PRAXIS MATH (Practice 3)
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? A. 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. B. The area of Figure 1 is equal to the area of Figure 2, and the perimeter of Figure 2 is greater than the parameter of Figure 1. C. The area of Figure 1 is greater than the area of Figure 2, and the perimeter of Figure 1 is greater than the parameter of Figure 2. D. 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.
(B) The question requires an understanding of area and perimeter. Since the two figures are composed of exactly the same sub parts, their areas are equal. Figure 2 features the hypotenuses of the two triangles, each of which contributes additional length to the perimeter of Figure 2.
Which of the following functions could be represented by the table shown? A. y = 2^x B. y = x^2 C. y = 2x D. y = 5x - 4
(B) The question requires an understanding of how to identify relationships between the corresponding terms of two numerical patterns. To find out which function could be represented by the table, one must substitute the values of x given in the table and verify which function gives the corresponding values of y. The function in (B) could be represented by the table because... 1^2 = 1 2^2 = 4 3^3 = 9 4^2 = 16 The functions in (A) and (C) could not be represented by the table because for x = 1, each y = 2. The function in (D) could not be represented by the table because for x = 2, it yields y = 6.
Which of the following graphs represents the solution set to the inequality 18b - 5 < 20b + 11?
(B) The question requires an understanding of how to interpret solutions of multi step one-variable linear equations and inequalities. The first step to find the solution set of the inequality is to use the addition property of inequality to add -20b + 5 to both sides of he inequality. This yields 18b - 5 - 20b + 5 < 20b + 11 - 20b + 5. The second step is to add like terms. This yields -2b < 16. The third step is to use the multiplication property of inequality to multiply both sides by - 1/2. One must not forget to flip the direction of the inequality sign when multiplying by a negative number. This yields (-1/2)(-2b)> (-1/2)(16), which is equivalent to b > -8. The line graph in (B) represents all numbers greater than -8.
Mr. Scythe has asked his students to come up with function rules for the following table of data. Adam says that the function rule is y = -x. Belinda says that the function rule is y = -x^2, and Chandra says that the function rule is y = - x^2 - 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
(B) 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 the y = -x to verify whether or not the substitution gives the correct output. This process must be repeated for both Belenda'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 (does not equal) -(-1)^2 = -1.
The figures shown are squares. Each side in Figure 1 has length 7, and Figure 2 has side lengths that are double those in Figure 1. How do the perimeter and area of Figure 1 compare with the perimeter and area of Figure 2. A. The perimeter and area of Figure 2 are double the perimeter and area of Figure 1 B. The perimeter and area of Figure 2 are four times the perimeter and area of Figure 1 C. The perimeter of Figure 2 is double the perimeter of Figure 1, and the area of Figure 2 is four times the area of Figure 1 D. The perimeter of Figure 2 is four times the perimeter of Figure 1, and the area of Figure 2 is eight times the area of Figure 1
(C) The question requires an understanding of how changes to dimensions change area and volume. If the dimensions of a figure double, the ratio of corresponding sides will be 1: 2. This same ratio will apply to the perimeter. In the figures shown, the perimeter of the smaller square is 28, and the perimeter of the larger square is 56. This results in a ratio of 28: 56, which can be simplified to 1: 2. The ratio of the areas of the squares with a side ratio of 1: 2 will be 1^1: 2^2, or 1: 4. The area of the smaller square is 49, and the area of the larger square will be 196. This results in a ratio of 49: 196, which can be simplified to 1: 4. Thus the perimeter is doubled, and the area is quadrupled.
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?
(C) The question requires an understanding of inequalities and the ability to solve them graphically. The given inequality is equivalent to x - 2 < -2 x - 2, which is equivalent to 3 x < 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 xy-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).
Mary has a rectangular garden in her backyard. The garden measures 5 3/4 feet wide by 7 1/2 feet long. What is the area of the garden? A. 26 1/2 square feet D 43 1/8 square feet
(D) The question requires an understanding of how to find the area and perimeters of polygons. If a rectangle has a length of L units and a width of W units, then its area is L x W square units. Since the garden has a length of 7 1/2 feet and a width of 5 3/4 feet, the area 7 1/2 x 5 3/4 = 15/2 x 23/4 =345/8 square feet, that is 43 1/8 square feet.
Which of the following could be used to describe the polygon shown? A. Regular and convex B. Regular and concave C. Irregular and convex D. Irregular and concave
(D) The question requires and understnding 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.
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 d 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
(A) 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 of d, or the number of days since the pool started to leak.
The perimeter of each of the seven regular hexagons in the figure shown is 18, what is the perimeter of the figures? A. 54 B. 63 C.108 D. 126
(A) 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 x 3, or 54.
Which word describes each angle in an equilateral triangle? A. Acute B. Obtuse C. Right D. Straight
(A) The question requires an understanding of how to classify angles based on their measure. An equilateral triangle is also equiangular: that is, all its angles have the same measure. Therefore, each angle has a measure of 180 / 3, or 60*. An acute angle is an angle that measures less than 90*. Therefore, the angles of an equilateral triangle are all acute.
Which of the following statements must be true about the two non-right angles of a right triangle? A. Both angles are acute B. One angle is acute and one is obtuse C. The angles are congruent D. Both angles are obtuse
(A) The question requires an understanding of how to classify angles based on their measure. The sum of the measures of the angles in a triangle is 180*. Since the right angle measures 90*, the otehr two angles must add up to the remaining 90*. Since both together make 90*, each individually must be less than 90* and therefore be acute.
The function f(x) = x^2 + 3 is represented by which table of values?
(A) The question requires an understanding of how to identify a relationship between the corresponding terms of two numerical patterns. A method to find out which table of values may represent the function f(x) = x^2 + 3 is to plug in the x values from each table in the function and verify whether the output matches the value of f(x) given the table. For x = 0, f(0) = 3, for x = -2, f(-2) = (-2)^2 + 3 = 4 + 3 = 7, for x = -1, f(-1) = (-1)^2 + 3 = 4 finally, for x = 3, f(3) = 9 + 3 = 12. The only table with all four correct points of values is the table in option A.
The first three figures in a pattern are shown. The 1st figure is composed of two triangles and one square. Each figure after the 1st figure is composed of two triangles and one square more than the preceding figure. How many line segments are in the 10th figure of the pattern? A. 35 B. 38 C. 41
(A) The question requires an understanding of how to identify and extend a pattern. The first figure has 8 line segments. Adding a square to each figure is equivalent to adding 3 line segments. So the number of line segments of the nth figure can be described by the equation f(n) = 5 + 3n, with n = 1, 2, 3,...Therefore the 10th figure of the pattern has f(n) = 5 + 3 x 10, or 35 line segments.
Which of the following inequalities is equivalent to the inequality 4x + 4 (<underlined) 9x + 8? A. x (>underlined) -4/5 B. x (<underlined) -4/5 C. x (>underlined) -12/5
(A) The question requires an understanding of how to solve multi step one-variable linear equations and inequalities. Using the addition property of inequality, the given inequality is equivalent to 4x + 4 + (-9x - 4) (<underlined) 9x + 8 + (-9x - 4). Simplifying like terms yields -5x (<underlined) 4. Using the multiplication property of inequality and taking into account the sign, -5x (<underlined) 4 is equivalent to (-1/5)(-5x) (>underlined) (-1/5)(4). Simplifying yields x(>underlined) -4/5.
A certain polygon has the following attributes. I. There are 2 pairs of parallel sides II. It is a quadrilateral III. One pair of parallel sides has length 2, and the other pair of parallel sides has length 4. Which one of the following types of polygons has all of the attributes listed? A. Parallelogram B. Rhombus C. Triangle D. Square
(A) The question requires an understanding of how to use attributes to classify or draw polygons and solids. A quadrilateral is a polygon with four sides. A parallelogram is a quadrilateral with two pairs of parallel sides. A rhombus is a parallelogram with all sides the same length. A square is a rhombus with at least one right angle. For attributes 1 and 2, the polygon is not a triangle. For attribute 3, the polygon is neither a rhombus nor a square. Therefore, the polygon must be a parallelogram.
The cost to rent a bus for a field trip is $34.25 per hour, and the duration of the trip is 4 hours and 45 min. Which of the following expressions is best for doing a mental calculation to closely estimate the total cost, in dollars, of renting the bus for the trip? A. 34 x 5 B. 34 x 4.75 C. 34.25 x 4.75 D. 35 x 5
(A) The question requires an understanding of how to use mental math, estimation, and rounding strategies to solve problems and determine reasonableness of results. The total cost of the trip can be calculated by multiplying the hourly rate by trip duration, in hours. The cost of the bus per hour is best estimated at $34, and the duration of the trip is best estimated as 5 hours. Therefore, the best expression to estimate the total cost using a mental calculation is 34 x 5.
The net shown above forms a right triangular prism. Which of the following represents the surface area of the right triangular prism? A. 84 B. 92 C. 96 D. 120
(A) The question requires an understanding of how to use nets to determine the surface area of three-dimensional figures. The surface area of the three-dimensional figure is the sum of the areas of its faces. The faces of the right triangular prism are 6 by 5 rectangle, a 6 by 4 rectangle, a 6 by 3 rectangle, and two congruent right triangles, each of which has sides of lengths 4 and 3. The areas of the rectangular faces are, respectively, 6 x 5, or 30; 6 x 4, or 24; and 6 x 3, or 18. The area of each of the triangular faces is 1/2 x 3 x 4, or 6. Therefore, the surface area of the figure is 30 + 24 + 18 + 2 x 6, or 84
Rodrigo left his workplace at 4:50 pm, and it took him 3/ 4 of an hour to get home. At what time did Rodrigo get home? A. 5:35 pm B. 5:45 pm C. 5:55 pm D. 6:05 pm
(A) This question requires an understanding of elapsed time. Since there are 60 minutes in an hour, it took Rodrigo 60 x 3/ 4, or 45 minutes, to get home. Rodrigo left at 4:50 pm. Since 50 + 45 = 95 minutes, or 1 hour and 35 minutes, Rodrigo got home at 5:35 pm.
In the formula d = r x t, if d = 60 and t remains constant, which of the following is equivalent to r? A. 60t B. 60/t C. t/ 60 D. D/ 60t
(B) The question requires an understanding of simple formulas and the ability to work with them. If d is equal to 60, d can be replaced with 60 in the equation, which will result in 60 = r x t. The question asks for determining which option is equivalent to r, so it is necessary to solve the equation for r. Since r is multiplied by t, both sides of the equation must be divided by t to isolate r. The result is 60/ r = t.
1, 2, 4 The first three terms of a certain sequence are shown. Which of the following mathematical relationships could describe the terms of the sequence? A. The first term is 1. Each subsequent term of the sequence is obtained by multiplying the fist constant quantity by the preceding term. B. The first term is 1. Each subsequent term of the sequence is obtained by adding a constant quantity to the preceding term. C. The first term is 1. Each subsequent term of the sequence is obtained by adding the preceding term and a quantity that increases by 1 with each new term. D. The first term is 1. Each subsequent term of the sequence is obtained by adding 1 to the square of the preceding term. E. The first term is 1. Each subsequent term of the sequence is obtained by squaring a number that is one greater than the number that was squared to obtain the preceding term.
(A, C) The question requires an understanding of how to make conjectures, predictions, or generalizations based on patterns. In the pattern described in option (A), the first term is 1, and if the constant described in the pattern is 2, then the first 3 terms of the sequence are 1, 2, and 4. Hence, the pattern described in option (A) could produce the three terms 1, 2, and 4, and if extended, the fourth term would be 8. In the pattern described in option (C), the first term is 1, and if the quantity that is added is initially 1, than the first three terms of the sequence are 1, 2, and 4. Hence the pattern described in option (C) could produce the three terms 1, 2, and 4, and, if extended, the fourth term would be 7. In option (B), the quantity that would add to the first term, 1, to produce the second term, 2 must be 1. Hence the first three terms produced by the pattern are 1, 2, and 3. The third term is 3, not 4, as required. In option (D), the terms produced by the pattern would be 1, 2, and 5. The third term is 5, not 4, as required. In option (E), the first three terms are 1, 4, and 9. The second and third term values, respectively, are not 2 and 4, as required.
In which quadrant is the point (-8, 2) located? A. Quadrant I B. Quadrant II C. Quadrant III D. Quadrant IV
(B) The question requires an understanding of the coordinate plane. Since points on the second quadrant have a negative x-coordinate and a positive y-coordinate, the point with coordinates (-8, 2) is located in quadrant II.
Which of the following is a statistical question? A. What is the daily high temperature for an August day in Cheyenne, Wyoming? B. How many speeches did George Washington make during his lifetime? C. How many minutes did Hannah spend talking on her phone on August 28, 1016? D. What was the average number of miles a week run by the members of the Hereford High School cross-country team last month?
(A, D) This question requires an understanding of how to identify statistical questions. A statistical question is one that can be answered by collecting data and where there will be variability in the data collected. To answer the question in (A), one must collect the daily high temperature for each day in August. Such values will vary. To answer the question in (D), one must collect the number of miles a week run by each of the members of the team during the past month. such variables will vary. The questions in (B, C) can be answered simply by counting.
In the figure shown, quadrilateral ABFG is a square and quadrilateral FCDE is a rectangle. Which of the following statements must be true about the figure? Select al that apply... A. G lies on the x-axis B. C lies on the y-axis C. A is in the first quadrant D. D is in the fourth quadrant E. The area of the polygon ABCDEFG is 27 square units F. The perimeter of the polygon ABCDEFG is 25 units
(A, D, and E) 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 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.
Which of the following is demonstrated by the figure shown? A. When the numerator stays the same and the denominator increases, the fraction increases B. When the numerator stays the same and the denominator increases, the fraction decreases C. When the denominator stays the same and the numerator increases, the fraction increases D. When the denominator stays the same and the numerator increases, the fraction decreases
(B) The question requires an understanding of fractions and how to use geometrical representations to compare fractions. All of the fractions shown are unit fractions; that is, fractions in which the numerator is 1. The models accompanying each of the four given fractions are called tape models. In a tape model, the length of the tape, represents one whole. This whole can then be divided into pieces of equal lengths, and the length of each piece represents a unit fraction. The way in which the models are organized and displayed shows that the length that represents the fractional part of the whole becomes shorter as the whole is subdivided into more parts of equal length. This is a pictorial representation that demonstrates that if the numerator of a set of fractions is fixed and does not change, the size of the number represented by the fractions will decrease as the denominators are increased.
A boxplot for a set of data is shown. Which of the following is true? A. The only outlier is 200 B. The only outlier is 1,000 C. The only outliers are 200, 700, and 1,000 D. All values greater than 500 or less than 300 are outliers
(B) The question requires an understanding of how to describe a set of data. The interquartile range is 500 - 300 = 200. Therefore any value less than 300 - (200 x 1.5) = 0 or greater than 500 + (200 x 1.5) = 800 is an outlier. The only outlier in the data set, ie., the data value less than 0 or greater than 800, is 1000.
Bob is filling water bottles for a bicycle race. The number of bottles, n, needed for the race is n = 2h +1, where h is the number of hours she expects to be racing. Which of the following statements is true about the variables n and h? A. n is the independent variable, and h is the dependent variable B. h is the independent variable, and n is the dependent variable. C. Both n and h are dependent variables. D. Both n and h are independent variables.
(B) The question requires an understanding of how to differentiate between dependent and independent variables in formulas. Since the number of hours Bob expects to be racing does not depend on how many water bottles he prepares, the number of hours h is the independent variable. Since the number of bottles prepared depends on how many hours Bob expects to be racing, the number of water bottles n is the dependent variable.
-1/2x - 6 > 4 - 3x Which of the following is the graph of the solutions to the inequality shown?
(B) The question requires an understanding of how to interpret solutions of multi step one-variable linear equations and inequalities. The inequality can be solved by first adding 6 and 3x to each side of the inequality and then adding like terms, resulting in 5/2x > 10. Multiplying each side by 2/5 yields x > 4. On the number line, this inequality corresponds to a graph of the numbers greater than 4 but not including 4. (Note open bubble)
The table shows the time it takes Larissa to burn 100 calories while performing each of three activities. Larissa's workout routine includes a 30-minute dance class, 10 minutes of running, and 15 minutes of walking. How many calories did Larissa burn to complete her workout? A. 375 B. 400 C. 425 D. 450
(B) The question requires an understanding of how to solve a unit-rate problem. Using the information on the chart, a 30-minute dance class would burn 100 x 2, or 200 calories; 10 minutes of the running would burn 100/ 8 x 10, or 125 calories; 15 minutes fo walking would burn 100/ 20 x 15, or 75 calories. Therefore Larissa burned a total of 200 + 125 + 75 = 400 calories
Two friends went out for lunch and decided to share the dessert. One of them ate 1/2 of the desert and the other ate 1/3 of the remaining part. What fraction of the desert was left over? A. 1/6 B. 1/3 C. 2/3 D. 5/6
(B) The question requires an understanding of how to solve multi step mathematical and real-world problems. The first friend ate 1/2 of the desert, while the second friend ate 1/3 of the remaining part; that is 1/3 (1 - 1/2), or 1/6. Altogether they ate 1/2 + 1/6 = 4/6, or 2/3 of the dessert. Therefore, the fraction left over is 1 - 2/3, or 1/3 of the dessert.
-3( x - 4) (>underlined) 9 Which of the following inequalities is equivalent to the inequality shown? A. x (<underlined) -1 B. x (<underlined) 1 C. x (>underlined) -1 D. x (>underlined) 1
(B) The question requires an understanding of how to solve multi step one-variable linear inequalities. Using the distributive property of multiplication over addition yields -3x + 12 (>underlined) 9. Adding -12 to both sides of the inequality and adding like terms yields -3x (>underlined) -3. Dividing both sides by -3 yields x (<underlined) 1, as the inequality sign must be reversed when multiplying or dividing by a negative number.
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
(B) 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.
Which of the following statements can be inferred from the graph shown? Select all that apply. A. For each country shown, exports to the United States increased each year from the previous year B. The country that had the greatest yearly exports to the United States for each of the years shown had a three-year export total between $11 billion and $12 billion C. The exports from Country A to the United States more than doubled from 1995 to 1997
(B, C) The question requires an understanding of bar graphs and the ability to read and interpret them. The scale is in billions of dollars and rises in increments of $0.5 billion. The exports from Country C decreased a small amount from 1995 to 1996, so the statement in (A) cannot be inferred from the graph. The statements in (B) and (C) can be inferred, since Country B had the greatest yearly exports, for a three-year total of about $11.5 billion. Also, the exports from Country A more than doubled, going from $2 billion to just over $4 billion.
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
(C) 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.
At an apple orchard, between 280 and 300 bushels of apples are picked each day during peak harvest season. There are between 42 and 48 pounds of apples in each bushel. Which of the following could be the number of pounds of apples picked a the orchard in one day during peak harvest season? A. 9,000 B. 11,000 C. 13,000 D. 15,000
(C) The question requires an understanding of how to recognize the reasonableness of a solution within the context of a given problem. The minimum number of pounds of apples picked in one day is 42 x 280 = 11,760. The maximum number of pounds of apples picked in one day is 48 x 300 = 14,400. The number in (C), 13,000 pounds, is the only number of pounds of apples greater than 11,760 and less than 14,400.
In the figure shown, which two lines form a pair of perpendicular lines? A. Line a and line b B. Line b and line c C. Line c and line d
(C) The question requires an understanding of how to use definitions to identify lines, rays, line segments, parallel lines, and perpendicular lines. Two lines in the plane are perpendicular if they form at least one right angle. The figure indicates that lines c and d for a right angle; therefore, line c and line d are perpendicular.
Ms. Gupta is making 3 batches of chocolate chip cookies for a picnic. Each batch requires 1 1/2 cups of sugar and 3 1/4 cups of flour. Which of the following is the best estimate of the total amount of sugar and flour Ms. Gupta uses for the cookies? A. Less than 9 cups B. Between 9 and 12 cups C. Between 12 and 15 cups D. More than 15 cups
(C) This question requires an understanding of flow to use mental math and estimation to solve problems and determine the reasonableness of results. Each batch of cookies requires a total of 1 1/2 + 3 1/4 = 4 3/4 cups of sugar and flour. This number is between 4 and 5, so three batches would require between 3 x 4 and 3 x 5 cups of flour and sugar, so the total is between 12 and 15 cups.
a = 5,000 (1 + r) The formula shown can be used to find the amount of money in dollars, a, in an account at the end of one year when $5,000 is invested at simple annual interest rate r for the year. Which of the following represents the independent variable in the formula? A. a B. 5,000 C. r D. 1 + r
(C) This question requires an understanding of how to differentiate between dependent and independent variables in formulas. In the given formula, there are two variables, a and r. The formula can be used to investigate how the amount of money a varies depending on the interest rate r. Therefore, the dependent variable is a and the independent variable is r.
Wal 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
(C) This question requires and understanding of basic probability. If a coin is fair, then the probability of tossing heads is the same as tossing tails. There are only two outcomes, so the probability of tossing tails is 1/ 2. The number 1/ 2 can also be written as 0.5.
A spinner is divided into 12 congruent sections. Each section is either red, blue, green, or yellow. The table shows the theoretical probability of landing on a color when spinning the spinner once. How many sections are blue? A. 2 B. 4 C. 5 D. 8
(C) The question requires an understanding of probability. The sample space consists of the possible outcomes of a spin which are red, blue, green or yellow. The sum of the probabilities of the possible outcomes in the sample space is 1; that is, 1/3 + x + 1/6 + 1/12 = 1, which is equivalent to 7/12 + x = 12/12. It follows that the probability x of landing on blue is 5/12. Therefore, 5 out of 12 sections of the spinner are blue.
The first two terms of the sequence shown are 2 and 3. Each subsequent term, beginning with third term is found by adding the two preceding terms and multiplying the sum by -2. What is the value of a5, the fifth term of the sequence? A. -14 B. -12 C. -10 D. -8
(D) 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 + 3 x -2. So the third term is -10. The fourth term is found by adding 3 + (-10) x -2 or -7 x -2 = 14. The fifth term is found by adding -10 + 14 x -2 or 4 x -2 = -8
Cube A has a volume of 1 cubic inch. The length of each side of cube B is 1 inch greater than the length of each side of cube A. The volume of cube B is how many times the volume of cube A? A. 2 times B. 3 times C. 4 times D. 8 times
(D) The question requires an understanding of how changes to dimensions change area and volume of three-dimensional shapes. Since the volume of cube A is 1 cubic inch, its sides must have a length of 1 inch. The length of each side in cube B is 1 inch greater than the 1 inch of each side of cube A, so each side in cube B has a length of 2 inches. The volume of cube B is thus 8 cubic inches, which is 8 times the volume of cube A.
Into how many equilateral triangles can a regular hexagon be decomposed? A. 3 B. 4 C. 5 D. 6
(D) The question requires an understanding of how to compose and decompose two-dimensional shapes. A regular hexagon can be inscribed in a circle. When segments are drawn from the center of he circle to the vertices of the hexagon, 6 triangles are formed. The triangles are congruent because of teh SSS Theorem. Moreover, the triangles are isosceles because, in each triangle, two of the sides are radi of the circle. In each triangle, teh angle that is opposed to the base measures 360*/ 6 =60*. Then, each base angle measures (180*-60*)/ 2 = 120*/ 2 = 60*. It follows that, in each triangle all angles have the same measurement; thus, the triangles are equilateral.
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
(D) 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 number because the unit is pieces of clothing which is positive and discrete unit. According to the word problem, Sara bought 6 shirts, 3 pairs of pants, and 1 1/2 sweaters, totaling 10 1/2 pieces of clothing. The solution is, therefore, not acceptable since it is not a natural number.
The boxplots shown compare the incomes of two professions. Based on the boxplots, which of the following statements is true? A. A nuclear engineers earn more than all police officers B. Exactly 50% of nuclear engineers earn more than all police officers C. The range of incomes for nuclear engineers is the same as that for police officers D. The median income for nuclear engineers is greater than the maximum income for police officers
(D) The question requires an understanding of how to interpret various displays of data. The top boxplot shows that the annual income of a nuclear engineer ranges from a minimum of approximately $50,000, with a median annual income of $70,000. The bottom boxplot shows that the annual income of a police officer ranges from a minimum of approximately $15,000 to a maximum of approximately $60,000, with a median annual income of approximately $50,000. Therefore, the median income for nuclear engineers is greater than the maximum income for police officers.
The table shows the cost of a membership to Gym B for the five possible membership lengths. Gym A has the same possible membership lengths, and the cost, y, in-dollars, of a membership to Gym A for x months is given by the equation 2y - 50x = 85. Which of the following is true about the cost, in dollars, of a membership to Gym A compared with the cost of a membership to Gym B? A. The cost of membership to Gym B is greater than the cost of a membership to Gym A for membership lengths of 6 months or less but is greater for membership lengths of greater than 6 months. B. The cost of a membership to Gym A includes the same initial membership fee as the cost of a membership t Gym B but a greater monthly fee. D. The cost of a membership to Gym B is greater than the cost of a membership to Gym A for any number of months.
(D) The question requires an understanding of how to use linear relationships represented by equations, tables, and graphs to solve problems.The table describes the costs of varying lengths of membership to Gym B and can be represented by the linear equation y = 25x + 50, where y is the cost of a membership lasting x months. The equation that describes the cost y of a membership to Gym A lasting for x months can be rewritten as y = 25x + 42.50. The monthly fees, represented by the slopes of the two linear equations, are equal for the two memberships. However, the y-intercept of the equation representing Gym B is greater than the y-intercept of the line representing Gym A. This can be interpreted to mean that the initial fee for Gym B is greater than the initial fee for Gym A. Since the monthly memberships are the same but Gym B has a greater initial fee, the membership cost for Gym B is always more expensive than the membership cost for Gym A for any number of months.
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 CD? A. 3 3/4 B. 1 3/4 C. 1 5/8 D. 1 3/8
(D) The question requires an understanding of measuring and comparing lengths of objects using standard tools. Line segment AB measures 3 6/8 inches, and line segment CD measures 2 3/8 inches. When subtracting the two lengths, line segment AB is 1 3/8 inches longer than line segment CD.
What is the area, in square inches, of the polygon shown? A. 21 B. 54 C. 1,008 D. 1,080
(D) The question requires an understanding of relative sizes of United States customary units. To find the area of the polygon in square inches, all measurements must first be converted to equivalent measurements in inches using the conversion that one foot is equivalent to 12 inches and 1 yard is equivalent to 3 feet. The lengths, in inches, of the labeled sides in the polygon are 36 inches, 18 inches, and 24 inches. The polygon can be decomposed into two rectangles; one having a length of 36 inches and a width of 18 inches, and the other having a length of 24 inches and a width of 18 inches. The first has an area of 36 x 18, or 648 square inches, and the second has an area of 24 x 18, or 432 square inches. The area of the polygon is the sum of the areas of these two rectangles, which equals 648 + 432, or 1,080 square inches.
On Greg's map, 1 inch represents 30 miles, and on Lori's map, 1 inch represents 20 miles. The area 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
(D) This 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 x width, base x height). A 1-inch square on Greg's map represents a square 30 miles on each side. The area of this square is 30 miles x 30 miles = 900 square miles. On Lori's map, the 1-inch square represents a square 20 miles on each side. The area of this square is 20 miles x 20 miles = 400 square miles. The difference between 900 - 400 = 500
The table shows the costs of supplies for a birthday party. Anton buys 6 packages of utensils and 4 packages of cups, 2 packages of plates, and 2 packages of tablecloths. Antons total purchase is subject to a 7.5% sales tax. How much will the party supplies cost Anton? A. $10.75 B. $23.65 C. $30.00 D. $32.25
(D) This question requires an understanding of how to solve multi step, mathematical and real-world problems using addition, subtraction, multiplication, and division of rational numbers. The cost before tax can be found by simplifying the expression 6 x 1.50 + 2 x 4 +2 x 2 + 2 x 4.50 obtaining $30. The taxes are 30 x 7.5/100 = 2.25 dollars. Therefore, the total cost is 30 + 2.25 dollars, that is, $32.25. Or you can find the tax by using 30 x 1.075 = $32.25
At a flower shop, there are 5 different kinds of flowers; tulips, Lillies, daiseys, carnations and roses. There are also 3 different colors of vases to hold the flowers: blue, green, and pink. If one kind of flower and one color of vase to hold them are to be selected at random, what is the probability that the selection will be Lillie's held in a pink vase? A. 2/8 B. 5/8 C. 3/16 D. 1/15
(D) The question requires an understanding of how to interpret probabilities relative to likelihood of occurrence. There are 15 possibilities (5 different kinds of flowers times 3 different colors of vases), so the probability of selecting Lillie's held in a pink vase is 1/15.
