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MATH 012/ MATH012 MIDTERM EXAM — KEY
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MATH 012/ MATH012 MIDTERM EXAM — KEY
1) Solve the equation below. Show all work following the methods discussed in class; if an equation includes fractions, clear the fractions in the first step. If the equation has a unique solution, please show the complete check of your answer.
2) Solve the equation below. Show all work following the methods discussed in class; if an equation includes fractions, clear the fractions in the first step. If the equation has a unique solution, please show the complete check of your answer.
3) Solve the equation below. Show all work following the methods discussed in class; if an equation includes fractions, clear the fractions in the first step. If the equation has a unique solution, please show the complete check of your answer.
4) Solve the inequality below. Show all work following the methods discussed in class; if an inequality includes fractions, clear the fractions in the first step. Write your answer in interval notation and graph the solution set on a number line.
5) Solve the inequality below. Show all work following the methods discussed in class; if an inequality includes fractions, clear the fractions in the first step. Write your answer in interval notation and graph the solution set on a number line.
6) James wins $900,000 (after taxes) in the lottery and decides to invest half of it in a 5-year CD that pays 5.25% interest compounded monthly. He invests the other half in a money market fund that retirement account that averages 8.37% interest compounded annually over the 5-year period. How much money will he have altogether in the two accounts at the end of the 5-year period?
7) The average annual tuition and fees at all 4-year institutions in the US in 2004 was $19,276 and in 2012 was $ 23,409. Let y be the average tuition and fees in the year x, where x = 0 represents the year 2004.
8) Given the equation 5x — 2y = 10:
9) Show all work as you perform the indicated operations and simplify the result:
10) Show all work as you perform the indicated operations and simplify the result. Write the answer with positive exponents only.
11) Show all work as you perform the indicated operations and simplify the result:
12) Show all work as you multiply the polynomials and simplify the result:
MATH 012/ MATH012 QUIZ 1 — KEY
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MATH 012/ MATH012 QUIZ 1 — KEY
1) Show all work following the methods discussed in class; if an equation includes fractions, clear the fractions in the first step. If the equation has a unique solution, please show the complete check of your answer.
2) Solve the equation below. Show all work following the methods discussed in class; if an equation includes fractions, clear the fractions in the first step. If the equation has a unique solution, please show the complete check of your answer.
3) Solve the equation below. Show all work following the methods discussed in class; if an equation includes fractions, clear the fractions in the first step. If the equation has a unique solution, please show the complete check of your answer.
4) Solve the equation below. Show all work following the methods discussed in class; if an equation includes fractions, clear the fractions in the first step. If the equation has a unique solution, please show the complete check of your answer.
5) Solve the equation below. Show all work following the methods discussed in class; if an equation includes fractions, clear the fractions in the first step. If the equation has a unique solution, please show the complete check of your answer.
6) The area of an oil spill on land varies directly as the volume of oil spilled. If a 35-gallon oil spill covers an area of 91 square feet, how many square feet would a 95-gallon oil spill cover?
7) In kick boxing, the energy needed to break a board of standard width and thickness varies inversely with the length of the board. If 5 Joules of energy are required to break a 12-inch board, how many Joules of energy are required to break a 20-inch board?
8) A plumber cut a 24-foot piece of pipe into two pieces. The length of the longer piece was three feet more than twice the length of the shorter piece. What was the length of each piece of pipe?
9) Briana left Amanda’s house and drove toward the ocean. One hour later, Amanda left, driving 14 mph faster than Briana in an effort to catch up with her. After two hours, Amanda caught up with Briana. What was each woman’s average rate?
10) Maura would like to have at least $350,000 saved for her daughter’s college education. If she invests $102,000 in an education account paying 7.05% interest compounded monthly, will she reach her goal in 18 years? Show all work to justify your answer and include appropriate units. The final amount in the account should be rounded to the nearest cent.
MATH 012/ MATH012 QUIZ 2 — KEY
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MATH 012/ MATH012 QUIZ 2 — KEY
1.
2. 1) Solve the inequality below. Write the solution set using interval notation and graph the solution set on a number line. If you are typing the quiz, you can review instructions for creating a number line from your keyboard attached in the Week 2 LEO News.
3. 2) Solve the compound inequality below. Write the solution set using interval notation and graph the solution set on a number line. If you are typing the quiz, you can review instructions for creating a number line from your keyboard attached in the Week 2 LEO News.
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 as you find ordered pairs.
4) 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 as you find ordered pairs.
5) Draw the line through the point (-2, 3) that is parallel to the y-axis. Write the equation of this line and state its slope.
6) Draw the line through the point (6, -4) that is parallel to the x-axis. Write the equation of this line and state its slope.
7) Given the linear equation 2x−7y 14, find the slope and y-intercept of the line. Write the slope in simplest form and the y-intercept as an ordered pair. Show all work below.
9) Write an equation in point-slope form of the line through the point (3, -5) perpendicular to the line with equation 2x + 9y = 18.
10) The number of Starbucks stores worldwide in 2010 was 16,858. In 2015, there were 23,043 Starbucks stores worldwide. Let y be the number of Starbucks stores worldwide in the year x, where x = 0 represents the year 2010.
MATH 012/ MATH012 QUIZ 3 — KEY
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MATH 012/ MATH012 QUIZ 3 — KEY
1. 1. Answer each of the questions below:
2. 2) Factor the greatest common factor (GCF) out of the expression below. Show all work, writing the complete expression in every step, and show the check by re-multiplication of the factors.
3) Factor by the method of grouping. Show all work, writing the complete expression in every step, and show the check by re-multiplication of the factors.
4) Factor by the method of grouping. Show all work, writing the complete expression in every step, and show the check by re-multiplication of the factors.
5) Factor completely. Show work following the methods discussed in Sections 6.1–6.4 of our text, and show the check by re-multiplication of the factors. If the polynomial is not factorable, write “prime.”
6) Factor completely. Show work following the methods discussed in Sections 6.1–6.4 of our text, and show the check by re-multiplication of the factors. If the polynomial is not factorable, write “prime.”
7) Factor completely. Show work following the methods discussed in Sections 6.1–6.4 of our text, and show the check by re-multiplication of the factors. If the polynomial is not factorable, write “prime.”
8) Solve the equation by the method of factoring discussed in Section 6.7 of our text.
9) Solve the equation by the method of factoring discussed in Section 6.7 of our text.
10) Solve the equation by the method of factoring discussed in Section 6.7 of our text.
MATH 012/ MATH012 QUIZ 4 — KEY
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MATH 012/ MATH012 QUIZ 4 — KEY
1. 1) Find the excluded values for the algebraic fraction:
2) Find the excluded values for the algebraic fraction:
3) Perform the indicated operation and simplify your answer:
4) Perform the indicated operation and simplify your answer:
5) Perform the indicated operation and simplify your answer:
6) Solve the equation by clearing fractions first. Then show the complete check of your solution(s). If an answer is an excluded value, please state that on your paper.
7) Solve the equation by clearing fractions first. Then show the complete check of your solution(s). If an answer is an excluded value, please state that on your paper.
8) Madeline worked 6 more overtime hours than Jacob one week. If Madeline worked 3 overtime hours for every 2 overtime hours that Jacob worked, for how many hours of overtime did each person work? Use a proportion to set up and solve the problem.
MATH 012/ MATH012 QUIZ 5 — KEY
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MATH 012/ MATH012 QUIZ 5 — KEY
1) Simplify the expression.
2) Show all work as you simplify the radical expression.
3) Show all work as you simplify the radical expression.
4) Perform the indicated operations and simplify the result.
5) Perform the indicated operations and simplify the result.
6) Perform the indicated operations and simplify the result.
7) Rationalize the denominator and simplify if possible:
8) Rationalize the denominator and simplify if possible:
9) Rationalize the denominator and simplify if possible:
10) Rewrite the expression using radical notation; then simplify the radical expression.