Praxis Core academic Skills for Educators: Mathematics Practice Test 2
harold has two containers that he has filled with water. one is a rectangular plastic box with a base of 16 sq inches, and the other is a cylindrical container with a base radius of 2 inches and a height of 11 inches. if the rectangular box is filled with water 9 inches from the bottom, and harold pours the water into the cylinder w/o spilling, what happens?
First determine the amount of water that can be held in each container by finding the volume of each. volume of water poured into the rectangular box is found by multiplying the area of the base by the height of the water: V = 16 in. sq x 9 in. = 144 in cubed. the total volume of the cylindrical container can be found by using the formula v= pieRsqxh, where r= radius of the base, h=height of the container, and pie=3.14 (plug in values into formula) answer is 138.16 in cube. becuz there is more water in the rectangular box, the cylinder will overflow when all the water is poured in. answer is: cylinder will overflow.
the sequence of numbers 0, 2, 2, 4, 6, 10, 16 follows a pattern. what comes next?
after the first two terms, each term is obtained by adding the preceding two terms in the sequence. following this pattern, the next term would be 10 + 16 = 26
Robert, Linda, Miguel, and sonja are friends. they all practice unique sports: one enjoys skiing, one enjoys fishing, one enjoys tennis, and one enjoys volleyball. the friend who fishes is miguel's neighbor. robert and linda dislike sports that use balls. sonja is older than both robert and the friend who fishes. who likes to fish?
linda does
out of 100 students polled at a local uni, 80 said they would favor being offered a course in web page development. if there are 30,000 students enrolled at this uni, how many would you expect to favor being offered such a course
80 stu out of the 100 polled would prefer this class, and 80 out of 100 is 80%. to find 80% of 30,000, multiply: 0.80 x 30,000 = 24, 000
D and M get a gext from a friend that their favorite donut shop is down to its last raspberry-custard donut. they race for it. both run at an average of 5 meters per second. if D cuts thru a field instead of following the lanes, by how many seconds will she beat M to the store.
D's route is the hypotenuse. solve for distance and divide by the rate to see how much sooner D arrives. with legs of 300 and 400 meters, the triangles hypotenuse will be 500 meters, the triangles hypotenuse will be 500 meters. subtract 500 from 700 to get 200, which is divided by 5 meters per second to get 40. D arrives 40 seconds sooner.
what is the formula for converting celsius to fahrenheit?
F=9/5C + 32
A triangle has two sides the measure 14 cm and 17 cm, what could be the length of the triangles third side?
`the length of the third side of the triangle must be less than the sum of the other two sides (17 + 14) and greater than their difference (17 - 14). this means that that the third side must be less than 31 and greater than 3. it could be 16, 25, 28 cm long`
There were 504 candies in a jar. between 8 and 9 o'clock, 1/8 of the candies were given out, between 9 and 10 , 2/9 of the remaining candies were given out. at 11 1/7 of the remaining candies are distributed. how many candies are left
answer is 294. when taking a fraction of some number, you are actually multiplying that number by the fraction. 1/8 x 504 = 63 (504-63=441) 2/9 x 441 = 98 (441 -98 = 343) 1/7 x 343 = 49 (343 - 49 = 294)
alicia drives a compact car that gets on average 28 miles for every gallon of gas. if she must drive 364 miles from los angeles to san fran, and gas costs on average 4.86 per gallon, approximately how much will she spend on gas.
answer is 63 dollars
a circle drawn on the floor has an area of 78.5 sq ft. what is the length of the diameter of this circle. use pie=3.14
area of a circle is A = pieRsq....solve to get 10 feet
The Astoria Main Street fair is raffling off a week long stay at a summer art camp. Sohail buys 4 raffle tickets for his son, Asad, and 3 times as many raffle tickets for his daughter Amara. if a total of 80 raffle tickets are sold for the art camp, what is the probability that Asad or Amara will win
because sohail bought 4 raffle tickets for asad and three times that for amara, he bought 4 x 3 = 12 tickets for amara, which means there were 16 tickets in total between the two of them. to find the probability of an event happening, the number of desired events must be put over the total number of events. in this case, there are 16 desired events (tickets belonging to asad or amara) and 80 total events (total number of tickets) probability can be written as a fraction or as a decimal (between 0 and 1), so 16/80 = 20
a factory operates 20 machines that make granola bars. each machine can make between 80 and 100 granola bars per minute. what is the number of granola bars produced per hour if all 20 machines are working at the same time.
calculate the minimum number and the max number of granola bars that the 20 machines can make per min. minimum number of bars each machine can make is 80, multiply 80 x 20 to get 1,600 max number of bars each machine can make is 100: 100 x 20 to get 2,000 minimum and max numbers are per minute: question asks for number per hour. to find the minimum and max numbers of bars made per hour, multiply both numbers by 60 because there are 60 min per hour: minimum: 1,600 x 60 = 96,000 max number: 2,000 x 60 = 120,000. find numbers between 96,000 and 120,000
Marvin wrapped a gift that is in a box that is a perfect cube with each side measuring d inches. Maya arrives with a gift that is also in a box that is a perfect cube, but the edge length of each side of her gift is twice as long as Marvin's gift. how many sq inches of wrapping paper, in terms of d, did Maya need to wrap her gift.
concepts to be considered here are area and surface area. the amt of paper needed to cover a cube is equivalent to the surface area of a cube. the surface area of a cube is the area of each face (d x d) x 6, which is dsq consider that each side length has doubled, and myas gift has a side length of 2d, which will in turn have 6 faces that are each 4dsq in area. the total surface area of maya's gift will be 6 x 4dsq = 24dsq
Ezra is purchasing sunscreen. the only bottle size is 25 ml. the instructions say that 5 ml cover 288 sq inches. his body surface is 20 sq feet. how many bottles does he need to purchase to cover himself.
convert sq inches to sq feet 288 sq inches is 2 sq feet (twice the product of 12 inches by 12 inches. then look at how many 5 ml applications are in a single bottle: 5. therefore, one bottle covers 10 sq feet. two bottles will exactly cover ezra's 20 sq foot body surface area.
During her shift at a busy restaurant, a chef uses 2 and 1/4 pounds of flour the first hour, 4 and 5/8 pounds of flour the second hour, and 1/2 pound of flour the third hour. how many pounds of flour does the chef use during these three hours
convert the two mixed numbers to improper fractions: 2 and 1/4 = 9/4, and 4 and 5/8 = 37/8. rewrite 1/2 as 4/8 and 9/4 as 18/8 so that all fractions have a common denominator. add the fractions to get 59/8
thirty percent of the students at a high school are involved in the vocal/instrumental music programs. if 15% of the musicians are in the choir, what percentage of the whole school is in the choir
decode the language to realize that you are being asked to find 15% of 30% of students who are in the music program. find find 15% of 30% first change the percentages to decimal form : 30%=0.30 and 15%=0.15, then multiply: 0.30 x 0.15 = 0.045. as a decimal, this is equivalent to 4.5%
one thousand students are participating in the regional math competition. an equal number of teams of 5 students are placed into 4 different gymnasiums. each team has one adult coach. to find the total number of people (students and coaches) in each gymnasium, you could`
divide 1,000 by 5, add that result to 1,000 and then divide that result by 4 because there are 1,000 st and there are 5 stu on a team, 1,000/5=200 teams. therefore there are a total of 1,000 + 200 = 1,200 people involved (because each of the 200 teams has one adult coach). 1,200 people/4 gymnasiums = 200 ppl in each gym
first year members of an auto club have to purchase the membership at the full price of 84.50, but those who were also members last year get a 15% discount. those who have been members for at least 3 years get an additonal 10% off the discounted price. how much does a person who has been a member for at least 3 years have to pay for his or her membership.
figure the problem in 2 steps: first find 15% off 84.50 and then find 10% off the membership price after the 15% discount: 15% of 84.50 = 0.15 x 84.50 = 12.68: 84.50 - 12.68 = 71.82. now calculate 90% of 71. 82 (remember if you save 10%, you need to pay 90%): 0.90 x 71.82 = 64.64
If Nyle ate 1/3 of a pizza, and nygel ate 2/5 of the pizza, what fraction of the pizza remains.
find common denominator, which is 15 convert fractions to find that nyles eats 5/15 of the pizza and nygel eats 6/15 of the pizza. add the fractions: 5/15 + 6/15 = 11/15 subtract 11/15 from a whole pizza to find out what fraction remains: 15/15 + 11/15 = 4/15
what is 2/3 divided by 5/12
in order to divide two fractions, multiply the fraction being divided into by the reciprocal of the fraction being divideded answer is 1 and 3/5
Ryan and kimberly spend a combined total of 12 hrs to begin the landscaping for a friend. the next week, jaime and janet spend another 18 hrs to finish the landscaping job. if ryan worked 3 times as many hours as kimberly, and jaime worked five more hours than ryan worked, how many hours did janet spend on landscaping
rep the work that r and k did by letting k's hours be k and ryan's hours be 3k their combined work would be represented as 3k + k =12. (k =3) k worked 3 hours and R worked 9 hours if jaime worked 5 more hours than R, that means he worked 14 hours, jaime and janet worked a total of 18 hours, that means that janet worked 4 hours
Fel spent 5.618 on rent this year and 5,085 the year before. she predicts that she will be paying approximately 6,163 next year. to the nearest 10, what is the best estimate of the total amt she will spend on rent during this three year span.
round each amt to the nearest ten and then add the rounded amts together: 5,618 rounds to 5,620; 5,085 rounds to 5,090, and 6,163 rounds to 6,160; add all to get 16,870. another approach is to add the numbers unrounded and then round the result to the nearest 10. when added the sum of the numbers before rounding is 16,866. this number is also equal to 16,870 when rounded to the nearest ten.
a certain county has an annual spending budget of about 490,000. the largest area of allocation is regional transportation. on which the country spends about 98,000 per year. write a fraction that portrays the portion of the budget spent on regional transportation with respect to the total annual budget of the county.
rounding to compatible numbers can help: 490,000 rounds to 500,000, and 98,000 rounds to 100,000. the question now becomes 100,000 compared to 500,000, which as a fraction is 100,000/500, 000 and simplifies to 1/5
tickets to the school play cost $7.50 for adults and $5 for children ages 12 and under. on sat and sun afternoon, there is special matinee price: $5.50 for adults and $3 for children ages 12 and under. Special group discounts are available for groups of 30 or more people. what information can be give from the passage?
the difference between the cost of a ticket to the school play for an adult on friday night and a ticket to the school play for a 13 year old on saturday afternoon
what was the percent decrease in cost of electricity usage from 1999 to 2000 for the engineering department. dollar amt consumed in 1999 was 1,000 dollar amt consumed in 2000 was 800
the engineering depts electricity usage decreased $200, from 1,000 to 800, in the period of 1999 to 2000. to calculate the percentage decrease between two numbers, divide the difference between the two numbers by the original number, so 200/1000 = 20/100, which is 20%
a floor rug in the shape of a circle has a diameter of 152 cm, what is the approximate area of the rug (1 cm = 0.39 inches)
the formula for the area of a circle is A= pieR sq, where r solve to get 5,776pie cm sq. convert into square inches by multiplying 5,776pie by 0.1521 (0.39 x 0.39) to get 878.53 pie in sq.
while competing in a swim meet. jose finished three one hundredths of a second ahead of his opponent. what is equivalent to this value
the hundredths place in a decimal is two places to the right of the decimal point. three one hundredths of a second is written as a decimal with the number 3 in the hundredths place: 0.03
vic and dahlia go to eat sushi together. he likes sea urchin, which costs $3 apiece. she likes eel, at $2.25 per. the bill without tax, drinks, or tip comes to $36, and each owes half. how many eel pieces did dahlia order
the key to this question is that the bill is even, so the answer choice will be a number that when multiplied by 2.35, the eel price, yields a product of 18, half the bill. it is also helpful to recognize that the su costs exactly one third more than the eel. since the bill divides evenly, the number of sea urchin pieces will be an integer that can be formed by adding 1/3rd to another integer. 8 is 1/3 more than 6
a jar of coins contains 8 dimes, 10 quarters, 3 nickels, and 9 pennies. what is the probability of selecting either a nickel or a penny if you draw one coin from the jar.
the probability of selecting a nickel or a penny is equal to the number of nickels and pennies in the jar divided by the total number of coins in the jar. there are 3 nickels and 9 pennies, so the number in the numerator ( or top) of the fraction is 12. there are a total of 30 coins in the jar, so the probability is 12/30, which reduces to 2/5
jesse ate 1/2 of a pizza and left the other half in his dorm room. dennis came by and ate 1/4 of what was left there. how much of the original pie did dennis eat.
the question being asked here is what is 1/4 of 1/2. the word of in math is an indication of multiplication. answer is 1/8
a train moving at a constant speed of 60 miles per hour leaves chicago for LA at time t=0. if LA is 2,000 miles from chicago, write an equation that describes the distance the train is from LA at any time t
the speed of the train is 60 miles per hour, so as each hour increases by one, the number of miles traveled increases by 60. therefore the distance the train is from Chicago would equal 60t because distance = rate x time. however as the train moves on, the distance from la decreases because the train is moving toward la, so there must be a function of -60t in the equation. at time t=0, the distance the train is from la is 2,000 miles, so the function is 2,000 - 60t
An aquarium has a base length of 12 inches and a width of 5 inches. if the aquarium is 10 inches tall, what is its total volume.
the volume of the aquarium, which is a rectangular prism, can be found by using the formla V = l x w x h, solve to get 600 cubic inches.
B keeps a drawer of unmatched blue socks and brown socks. he keeps 11 blue socks and 10 brown socks. what is the percent likelihood that the sock he pulls is a match if he draws blue first
this is a probability question with a percent conversion. there are 21 socks in all; after pulling one blue, there are an even number of blue socks and brown socks left in the drawer. the percent likelihood then is a conversioin of the fraction 10/20 or 50 percent.
Eva has exactly 1,632 hours until her v action begins. how many days are there before her vacation begins>?
this problem requires you to convert a smaller unit to a largest unit, which is done by dividing: 1,632 / 24 hrs per day = 68 days.
Ridgefield stadium has a total of 36,042 seats. at the first home game of the year, every seat was sold out, and 16,534 of the people in attendance were male. approximately how many more women attended this game than men.
this question contains approximately, so you should estimate to find the answer. round the numbers to 36,000 and 16,500 then solve. answer is 3,000
The average high temperature for the first five days in july was 90 degrees. If the temperature for the first four days were 95 degrees, 85 degrees, 88 degrees, and 84 degrees, respectively, what was the temp on the fifth day
to find the average of the numbers, divide the sum of the numbers by the number of terms being averaged. in this case, x represents the temp on the fifth day, and set the expression equal to the average temp for the five days, which was 90 = 95 + 85+ 88+84+x= 352 + x over 5 cross multiply to get 450 = 352/x. subtract 352 from each side to get x = 98. this problem could also be solved by trying each of the answer choices to see which one results in an average of 90 degrees. when 98 is added to the temperatures for the first four days, the sum is 450 divided by 5 is equal to 90
