PRAXIS MATH (practice 2)
The formula V = IR relates the voltage V, in volts, to the current I, in amps, and the resistance R, in ohms, in a circuit. What is the current produced by a 9-volt battery in a circuit with 4 ohms of resistance? A. 1.50 amps B. 2.00 amps C. 2.25 amps D. 2.50 amps
(C) The question requires an understanding of how to use formulas to determine unknown quantities. Since V = 9 volts and R = ohms, I = V/R = 9/4 = 2.25 amps.
What is the prime factorization of 180? A. 3^2 x 4 x 5 B. 2^2 x 5 x 9 C. 2^2 x 3^3 x 5 D. 2 x 3^2 x 10
(C) The question requires an understanding of how to identify prime and composite numbers. Since 180 = 2 x 90 = 2 x 2 x 45 = 2 x 2 x 3 x 15 = 2 x 2 x 3 x 3 x 5, the prime factorization of 180 = 2^2 x 3^2 x 5.
(2x + 5x -2) - (x + y - 3y - 5x + 2) Which of the following is equivalent to the expression shown? A. 11x + 2y - 4 B. 3x - 2y - 4 C. 11x - 2y
(A) The question requires an understanding of how to add and subtract linear algebraic expressions. Adding like terms in the given expression yields the equivalent expression (7x - 2) - (-4x - 2y + 2), which is equivalent to 7x - 2 + 4x + 2y - 2. Adding like terms again yields 11x + 2y - 4
(2a - a + 3) - (-5a + 6a + 2) Which of the following is equivalent to the expression shown? A. 1 B. 5 C.3
(A) The question requires an understanding of how to add and subtract linear algebraic expressions. In fact, (2a - a + 3) -( -5a + 6a + 2) = a + 3 - (a + 2) = a + 3 - a - 2 = 1.
Tony made 1,500 mil of lemonade for a party. Which of the following represents the amount of lemonade in, in lit, that Tony made? A. 1.5 B. 15 C. 150 D. 15,000
(A) The question requires an understanding of how to convert units within the metric system. Since 1 l is equivalent to 1,000 ml, it follows that 1 ml is equivalent to 0.001 l. Therefore, 1,500 ml are equivalent to 1,500 x 0.001, or 1.5 l.
A salesperson records data consisting of total sales each day for one year. In the least and greatest total sales values are deleted from the data set, which of the following is most likely true about the effect of the deletion? A. The range and mean of the data set will change, but not the median B. The range and median of the data set will change, but not the mean C. The median and mean of the data set will change, but not the range D. The mean, median, and range of the data set will all change
(A) The question requires an understanding of how to determine how changes in data affect measures of center or range. The range is the difference between the greatest and the least values. Removing the greatest and least values will decrease the range. The mean is the sum of the daily values divided by the number of days. Removing the greatest and the lest values will likely affect the mean by shifting it toward the value of the two that was closer to the mean before the removal. The median is the value of the data point that is in the middle when the values in the data set are arranged in numerical order. Since the least value is at the left of the meridian and the greatest value is at the right of the median, removing those values will not affect the median.
Which of the following addition sentences represents the model shown? A. -5 + 1 = -4 B. -3 + (-1) = -4 C. 5 + (-1) = 4 D. 6 + (-2) = 4
(A) The question requires an understanding of how to represent rational numbers and their operations in different ways. The first box shows 5 counters with a minus sign and 1 counter with a plus sign; that is, -5 + 1. The middle box shows that -5 +1 is equivalent to -4 +(-1 + 1) and that -1 + 1 can be removed as it is equivalent to 0. The last box shows that -4 + 0 is equivalent to -4.
The surface area of a cube is 54 in^2. What is the volume of the cube? A. 27 in^3 B. 54 in^3 C. 81 in^3 D. 108 in^3
(A) The question requires an understanding of how to solve problems involving elapsed time, money, length, volume, and mass. If the length of the side of the cute is in s in, then its surface area is 6s^2 in^2. Since the surface area is 54 in^2, then the length of the side of the cube, in inches, can be found by solving the equation 6s^2 = 54, which yields s = 3. The volume of the cube can then be found by solving the equation v = s^3, thus v =3^3. Therefore the volume is 27 in^3
1 - 2 5/6 What is the value of the expression shown? A. -1 5/6 B. -1/6 C. 1/6 D. 6/1
(A) The question requires an understanding of various strategies and algorithms used to perform operations on rational numbers. The given expression is equivalent to 6/6 - 17/ 6 = -11/6, or -1 5/6
In the xy-plane, point A has coordinates (2, 1) and the point B has coordinates (5,1). Which of the one following could be the coordinates for point C so that the area of triangle ABC is equal to 9 sq units? A. (5,7) B. (5,4) C. (5,2) D. (5,1)
(A) The question requires an understanding of how to solve problems by plotting points and drawing polygons in the coordinate plane. The formula for the area of a triangle is A = 1/2 x b x h where b is the length of a side of the triangle that is used as the base and h is the length of the height relative to the side chosen as a base. Since the coordinates of points a and b are given and the segment ab is parallel to the x-axis, the length of side ab can be easily computed, making ab the best choice for the base of the triangle. The length of segment ab is (5 - 2), or 3 units. Substituting the value of 9 for a and the value of 3 for b the formula yields 9 = 1/2 x 3 x h, that is, h = 6. Therefore, the length of the height of the triangle relative to side ab must be 6. Since ab is parallel to the x-axis, point c must be on the line with equation 7 = 7 or on the line with the equation y = -5; that is, it must have a y- coordinate of either 7, or -5.
The population of a certain city was 50,000 people. One year later, the population of the same city grew to 50,600. What was the percent increase in the city's population in that one year period? A. 0.6% B. 1.2% C. 6% D. 12%
(B) The question requires an understanding of computing percent increase. The increase in the population of the city is 50,600 - 50,000 = 600 people. The value of the fraction 600/50,000 gives the percent increase based on the population before the increase occurred. The fraction is equivalent to the decimal 0.012, which is equivalent to 1.2 percent. (convert decimal to percent move decimal point two places to the right)
At a yard sale. Tensile sold drinking glasses for $2.00 each and plates for $3.50 each. Nicholas spent a total of $18.00 on drinking glasses and plates at Tenille's yard sale. If Nicholas bought at least one glass and one plate, how many drinking glasses did he buy? A. 1 B. 2 C. 3 D. 4
(B) The question requires an understanding of equations and the ability to translate a word problem into an equation. If x represents the number of glasses and y represents the number of plates that Nicholas bought, then 2x + 3.5y = 18. Both x and y must be integers. Therefore 18 - 2x must be a multiple of 3.5. The possible multiples of 3.5 for this problem are 3.5, 7, 10.5, 14 and 17.5. The only multiple of 3.5 that is equivalent to 18 - 2x as an integer is 14. Thus x = 2 (x = drinking glasses, y = number of plates...2x + 3.5y = 18)
In a certain year, 5 percent of the 2,800 employees of a company had a perfect attendance record. Which of the following computations can be used to determine the number of employees with a perfect attendance record? A. 1/40 x 2,800 B. 1/20 x 2,800 C. 1/5 x 2,800
(B) The question requires an understanding of fractions, percentages, and decimals and the ability to recognize equivalence among them. Since 5 percent means 5-one-hundredths, 5 percent is equivalent to 0.05 or 5 divided by 100, 5/100, which simplifies to 1/20. To find 5 percent of 2,800 employees, multiply 2,800 by 0.05 or 1/20.
Which list of numbers is ordered from least to greatest? A. 9/25, 0.35, 2/5, 0.35 (line over number) B. 0.35, 0.35 (line over number), 9/25, 2/5 C. 2/5, 9/25, 0.35, 0.35 (line over number)
(B) The question requires an understanding of how to compare and order rational numbers. One way to compare the four numbers is by finding the decimal equivalent of the fractions. The fraction 9/25 is equivalent to 0.36, the fraction 2/5 is equivalent to 0.4. The decimal number 0.35 (line over number) is equivalent to 0.353536..., where the digits 35 repeat indefinitely. Therefore the order from least to greatest is (B).
Lilly, Madelyn, Natalie, and Olivia each walked from their houses to the mall. Lilly walked 1/ 4 mile, Madelyn walked 3/ 8 mile, Natalie walked 5/ 6 mile, and Olivia walked 7/ 12 mile. Which list shows these distances in order from least to greatest? A. 1/ 4, 3/ 8, 5/ 6, 7/ 12 B. 1/ 4, 3/ 8, 7/ 12, 5/ 6
(B) The question requires an understanding of how to compare, classify, and order rational numbers. The distances can be ordered by rewriting all fractions as equivalent fractions with the common denominator 24. Since 1/4 = 6/ 24, 3/ 8 = 9/ 24, 5/ 6 = 20/ 24, and 7/ 12 = 14/ 24, the correct order from least to greatest distance is (B).
What is the least common multiple of 12, 20, and 30? A 2 B. 60 C. 240 D 360
(B) The question requires an understanding of how to find factors and multiples on numbers. The prime factorization of 12 is 2^2 x 3, the prime factorization of 20 is 2^2 x 5, and the prime factorization of 30 is 2 x 3 x 5. Therefore, the least common multiple of the three numbers is 2^2 x 3 x 5 = 60.
9, 11, 1, 4, 7, 12, 10, 4, 9, 2, 5, 9, 8 The list shows the number of books each of the 13 students in a class read over the summer. The teacher wants to summarize the data using the boxplot shown. What is the value of C on this boxplot? A. 7 B. 8 C. 9
(B) The question requires an understanding of how to identify, construct, and complete a boxplot that correctly represents given data. Point C on the boxplot is the median of the data. To find the median, that data points must be reordered from least to greatest, which yields 1, 2, 4, 4, 5, 7, 8, 9, 9, 9, 10, 11, 12. The median is the 7th data point, which is 8.
In the sequence of figures shown, the first term is made of a single square and each successive term is made by adding one cross and one square to the preceding term. To form each square, 4 line segments are needed, and to form each cross, 2 line segments are needed. Which of the following expressions can be used to find the number of line segments needed to form the nth term in the sequence of figures? A. n + 6 B. 6n - 2 C. n^2 + 3n
(B) The question requires an understanding of how to identify, extend, describe, or generate number and shape patterns. The nth figure includes n squares made up of 4 line segments and n-1 crosses made up of 2 line segments. Therefore, the number of line segments required for the nth figure is equal to 4n + 2(n - 1), which simplifies to 6n - 2.
On a major league roster of 25 players, three players have a yearly salary of $15 million each two players have a quarterly salary of $10 million each, and the remaining players have a yearly salary of $1 million each. Which of the following best represents a typical player's yearly salary? A Mean B. Median C. Mode
(B) The question requires an understanding of how to recognize which measure of center best describes a set of data. The median salary is $1 million and represents nearly all (80%) of the player's salaries on the team. The mean is $3.4 million and does not represent a typical yearly salary since the five salaries that are very high cause the mean to be far from the typical player salary. The mode is not unique, and the range is not a measure of center.
A wholesale nut company makes 10-lb and 25-lb bags of trail mix. For the 10-lb bag the company uses 3-lb of raisins, and the rest is nuts. If the proportion of raisins to nuts is the same for the 25-lb bag as in the 10-lb bag, how many pounds of nuts does the company need fo the 25-lb bag? A. 7.5 B. 17.5 C. 18.5 D. 22.0
(B) The question requires an understanding of how to use proportional relationships to solve ratio and percent problems. If 3 lb of raisins are used in the 10-lb moisture, then 7 lb of nuts are used in the mixture, giving a ration of pounds to nuts to pounds of total mixture of 7:10. This is taken from the word problem where it asks how many pounds of nuts. Using x to represent the number of pounds of nuts in the 25-lb mixture. Then 7/10 = x/25, cross multiply and isolate x, x = 17.5
All small rectangles contained in rectangle ABCD shown have the same area. How many of the small rectangles must be shaded so that 38 percent of the area of rectangle ABCD is shaded? A. 12 B. 19 C. 31
(B) The question requires an understanding of percent as a rate per 100. There are 50 congruent small rectangles in ABCD. If 38% of the area of ABCD is shaded, then 38/100 x 50, or 19 small rectangles, must be shaded. (50 is all the rectangles)
A window's size is 8 feet by 4 feet. Which of the following units is most appropriate to use to convert the dimensions to metric units? A. Kilometers B. Meters C. Millimeters D. Nanometers
(B) The question requires an understanding of relative sizes of United States customary units to metric units. Since 1 meter is approximately 3.28 feet, meters are the most appropriate unit to use to convert 8 feet and 4 feet to metric units.
Which of the following is equivalent to 1/4 / 1/8? A. 1/4 x 1/8 B. 1/4 x 8 C. 4 x 1/8 D. 4 x 8
(B) The question requires an understanding of various strategies and algorithms use to perform operations on rational numbers. Dividing a fraction by a fraction is equivalent to multiplying the first fraction by the reciprocal of the second fraction. The reciprocal of 1/8 is 8/1 or 8.
In the coordinate plane shown, which point is located in Quadrant I? A. A B. B C. C D. D
(B) This question requires an understanding of how to identify the x-axis, the y-axis, the origin, and the four quadrants in the coordinate plane. The x-axis and the y-axis intersect at the origin and divide the coordinate plane into four quadrants. Quadrant I is the quadrant above the x-axis and to the right of the y-axis. Point B is the only point that lies within this quadrant.
7, 9, 10, 11, 14, 15, 15, 15, 17, 18, 18, 20, 26, 26, 27, 28, 30 The list shows the times spent eating lunch for the 17 students in Ms. Begay's class. Which of the following statements about the times must be true? A. The mode is 17 min B. The median is 17 min C. The mean is 18 min C. The median is 18 min
(B, C) The question requires an understanding of solving problems involving measures of center (mean, median, and mode) and range. The list is already ordering and contains 17 numbers, so the ninth number, which is 17, is the median since it has 8 numbers above it and 8 below it in the ordered list. The sum of all 17 numbers is 306, and the mean is found by dividing 306 by 17. This yields a men of 18. Hence both options (B, C) are correct. The mode is the value that occurs most frequently in the list, so that is 15, and hence option (A) is incorrect. The range is 30 - 7 = 23, so option (D) is incorrect.
30M + 15R = 900 In a certain year, Rod earned a total of $900 mowing lawns and raking leaves for his neighbors. He received $30 for each lawn he mowed and $15 for each job raking leaves he had. In the formula ab/of M represents the number of lawns Rod mowed for his neighbors and R represents the number of jobs raking leaves he had during the year. If Rod mowed 15 lawns that year, how many jobs raking leaves did he have? A. 15 B. 20 C. 30 D. 90
(C) The question requires an understanding o how to use formulas to determine the unknown quantities. Since Rod mowed 15 lawns, M = 15. Plugging the number into the formula yields 30 x 15 + 15r = 900. Solving for R yields R = 900-450/15. Therefore R = 30. (15 x 30 =450, 450/15 = 30)
Bill went to sleep at 9:57 pm and woke the next morning at 6.28 am. For how many hours and minutes did he sleep? A. 9 hours and 31 min B. 9 hours and 25 min C. 8 hours and 31 min D. 8 hours and 25 min
(C) The question requires an understanding of calculating with standard units of time. Bill slept for 3 min from 9.57 pm until 10 pm and for 2 hours from 10 pm until 12 am. Then he slept another 6 hours and 28 min until 6.28 am. This adds up to 8 hours and 31 min.
Which of the following is the product of two even numbers and an odd number, each of which is greater than 1? A. 15 B. 16 C. 20 D. 21
(C) The question requires an understanding of factors of natural numbers. The question requires a determination of the number that has two even factors and one odd factor. The even numbers need not be unique. In (C), 20 = 2 x 2 x 5, 20 can be written as the product of 2, 2, and 5, so 20 can be written as the product of two even numbers and one odd number. In (A), 15 = 3 x 5, and in (D), 21 = 3 x 7; 15 and 21 do not have any even factors. In (B), 16 = 2 x 2 x 2 x 2. 16 does not have any odd factors.
5 1/4% is equivalent to which of the following ? A. 5.25 B. 0.525 C. 0.0525 D. 0.00525
(C) The question requires an understanding of how to convert between fractions, decimals, and percents. The fraction 1/4 can be converted to 0.25 so that the original percent can be written as 5.25%. Since 5.25% is equivalent to 5.25/100, to convert 5.25% to a decimal number, one must divide 5.25 by 100. This means that 5.25% is equivalent to 0.0525.
Each row of the table shows equivalent measurements. Based on equivalent measurements, which of the following quantities is greatest? A. 12 tb B. 7/8 cup C. 8 fl oz D. 45 tsp
(C) The question requires an understanding of how to convert units within the U.S. customary system. To answer the question, one can convert all measurements to the same unit, for example, tablespoons. The quantity in (A) is already 12 tb. The quantity in (B) is 7/8 c which is equivalent to 7/8 x 16, or 14 tb. The quantity in (C) is 8 fl oz, which is equivalent to 8 x 2, or 16 tb. Lastly, the quantity in (D) is 45 tsp, which is equivalent to 45 x 1/3, or 15 tb. (See conversion chart on next slide)
90, 90, 95, 90, 85, 90 Caleb's scores for the first 6 quizzes in his algebra class are shown above, if he receives a score of 95 on the 7th quiz, which of the following statements will be true? A. The average (mean) of the 7 quiz scores is less then the average of the first 6 quiz scores. B. The mode of the 7 quiz scores is greater than the mode of the first 6 quiz scores. C. The median of the 7 quiz scores is equal to the median of the first 6 quiz scores. D. The range of the 7 quiz scores is greater than the range of he fist 6 quiz scores.
(C) The question requires an understanding of how to determine how changes in data affect measures of center or range. Placing the first 6 quiz scores in order gives 85, 90, 90, 90, and 95. Since the two middle numbers are both 90, and the range is 10. After adding 95 to the list, the median remains 90. The mode and mean are also 90, and the range is 10. After adding 95 to the list, the median remains 90, the mode remains 90, and the range remains 10. Only the mean is affected by adding 95 to the list. Since 95 is greater than 90, that is, the mean of the first 6 quiz scores, the mean of the 7 quiz scores is greater than the mean of the first 6 quiz scores. Therefore, of the given statements, the only true statement is that the two medians are equal.
1, 1, 2, 3, 5, 8 The first six terms of a sequence are shown. Which of the following formulas can be used to find the terms of the sequence?
(C) The question requires an understanding of how to make conjectures, predictions, or generalizations based on patterns. The only formula that yields a sequence whose terms are those shown is the one in (C), in which the first two terms are defined as 1 and each subsequent term is the sum of the two terms immediately preceding it. The formula in (A) yields a sequence in which every term is 1. The formula in (B) yields a sequence in which the first two terms are 1 and 2. The formula in (D) yields a sequence in which the first four terms are 1, 1, 2, and 4.
A machine that works at a constant rate processes 18 pounds of fruit every 3 hours. At this rate how many hours does it take to process 72 pounds of fruit? A. 4 B. 10 C. 12 D. 15
(C) The question requires an understanding of how to solve unit-rate problems. One must first find the unit rate by dividing 18 pounds by 3 hours, resulting in 6 lbs/hr. Then one must divide 72 lbs by 6 lbs/hr to determine how many hours it will take to process 72 lbs of fruit. Since 72 / 6 = 12, it will take 12 hours to process 72 lbs of fruit.
A basket contains A apples and P pears, and there are two fewer apples than three times the number of pears. Which of the following equations can be used to represent algebraically the relationship between the number of apples and the number of pears in the basket? A. A = 2 - 3P B. A - 2 = 3P C. A + 2 = 3P D. 3A = P - 2
(C) The question requires an understanding of how to translate between verbal statements and algebraic equations. The basket contains two fewer apples than three times the number of pairs, so if here were two more apples, there would be as many apples as three times the number of pears. Therefore A + 2 = 3P
Bob has been reading a 600-page novel at a constant rate. The graph shows the number of pages he has read after x days of reading. If he continues reading at the same rate, how many days will it take for him to read the novel from beginning to end? A. 4 B. 6 C. 8 D. 12
(C) The question requires an understanding of how to use linear relationships represented by a graph to solve problems. The graph shows that Bob has read 150 pages in 2 days and that he has read 300 pages in 4 days. Therefore, Bob has been reading the novel at a constant rate of 75 pages per day. If he continues to read at the same rate, he will finish reading the novel in 600/ 75 = 8 (days)
A painter used 1 1/2 cans of paint to paint 2/3 of a room. At this rate , how much more paint does the painter need to paint the remainder of the room? A. 1/3 can B. 1/2 can C. 3/4 can D. 1 can
(C) The question requires an understanding of how to use proportional relationships to solve ration an percent problems. Since the painter has already painted 2/3 of the room, the painter still needs to paint 1- 2/3 or 1/3 of the room. To determine the amount of paint x needed to paint the rest of the room, one can set up the proportion 1 1/2: 2/3 = x : 1/3, which yields the equation 2/3 x = (1 1/2) x 1/3. Simplifying the right side of the equation yields 2/3 x = 1/2. Therefore, x = 3/2 x 1/2; that is, x = 3/4.
Rosa left a 20% tip on a restaurant bill of $47.30. What amount did Rosa leave for the tip? A. $0.95 B. $4.73 C. $9.46 D. $14.19
(C) The question requires an understanding of percent as a rate per 100. The tip is 20% of $47.30, and it can be found by multiplying 47.30 by 20/100, which yields $9.46. Alternatively, to find 20% of $47.30, 0.2 x 47.30 = 9.46.
What is the greatest odd factor of the number 2, 112? A. 3 B. 21 C. 33 D. 111
(C) The question requires an understanding of prime factorization of a number. The prime factorization of 2,112 is 2^5 x 3 x 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 x 11 which is 33.
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, Statue of Liberty must be within which of the following ranges? A. 115 meters to 120 meters B. 105 meters to 110 meters C. 90 meters to 95 meters D. 60 meters to 65 meters
(C) The question requires an understanding of proportions. The ratio between the height of the Statue of Liberty and the length of its shadow is equal t the ratio between the height of the pole and the length of its shadow. The proportion will look like this (where L represents the height of the Statue of Liberty): L/37 = 5/2. Multiplying both sides by 37 and then simplifying both sides of the equation gives you L = 92.5 m. Note that other proportions can be set up, such as the height (L) divided by pole height (5 meters) equals state shadow length (37 meters) divided by pole shadow length (2 meters). This will also give the correct result.
Tasha has T books, and Aisha has A books. Aisha has twice as many books as Tasha, and altogether they have 30 books. Which of the following proportions can be used to find out how many books Aisha has? A. A : T = 2 : 3 B. T : A = 2 : 3 C. A : (T + A) = 2 : 3 D. T : (T + A) = 2 : 3
(C) The question requires an understanding of ratios and unit rates to describe relationships between quantities. Since Aisha has two as many books as Tasha, the ratio of T : A is equal to 1 : 2 that is, Tasha has one-third of the books, while Aisha has two-thirds. Therefore, the ratio of Aisha's books. A, and the total T + A is 2 : 3.
A shopper purchases one of each of the items on the list above at the prices indicated. Which of the following is closest to the change the shopper would receive after paying with a $20.00 bill? (Assume there is no sales tax) A. $9 B. $10 C. $12 D. $13
(C) The question requires an understating of addition of rational numbers. You can add the prices of the groceries and get a total of $8.28. Subtracting this amount from $20.00 gives you the amount of change $11.72, which is closest to $12.00.
Some values of the linear function ƒ are given in the table shown. What is the value of ƒ(100) ? A. 30 B. 36 C. 40 D. 48
(C) The question requires an understanding of finding patterns in data. Since 18-12/45-30 = 6/15 = 2/5, the value of ƒ(x) increases by 2 units for every 5-unit increase in the value of x. The value of x increases by 40 units from 60 to 100, so the value of ƒ(x) must increase by 16 units between ƒ(60) and ƒ(100). Since ƒ(60) =24, ƒ(100) = 24 + 16 = 40
A pencil is 18 cm in length. How long is the pencil in millimeters? A. 0.18 B. 1.8 C. 180 D. 1,800
(C) The question requires an understanding of the metric system. Since 1 cm equals 10 mm, 18 cm equals 180 mm. (18 x 10)
Which of the following expresses 3/16 as a percent? A. 0.1875% B. 1.875% C. 5.33% D. 18.75%
(D) 3/16 x 100 = 18.75
What is the prime factorization of 3,780? A. 2 x 5 x 6 x 7 x 9 B. 3 x 4 x 5 x 7 x 9 C. 2 x 3 x 6 x 7 x 15 D. 2 x 2 x 3 x 3 x 3 x 5 x 7
(D) The question requires an understanding of how to identify and use prime and composite numbers. The prime factorization of a number is that number written as a product of its prime factors. The prime factors of 3,780 are (D).
A unit square is partitioned into identical parts having equal areas. One of the parts is removed from the square, and a shape is formed by the parts that remain after the removal. For which part of the following areas of the removed part will the shape that is formed have the greatest area? A. 1/4 B. 1/5 C. 1/6 D. 1/7
(D) The question requires an understanding of how to recognize concepts of rational numbers and their operations. If the unit square is partitioned in n parts having equal area, the area of each part is 1/ n. Therefore the area of the shape that is formed when removing one of the identical parts is 1 - 1/ n. The smaller is the area of the removed part, the greater is the area of the shape that is left. Since 1/ 7 is the smallest of the four fractions listed, the shape that has the greatest area is the one that is left by removing a part with area 1/ 7.
8 + 24 / 4 x (6 - 4) Which of the following is equivalent to the expression shown? A. 5 B. 11 C. 16 D. 20
(D) The question requires an understanding of how to solve problems using the order of operations. Using the order of operations, the first step is performing the subtraction within the parenthesis, which yields 8 + 24 / 4 x 2. The second step is performing the division, which yields 8 + 6 x 2. The third step is performing the multiplication, which yields 8 + 12. Finally, the fourth step is performing the addition, which yields 20.
0.7 is 1/1,000 of what number? A. 0.0007 B. 0.007 C. 70 D. 700
(D) The question requires an understanding of place value by recognizing that a digit in one place represents ten times what it represents in the place to its right and one-tenth of what it represents in the place to its left and the ability to extend this concept several places to the right or left. If 0.7 is 1/1,000 of a number n then n, then 0.7 = 1/ 1,000 n. Therefore, n = 0.7 x 1,000. Working backward, one can also observe that the decimal point moves three places to the left when finding one-thousandths of a number.
Which of the following lists shows all the factors of 24? A. 2, 3 B. 3, 4 ,6, 8 C. 2, 3, 4, 6, 8, 12 D. 1, 2, 3, 4, 6, 8, 12, 24
(D) The question requires an understanding of the factors and multiples of a number. Given a natural number n, a natural number less than or equal to n is a factor of n if and only n is divisible by that number. Since 1 x 24 = 24, 2 x 12 = 24, 3 x 8 = 24, and 4 x 6 = 24, the factors of 24 are (D) *include 1 and itself too!!
The Clearbrook Wildcats basketball team scored an average of 77 points in four games. In the first game, the team scored 70, 76, and 82 points. How many points did they score in their last game? A. 70 B. 76 C. 77 D. 80
(D) This question requires an understanding of average (or mean) and the ability to set up and solve several computations. An average of 77 points in the four games means that they scored a total of 77 times 4, or 308 points. Since the scores for the first three games are given as 70, 76, and 82 points, it is necessary to add these up (288 points) and subtract them from the four-game total of 308 points. This leaves 80 points for the last game's score.
Conversation chart measurements
Conversation chart measurements
In a set of number cubes, the length of the edge of each number cute is 2/3 inch. It takes 27 of these number cubes to completely fill a box in the shape of a cube. What is the volume, in cubic inches, of the box?
The correct answer is 8. The question requires an understanding of how to find the volume of the right rectangular prism. If 27 number cubes fit in the cubical box, there must be 3 layers of number cubes, with each layer consisting of 3 rows of 3 number cubes. With 3 number cubes, each having edge length 2/3 inch, along one edge of the box, each edge of the box is 3 x 2/3 = 2 inches in length. The volume of the box is thus 2^3 = 8 cubic inches. Another approach is to find the volume of each number cube first. The volume of each number cube is (2/3)^3, or 8/ 27 cubic inches. Since there are 27 number cubes in the box, the volume of the box is 8/ 27 x 27, or 8 cubic inches.
R = 5b In a flower shop, there are 5 roses in every bouquet. The equation shown give the number of roses r used to make b bouquets. Select the appropriate choices to correctly complete each sentence. Dependent or independent variable: B is (___________) variable R is (___________) variable
The quesion requires an understanding of how to differentate between dependent and independent variables in a forumula. In the given formula there are two variables b and r. Since the formula invesigates how the number of roses r used increases depending on the number of boquets b, the dependent variable is r and the independent variable is b.
The following graphs best represents the relationship between x and y in the table shown.
The question requires an understanding of representing points in the xy-coordinate plane. the ordered pairs in the table can be represented in the xy-coordinate plane as four points on a line. The point (-5,0) is one of the points on the line and indicates that the line crosses the x-axis at -5. The only one of the graphs shown that is a line that meets this condition is the graph in option (A)
