Solve Systems of Equations

Several of you requested some review of graphing linear equations.  Systems of Equations Video links from openalgebra.com

Click on video links.
Slope Intercept Form 1:38
Standard Form – Graph using intercepts 1:54
Horizontal & Vertical Lines 1:11
Graph Linear Inequality 2:50
Solutions to Linear Inequality 3:13

Solving Systems of Equations and scroll down to section 3 for examples of various methods of solving systems.

Cramer’s Rule Notes / Practice Problems

INB 37 10/16/14

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Intro to Matrices

You may choose to watch this video and create notes for INB 17 (Intro to Matrices) & INB 19 (Matrix Multiplication)

Or use the following videos and outline.

INB 17
Intro to Matrix Operations

I. Watch video 0-3:25 and stop.

Pause throughout to jot any notes, examples you wish to record.

II. Answer these 5 questions in your INB.
a. What is a matrix?
b. How do you define the size?
c. In order to add or subtract what must be true?
d. Explain how to add or subtract two matrices.
e. Why do you think they call it scalar multiplication?

III. Practice these 4 problems.
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And check, then record results on green organizer.
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INB 19
Matrix Multiplication

I. Watch video from 3:26 to 9:04.

Pause as needed to jot down any notes and examples.

II. Complete these 6 questions.
a. When can 2 matrices be multiplied?
b. How can we tell the dimensions of our answer matrix?
c.  Give dimensions of 2 matrices that can be multiplied.
d.  What is the dimension of their answer matrix?
e.  Give dimensions of 2 matrices that cannot be multiplied.
f. Multiply Practice (handout from class).

Sample Notes for INB 19
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INB 21
Evaluating Determininants
2×2 Matrix (2:45)
3×3 Matrix (3:29)
Finding Area video.
Copy examples from videos into notes.

1. Give an example of a square matrix. Why is it called a square matrix?
2. Show how to find the determinatn of a 2 x 2 matrix.
3. To find the determinant of a 2×2 square matrix, does it matter if you take bc-ad instead of ad-bc? Why/Why not?
4. How can you use the determinant of a matrix to find the area of a triangle?
5. If you apply a scalar of 2 to your triangle coordinates matrix, how does it affect the determinant value?

INB 23
Why Inverses?
Enigma Code video.

Video for Finding 2×2 inverses Notes/Examples. (4:24)

INB 25
Using Technology in Class Notes

Remainder Theorem INB 90 1/14/13

INB 81 – ACT Geometry Review:

#1, #2

#1, #2

#3, #4

#3, #4

 

 

 

 

 

Monday 1/14/13 In Class Notes / Examples:

Friday we “discovered” that we could substitude “a” into our polynomial and the result would be the remainder if we divided by (x-a).

Today, we’re answering the question “When we use  Remainder Theorem, what is this really telling us?”

INB page 90 “More Remainder Theorem”

We graphed the given polynomial as a function in our graphing calculators.  Noted the x-intercepts. "Created" factors from our x-intercepts, then graphed our factors to see the graphed resulted in the same thing.

We graphed the given polynomial as a function in our graphing calculators. Noted the x-intercepts. “Created” factors from our x-intercepts, then graphed our factors to see the graphed resulted in the same thing.

 
We used the remainder theorem to show that (x+5) was indeed a factor!

We used the remainder theorem to show that (x+5) was indeed a factor!

Again, we used the Remainder Theorem to show (x-1) was NOT a factor.  Students already noted it was not an x-intercept on the graph.

Assignment/Practice due Tuesday:  

remaindertheorempractice11413

Algebra 2 1/8/13 Long Division with Polynomials

Cool Math – Division of Polynomials examples of Monday – Wednesday skills.

1/7/13 Dividing Polynomials by Monomials (wkst 51 practice)
Video:

Polynomial divided by monomial: Polynomial divided by monomial

1/8/13 – 1/9/13 long division polynomials skills practice handout (assigned odds only)
video:

Polynomial Division: Polynomial Division

1/10/13 Synthetic Division for Polynomials (assign evens from handout above 1/8/13
video:

Synthetic Division: Basic algorithm for Synthetic Division

11/11/13 Mistake Game! and Polynomial Review Stations

Cool Math – Division of Polynomials examples