AR.Math.Content.HSN.RN: The Real Number System

AR.Math.Content.HSN.RN.A: Extend the properties of exponents to rational exponents

AR.Math.Content.HSN.RN.A.1: Explain how extending the properties of integer exponents to rational exponents provides an alternative notation for radicals.

Exponents and Power Rules

AR.Math.Content.HSN.RN.B: Use properties of rational and irrational numbers

AR.Math.Content.HSN.RN.B.4: Simplify radical expressions. Perform operations (add, subtract, multiply, and divide) with radical expressions. Rationalize denominators and/or numerators.

Operations with Radical Expressions
Simplifying Radical Expressions

AR.Math.Content.HSN.CN: The Complex Number System

AR.Math.Content.HSN.CN.A: Perform arithmetic operations with complex numbers

AR.Math.Content.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.

Points in the Complex Plane
Roots of a Quadratic

AR.Math.Content.HSN.CN.A.2: Use the relation i² = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

Points in the Complex Plane

AR.Math.Content.HSN.CN.A.3: Find the conjugate of a complex number. Use conjugates to find quotients of complex numbers. Use conjugates to find moduli.

Points in the Complex Plane
Roots of a Quadratic

AR.Math.Content.HSN.CN.B: Represent complex numbers and their operations on the complex plane

AR.Math.Content.HSN.CN.B.4: Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers). Explain why the rectangular and polar forms of a given complex number represent the same number.

Points in the Complex Plane

AR.Math.Content.HSN.CN.B.5: Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of geometrical representation for computation.

Points in the Complex Plane

AR.Math.Content.HSN.CN.C: Use complex numbers in polynomial identities and equations

AR.Math.Content.HSN.CN.C.7: Solve quadratic equations with real coefficients that have real or complex solutions.

Points in the Complex Plane
Roots of a Quadratic

AR.Math.Content.HSN.VM: Vector and Matrix Quantities

AR.Math.Content.HSN.VM.A: Represent and model with vector quantities

AR.Math.Content.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).

Adding Vectors
Vectors

AR.Math.Content.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.

Vectors

AR.Math.Content.HSN.VM.A.3: Solve problems involving velocity and other quantities that can be represented by vectors.

2D Collisions
Golf Range

AR.Math.Content.HSN.VM.B: Perform operations on vectors

AR.Math.Content.HSN.VM.B.4: Add and subtract vectors. 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. Given 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. Perform vector subtraction component-wise.

Adding Vectors
Vectors

AR.Math.Content.HSN.VM.B.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, 𝘷 subscript 𝘺) = (𝘤𝘷ₓ, 𝘤𝘷 subscript 𝘺). 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).

Dilations
Vectors

AR.Math.Content.HSN.VM.C: Perform operations on matrices and use matrices in applications

AR.Math.Content.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).

Dilations