# Pre-Calculus Unit 7: Vectors

**In this unit, stud****ents 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**

**Sample Test**

*P**re-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**

**Sample Assessment:**

**Pre-Calculus Unit 5: Trigonometric Identities**

**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:**

**Sample Assessment:**

*Pre-Calculus Unit 4: Trig Graphs*

*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:**

**Example Summative:**

**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:**

Pre-requisite skills: review: https://cobbteachingandlearningsystem.cobbk12.org/Workspace.aspx?wsid=30252&wstid=3&cpid=30202#ContentTab%5CUnit%20Resources%5C349705

Sample post test: https://cobbteachingandlearningsystem.cobbk12.org/Workspace.aspx?wsid=30252&wstid=3&cpid=30202#ContentTab%5CUnit%20Resources%5C349705

**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:**

- Sample prerequisite skills: https://cobbteachingandlearningsystem.cobbk12.org/GetFile.aspx?f=ac599628-109d-43d3-931b-0dfc45c90196&t=v
- Sample Unit test: https://cobbteachingandlearningsystem.cobbk12.org/GetFile.aspx?f=d8a4d6ba-8481-48d1-be60-a82390abdadb&t=v

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