Title: Readiness Exam
Course: Technical Math for Industry

Q: An astronomer calculates that a far away galaxy contains 351,472 stars. What does the digit 3 represent in this number?
- Three hundred thousand (Correct. In the number 351,472, the number 3 is in the hundred thousands place, so it represents three hundred thousand.)
- Three hundred million (Incorrect. Beginning with the digit 2 and proceeding to the left, count the place value of each number according to the following patterns: ones, tens, hundreds. If you follow this pattern, what is the place value of the digit 3?)
- Three thousand (Incorrect. Beginning with the digit 2 and proceeding to the left, count the place value of each number according to the following patterns: ones, tens, hundreds. If you follow this pattern, what is the place value of the digit 3?)
- Three million (Incorrect. Beginning with the digit 2 and proceeding to the left, count the place value of each number according to the following patterns: ones, tens, hundreds. If you follow this pattern, what is the place value of the digit 3?)
A: Three hundred thousand

Q: A computer mapping program determined that the distance between Hemali's house and her school was 2.95 miles. What is the value of the digit 5 in this number?
- Five hundredths (Correct. In the number 2.95, the number 5 is in the hundredths place, so it represents five hundredths.)
- Five tenths (Incorrect. Notice this number is a decimal, and that the 5 is to the right of the decimal point. The digit 9 is in the tenths place. What does this mean for the value of the digit 5?)
- Five thousandths (Incorrect. Notice this number is a decimal, and that the 5 is to the right of the decimal point. The digit 9 is in the tenths place. What does this mean for the value of the digit 5?)
- Five ones (Incorrect. Notice this number is a decimal, and that the 5 is to the right of the decimal point. The digit 9 is in the tenths place. What does this mean for the value of the digit 5?)
A: Five hundredths

Q: Pick the math symbol that should replace ? to make a true sentence.

432   ?   2120
A: (a choice with no text)
If right: Correct. 432 is less than 2120 so is correct.
If wrong: Incorrect. Which symbol indicates that 432 is less than 2120?
If wrong: Incorrect. Which symbol indicates that 432 is less than 2120?
If wrong: Incorrect. Which symbol indicates that 432 is less than 2120?

Q: Which of the choices below correctly ranks the values from least to greatest?
- 1%, , 33%, .85 (Incorrect. Try representing each quantity as a fraction and then compare all of them. The decimal 0.85 can be represented , 1% can be represented as , and 33% can be represented as .)
- .85, , 33%, 1% (Incorrect. Try representing each quantity as a fraction and then compare all of them. The decimal 0.85 can be represented , 1% can be represented as , and 33% can be represented as .)
- 33%, 1%, , .85 (Incorrect. Try representing each quantity as a fraction and then compare all of them. The decimal 0.85 can be represented , 1% can be represented as , and 33% can be represented as .)
- 1%, 33%, , .85 (Correct. In this list, 0.85 is the greatest quantity, and 1% is the least.)
A: 1%, 33%, , .85

Q: Which of the choices below correctly shows to location of -7 on a number line?
A: (a choice with no text)
If wrong: Incorrect. Remember that positive numbers will be placed to the right of the number 0, and negative numbers are placed to the left of 0. This means -7 will be placed 7 spots to the left of 0.
If right: Correct. On this number line, -7 will be 7 spots to the left of 0.
If wrong: Incorrect. Remember that positive numbers will be placed to the right of the number 0, and negative numbers are placed to the left of 0. This means -7 will be placed 7 spots to the left of 0.
If wrong: Incorrect. Remember that positive numbers will be placed to the right of the number 0, and negative numbers are placed to the left of 0. This means -7 will be placed 7 spots to the left of 0.

Q: There are 12 inches in one foot, and 5,280 feet in one mile. How many inches are in 2 miles?
- 880 inches (Incorrect. To find the number of inches in 1 mile, you can multiply . How many inches are there in 2 miles?)
- 63,360 inches (Incorrect. To find the number of inches in 1 mile, you can multiply . How many inches are there in 2 miles?)
- 440 inches (Incorrect. To find the number of inches in 1 mile, you can multiply . How many inches are there in 2 miles?)
- 126,720 inches (Correct. Multiplying you find that there are 126,720 inches in 2 miles.)
A: 126,720 inches

Q: There are 44 players on the high school football team. The team uses buses to travel to games. If each bus can hold 20 players, how many buses does the team need to travel to the game?
- 2.5 (Incorrect. One bus can hold 20 players, while 2 buses can hold 40 players. How many buses does the team need for 44 players? Keep in mind that you cannot hire a fractional amount of buses.)
- 3 (Correct. Two buses will be completely full, and the third bus will hold only 4 players.)
- 3.5 (Incorrect. One bus can hold 20 players, while 2 buses can hold 40 players. How many buses does the team need for 44 players? Keep in mind that you cannot hire a fractional amount of buses.)
- 2 (Incorrect. One bus can hold 20 players, while 2 buses can hold 40 players. How many buses does the team need for 44 players? Keep in mind that you cannot hire a fractional amount of buses.)
A: 3

Q: What is the greatest common factor of 36 and 48?
- 4 (Incorrect. 4 is a common factor of 36 and 48, but it is not the greatest common factor.)
- 12 (Correct. 12 is the largest number that is a factor of both 36 and 48.)
- 288 (Incorrect. 288 is the lowest common multiple of 36 and 48, not the greatest common factor.)
- 20 (Incorrect. Neither 36 nor 48 is divisible by 20.)
A: 12

Q: Find the perimeter of the trapezoid.
- 1,000 (Incorrect. Try lining the numbers up vertically, paying attention to place value, and add them again.)
- 1,200 (Incorrect. Try lining the numbers up vertically, paying attention to place value, and add them again.)
- 250,000 (Incorrect. Try lining the numbers up vertically, paying attention to place value, and add them again.)
- 2,200 (Correct. You added the lengths of the sides together successfully.)
A: 2,200

Q: Subtract:
- 4,034 (Incorrect. Try lining the numbers up vertically, paying attention to place value, and subtract them again. You may need to use "borrowing" or "regrouping" to solve this problem.)
- 13,901 (Incorrect. Try lining the numbers up vertically, paying attention to place value, and subtract them again. You may need to use "borrowing" or "regrouping" to solve this problem.)
- 12,217 (Incorrect. Try lining the numbers up vertically, paying attention to place value, and subtract them again. You may need to use "borrowing" or "regrouping" to solve this problem.)
- 12,107 (Correct. The difference when subtracting these numbers is 12,107.)
A: 12,107

Q: What value of n makes the following equation true?
- 2 (Incorrect. Substitute each of the answer choices in for n in the equation (make sure to do it twice; once for each n) and see which value makes the equation true.)
- 40 (Correct. When , then the statement is true.)
- 30 (Incorrect. Substitute each of the answer choices in for n in the equation (make sure to do it twice; once for each n) and see which value makes the equation true.)
- 160 (Incorrect. Substitute each of the answer choices in for n in the equation (make sure to do it twice; once for each n) and see which value makes the equation true.)
A: 40

Q: For her birthday, Joanne received a $20 gift card to an online music store. If she purchased $12.99 worth of music, how much money remains on the gift card?
- $10.01 (Incorrect. To solve this problem, you need to subtract 12.99 from 20. Remember that you can think of 20 as 20.00, and then line up the decimal points and subtract.)
- $12.99 (Incorrect. To solve this problem, you need to subtract 12.99 from 20. Remember that you can think of 20 as 20.00, and then line up the decimal points and subtract.)
- $8.99 (Incorrect. To solve this problem, you need to subtract 12.99 from 20. Remember that you can think of 20 as 20.00, and then line up the decimal points and subtract.)
- $7.01 (Correct. Subtracting 12.99 from 20, you found a difference of 7.01.)
A: $7.01

Q: Add
- 77.77 (Correct. You successfully added these two decimal numbers.)
- 77 (Incorrect. Try lining the numbers up vertically, paying attention to place value, and add them again.)
- 113 (Incorrect. Try lining the numbers up vertically, paying attention to place value, and add them again.)
- 41.72 (Incorrect. Try lining the numbers up vertically, paying attention to place value, and add them again.)
A: 77.77

Q: What is the area of the figure below?
- 400 ft^2 (Incorrect. Try breaking the figure into two sections--rectangle and a square. What is the area of each figure?)
- 80 ft^2 (Incorrect. Try breaking the figure into two sections--rectangle and a square. What is the area of each figure?)
- 300 ft^2 (Correct. The area of the section on the left is 20 ft 10 ft = 200 ft^2, and the area of the section on the right is 10 ft 10 ft = 100 ft^2, so the total is 200 ft^2 + 100 ft^2 = 300 ft^2.)
- 200 ft^2 (Incorrect. Try breaking the figure into two sections--rectangle and a square. What is the area of each figure?)
A: 300 ft^2

Q: Which of the numerical representations below does NOT match the label on the right?
- , 56 divided by 7 (Incorrect.)
- , 56 divided by 7 (Incorrect.)
- ,  7 divided by 56 (Incorrect.)
- , 56 divided by 7 (Correct.)
A: , 56 divided by 7

Q: Find the value of .
- 43 (Incorrect. Remember that means .)
- 12 (Incorrect. Remember that means .)
- 256 (Incorrect. Remember that means .)
- 64 (Correct. .)
A: 64

Q: Write in exponential notation.
- 1,000,000 (Incorrect. Count the number of times 10 is used in the multiplication, which is 6, to find the exponent. Then express the number as a base and an exponent.)
- 60 (Incorrect. Count the number of times 10 is used in the multiplication, which is 6, to find the exponent. Then express the number as a base and an exponent.)
A: (a choice with no text)
If right: Correct. The base is 10 since that is the number that is being multiplied by itself. The exponent is 6 since the factor 10 appears 6 times.
If wrong: Incorrect. Count the number of times 10 is used in the multiplication, which is 6, to find the exponent. Then express the number as a base and an exponent.

Q: Simplify: .
- 28 (Incorrect. Simplify the expression in parentheses first, then apply the exponent, and then perform the subtraction.)
- 71 (Incorrect. Simplify the expression in parentheses first, then apply the exponent, and then perform the subtraction.)
- 68 (Correct. You applied the order of operations correctly: .)
- 156 (Incorrect. Simplify the expression in parentheses first, then apply the exponent, and then perform the subtraction.)
A: 68

Q: Simplify:
- 17 (Correct. You applied the order of operations correctly:)
- 32 (Incorrect. Make sure to follow the order of operations. Compute the addition in parentheses first. Then, perform division. Finally, add from left to right.)
- 11 (Incorrect. Make sure to follow the order of operations. Compute the addition in parentheses first. Then, perform division. Finally, add from left to right.)
- 19 (Incorrect. Make sure to follow the order of operations. Compute the addition in parentheses first. Then, perform division. Finally, add from left to right.)
A: 17

Q: Joe rolls a six-sided cube whose faces are each a different color: white, black, red, green, yellow, and blue. What is the probability that Joe rolls the cube and it lands on green?
A: (a choice with no text)
If wrong: Incorrect. Each color has an even chance of being rolled. If there are 6 possible outcomes, what is the probability that any one of those is rolled?
If wrong: Incorrect. Each color has an even chance of being rolled. If there are 6 possible outcomes, what is the probability that any one of those is rolled?
If right: Correct. There is an equal chance of each color being rolled, so the probability that he rolls a green is .
If wrong: Incorrect. Each color has an even chance of being rolled. If there are 6 possible outcomes, what is the probability that any one of those is rolled?

Q: Which of following pairs of values complete the table below?
- Input = 4, Output = 1 (Incorrect. Look at the patterns in the input and output columns. How much is the input changing between 1 and 2? 2 and 3? How much is the output changing between 10 and 8? 8 and 6? Use this information to find the missing values.)
- Input = 2, Output = 1 (Incorrect. Look at the patterns in the input and output columns. How much is the input changing between 1 and 2? 2 and 3? How much is the output changing between 10 and 8? 8 and 6? Use this information to find the missing values.)
- Input = 4, Output = 0 (Incorrect. Look at the patterns in the input and output columns. How much is the input changing between 1 and 2? 2 and 3? How much is the output changing between 10 and 8? 8 and 6? Use this information to find the missing values.)
- Input = 4, Output = 2 (Correct. As the input increases by 1, the output decreases by 2.)
A: Input = 4, Output = 2

Q: Samuel has written a short computer program for a math project. Given any number from 1-10, the program will add 1 to the number, then double it, and then subtract 5. If Samuel enters the number "7" into his program, what number will the program produce?
- 10 (Incorrect. The computer program's first step would be to take the entered number, , and add . Then it would take that sum , multiply it by and then subtract from the product.)
- 21 (Incorrect. The computer program's first step would be to take the entered number, , and add . Then it would take that sum , multiply it by and then subtract from the product.)
- 11 (Correct. You found that the computer program would do the following operations: , , and finally . The program would produce the number .)
- 4 (Incorrect. The computer program's first step would be to take the entered number, , and add . Then it would take that sum , multiply it by and then subtract from the product.)
A: 11

Q: Ellie has created a "number machine" for a math project. Given any number, the machine will add 2, multiply by 6, and then divide by 3. If Ellie enters the number "4" into his program, what number will the program produce?
- 14 (Incorrect. The program's first step would be to take the entered number, 4, and add 2. Then it would take that sum () and multiply it by 6. Can you figure out what the final step--and end result--would be?)
- 12 (Correct. Following the machine, you found that it would do the following operations: , , and finally . The program would produce the number 11.)
- 18 (Incorrect. The program's first step would be to take the entered number, 4, and add 2. Then it would take that sum () and multiply it by 6. Can you figure out what the final step--and end result--would be?)
- 10 (Incorrect. The program's first step would be to take the entered number, 4, and add 2. Then it would take that sum () and multiply it by 6. Can you figure out what the final step--and end result--would be?)
A: 12

Q: Identify the number that completes the pattern.

3, 6, 9, ___, 15, 18
- 14 (Incorrect. In this pattern, each term grows by 3. What does this mean for the missing term?)
- 13 (Incorrect. In this pattern, each term grows by 3. What does this mean for the missing term?)
- 12 (Correct. In this pattern, each term grows by 3, so the missing term will be , or 12.)
- 10 (Incorrect. In this pattern, each term grows by 3. What does this mean for the missing term?)
A: 12

Q: Identify the number that completes the pattern.

729, 243, 81, ___, 9, 3
- 45 (Incorrect. In this pattern, divide each term by 3 to get the next term. What does this mean for the missing term?)
- 15 (Incorrect. In this pattern, divide each term by 3 to get the next term. What does this mean for the missing term?)
- 75 (Incorrect. In this pattern, divide each term by 3 to get the next term. What does this mean for the missing term?)
- 27 (Correct. In this pattern, each term is of the term before it. The missing term will be , or 27.)
A: 27

Q: Subtract: .
A: (a choice with no text)
If wrong: Incorrect. Rewrite as , and then subtract .
If wrong: Incorrect. Rewrite as , and then subtract .
If wrong: Incorrect. Rewrite as , and then subtract .
If right: Correct. .

Q: Divide: .
A: (a choice with no text)
If wrong: Incorrect. Try rewriting as , and then multiply.
If wrong: Incorrect. Try rewriting as , and then multiply.
If right: Correct. can be rewritten as , which equals .
If wrong: Incorrect. Try rewriting as , and then multiply.

Q: Solve:
- -7 (Correct. can be rewritten , which is equal to -7.)
- 1 (Incorrect. Evaluate first, and then add that quantity to -3.)
- -11 (Incorrect. Evaluate first, and then add that quantity to -3.)
- -5 (Incorrect. Evaluate first, and then add that quantity to -3.)
A: -7