HS Number & Quantity Math
The Complex Number System (CN)
Standards in this strand:
Perform arithmetic operations with complex numbers
HSN.CN.A.1 | 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. | 0 Lesson(s) |
HSN.CN.A.2 | Use the relation i2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. | 0 Lesson(s) |
HSN.CN.A.3 | (+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. | 0 Lesson(s) |
Represent complex numbers and their operations on the complex plane
HSN.CN.B.4 |
(+) 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.
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HSN.CN.B.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 120°. | 0 Lesson(s) |
HSN.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. | 0 Lesson(s) |
Use complex numbers in polynomial identities and equations
HSN.CN.C.7 | Solve quadratic equations with real coefficients that have complex solutions. | 0 Lesson(s) |
HSN.CN.C.8 | (+) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x - 2i). | 0 Lesson(s) |
HSN.CN.C.9 | (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. | 0 Lesson(s) |
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HS Number & Quantity Math
Quantities (Q)
Standards in this strand:
Reason quantitatively and use units to solve problems
HSN.Q.A.1 | Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. | 0 Lesson(s) |
HSN.Q.A.2 | Define appropriate quantities for the purpose of descriptive modeling. | 0 Lesson(s) |
HSN.Q.A.3 | Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. | 0 Lesson(s) |
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HS Number & Quantity Math
The Real Number System (RN)
Standards in this strand:
Extend the properties of exponents to rational exponents
HSN.RN.A.1 | 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. | 0 Lesson(s) |
HSN.RN.A.2 | Rewrite expressions involving radicals and rational exponents using the properties of exponents. | 0 Lesson(s) |
Use properties of rational and irrational numbers
HSN.RN.B.3 | 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. | 0 Lesson(s) |
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HS Number & Quantity Math
Vector & Matrix Quantities (VM)
Standards in this strand:
Represent and model with vector quantities
HSN.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 (e.g., v, |v|, ||v||, v).
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HSN.VM.A.2 | (+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. | 0 Lesson(s) |
HSN.VM.A.3 | (+) Solve problems involving velocity and other quantities that can be represented by vectors. | 0 Lesson(s) |
Perform operations on vectors
HSN.VM.B.4 | (+) Add and subtract vectors. | 0 Lesson(s) |
HSN.VM.B.4.a | Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes. | 0 Lesson(s) |
HSN.VM.B.4.b | Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum. | 0 Lesson(s) |
HSN.VM.B.4.c | Understand vector subtraction v - w as v + (-w), where -w is the additive inverse ofw, 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. | 0 Lesson(s) |
HSN.VM.B.5 |
(+) Multiply a vector by a scalar.
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HSN.VM.B.5.a | 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). | 0 Lesson(s) |
HSN.VM.B.5.b |
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).
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Perform operations on matrices and use matrices in applications
HSN.VM.C.6 | (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. | 0 Lesson(s) |
HSN.VM.C.7 | (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. | 0 Lesson(s) |
HSN.VM.C.8 | (+) Add, subtract, and multiply matrices of appropriate dimensions. | 0 Lesson(s) |
HSN.VM.C.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. | 0 Lesson(s) |
HSN.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. | 0 Lesson(s) |
HSN.VM.C.11 | Students should know what the zero and identity matrices are and how they’re used in matrix addition and multiplication. First, we’ll start with zero. It’s a great number, right? You can add zero to anything, and you’ll just get the same number back. For instance, 6 + 0 = 6 and 0 + 19 = 19. It’s called the additive identity because we can add zero to any number without changing that number’s “identity.” (So when it goes to see a move that’s rated R, adding zero won’t help it if it’s under 17.) In a similar fashion, 1 is the multiplicative identity. We can multiply any number by 1 and not change the “identity” of the number. For example, 3444 × 1 = 3444 and 1 × 7 = 7. Yeah, but that’s the realm of numbers. We’re talking about matrices, here. Students should know that the zero matrix is exactly what they think it is: a matrix filled with zeros. When added to any other matrix, it yields the other matrix as the sum. | 0 Lesson(s) |
HSN.VM.C.12 | (+) Work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area. | 0 Lesson(s) |
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