### 1: The Real Number System

#### 1.1: Extend the properties of exponents to rational exponents.

KY.HS.N.2: Rewrite expressions involving radicals and rational exponents using the properties of exponents.

### 2: Quantities

#### 2.1: Reason quantitatively and use units to solve problems.

KY.HS.N.4: Use units in context as a way to understand problems and to guide the solution of multi-step problems;

KY.HS.N.4.a: Choose and interpret units consistently in formulas;

KY.HS.N.4.b: Choose and interpret the scale and the origin in graphs and data displays.

KY.HS.N.5: Define appropriate units in context for the purpose of descriptive modeling.

KY.HS.N.6: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

### 3: The Complex Number System

#### 3.1: Perform arithmetic operations with complex numbers.

KY.HS.N.7: Understanding properties of complex numbers.

KY.HS.N.7.a: 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.

KY.HS.N.7.b: Use the relation i² = –1 and the commutative, associative and distributive properties to add, subtract and multiply complex numbers.

KY.HS.N.7.c: Find the conjugate of a complex number and use it to find the quotient of complex numbers.

#### 3.2: Represent complex numbers and their operations on the complex plane.

KY.HS.N.8: Understanding representations of complex numbers using the complex plane.

KY.HS.N.8.a: 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.

KY.HS.N.8.b: Represent addition, subtraction, multiplication, modulus and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.

#### 3.3: Use complex numbers in polynomial identities and equations.

KY.HS.N.9: Solve quadratic equations with real coefficients that have complex solutions.

KY.HS.N.10: Extend polynomial identities to the complex numbers.

KY.HS.N.10.1: When multiplying complex binomials, students recognize and understand the value of i² as -1 and fluently simplify each polynomial appropriately navigating between the real number system and complex numbers. One example of this might be that students should understand that it would be appropriate to rewrite x² + 4 as (x + 2i)(x – 2i).

### 4: Vector and Matrix Quantities

#### 4.1: Represent and model with vector quantities.

KY.HS.N.12: Understand and apply properties of vectors.

KY.HS.N.12.a: 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.

KY.HS.N.12.b: Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

KY.HS.N.12.c: Solve problems involving velocity and other quantities that can be represented by vectors.

#### 4.2: Perform operations on vectors.

KY.HS.N.13: Perform operations with vectors (addition, subtraction and multiplication by a scalar).

KY.HS.N.13.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.

KY.HS.N.13.b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

KY.HS.N.13.c: 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.

KY.HS.N.13.d: Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise.

KY.HS.N.13.e: Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v is not equal to 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).

#### 4.3: Perform operations on matrices and use matrices in applications.

KY.HS.N.14: Use matrices to represent and manipulate data.

KY.HS.N.15: Perform operations with matrices.

KY.HS.N.15.a: Add, subtract and multiply matrices of appropriate dimensions.

KY.HS.N.15.b: Multiply matrices by scalars to produce new matrices.

KY.HS.N.16: Understand properties of square and identity matrices.

KY.HS.N.16.b: 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.

KY.HS.N.16.c: Work with 2 × 2 matrices as transformations of the plane and interpret the absolute value of the determinant in terms of area.

Correlation last revised: 1/22/2020

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.