Algebra 2 Portfolio

Algebra II Portfolio

1.

Students will type each California State Standard at the top of the page (start a new page for each standard, you can copy and paste it from my web site).

2.

The student will then write one or more paragraphs explaining what the standard is about (each student’s own words). The amount of paragraphs depends on the amount of examples that I require for each standard. The student can explain in detail an actual problem for which this standard addresses. All paragraphs must be at the beginning of each page. The examples should be at the end of each standard.

3.

Each standard must include the correct number of problem that I have assigned to each student these problems cover every aspect of the standard. The examples must be explained in detail and I expect to see notes on the side of the problem clarifying these details. The examples will not be graded if they are written in pencil (color pencils are accepted, be creative).

4.

All work must be typed using double spacing. The size of the font must be 12 (not smaller or bigger). The only things that can be done by hand (no points deducted) are the examples. All pages must include a header and footer. The header page must have the student’s complete name and the period number. The footer must include the page number (lower right hand corner).

5.

The final portfolio must include a cover page with the title “Algebra II or Geometry Portfolio”, the school year, student’s name and teacher’s name (Mr.Negrete). You should include a table of content with the list of the state standards and the page numbers that these can be found in. Beside these guidelines your cover page can be decorated in any fashion that you desire.

6.

I prefer that you purchase a 3 ring ½” binder that has a cover pouch so you can insert your cover page. The portfolio will have a preliminary grade after “turkey weekend” then you will turn it in on the day of the Final Semester Test. Students must have their portfolio bounded together; staples or manila folders will not be accepted. The bounded can be done as a book or as a spiral (these services are done at Kinko’s).

Examples per Standard

Ca Standard 1.0 Absolute value in inequalities (Explain in detail the steps, explain when the inequality changes its direction, and also explain when we separate the inequality). Examples: 1. 4

3x 1

2

2. 6 52 x 3

3. 2

2x 5 3

4

3 5

Absolute value in equality (Explain in detail the steps and when we separate the equality). Examples: 1. 2

2. 4

2x 5 3

3 5

3x 1

3. 6 52 x 3

2 4

Ca Standard 2.0 Solve a system of inequalities using the graphing method (Explain each step, how to graph it, how to shade it and where is the solution). Examples: 1. y - 3x > -1 y+x

4

1 - x 2 2 3 y> x 2 2

2. y

3. y - 2 < x y - 3 > 2x

Solve a system of three equations with three variables using the elimination method. (This one you have notes in your composition book, do not copy rewrite them using your own words and make). Examples: 1. x + 2y - 4z = 6 2x - 3y + z = 11 3x - 5y - 3z = 1 2. x + y - 2z = 0 x - y - 4z = 2 2x - y - 5z = -1 3. 5x + 3y + 2z = -2 3x - y - z = -4 x + 2y + 3z = 1

Solve a system of three equations with three variables using Cramer’s rule (how do you set up the matrices d, dx, dy and dz. Explain how to solve the determinant d, dx, dy and dz. Then explain how to solve for x, y and z). Examples: 1. 5x + 3y + 2z = -2 3x - y - z = -4 x + 2y + 3z = 1 2. x + 2y - 4z = 6 2x - 3y + z = 11 3x - 5y - 3z = 1 3. x + y - 2z = 0 x - y - 4z = 2 2x - y - 5z = -1

Ca Standard 3.0 Multiplying Polynomials (explain the laws of exponents, vertical method and the horizontal method). Examples:

1. (3- k 2 )(2 k 2 2. (y 2

k4)

2 y 1)( y 2

3. (3s + 2t)(s3 3st 2

y 1) 2t 3 )

Dividing Polynomials using Long Division (This one you have notes in your composition book, do not copy rewrite them using your own words and make). Examples:

1.

2.

3.

x5

2x4

x4 x3 x2 1 x2 x 1 x 3 y x 2 y 2 4 xy 3 4 y 4 2 x 2 xy 2 y 2

2 p 3 2q 3 pq 2 2p q

p2q

Synthetic Division (This one you have notes in your composition book, do not copy rewrite them using your own words and make). Examples: 1.

2 x 3 3x 2 14 x 14 x 3

2.

x 3 7 x 2 15x 14 x 2

3.

3x 4

2x3 2x2 x 1

3x 2

Remainder Theorem (Describe this theorem in a couple of sentences). Examples: 1. P ( x )

5x 3 2 x 6; c

2. P ( x )

3x 3

3. P ( x )

2 x 3 5x 2

x2

3

4 x 3; c x 2; c

3 2

Factor Theorem (Describe this theorem in a couple of sentences). Examples: 1. x 3; P ( x )

2 x 3 11x 2 16 x 6

2. x 4; P ( x )

3x 3 15x 2 10 x 8

3. x 3; P ( x )

5x 3 19 x 2

9x 9

Ca Standard 4.0 Perfect Square trinomials (1- Describe how do you know it’s a perfect square trinomial 2- Describe how to get find factors/answer.) Examples:

1. 9 s2

24 s 16

2. 16 x 2 3. 4 s2

40 xy 25 y 2 4s 1

Difference of Squares (1- Describe how do you know it’s a difference of squares. 2- Describe how to find the factors/answer.) Examples:

1. 8b 3

2b

2. 9n 2

4

3.

121x 2 1

Sum of a Cube (1- Describe how do you know it’s a sum of cubes 2- Describe how to find the factors/answer.) Examples:

1. x 6 8 y 3 2. 125x 6

y6

3. 216a 3 125 Difference of a Cube (1- Describe how do you know it’s a difference of cubes 2Describe how to find the factors/answer) Examples: 1. 216a 3 125 2. x 6 8 y 3 3. 125x 6

y6

Ca Standard 5.0 Paragraph 1- Explain how to plot complex numbers and how to find their absolute value (magnitude). Examples: Graph them find the absolute values. Make sure your graph shows the coordinates and the absolute value on the graph. Examples 1-

2i (3 2i )

2-

i (4 6i )

3-

2i ( 3 3i )

Ca Standard 6.0 Paragraph 1- Explain how to simplify complex numbers. Explain what is the conjugate. 1.

2.

3.

8 3i 1 5 4 -4

Paragraph 2- Explain adding, subtracting, multiplying and dividing with complex numbers.

Examples 1- 2i 12 i

2-

3 i 3 2i

3-

3 4i 1 i

Ca Standard 7.0 Explain how to add or subtract fractions that have different denominator. These denominators can be numbers, variables or binomials. (Look at the examples to make sure that you explain all the details).

Examples : 1.

2.

3.

x x-1

1 x 1 1

u

2

1 2u

u

1

2

4

1

y 1

y

2

y

Explain how to simplify complex fractions. (What are the steps to solve this).

Examples : 1

1.

r r

s

2.

x -1 x 2

3.

ab 1 1 b1 a1

s

1

y y

1 2

Ca Standard 8.0 Explain how to solve quadratic equations by completing the square. Make up a story about the quadratic equation. Explain how to solve complex equations (hidden quadratic equations).

Examples Solve by completing the square. 1.

a2

4a 1 0

2.

c2

c 3

3.

z2

3z 2

0

0

Examples Solve the complex equations (hidden equations) . 1.

a4

2a 2 15

2.

b 3 b 10

0

3.

y4

0

6y2

5

0

Ca Standard 9.0 Explain what does a, h and k represent in the quadratic equation in the form of y – k = a ( x2 – h )2 . Also explain what will change in the graph if we change a, h and k.

Examples Explain all the changes from one equation t o the next equation.( What happened to the vertex , how does it open and is it thicker or thinner ). 1.

y 1

2( x 5) 2

y 3

2( x 2) 2

2.

y 5

1 ( x 1) 2 2

y 5

1 ( x 1) 2 3

3.

y 4

1 ( x 2) 2 3

y 4

3( x 2) 2

Ca Standard 10.0 No paragraph for this standard. Graph the examples and make sure you label everything (the axis of symmetry, find the y-intercepts, find the solutions and the maxima or minima of the function.

Examples : Graph and label, determine the y - intercepts , solutions and any maxima or minima. 1.

y 1

2( x 5) 2

2.

y 5

1 ( x 1) 2 2

3.

y 4

1 ( x 2) 2 3