Hello
Since most of you finished yesterdays' exam before class ended, I gave you some brain teasers and I told you I would post the answers this weekend. I will post them in separate posts.
Mr. Rice is gardening and he needs to mix some fertilizer with 7 quarts of water. He has two buckets that hold exactly 3 quarts and 8 quarts, respectively. Describe or illustrate a procedure that will give Mr. Rice exactly 7 quarts of water in the 8 quart bucket.
1. Fill the 8 quart bucket
2. Fill the 3 quart bucket from the 8 quart bucket (you now have 5 quarts in the 8 quart bucket).
3. Empty the 3 quart bucket.
4. Fill the 3 quart bucket from the 8 quart bucket (you now have 2 quarts in the 8 quart bucket).
5. Empty the 3 quart bucket.
6. Pour the 2 quarts from the 8 quart bucket into the 3 quart bucket (the 8 quart bucket is now empty).
7. Refill the 8 quart bucket.
8. Since the 3 quart bucket has 2 quarts in it, pour 1 quart from the 8 quart bucket into the 3 quart bucket. You now have exactly 7 quarts in the 8 quart bucket!!!!
Saturday, July 30, 2011
Tuesday, July 26, 2011
Review Sheet #1
Here is some review questions. I was not able get the tables to line up. We will go over this tomorrow and I will have more review questions for you in class, plus homework tomorrow.
1. Simplify the following expression (4x-5)- (9x-7)
2. The cost to buy water for a camping trip is determined by the formula T=q(p+t). In this formula T is the total cost of the water, q is the number of quarts of water bought, p is the price per quart, and t is the tax on each quart. Solve the equation for p.
3. Solve for x: 15(x-3)- x/(3 )=10x+25
4. What is the equation of the line that passes through the points (-5, 4) and (6, -51)?
5. What is the slope of the line that is perpendicular to the graph 2y = -6x+8?
6. Find the solution for the following system of linear equations:
5x+3y=5
2x+4y=16
7. Draw the number line that represents all of the solutions of the inequality |x+3|>6
8. Solve for x: 4^x= 〖256〗^2
9. The students recorded how long it took them to walk up the stairs at Rainier Beach High School.
Student Number of Stairs Time in Seconds
Thea 15 6
Adriana 40 16
Imani 20 8
Quan 25 10
Diamond 10 4
What is the equation that represents the data in the table?
10. Let f(x)= x^2- 6x+34. What is the value of x that makes f(x)=50 true?
11. The fuel gauge on Mr. Rice’s car showed that the tank was 2/3 full. After he added 2 gallons of fuel to the tank, the gauge indicated it was now 3/4 full. How many gallons of fuel does Mr. Rice’s car gas tank hold?
12. What binomial are factors of x^2 - 10x - 24?
13. When each side of a square is increased by 12 inches, the resulting area is four times as great as it would have been if each side had been increased by 4 inches. What is the area of the original square?
14. During the last few years, a high school has experienced changes in student enrollment and the number of students taking calculus.
Year 1 2 3 4 5
Total Enrollment 1,250 1,289 1,362 1,439 1,540
Enrollment in Calculus 512 515 530 547 568
Ms. Riggin says interest is Calculus is increasing. Explain how the data from the table supports her statement.
Mr. Rice says interest is Calculus is decreasing. Explain how the data from the table supports his statement.
15. The distance from the Sun to Mars is 2.49*〖10〗^8 kilometers. The distance from the Sun to the Earth is 5.77*〖10〗^7 kilometers. How far is it from the Earth to Mars?
16. What is the x-intercept of the graph of the equation y = (x-250)/50 ?
17. Consider the expression 3(n-2)^3 - 3.
What are the values of the expression when n=1, 2, and 3?
18. Alexis, Mary, Ambera and Michaela compared answers to a problem from a Mr. Rice quiz.
Alexis’s answer was 7
Mary’s answer was √81
Ambera’s answer was √64
Michaela’s answer was √73
Whose answer was closest to 8.5?
19. Solve for x. 1/3 x + 60 - 5x = 2x
20. The age of each adult in a group is exactly double the age, in years, of each student in the group.
Student ages: 19, 17, 20, 21, 22, 18, 22
Compare the mean and the range of each group. What do you notice?
21. Let f(x)= 7√(63+x^3 ). What is the value of f(-3)?
22. Find the roots of this quadratic equation: y = 3x^2 + 3x - 18
23. Solve for x: (3^x )^2 = 6561
24. Mr. Rice has some savings. He decides to invest the savings. The formula for the account is: V=P(1+r)^t.
V = the future value of the money
P = the amount of the deposit
r = the annual interest rate
t = time in years.
How much money will Mr. Rice have if he invests $750 for 4 years at 7% annual interest?
25. Joey is writing a report about the future of technology in public education. He found the following information about computers at RBHS.
School Year Students per Computer
2007 – 2008 15.6
2008 – 2009 11.7
2009 – 2010 8.5
2010 – 2011 7.4
Based on the above data, what sort of prediction can you make about computers at RBHS?
26. Find f(3) when f(x)=2(|x-12|+ 6).
27. What is the exponential function that fits the ordered pairs is the table below?
x 0 1 2 3
f(x) 16 24 36 54
28. When Mrs. Rice goes for her morning walk she takes 9,000 steps to cover 4 miles. Write the equation that represents the relationship between the number of miles walked, M, and the number of steps taken, s.
29. What is the cube of 4x^2?
30. Consider the following table the shows the force applied to a piece of rope and how far it will stretch.
Force Length (mm)
0.0 5
1.5 8
3.0 11
4.5 14
Based on the pattern, what is the force required to stretch the rope 20mm?
31. Solve the following system of linear equations:
3x-2y=4
4x-3y=7
32. The yield for a cotton crop will increase at a constant rate with additional rain
Additional Rain (in.) Cotton Yield (bushels)
1.75 50.25
2.50 60.75
What is the expression that represents the rate of change of expected cotton yield to additional rain?
33. Mr. Rice is going to save some money. He is going to deposit an equal amount of money into a savings account until he has saved $1,100. The amount of money, y in the account after x months can be expressed by the equation y= 55x + 440.
What does the y-intercept of the equation above represent?
1. Simplify the following expression (4x-5)- (9x-7)
2. The cost to buy water for a camping trip is determined by the formula T=q(p+t). In this formula T is the total cost of the water, q is the number of quarts of water bought, p is the price per quart, and t is the tax on each quart. Solve the equation for p.
3. Solve for x: 15(x-3)- x/(3 )=10x+25
4. What is the equation of the line that passes through the points (-5, 4) and (6, -51)?
5. What is the slope of the line that is perpendicular to the graph 2y = -6x+8?
6. Find the solution for the following system of linear equations:
5x+3y=5
2x+4y=16
7. Draw the number line that represents all of the solutions of the inequality |x+3|>6
8. Solve for x: 4^x= 〖256〗^2
9. The students recorded how long it took them to walk up the stairs at Rainier Beach High School.
Student Number of Stairs Time in Seconds
Thea 15 6
Adriana 40 16
Imani 20 8
Quan 25 10
Diamond 10 4
What is the equation that represents the data in the table?
10. Let f(x)= x^2- 6x+34. What is the value of x that makes f(x)=50 true?
11. The fuel gauge on Mr. Rice’s car showed that the tank was 2/3 full. After he added 2 gallons of fuel to the tank, the gauge indicated it was now 3/4 full. How many gallons of fuel does Mr. Rice’s car gas tank hold?
12. What binomial are factors of x^2 - 10x - 24?
13. When each side of a square is increased by 12 inches, the resulting area is four times as great as it would have been if each side had been increased by 4 inches. What is the area of the original square?
14. During the last few years, a high school has experienced changes in student enrollment and the number of students taking calculus.
Year 1 2 3 4 5
Total Enrollment 1,250 1,289 1,362 1,439 1,540
Enrollment in Calculus 512 515 530 547 568
Ms. Riggin says interest is Calculus is increasing. Explain how the data from the table supports her statement.
Mr. Rice says interest is Calculus is decreasing. Explain how the data from the table supports his statement.
15. The distance from the Sun to Mars is 2.49*〖10〗^8 kilometers. The distance from the Sun to the Earth is 5.77*〖10〗^7 kilometers. How far is it from the Earth to Mars?
16. What is the x-intercept of the graph of the equation y = (x-250)/50 ?
17. Consider the expression 3(n-2)^3 - 3.
What are the values of the expression when n=1, 2, and 3?
18. Alexis, Mary, Ambera and Michaela compared answers to a problem from a Mr. Rice quiz.
Alexis’s answer was 7
Mary’s answer was √81
Ambera’s answer was √64
Michaela’s answer was √73
Whose answer was closest to 8.5?
19. Solve for x. 1/3 x + 60 - 5x = 2x
20. The age of each adult in a group is exactly double the age, in years, of each student in the group.
Student ages: 19, 17, 20, 21, 22, 18, 22
Compare the mean and the range of each group. What do you notice?
21. Let f(x)= 7√(63+x^3 ). What is the value of f(-3)?
22. Find the roots of this quadratic equation: y = 3x^2 + 3x - 18
23. Solve for x: (3^x )^2 = 6561
24. Mr. Rice has some savings. He decides to invest the savings. The formula for the account is: V=P(1+r)^t.
V = the future value of the money
P = the amount of the deposit
r = the annual interest rate
t = time in years.
How much money will Mr. Rice have if he invests $750 for 4 years at 7% annual interest?
25. Joey is writing a report about the future of technology in public education. He found the following information about computers at RBHS.
School Year Students per Computer
2007 – 2008 15.6
2008 – 2009 11.7
2009 – 2010 8.5
2010 – 2011 7.4
Based on the above data, what sort of prediction can you make about computers at RBHS?
26. Find f(3) when f(x)=2(|x-12|+ 6).
27. What is the exponential function that fits the ordered pairs is the table below?
x 0 1 2 3
f(x) 16 24 36 54
28. When Mrs. Rice goes for her morning walk she takes 9,000 steps to cover 4 miles. Write the equation that represents the relationship between the number of miles walked, M, and the number of steps taken, s.
29. What is the cube of 4x^2?
30. Consider the following table the shows the force applied to a piece of rope and how far it will stretch.
Force Length (mm)
0.0 5
1.5 8
3.0 11
4.5 14
Based on the pattern, what is the force required to stretch the rope 20mm?
31. Solve the following system of linear equations:
3x-2y=4
4x-3y=7
32. The yield for a cotton crop will increase at a constant rate with additional rain
Additional Rain (in.) Cotton Yield (bushels)
1.75 50.25
2.50 60.75
What is the expression that represents the rate of change of expected cotton yield to additional rain?
33. Mr. Rice is going to save some money. He is going to deposit an equal amount of money into a savings account until he has saved $1,100. The amount of money, y in the account after x months can be expressed by the equation y= 55x + 440.
What does the y-intercept of the equation above represent?
Friday, July 22, 2011
Tuesday, July 26th
Today is the last day of new instruction. We will be spending the rest of the week preparing for the district assessment. We have covered a large amount of material in a short period of time. I encourage all of you to review the videos of any material you are weak on. Make sure to bring any questions you may have to class.
Day 17 – July 26 – Tuesday – Chapter 11 – Rational Expressions and Functions
11.1 Simplifying Rational Expressions
Simplify Rational Expressions
11.2 Multiplying and Dividing Rational Expressions
Multiplying Rational Expressions
Dividing Rational Expressions
Day 17 – July 26 – Tuesday – Chapter 11 – Rational Expressions and Functions
11.1 Simplifying Rational Expressions
Simplify Rational Expressions
11.2 Multiplying and Dividing Rational Expressions
Multiplying Rational Expressions
Dividing Rational Expressions
Monday, July 25th
We are in the final week. We will be covering new material on Monday and Tuesday. Wednesday and Thursday are going to be review days, and we will take the district assessment on Friday.
Day 16 – July 25 – Monday – Chapter 9 – Quadratic Functions and Equations
9.6 The Quadratic Formula and the Discriminant
Quadratic Formula 1Quadratic Formula 2
Quadratic Formula 3The Discriminant
9.7 Linear, Quadratic, & Exponential Models
Linear, Quadratic & Exponential Models
Day 16 – July 25 – Monday – Chapter 9 – Quadratic Functions and Equations
9.6 The Quadratic Formula and the Discriminant
Quadratic Formula 1Quadratic Formula 2
Quadratic Formula 3The Discriminant
9.7 Linear, Quadratic, & Exponential Models
Linear, Quadratic & Exponential Models
Wednesday, July 20, 2011
Friday, July 22nd
We are continuing to work on Chapter 9. You will be receiving a homework assignment that will be practice for the district assessment on the last day of class.
Day 15 – July 22 – Friday – Chapter 9 – Quadratic Functions and Equations
9.4 Factoring to Solve Quadratic Equations
Factoring Quadratics to Solve 1
Factoring Quadratics to Solve 2
Factoring Quadratics to Solve 3
9.5 Completing the Square
Complete the Square 1
Complete the Square 2
Complete the Square 3
Complete the Square 4
Complete the Square 5
Day 15 – July 22 – Friday – Chapter 9 – Quadratic Functions and Equations
9.4 Factoring to Solve Quadratic Equations
Factoring Quadratics to Solve 1
Factoring Quadratics to Solve 2
Factoring Quadratics to Solve 3
9.5 Completing the Square
Complete the Square 1
Complete the Square 2
Complete the Square 3
Complete the Square 4
Complete the Square 5
Thursday, July 21
We are starting Chapter 9, which is all about quadratics. We know where the word quadratic comes from, thanks to Naomi.
Day 14 – July 21 – Thursday – Chapter 9 – Quadratic Functions and Equations
9.1 Quadratic Graphs and Their Properties
Quadratic Graphs 1
Quadratic Graphs 2
9.2 Quadratic Functions
9.3 Solving Quadratic Equations
Solving Quadratics
Day 14 – July 21 – Thursday – Chapter 9 – Quadratic Functions and Equations
9.1 Quadratic Graphs and Their Properties
Quadratic Graphs 1
Quadratic Graphs 2
9.2 Quadratic Functions
9.3 Solving Quadratic Equations
Solving Quadratics
Monday, July 18, 2011
Wednesday, July 20th
I am posting Wednesday's videos because I will not be able to post these tomorrow, since I will be at the memorial service for a high school friend. Please watch these before class on Wednesday. This is the end of chapter 8.
Day 13 – July 20 – Wednesday – Chapter 8 – Polynomials & Factoring
8.7 Factoring Special Cases
Perfect Square Trinomials
Factoring Difference of Squares
8.8 Factoring by Grouping
Factor by Grouping 2
Day 13 – July 20 – Wednesday – Chapter 8 – Polynomials & Factoring
8.7 Factoring Special Cases
Perfect Square Trinomials
Factoring Difference of Squares
8.8 Factoring by Grouping
Factor by Grouping 2
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