PRAXIS MATH

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?

$12

Which of the following are equivalent to dividing 288 by 24? (288 / 4) / 6 2(144 / 24) (144 /12) + (144 / 12) (240 / 24) + (48 /24)

(288 / 4) / 6 2(144 / 24) (240 / 24) + (48 /24)

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

(ab) c = a(bc)

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.

G is the dependent variable because the volume is dependent on the number of days D.

Which of the following graphs best represents the relationship between x and y in the table shown? x y - 10 -5 -5 0 5 10 10 15

Graph A

Which of the following could be used to describe the polygon shown? - Regular and convex - Regular and concave - Irregular and convex - Irregular and concave

Irregular and Concave The question requires an understanding of polygons and their properties. The polygon can be described as irregular because its sides are of different lengths, and the polygon can be described as concave because it is possible to connect two vertices of the polygon with a segment that is not contained in the interior of the polygon.

In which quadrant is the point (-8,2) located?

Quadrant II

In the number 567,894, what is the value of the digit 6?

Sixty Thousand

Which of the following graphs in the xy-plane could be used to solve graphically the inequality x- 2 < -2(x + 1) and shows the solution to the inequality?

The question requires an understanding of inequalities and the ability to solve them graphically. The given inequality is equivalent to x−2<−2x−2, which is equivalent to 3x<0, which yields x<0. A way to solve the given inequality graphically is to consider the equations y=x−2 and y=−2(x+1). The graphs of the two equations in the xy-coordinate plane are lines. The solution to the inequality is the set of points (a,0) on the x-axis for which the point (a, a−2) is "below" the point (a,−2(a+1)); that is, when the graph of the line y=x−2 is "below" the graph of the line y=−2(x+1).

A two-dimensional net of a certain three-dimensional figure includes five faces, nine edges, and six vertices. What three-dimensional figures is represented by the net?

Triangular Prism Understand three-dimensional object. 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.

What is demonstrated by the figure shown?

When the numerator stays the same and the denominator increases, the fraction decreases.

If one cup of soup costs 2 dollars, which of the following represents the number of cups of soup that can be purchased with d dollars? 2d d/2 d/100 x 2 100 x d/ 2

d/2

If 125 + 4x = 4y, what is x in terms of y?

x=(7y−125)÷4 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=7y125+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=7y125+4x=7y yields 4x=7y−1254x=7y−125. Dividing both sides of 4x=7y−1254x=7y−125 by 4 yields x=(7y−125)÷4x=(7y−125)÷4. The variable x is now expressed in terms of y.

3x^5 + 7x^3 - 5 Which of the following lists the coefficients and degrees of the terms in the polynomial shown?

Coefficients: 3, 7, -5 Degrees: 5,3,0

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?

10

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?

17.5

What percent does 3/16 express?

18.75 3/16 x 100 = 18.75

A pencil is 18 centimeters in length. How long is the pencil in millimeters?

180

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?

2 If x represents the number of glasses and y represents the number of plates that Nicholas bought, then 2x+3.5y=182x+3.5y=18. Both x and y must be integers. Therefore, 18−2x18−2x 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 18−2x18−2x as an integer is 14. Thus, x=2.

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 28x+10028x+100. What is equivalent to Kyle's expression?

4(7x + 25) Since both 28 and 100 are divisible by 4, 4 is a factor of the expression 28x+10028x+100. To arrive at the equivalent expression given in (A), the distributive property was applied to 28x+10028x+100. In fact, 28x+100=4×7x+4×25=4(7x+25)28x+100=4×7x+4×25=4(7x+25).

Some values of the linear function F are given in the table shown. What is the value of F(100)?

40

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, ...

486

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?

5

What is equal to 5 (10^0)?

5

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?

500

Which of the following has the greatest value? 5 thousand 53 hundreds 506 tens 5,100 ones

53 hundreds

If the perimeter of each of the seven regular hexagons in the figure shown is 18, what is the perimeter of the figure?

54

In the formula d = r x t, if d equals 60 and t remains constant, which of the following is equivalent to r?

60/t

2, 3, a3 , a4 , a5 , ... The first two terms of the sequence shown are 2 and 3. Each subsequent term, beginning with the third, is found by adding the two preceding terms and multiplying the sum by−2-2. What is the value ofa5, the fifth term of the sequence?

-8 The question requires an understanding of following a rule to continue a sequence of numbers. The first term is 2, the second term is 3, and the third term is found by adding 2 and 3 and multiplying the result by −2-2. So the third term is −10-10. The fourth term is found by adding 3 and −10-10 and multiplying the sum by −2-2. The fourth term is, therefore −7-7 times −2-2, or 14. The fifth term is found by adding −10-10 and 14 and multiplying the sum by −2-2. The fifth term is, therefore, 4 times −2-2, or −8-8.

Which of the following number is the least? 0.103 0.1041 0.1005 0.11

0.1005

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 ?

0.5

The figure shows a ruler with inches marked and two line segments drawn. To the nearest eighth of an inch, how much longer, in inches, is the length of AB than the length of CD?

1 3/8

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?

1.2%

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?

1/20 x 2800

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

20

3y + 2y What is the value of the algebraic expression shown when y = 5?

25

What is equal to 4(5 - 2)^2 - 2^3?

28

What is the greatest odd factor of the number 2,112?

33 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.

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?

73 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.

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?

8 hours and 31 minutes

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?

80

Consider the algorithm shown. Step 1: Select a numerical value for the variable k. Step 2: Add 3 to k. Step 3: Multiply the result by 8. Step 4: Cube the result. Step 5: End. Executing the algorithm shown is equivalent to evaluating which of the following algebraic expressions?

8^3 (k + 3)^3

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?

90 meters to 95 meters

In the figure shown, quadrilateral ABFG is a square, and quadrilateral FCDE is a rectangle. What statements must be true about the figure? Options: - G lies on the x-axis - C lies on the y- axis - A is in the first quadrant - D is in the fourth quadrant - The area of the polygon ABCDEFG is 27 square units - The perimeter of the polygon ABCDEFG is 25 units.

A. G lies on the x-axis. D. D is in the fourth quadrant. E. The area of the polygon ABCDEFG is 27 square units. Options (A), (D), and (E) are correct. The question requires an understanding of the coordinate plane and area of polygons. Since the x-axis is the horizontal axis, point G lies on the x-axis and has coordinates (-3, 0). The points in the fourth quadrant have a positive x-coordinate and a negative y-coordinate. Since point D has coordinates (4, -3), point D is in the fourth quadrant. The polygon is made of a square, a right triangle, and a rectangle. The length of the side of the square is 3 units; therefore, the area of the square is 9 square units. The lengths of the sides of the right triangle are 3 and 4 units, respectively; therefore, the area of the right triangle is 6 square units. The lengths of the sides of the rectangle are also 3 and 4 units, respectively; therefore, the area of the rectangle is 12 square units. Finally, the area of the polygon is the sum of the areas of its parts; that is, 9 + 6 + 12, or 27 square units.

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?

Adam's and Chandra's only

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.

Because of the real-world context, the solution must belong to the set of all natural numbers; therefore, the solution is not acceptable. 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 112112 sweaters, totaling 10121012 pieces of clothing. The solution is, therefore, not acceptable since it is not a natural number.

The rectangular region shown in Figure 1 is cut along the dotted line and reassembled as shown in Figure 2. Which of the following statements about the area and perimeter of Figure 1 and Figure 2 is true? - The area of Figure 1 is equal to the area of Figure 2, and the perimeter of Figure 1 is equal to the perimeter of Figure 2. - The area of Figure 1 is equal to the area of Figure 2, and the perimeter of Figure 2 is greater than the perimeter of Figure 1. - The area of Figure 1 is greater than the area of Figure 2, and the perimeter of Figure 1 is greater than the perimeter of Figure 2. - The area of Figure 1 is greater than the area of Figure 2, and the perimeter of Figure 1 is equal to the perimeter of Figure 2.

The area of Figure 1 is equal to the area of Figure 2, and the perimeter of Figure 2 is greater than the perimeter of Figure 1.

Which of the following can be inferred from the graph shown? - For each country shown, exports to the US increased each year from the previous year. - The country that had the greatest yearly exports to the US for each of the years shown had a three-year export total between $11 billion and $12 billion - The exports from Country A to the US more than doubled from 1995 to 1997.

The country that had the greatest yearly exports to the US for each of the years shown had a three-year export total between $11 billion and $12 billion. The exports from Country A to the US more than doubled from 1995 to 1997.

15 (4 + 3) = 15 x 4 + 15 x 3 The equation shown demonstrates which of the following?

The distributive property of multiplication over addition.