# Pre-Calculus Unit 7: Vectors

In this unit, students will:

• Recognize vectors as mathematical objects having both magnitude and direction.
• Add / Subtract vectors using a variety of methods: end to end, parallelogram, and component wise.
• Multiply vectors by a scalar.
• Interpret operations on vectors (+, –, ×) geometrically.
• Understand why the magnitude of the sum of two vectors is usually less than (sometimes equal to) the sum of their magnitudes
• Use vectors to solve problems.
• Apply matrix transformations to vectors.
• Plot complex numbers in the complex plane.
• write complex numbers in rectangular and polar form
• Interpret operations on complex numbers (+, –, ×, ÷, conjugate) geometrically.
• Use the complex plane to find the distance between two complex numbers.
• Use the complex plane to find the average of two complex numbers.

Pre-requisite skills

https://cobbteachingandlearningsystem.cobbk12.org/GetFile.aspx?f=d627a419-46a0-de01-3976-6ea80965d845&t=v

Sample Test

https://cobbteachingandlearningsystem.cobbk12.org/GetFile.aspx?f=b5cad819-b3c9-4d56-9301-19e021091d13&t=v

### Pre-Calculus Unit 6:  Triangles

In this unit, students will:
• Expand the use of trigonometric functions beyond right triangles into more general triangles.
• Develop the trigonometric formula for area of a triangle.
• Use the Laws of Sines and Cosines to solve problems.

Pre-requisite skills

https://cobbteachingandlearningsystem.cobbk12.org/GetFile.aspx?f=f1faa509-8023-8147-19eb-ca747c397487&t=v

Sample Assessment:

https://cobbteachingandlearningsystem.cobbk12.org/GetFile.aspx?f=16b8fdfe-d100-d9e9-51c9-eda9153f05e9&t=v

### Pre-Calculus Unit 5:  Trigonometric Identities

In this unit, students will:
• Build upon their work with trigonometric identities with addition and subtraction formulas.
• Will look at addition and subtraction formulas geometrically.
• Prove addition and subtraction formulas.
• Use addition and subtraction formulas to solve problems.

Pre-requisite skills:

https://cobbteachingandlearningsystem.cobbk12.org/GetFile.aspx?f=c99ba0eb-8eff-7cf9-0543-42942a5b2e0f&t=v

Sample Assessment:

https://cobbteachingandlearningsystem.cobbk12.org/GetFile.aspx?f=891d83e8-9cd3-50c8-31db-1a594a62d624&t=v

### Pre-Calculus Unit 4: Trig Graphs

Objectives:

• Realize transformations of y = sin(x) and y = cos(x) behave just as transformations of other parent functions.
• Learn that the concepts of amplitude, midline, frequency, and period are related to the transformations of trigonometric functions.
• Learn how to look at a graph of a transformed sine or cosine function and to write a function to represent that graph explore several real-world settings and represent the situation with a trigonometric function that can be used to answer questions about the situation.
• Pre-requisite skills:

https://cobbteachingandlearningsystem.cobbk12.org/GetFile.aspx?f=54191593-36a0-3561-5c0e-8b6e0718aa35&t=v

Example Summative:

https://cobbteachingandlearningsystem.cobbk12.org/GetFile.aspx?f=6c148771-d987-4dbf-7f96-3b505fcf7efc&t=v

PreCalculus Unit 3: Basic Trig

In this unit, students will:

• Expand their understanding of angle with the concept of a rotation angle.
• Explore the definition of radian.
• Define angles in standard position and consider them in relationship to the unit circle.
• Make connections to see how a real number is connected to the radian measure of an angle in standard position which is connected to an intercepted arc on the unit circle which is connected to a terminal point of this arc whose coordinates are connected to the sine and cosine functions.
• Gain a better understanding of the unit circle and its connection to trigonometric functions.

Unit Two – Conics

In this unit, students will:
• Build upon the understanding of the algebraic representations of circles and parabolas.
• Develop the understanding of the geometric description and equations for the conic sections, parabolas, ellipses, and hyperbolas.

Resources:

Unit One – Matrices

In this unit students will:

• Represent and manipulate data using matrices.
• Define the order of a matrix as the number of rows by the number of columns.
• Add and subtract matrices and know these operations are possible only when the dimensions are equal.
• Recognize that matrix addition and subtraction are commutative.
• Multiply matrices by a scalar and understand the distributive and associative properties apply to matrices.
• Multiply matrices and know when the operation is defined.
• Recognize that matrix multiplication is not commutative.
• Understand and apply the properties of a zero matrix.
• Understand and apply the properties of an identity matrix.
• Find the determinant of a square matrix and understand that it is a nonzero value if and only if the matrix has an inverse.
• Use 2 X 2 matrices as transformations of a plane and determine the area of the plane using the determinant
• Write a system of linear equations as a matrix equation and use the inverse of the coefficient matrix to solve the system.

Resources: