07 Jan 8) Rationalize the denominator

Quiz 1

Math 012 Quiz 1

Professor: Dr. John Uccellini

Instructions:

The quiz is worth 50 points. Your score on the quiz will be converted to a percentage and posted in your Grade book.

This quiz is open book and open notes, and you may take as long as you like on it provided that you submit the quiz no later than the due date posted in our course schedule of the syllabus. You may refer to your textbook, notes, and online classroom materials, but you may not consult anyone or any online resources.

You should show all of your work to receive full credit. If you do not show work, you may earn only partial or no credit.

Please type your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is also acceptable. Be sure to include your name in the document.

If you have any questions, please contact me by e-mail ([email protected]).

Please remember to show ALL of your work on every problem. If there is no work to show, then include a sentence or two explaining your answer.

Here are the basic rules of showing work:

Each step should show the complete expression or equation rather than a piece of it.

Each new step should follow logically from the previous step, following rules of algebra.

Each new step should be beneath the previous step.

The equal sign, =, should only connect equal numbers or expressions.

If you have questions about showing work, please ask.

Name_______________________________ Math 012 Quiz #1 50 Points

Sections 1.3 – 1.5, 1.7, 1.8, 1.10, 10.6

Solve the following equations showing all work to support your answer. (5 points each)

a.

b.

c. x/2-1=2/3 x-3

d. 10x-2(x+4)=8(x-2)+8

e. S=2?rh-2?r^(2 ),solve for h

f. 0.25y+0.10(y-3)=1.1

Instructions for # 2 and #3. Please include the following in your work on each word problem:

a) A statement defining any unknown quantities in the problem in terms of variables.

b) An equation involving the variable(s) corresponding to the information given in the problem.

c) A complete solution to the equation, showing all work.

d) A complete answer to the question asked, including appropriate units.

The perimeter of a triangle measures 82 feet. All three sides are of different lengths. The longest side is 12 feet less than three times the length of the smallest side. The middle length side is 26 feet. Find the length of the smallest and longest side. Show all work to support your answer. (5 points)

Two brothers decide to invest in a business venture. Their initial investment is $100,000. The younger brother invested $43,000 less than the older brother. What were their respective investments? Show all your work to support your answer. (5 points)

The Combined Gas Law from chemistry states that ratio between product of the pressure, P, and the volume, V, and the quotient of the temperature, T, for any gas remains constant. The formula is given by: where k is a constant.

Solve the Combined Gas Law for the volume, V. Show your work. (3 pts.)

If the constant k is 10.13, the pressure 8 litres and the temperature 300 degrees Kelvin, find the volume of the gas? Round your answer to three decimal places. (2 pts)

The formula for compound interest is given by the formula:

Where P is the initial investment, r is the rate of interest expressed as a decimal, t is the time of the investment is years, n is the number of compounding periods in one year and A is the amount of the investment after t years.

Which investment will have the highest yield,

a. $1000 invested at 3% interest compounded semiannually for 10 years or

b. $1000 invested at 2% interest compounded monthly for 10 years? Show work to support your answer. Round your answer to two decimal places. (5 pts)

Quiz 2

Math 012 Quiz 2 Sections 2.1 – 2.5, 3.1, 3.2, Linear Modeling

Professor: Dr. John Uccellini

Instructions:

The quiz is worth 50 points. Your score on the quiz will be converted to a percentage and posted in your assignment folder with comments.

This quiz is open book and open notes, and you may take as long as you like on it provided that you submit the quiz no later than the due date posted in our course schedule of the syllabus. You may refer to your textbook, notes, and online classroom materials, but you may not consult anyone or use any other online resources.

You must show all of your work to receive full credit. If a problem does not seem to require work, write a sentence or two to justify your answer.

Please type your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is also acceptable. Be sure to include your name in the document. Review instructions for submitting your quiz in the Quizzes Module.

If you have any questions, please contact me by e-mail ([email protected]).

Please remember to show all work on every problem.

Name________________________________

1) Given:

Solve for x. (3 points)

Express your answer in Interval Notation. (1 point)

Graph your answer to part a. (1 point)

2) Given -1? (2x )/3+ 5 < 2 Solve for x. (3 points) Express your answer in Interval Notation. (1 point) Graph your answer to part a. (1 point) 3) Find at least three ordered pairs that satisfy the following equation and graph the line through them. You may use the grid provided or create your own graph. Show all work. (5pts) 4x+3y=12 Find at least three ordered pairs that satisfy the following equation and graph the line through them. You may use the grid provided or create your own graph. Show all work. (5pts) 2x-y=4 Draw the line through the point (-2,6) that is parallel to the x-axis. You may use the grid provided or create your own graph. (2 pts) Write the equation of this line (2 pts): ___________________ State the slope of this line (1 pt): _______________________ Draw the line through the point (7,-4) that is parallel to the y-axis.You may use the grid provided or create your own graph. (2 pts) Write the equation of this line (2 pts): ___________________ State the slope of this line (1 pt): _______________________ Given the linear equation 6x+12y=-4, Find the slope and express it in simplest form. Show all work. (3 pts) Find the y-intercept and express it as an ordered pair. Show all work. (2 pts) Given the ordered pairs (2,-3) and (8,0). Show all work. (1 point each) Find the slope of the line through the two ordered pairs. Write the equation in point-slope form of the line through the ordered pairs. Convert the equation toslope intercept form. Convert the equation to standard form, Ax + By = C, where A, B, C are integers. Graph the equation. You may use the axes provided or create one of your own. Write an equation in point-slope form of the line through the point (9,-1) perpendicular to the line with equation: x+5y=5. Show all work. (5 pts) The median sale price of new homes sold in the United States in 2007 was $248,000. In 2010, the median price decreased to $222,000. Let y be the median new home sale price in the year x, where x = 0 represents the year 2007. Write a linear equation that models the change in the median new home price in terms of x. [Hint: the line must pass through the points (0, 248000) and (3, 222000)]. (3 pts) b) Explain what the slope for this line means in the context of the problem. (1pt) c)Use this equation to predict the median new home price in the year 2016. (1 pt) Bonus: Write an equation in point-slope for of the line through the point (-1,2) parallel to the line with equation 4x - 3y = 1. Show all work. (5 pts.) End of quiz: please remember to sign and date the statement in the box on the first page of the quiz. Quiz 3 Math 012 Quiz 3 Professor: Dr. John Uccellini Instructions: The quiz is worth 50 points. There are 10 problems, each worth 5 points. Your score on the quiz will be converted to a percentage and posted in your assignment folder with comments. This quiz is open book and open notes, and you may take as long as you like on it provided that you submit the quiz no later than the due date posted in our course schedule of the syllabus. You may refer to your textbook, notes, and online classroom materials, but you may not consult anyone or any other online resources. You must show all of your work to receive full credit. If a problem does not seem to require work, write a sentence or two to justify your answer. Please type your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is also acceptable. Be sure to include your name in the document. Review instructions for submitting your quiz in the Unit Quizzes Module. If you have any questions, please contact me by e-mail ([email protected]). Please remember to show all of your work. Name________________________________ 1. Answer each of the questions below: (1 pt. each) a) Write the number in scientific notation: 360,559,112 b) Write the number in scientific notation: 0.00000631 c) Write the number in standard notation, without exponents: d) Write the number in standard notation, without exponents: e) Simplify: 2) Simplify. Write the answer using positive exponents only. (5 pts) (2x^3 y^(-2) z)(5x^4 y^2 z^7 ) 3) Simplify. Write the answer using positive exponents only. (5 pts) 4) Simplify. Write the answer using positive exponents only. (5 pts) 5) Perform the indicated operations and simplify: (5 pts) 6) Perform the indicated operations and simplify: (5pts) (6x-4y^2 )(6x+4y^2 ) 7) Perform the indicated operations and simplify: (5 pts) 8) Factor completely. Show work following the method discussed in Sections 6.1 and 6.3 of our text, and show the check by re-multiplication of the factors. If the polynomial is not factorable, write “prime.” (5 pts) 9) Solve the equation by the method of factoring. Use the factoring technique discussed in Section 6.4 of our text, and solve following the methods discussed in Section 6.7. (5 pts) 2x^2+9x-5=0 10) Solve the equation by the method of factoring. Use the factoring technique discussed in Section 6.4 of our text, and solve following the methods discussed in Section 6.7. (5 pts) 30x^2=3x+9 Bonus: Perform the indicated operations and simplify. Show work to support your answer. (5 pts) End of quiz: please remember to sign and date the statement in the box on the first page of the quiz. Quiz 4 Math 012 Quiz 4 Professor: Dr. John Uccellini Instructions: The quiz is worth 50 points. There are 10 problems, each worth 5 points. Your score on the quiz will be converted to a percentage and posted in your assignment folder with comments. This quiz is open book and open notes, and you may take as long as you like on it provided that you submit the quiz no later than the due date posted in our course schedule of the syllabus. You may refer to your textbook, notes, and online classroom materials, but you may not consult anyone or use any other online resources. You must show all of your work to receive full credit. If a problem does not seem to require work, write a sentence or two to justify your answer. Please type your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is also acceptable. Be sure to include your name in the document. Review instructions for submitting your quiz in the Unit Quizzes Module. If you have any questions, please contact me by e-mail ([email protected]). Please remember to show all of your work. \ Name________________________________ 1) Find the excluded values for the algebraic fraction: (5 pts) 2) Find the excluded values for the algebraic fraction: (5 pts) 3) Perform the indicated operation and simplify your answer: (5 pts) (8x^2)/(12x-18)×(14x-21)/(2x^2 ) 4) Perform the indicated operation and simplify your answer: (5 pts) 5) Perform the indicated operation and simplify your answer: (5 pts) 6) Perform the indicated operation and simplify your answer: (5 pts) 7) Solve the equation and show the check of your solution(s). If an answer is an excluded value, please state than on your paper. Use the method discussed in Section 7.7 of our text, clearing fractions from the equation first. (5 pts) 8) Solve the equation and show the check of your solution(s). If an answer is an excluded value, please state that on your paper. Use the method discussed in Section 7.7 of our text, clearing fractions from the equation first. (5 pts) 9) The daily supply of oxygen for one person is provided by 625 square feet of lawn. The Chateau de Versailles’ lawn is 10,890,000 square feet. A lawn of this size would be able to provide the daily oxygen supply for how many people? (5 pts) 10) Two mail sorting machines are in use by a local postal office. The newer machine sorts 300 more letters per minute than the old machine. If the new machine runs 50 minutes for every 40 minutes the old machine runs, how many letters does each machine sort in a minute? ( 5 pts) Bonus: Simplify the expression below. Show all work to support you answer. (5 pts) End of quiz: please remember to sign and date the statement in the box on the first page of the quiz. Quiz 5 Math 012 Quiz 5 Sections: 8.1 – 8.6 Professor: Dr. John Uccellini Instructions: The quiz is worth 50 points. There are 10 problems, each worth 5 points. Your score on the quiz will be converted to a percentage and posted in your assignment folder with comments. This quiz is open book and open notes, and you may take as long as you like on it provided that you submit the quiz no later than the due date posted in our course schedule of the syllabus. You may refer to your textbook, notes, and online classroom materials, but you may not consult anyone or use any other online resources. You must show all of your work to receive full credit. If a problem does not seem to require work, write a sentence or two to justify your answer. Please type your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is also acceptable. Be sure to include your name in the document. Review instructions for submitting your quiz in the Unit Quizzes Module. If you have any questions, please contact me by e-mail ([email protected]). Please remember to show all of your work. Name________________________________ 1) Simplify the expression. Show all work to support your answer. Check you answer by raising it back to the 2nd power. 2) Simplify the expression. Show all work to support your answer. 3) Simplify the expression. Show all work to support your answer. ?(625x^(12 ) ? y?^8 z^36 ) 4) Perform the indicated operations and simplify if possible. Show all work to support your answer. 5) Perform the indicated operation. Show all work to support your answer. (3-2?5)(4?5-2) 6) Perform the indicated operation. Show all work to support your answer. 7) Rationalize the denominator and simplify if possible. Show all work to support your answer. 8) Rationalize the denominator and simplify if possible. Show all work to support your answer. 9) Rationalize the denominator and simplify if possible. Show all work to support your answer. (-19)/(2?7+3) 10) Use radical notation to rewrite the following expression. Simplify if possible and show all work. (81)^(3?4)-(27)^(4?3) Bonus: Simplify. Your answer should contain only positive exponents. Show all work. Up to 5 bonus points. End of quiz: please remember to sign and date the statement in the box on the first page of the quiz.