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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
ALGEBRA II OVER II MATH NOTES
SECTION 2-6 I. Special Functions
A. Set
-Page 105 (44-52)
B. Definition(s)/Property (s)
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.
6. Check your progress #3 page 98.
7. Example 4 page 98.
8. Check your progress #4 page 98.
D. Guided Practice
-Study Guide and Intervention 2-6
- Skills Practice 2-6
E. Independent Practice
-2-6 Practice Sheet
ALGEBRA II OVER II MATH NOTES
SECTION 2-7 I. Graphing Inequalities
A. Set
-Page 105 (44-52)
B. Definition(s)/Property (s)
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
-Study Guide and Intervention 2-7
E. Independent Practice
-Page 104 (10-21) Day 1
-Page 104 (22-34) Day 2
-2-7 Practice Sheet
ALGEBRA II OVER II MATH NOTES
SECTION 3-1 II. Solving Systems of Equations by Graphing
A. Set
-Page 122 (49-57)
B. Definition(s)/Property (s)
1. System of Equations -
2. Consistent -
3. Inconsistent-
4. Independent-
5. Dependent-
6. Concept Summary Page 119-
C. Example(s)
1. Example 1 page 116.
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
-Study Guide and Intervention 3-1
E. Independent Practice
-Page 120 (13-32, 34, 36, 38)
-3-1 Practice Sheet
ALGEBRA II OVER II MATH NOTES
SECTION 3-2 I. Solving Systems of Equations Algebraically
A. Set
-Page 129 (52-63)
B. Definition(s)/Property (s)
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
-Study Guide and Intervention 3-2
E. Independent Practice
-Day 1Page 127 (12-27)
-Day 2 Page 128 (28-42)
-3-2 Practice Sheet
ALGEBRA II OVER II MATH NOTES
SECTION 3-3 I. Solving Systems of Inequalities by Graphing
A. Set
-Page 135 (43-48)
B. Definition(s)/Property (s)
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
-Study Guide and Intervention 3-3
E. Independent Practice
-Day 1Page 133 (9-25)
-Day 2 Page 128 (26-36, 38)
-3-3 Practice Sheet
ALGEBRA II OVER II MATH NOTES
SECTION 4-1 III. Introduction to Matrices
A. Set
-Page 135 (43-48)
B. Definition(s)/Property (s)
1. Matrix –
2. Element-
3. Dimensions-
4. Row Matrix-
5. Column Matrix-
6. Square Matrix-
7. Zero Matrix-
8. Equal Matrices-
C. Example(s)
1. Example 1 page 162.
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.
5. Example 3 page 164.
6. Check your progress #3 page164.
D. Guided Practice
-Study Guide and Intervention 4-1 and Lesson
Reading Guide
E. Independent Practice
-
ALGEBRA II OVER II MATH NOTES
SECTION 4-2 I. Operations with Matrices
A. Set
-Page 173 (1-4)
B. Definition(s)/Property (s)
1. Addition and Subtraction of Matrices–
2. Scalar Multiplication-
3. Properties of Matrix Operations-
C. Example(s)
1. Example 1 page 169.
2. Check your progress page 169.
3. Find A - B
A= 9 2 B= 3 6
-4 7 8 -2
4. Check your progress pg. 170 #2.
5. Example 3 page 170.
6. If: A= 2 8 -3 Find 3A
5 -9 2
7. Check your progress #4, Page 171.
8. Example 5 and check your progress, page 172.
D. Guided Practice
-Study Guide and Intervention 4-2 and Lesson
Reading Guide
E. Independent Practice
-Practice Sheet 4-2
ALGEBRA II OVER II MATH NOTES
SECTION 4-3 I. Multiplying Matrices
A. Set
-Page 176 (50-55)
B. Definition(s)/Property (s)
1. Multiplying Matrices–
2. Properties of Matrix Multiplication-
C. Example(s)
1. Example 1 page 177.
2. Check your progress page 177.
3. Find RS if:
R= 2 -1 S= 3 -9
3 4 5 7
4. Check your progress pg. 178 #2.
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
-Study Guide and Intervention 4-3 and Lesson
Reading Guide
E. Independent Practice
-Practice Sheet 4-3
ALGEBRA II OVER II MATH NOTES
SECTION 4-8 I. Using Matrices to Solve Systems of Equations
A. Set
-Page 215 (60-62)
B. Definition(s)/Property (s)
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
2. Example 2 page 217.
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 Page 219.
D. Guided Practice
-Study Guide and Intervention 4-8 and Lesson
Reading Guide
E. Independent Practice
-Practice Sheet 4-8