ATI TEAS: Mathematics

3x/5 - 2 = x + 1/3 Solve the equation above for x. Which of the following is correct? a. -35/6 b. -6/35 c. 6/35 d. 35/6

a. -35/6 The least common denominator of 3x/5, -2, x, and 1/3 is 15. The equation can be rewritten as: 9x/15 - 30/15 = 15x/15 + 5/15 -35/15 = 6x/15 This means -35 = 6x x = -35/6.

A patient in a hospital is prescribed .52mL of medication. The patient has received .371mL. Which of the following is the amount of medication remaining to be administered? a. 0.149 mL b. 0.249 mL c. 0.251 mL d. 0.319 mL

a. 0.149 mL 0.520 - 0.371 = 0.149

What is the approximate height in meters of a person who is 6 feet tall? a. 1.8 m b. 2.6 m c. 7.18 m d. 18 m

a. 1.8 m 1 foot = .3m

Which of the following is the equivalent percent for 66/33? a. 200% b. 50% c. 0.5% d. 0.02%

a. 200% 66/33 = 2 2 x 100 = 200%

Two times a number is less than four more than that number. Which of the following inequalities correctly represents the sentence above? a. 2x < x + 4 b. 2x > x + 4 c. 2x + 4 > x d. 2x + 4 < x

a. 2x < x + 4

The television is discounted at 20% in a sale. A shopper has a coupon for an additional 15% off the sale price. Which of the following is the total percent discount from the original price of the television? a. 32% b. 35% c. 65% d. 68%

a. 32% The television is discounted 20%. Therefore, it is being sold for 80% of the original price. The additional 15% discount is applied to the discounted price, and 15% of 80% is 12%. This discount is in addition to the original 20% discount. Therefore, 20% plus 12% equals 32%.

One rectangle is 4 cm by 5 cm. one is 3 cm by 6 cm. one is 2 cm by 3 cm. Which of the following is the area of the irregular polygon above? a. 44 square cm b. 45 square cm c. 34 square cm d. 54 square cm

a. 44 square cm One rectangle is 4 cm by 5 cm; one is 3 cm by 6 cm; and one is 2 cm by 3 cm. Area is length times width, so 20 cm2 + 18 cm2 + 6 cm2 = 44 cm2

A science student is comparing the mass of several items. Which of the following is a reasonable estimation of the mass of a standard bowling ball? a. 5 kilograms b. 5 grams c. 5 decagrams d. 5 milligrams

a. 5 kilograms 1 kg = 2.2 lb 5kg = 11 lbs about the average bowling ball

81ft^2=_____yd^2 Which of the following converts the units above correctly?(Note: 1 yd =3ft) a. 9 b. 27 c. 243 d. 729

a. 9 There are 3 feet to a yard and 9 square feet to a square yard. 81ft^2 /x= 9ft^2/1

A customer purchases apples, bananas, and oranges at a local fruit stand everyday. They would like to keep track of how many pieces of each fruit they buy each week. Which of the following graphical representations would be best to use for this purpose? a. Bar graph b. Pie chart c. Line graph d. Stem-and-leaf plot

a. Bar graph A bar graph is a type of frequency graph that is appropriate for displaying and comparing discrete data.

Let x represent the length of one side of a rectangle with a perimeter of 200. Which of the following expressions describes the area of the rectangle? a. x(100 - x) b. 2x(100 - x) c. x(200 - x) d. 2x(200 - x)

a. x(100 - x) The area of a rectangle is the product of the length times the width. Since the perimeter of the rectangle is 200, one length + one width = 100. If one side is x, the adjacent side must be 100 - x.

An employee at a restaurant makes $ 14.50 per hour. if the employee works 150 hours during a pay day period. Which of the following represents the employee's gross earnings for the pay periods? a. $1,645.00 b. $2,175.00 c. $2,250.00 d. $2,100.50

b. $2,175.00 $14.50 x 150 = $2,175

A family had $7,564 in a bank account set aside for home repairs. Over the last few months, they spent $1,244 repairing their furnace, spent $756 replacing a window, and deposited $1,503 into the account. Which of the following Amounts is the current balance of the bank account? a. $4,061 b. $7,067 c. $5,564 d. $7,823

b. $7,067 $7,564 - $1,244 - $756 + $1,503 = $7,067

Which of the following is the product of .05 and .7? a. 0.0035 b. 0.035 c. 0.35 d. 3.5

b. 0.035 product means multiply

Which of the following is the decimal equivalent of 3/5? a. 0.06 b. 0.6 c. 6 d. 60

b. 0.6 The fraction 3/5 is equivalent to the fraction 6/10 = .6 or use calculator

Which of the following is the fractional equivalent of 1.7%? a. 1/7 b. 17/1,000 c. 1/17 d. 17/100

b. 17/1,000 1.7% = .017 = 17/1,000

Which of the following is the product of .003 and 800? a. 0.24 b. 2.4 c .24 d .240

b. 2.4

Which of the following is the solution to 2 1/2 / 3 3/4? a. 8/75 b. 2/3 c. 1 1/2 d. 9 3/8

b. 2/3 Both fractions should be rewritten as improper fractions in order to represent division as multiplication by the reciprocal. The expression can then be written as 5/2 x 4/15, which simplifies to 2/3.

A $75 sweater is discounted by $15. Which of the following is the percent of the discount? a. 15% b. 20% c. 80% d. 85%

b. 20% To determine the percent of the discount, take the discount amount ($15) and divide by the original price ($75). This equals 0.2, which is equivalent to 20%.

Which of the following is a fractional equivalent of 6 2/3% a. 11/300 b. 20/300 c. 3/20 d. 20/3

b. 20/300 To convert from a fractional percent, first change the percent to an improper fraction (20/3). Then divide by 100 (which is equivalent to multiplying by 1/100), which equals 20/300.

Paint brushes cost $2 each and tubes of paint cost $3 each. If Sanjan Has $36 on paint supplies, which of the following inequalities represents how many paint brushes (b) and how many tubes of paint (t) can he buy? a. 3b + 2t ≤ 36 b. 2b + 3t ≤ 36 c. 2b + 3t ≥ 36 d. 3b + 2t ≥ 36

b. 2b + 3t ≤ 36

Which of the following is the value below rounded to the nearest thousandth? 34,582.29176 a. 35,000.00000 b. 34,582.29200 c. 34,582.29100 d. 34,582.29000

b. 34,582.29200

7 students in a class of 20 mad a perfect score on a quiz. Which of the the following is the percent of students who made the perfect score? a. 2.9% b. 35% c. 53.8% d. 65%

b. 35% 7/20 = .35 or 35%

The original price of an item is $3.75. If the discounted price is to $2.25, which of the following is the percent of the discount? a. 33% b. 40% c. 60% d. 67%

b. 40% $3.75 - $2.25 = $1.50 $1.50/$.75 = .4 or 40%

The average diameter of 1 tennis ball in a package of 3 is 6.8 cm. Which of the following is the combined volume of three tennis balls? Use 3.14 for pi and round your final answer to the nearest hundredth. (V = 4/3 pi r^3) a. 164.55 cm3 b. 493.66 cm3 c. 1,316.42 cm3 d. 3,949.27 cm3

b. 493.66 cm3 r = 6.8/2 = 3.4 3.4^3 x 3.14 x 4/3 =164.55 164.55 x 3 tennis balls = 493.66 cm3

A contractor builds a fence to surround a rectangular garden. The length of the fence is 5 feet more than the width, W. Which of the following expressions represents the amount of fencing the contractor will need to complete the project? a. 2W + 5 b. 4W + 10 c. 6W d. 12W

b. 4W + 10 This option is the result of representing the width as W and the length as W + 5. Because the rectangle has opposite sides of equal length, the perimeter is equal to 2W + 2(W + 5), or 4W + 10.

Mary was planning a trip to Western Samoa. Before going, she did some research and learned that the exchange rate is 6 Tala for $2. How many Tala would she get if she exchanged $325? a. 650 Tala b. 975 Tala c. 162.5 Tala d. 1,950 Tala

b. 975 Tala 6 Tala/$2 = x/$325 OR 3 tala per $1 = $325 x 3

A student filled a beaker with boiling water and another Beaker with ice water. Every 1 minute, the Student Records the temperature in each beaker. In order to determine the exact time the temperature in the two beakers will be equal, which of the following graphical representations should be used to organize the data? a. Bar graph b. Line graph c. Histogram d. Scatterplot

b. Line graph

(x+3)^3 = 3 Which of the following is the correct solution to the equation above? a. x = 3 ± √3 b. x = -3 ± √3 c. x = -6 d. x = 6

b. x = -3 ± √3

The sales tax for a purchase equals $7.00. The sales tax rate is 6.25%. Which of the following is the price of the purchase before tax? a. $11.20 b. $43.75 c. $112.00 d. $119.00

c. $112.00 112 x .0625 = 7

8 - 12z = 92 solve the equation for z. Which of the following is correct? a. -81/3 b. 7 c. -7 d. 81/3

c. -7 This is the result of subtracting 8 from both sides of the equation, then dividing the remaining values by -12. The quotient is negative, because a positive divided by a negative results in a negative value.

A city assesses a transportation tax of 3/5 of a penny on each dollar. What percent of each dollar is collected by this tax? a. 0.006% b. 0.06% c. 0.6% d. 6.0%

c. 0.6% 3/5 of a penny is equivalent to 6/10, or 0.6 pennies. Since there are 100 pennies in a dollar, dividing 0.6 by 100 results in 0.006 dollars. To convert to a percent, multiply by 100, resulting in 0.6%

True school districts are combining to form a new district. School district A has 6,798 students. school district B has 8,976 students. Which of the following will be the combined enrollment of the new school district? a. 13,596 b. 14,874 c. 15,774 d. 17,952

c. 15,774 add

Solve the following equation for x. 10-4x=2 a. -3 b. -2 c. 2 d. 3

c. 2

A landscaper wants the length and width of the lawn each increased by 20%. The current dimensions of the lawn are 18 ft by 24 ft. Which of the following are the dimensions of the new line? a. 19.8 feet x 26.4 feet b. 20 feet x 26 feet c. 21.6 feet x 28.8 feet d. 23 feet x 29 feet

c. 21.6 feet x 28.8 feet Because the landscaper wants to increase the dimensions by 20%, they should multiply each dimension by 1.2, or 120%.

A doctor sees each patient for 20min during a typical appointment. How many patients can the doctor see in a typical 7.5 hr day? a. 15 b. 23 c. 22 d. 150

c. 22 1 patient/20 min = x/450 min. 3 pt per hr (20x3=60 1 hr) 3x7.5 = 22.5

A recipe for a pizza that serves 12 people calls for 2 cups of shredded cheese. If a bag of shredded cheese contains 3 cups, what is the minimum number of bags required to make pizza for 48 people? a. 1 b. 2 c. 3 d. 4

c. 3 12 x 4 = 48 2 x 4 = 8 cups needed 8/3 = 2.6 need 3 bags

2 5/9 + 1 2/18 Simplify the expression above. Which of the following is correct? a. 3 7/27 b. 3 7/18 c. 3 2/3 d. 3 7/9

c. 3 2/3 2 + 5/9 + 1 + 2/18 = 2 + 5/9 + 1 + 1/9 = 3 + 6/9 = 32/3 or place into decimals

A basketball player attempts 15 shots during a game. The player misses seven shots. Which of the following is the percentage of shots the player made, rounded to the nearest percent? a. 19% b. 47% c. 53% d. 21%

c. 53% 15-7 = 8 shots made 8/15 = .53 or 53%

There are 100 student in the freshman class of a high school .THREE-TENTHS of the class is going on a field trip today. Which of the the following is the number of freshmen who will be staying at school? a. 3 b. 30 c. 70 d. 97

c. 70 If 3/10 of the students are going on the field trip, then 7/10 must be staying at school. Take the total number of students (100) and multiply by 7/10, which equals 70.

-7(y-4)=-y-26 Which of the following correctly solves the equation above for y? a. y = 16 b. y = -1/3 c. y = 11/3 d .y = 9

d .y = 9

A customer at a restaurant leaves $80 on the table to pay for the food, a 15% tip, and 80% sales tax. If both tip and sales tax are calculated from the cost of the food, which of the following with the cost of the food, rounded to the nearest cent? a. $57.00 b. $61.60 c. $62.56 d. $65.04

d. $65.04 x + 0.15x + 0.08x = 80

Which of the following is the equivalent percent for 12.5? a. .125% b. 12.5% c. 125% d. 1,250%

d. 1,250% When converting from a decimal to a percent, multiply by 100.

The average speed a NASA space shuttle travels is 17,500 miles per hour. The distance the space shuttle traveled is 238,855 miles. What is the travel time of the space shuttle? a. 43.2 hr b. 27.2 hr c. 6.8 hr d. 13.6 hr

d. 13.6 hr 238,855/17,500 miles/hr = approximately 13.6 hours.

16 out of 64 students in a Physics class received a grade of "A" for the class. Which of the following is the percent of students who received an "A"? a. 20% b. 40% c. 33% d. 25%

d. 25% 16/64 = .25 or 25%

Half a circle. Diameter = 10 (r=5 for half) Which of the following is the accurate calculation of the perimeter of the object above? (use 3.14 for pi) a. 20.7 cm b. 41.4 cm c. 39.3 cm d. 25.7 cm

d. 25.7 cm This is the calculation of half the circumference of the circle (10 x 3.14/2) added to the length of the diameter (5 x 2).

A box has a length of 2 1/2 feet, a width of 3 1/3 feet, and a height of 4 1/4 feet. The formula for volume is length X width X height. Which of the following is the volume of the box in cubic feet? a. 10 1/12 feet^3 b. 24 1/24 feet^3 c. 24 3/9 feet^3 d. 35 5/12 feet^3

d. 35 5/12 feet^3 By converting mixed numbers to improper fractions, the improper fractions can then be multiplied and finally converted back into a mixed number.

In a community, 3/8 of the population has children that attend school. Which of the following is the percentage of the population that has children in school? a. 0.00375% b. 0.375% c. 3.75% d. 37.5%

d. 37.5% 3/8 = .375 or 37.5%

The shopper at a local grocery store weighs a bag of apples. the weight is 2.4 pounds (lb). Which of the the following is the weight of the apples? ( NOTE: 1 lb = 16 oz) a. 14.4 oz b. 19.2 oz c. 28.8 oz d. 38.4 oz

d. 38.4 oz x/2.4lb = 16oz/1lb Another way to solve this problem is to multiply 2.4 X 16 ounces.

3 2/4 X 1 1/2 Simplify the expression above. Which of the following is correct? a. 2 1/3 b. 3 1/4 c. 3 1/2 d. 5 1/4

d. 5 1/4 When multiplying mixed numbers, first change the mixed numbers to improper fractions (14/4 × 3/2). Then multiply the numerators together and the denominators together and simplify the result (42/8 = 51/4).

A holiday punch recipe calls for 1,500 mL of fruit punch, 375mL of pineapple juice, and 1 L of ginger ale. How many liters of punch will this recipe yield if doubled? a. 12.5 L b. 3.05 L c. 2.875 L d. 5.75 L

d. 5.75 L 1,500 mL = 1.5 mL 375 mL = .375 mL

Exactly how many hourly rates are less than the mean value? 9, 10, 11.75, 14, 15.5, 16, 18.75, 21.25, 22, 38, 42. a. 4 b. 5 c. 6 d. 7

d. 7 add all numbers and divide by total numbers (11) then see how many are below that

A state trooper recorded and collected speeds of several cars at a set location on a local highway. The speeds in miles per hour recorded below. Which of the following is the median of the data set? 73, 81, 68, 75, 90, 78, 75, 82, 77, 71 a. 77 b. 22 c. 75 d. 76

d. 76 The median is the middle number when the data is ordered from least to greatest. Since this set has 10 values, it is the average of the 5th and 6th values.

A basic cell phone plan costs $50 per month and includes 200 minutes of call time. If the customer uses more than 200 minutes in a month, they are charged an additional $.03 per minute used. If n represents the minutes used, which of the following represents the monthly cost (c) when more than 200 minutes are used? a. C = 50 + 0.03(n) b. C = 50 + 0.03(n + 200) c. C = 50 + 0.03(n - 200) d. C = 50 + 0.03(200 - n)

d. C = 50 + 0.03(200 - n) If more than 200 minutes are used, the cost will equal $50 plus $0.03 times the difference between the number of minutes used and 200.

The sum of two numbers is 20. Which of the following equation states that the product of one number and the square of the other number is 50? a. x^2(x + 20) = 50 b. x(20 + x)^2 = 50 c. x(x - 20)^2 = 50 d. x^2(20 - x) = 50

d. x^2(20 - x) = 50 Let x equal one number, then 20 - x equals the other number. The phrase "the product of one number and the square of the other is 50" could be represented by either x2(20 - x) = 50 or x(20 - x)2 = 50.