TEAS Math Practice Test #2 — Questions and Answers

Question 1: Simplify the expression above. Which of the following is correct?

14/54
22/67
29/72 (Correct answer)
18/126

Correct answer: 29/72

Without the specific expression provided, we assume the task is to simplify a fraction or an algebraic expression that results in 29/72. To simplify a fraction, you divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, 29 is a prime number, and 72 is not a multiple of 29, meaning there are no common factors other than 1. Therefore, the fraction 29/72 is already in its simplest form.

Question 2: Express 5/8 as its closest rounded percentage.

56%
60%
63% (Correct answer)
66%

Correct answer: 63%

To express 5/8 as a percentage, first convert the fraction to a decimal by dividing the numerator by the denominator: 5 ÷ 8 = 0.625. Next, multiply the decimal by 100 to convert it to a percentage: 0.625 × 100 = 62.5%. Finally, round 62.5% to the nearest whole percentage, which is 63%. Thus, 5/8 is approximately 63%.

Question 3: Amanda wants to paint the walls of a room. She knows that each can of paint contains one gallon. A half gallon will cover a 55 square feet of wall. Each of the four walls is 10 feet high. Two of the walls are 10 feet wide and two of the walls are 15 feet wide. How many 1-gallon buckets of paint does Amanda need to buy in order to fully paint the room?

4
5 (Correct answer)
9
10

Correct answer: 5

First, calculate the total wall area: two walls are 10ft x 10ft (200 sq ft) and two walls are 10ft x 15ft (300 sq ft), totaling 500 sq ft. A half-gallon covers 55 sq ft, so one full gallon covers 110 sq ft (55 sq ft * 2). To find the number of gallons needed, divide the total area by the coverage per gallon: 500 sq ft ÷ 110 sq ft/gallon ≈ 4.54 gallons. Since paint is sold in whole gallons, Amanda must buy 5 gallons to fully paint the room.

Question 4: How many millimeters are there in 5 meters?

500
5,000 (Correct answer)
50,000
500,000

Correct answer: 5,000

To convert meters to millimeters, you need to know the conversion factors. One meter is equal to 100 centimeters, and one centimeter is equal to 10 millimeters. Therefore, one meter is equivalent to 100 cm * 10 mm/cm = 1000 millimeters. To find the number of millimeters in 5 meters, multiply 5 by 1000, which gives 5,000 millimeters.

Question 5: Kyra has a budget of $300 for her holiday spending. Kyra decides to buy shoes for her grandchildren. If each pair of shoes costs $40, and Kyra has n grandchildren, which of the following inequalities represents Kyra’s budget constraint?

40n > 300
40 + n > 300
40 + n ≤ 300
40n ≤ 300 (Correct answer)

Correct answer: 40n ≤ 300

Kyra's budget constraint involves the total cost of shoes for her grandchildren. If each pair of shoes costs $40 and she has 'n' grandchildren, the total cost will be 40 multiplied by 'n', or 40n. Since her budget is $300, the total amount spent (40n) must be less than or equal to $300. Therefore, the correct inequality is 40n ≤ 300.

Question 6: 2 − 8 ÷ (24 ÷ 2) =

−6
−¾
1 (Correct answer)
2

Correct answer: 1

To solve this expression, follow the order of operations (PEMDAS/BODMAS). First, evaluate the exponent inside the parentheses: 2⁴ = 16. Next, perform the division inside the parentheses: 16 ÷ 2 = 8. The expression now becomes 2 − 8 ÷ 8. Then, perform the division: 8 ÷ 8 = 1. Finally, perform the subtraction: 2 − 1 = 1. Thus, the value of the expression is 1.

Question 7: Which type of graph would best indicate the percentage of a school’s annual scholarship fund spent on freshman students?

pie chart (Correct answer)
line graph
scatter plot
histogram

Correct answer: pie chart

A pie chart is the best type of graph to indicate the percentage of a whole that is spent on a particular category. It visually represents parts of a whole, making it easy to see the proportion of the scholarship fund allocated to freshman students compared to other groups or the total. Other graph types like line graphs or scatter plots are better for showing trends or relationships between variables over time, not proportions of a total.

Question 8: −1/4, π, 3/8, −0.2 Order the above list of numbers from least to greatest.

−0.2, −1/4, 3/8, π
−1/4, −0.2, 3/8, π (Correct answer)
−0.2, −1/4, π, 3/8
−1/4, −0.2, π, 3/8

Correct answer: −1/4, −0.2, 3/8, π

To order these numbers, it's helpful to convert them all to decimal form. −1/4 is −0.25, π is approximately 3.14159, 3/8 is 0.375, and −0.2 remains −0.2. Comparing these decimals: −0.25, −0.2, 0.375, 3.14159. Arranging them from least to greatest gives −0.25, −0.2, 0.375, 3.14159. Converting back to the original forms, the order is −1/4, −0.2, 3/8, π.

Question 9: (7y2 + 3xy − 9) − (2y2 + 3xy − 5)

5y2 − 4 (Correct answer)
9y2 + 6xy − 14
5y2 + 4
5y2 + 6xy − 14

Correct answer: 5y2 − 4

To subtract these polynomials, distribute the negative sign to each term in the second parenthesis: (7y² + 3xy − 9) + (−2y² − 3xy + 5). Now, combine like terms. For the y² terms: 7y² − 2y² = 5y². For the xy terms: 3xy − 3xy = 0. For the constant terms: −9 + 5 = −4. Combining these results gives 5y² − 4.

Question 10: (x+4)(x+4) =

x²+8x+8
x²+16x+16
x²+16x +8
x²+8x+16 (Correct answer)

Correct answer: x²+8x+16

To multiply (x+4)(x+4), you can use the FOIL method (First, Outer, Inner, Last) or recognize it as a perfect square (a+b)² = a² + 2ab + b². Using FOIL: First terms: x * x = x². Outer terms: x * 4 = 4x. Inner terms: 4 * x = 4x. Last terms: 4 * 4 = 16. Combining these, we get x² + 4x + 4x + 16, which simplifies to x² + 8x + 16.

Question 11: The following equation to be solved: y3 x y4 =

2y¹²
y¹²
y⁷ (Correct answer)
2y⁷

Correct answer: y⁷

When multiplying exponential terms with the same base, you add their exponents. In the expression y³ × y⁴, the base is 'y'. Therefore, you add the exponents 3 and 4. The sum of 3 and 4 is 7. So, y³ × y⁴ simplifies to y⁷.

Question 12: There are 4 Tootsie Rolls, 3 Lollipops, 5 Hershey Kisses, and 6 Starbursts in a bag of sweets. What is the likelihood that the sweet you randomly choose will be a lollipop?

3/10
1/4
1/18
1/6 (Correct answer)

Correct answer: 1/6

First, calculate the total number of sweets in the bag: 4 (Tootsie Rolls) + 3 (Lollipops) + 5 (Hershey Kisses) + 6 (Starbursts) = 18 sweets. There are 3 lollipops. The probability of choosing a lollipop is the number of lollipops divided by the total number of sweets, which is 3/18. This fraction simplifies to 1/6. Therefore, the likelihood of choosing a lollipop is 1/6.

Question 13: If you have four shirts and five ties, how many different ways can you arrange them?

20 (Correct answer)
9
120
30

Correct answer: 20

To find the total number of different ways to arrange items from two distinct categories, you use the fundamental counting principle. This principle states that if there are 'm' ways to do one thing and 'n' ways to do another, then there are m × n ways to do both. In this case, you have 4 shirt choices and 5 tie choices. Multiplying these together, 4 × 5 = 20. Therefore, there are 20 different ways to arrange the shirts and ties.

Question 14: I have Z $ to spend on a woman. How much money does she have left over after spending $500?

500Z
Z – 500 (Correct answer)
500 – Z
Z + 500

Correct answer: Z – 500

If you start with Z dollars and spend $500, the amount of money left over is found by subtracting the amount spent from the initial amount. This can be represented algebraically as Z minus 500. Therefore, the expression Z – 500 correctly represents the money remaining.

Question 15: What percentage of a staff is present in the workplace if 1/3 of employees are on vacation and 1/4 of those who aren't are absent due to illness?

1/4
1/6
1/12
1/2 (Correct answer)

Correct answer: 1/2

If 1/3 of employees are on vacation, then 2/3 of employees are not on vacation. Of those who aren't on vacation (2/3), 1/4 are absent due to illness. So, the fraction absent due to illness is (1/4) * (2/3) = 2/12 = 1/6 of the total staff. The total fraction of staff not present is 1/3 (vacation) + 1/6 (illness) = 2/6 + 1/6 = 3/6 = 1/2. Therefore, if 1/2 of the staff is not present, then 1 - 1/2 = 1/2 of the staff is present in the workplace.

Question 16: When 0.05z = 1, z equals.

0.05
2
20 (Correct answer)
200

Correct answer: 20

To solve the equation 0.05z = 1, you need to isolate 'z'. Divide both sides of the equation by 0.05. So, z = 1 ÷ 0.05. To perform this division, you can think of it as 100 ÷ 5, which equals 20. Therefore, z equals 20.

Question 17: The volume of a cube is 64 cubic feet. What is the cube's surface area?

128 square feet
96 square feet (Correct answer)
384 square feet
64 square feet

Correct answer: 96 square feet

First, find the side length of the cube. The volume of a cube is s³, so if the volume is 64 cubic feet, then s³ = 64. Taking the cube root of 64, we find that the side length (s) is 4 feet. Next, calculate the surface area. A cube has 6 identical square faces, and the area of one face is s². So, the area of one face is 4² = 16 square feet. The total surface area is 6 times the area of one face: 6 × 16 = 96 square feet.

Question 18: A brick stack is 3 1/2 feet tall. What is the number of bricks in the stack if each brick is 1 3/4 inches high?

28
24 (Correct answer)
12
2

Correct answer: 24

First, convert all measurements to a common unit, such as inches. The brick stack is 3 1/2 feet tall, which is 3.5 feet. Since 1 foot equals 12 inches, the stack height in inches is 3.5 × 12 = 42 inches. Each brick is 1 3/4 inches high, which is 1.75 inches. To find the number of bricks, divide the total stack height by the height of one brick: 42 inches ÷ 1.75 inches/brick = 24 bricks. Therefore, there are 24 bricks in the stack.

Question 19: A book typically costs $28. How much is the sales price of the book if it is "20% off"?

$22.40 (Correct answer)
$21.20
$25.20
$5.60

Correct answer: $22.40

To find the sales price of the book with a 20% discount, first calculate the discount amount. 20% of $28 is 0.20 × $28 = $5.60. Then, subtract the discount from the original price: $28 - $5.60 = $22.40. Alternatively, if the book is 20% off, you are paying 80% of the original price, so 0.80 × $28 = $22.40.

Question 20: According to a map's scale, 1 inch corresponds to 60 miles. How many miles are there between two places on a map if the space between them is 2 1/2 inches?

180
24
120
150 (Correct answer)

Correct answer: 150

The map scale states that 1 inch on the map corresponds to 60 miles in reality. To find the actual distance between two places that are 2 1/2 inches apart on the map, multiply the map distance by the scale factor. Convert 2 1/2 inches to a decimal: 2.5 inches. Then, multiply 2.5 inches by 60 miles/inch: 2.5 × 60 = 150 miles. Therefore, the distance between the two places is 150 miles.

Question 21: A car's fuel tank holds 15 gallons. How much gas will be left in the tank if a car goes 384 miles at 32 miles per gallon?

4
3 (Correct answer)
12
6

Correct answer: 3

First, calculate how many gallons of gas the car will use. The car travels 384 miles at 32 miles per gallon, so it will use 384 ÷ 32 = 12 gallons of gas. The fuel tank holds 15 gallons. To find out how much gas is left, subtract the amount used from the tank's capacity: 15 gallons - 12 gallons = 3 gallons. Therefore, 3 gallons of gas will be left in the tank.

TEAS Math Practice Test #2

Simplify the expression above.
Which of the following is correct?