Title: Unit 2 Quiz
Course: Technical Math for Industry

Q: Which of the following will isolate the variable in the expression  ?
- Divide by 6, then subtract 12. (Incorrect. Dividing by 6 is an appropriate first step, because you end up with the expression . However, subtracting 12 is incorrect. In this case, you would need to subtract 2, and not 12, to isolate the variable. You probably forgot to divide the 12 by 6.)
- Multiply by 6, then add 12. (Isolating the variable requires performing the inverse of each operation in the correct order. The inverse of +12 is -12, so you need to subtract 12. This results in 6q. The inverse of multiplying by 6 is dividing by 6, which gives you q by itself. So the correct method is to subtract 12, and then divide by 6.)
- Subtract 12, then divide by 6. (Correct. By subtracting 12 first, you are performing the inverse of +12, resulting in the expression 6q. By dividing by 6, you are performing the inverse of multiplying by 6, and completely isolating the variable h..)
- Add 12, then multiply by 6. (Isolating the variable requires performing the inverse of each operation in the correct order. The inverse of +12 is -12, so you need to subtract 12. This results in 6q. The inverse of multiplying by 6 is dividing by 6, which gives you q by itself. So the correct method is to subtract 12, and then divide by 6.)
A: Subtract 12, then divide by 6.

Q: Which of the following operations will isolate the variable in the expression ?
- Divide 8, then subtract 9. (Incorrect. The first step is a valid one and results in . However, subtracting 9 results in . You probably forgot to divide 9 by 8 when you divided 8x by 8, and you then subtracted again instead of using the inverse of subtracting. Isolating the variable requires performing the same operation to all parts of the expression, and in the correct order. The inverse of -9 is + 9, so you would add 9, resulting in 8x. You would then perform the inverse of multiplying by 8, which is dividing by 8. This method would isolate x. So the correct method is to add 9, and then multiply divide by 8.)
- Add 9, then multiply by 8. (Incorrect. Your first step is an effective one. The inverse of subtracting 9 is adding 9, so adding 9 cancels the -9 and results in 8x. However, multiplying by x gives you 64x. To simplify this properly, the second step should be performing the inverse of multiplying by 8, which is dividing x by 8. So to isolate x, you can add 9 and divide by 8.)
- Divide by 8, then add 9. (Incorrect. The first step is a valid one and results in . However, adding 9 results in . You probably forgot to divide 9 by 8 when you divided 8x by 8. Isolating the variable requires performing the same operation to all parts of the expression. Performing the steps you went through in reverse order works, though, because you are using the inverse of the operations in the expression. The inverse of -9 is + 9, so you would add 9. You would then perform the inverse of multiplying by 8, which is dividing by 8. So the correct method is to add 9, and then multiply divide by 8.)
- Add 9, then divide by 8. (Correct. You successfully performed the inverse of the operations in the expression. Adding 9 results in an answer of 8x, and dividing by 8 yields x by itself.)
A: Add 9, then divide by 8.

Q: Which of the following methods will solve the equation   ?
- Subtract 6 from both sides and then multiply both sides by 3. (Correct. You can isolate a variable by using inverse operations to first remove other terms in the expression and then to clear the coefficient of the variable. As long as the same operations are done to both sides of the equation, equality is maintained.)
- Multiply both sides of the equation by 3 and then subtract 6 from both sides. (Incorrect. Your first step is a valid one, and results in . However, subtracting 6 from both sides results in , which does not simplify the fraction. You probably forgot to multiply 6 by 3 when you multiplied by 3. Isolating the variable requires performing the inverse of the operations in the correct order. The correct answer is to subtract 6 from both sides first, and then multiply both sides by 3.)
- Subtract 6 the left side of the equation and multiply the right side by 3. (Incorrect. The equality of an expression is lost if the same operations are not done to both sides of the equation. The correct answer is to subtract 6 from both sides of the equation and then multiply both sides by 3.)
- Add 6 to both sides of the equation and multiply both sides by . (Incorrect. Isolating the variable requires performing the inverse of the operations in the correct order. The correct answer is to subtract 6 from both sides first, and then multiply both sides by 3.)
A: Subtract 6 from both sides and then multiply both sides by 3.

Q: Which of the following methods would you use to solve the equation ?
- Subtract 31 from both sides and divide both sides by 4. (Incorrect. You need to isolate the variable by performing the reverse of the operations shown in the problem. The steps also must be done to each side of the equation, and in the correct order. The correct answer is to subtract 3 from both sides, and then divide both sides by 4.)
- Subtract 3 from both sides, and then divide both sides by 4. (Correct. You performed the correct operations to both sides of the equation, and in the correct order.)
- Add 3 to both sides, and then multiply both sides by 4. (Incorrect. You need to isolate the variable by performing the reverse of the operations shown in the problem. The steps also must be done to each side of the equation, and in the correct order. The correct answer is to subtract 3 from both sides, and then divide both sides by 4.)
- Divide both sides by 4, then add 3 to both sides. (Incorrect. You need to isolate the variable by performing the reverse of the operations shown in the problem. The steps also must be done to each side of the equation, and in the correct order. The correct answer is to subtract 3 from both sides, and then divide both sides by 4.)
A: Subtract 3 from both sides, and then divide both sides by 4.

Q: Which of the following methods would you use to solve the equation 36x - 9 = 63?
- Add 9 to both sides, and then divide both sides by 36. (Correct. By adding 9 to both sides, and dividing both sides by 36, you perform the inverse of the operations in the problem, and isolate the variable. By following this procedure, you should find that x = 2.)
- Subtract 9 from the left side, and divide the right side by 36 (Incorrect. You need to isolate the variable by performing the reverse of the operations shown to both sides of the equation. The correct answer is to add 9 to both sides, and then divide both sides by 36.)
- Add 9 to the left side, and multiply the right side by 36 (Incorrect. You need to isolate the variable by performing the reverse of the operations shown to both sides of the equation. The correct answer is to add 9 to both sides, and then divide both sides by 36.)
- Subtract 9 from both sides, and then multiply both sides by 36 (Incorrect. You need to isolate the variable by performing the reverse of the operations shown to both sides of the equation. The correct answer is to add 9 to both sides, and then divide both sides by 36.)
A: Add 9 to both sides, and then divide both sides by 36.

Q: In which of the following equations is the distributive property correctly applied to the equation p(q + 3) = 5?
- pq + 3p = 5 (Correct. The Distributive Property states that when a number multiplies an expression inside parentheses, you can distribute the multiplication to each term of the expression individually.)
- pq + 3p = 5p (Incorrect. Multiplication occurs with only the terms inside the parenthesis, not the other parts of the equation.)
- 3 + q = 5p (Incorrect. Multiplication occurs with only the terms inside the parenthesis, not the other parts of the equation. All of the terms inside the parentheses must be multiplied by the value outside.)
A: pq + 3p = 5
If wrong: Incorrect. All of the terms inside the parentheses must be multiplied by the value outside.

Q: In order to clear away the fractions from , which of the following numbers can we use to multiply both sides of the equation?
- 62 (Incorrect. In this case, you must clear the fraction by multiplying them by a common denominator. 62 is not a common denominator of 9 and 5.)
- 45 (Correct. 45 is the lowest common denominator of 9 and 5 so you can multiply both sides of the equation by this number to clear away the fractions.)
- 15 (Incorrect. In this case, you must clear the fraction by multiplying them by a common denominator. 15 is not a common denominator of 9 and 5.)
- 95 (Incorrect. In this case, you must clear the fraction by multiplying them by a common denominator. 95 is not a common denominator of 9 and 5.)
A: 45

Q: Which of the equations listed below is equivalent to:
A: (a choice with no text)
If wrong: Incorrect. When applying the Distributive Property, multiplication occurs with only the terms inside the parenthesis, not the other parts of the equation. Here, you multiplied but not or .
If wrong: Incorrect. When applying the Distributive Property, all of the terms inside the parentheses must be multiplied by the value outside. Here, you multiplied both and by 9; try multiplying both terms by 18.
If wrong: Incorrect. When applying the Distributive Property, multiplication occurs with only the terms inside the parenthesis, not the other parts of the equation.
If right: Correct. All of the terms inside the parentheses have been multiplied by the correct value outside.

Q: In which of the following equations is the Distributive Property correctly applied to the equation ?
A: (a choice with no text)
If wrong: Incorrect. When applying the Distributive Property, all of the terms inside the parentheses must be multiplied by the value outside. Here, you have multiplied but not .
If right: Correct. All of the terms inside the parentheses, (90q + 36), have been multiplied by the value 2p.
If wrong: Incorrect. When applying the Distributive Property, multiplication occurs with only the terms inside the parenthesis, not the other parts of the equation.
If wrong: Incorrect. When applying the Distributive Property, multiplication occurs with only the terms inside the parenthesis, not the other parts of the equation.

Q: Multiply using the distributive property.
A: (a choice with no text)
If right: Correct. All of the terms within the parentheses have been multiplied by the term on the outside of the parentheses.
If wrong: Incorrect. Remember that each term within the parentheses must be multiplied by the expression on the outside of the parentheses. You can think of the expression as .
If wrong: Incorrect. Remember that each term within the parentheses must be multiplied by the expression on the outside of the parentheses. You can think of the expression as .
If wrong: Incorrect. Remember that each term within the parentheses must be multiplied by the expression on the outside of the parentheses. You can think of the expression as .

Q: Jordan's sporting goods store had 75 basketballs. Before selling any, they added an unknown number of basketballs to their stock, resulting in 136 basketballs total.

Which of the following equations best represents this situation?
A: (a choice with no text)
If wrong: Incorrect. Remember that unknown refers to the variable, and added implies addition, and total indicates the total number of basketballs.If they began with 75, how many did they add to get to 136?
If wrong: Incorrect. Remember that unknown refers to the variable, and added implies addition, and total indicates the total number of basketballs.If they began with 75, how many did they add to get to 136?
If wrong: Incorrect. Remember that unknown refers to the variable, and added implies addition, and total indicates the total number of basketballs.If they began with 75, how many did they add to get to 136?
If right: Correct. You put the variable and the two numbers in the proper positions.

Q: At the Galapagos Islands, Dr. Owen finds 102 giant tortoise eggs that he brings back to his research center to be hatched in safety. At the research center, six of the eggs hatch, and the hatchlings are placed in a nursery. Dr. Owen places equal but unknown numbers of the remaining eggs in eight different labs.

Which of the following equations best represents this situation?
A: (a choice with no text)
If wrong: Incorrect. The eggs that hatch should be subtracted from the original total of 102, resulting in the expression 102-6. The variable x represents the number of eggs in each lab, and the coefficient 8 is placed in front of the x to represent the number of labs. Try putting this information together and identifying the correct equation.
If right: Correct. The coefficient, variable, and two constants are placed in the proper positions.
If wrong: Incorrect. The eggs that hatch should be subtracted from the original total of 102, resulting in the expression 102-6. The variable x represents the number of eggs in each lab, and the coefficient 8 is placed in front of the x to represent the number of labs. Try putting this information together and identifying the correct equation.
If wrong: Incorrect. The eggs that hatch should be subtracted from the original total of 102, resulting in the expression 102-6. The variable x represents the number of eggs in each lab, and the coefficient 8 is placed in front of the x to represent the number of labs. Try putting this information together and identifying the correct equation.

Q: A bus has 16 rows of seats. It is completely full, and each row has an equal but unknown number of kids. After fourteen kids get off the bus, only 50 kids remain on the bus.

Which of the following equations best represents this situation?
A: (a choice with no text)
If wrong: Incorrect. Use the variable x to represent the number of kids in each row when the bus is full. Because there are 16 rows, the total number of kids on the full bus can be represented by 16x. Think about how many kids get off, and then how many are left. How are these quantities represented in the equation?
If wrong: Incorrect. Use the variable x to represent the number of kids in each row when the bus is full. Because there are 16 rows, the total number of kids on the full bus can be represented by 16x. Think about how many kids get off, and then how many are left. How are these quantities represented in the equation?
If wrong: Incorrect. Use the variable x to represent the number of kids in each row when the bus is full. Because there are 16 rows, the total number of kids on the full bus can be represented by 16x. Think about how many kids get off, and then how many are left. How are these quantities represented in the equation?
If right: Correct. The variable, coefficient, and constants are placed correctly in the equation.

Q: Two opponents playing chess start out with 32 pieces on the chess board. Each person loses an equal amount of pieces over 15 minutes. By this time, only 20 pieces remain. How many pieces did each person lose?

Translate this word problem into an equation, using x to represent the number of pieces that each person lost.
A: (a choice with no text)
If wrong: Incorrect. Remember that the game started with 32 pieces and each person lost x amount of pieces. The number of pieces lost is ; what number do you think this expression should be set equal to?
If wrong: Incorrect. Remember that the game started with 32 pieces and each person lost x amount of pieces. The number of pieces lost is ; what number do you think this expression should be set equal to?
If right: Correct. The variable, coefficient, and constants are all in the proper positions.
If wrong: Incorrect. Remember that the game started with 32 pieces and each person lost x amount of pieces. The number of pieces lost is ; what number do you think this expression should be set equal to?

Q: A boy has four slices of pizza. Each slice has an equal number of green pepper pieces. He adds on three green pepper pieces to his slices of pizza and ends up with 27 total pieces of green pepper on it. How many pieces of green pepper were on each slice of pizza in the beginning?

Translate this problem into an equation, using x to represent the number of green peppers on a given slice.
A: (a choice with no text)
If wrong: Incorrect. Because x represents the unknown number of green pepper pieces on each slice, the number of green pepper pieces on four slices of pizza can be represented by 4x. How many pieces did he add to the 4x? How many pieces did he have at the end?
If right: Correct. The coefficient, variable, and constant are in the right place.
If wrong: Incorrect. Because x represents the unknown number of green pepper pieces on each slice, the number of green pepper pieces on four slices of pizza can be represented by 4x. How many pieces did he add to the 4x? How many pieces did he have at the end?
If wrong: Incorrect. Because x represents the unknown number of green pepper pieces on each slice, the number of green pepper pieces on four slices of pizza can be represented by 4x. How many pieces did he add to the 4x? How many pieces did he have at the end?

Q: Rewrite the formula for the area of a trapezoid to solve for the height, h.
A: (a choice with no text)
If wrong: Incorrect. To solve for h, begin by multiplying both sides by 2. What do you have to divide by in order to isolate h?
If wrong: Incorrect. To solve for h, begin by multiplying both sides by 2. What do you have to divide by in order to isolate h?
If wrong: Incorrect. To solve for h, begin by multiplying both sides by 2. What do you have to divide by in order to isolate h?
If right: Correct. Multiplying both sides by 2 and then dividing by will isolate h on one side of the equation.

Q: Rewrite the formula for initial velocity to solve for final velocity, .
A: (a choice with no text)
If right: Correct. To find , add to both sides of the equation.
If wrong: Incorrect. In order to isolate , what do you have to move to the other side of the equaton?
If wrong: Incorrect. In order to isolate , what do you have to move to the other side of the equaton?
If wrong: Incorrect. In order to isolate , what do you have to move to the other side of the equaton?

Q: Rewrite the formula for volume to solve for moles, n.
A: (a choice with no text)
If right: Correct. To solve for n, multiply the equation by P and then divide by .
If wrong: Incorrect. To solve for n, begin by multipling both sides by P. What do you have to divide by in order to isolate n?
If wrong: Incorrect. To solve for n, begin by multipling both sides by P. What do you have to divide by in order to isolate n?
If wrong: Incorrect. To solve for n, begin by multipling both sides by P. What do you have to divide by in order to isolate n?

Q: The potential energy (PE) of an object is equal to its mass multiplied by acceleration due to gravity multiplied by its height. In mathematical terms, this is represented by the formula:

Rewrite this equation to solve for height, h.
A: (a choice with no text)
If wrong: Incorrect. In this formula, the variables m, g, and h are all multiplied together. What operation can you use to "undo" multiplication in order to isolate the h?
If right: Correct. To solve for h, divide both sides of the equation by mg.
If wrong: Incorrect. In this formula, the variables m, g, and h are all multiplied together. What operation can you use to "undo" multiplication in order to isolate the h?
If wrong: Incorrect. In this formula, the variables m, g, and h are all multiplied together. What operation can you use to "undo" multiplication in order to isolate the h?

Q: Rewrite the formula for the perimeter of an isosceles triangle to solve for the length of one of the identical sides, a.
A: (a choice with no text)
If wrong: Incorrect. Imagine you have an isosceles triangle with a perimeter of 33 and a base length of 17. How long is each of the identical sides? How do you know?
If right: Correct. To find the length of a, you can subtract b from p and divide by 2.
If wrong: Incorrect. Imagine you have an isosceles triangle with a perimeter of 33 and a base length of 17. How long is each of the identical sides? How do you know?
If wrong: Incorrect. Imagine you have an isosceles triangle with a perimeter of 33 and a base length of 17. How long is each of the identical sides? How do you know?

Q: Which of the following is the correct value of | -45 + 33 | - 7?
- 71 (The absolute value of a number is always positive or zero. If the original number is negative, its absolute value is that number without the negative sign. In this case, | - 45 + 33 | - 7 = | -12 | - 7 = 12 - 7.)
- 5 (Correct. | -45 + 33 | - 7 = | -12 | - 7 = 12 - 7 = 5.)
- 78 (The absolute value of a number is always positive or zero. If the original number is negative, its absolute value is that number without the negative sign. In this case, | - 45 + 33 | - 7 = | -12 | - 7 = 12 - 7.)
- -19 (The absolute value of a number is always positive or zero. If the original number is negative, its absolute value is that number without the negative sign. In this case, | - 45 + 33 | - 7 = | -12 | - 7 = 12 - 7.)
A: 5

Q: What point on the number line is
- 15 (Incorrect. The expression . What is the absolute value of -10? What do you get when you multiply it by 2?)
- 5 (Incorrect. The expression . What is the absolute value of -10? What do you get when you multiply it by 2?)
- 20 (Correct. The absolute value of)
- 40 (Incorrect. The expression . What is the absolute value of -10? What do you get when you multiply it by 2?)
A: 20

Q: If , which of the following points on this number line is
- 68 (Incorrect. For , the quantity can be written as , or Does this help you think about the problem?)
- 12 (Incorrect. For , the quantity can be written as , or Does this help you think about the problem?)
- 8 (Correct. When you evaluate for you get 8.)
- 0 (Incorrect. For , the quantity can be written as , or Does this help you think about the problem?)
A: 8

Q: Which values for n will make a true equation?
- -24 and 24 (Incorrect. ; how can you use this fact to help you solve this problem?)
- -9 and 9 (Correct. These values make the equation true.)
- 0 (Incorrect. ; how can you use this fact to help you solve this problem?)
- -6 and 6 (Incorrect. ; how can you use this fact to help you solve this problem?)
A: -9 and 9

Q: Which values for t make  a true equation?
- -5 and 5 (Incorrect. . Which values for t can make ?)
- -1 and 1 (Correct. Those values for t make the equation true.)
- 0 (Incorrect. . Which values for t can make ?)
- -4 and 4 (Incorrect. . Which values for t can make ?)
A: -1 and 1

Q: Which of the following number lines show the correct solution to the equation ?
A: (a choice with no text)
If wrong: Incorrect. Begin by multiplying both sides of the equation by -4, and then solve the equation for k.
If wrong: Incorrect. Begin by multiplying both sides of the equation by -4, and then solve the equation for k.
If right: Correct. When k = 2 or -2, the equation is true.
If wrong: Incorrect. Begin by multiplying both sides of the equation by -4, and then solve the equation for k.

Q: Which of the following number lines show the correct solution to the equation ?
A: (a choice with no text)
If wrong: Incorrect. Begin by multiplying both sides by 15, and then solve the equation .
If right: Correct. When x equals -5 or 5, this is a true statement.
If wrong: Incorrect. Begin by multiplying both sides by 15, and then solve the equation .
If wrong: Incorrect. Begin by multiplying both sides by 15, and then solve the equation .

Q: Which of the following is the correct solution for ?
- x = -12, 12 (Incorrect. There are two possible values for x here: one postive, and one negative. You know that ; what values can x be so that ?)
- x = -4 (Incorrect. There are two possible values for x here: one postive, and one negative. You know that ; what values can x be so that ?)
- x = 8 (Incorrect. There are two possible values for x here: one postive, and one negative. You know that ; what values can x be so that ?)
- x = -4, 4 (Correct. Both 4 and -4 have an absolute value of 4, so both are possible values for x.)
A: x = -4, 4