Domain
|
Standard
|
Cluster
|
Text of Objective
|
Web Resource
|
Instructions for Use
|
Number and Quantity: The Real Number System
|
N.RN.1
|
Extend the properties of exponents to rational exponents.
|
Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.
|
Rational Exponents
|
|
N.RN.2
|
Rewrite expressions involving radicals and rational exponents using the properties of exponents.
|
Virtual Math Lab
|
|
N.RN.3
|
Use properties of rational and irrational numbers.
|
Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
|
|
|
Number and Quantity: Quantities
|
N.Q.1
|
Reason quantitatively and use units to solve problems.
|
Use units as a way to understand problems and to guide the solution of multi-steps problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
|
|
|
N.Q.2
|
Define appropriate quantities for the purpose of descriptive modeling.
|
|
|
N.Q.3
|
Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
|
|
|
Number and Quantity: The Complex Number System
|
N.CN.1
|
Perform arithmetic operations with complex numbers.
|
Know there is a complex number i such that i2 = -1, and every complex number has the form a + bi with a and b real.
|
|
|
N.CN.2
|
Use the relation i2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
|
|
|
N.CN.3
|
(+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
|
|
|
N.CN.4
|
Represent complex numbers and their operations on the complex plane.
|
(+) 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.
|
|
|
N.CN.5
|
(+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (-1 + √3 i)3 = 8 because (-1 + √3 i) has modulus 2 and argument 120ᵒ.
|
|
|
N.CN.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.7
|
Use complex numbers in polynomial identities and equations.
|
Solve quadratic equations with real coefficients that have complex solutions.
|
|
|
N.CN.8
|
(+) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x – 2i).
|
|
|
N.CN.9
|
(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
|
|
|
Number and Quantity: Vector and Matrix Quantities
|
N.VM.1
|
Represent and model with vector quantities.
|
(+) 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 (e.g., v, lvl, l׀v׀׀, v).
|
|
|
N.VM.2
|
(+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
|
|
|
N.VM.3
|
(+) Solve problems involving velocity and other quantities that can be represented by vectors.
|
|
|
N.VM.4
|
Perform operations on vectors
|
(+) Add and subtract vectors
- Add vectors end-to-end, component-wise, and by parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.·
- Give two vectors in magnitude and direction form, determine the magnitude and direction of their sum.·
- 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·
|
|
|
N.VM.5
|
(+) Multiply a vector by a scalar.
- Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy).·
- 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).
|
|
|
N.VM.6
|
Perform operations on matrices and use matrices in applications.
|
(+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.
|
|
|
N.VM.7
|
(+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.
|
|
|
N.VM.8
|
(+) Add, subtract, and multiply matrices of appropriate dimensions.
|
|
|
|
N.VM.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.
|
|
|
N.VM.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.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.12
|
(+) Work with 2 x 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.
|
|
|
|
|
|
|
|
|
Comments (0)
You don't have permission to comment on this page.