarithms
  • Natural log: ln
  • Evaluating logarithms using change-of-base formula
  • Converting from exponential form to logarithmic form
• 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.
  • Find the exact value of trigonometric ratios
  • Solving expressions using 45-45-90 special right triangles
  • Solving expressions using 30-60-90 special right triangles
• 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.
  • Pythagorean identities
• NY.F-TF.C.9+Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
  • Sum and difference identities
  • Double-angle identities
  • Cofunction identities
• 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.
  • Area of triangles: 1/2 a*b sin(C)
• NY.G-SRT.D.10+Prove the Laws of Sines and Cosines and use them to solve problems.
  • Law of sines
  • Law of cosines
• 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.
  • Applications of the sine law and cosine law