algebra ii over ii math notes section 2-5€¦ · algebra ii over ii math notes section 2-5 i....

ALGEBRA II OVER II MATH NOTES

SECTION 2-5 I. Statistics: Using Scatter Plots

A. Set

-Page 91 (23-35)

B. Definition(s)/Property (s)

1. Bivariate Data -

2. Scatter Plot-

3. Positive, Negative and No Correlation-

4. Line of Fit-

5. Prediction Equation-

C. Example(s)

1. Example 1 Page 87.

2. Page 88 Check Your Progress.

D. Guided Practice

-Study Guide and Intervention 2-5

E. Independent Practice

-Page 93 (1-16)

-2-5 Practice Sheet


SECTION 2-6 I. Special Functions

A. Set

-Page 105 (44-52)


1. Step Function -

2. Greatest Integer Function -

3. Constant Function-

4. Identity Function-

5. Piecewise Function-

6. Absolute Value Function-

7. Know Concept Summary Page 98-

C. Example(s)

1. The No Leak Plumbing Repair Company charges

$60/hr. or any fraction thereof for labor. Draw a

graph that represents the situation.

2. Check your progress #1 page 96.

3. Graph f(x) = |x| + 1 and g(x) = |x| - 2 on the same

coordinate plane. Determine the similarities and

differences in the two graphs.

4. Graphing Calculator Lab page 97.

5. Example 3 page 98.




D. Guided Practice


- Skills Practice 2-6


-2-6 Practice Sheet


SECTION 2-7 I. Graphing Inequalities

A. Set

-Page 105 (44-52)


1. Boundary -

2. Test Area -

3. Dotted Line-

4. Solid Line-

C. Example(s)

1. Graph 2x + 3y > 6.

2. Graph 3x + 1/2 y ≥ 2.

3. Example 2 and Check Your Progress Page 103.

4. Graph f(x) < 2|x| - 3

D. Guided Practice



-Page 104 (10-21) Day 1

-Page 104 (22-34) Day 2

-2-7 Practice Sheet


SECTION 3-1 II. Solving Systems of Equations by Graphing

A. Set

-Page 122 (49-57)


1. System of Equations -

2. Consistent -

3. Inconsistent-

4. Independent-

5. Dependent-

6. Concept Summary Page 119-

C. Example(s)


2. Solve by graphing.

a)2x + y =5 b) x + y = 3

x – y =1 -2x + y = -6

c) x – 2y = 0 d) 4x + 1/3 y = 8

x + y = 6 3x + y = 6

3. Example 3 and Check Your Progress Page 117-

118.

4. A service club is selling copies of its holiday

cookbook to raise funds for a project. The

printer’s set-up charge is $200, and each book

coast $2 to print. The cookbooks will sell for $6

each. How many must the club sell before it

makes a profit?

5. Example 4 and check your progress.

6. Example 5.

7. Graph the system of equations and describe it as

consistent and independent, consistent and

dependent, or inconsistent.

a)15 x – 6y = 0 b)y – 4/3 x = -2 c) y – 4/3 x = -2

5x – 2y = 10 y + ¾ x = -2 y – 4/3 x = 3

D. Guided Practice



-Page 120 (13-32, 34, 36, 38)

-3-1 Practice Sheet


SECTION 3-2 I. Solving Systems of Equations Algebraically

A. Set

-Page 129 (52-63)


1. Substitution Method -

2. Elimination Method-

C. Example(s)

1. Use substitution to solve the following system of

equations.

a) x + 2y = 8 b) x + 4y = 26

x/2 – y = 18 x – 5y = -10

c) 7y= 26 + 11x

x – 3y = 0

2. Example 2 and check your progress page 124-

125.

3. Use the elimination to method to solve the

following systems of equations.

a) 2x + y =4 b) 5b = 20 + 2a

3x + y =8 2a + 4b = 7

c) -3x + 5y = 12 d) 8y = 2x + 48

6x – 10 y = -21 y – x/4 = 6

D. Guided Practice



-Day 1Page 127 (12-27)

-Day 2 Page 128 (28-42)

-3-2 Practice Sheet


SECTION 3-3 I. Solving Systems of Inequalities by Graphing

A. Set

-Page 135 (43-48)


1. System of Inequalities -

C. Example(s)

1. Solve each system of inequalities.

a) y≥ 2x - 3 b) y ≤ -x + 1 c) y ≥ -3x/4 + 1

y < -x + 2 |x + 1| < 3 y ≤ -3x/4 -2

2. Example 3 and check your progress page 131.

3. Find the coordinates of the vertices of the figure

formed by 2x – y ≥ -1, x + y ≤ 4, and x + 4y ≥ 4.

4. Check your progress pg. 132

D. Guided Practice



-Day 13 (9-25)

-Day 2 Page 128 (26-36, 38)

-3-3 Practice Sheet


SECTION 4-1 III. Introduction to Matrices

A. Set

-Page 135 (43-48)


1. Matrix –

2. Element-

3. Dimensions-

4. Row Matrix-

5. Column Matrix-

6. Square Matrix-

7. Zero Matrix-

8. Equal Matrices-

C. Example(s)


2. Check your progress page 163.

3. State the dimensions of matrix B if

B= 1 -3

-5 18

0 -2

4. Check your progress pg. 163 #2.


6. Check your progress #3 page164.

D. Guided Practice

-Study Guide and Intervention 4-1 and Lesson

Reading Guide


-


SECTION 4-2 I. Operations with Matrices

A. Set

-Page 173 (1-4)


1. Addition and Subtraction of Matrices–

2. Scalar Multiplication-

3. Properties of Matrix Operations-

C. Example(s)



3. Find A - B

A= 9 2 B= 3 6

-4 7 8 -2



6. If: A= 2 8 -3 Find 3A

5 -9 2

7. Check your progress #4, 1.

8. Example 5 and check your progress, page 172.

D. Guided Practice


Reading Guide


-Practice Sheet 4-2


SECTION 4-3 I. Multiplying Matrices

A. Set

-Page 176 (50-55)


1. Multiplying Matrices–

2. Properties of Matrix Multiplication-

C. Example(s)



3. Find RS if:

R= 2 -1 S= 3 -9

3 4 5 7


5. Example 3 page 179 and check your progress.

6. Example 4 and check your progress Page 180.

7. Example 5 and check your progress page 181.

D. Guided Practice


Reading Guide


-Practice Sheet 4-3


SECTION 4-8 I. Using Matrices to Solve Systems of Equations

A. Set

-Page 215 (60-62)


1. Matrix Equation–

C. Example(s)

1. Write a matrix equation for the system of

equations.

a) 5x – 6y = -47 b) 2x + 4y = 7

3x + 2y = -17 3x – y = 6


3. The formula for propane is C3H8, and its atomic

weight is 44 amu. Butane is C4H10, and its atomic

weight is 58 amu. Write a system of equations

for the weight of each. Then write a matrix

equation for the system of equations.

4. Use a matrix equation to solve each system of

equations.

a. 6x + 2y =11 b) 6a – 9b = -18

3x – 8y = 1 8a – 12b = 24

c) -2x + 3y = -7 d) 2x – 4y = -24

4x – 8y = 16 3x – 6y = -12

5. Graphing Calculator Lab 9.

D. Guided Practice


Reading Guide


-Practice Sheet 4-8

algebra ii over ii math notes section 2-5€¦ · algebra ii over ii math notes section 2-5 i....

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