Praxis Core I - Math Review Test

Click on your choices. Question: A triangle has sides of length 4, 7, and x. Which of the following could be the value of x ? Indicate all such values. A. 2.9 B. 4.5 C. 6.25 D. 7 E.12

Correct Answer: B, C, D The correct answers are (B), (C), and (D). The triangle inequality states that the length of the longest side of a triangle must be less than the sum of the lengths of the other two sides. Examination of each case is required. If x = 2.9, then the sum of 2.9 + 4 = 6.9, which is less than the longer side of 7, so (A) cannot be a value of x. If x = 4.5, then the sum of 4.5 + 4 = 8.5, which is longer than the longest side of 7, so (B) could be a value of x. If x = 6.25, then the sum of 6.25 + 4 = 10.25, which is longer than the longest side of 7, so (C) could be a value of x. If x = 7, then it would be an isosceles triangle with lengths of 7 for two of the sides, and a length of 4 for the other side, so (D) could be a value of x. If x = 12, then the longest side of the triangle would now be 12 and the other two sides would have to sum to be larger than 12. Since 4 + 7 = 11, which is less than 12, (E) cannot be a value of x.

Click on your choices. Question: Which of the following questions are statistical questions? Indicate all such questions. A.How long is Mike's foot? B.When do university students eat lunch? C.What is the weight of John's math textbook? D.How many coffee drinks do customers at a coffee shop order?

Correct Answer: B, D The correct answers are (B) and (D). A statistical question is a question that one would expect to get a variety of answers for and not just a single answer. (A) would give only a single answer for the length of Mike's foot and (C) would give only a single answer for the weight of John's math textbook, so they are not statistical questions. For (B) and (D), one would expect to get a variety of answers, so they are statistical questions.

Answer the question below by clicking on the correct response. Question: James walked 212212 miles in 2323 of an hour. What was his average speed, in miles per hour? A. 314314 B. 312312 C. 334334 D. 378378 E. 414

Correct Answer: C 21223=5223=52(32)23(32)=1541=154=334miles per hour.

Answer the question below by clicking on the correct response. Question: In the last step of a computation, Evelyn added 290 instead of subtracting 290. What one number can Evelyn subtract from her final result of 3,710 so that the correct result of the computation is displayed on the calculator and she does not have to clear her calculator and start over? A. 290 B. 435 C. 580 D. 855 E. 870

Correct Answer: C Option (C) is correct. Since Evelyn added 290 to a number instead of subtracting 290 from the number, the number would be off by 290 + 290 = 580. The final result of 3,710 would need to have 580 subtracted from it in order for the calculation to be corrected on her calculator.

Answer the question below by clicking on the correct response. Question: Of the following, which is most likely to be the height of a high school athlete? A. 3 yards B. 10 feet C. 124 inches D. 200 centimeters E. 400 millimeters

Correct Answer: D Option (D) is correct. 200 centimeters is approximately 6.5 feet, which would be a reasonable height for a high school athlete. None of the other options are plausible, as (A) through (C) are 9 feet or greater, and 400 millimeters is too small.

Answer the question below by clicking on the correct response. Question:P is 6 times Q, and Q is 2 less than 9 times R. Which of the following statements describes the relationship between P and R ? A. P is 2 less than 15 times R. B. P is 2 less than 54 times R. C. P is 12 less than 15 times R. D. P is 12 less than 54 times R. E. P is 18 less than 15 times R.

Correct Answer: D Option (D) is correct. By translating each word expression, P is 6 times Q, or P=6Q and Q is 2 less than 9 times R, which means Q=9R−2. To describe the relationship between P and R, substitute the value of Q into P's equation. P=6QP=6(9R−2)P=54R−12 Therefore, P is 12 less than 54 times R.

Answer the question below by clicking on the correct response. Question: On a map that is drawn to scale, 6 inches represents a distance of d miles. Which of the following represents the distance, in inches, of d+1d+1 miles on the map? A. d(d+1)6d(d+1)6 B. 6(d+1)d6(d+1)d C. d+16dd+16d D. 6dd+16dd+1 E. 6d(d+1)

Correct Answer: B Option (B) is correct. The given ratio of 6 inches represents d miles can be written as 6d. Another ratio must be written for the distance d + 1 , but since the distance for d + 1 is not known, it can be called x, since that is what is being solved for in the problem. This leads to the equation 6d=xd+1. Cross-multiplication can be used to solve and gives 6(d+1)=dx. Dividing both sides by d to isolate x, gives x=6(d+1)d.

Click on each box and type in a number. Backspace to erase. Question: The figure above shows a right circular cone with base radius 6 and height 20. The shaded portion of the figure is a right circular cone with height 10. The volume of the smaller cone is what fraction of the volume of the larger cone? (The volume of a right circular cone with base radius r and height h is 13πr2h .) Numerator value = 9 Denominator value of = 3

Correct Answer: 18 On the larger cone, the radius r1 is 6 when the height h1 is 20. The smaller shaded cone is similar to the larger cone, so rules for similarity can be used to determine the radius of the smaller cone. Since the height of the smaller cone h2 given is 10, which is half of the larger cone's height of 20, the radius of the smaller cone r2 should be half the radius of the larger cone, which is half of 6, or 3. The question asks what fraction of the volume the smaller cone is compared to the larger cone, which leads to the following ratio, set up using the volume formula for each cone that was given in the problem. VolumeofsmallconeVolumeoflargecone=13πr22h213πr21h1=13π(3)21013π(6)220=(9)10(36)20=90720=18

Click on each box and type in a number. Backspace to erase. Question: Allison works for a computer software company. She earns $225 per week plus $25 for each software package that she sells that week. If she wants to earn at least $400 this week, what is the minimum number of software packages that she must sell this week? 7 software packages

Correct Answer: 7 According to the information given, Allison earns $225 per week plus an additional $25 for each software packages she sells. In order to solve for the minimum number of packages she must sell to earn $400 in a week, the following inequality is used: 25p+225≥400, where p = the number of software packages. Solving for p, 25p≥175p≥7 Allison must sell a minimum of 7 software packages that week to earn at least $400.

Click on each box and type in a number. Backspace to erase. Question: The ages, in years, of 6 cars in a parking lot are 6, 14, 5, 1, 8, and x. If the average (arithmetic mean) of the 6 ages is 7 years, what is the value of x ? x = 8

Correct Answer: 8 To find the average of a group of numbers, sum the numbers and divide by the number of items that were summed. The average for the group of six cars in the parking lot is 7 years, and the age of one car is not known and is called x, which leads to the equation 6+14+5+1+8+x6=7. Multiplying both sides of the equation by 6 and summing the numbers gives the equation 34+x=42. Subtracting 34 from each side gives x=8. So, the car with the unknown age must be 8 years.

Answer the question below by clicking on the correct response. The figure shows a pictograph titled Number of Pies Sold. Each pie shown in the pictograph represents 15 pies.The pictograph has three rows. The first row is labeled Blueberry and four pies are shown. The second row is labeled Peach and three pies are shown. The third row is labeled Pineapple and five pies are shown. Question: The pictograph above shows the number of pies sold one day at a certain bakery. Blueberry pies sold for $4.50 each, peach pies sold for $4.00 each, and the total sales of all three types of pies was $825.00. If each pineapple pie sold for d dollars, what is the value of d ? A. $5.00 B. $4.75 C. $4.50 D. $4.25 E. $4.00

Correct Answer: A Option (A) is correct. According to the pictograph, each pie shown represents 15 pies and the # of blueberry pies + the # of peach pies + the # of pineapple pies gives total sales earned. BB = the number of blueberry pies PP = the number of peach pies dd = the dollar amount of each pineapple pie Since each blueberry pie sold for $4.50, each peach pie sold for $4.00, and the total sales of all three types of pies is $825.00, the dollar amount each pineapple pie sold for can be determined by substituting the above values into the equation: 15⋅4.50(B)+15⋅4.00(P)+15d(N)=82515⋅4.50(4)+15⋅4.00(3)+15⋅d(5)=825 270 +180 +75dd = 825 75dd +450 = 825 75d+450−450=825−450 75dd = 375 75d75=37575 dd = 5 = $5 The dollar amount each pineapple pie sold for is $5.00.

Answer the question below by clicking on the correct response. Question: Last Monday Craig walked at a constant rate of 3 miles per hour from his home to the bank. He stayed at the bank for 15 minutes, and then jogged home at a constant rate of 6 miles per hour. If the bank is 0.5 mile from his home, which of the following graphs best represents the relationship between Craig's distance from home d, in miles, and time t, in minutes? A. The graph starts from the origin, moves 2 gridlines to the right and 2 gridlines up to the point with the coordinates 10, zero point five zero, moves horizontally 3 gridlines to the right to the point with the coordinates 25, zero point five zero, and then slants one gridline to the right and 2 gridlines down to end at the point on the horizontal axis with the coordinates 30, zero. B. The graph starts from the origin, moves one gridline to the right and 2 gridlines up to the point with the coordinates 5, zero point five zero, moves horizontally 3 gridlines to the right to the point with the coordinates 20, zero point five zero, and then slants 2 gridlines to the right and 2 gridlines down to end at the point on the horizontal axis with the coordinates 30, zero. C. The graph starts from the origin, moves 2 gridlines to the right and 3 gridlines up to the point with the coordinates 10, zero point seven five, moves horizontally 3 gridlines to the right to the point with the coordinates 25, zero point seven five, and then slants one gridline to the right and 3 gridlines down to end at the point on the horizontal axis with the coordinates 30, zero. D. The graph starts from the origin, moves one gridline to the right and 3 gridlines up to the point with the coordinates 5, zero point seven five, moves horizontally 3 gridlines to the right to the point with the coordinates 20, zero point seven five, and then slants 2 gridlines to the right and 3 gridlines down to end at the point on the horizontal axis with the coordinates 30, zero. E. The graph starts from the origin, moves 2 gridlines to the right and 2 gridlines up to the point with the coordinates 10, zero point five zero, moves horizontally 2 gridlines to the right to the point with the coordinates 20, zero point five zero, and then slants 2 gridlines to the right and 2 gridlines down to end at the point on the horizontal axis with the coordinates 30, zero.

Correct Answer: A Option (A) is correct. If Craig walks at a rate of 3 miles per hour, he travels 1 mile in 20 minutes (13 hour) and therefore travels the distance to the bank (0.5 miles) in 10 minutes. If Craig stays at the bank for 15 minutes, his distance does not change from 10 minutes to 25 minutes. If Craig jogs at a rate of 6 miles per hour, he jogs 1 mile in 10 minutes and therefore jogs the 0.5 mile distance home in the last 5 minutes. None of the other graphs correctly demonstrates each part of Craig's trip.

Answer the question below by clicking on the correct response. Question: Which of the following scatterplots most strongly suggests a negative linear relationship between x and y? A. All five answer choices are the scatter plots in the xy-plane, where the horizontal axis is labeled x, the vertical axis is labeled y, and the origin is labeled O. The number 10 appears on the x-axis as well as on the y-axis. Each of the scatter plots consists of about 17 data points except answer choice E that has only 7 data points, where the data points are clustered in a certain pattern. The description in each answer choice describes each pattern; The cluster is in quadrant one. It starts in the upper-left corner, goes downward and to the right, and ends in the lower-right corner. B. The cluster is in quadrant one and quadrant two. It starts in the upper-left corner in quadrant two, goes downward and to the right crossing the y-axis, and then goes upward and to the right, and extend towards the upper-right corner in quadrant one. C. The cluster is in quadrant one and quadrant two. It starts in quadrant two near the origin, goes steeply upward and to the right crossing the y-axis, and then goes down and to the right, and extend towards the lower-right corner in quadrant one. D. The cluster is in quadrant two. It starts in the lower-left corner, goes upward and to the right, and stops in the upper-right corner next to the y-axis. E. The cluster is in quadrant one. It falls on a horizontal line.

Correct Answer: A Option (A) is correct. Reading the graph from left to right shows that as the values of x increase the corresponding values of y decrease. If a line of best fit is drawn, the line would show a trend of points going down as you move to the right, which infers a negative slope. A negative slope means a negative correlation. Therefore, there is a strong negative correlation because the points are very close to the line of best fit.

Answer the question below by clicking on the correct response. The figure shows the graph of Line L in the xy-plane, where the horizontal axis is labled x, the vertical axis is labled y, and the origin is labeled O. The numbers 15 and 30 appear on the x-axis, and the numbers 20 and 40 appear on the y-axis. Line L starts at the orgin and passes through two points, one with the coordinates 15, 20, and another with the coordinates 30, 40. Question: The graph of line ℓℓ is shown in the xy-plane above. The point on line ℓℓ that has x-coordinate 75 is not shown. What is the y-coordinate of that point? A. 100 B. 95 C. 75 D. 70 E. 65

Correct Answer: A Option (A) is correct. The change in the y-value was 20 when the x-value changed from 0 to 15, and from 15 to 30. For every change in 15 for the x-value of a coordinate, the y-value of the coordinate will change by 20. When x changes from 0 to 75, it would have five increases of 15, so the y-value also must have five increases of 20, or a change of 100.

Answer the question below by clicking on the correct response. Question: A bag contains a number of solid-colored marbles, of which 6 are red, 7 are blue, and the rest are yellow. If a person were to draw a marble at random from the bag, the probability that the marble drawn would be red is 14 . How many yellow marbles are in the bag? A. 11 B. 12 C. 13 D. 14 E. 15

Correct Answer: A Option (A) is correct. The probability of drawing a red marble is 14 and there are 6 red marbles in the bag, which means that there are a total of 24 marbles in the bag, since 624=14. There are 6 red and 7 blue marbles in the bag, hence 24−6−7=11, so there must be 11 yellow marbles in the bag.

Answer the question below by clicking on the correct response. Question: The ratio of the number of adults to the number of children on a certain bus tour was 4 to 22. If the total number of passengers on the bus tour was 91, how many adults were on the tour? A. 14 B. 48 C. 65 D. 69 E. 77

Correct Answer: A Option (A) is correct. The ratio of 4 to 22 can also be expressed as 2 to 11, or 2x to 11x, where 2x represents the number of adults and 11x represents the number of children. Since the total number of adults and children is 2x+11x=91, solving the equation yields x=7, and the number of adults is 2(7)=14.

Click on your choices. 14,98,2312,k,π14,98,2312,k,π Question: The five numbers shown above are listed in order from least to greatest. Which of the following could be the value of k ? Indicate all such values. A.2 B.516516 C.238238 D.7‾√7 E.17‾‾‾√

Correct Answer: A, C, D The correct answers are (A), (C), and (D). This problem can be answered using estimation. The value of k lies between 2312 (a number slightly less than 2 ) and π (a number slightly more than 3). Since 516<1 and 17‾‾‾√>4, they can be eliminated easily. The other three choices are greater than or equal to 2 and less than 3, which are in the necessary interval.

Answer the question below by clicking on the correct response. 4r+10b4r+10b Question: The expression above represents the total amount, in dollars, earned by selling r rolls of gift wrap and b boxes of greeting cards. A freshman class earned a total of $958 by selling both gift wrap and greeting cards. The amount earned by selling the greeting cards is what fraction of the total amount earned? A. b958b958 B. 10b95810b958 C. r958r958 D. 4r9584r958 E. 4r+10b958

Correct Answer: B Option (B) is correct. A freshman class earned a total of $958 selling gift wrap and greeting cards. Using the expression given, r rolls plus b boxes of greeting cards equals total dollars earned. 4r+10b=958 The amount earned by selling the greeting cards is: greeting cardstotal $ earned=10b958.

Answer the question below by clicking on the correct response. Question: On a certain day, the temperature was 37°F37°F at 10 A.M. and 52°F52°F at 3 P.M. If the temperature rose at a constant rate from 10 A.M. to 3 P.M. on that day, what was the temperature at noon? A. 42°F42°F B. 43°F43°F C. 44°F44°F D. 45°F45°F E. 46°F46°F

Correct Answer: B Option (B) is correct. On a certain day, the temperature at 10 A.M was 37° F and at 3 P.M. was 52° F. Since the temperature throughout the 5-hour time period increased at a constant rate, each hour, the temperature increased the same amount. 52−375=155=3 gives the amount in which the temperature increased each hour. The table below shows the time and corresponding temperature each hour. Time Temperature (degrees F) 10 A.M. 37° 11 A.M. 40° 12 noon 43° 1 P.M. 46° 2 P.M. 49° 3 P.M. 52° At noon, the temperature was 43° F.

Answer the question below by clicking on the correct response. Robert sets up a conversion as follows: 4miles×5,280feet1mile×12inches1foot4miles×5,280feet1mile×12inches1foot Question: Which of the following conversions is he performing? A. Miles to feet B. Miles to inches C. Feet to miles D. Inches to miles E. Inches to feet

Correct Answer: B Option (B) is correct. Robert begins his conversion with 4 miles. He converted 4 miles into an equivalent number of feet by multiplying 4 by the number of feet that are in 1 mile. He then converted the number of feet in 4 miles into an equivalent number of inches by multiplying the number of feet by the number of inches that are in 1 foot. Therefore, Robert converted miles to inches.

Answer the question below by clicking on the correct response. Question: If the speed of light is 1,080,000,000 kilometers per hour, how far does light travel in 100 hours? A. 1.08×1091.08×109 kilometers B. 1.08×10111.08×1011 kilometers C. 1.08×10131.08×1013 kilometers D. 10.8×101410.8×1014 kilometers E. 108×1015108×1015 kilometers

Correct Answer: B Option (B) is correct. The number 1,080,000,000 can be written in scientific notation as 1.08×109. Multiplying any number by 100 would have the same effect as adding two zeros to the number, thus increasing the exponent by 2, so light travels 1.08×1011 km in 100 hours.

Answer the question below by clicking on the correct response. Question: The total cost, t, in dollars, for c children to attend a camp is estimated by the equation t=650c+5,600t=650c+5,600. If $20,000 is available to pay for children to attend the camp what is the greatest number of children that can attend the camp? A. 21 B. 22 C. 23 D. 24 E. 25

Correct Answer: B Option (B) is correct. Using the equation, the total cost t for c children to attend a camp is given by t = 650c + 5,600, where the total cost is a maximum of $20,000 available to pay for a certain number of children to attend camp. t = 650c + 5,600 20,000 = 650c + 5,600 14,400 = 650c 14,400650=c c ≈ 22.15 Although there is a remainder, c represents the number of children. Since you cannot have a part of a person, 22 is the greatest number of children that can attend the camp using $20,000.

Answer the question below by clicking on the correct response. The figure is a pie chart titled Distribution of Coins Owned by Four Collectors Before Trading. The pie chart is divided into four sections labeled, starting from the upper-left corner in clockwise, Cristina 34%; Greg 14%; Lisa 24%, and Jon 28%. Question: Cristina, Greg, Lisa, and Jon are coin collectors, and together they have a total of 2,250 coins. They decided to meet and trade coins. The pie chart above shows the distribution of the 2,250 coins before trading. At the end of trading, Cristina has 32 percent, Lisa has 22 percent, and Jon has 26 percent of the total number of coins owned by the four collectors. How many more coins does Greg have at the end of trading than he had before the trading began? A. 115 B. 120 C. 135 D. 140 E. 145

Correct Answer: C Option (C) is correct. Before trading coins, Greg had 14% of the 2,250 coins, or he had 0.14(2,250) = 315 coins. After trading, the combined percentages of coins owned by Cristina, Lisa, and Jon are 32% + 22% + 26% = 80%. So, Greg must have 100% - 80% = 20%, or Greg now has 20% of all of the 2,250 coins. After trading Greg has 0.20(2,250) = 450 coins. To figure how many coins more he had after trading than before, subtract 450 - 315 = 135, or Greg has 135 more coins after trading.

Answer the question below by clicking on the correct response. Question: Which of the following dot plots represents a distribution of nine values of x in which the mean of the distribution is greater than the median of the distribution? A. All five answer choices are number lines. In each answer choice, the number line is labeled x and the numbers one, two, three, four, and five appear along the number line. There are dots placed above some of the numbers for each answer choice; There is one dot above the number one, two dots above the number two, three dots above the number three, two dots above the number four, and one dot above the number five. B. There are two dots above the number one, one dot above the number two, three dots above the number three, two dots above the number four, and one dot above the number five. C. There is one dot above the number one, two dots above the number two, three dots above the number three, one dot above the number four, and two dots above the number five. D. There is one dot above the number one, three dots above the number two, three dots above the number three, one dot above the number four, and one dot above the number five. E. There are no dots above the number one, three dots above the number two, three dots above the number three, three dots above the number four, and no dots above the number five.

Correct Answer: C Option (C) is correct. Each of the dot plots has a median of 3. By observation, the mean of options (A) and (E) are 3, and the mean of options (B) and (D) are both less than 3. The mean of option (C), or any of the options, can be found rigorously by first finding the sum of the 9 values in the dot plot, for option (C), sum = 1 + 2 + 2 + 3 + 3 + 3 + 4 + 5 + 5 = 28, then dividing the sum by 9, so 289=319.

Answer the question below by clicking on the correct response. The figure shows a circle on an xy-coordinate plane with origin O. The circle has center O and intersects the positive x-axis between two point two units and two point four units. Question: Which of the following best approximates the area of the circle shown in the graph above? A. 8 B. 13 C. 18 D. 23 E. 28

Correct Answer: C Option (C) is correct. From the xy-plane in which the circle is graphed, it can be concluded that the radius is approximately 2.4. The formula for the area of a circle is A=πr2, where A is the area, r is the radius, and π is approximately 3.14. If 2.4 is substituted into the formula for the radius and 3.14 for π, A=(2.4)2(3.14)=18.0864.

Answer the question below by clicking on the correct response. Question: Which of the following sequence of steps, when completed, will solve the equation −6+3y=1−6+3y=1 for y ? A. Subtract 1 from both sides of the equation, then divide both sides of the new equation by −6−6. B. Subtract 1 from both sides of the equation, then divide both sides by 6. C. Add 6 to both sides of the equation, then divide both sides by 3. D. Add 6 to both sides, then subtract 3 from both sides. E. Divide both sides of the equation by 3, then subtract 6 from both sides.

Correct Answer: C Option (C) is correct. None of the other sequences would result in a correct solution.

Answer the question below by clicking on the correct response. The figure shows a number line. The numbers negative two, negative one, zero, one, and two are labeled on the number line. There are three equally spaced tick marks between each two consecutive numbers. There are seven points labeled with letters on the number line. From left to right: Point P is located one tick mark to the right of negative two; Point A is located one tick mark to the right of negative one; Point Q is located two tick marks to the right of negative one and one tick mark to the right of point A; Point B is located two tick marks to the right of zero; Point C is located three tick marks to the right of zero, one tick mark to the right of point B, and one tick mark to the left of 1; Point D is located one tick mark to the right of one; Point E is located three tick marks to the right of one, two tick marks to the right of point D, and one tick mark to the left of 2. Question: The number line above shows 7 points, each of them labeled with a letter of the alphabet. The product of the coordinate of point P and the coordinate of point Q is closest to the coordinate of which of the following points? A. A B. B C. C D. D E. E

Correct Answer: C Option (C) is correct. Point P is -1.75 on the number line and point Q is -0.50 on the number line. The product of these is (−1.75)(-0.50)=0.875. This would be slightly to the right of point C which is at 0.75, thus making it the closest point to the result.

Answer the question below by clicking on the correct response. The figure shows a triangle ABC in the xy-plane, where the horizontal axis is labeled x, the vertical axis is labeled y. There are horizontal gridlines indicating units on the x-axis and vertical gridlines indicating units on the y-axis. Vertex A is three units to the left of the y-axis and one unit above the x-axis; vertex B is one unit to the left of the y-axis and three units above the x-axis; vertex C is one unit to the left of the y-axis and one unit above the x-axis.Triangle ABC in the xy-plane above will be translated 3 units to the right and then 2 units down. What point will correspond to vertex A after these translations? A. (−1, −1)(−1, −1) B. (−1, 0)(−1, 0) C. (0, 0)(0, 0) D. (0, −1)(0, −1) E. (1, 1)

Correct Answer: D Option (D) is correct. A horizontal translation changes the x-coordinate, and a vertical translation changes the y-coordinate. Translating 3 units to the right adds 3 to the x-coordinate. Translating 2 units down subtracts 2 from the y-coordinate. Since the coordinates of vertex A are (−3, 1), the coordinates corresponding to vertex A after translation are (−3 + 3, 1 − 2), or (0, −1).

Answer the question below by clicking on the correct response. Question: Last year 45 percent of the total number of complaints made to a telephone company were about billing errors. In which of the following circle graphs does the shaded area represent the fraction of the total number of complaints made that were about billing errors last year? A. The graph has one-quarter of the circular region shaded. B. The graph has approximately one-third of the circular region shaded. C. The graph has three-quarters of the circular region shaded. D. The graph has slightly less than half of the circular region shaded. E. The graph has slightly more than half of the circular region shaded.

Correct Answer: D Option (D) is correct. Because 45 percent of a circle can be calculated by multiplying (.45)(360)=162, the correct answer is represented by a graph that is 18 degrees less than a semicircle (180 degrees). The answer can also be determined by estimation, since 45 percent is slightly less than half (50 percent), only (D) is sufficiently close to half of the circle.

Answer the question below by clicking on the correct response. Question: A landscaping service needs to apply fertilizer to 5 lawns, each having an area of 7,800 square feet. One bag of fertilizer covers 2,500 square feet. What is the least number of bags of fertilizer that must be used? A. 13 B. 14 C. 15 D. 16 E. 17

Correct Answer: D Option (D) is correct. Each lawn the landscaper must fertilize has an area of 7,800 square feet. Since there are 5 lawns, the landscaper must have enough fertilizer to cover 7,800⋅5=39,000 square feet of lawn. Each bag of fertilizer covers 2,500 square feet of lawn. To find the number of bags needed, divide the total area of lawns by 2,500 square feet. 39,0002,500=15.6 Since 15.6 is not enough to cover all the lawns, the number of bags must be rounded up. Therefore, the total number of bags needed to cover the 5 lawns is 16 bags.

Answer the question below by clicking on the correct response. Question: A large wheel has a diameter of 30 inches, and a small wheel has a diameter of 20 inches. How many revolutions does the small wheel need to make to travel the same distance that the large wheel travels in 240 revolutions? A. 160 B. 240 C. 320 D. 360 E. 420

Correct Answer: D Option (D) is correct. For each revolution of either wheel, the distance that the wheel would travel is equal to the wheel's circumference, which can be found using either C=2πr or C=πd, where C is the circumference, r is the radius, and d is the diameter. Since we are given the diameter, the latter will be used. The larger wheel travels a total distance of 240 times the circumference of the larger wheel which is 240(30π)=7,200π. The smaller wheel has a circumference of 20π. To figure how many revolutions the smaller wheel would need to go so that it would travel the same distance of 7,200π that the larger wheel travelled, 7,200π20π=360. Or, the smaller wheel would need to make 360 revolutions to travel the same distance that the larger wheel could travel in 240 revolutions.

Answer the question below by clicking on the correct response. The figure shows a rectangle with the vertical length labeled 7 feet and the horizontal width labeled 5 feet. A diagonal of the rectangle extends from the upper left corner to the lower right corner. The remaining two corners have a right angle symbol. Question: A carpenter wants to build a diagonal brace for a rectangular gate that is 5 feet wide and 7 feet high, as shown in the figure. Approximately what is the length, in feet, of the diagonal brace? A. 5.5 B. 6.5 C. 7.5 D. 8.5 E. 9.5

Correct Answer: D Option (D) is correct. Since the gate shown is rectangular, the unknown length of the diagonal brace can be found using the Pythagorean theorem. a2+b2=c2, where a = 7 feet, b = 5 feet, and c is the length of the diagonal brace. 72+52=c2 49+25=c2 74=c2 74‾‾‾√=c c≈8.6 feet

Answer the question below by clicking on the correct response. 1.4, 1.8, 2.2, 2.0, 1.0, 1.9, 1.2, 2.1, 1.7 Question: What is the median of the numbers in the list above? A. 1.2 B. 1.4 C. 1.7 D. 1.8 E. 1.9

Correct Answer: D Option (D) is correct. The median of an ordered set of data is the number positioned where there are an equal number less than the number and greater than the number (that is, the number in the "middle"). Rearranging the nine numbers from least to greatest, the list becomes 1.0, 1.2, 1.4, 1.7, 1.8, 1.9, 2.0, 2.1, 2.2, where 1.8 is the fifth (middle) number in the list.

Answer the question below by clicking on the correct response. Question: The price of a coat was reduced from $90 to $72 at the end of the season. By what percent was the price of the coat reduced? A. 8% B. 10% C. 18% D. 20% E. 25%

Correct Answer: D Option (D) is correct. The original price of the coat was $90, and the sale price was $72, so the amount of the discount would be 90−72=18. Amount of Discount = Original Price × Percent Discount, which gives 18=90x, or x=1890=0.20=20%.

Answer the question below by clicking on the correct response. Question: Of the 25 fish in a tropical fish tank, 10 are guppies, 4 are swordtails, and the rest are tetras. One fish is to be randomly selected from the fish tank. What is the probability that the fish selected will not be a guppy? A. 2525 B. 11251125 C. 14251425 D. 3535 E. 2125

Correct Answer: D Option (D) is correct. The required probability is given by: number of fish that are not guppiestotal number of fish . Since there are 10 guppies out of the 25 fish, 15 are not guppies, and the probability is 1525=35 .

Answer the question below by clicking on the correct response. Question: Jermaine promised to donate a total of z dollars to a charity by donating x dollars immediately and then donating a fixed constant amount of dollars each month for m months. Which of the following expressions represents the fixed constant amount of dollars Jermaine promised to donate each month? A. z−xmz−xm B. z−mxz−mx C. zx−mzx−m D. z−xmz−xm E. zm−x

Correct Answer: D Option (D) is correct. The total amount that Jermaine promised to donate is z dollars. He will donate x dollars immediately and a fixed amount monthly over m months. The amount he will have left to pay after donating x dollars can be expressed as z−x. This amount is to be spread out over m months, so each month Jermaine would owe z−xm dollars to the charity.

Answer the question below by clicking on the correct response. The figure shows an arch that consists of 5 nearly congruent stones laid end-to-end with no space between them. Each of the 5 stones is in the shape of a right prism with trapezoid bases. The thickness of each prism is 3 feet, each of the trapezoidal bases of each prism has lengths 10 feet and 14 feet, and the height of each trapezoid is 12 feet. Question: The arch above is constructed of 5 nearly congruent stones, each of which is in the shape of a right prism with trapezoid bases. Based on the approximate measurements provided, which of the following best approximates the volume of the entire arch? (The area of a trapezoid with bases b1b1 and b2b2 and height h is 12(b1+b2)h12(b1+b2)h.) A. 900 cubic feet B. 1,050 cubic feet C. 1,140 cubic feet D. 2,160 cubic feet E. 4,320 cubic feet

Correct Answer: D Option (D) is correct. The volume of a right trapezoidal prism is equal to the height of the prism times the base area of the trapezoid, and is given by the formula V=12(b1+b2)⋅h⋅l, where b1 and b2 are the trapezoid bases, h = the height of the trapezoid, and l = the height of the prism. By substituting the values given: V=12(b1+b2)⋅h⋅l V=12(14+10)⋅12⋅3 V= 432 One trapezoidal stone is 432 cubic feet. Since there are 5 nearly congruent stones, 432⋅5=2,160. Therefore, the entire arch is approximately 2,160 cubic feet.

Answer the question below by clicking on the correct response. Question: A principal of a certain high school wants to ask a sample of students how they feel about a new school policy that will drop football as a varsity sport. Which of the following methods of selecting the sample will yield the most valid information about the feelings of all the students at the school? A. Interviewing twelfth-grade students on campus at random as they change classes B. Selecting a random sample of current football players C. Choosing two students at random from each science class on a given day D. Sending a questionnaire to all students currently enrolled and using the returned questionnaires as the sample E. Selecting a random sample from a list of all students currently enrolled at the school

Correct Answer: E Option (E) is correct. A list of students currently enrolled gives a population where the group of students fit a particular description or set of conditions. Since the principal wants to ask a sample of students, a random sample where each member of this population has an equal chance of being included will give the principal an idea of what the entire population might look like.

Answer the question below by clicking on the correct response. The figure shows a line in the xy-plane, where the horizontal axis is labeled x and the vertical axis is labeled y, and the origin has the coordinates (zero, zero). The numbers zero to 36 , in increments of 6, appear along the x-axis, and the numbers from zero to 45, in increments of 5, appear along the y-axis. There are horizontal gridlines and vertical gridlines at those numbers. The line starts at a point between 5 and 10 on the y-axis and passes through a point with the coordinates (30, 45). Of the points the line passes through on the gridlines, two have the coordinates (6, 15) and (18, 30). All five answer choices are 2-column tables. The first column is labeled x and the second column is labeled y. There are 4 pairs of values for x and y in each answer choice. Question: The graph of a linear equation is shown in the xy-plane above. Which of the following tables of values corresponds to the graph? A. Pair 1: x equals 6, and y equals 10; Pair 2: x equals 12, and y equals 22; Pair 3: x equals 18, and y equals 34; Pair 4: x equals 24, and y equals 46 B. Pair 1: x equals 6, and y equals 18.5; Pair 2: x equals 12, and y equals 28; Pair 3: x equals 18, and y equals 37.5; Pair 4: x equals 24, and y equals 47 C. Pair 1: x equals 6, and y equals 15; Pair 2: x equals 12, and y equals 24; Pair 3: x equals 18, and y equals 36; Pair 4: x equals 24, and y equals 45 D. Pair 1: x equals 0, and y equals 10; Pair 2: x equals 6, and y equals 15; Pair 3: x equals 12, and y equals 27; Pair 4: x equals 18, and y equals 39 E. Pair 1: x equals 6, and y equals 15; Pair 2: x equals 12, and y equals 22.5; Pair 3: x equals 18, and y equals 30; Pair 4: x equals 24, and y equals 37.5

Correct Answer: E Option (E) is correct. According to the graph, the following (x,y) points can be found on the line: (6,15),(18,30), and (30,45). In (E), two of those three points are found in the table. To ensure the rest of the coordinate points are found on the line, use the graph to check that the rest of the points lie on the line.

Answer the question below by clicking on the correct response. The figure is a bar graph with 5 bars. The horizontal axis is labeled Number of Errors, and the vertical axis is labeled Number of Business Letters. The 5 vertical bars are labeled from left to right, zero, one, 2, 3, and 4 or more on the horizontal axis, and the height of each bar represents the number of business letters. The numbers from zero to 30, in increments of 3, appear along the vertical axis, and there are horizontal gridlines at those numbers. According to the bar graph, the numbers of business letters with errors zero to 4 or more are as follows: Zero error, 27 letters; 1 error, 15 letters; 2 errors, 6 letters; 3 errors, 3 letters; 4 or more errors, 3 letters Question: A total of 54 business letters at a certain company were inspected for errors. The graph above shows the number of letters with either 0, 1, 2, 3, or 4 or more errors. How many of the 54 letters contained at most 2 errors? A. 6 B. 12 C. 24 D. 42 E. 48

Correct Answer: E Option (E) is correct. According to the graph, the three columns with 0, 1, and 2 errors are the only letters that need to be considered of the 54 business letters. There are 27 letters with 0 errors, 15 letters with 1 error, and 6 letters with 2 errors. 27+15+6=48 In total, 48 letters contain at most 2 errors.

Answer the question below by clicking on the correct response. Question: If x+z=15x+z=15 and w+y=10w+y=10, what is the value of (3w+3y)(2x+2z)(3w+3y)(2x+2z) ? A. 150 B. 300 C. 450 D. 600 E. 900

Correct Answer: E Option (E) is correct. In the expression (3w+3y)(2x+2z), a factor of 3 can be factored from the first parenthetical and a factor of 2 can be factored from the second parenthetical. 3(w+y)⋅2(x+z) The values of x+z and w+y can be substituted so that: 3(w+y)⋅2(x+z)=3(10)⋅2(15)=30⋅30=900.

Answer the question below by clicking on the correct response. Question: If 17x−2=117x−2=1, then x=x= A. -7 B. 3 C. 9 D. 15 E. 21

Correct Answer: E Option (E) is correct. Solve this equation by first adding 2 to both sides, resulting in an equivalent equation 17x=3. Multiplying both sides of this equation by 7 yields 7(17x)=7(3) or x=21.

Answer the question below by clicking on the correct response. Question: The median and range of 15 measurements are 18 and 5, respectively. If 3 is subtracted from each of the 15 measurements, which of the following statements regarding the median and range of the modified 15 measurements must be true? A. The median and range will both decrease. B. The median and range will both stay the same. C. The median will stay the same, but the range will decrease. D. The median will stay the same, but the range will increase. E. The median will decrease, but the range will stay the same.

Correct Answer: E Option (E) is correct. The given median is 18 and the range is 5 for a set of measurements. If each number were to be reduced by 3, and since the median is a member of the set, it too would be reduced by 3. So the new median would be 15. The range is the largest number in the set minus the smallest number in the set. If the range was 5 before subtracting 3 from each member of the set, the range should still be 5 for the new set of numbers. The difference would be the same, hence the range is still 5.

Answer the question below by clicking on the correct response. The figure shows a right triangle ABC. The length of horizontal side AC is 12, the length of vertical side BC is 5, and there is a right angle symbol at angle C. Question: Which of the following statements is true about right triangle ABC above? A. The measure of angle A is 45°45°. B. The sum of the measures of angle A and angle B is 70°70°. C. The area of the triangle is 6060. D. The length of side AB is 1717. E. The perimeter of the triangle is 3030.

Correct Answer: E Option (E) is correct. The triangle shown is a right triangle with sides of length 5 and 12. This is recognized as a 5 - 12 - 13 right triangle. Or, the Pythagorean theorem could be used to find the length of the missing side. The Pythagorean theorem is c2=a2+b2, where c is the length of the hypotenuse (the side opposite the 90° angle) and sides a and b are the lengths of the other two sides. c2=(5)2+(12)2=25+144=169. Then, c2‾‾√=169‾‾‾‾√, or c = 13. The perimeter would be 12 + 5 + 13, or 30. None of the other options are true.

Answer the question below by clicking on the correct response. Question: Which of the following is equivalent to x2+y3x2+y3 ? A. x+y5x+y5 B. x+y6x+y6 C. 3x+2y3x+2y D. 3x+2y53x+2y5 E. 3x+2y6

Correct Answer: E Option (E) is correct. To add fractions they must have a common denominator. The least common denominator for 2 and 3 is 6. Each fraction can be written in an equivalent form with the common denominator of 6 thus, x(3)2(3)=3x6 and y(2)3(2)=2y6. Adding the two equivalent forms of the fraction gives 3x6+2y6=3x+2y6.

Answer the question below by clicking on the correct response. 12.1, 12.3, 11.9, 11.6, 11.2, 11.4, 11.1, 11.3, 11.2 Question: Marcy ran the 100-meter dash 9 times in competitions during the spring. Her times, in seconds, are listed above. What is the range of Marcy's times, in seconds? A. 0.8 B. 0.9 C. 1.0 D. 1.1 E. 1.2

Correct Answer: E Option (E) is correct. To find the range of Marcy's times, one strategy is to list Marcy's nine 100-meter dash times from least to greatest to easily find the fastest and slowest times she ran. Her times are as follows: 11.1, 11.2, 11.2, 11.3, 11.4, 11.6, 11.9, 12.1, and 12.3. Her slowest time was 12.3 seconds and her fastest time was 11.1 seconds. To find the range, find the difference between the fastest time ran and the slowest time ran within the data set. Therefore, 12.3−11.1=1.2 seconds.