**Hard Math Problems For 12th Graders** – Do you want solving math issues? Take this twelfth Grade’s toughest Math quiz and notice how properly you apprehend the calculation and formula.

Mathematics is a natural and easy idea, but it could get complex. Math is likewise interesting but can occasionally get hectic.

Are you organised to tackle a hard and fast of exceptionally complicated mat questions? Fasten your seat belts, and let’s skip at the math-filled curler coaster! All the nice for a great score in this math quiz.

**Suggested Read:** algebra functions and data analysis

**Hard Math Problems For 12th Graders** – Questions and Answers

· **1. **

Which is the smallest?

- A.
- -1
- B.
- -half of
- C.
- 0
- D.
- 3

** Simplify: (4 – five) – (13 – 18 + 2).**

- A.
- -1
- B.
- –2
- C.
- 1
- D.
- 2

**3-260**

**D.****1**

**Multiply: (x – 4)(x + five)**

**o A. **

**x**^{2}**+ 5x – 20****B.****X**^{2}**– 4x – 20****C.****x**^{2}**– x – 20****D.****X**^{2}**+ x – 20**

**Factor: 5x**^{2}** – 15x – 20**

**A.****five(x-4)(x+1)****B.****-2(x-four)(x+five)****C.****-5(x+4)(x-1)****D.****five(x+four)(x+1)**

**Factor: 3y(x – 3) -2(x – 3)**

**A.****(x – three)(x – three)****B.****(x – three)**^{2}**C.****(x – 3)(3y – 2)****D.****3y(x – three)**

**Solve for x: 2x – y = (3/4)x + 6**

**A.****(y + 6)/five****B.****4(y + 6)/five****C.****(y + 6)****D.****four(y – 6)/five**

**Simplify:(4x**^{2}** – 2x) – (-5x**^{2}** – 8x)**

**A.****9x(3x + 2)****B.****8x(3x + 2)****C.****4x(3x + 2)****D.****3x(3x + 2)**

**What is the radius of a circle that has a circumference of 3.14 meters?**

**A.****0.2 meter****B.****0.Three meter****C.****zero.Four meter****D.****0.Five meter**

** Factor: 3x**^{four}**y**^{three}** – 48y**^{three}

**A.****3y**^{3}**(x**^{2}**+ 4)(x + 2)(x -2)****B.****4y**^{3}**(x**^{2}**+ four)(x + 2)(x -2)****C.****3y**^{three}**(x**^{2}**+ three)(x + 2)(x -2)****D.****3y**^{three}(x^{2}+ three)(x + 1)(x -1)

**Suggested Read:** Math kangaroo past papers

**100 Difficult Phrase Troubles in algebra **

**The charge of petrol rises by way of 2 cents a liter. Final week a man offered 20 liters on the old price. This week he sold 10 liters at the latest fee. Altogether, the petrol costs $9.20. What changed into the antique charge for 1 liter?**

**Teachers divided college students into organizations of 3. Each organization of 3 wrote a file that had 9 pictures in it. The university college students used 585 pics altogether. How many university college students were there in all?**

**Vera and Vikki are sisters. Vera is four years vintage and Vikki is 13 years antique. What age will every sister be whilst Vikki is twice as vintage as Vera?**

**A can do a piece in 14 days and operating collectively A and B can do the equal work in 10 days. In what time can B on my own do the art work?**

**7 employees could make 210 pairs of cup in 6 days. How many people are required to make 450 pairs of cup in 10 days?**

**Ten years within the past the ratio many of the a long time of Mohan and Suman was three:5. 11 years for that reason it will be 11:sixteen. What is the existing age of Mohan?**

**The ratio of ladies to boys in class is nine to 7 and there are 80 students within the beauty. How many girls are within the elegance?**

**One ounce of answer X consists of simplest components a and b in a ratio of 2:3. One ounce of answer Y incorporates best components a and b in a ratio of 1:2. If answer Z is created via blending answers X and Y in a ratio of three:eleven, then 2520 ounces of solution Z consists of how many oz. Of a?**

**This week Bob puts gasoline in his truck even as the tank emerge as approximately 1/2 empty. Five days later, bob places fuel all over again whilst the tank became about 3 fourths full. If Bob Bought 24 gallons of fuel, how many gallons does the tank keep?**

**A enterprise airplane flying with a velocity of 7-hundred mi/h is detected one thousand miles away with a radar. Half an hour later an interceptor aircraft flying with a pace of 800 mi/h is dispatched. How long will it take the interceptor aircraft to meet with the alternative aircraft?**

**There are 40 pigs and chickens in a farmyard. Joseph counted 100 legs in all. How many pigs and how many chickens are there?**

**The pinnacle of a container is a rectangle with a perimeter of seventy two inches. If the container is eight inches high, what dimensions will provide the most quantity?**

**You are elevating coins for a charity. Someone made a fixed donation of 500. Then, you require every player to make a pledge of 25 bucks. What is the minimum amount of cash raised if there are 224 contributors.**

**The sum of high first-rate numbers is 4 and the sum in their squares is 28. What are the two numbers?**

**Flying in the direction of the jet circulate, a jet travels 1880 mi in four hours. Flying with the jet stream, the equal jet travels 5820 mi in 6 hours. What is the fee of the jet in nevertheless air and what’s the rate of the jet movement?**

**16. Jenna and her buddy, Khalil, are having a competition to see who can keep the maximum coins. Jenna has already saved $a hundred and ten and each week she saves an extra $20. Khalil has already saved $eighty and every week he saves a similarly $25. Let x represent the variety of weeks and y represent the overall amount of money saved. Determine in what number of weeks Jenna and Khalil can have the identical amount of money.**

**The sum of three consecutive phrases of a geometric series is 104 and their product is 13824.Locate the phrases.**

**The sum of the number one and ultimate of 4 consecutive odd integers is fifty . What are the 4 integers?**

**A gymnasium expenses a one-time initiation rate and a monthly fee. John paid a hundred bucks for 2 months of membership. However, Peter paid 200 for 6 months of club. How tons will Sylvia pay for 1 year of club?**

**The sum of satisfactory numbers is four and the sum in their cubes is 28. What is the fabricated from the two numbers?**

**A man selling computer components realizes that after he sells 16 computer additives, his earning is $1700. When he sells 56 laptop parts, his incomes is $4300. What will the incomes be if the individual sells 30 pc systems factors?**

**A man has 15 cash in his pockets. These cash are dimes and quarters that upload up 2.Four greenbacks. How many quarters and how many dimes does the man have?**

**The lengths of the sides of a triangle are inside the ratio 4:3:5. Find the lengths of the rims if the perimeter is 18 inches.**

**The ratio of base to peak of a equilateral triangle is 3:4. If the place of the triangle is 6, what is the fringe of the triangle?**

**The percent pass returned price of a boom fund, income fund, and money market are 10%, 7%, and five% respectively. Suppose you have got were given 3200 to make investments and also you want to position two times as a lot inside the increase fund as inside the money market to maximize your cross returned. How have to you invest to get a go back of 250 dollars in 1 year?**

**A shark turn out to be caught whose tail weighted 2 hundred kilos. The head of the shark weighted as lots as its tail plus 1/2 of its frame. Its body weighted as loads as its head and tail. What is the burden of the shark?**

**The rectangular root of a number of plus is just like the amount. What is the variety?**

**Suppose you’ve got a reduction worth 6 bucks off any object at a mall. You pass to a store on the mall that offers a 20% good deal. What do you need to do to keep the most money?**

**Suppose your grades on three math tests are eighty, 90 three, and ninety one. What grade do you need for your next examination to have as a minimum a ninety not unusual on the four tests?**

**Peter has a photograph that is 5 inches extensive and six inches lengthy. She enlarged each facet by way of the use of the equal quantity. By how masses became the image enlarged if the brand new place is 182 square inches?**

**31. The price to deliver a e-book is 1200 to get began out plus nine bucks in line with e-book. The e-book sells for 15 greenbacks every. How many books want to be sold to make a income?**

**Store A sells CDs for 2 dollars each in case you pay a one-time rate of 104 greenbacks. Store B gives 12 unfastened CDs and charges 10 dollars for each more CD. How many CD want to you purchase so it’s going to fee the identical under each plans?**

**When four is introduced to two numbers, the ratio is 5:6. When four is subtracted from the 2 numbers, the ratio is 1:2. Find the two numbers.**

**A preserve proprietor desires to promote hundred pounds of pistachios and walnuts blended collectively. Walnuts charge 4 greenbacks in line with pound and pistachio cost 6 dollars consistent with kilos. How many pounds of each shape of nuts need to be mixed if the store owner will rate five greenbacks for the combination?**

**A cereal area producer makes 32-ounce containers of cereal. In a surely best global, the sector can be 32-ounce on every occasion is made. However, for the reason that global isn’t perfect, they allow a difference of 0.06 ounce. Find the variety of best size for the cereal field.**

**A man weighing six hundred kg has been dropping three.12% of his weight every month with a few heavy carrying activities and eating the proper meals. What will the person weigh after 20 months?**

**An object is thrown into the air at a peak of 60 feet. After 1 2d and a couple of 2nd, the object is 88 toes and eighty four toes in the air respectively. What is the preliminary pace of the object?**

**A transit is 2 hundred feet from the bottom of a building. There is guy fame on top of the constructing. The angles of elevation from the top and backside of the person are forty five tiers and 44 levels. What is the height of the individual?**

**A lemonade includes 6% of lemon juice and a strawberry juice includes 15% natural fruit juice. How an lousy lot of every kind need to be mixed together to get a four Liters of a ten% concentration of fruit juice?**

**Ellen can wash her automobile in 60 minutes. Her older sister Sarah can do the equal job in 45 minutes. How prolonged will it take inside the occasion that they wash the car collectively?**

**Suggested Read:** basic geometry worksheets pdf

**A plane flies 500 mi/h. The aircraft can journey 1100 miles with the wind in the same amount of time as it travels 900 miles towards the wind. What is the velocity of the wind?**

**A business company produces bins which are 5 toes lengthy, 4 ft giant, and 3 feet high. The organisation wants to growth every dimension through the equal quantity simply so the new quantity is two times as big. How a good deal is the boom in dimension?**

**James invested half of of his money in land, a 10th in stock, and a twentieth in saving bonds. Then, he positioned the final 21000 in a CD. How a whole lot money did James saved or invested?**

**The motherboards for a pc pc can be artificial for 50 dollars every. The improvement charge is 250000. The first 20 motherboard are samples and could not be offered. How many salable motherboards will yield a mean cost of 6325 dollars?**

**How plenty of a 70% orange juice drink want to be mixed with forty four gallons of a 20% orange juice drink to acquire a combination this is 50% orange juice?**

**A organisation sells nuts in bulk portions. When offered in bulk, peanuts sell ****for $1.20 in keeping with pound, almonds for $ 2.20 in keeping with pound, and cashews for $three.20 in line with pound. Suppose a sturdy point maintain needs a combination of 280 kilos in order to charge $2.59 in step with pound. Find the variety of kilos of every type of nut if the sum of the wide sort of kilos of almonds and cashews is 3 times the variety of kilos of peanuts. Round your answers to the closest pound.**

**A Basketball participant has efficiently made 36 of his final forty eight unfastened throws. Find the extensive kind of consecutive free throws the participant needs to boom his achievement fee to eighty%.**

**John can wash cars 3 times as speedy as his son Erick. Working together, they want to scrub 30 cars in 6 hours. How many hours will it takes each of them running by myself?**

**In a university, approximately 36% of pupil are beneath a long time antique and 15% are over forty years antique. What is the opportunity that a scholar selected at random is beneath many years vintage or over 40 years?**

**Twice quite a few plus the rectangular root of the amount is twelve minus the square root of the range.**

**The mild depth, I , of a mild bulb varies inversely because the square of the space from the bulb. A a distance of 3 meters from the bulb, I = 1.Five W/m^2 . What is the mild intensity at a distance of two meters from the bulb?**

**The lengths of aspects of a triangle are 2 and 6. Find the variety of values for the feasible lengths of the 1/3 aspect.**

**Find three consecutive integers such that one 1/2 in their sum is among 15 and 21.**

**After you open a e-book, you be aware that the made of the two net web page numbers at the coping with pages is 650. What are the two net web page numbers?**

**Suppose you begin with a number of. You multiply the amount by way of using three, upload 7, divide by using way of ½, subtract 5, and then divide through 12. The cease result is 5. What extensive variety did you begin with?**

**You have 156 toes of fencing to surround a square garden. You need the garden to be five instances so long as it’s miles extensive. Find the dimensions of the lawn.**

**The quantity of water a dripping faucet wastes water varies without delay with the amount of time the tap drips. If the tap drips 2 cups of water every 6 mins, find out how prolonged it’ll take the faucet to drip 10.6465 liters of water.**

**A washing gadget expenses 25% more than a dryer. If the shop clerk gave a ten% good deal for the dryer and a 20% bargain for the washing machine, how a good deal is the washing machine earlier than the good deal in case you paid 1900 greenbacks.**

**Baking a tray of blueberry desserts takes four cups of milk and three cups of wheat flour. A tray of pumpkin desserts takes 2 cups of milk and 3 cups of wheat flour. A baker has 16 cups of milk and 15 cups of wheat flour. You make three bucks income in keeping with tray of blueberry truffles and multiple bucks earnings consistent with tray of pumpkin desserts. How many trays of every type of desserts must you are making to maximize profit?**

**A company located that -2p + one thousand models the huge kind of TVs bought constant with month in which p may be set as low as 200 or as excessive as three hundred. How can the agency maximise the sales?**

**More difficult word problems in algebra**

**Your buddies say that he has $2.40 in identical numbers of quarters, dimes, and nickels. How many of each coin does he have?**

**I am a -digit range whose digit within the 10th area is 1 less than two times the digit in the ones region. When the digit in the tenth place is divided by way of the use of the digit inside the ones location, The quotient is 1 and the the rest is four. What amount am I?**

**A -digit wide range is formed by way of randomly choosing from the digits 2, four, five, and seven without opportunity. What is the opportunity that a -digit amount consists of a 2 or a 7?**

**Suppose you interview 30 ladies and 20 adult males at your university to find out who among them are using an electric toothbrush. Your survey observed that most effective 2 guys use an electric toothbrush whilst 6 girls use it. What is the possibility that a respondent did now not use an electric powered toothbrush for the purpose that the respondent is a female?**

**Suggested Read:** algebra 2 formula sheet pdf

**An organization can pay 15 dollars in line with hour plus a further 5 dollars steady with hour for each hour worked beyond eight hours as much as a maximum daily revenue of 220 greenbacks. Find a piecewise characteristic that fashions this case.**

**Divide me thru 7, the the relaxation is five. Divide me with the aid of three, the the rest is 1 and my quotient is two less than 3 times my previous quotient. What range am I?**

**A organization making luggage have those necessities to comply with. The length is 15 inches more than the depth and the sum of length, width, and depth won’t exceed 50 inches. What is the most charge for the depth if the manufacturer will quality use whole numbers?**

**To make an open area, a man cuts identical squares from every nook of a sheet of steel that is 12 inches big and sixteen inches long. Find an expression for the extent in phrases of x.**

**Ten candidates are going for walks for president, vice-president, and secretary in the students authorities. You also can vote for as many as three applicants. In how many ways can you vote for three or fewer applicants?**

**The 1/2-lifestyles of a medicine prescribed by using a medical doctor is 6 hours. How many mg of this medication is left after 78 hours if the doctor prescribed a hundred mg?**

**Suppose you roll a red huge variety dice and a yellow range dice. Find P(pink 2, yellow 2) and the probability to get any matching pairs of numbers.**

**A movie theater in a small town commonly open its doorways 3 days in a row and then closes day after today for upkeep. Another film theater 3 miles away open 4 days in a row and then closes the following day for the same cause. Suppose each film theaters are closed nowadays and these days is Wednesday, whilst is the subsequent time they’ll each be closed over again on the same day?**

**An investor invests 5000 dollars at 10% and the rest at 5%. How masses have become invested at 5% if the yield is one-fifth of the quantity invested at at 10%?**

**20000 university college students took a standardized math take a look at. The ratings at the test are normally dispensed, with a median rating of 80 five and a elegant deviation of 5. About how many college students scored between ninety and 95?**

**A satellite tv for laptop, placed 2400 km above Earth’s floor, is in circular orbit around the earth. If it takes the satellite three hours to complete 1 orbit, how an extended manner is the satellite tv for pc after 1 hour?**

**In a collection of 10 human beings, what’s the possibility that at the least human beings inside the company have the same birthday?**

**During a fundraising for cancer at a gala, absolutely everyone shakes palms with everyone else within the room earlier than the occasion and after the occasion is finished. If n people attended the gala, what number of particular handshakes arise?**

**Two cubes have component lengths which may be equal to 2x and 4x. How regularly extra than the surface of the small cube is the ground vicinity of the large cube?**

**Suppose you have were given a interest in a eating place on the way to pay $8 regular with hour. You actually have a procedure at Walmart that pays $10 in keeping with hour. You want to earn as a minimum 2 hundred in step with week. However, you need to work no more than 25 hours in keeping with week . Show 3 fantastic methods you may work at every hobby.**

**Two enterprise offer tutoring offerings. Company A realizes that when they teach for 3 hours, they make 45 greenbacks. When they coach for 7 hours they make one hundred and 5 hours.**

**Company B realizes that when they instruct for two hours, they make 34 bucks. When they instruct for six hours they make 102 hours. Assuming that the style of hours university college students sign for tutoring is the equal for both agency, which company will generate more income?**

**You need to fence a square area for youngsters in the out of doors. To store on fences, you will use the lower back of your private home as one of the four sides. Find the possible dimensions if the residence is 60 toes large and also you want to apply at least 160 toes of fencing.**

**When more than a few in stepped forward by using 20%, the stop end result is the equal at the same time as it is reduced with the aid of 10% plus 12. What is the quantity?**

**The average of 3 numbers is 47. The largest range is five more than two times the smallest. The range is 35. What are the three numbers?**

**The percentage of boom of numerous from its original amount to 36 is 80%. What is the specific amount of the number?**

**Suggested Read:** geometry formulas pdf

**eighty five. When Peter drives to artwork, he averages forty five miles consistent with hour due to traffic. On the manner lower back home, he averages 60 miles consistent with hour because of the truth site traffic isn’t always as horrific. The overall tour time is 2 hours. How a long way is Peter’s house from paintings?**

**An advertising corporation takes 20% from all income that it generates for its associates. If the pals were paid 15200 dollars this month, how tons income did the advertising and marketing agency generate this month?**

**A organization’s sales can be modeled with a quadratic equation. The enterprise determined that when they sell each 2 or or 12 objects, the sales is 0. How a whole lot is the income when they promote 20 devices?**

**A ball bounced 4 times, reaching 3-fourths of its preceding top with each bounce. After the fourth leap, the ball reached a top of 25 cm. How immoderate became the ball at the same time as it changed into dropped?**

**A rental organization prices 40 dollars steady with day plus $zero.30 in line with mile. You hire a automobile and drop it off four days later. How many miles did you force the auto if you paid 325.Five bucks which blanketed a 5% income tax?**

**Two college students depart university at the same time and adventure in contrary commands along the same road. One walk at a charge of 3 mi/h. The different bikes at a charge of eight. Five mi/h. After how lengthy will they be 23 miles part?**

**Brown has the equal quantity of brothers as sisters. His sister Sylvia as two instances as many brothers as sisters. How many kids are inside the circle of relatives?**

**Ethan has the identical wide sort of male classmates as female classmates. His classmate Olivia has three-fourths as many woman classmates as male classmates. How many college college students are in the beauty?**

**Noah desires to proportion a positive sum of money with 10 human beings. However, at the last minute, he’s thinking about decreasing the amount through 20 so he can preserve 20 for himself and share the cash with best 5 people. How loads money is Noah looking to percentage if anyone although receives the equal quantity?**

**The square root of me plus the square root of me is me. Who am I?**

**A cash drawer consists of a hundred and sixty bills, all 10s and 50s. If the general value of the 10s and 50s is $1,760. How many of every form of bill are in the drawer?**

**You want to make 28 grams of protein snack combo made with peanuts and granola. Peanuts incorporate 7 grams of protein according to ounce and granola incorporate 3 grams of protein consistent with ounce. How many ounces of granola have to you operate for 1 ounce of peanuts?**

**The period of a square prism is quadrupled, the width is doubled, and the height is lessen in half of of. If V is the extent of the square prism before the modification, express the amount after the amendment in phrases of V.**

**A car condo has CD gamers in eighty five% of its motors. The CD gamers are randomly allocated throughout the fleet of vehicles. If a person rents 4 cars, what is the opportunity that at least three of them will have CD game enthusiasts?**

**Jacob’s hourly salary is four times as an entire lot as Noah. When Jacob were given a growth of two dollars, Noah ordinary a contemporary position which can pay him 2 bucks a lot less in step with hour. Jacob now earns five times as tons cash as Noah. How lots coins do they make according to hour after Jacob were given the beautify?**

**You very own a catering corporation that makes place of know-how cakes. Your organization has decided to create 3 styles of cakes. To create these cakes, it takes a crew that includes a decorator, a baker, and a layout representative. Cake A takes the decorator 9 hours, the baker 6 hours, and the layout representative 1 hour to finish.**

**Cake B takes the decorator 10 hours, the baker 4 hours, and the layout consultant 2 hours. Cake C takes the decorator 12 hours, the baker 4 hour, and the layout representative 1 hour.**

**Without hiring extra employees, there are 398 decorator hours available, 164 baker hours available, and fifty eight layout representative hours to be had. How many of each sort of cake may be created?**

**Suggested Read:** algebra 2 cheat sheet pdf