ATI TEAS MATH PRACTICE TEST QUESTIONS AND ANSWERS

ATI TEAS MATH PRACTICE TEST QUESTIONS AND ANSWERS The ATI TEAS Math test is a challenging test that focuses on numbers and operations, data interpretation, algebra, and measurement. All of the practice questions include answers and detailed explanations. Question 1 CORRECT 5,344 − 57 Simplify the expression above. Which of the following is correct? A 5,277 B 5,283 C 5,287 D 5,288 Question 1 Explanation: The correct answer is (C). Remember that calculators are not permitted on the TEAS math test, so make sure you are able to subtract large numbers without using a calculator. (subtraction by regrouping) Question 2 CORRECT 3(x − 4) = 18 Solve the equation above. Which of the following is correct? A x = 3/2 B x = 22/3 C x = 6 x = 10 Question 2 Explanation: The correct answer is (D). First divide both sides by 3: 3(x − 4) = 18 x − 4 = 18/3 x − 4 = 6 Then solve for x: x − 4 = 6 x = 6 + 4 x = 10 Question 3 CORRECT The above is known as what type of graph? A Line Graph Scatterplot C Bar Graph D Histogram Question 3 Explanation: The correct answer is (B). The above graph is known as a scatterplot, which is a plot of points on x and y axes. In this case, each point would have an x value equal to the temperature in degrees Celsius, and a y value equal to the amount of money in dollars. Question 4 CORRECT (5x − 1) (3x + 2) Simplify the expression above. Which of the following is correct? A 15x2 − 7x + 3 15x2 + 7x − 2 C 15x2 + 7x − 3 D 15x2 − 7x − 2 Question 4 Explanation: The correct answer is (B). The “FOIL method” is the easiest way to remember how to multiply two-termed expressions. Multiply the First two terms, then the Outer two terms, then the Inner two terms, and then the Last two terms, then sum all four to arrive at the answer: 15x2 + 10x − 3x − 2 = 15x2 + 7x − 2 Question 5 CORRECT Timmy can usually make six paper airplanes in an hour. However, if he gets interrupted by his parents, he can only make four per hour. His friend John can make seven paper airplanes per hour. One day, Timmy and John decide to have a three-hour long contest to see who can make the most paper airplanes. During the contest, Timmy is interrupted once every hour. John also had to take a break and do chores for an hour. How many more paper airplanes does the winner make? A 1 2 C 3 D 4 Question 5 Explanation: The correct answer is (B). Because Timmy is interrupted during each hour, he can only make four paper airplanes per hour, multiplied by 3 hours, for a total of 12 airplanes. John makes seven paper airplanes during the two hours he works without chores, for a total of 14 airplanes. 14 airplanes minus 12 airplanes equals 2. Question 6 CORRECT If a car travels 360 kilometers in 5 hours, how far will it travel in 9 hours? A 72 B 268 C 426 648 Question 6 Explanation: The correct answer is (D). Given that it took 5 hours to travel 360km, we can set up a ratio equation to figure out how far the car will travel in 9 hours. 360/5 = x/9 72 = x/9 72*9 = x x = 648 Question 7 CORRECT What degrees Fahrenheit is it at 30 degrees Celsius? Note: °F = (°C * 9/5) + 32 86 B 89 C 92 D 95 Question 7 Explanation: The correct answer is (A). Plug in °C = 30 into the given formula and solve for °F: °F = (°C * 9/5) + 32 °F = (30 * 9/5) + 32 °F = 54 + 32 °F = 86 Question 8 CORRECT A toy manufacturer makes 15,000 toys a year. The company randomly selects 300 of the toys to sample for inspection. The company discovers that there are 5 faulty toys in the sample. Based on the sample, how many of the 15,000 total toys are likely to be faulty? A 25 250 C 300 D 600 Question 8 Explanation: The sample indicates that 5 out of every 300 randomly selected toys will be faulty. Consequently, a proportion can be set up that relates the unknown number of faulty toys in the total number of toys to the ratio of faulty toys to the sample. Stated otherwise: T is the unknown number of faulty toys in the total. Multiply both sides by 15,000 and then divide the left hand side by 300 to solve for T: Question 9 CORRECT At a comic book store, Robert purchased three comics for $2.65 each. If he paid with a $20 bill, how much change did he receive? A $10.95 $12.05 C $13.15 D $13.85 Question 9 Explanation: The correct answer is (B). Three comics at $2.65 would equal a total of $7.95. The change would equal $20 − $7.95 = $12.05. Question 10 CORRECT Simplify the expression above. Which of the following is correct? A 14/54 B 22/67 29/72 D 18/126 Question 10 Explanation: The correct answer is (C). 7¼ can be expressed as 29/4. 29/4 x 1/18 = 29/(4 x 18) = 29/72. Question 11 CORRECT Express 5/8 as its closest rounded percentage. A 56% B 60% 63% D 66% Question 11 Explanation: The correct answer is (C). 5 ÷ 8 = 0.625, which equals 62.5%. Rounding up gives us 63%. Question 12 CORRECT 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? A 4 5 C 9 D 10 Question 12 Explanation: The correct answer is (B). First, we must calculate the area of the walls Amanda wants to paint. Two of the walls are 10 x 10 and two of the walls are 10 x 15: 2 (10 x 10) = 200 2 (10 x 15) = 300 So the total square footage of the walls is 500. If a half gallon of paint will cover 55 square feet, then each gallon will cover 110 square feet. Four gallons would only cover 440 square feet. Five gallons will cover 550 square feet, which will be enough for all 500 square feet of walls. Question 13 CORRECT How many millimeters are there in 5 meters? A 500 5,000 C 50,000 D 500,000 Question 13 Explanation: The correct answer is (B). The prefix “milli-” means 1,000. There are 1,000 millimeters in 1 meter, so there are 5,000 millimeters in 5 meters. Question 14 CORRECT 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 ngrandchildren, which of the following inequalities represents Kyra’s budget constraint? A 40n > 300 B 40 + n > 300 C 40 + n ≤ 300 40n ≤ 300 Question 14 Explanation: The correct answer is (D). If Kyra buys n pairs of shoes at a cost of $40 each, she pays $40n. Since she only has $300 to spend, $40nmust be less than or equal to $300: 40n ≤ 300 Question 15 CORRECT 2 − 8 ÷ (24 ÷ 2) = Simplify the expression above. Which of the following is correct? A −6 B −¾ 1 D 2 Question 15 Explanation: The correct answer is (C). Remember your order of operations: • Complete operations within parentheses first. • Calculate exponents. • Then multiply and divide in order from left to right. • Then add and subtract in order from left to right. 2 − 8 ÷ (24 ÷ 2) = 2 − 8 ÷ (16 ÷ 2) = 2 − 8 ÷ 8 = 2 − 1 = 1 Question 16 CORRECT Which type of graph would best indicate the percentage of a school’s annual scholarship fund spent on freshman students? pie chart B line graph C scatter plot D histogram Question 16 Explanation: The correct answer is (A). A pie chart represents percentages of a total, and would thus be the best graphic representation of a budget breakdown. Question 17 CORRECT −1/4, π, 3/8, −0.2 Order the above list of numbers from least to greatest. Which of the following is correct? A −0.2, −1/4, 3/8, π −1/4, −0.2, 3/8, π C −0.2, −1/4, π, 3/8 D −1/4, −0.2, π, 3/8 Question 17 Explanation: The correct answer is (B). The smallest number is the greatest negative value: −1/4 (−0.25). The next smallest is −0.2 (−1/5). The largest value is π, or approximately 3.14. Question 18 CORRECT Simplify: (7y2 + 3xy − 9) − (2y2 + 3xy − 5) 5y2 − 4 B 9y2 + 6xy − 14 C 5y2 + 4 D 5y2 + 6xy − 14 Question 18 Explanation: The correct answer is (A). When subtracting polynomials the first step is to distribute the negative sign through the parentheses. This changes the sign on each term inside the parentheses: 7y2 + 3xy − 9 − 2y2 − 3xy + 5 Arrange like terms next to each other (optional): 7y2 − 2y2+ 3xy − 3xy − 9 + 5 Combine like terms to compute the answer: 5y2 − 4 Question 19 CORRECT | 2x − 5 | = 19 Which of the following is the solution set for the equation above? A {−7, −12} B {7, 12} {−7, 12} D {7, −12} Question 19 Explanation: The correct answer is (C). Absolute value equations can be rewritten in two ways to solve: 2x − 5 = 19 and 2x − 5 = −19. Solve both: 2x − 5 = 19 2x = 24 X = 12 2x − 5 = −19 2x = −14 x = −7 The two solutions and −7 and 12. Question 20 CORRECT If Maria left a $10.16 tip on a breakfast that cost $86.89, approximately what percentage was the tip? 12% B 17% C 25% D 31% Question 20 Explanation: The correct answer is (A). The easiest way to answer this question is to round the numbers. Let’s say the tip is $10 and the total was $87. $10/$87 = approximately 11%. (A) is the closest answer to our approximation. Question 21 CORRECT A nurse working at a medical clinic earns $17.81 per hour. The nurse works three 8-hour shifts and one 12-hour shift every week, and is paid weekly. Weekly deductions are: federal tax $102.80, state tax $24.58, federal insurance $18.13, and family health insurance $52.15. What is the nurse's take-home pay each week? A $158.54 $443.50 C $514.74 D $641.16 Question 21 Explanation: The correct answer is (B). First you must calculate how many hours the nurse works each week. Three 8-hour shifts plus one 12-hour shift equals 36 hours per week. Beginning Salary = 36 x $17.81 = $641.16 Deductions = $102.80 + $24.58 + $18.13 + $52.15 = $197.66 Take-Home Pay = $641.16 − $197.66 = $443.50 Question 22 CORRECT How many imperial gallons are there in 1,400 liters? Note: 1 kiloliter = 220 imperial gallons 308 B 3,080 C 30,800 D 308,000 Question 22 Explanation: The correct answer is (A). There are 1,000 liters in 1 kiloliter: 1,400 liters = 1.4 kiloliters. 1.4 x 220 = 308 imperial gallons Question 23 CORRECT Derek purchased concert tickets in the month of June for $73, $66, $96, $17, and $66 dollars. Which of the following is an accurate estimate of the total amount he spent on concert tickets in June? A $300 $330 C $360 D $400 Question 23 Explanation: The correct answer is (B). The easiest way to make an estimate is to round each number so there is only one nonzero digit. Then you can easily add up the numbers: 73 ≈ 70 66 ≈ 70 96 ≈ 100 17 ≈ 20 66 ≈ 70 Adding these numbers together yields $330. Question 24 CORRECT 5y − 8 > 32 Solve the inequality above. Which of the following is correct? y > 8 B y < 8 C y > 6 D y < 6 Question 24 Explanation: The correct answer is (A). To solve an inequality, simply treat the inequality symbol as if it’s an equals sign: 5y − 8 > 32 5y > 40 y > 8 Question 25 CORRECT There are 48 students studying foreign language at the community college. If the only two foreign languages offered are French and Spanish, and 28 students are studying French, which of the following represents the ratio of students studying Spanish to the total number of foreign language students? A 2/7 B 1/2 C 1/3 5/12 Question 25 Explanation: The correct answer is (D). If there are 48 total, and 28 study French, then 20 study Spanish. The ratio of 20 to 48 = 10/24 = 5/12. Question 26 CORRECT What is 181.5% of 18? A 3.267 B 14.67 32.67 D 3267 Question 26 Explanation: The correct answer is (C). First you must convert the fraction to a decimal by moving the decimal point 2 places to the left, which gives you 1.815. Then multiply this by 18. 1.815 x 18 = 32.67 Question 27 CORRECT Which of the following is equivalent to 0.0009? A 0.0009% B 0.009% 0.09% D 0.9% Question 27 Explanation: The correct answer is (C). In order to convert a decimal to a percent you need to move the decimal point two places to the right and add the percent symbol. Question 28 CORRECT A father is planning a birthday party for his son. He is expecting a total attendance of 7 adults and 13 children. Food costs will be $11.00 for each adult and $5.00 for each child. He will also need to spend $2.00 per child for party favors. Which of the following is the total cost of the birthday party? A $142.00 $168.00 C $182.00 D $192.00 Question 28 Explanation: The correct answer is (B). The cost for each adult will be $11.00. 7 x 11 = 77 The cost for each child will be $7.00 ($5.00 for food plus $2.00 for the party favors). 13 x 7 = 91 So the total cost will be 77 + 91, which is 168. Question 29 CORRECT 7 x 4 + (9 − 6) + 13 Simplify the expression above. Which of the following is correct? A 34 B 37 C 41 44 Question 29 Explanation: The correct answer is (D). According to the order of operations, do what is inside the parenthesis first: 7 x 4 + (3) + 13 Next, move left to right, doing any multiplication or division: 28 + 3 + 13 Finally, move left to right, doing any addition or subtraction: 31 + 13 = 44 Question 30 CORRECT Write the number 1906 in Roman numerals. A MCMLXVIII B MCMXVI MCMVI D XIXVI Question 30 Explanation: The correct answer is (C). In the Roman numeral system, M = 1000, D = 500, C = 100, L = 50, X = 10, V = 5, and I = 1. The ones, tens, hundreds and thousands must be treated as separate items. If a smaller item precedes a larger item, as in CM, it is treated as the difference of the two, so CM = 1000 − 100 = 900. 1000=M 900= CM 6=VI Question 31 A B C D