Math Praxis 5511

Which of the following problems demonstrates the associative property of multiplication? A. 2(3+4)=2(3)+2(4) B. (3x6)x2=(4x3)x3 C. (2x3)x4=2x(3x4) D. 6x4=4x6

C. (2x3)x4=2x(3x4)

2001 - 9.8 2002 - 9.8 2003 - 9.7 2004 - 10.5 2005 - x Numbers of Acres of wheat planted (in millions) The average (arithmetic mean) number of acres of wheat planted in State K for the years shown in the table was 10.0 million acres. Which of the following is closest to the value of x? A. 9.8 B. 10.0 C. 10.2 D. 10.5

C. 10.2 9.8+9.8+9.7+10.5+x/5 = 10.0 x = (5)(10) - (9.8+9.8+9.7+10.5) = 50 - 39.8 = 10.2

Aidan has a plastic container in the shape of a square pyramid. He wants to fill the container with chocolate candies. If the base has a side length of 6 inches and the height of the container is 9 inches, how many cubic inches of space may be filled with candies? A. 98 B. 102 C. 108 D. 112

C. 108 V=1/3(Bh) - B is for base h is for height Base = area = side x side

5 minutes - 3 students 10 minutes - 7 students 15 minutes - 5 students 20 minutes - 8 students 25 minutes - 15 students 30 minutes - 13 students 35 minutes - 7 students 40 minutes - 2 students 45 minutes - 0 students The chart above shows the time, in minutes, that all the fourth-grade students attending Haddon Elementary School spent reading one day last week. How many students read less than 20 minutes on that day? A. 0 B. 8 C.15 D.23

C. 15

Cards in a deck are worth either two points or one point. In a game, a player earns points by drawing cards from the deck. One player drew nine times as many two-point cards as one-point cards and scored a total of 38 points. How many two-point cards did the player draw? A. 2 B. 9 C.18 D.19

C. 18 T=9u Total score = 38=2T+U 38=2(9U)+U=18U+U=19U 38=19U U=2 So, T=9(2) T=18

In a pack of 20 jellybeans, there are two licorice and four cinnamon flavored jellybeans. What is the probability of choosing a licorice jellybean followed by a cinnamon jellybean? A. 2/5 B. 8/20 C. 2/95 D. 1/50

C. 2/95 2/20 (4/19)

A zoo will build a new enclosure for birds in the shape of a rectangular prism. The height of the bird enclosure will be 120 feet, and the perimeter of the rectangular base will be 240 feet. What is the maximum volume that the bird enclosure can have? A. 28,800 cubic feet B.324,000 cubic feet C.432,000 cubic feet D.864,000 cubic feet

C. 432,000 cubic feet sum of length and width must be 120 feet - so length and width must be 60 each height x width x length 120 x 60 x60 = 432,000

The diameter of a human red blood cell ranges between 6.2 and 8.2 thousandths of a millimeter. Which of the following is an equivalent measure of the diameter of a human red blood cell? A.Between 0.62 and 0.82 millimeter B.Between 0.062 and 0.082 millimeter C.Between 0.0062 and 0.0082 millimeter D.Between 0.00062 and 0.00082 millimeter

C. Between 0.0062 and 0.0082 milimeter 6.2(1/10^3) = 0.0062 and 8.2(1/10^3) = 0.0082

Which of the following activities is most appropriate for developing a 1st grader's concept of measuring objects? A. measuring the height of the pencil sharpener using a meter stick? B. measuring the length of the chalkboard using a tape measure C. measuring the width of their desk using dominoes placed end to end D. measuring the circumference of the trash can using a cloth tape

C. measuring the width of their desk using dominoes placed end to end

Steve received $100.00 for his birthday on Thursday and spent the whole amount over the following three days, Friday, Saturday, and Sunday. The ratio of the amount he spent on Friday to the amount he spent on Saturday to the amount he spent on Sunday was 5:4:16. How much did Steve spend on Sunday? A.$16 B.$20 C.$32 D.$64

D. $64 5+4+16= 25 parts of $100 Friday: 100x5/25=$20 Saturday: 100x4/25=$16 Sunday: 100x16/25=$64

Megan bought a watch in a store. The watch was on sale for 20 percent off the original price. Megan has the store credit card and she received an additional 15 percent off the discounted price. On the final sale the store applied a sales tax of 7 percent. If the original price of the watch was $100, what price did Megan pay for the watch? A.$28.00 B.$69.55 C.$72.00 D.$72.76

D. $72.76 100 (.8) = 80 80 (.85) = 68 68 (1.07) = 72.76

What is the constant of proportionality represented by the table below: 2 for -8 5 for -20 7 for -28 10 for -40 11 for -44 A. -12 B. -8 C. -6 D. -4

D. -4

During a unit on geometry, Ms. Nifong instructs her students to sketch two congruent polygons. Which of the following sketches completes this task correctly? A. Two rectangles with the same perimeter B. Two polygons with the same shape C. Two polygons with the same side lenghts D. Two squares with the same area

D. Two squares with the same area congruent means same shape and same size

Samantha drove 90 miles in 3 hours and then stopped for lunch. After lunch she drove 240 miles in 4 hours. What was Samantha's average speed during the time she was driving, rounded to the nearest integer?

47 miles per hour 90 + 240 / 3 + 4 = 330/7 = 47 1/7 mph

Will bought a book on sale for 25% off the original price. The original price of the book was $25.99 and the total amount paid included a 6% sales tax. Which of the following represents the total amount Will paid for the book, in dollars? A.(25.99)(0.75)(1.06)(25.99)(0.75)(1.06) B.(25.99)(0.25)(1.06)(25.99)(0.25)(1.06) C.(25.99)(0.75)(0.06)(25.99)(0.75)(0.06) D.(25.99)(0.25)(0.06)

A. (25.99)(0.75)(1.06) (25.99)(1-25/100) = 25.99(0.75) Sales tax is 6% - represented by 1.06

. A dartboard consists of two concentric circles with radii of 3 inches and 6 inches. If a dart is thrown onto the board, what is the probability the dart will land in the inner circle? A. 1/4 B. 1/2 C. 1/3 D. 1/5

A. 1/4 Ratio of inner circle to the area of outer circle 3/2:6/2

Andrea must administer 1/12 of a medicine bottle to a patient. If the bottle contains 3 4/10 fluid ounces of medicine, how much medicine should be administered? A. 17/60 FLoz B. 15/62 FLoz C. 3/19 FLoz D. 17/67 FLoz

A. 17/60 FLoz 1/12 (34/10) = 34/120 = 17/60

A glass manufacturer shipped 250 bottles from their factory to a customer in New York. Upon arrival, the customer found that 10 percent of the bottles had been broken during shipping. How many of the bottles were NOT broken? A. 225 B. 200 C. 175 D. 25

A. 225 90 percent of 250 = 225

Which of the following options represents equivalency between mathematical expressions? A. 3+x+3x+3+x=5x+6 B. 7x-2x=9x C.2y+2y+2y=6y^2 D. 2.5(x+2)=2.5x+2

A. 3+x+3x+3+x=5x+6

Monday - $25.00 Tuesday - $26.50 Wednesday - $ 20.50 Thursday - $19.50 The graph shows the closing price of Company X's stock on 4 days last week, Monday through Thursday. The average (arithmetic mean) closing price of the stock for 5 days last week, Monday through Friday, was $23.30. On which day was the closing price of Company X's stock the same as the closing price on Friday? A.Monday B.Tuesday C.Wednesday D.Thursday

A. Monday 23.30 = 25.00+26.50+20.50+19.50+x/5 5(23.30) = 91.50 +x x = 25.00

A teacher asks her student to find the error in this algebra problem. What is the error? 3x+4x=(2^2+1)+2(2) 7x=5+2)2) 7x=7(2) 7x=14 x=2 A. The student incorrectly added before multiplying B. The student incorrectly multiplied before adding C. The student incorrectly multiplied the exponent D. The student incorrectly combined like terms

A. The student incorrectly added before multiplying

Store A: $1.10 Store B: $1.25 Store C: $1.10 Store D: $ 1.25 Store E: $1.25 Store F: $1.15 Store G: $1.00 Luis noted the price of a particular candy bar at 7 different stores and recorded the prices as shown above. What is the median of the prices Luis recorded? A. $1.12 B. $1.15 C. $1.18 D. $1.25

B. $1.15

Three friends at a restaurant got the bill that included two appetizers for $12.25 each, three main dishes for $17.50 each, and two desserts for $7.75 each. The three friends agreed to add a 15 percent tip and each pay 1/3 of the total bill. Which of the following is the best estimate of how much each of the three friends will pay? A.$26 B.$36 C.$56 D.$96

B. $36 12x2+18x3+8x2+54 = 94 94(.15) = 14 94+14=108 108/3 = $36

There are 5 students in the Chess Club, and 2 students will be selected at random to represent the club in a statewide competition. How many possible selections of groups of 2 students are possible? A. 5 B. 10 C. 60 D.120

B. 10 n!/(k!(n-k)! 5!/2!(5-2)!= (5)(4)(3)(2)(1)/((2)(1))((3)(2)(1)) = 120/12 = 10

1 volume = 2.5 mass (grams) 2 volume = 5.5 mass (grams) 3 volume= 8.5 mass (grams) A class recorded measurements of the volume and mass of three samples of a certain substance on the graph shown. The students noticed that the three points appear to lie on a line. The students drew a trend line that connects the three points and used the trend line to estimate the volume and mass for other samples of the substance. Based on the trend line, which of the following is the best estimate of the mass of a sample with a volume of 4 cubic centimeters? A.10.0 grams B.11.5 grams C.14.0 grams D.15.5 grams

B. 11.5 grams formula of the line: y=3x-0.5 x= volume y= mass x=4, then mass is y=(3)(4)-0.5=12-0.5=11.5 grams

The United States five-cent coin is made of metal that is comprised of 1/4 nickel and 3/4 copper. The mass of each five-cent coin is 5 grams. How many grams of nickel are needed to make 100 five-cent coins? A. 75 grams B.125 grams C.250 grams D.375 grams

B. 125 grams (5)(100) = 500 grams 1/4 (500) = 125 grams

A ball has a diameter of 7 inches. Which of the following best represents the volume? A. 165.7 in^3 B. 179.6 in^3 C. 184.5 in^3 D. 192.3 in^3

B. 179.6 in^3 Find radius - divide 7 by 2 Volume = 4/3(pi)(radius)^3

For each meal purchased at a restaurant, all customers are allowed to randomly select one of three discount tickets. The tickets are all equally likely to be selected and consist of discounts for $1, $3, or $5 on the next purchase of a meal. A customer purchased two meals. The customer will select one discount ticket, replace it, and then select a second discount ticket. What is the probability that the customer will select two tickets with discounts of $3 and $5? A.1/9 B. 2/9 C. 1/3 D. 2/3

B. 2/9 (1,1), (1,3), (1,5), (3,1), (3,3), (3,5), (5,1), (5,3), (5,5) Only winning would be (5,3) and (3,5)

Mr. Orr asks his class to use inductive reasoning as to determine the pattern in this series of numbers. Which number is next in this series? 2,5,10,17, ____ A. 25 B. 26 C. 22 D. 24

B. 26 - adding by odd numbers

Jean participated in two stages of a bicycling race. The first stage was 400 kilometers, and his average speed was 25 kilometers per hour. The second stage was 360 kilometers, and his average speed was 24 kilometers per hour. What was Jean's total time cycling in the two stages? A. 30 hours B. 31 hours C. 32 hours D. 33 hours

B. 31 hours 400 kilometers/25 kilometers per hours = 16 hours during second stage 360 kilometers/ 24 kilometers per hours = 15 hours 15+16=31 hours

Zeke drove from his house to a furniture store in Atlanta and then back home along the same route. it took Zeke 3 hours to drive to the store. by driving an average of 20 mph faster on his return trip, Zeke was able to save an hour of driving time. what was Zeke's average driving speed on his round trip? A. 24mph B. 48 mph C. 50 mph D. 60 mph

B. 48 mph

The circumference of the circular Ferris Wheel shown is 544 yards. Which of the following is closest to the diameter of the Ferris Wheel in feet? A. 260 B. 519 C. 1,040 D. 5,124

B. 519 feet Radius = 544/2pi = 86.58 yards Diameter = 2(86.58) = 173.16 1 yard = 3 feet (173.16)(3) = 519.48

Which of the following describes how to find the volume of a regular solid prism? A. Find the perimeter of the base of the prism and multiply by the height of the prism B. Find the area of the base of the prism and multiply by the height of the prism C. Find the sum of the areas of the faces and multiply by the length of the prism D. Find the sum of the areas of the lateral faces and multiply by the number of faces

B. Find the area of the base of the prism and multiply by the height of the prism

During an activity Mrs. Schwartz instructs her students to place groups of coins in order of decreasing value. Which of the following students correctly completed this activity. A. Henry - Group 1: 2 dimes, 2 nickels, 4 pennies; group 2: 1 dime, 3 nickels, 2 pennies; groups 3: 1 dime, 2 nickels, 7 pennies B. Graham - Group 1; 1 dime, 5 nickels, and 5 pennies, Group 2; 2 dimes, 2 nickels, 8 pennies, Group 3; 1 dime 2 nickels, 9 pennies C. Landon - Group 1; 3 dimes, 4 nickels and 9 pennies, Group 2; 2 dimes, 4 nickels, 3 pennies, Group 3; 1 dime, 9 nickels, 4 pennies D. Elizabeth - Group 1; 2 dimes, 3 nickels, 6 pennies, Group 2; 2 dimes, 4 nickels, 1 penny, Group 3; 1 dime, 1 nickel, 7 pennies

B. Graham - Group 1; 1 dime, 5 nickels, and 5 pennies, Group 2; 2 dimes, 2 nickels, 8 pennies, Group 3; 1 dime 2 nickels, 9 pennies

Kendra's annual income is $40,000 She spends: travel - 15% savings - 10% groceries - 20% leisure - 17% rent and utilities - 38% Which statement is true? A. The amount of money she spends on travel and savings is more than $11,000 B. The amount of money she spends on rent and utilities is approximately $15,000 C. The amount of money she spends on groceries and savings is more than $13,000 D. The amount of money she spends on leisure is less than $5,000

B. The amount of money she spends on rent and utilities is approximately $15,000

The length of a rectangle is 5ab feet and the width is 3ab feet, where a and b are positive constants. Which of the following statements is true? Select all that apply. A.The perimeter of the rectangle is 8ab feet. B.The perimeter of the rectangle is 16ab feet. C.The area of the rectangle is 15a^2b^2 square feet. D.The area of the rectangle is 125a^3b^3 square feet.

B. The perimeter of the rectangle is 16ab feet C. The area of the rectangle is 15a^2b^2 square feet perimeter: 2(5ab+3ab) = 16ab area: 5(ab)(3ab) = 15a^2b^2

Which of these would be illustrate change over time? A. pie chart B. line graph C. box and whisker plot D. venn diagram

B. line graph

For which of these does a rotation of 120 degrees about the center of the polygon map the polygon onto itself? A. square B. regular hexagon C. regular octagon D. regular decagon

B. regular hexagon

Mandy can buy 4 containers of yogurt and 3 boxes of crackers for $9.55. She can buy 2 containers of yogurt and 2 boxes of crackers for $5.90. How much does one box of crackers cost? A. $1.75 B. $2.00 C. $2.25 D. $2.50

C. $2.25 4x+3y=$9.55 2x+2y=$5.90 4x+3y=9.55/2x+2y=5.90(-2) 4x+3y=9.55 -4x-4y=-11.80 Add together -y=-2.25 or y=2.25

Amy saves $450 every 3 months. How much does she save after 3 years? A. $4800 B.$5200 C. $5400 D. $5800

C. $5400 450(4)=1800 (3) = 5400

A topographic map of mountain trails has a scale of 1:70,000 inches. One of the trails on the map is 18 inches long. Which of the following is the best estimate of the length of the trail, in miles, on the ground? (12 inches = 1 foot and 5,280 feet = 1 mile.) A. 0.9 B. 2.0 C.20.0 D.23.9

C. 20.0 18x70,000 = 1,260,000 1,260,000 x 1 foot/12 inches x 1 mile/5,280 feet = 20.0 miles

During each 8-hour workday, Fred estimates that he spends about 15% of his time filling out payroll forms. If Fred works 5 days each week and 50 weeks each year, based on his approximation, which of the following is the best estimate of the number of hours Fred spends filling out payroll forms each year? A. 3 B. 30 C. 300 D.3,000

C. 300 (15/100)(8 hours/1 day)(5 days/ 1 week)(50 weeks/ 1 year) = 300 hours/ 1 year

Which system of linear inequalities has no solution? A. x-y<3 and x-y>=-3 B. y<=6-2x and 1/3y+2/3x>=2 C.6x+2y<=12 and 3x >= 8-y D. x+4y<=-8 and y + 4x>-8

C. 6x+27<=12 and 3x>+8-y Parallel lines

Kellie puts 6 blue marbles, 7 green marbles, and 8 red marbles in a small box. She shakes the box and selects a marble at random, which is green. Kellie sets aside the green marble, shakes the box, and selects a second marble at random. What is the probability that the second marble selected will be green or red? A. 2/3 B. 3/4 C. 7/10 D. 15/21

C. 7/10 (6+8)/20 = 14/20 =7/10

Which number comes next in the sequence? 16,24,34,46,60 A. 72 B. 74 C. 76 D. 56

C. 76

A company charges $0.25 per square yard to remove snow after a storm. How much will the company charge to remove snow from a driveway that is 12 yards long and 7 yards wide and a sidewalk that is 40 yards long and 1 yard wide? A.$10.75 B.$19.50 C.$21.00 D.$31.00

D. $31.00 area of driveway: 12x7=84sqyards area of sidewalk: 40x1=40sqyards 84+40=124sqyards .25(124)=31.00

Marlon pays $45 for a jacket that has been marked down 25%. What is the original cost of the jacket? A. $80 B. $75 C. $65 D. $60

D. $60 45=0.75x

At a fruit store, apples cost $1.19 per pound, and 4 oranges cost $1.00. If a customer bought x pounds of apples and y oranges, which of the following expressions represents the total amount paid, in dollars? A. 2.19 (x+y/4) B. 2.19 (x+y) C. 1.19x+1.00y D. 1.19x +.25y

D. 1.19x+.25y 1.19x+1.00y/4 = .25y

Kim's current monthly rent is $800. She is moving to another apartment complex, where the monthly rent will be $1100. What is the percent increase in her monthly rent amount? A. 25.5% B. 27% C. 35% D. 37.5%

D. 37.5% 1100-800 = 300 300/800=.375 .375(100)=37.5%

2013: $59 stock price per share 2014: $62 stock price per share The table shows the price per share for a certain stock on January 1st for the years 2013 and 2014. What was the percent change in the price of the stock, rounded to the nearest whole percent, from 2013 to 2013? A. 2% B. 3% C. 4% D. 5%

D. 5% (62-59/59)(100) = 5.08%

If a machine working at a constant rate makes 33 1/3 aluminum cans each second, how many hours will it take for the machine to make 612,000 cans? A.306.3 hours B.306.0 hours C. 30.6 hours D. 5.1 hours

D. 5.1 hours 33 1/3 = 100/3 cans per minute or 100/3 x 60 x 60 = 120,000 cans per hour 612,000/120,000 = 5.1 hours

Monika has a bag containing red, green, blue, black, and yellow chips. If Monika selects a chip at random from the bag, the probability that a yellow chip will be selected is 1/12. If there are 5 yellow chips in the bag, what is the total number of chips in the bag? A.12 B.24 C.48 D.60

D. 60 yellow chip - 5/T 5/T=1/12 5(12)=T(1) = T= 60

Male: Dog - 42 Cat - 10 Total - 52 Female: Dog - 9 Cat - 39 Total - 48 Total: Dog - 51 Cat - 49 Total - 100 The numbers of male and female dogs and cats on a farm in categorized in the table shown. What percentage of the female animals on the farm are cats? A. 18.75% B. 39.00% C. 79.59% D. 81.25%

D. 81.25% 39/48 = 0.8125 = 81.25%

Mr. Alejo is teaching a unit on fractions to her 3rd grade class. Some students are completing an activity in identifying the parts of a fraction. Others are completing an activity on equivalent fractions. Another group of students is completing an activity on adding and subtracting fractions. Which of the following instruction methods describes the various readiness levels Mr. Alejo is incorporating? A. collaborative learning B. small group instruction C. nonlinguistic representations D. differentiated instruction

D. differentiated instruction

Miss Wise asks her students to work in pairs to construct venn diagrams which classify rational numbers, irrational numbers, real numbers, and integers. As she walks around the room to observe their progress, which of the following criterion could she use to assess the students' understanding of these sets of numbers? A. the set of integers should include the other three sets B. the set of rational numbers should include the other three sets C. the set of irrational numbers should include the other three sets D. The set of real numbers should include the other three sets

D. the set of real numbers should include the other three sets - real numbers are irrational, rational, and integers.

Mr. Saver, a 2nd grade teacher, notices that a few of his students are struggling with the concept of borrowing when subtracting two-digit numbers. Which of the following activities would best help students understand this concept of borrowing? A. the teacher works subtraction problems on the whiteboard B. the students watch a children's video about borrowing C. the students complete a worksheet with subtraction problems D. the students use cardboard manipulatives to model subtraction problems

D. the students use cardboard manipulatives to model subtraction problems

Coach Weybright's 6th grade basketball team has played 36 games this season. The ratio of wins to losses is 2:1. If x represents the number of wins, which of the following proportions can be used to determine the number of wins? A. x/36 = 2/1 B. x/2 = 1/36 C. x/3 = 36/2 D. x/36 = 2/3

D. x/36 = 2/3 2/3 is wins to total games played

How do you find the line of symmetry in a figure?

Find the points of x-axis and y-axis

What are congruent angles?

angles that have the same measure