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Georgia 
Unit 7 Frameworks  Vectors 
All of Unit 7 
Unit 71: 
Basic Vector Forms (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)
MGSE912.N.VM.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).
MGSE912.N.VM.2 Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
MGSE912.N.VM.3: Solve problems involving velocity and other quantities that can be represented by vectors.
Video Lessons: (p1, p2, p3, p4, p5)
Sample Quiz:(Interactive, PDF)


Unit 72: 
Basic Vector Operations (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)
MGSE912.N.VM.4 :Add and subtract vectors.
MGSE912.N.VM4a: Add vectors endtoend, componentwise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.
MGSE912.N.VM4b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
MGSE912.N.VM4c: 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 componentwise.
MGSE912.N.VM.5 :Multiply a vector by a scalar
MGSE912.N.VM.5a: Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication componentwise, e.g., as c(vx, vy) = (cvx, cvy).
MGSE912.N.VM.5b: Compute the magnitude of a scalar multiple cv using cv = cv. Compute the direction of cv knowing that when cv = 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).
Video Lessons: (p1, p2, p3, p4a, p4b, p5a, p5b)
Sample Quiz:(Interactive, PDF)


Unit 73: 
Vector Matrix Transforms (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)
MGSE912.N.VM.11 :Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.
Video Lessons: (p1, p2)
Sample Quiz:(Interactive, PDF) 

Unit 74 : 
(OPTIONAL) 3D  Vectors (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)
MGSE912.N.VM.4 :Add and subtract vectors.
MGSE912.N.VM4a: Add vectors endtoend, componentwise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.
MGSE912.N.VM4b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
MGSE912.N.VM4c: 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 componentwise.
MGSE912.N.VM.5 :Multiply a vector by a scalar
MGSE912.N.VM.5a: Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication componentwise, e.g., as c(vx, vy) = (cvx, cvy).
MGSE912.N.VM.5b: Compute the magnitude of a scalar multiple cv using cv = cv. Compute the direction of cv knowing that when cv = 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).
3Dimensional Vector Spherical Form Sketch (GSP)
Video Lessons: (p1, p2, p3, p4)
Sample Quiz:(Interactive, PDF) 

Unit 75: 
(OPTIONAL)Adv.Vector Operations(Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)
MGSE912.N.VM.11 :Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.
 Dot Products
 Cross Products
 Angle Betweewn Vectors
Cross Product in 3d Sketch (GSP)
Video Lessons: (p1, p2, p3a, p3b, p4)
Sample Quiz:(Interactive, PDF)


Unit 76 : 
(Review) Complex Numbers(Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)
MGSE912.N.CN.3:Find the conjugate of a complex number; use the conjugate to find the absolute value (modulus) and quotient of complex numbers.
MGSE912.N.CN.1 (Algebra 2): Understand there is a complex number i such that i^2= −1, and every complex number has the form a + bi where a and b are real numbers.
MGSE912.N.CN.2 (Algebra 2): Use the relation i^2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
MGSE912.N.CN.3 (Algebra 2): Find the conjugate of a complex number; use the conjugate to find the absolute value (modulus) and quotient of complex numbers.
Video Lessons: (p1, p2, p3, p4)
Sample Quiz:(Interactive, PDF)


Unit 77: 
Complex Plane (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)
MGSE912.N.CN.3:Find the conjugate of a complex number; use the conjugate to find the absolute value (modulus) and quotient of complex numbers.
MGSE912.N.CN.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.
MGSE912.N.CN.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 + √3i)3 = 8 because (1 + √3i) has modulus 2 and argument 120°.
MGSE912.N.CN.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.
Video Lessons: (p1, p2a, p2b, p3, p4)
Sample Quiz:(Interactive, PDF)
"Imaginary Numbers Are Real"
Video Series
(by Welch Labs):
(parts: p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, p11, p12, p13)




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