TEAS Practice (Math Portion)
V (Roman numeral)
5 (roman numeral)
Express 5.6 meters as a percentage of 8 meters.
5.6 over 8, times (x) 100 =70%
L (roman numeral)
50 (roman numeral)
D (Roman Numeral)
500 (roman numeral)
John, Lucy and Emma share 60 pencils in the ratio 4:5:6. How many pencils does Lucy receive?
60 pencils are distributed to John, Lucy and Emma in the proportion of 4:5:6. First, add the numbers given in the proportion to get a denominator to use, in this case: 4 + 5 + 6 = 15. Then, use 15 as the denominator to express each part in a fraction: John gets 415 of the 60 pencils. Lucy gets 515 of the 60 pencils. Emma gets 615 of the 60 pencils. Multiply Lucy's fraction by the total number of pencils (60) to get the number of Lucy's pencils: 5 (15)(60)=20pencils
I (Roman numeral)
1 (roman numeral)
a unit rate should have a
1 in the denominator
kilogram (kg)
A 5 pound bag of sugar weighs just over 2 kilograms
1 liter contains
1,000 milliliters or 1,000 cubic centimeters
milligram (mg)
1/1000 of a gram
deca
10
X (Roman numeral)
10 (roman numeral)
C (Roman Numeral)
100 (roman numeral)
kilo
1000
M (Roman Numeral)
1000 roman numeral
The area of one face of a cube is 49 square centimeters. What is the total length of all its edges?
A cube has 6 faces (sometimes called sides), all with equal areas, all square-shaped. A cube has 12 edges and all of these have equal lengths. (The edges are the borders of the square faces, so each would be the same length as one dimension of any face (7 cm).) A face has an area. This is the area of a face: (lengthofface)(lengthofface)=(lengthofface)2 49=(lengthofface)2 lengthofface=4-√9=7cm So, the total length of all edges: 7cm⋅12edges=84cm
Sam, Paul, and Dean share a sum of money in the ratio 14:16:18 respectively. Given that Sam receives $2100, how much does Dean receive?
A sum of money is distributed to Sam, Paul and Dean in the proportion of 14:16:18. Add the 3 proportions to get a total of 48. Sam receives $2100, representing 1448 of the total money. 2100=14 48⋅Total 2100(48 14)=Total To compute Dean's share, which represents 18 48 of the total: 18 48⋅Total (18 48)[2100(48 4)] 18 14(2100)=2700
formula for area of a square
A= lxl=1^2
Area of a trapezoid
A=1/2h(b1+b2)
formula for area of a triangle
A=½ x b x h
Area of a circle
A=πr²
How to find the median
Arrange the numbers in numerical order. The middle number is the median. If there are two middle numbers you need to add both numbers and divide by 2.
Circumference Formula
C = 2πr
fraction to decimal
Divide numerator by denominator
decimal to fraction
Ex) 2.36 move decimal to make a whole number 236 and count how many decimal places were moved then place a one in the denominator and add zeros to however many decimals were moved =236/100 if number is less than 1 (0.36) just use 36 as the whole number and move decimal places =36/100
Solve the inequality 17 - 2a < 10.
Isolate the variable by undoing the operations performed on it to solve the inequality. Remember that multiplication or division of an inequality by a negative value switches the direction of the inequality sign. 17-2a<10 Subtract both sides by 17: −2a<−7 Divide both sides by −2, remembering to switch the direction of the inequality sign: a>3.5
formula for area of a rectangle
Length x Width
how to find the area
Length x Width
In a competition, three teams, A, B and C, scored a total of 150 points. If A scored 40% of this total and B scored four times as many points as C, what were the number of points scored by B?
Let a be the points earned by A, b be the points scored by B, and c be the points scored by C. 40 a 100=150 (40 100)(150)=a a=60points b = 4c 150=a+b+c 150=60+4c+c 150=60+5c 5c=150-60 c=90 5 c = 18 points b=4c=4(18) b = 72 points
Given that 5 cm on a map represents 4 km on the ground, calculate the distance in km between two points, which are 8 cm apart on the map.
Let x represent the distance you are trying to find (in km). The quickest way to solve for x is to create a proportion with the quantities you do know. km on land==km on land cm on map=cm on map Substitute the numbers you know: 4=x 5=8 This would be read: "4 km is to 5 cm, as x km is to 8 cm. Cross-multiply to get this equation: 4⋅8=5x Solve: 32=5x 6.4=x (6.4)(5)=32
Meter (m)
The average adult is 1.5 to 2 meters tall
Kilometer (km)
The average adult walks 1 km in about 15 minutes
which of the following is the percent equivalent of 0.0016?
Multiply 0.0016 (times) 100 to get 0.16%
What degrees Fahrenheit is it at 30 degrees Celsius?
Note: °F = (°C * 9/5) + 32 °F = (°C * 9/5) + 32 °F = (30 * 9/5) + 32 °F = 54 + 32 °F = 86
Express as a single fraction in its simplest form: 3(2x−1)−4(5x+2)
Since this is subtraction of 2 fractions with different denominators, determine their least common denominator, in this case, the LCD is: (2x-1)(5x+2) Proceed to subtraction: 3(2x-1)-4(5x+2) [3(5x+2)-4(2x−1)](2x−1)(5x+2) [15x+6-8x+4](2x−1)(5x+2) [15x-8x+6+4](2x−1)(5x+2) (7x+10)(2x−1)(5x+2)
The price of a pencil box increased from $25 to $26.50. What is the percentage increase in the price?
Subtract to find the difference or increase in price $26.50−$25.00=$1.50 Divide the increase with the previous price to compute for the rate of increase $1.50÷$25.00=0.06 Convert decimal to percentage form 0.06⋅100%=6%
If 42.8 kg is divided into two parts, in a ratio of 7:2, how many kg is the smaller share?
The 42.8 kg item is divided into 2 parts or shares, in the proportion of 7:2. First, add the numbers given in the proportion to get a denominator to use, in this case: 7 + 2 = 9. Then, the two parts can be represented as 7 over 9 and 2 over 9, making a whole 9 over 9. Of the two parts, the smaller part or share is 2 over 9 of 42.8 kg. Multiply this fraction by the total amount of kg to get the amount in the smaller part. (29)(42.8kg)=9.51kg
Which type of graph would best indicate the percentage of a school's annual scholarship fund spent on freshman students?
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.
If Maria left a $10.16 tip on a breakfast that cost $86.89, approximately what percentage was the tip?
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.
Simplify: (7y2 + 3xy − 9) − (2y2 + 3xy − 5)
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
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?
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.
How many millimeters are there in 5 meters?
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.
| 2x − 5 | = 19 Which of the following is the solution set for the equation above?
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.
What is 181.5% of 18?
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
2 − 8 ÷ (24 ÷ 2) = Simplify the expression above. Which of the following is correct
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
3(x − 4) = 18 Solve the equation above. Which of the following is correct?
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
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?
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, $40n must be less than or equal to $300: 40n ≤ 300
A side of a square is 2.5 cm long. What is the area of square?
The formula for solving the area of a square is: A = s x s (where s is the length of one side) A = 2.5 x 2.5 = 6.25 square centimeters
A tank is 12 cm high with a square base. Its sides are 10 centimeters wide. What is the volume of the tank in cubic centimeters?
The formula for the volume of a rectangular solid is: Volume = length ⋅ width ⋅ height V=10⋅10⋅12=1200
A teacher has a rectangular piece of paper which is 52 cm long and 38 cm wide. She cuts the paper into squares, each measuring 5 cm by 5 cm. What is the largest number of whole squares she cuts?
The key to solving this problem is realizing that you are looking for the number of whole, 5 x 5 cm squares that can be cut from this paper. There will be paper left over, since the dimensions of the paper are not exactly divisible by 5 cm. There will be only 7 rows of squares possible along the 38-cm side, because 38÷5=7.6. This is rounded to 7 because the .6 would only provide a 3 cm side and we need 5 cm sides. The 3 cm would be a leftover scrap, not useful for cutting another square. Similarly, there will be only 10 columns of squares possible along the 52-cm side, because 52÷5=10.4 or 10. (The extra 2 cm is also not enough for a square side.) 10⋅7=70 whole, 5 x 5 cm squares
Given that 6x = 7y, find the ratio x : y.
The ratio of x : y is equivalent to x divided by y, or xy. Rearrange the original equation so that only xy is on one side of the equal sign. 6x=7y Dividing both sides by 6 to find: x=7y 6 Dividing both sides by y to produce the desired format of xy: x=7 y=6 x:y is 7:6
What is the number of sides of a regular polygon whose interior angles are 156∘ each? (Remember, the sum of exterior angles of any polygon is 360∘.)
The sum of exterior angles of any polygon is always equal to 360 degrees, hence: Exterior angle measurement in degrees x n = 360 where n is the number of angles (which is also the number of sides). Also, for a given interior angle, the exterior angle = 180 - interior angle In the problem: the exterior angle = 180 - 156 = 24 degrees From the formula given above and measurement of the exterior angle computed: 24n = 360 n=360÷24=15
Gram (g)
The weight of one aspirin tablet
In a sale, all prices are reduced by 40%. Calculate the original price of an article whose sale price is $42.
Think: If prices are reduced by 40%, then the customer is paying 60% of the original cost. This 60% is $42 and we need to find the original price. Let x be the original price of the article. To develop a proportion for solving, say "60% is to 100% as $42 is to x" and write that in proportion form: Cross-multiply to get a solvable equation: 60x=42 Divide both sides by 60 to get 70. The original price was $70.
Percent to Decimal
divide by 100
Given that a:12 = 4:10, find the value of a.
a:12 = 4:10 can also be stated mathematically as: a=4 12=10 Cross-multiply to solve: 10a=48 Divide both sides by 10 to get a alone on one side of the equation. 10a=48 10 =10 a=48 10 Reduce to lowest terms by dividing top and bottom numbers by the greatest common factor: a=48÷2 10÷2=24 5
how to find the mean
add up all the numbers, then divide by how many numbers there are
percent to fraction
divide by 100
To convert from a ratio to percent
divide the first number, by the second number, and multiply by 100
Area of a parallelogram
base x height
How to find range
biggest number - smallest number
Fraction to Percent
divide the top number by the bottom number. then multiply the result by 100, and add the "%" sign.
Volume is measured in
cubic units
deci
one tenth (1/10)
milli
one thousandth (1/1000)
centi
one/hundredth
How to find volume
length x width x height or mass ÷ density
decimal to percent
multiply by 100
length of an arc of a circle
s=(degrees/360)(2pi(r)
millimeter (mm)
the thickness of a dime
centimeter (cm)
the width of an average pinkie fingernail
a rate must have
units attached
degrees Celsius
zero is freezing, 10 is not, 20 is warm, 30 is hot!