Math Praxis (practice test and answers)

Option (B) is correct. The question requires an understanding of three-dimensional geometry. Triangular pyramids and rectangular prisms have four and six faces, respectively. Triangular prisms have five faces: two are triangles, and three are quadrilaterals. Rectangular pyramids also have five faces: one is a rectangle, and four are triangles. Triangular prisms have nine edges, while rectangular pyramids only have eight edges.

A two-dimensional net of a certain three-dimensional figure includes five faces, nine edges, and six vertices. Which of the following three-dimensional figures is represented by the net? A. Triangular pyramid B. Triangular prism C. Rectangular pyramid D. Rectangular prism

Option (C) is correct. The question requires an understanding of calculating with standard units of time. Bill slept for 3 minutes from 9:57 P.M. until 10:00 P.M. and for 2 hours from 10:00 P.M. until 12:00 A.M. (midnight). Then he slept another 6 hours and 28 minutes until 6:28 A.M. This adds up to 8 hours and 31 minutes.

Bill went to sleep at 9:57 P.M. and awoke the next morning at 6:28 A.M. For how many hours and minutes did he sleep? A.9 hours and 31 minutes B.9 hours and 25 minutes C.8 hours and 31 minutes D.8 hours and 25 minutes

Correct Answer: D Option (D) is correct. The question requires an understanding of percent and percentages. To convert a fraction to a percent, it is necessary to multiply the fraction by 100 and add a percent symbol. Since 316×100=18.75 3 16 × 100 = 18.75, 3 16 is equivalent to 18.75%.

Answer the question below by clicking on the correct response. Question: Which of the following expresses 3/16 3 16 as a percent? A. 0.1875% B. 1.875% C. 5.33% D. 18.75%

Option (B) is correct. The question requires an understanding of equations and the ability to translate a word problem into an equation. If x represents the number of glasses and y represents the number of plates that Nicholas bought, then 2x + 3.5y = 18. Both x and y must be integers. Therefore, 18−2x must be a multiple of 3.5. The possible multiples of 3.5 for this problem are 3.5, 7, 10.5, 14, and 17.5. The only multiple of 3.5 that is equivalent to 18−2x as an integer is 14. Thus, x=2.

At a yard sale, Tenille sold drinking glasses for $2.00 each and plates for $3.50 each. Nicholas spent a total of $18.00 on drinking glasses and plates at Tenille's yard sale. If Nicholas bought at least one glass and one plate, how many drinking glasses did he buy? A.1 B.2 C.3 D.4

Option (C) is correct. The question requires an understanding of finding patterns in data. Since 18−12/45−30 = 6/15= 2/5 the value of f(x) increases by 2 units for every 5-unit increase in the value of x. The value of x increases by 40 units from 60 to 100, so the value of f(x) must increase by 16 units between f(60).

x f(x) 100 60 24 45 18 30 12 Some values of the linear function f are given in the table shown. What is the value of f(100)? A. 30 B. 36 C. 40 D. 48

Option (B) is correct. The question requires an understanding of how to use proportional relationships to solve ratio and percent problems. If 3 pounds of raisins are used in the 10-pound mixture, then 7 pounds of nuts are used in the mixture, giving a ratio of pounds of nuts to pounds of total mixture of 7:10. So 70% of the total number of pounds in the mixture consists of nuts. Since the ratio of pounds of nuts to pounds of total mixture in the 25-pound mixture is the same, then 70% of 25, or 17.5, gives the number of pounds of nuts in the 25-pound mixture. The problem could also be solved by setting up a proportion using x to represent the number of pounds of nuts in the 25-pound mixture. Then 7/10 = x/25 and solving for x yields 17.5.

A wholesale nut company makes 10-pound and 25-pound bags of trail mix. For the 10-pound bag, the company uses 3 pounds of raisins, and the rest is nuts. If the proportion of raisins to nuts is the same in the 25-pound bag as in the 10-pound bag, how many pounds of nuts does the company need for the 25-pound bag? A. 7.5 B.17.5 C.18.5 D.22.0

Option (A) is correct. The question requires an understanding of place value systems. The value of the number represented by the 7 in Elisa's number is 700,000, or 7×10^5 while the value of the number represented by the 7 in Troy's number is 70,000, or 7×10^4. Therefore, the value of the former is 10 times as great as the value of latter.

Elisa's number: 5,723,683 Troy's number: 2,678,533 Both Elisa and Troy wrote a number, as shown. The digit 7 in Elisa's number represents how many times what the digit 7 represents in Troy's number? A. 10 B. 100 C. 1,000 D. 10,000

Option (C) is correct. The question requires an understanding of solving an equation for a given variable. To find x in terms of y, the equation 125+4x=7y must be transformed so that the variable x is isolated, or by itself, on one side of the equal sign. Subtracting 125 from both sides of 125+4x=7y yields 4x=7y−125. Dividing both sides of 4x=7y−125 by 4 yields x=(7y−125)÷4. The variable x is now expressed in terms of y.

If 125+4x=7y what is x in terms of y ? A.x=4(7y−125) B.x=4(7y+125) C.x=(7y−125)÷4 D.x=(7y+125)÷4

Option (D) is correct. The question requires an understanding of how to evaluate the reasonableness of a solution to a contextual word problem. The solution to the given word problem must belong to the set of all natural numbers because the unit is pieces of clothing, which is a positive and discrete unit. According to the word problem, Sara bought 6 shirts, 3 pairs of pants, and sweaters, totaling 10 and 1/2 pieces of clothing. The solution is, therefore, not acceptable since it is not a natural number.

Sara went to the store to buy some clothes. She bought six shirts, half as many pairs of pants as shirts, and a fourth as many sweaters as shirts. How many pieces of clothing did Sara buy? Which of the following statements about the solution to the word problem shown must be true? A. Because of the real-world context, the solution must belong to the set of all rational positive numbers; therefore, the solution is acceptable. B. Because of the real-world context, the solution must belong to the set of all rational positive numbers; therefore, the solution is not acceptable. C. Because of the real-world context, the solution must belong to the set of all natural numbers; therefore, the solution is acceptable. D. Because of the real-world context, the solution must belong to the set of all natural numbers; therefore, the solution is not acceptable.

Option (C) is correct. The question requires an understanding of the metric system. Since 1 centimeter equals 10 millimeters, 18 centimeters equal 180 millimeters.

A pencil is 18 centimeters in length. How long is the pencil in millimeters? A. 0.18 B. 1.8 C. 180 D. 1,800

Option (C) is correct. The question requires an understanding of patterns and the ability to find and use a pattern rule. A geometric sequence is a sequence for which the ratio between consecutive terms is constant. The generic rule for a geometric sequence can be written as an=a1(r)n−1 for n≥1 where a1 is the initial term and r is the ratio. In this case the initial term is 2 and the ratio is 3, so the sequence rule can be expressed as an=2(3)n−1 for n≥1 Another way of representing the same sequence is a1=2 and an=3an−1 for n≥2 The next number in the sequence is then a6 = 3a^5 = 3×162 = 486.

If the geometric sequence below continues to increase in the same way, what is the next number in the sequence? 2, 6, 18, 54, 162, ... A.243 B.324 C.486 D.729

Option (A) is correct. The question requires an understanding of geometric reasoning. Since each of the small hexagons in the figure is regular, each hexagon's sides are equal in length. Therefore, the length of any one hexagon's side is 18÷6 or 3. The perimeter of the large figure shown is found by multiplying the number of exposed hexagon's sides by the length of one hexagon side. There are 18 exposed sides, and each one is 3 units long. Therefore, the perimeter of the figure is 18×3 or 54.

If the perimeter of each of the seven regular hexagons in the figure shown is 18, what is the perimeter of the figure? A. 54 B. 63 C.108 D.126

Option (B) is correct. The question requires an understanding of fractions, percentages, and decimals and the ability to recognize equivalence among them. Since 5 percent means 5 one-hundredths, 5 percent is equivalent to 0.05, or 5 divided by 100, 5/100 5 100 ,which simplifies to 1 20 To find 5 percent of 2,800 employees, it is necessary to multiply 2,800 by either 0.05 or 1/20.

In a certain year, 5 percent of the 2,800 employees of a company had a perfect attendance record. Which of the following computations can be used to determine the number of employees with a perfect attendance record? A. 1/40 x 2,800 B. 1/20 x 2,800 C. 1/5 x 2,800 D. 5 x 2,800

Option (D) is correct. The question requires an understanding of place value systems. Reading the number from left to right, the digit 4 is in the ones position and has a value of 4. The digit 9 is in the tens position and has a value of 90. The digit 8 is in the hundreds position and has a value of 800. The digit 7 is in the thousands position and has a value of 7,000. The digit 6 is in the ten-thousands position and has a value of 60,000.

In the number 567,894, what is the value of the digit 6 ? A.Sixty B.Ten thousand C.Six thousand D.Sixty thousand

Option (C) is correct. The question requires an understanding of addition of rational numbers. You can add the prices of the groceries and get a total of $8.28. Subtracting this amount from $20 gives you the amount of change $11.72, which is closest to $12.

Item Price Cheese $1.63 Milk $1.19 Juice $1.99 Cereal $1.19 Bread $0.89 Butter $1.39 A shopper purchases one of each of the items in the list above at the prices indicated. Which of the following is closest to the change the shopper would receive after paying with a $20 bill? (Assume there is no sales tax.) A.$10 B.$11 C.$12 D.$13

Option (A) is correct. The question requires an understanding of algebraic expressions and the ability to manipulate them. Since both 28 and 100 are divisible by 4, 4 is a factor of the expression 28x+100 To arrive at the equivalent expression given in (A), the distributive property was applied to 28x+100 In fact, 28x+100=4×7x+4×25=4(7x+25)

Kyle's father set up a savings account for him with an initial balance of $100. Since then, Kyle has been depositing $28 into the account each week. Kyle represents the amount of money he has saved after x weeks by the expression Which of the following is equivalent to Kyle's expression? A.) 4(7x+25) B.) 7(4x+100) C.) 7(4x+25) D.) 4(7x+100)

Option (B) is correct. The question requires an understanding of the concept of function and its definition. A function is a rule that establishes a relationship between two quantities: the input and the output. To find out whether or not Adam's function could be the rule for the given table, it is necessary to substitute each pair of values, (0,0) and (−1,1) into y= −x to verify whether or not the substitution gives the correct output. This process must be repeated for both Belinda's function and for Chandra's function. It is easy to see that (0,0) satisfies all three rules. Since 1= −(−1) the pair (−1,1) satisfies Adam's function rule. Since 1 = − (−1) ^2 − 2(−1) = − 1+2 = 1 the pair (−1,1) also satisfies Chandra's function rule. The pair (−1,1) does not satisfy Belinda's rule, since 1 ≠ − (−1)^2 = −1

Mr. Smythe has asked his students to come up with function rules for the following table of data. x y -1 1 0 0 Adam says that the function rule is y = −x Belinda says that the function rule is y = −x2 and Chandra says that the function rule is y=−x2−2x Which of the three equations could be the function rule for the table? A. Adam's only B. Adam's and Chandra's only C. Belinda's and Chandra's only D. Adam's, Belinda's, and Chandra's

Option (D) is correct. The question requires an understanding of calculating areas using standard, real-world miles on a map. Area is a two-dimensional representation of a surface (length times width, base times height, etc.). A 1-inch by 1-inch square on Greg's map represents a square 30 miles on each side. The area of this square is 30 miles multiplied by 30 miles, or 900 square miles. On Lori's map, the 1-inch by 1-inch square represents a square 20 miles on each side. The area of this square is 20 miles multiplied by 20 miles, or 400 square miles. The difference between these is 500 square miles.

On Greg's map, 1 inch represents 30 miles, and on Lori's map, 1 inch represents 20 miles. The area of a 1-inch by 1-inch square represents how many more square miles on Greg's map than on Lori's map? A.100 B.250 C.400 D.500

Option (D) is correct. The question requires an understanding of average (or arithmetic mean) and the ability to set up and solve several computations. An average of 77 points in four games means that they scored a total of 77 x 4, or 308 points. Since the scores for the first three games are given as 70, 76, and 82 points, it is necessary to add these up (228 points) and subtract from the four-game total of 308 points. This leaves 80 points for the last game's score.

The Clearbrook Wildcats basketball team scored an average of 77 points in four games. In the first three games, the team scored 70, 76, and 82 points. How many points did they score in their last game? A.70 B.76 C.77 D.80

Option (C) is correct. The question requires an understanding of proportions. The ratio between the height of the Statue of Liberty and the length of its shadow is equal to the ratio between the height of the pole and the length of its shadow. The proportion will look like this (where L represents the height of the Statue of Liberty): L37 = 52 Multiplying both sides by 37 and then simplifying both sides of the equation gives you L=92.5 Note that other proportions can be set up, such as statue height (L) divided by pole height (5 meters) equals statue shadow length (37 meters) divided by pole shadow length (2 meters). This will also give the correct result.

The Statue of Liberty casts a shadow that is 37 meters long at the same time that a nearby vertical 5-meter pole casts a shadow that is 2 meters long. Based on shadow height, the height, in meters, of the Statue of Liberty must be within which of the following ranges? A.115 meters to 120 meters B.105 meters to 110 meters C. 90 meters to 95 meters D. 60 meters to 65 meters

Option (A) is correct. The question requires an understanding of dependent and independent variables within various formulas. The input of a function is referred to as the independent variable because the input can be any number. In this instance, the output, referred to as the dependent variable, is the number of gallons g remaining in the pool, because the volume depends on the input variable d, or the number of days since the pool started to leak.

The community pool has a capacity of 50,000 gallons. It is leaking at a rate of 450 gallons per day. The equation g = 50,000 - 450d can be used to find the number of gallons g remaining in the pool after d days. Which of the following statements is true? A. g is the dependent variable because the volume is dependent on the number of days d. B. g is the independent variable because it is what needs to be found. C. d is the dependent variable because it is being multiplied by the independent rate of 450. D. Dependent and independent variables cannot be determined in this situation because the equation is linear.

Option (B) is correct. The question requires an understanding of computing percent increase. The increase in the population of the city is 50,600−50,000=600 people. The value of the fraction 600/50,000 gives the percent increase based on the population before the increase occurred. The fraction is equivalent to the decimal 0.012, which is equivalent to 1.2 percent.

The population of a certain city was 50,000 people. One year later, the population of the same city grew to 50,600. What was the percent increase in the city's population in that one-year period? A. 0.6% B. 1.2% C. 6% D.12%

The correct answer is 5. The question requires an understanding of rounding strategies for reasonableness of results. The word problem can be solved by performing the division 1,944 ÷ 450, which yields 4.32. Since the result represents the number of trucks needed, the result must be rounded to an integer. Rounding down to 4 would yield the wrong answer since 4 × 450 = 1,800, so Tom would be able to ship up to 1,800 boxes of shoes with 4 trucks. Rounding up to 5 would yield the right answer since 5 × 450 = 2,250. Since with 5 trucks Tom would be able to ship up to 2,250 boxes of shoes, he would also be able to ship 1,944.

Tom's company has to ship 1,944 boxes of shoes. If a truck can hold 450 boxes, how many trucks does he need to ship all the boxes?

Option (C) is correct. This question requires an understanding of basic probability. If a coin is fair, the probability of tossing heads is the same as the probability of tossing tails. There are only two possible outcomes, so the probability of tossing tails is 1/2. The number 1/2 can also be written as 0.5. Please note that since each toss of the coin is an independent event, which means that the previous results do not affect the current toss of the coin, each time the coin is tossed, the probabilities of H or T would always be the same, 0.5.

Wai tossed a fair coin 9 times with an outcome of H H T T T T H H H, where H means heads and T means tails. What is the probability that the next toss will be T ? A.0.2 B.0.4 C.0.5 D.1.0

Option (C) is correct. The question requires an understanding of basic statistical concepts. The range is obtained by subtracting the smallest value, 44, from the largest value, 125. In order to modify the mean and median but not the range, the number of customers that shopped at the store during the tenth week must be greater or equal to 44 and less than or equal to 125.

Week Customers 1 52 2 79 3 44 4 110 5 90 6 68 7 125 8 96 9 88 Bobby runs a small store. The total number of customers who shopped at the store during each of nine consecutive weeks is recorded in the chart shown. If the number of customers who shopped at the store during the tenth week were included in the data, the mean and median of the data would change but the range would not change. Which of the following could be the number of customers who shopped at the store during the tenth week? A. 39 B. 41 C. 73 D.132

Option (B) is correct. The question requires an understanding of place value. By writing each of the answer choices as a numeral, you can compare the four numbers and decide which is the greatest. 5 thousands is the same as 5 times 1,000, or 5,000. 53 hundreds is the same as 53 times 100, or 5,300. 506 tens is the same as 506 times 10, or 5,060. 5,100 ones is the same as 5,100 times 1, or 5,100. 53 hundreds is the greatest of the numbers given.

Which of the following has the greatest value? A. 5 thousands B. 53 hundreds C. 506 tens D.5,100 ones

Option (C) is correct. The question requires an understanding of prime factorization of a number. The prime factorization of 2,112 is 2^6×3×11 Since 3 and 11 are the only odd prime factors of 2,112, the greatest odd factor is given by the product of 3 and 11, or 3×11, or 33.

What is the greatest odd factor of the number 2,112 ? A. 3 B. 21 C. 33 D.111

Option (C) is correct. The question requires an understanding of algebraic properties. The associative property of multiplication concerns the order in which the multiplications are performed when three or more numbers are multiplied, which can be changed by inserting or removing grouping symbols such as parentheses. If the same factors are present, and in the same order, but the grouping symbols dictate that the order in which the multiplications are performed has changed, then the associative property of multiplication has been applied. In ab+c=ba+c ab+c=c+ab and a(b+c)=ab+bc there are only products with two factors in each, so the associative property of multiplication cannot be applied. In (ab)c=a(bc) the parentheses dictate that on the left side, a and b are multiplied first, and then the result is multiplied by c, and that on the right side, b and c are multiplied first, and then a is multiplied by this result. The fact that the end results on each side are equal is guaranteed by the associative property of multiplication.

Which of the following is an example of the associative property of multiplication? A. ab+c = ba+c B. ab+c = c+ab C. (ab)c = a(bc) D. a(b+c) = ab+ac

Option (B) is correct. The question requires an understanding of the order of operations. The first step to simplify the expression 4(5−2)^2 − 2^3 is the evaluation of the subtraction within the parentheses; the expression is equivalent to 4 × 3^2 − 2^3 The second step is the evaluation of the powers; the expression is equivalent to 4×9−8 The third step is the evaluation of the multiplication; the expression is equivalent to 36−8 The final step is the evaluation of the subtraction; the expression is equivalent to 28.

Which of the following is equal to 4(5−2)^2 − 2^3 (^ means the digit after ^ is an exponent) A. 16 B. 28 C. 76 D.136

Option (C) is correct. The question requires an understanding of the place value system and powers of 10. Since 10^0=1 the expression 5(10^0) is equal to 5×1 or 5.

Which of the following is equal to 5(10^0)? A. 0 B. 1 C. 5 D.50

Option (C) is correct. The question requires an understanding of factors of natural numbers. The question requires a determination of the number that has two even factors and one odd factor. The even numbers need not be unique. In (C), 20=2×2×5 ; 20 can be written as the product of 2, 2, and 5, so 20 can be written as the product of two even numbers and one odd number. In (A), 15=3×5 and in (D), 21=3×7 15 and 21 do not have any even factors. In (B), 16=2×2×2×2 ; 16 does not have any odd factors.

Which of the following is the product of two even numbers and an odd number, each of which is greater than 1 ? A.15 B.16 C.20 D.21

Option (A) is correct. The question requires an understanding of algebraic terminology. The coefficients of the terms of a polynomial are the numbers by which the variables are multiplied. The degrees of the terms of a polynomial are the exponents to which the variables are raised. Therefore, the coefficients are 3, 7, and −5 and the degrees are 5, 3, and 0.

Which of the following lists the coefficients and degrees of the terms in the polynomial shown? A.Coefficients: 3, 7, −5; Degrees: 5, 3, 0 B.Coefficients: 3, 7, −5; Degrees: 5, 3, 1 C.Coefficients: 5, 3, 0; Degrees: 3, 7, −5 D.Coefficients: 5, 3, 1; Degrees: 3, 7, −5

Option (C) is correct. The question requires an understanding of place value. To compare the four numbers in the options, the digits that determine place value must be compared moving left to right beginning with the digit in the tenths place. The digit 1 is in the tenths place of each number, so one must compare the digit in the hundredths place of each number. The digit 1 in the hundredths place of the number in (D) is greater than the digit 0 in the hundredths place of each of the numbers in (A), (B), and (C), so the number in (D) is the greatest. In the thousandths place, the number in (C) has a digit of 0, while the numbers in (A) and (B) have digits of 3 and 4, respectively. The number in (C) is thus less than the numbers in (A) and (B), making the number in (C) the least of the four numbers. Another way to approach this kind of problem is to add a zero to the end of 0.103 in (A) and two zeros to the end of 0.11 in (D) so that all four choices represent a value in ten-thousandths. This does not change the numbers' values, but makes it easier to determine that (D) is the greatest, being equal to 1,100 ten-thousandths, and (C) is the least, being equal to 1,005 ten-thousandths.

Which of the following numbers is least? A.0.103 B.0.1041 C.0.1005 D.0.11