Math Unsolved Questions

In math unsolved questions students can try to practice the given questions and find the exact solution of various types of questions from different topics. These questions will help you to increase your skills to recognize different formula and their uses. A large number of objectives questions have also been included which will help students quickly test their knowledge and skill.

Math Unsolved Questions :

1. If you add the two digits of the mystery number and then multiply the sum by 7, the answer is the mystery number. Find three or more numbers that fit this pattern.

2. You are taking a course that has 4 exams. the first three tests are 100 points each, and the final exam is 200 points. to get an A you need to score at least 90%. If your first three scores were 87, 92, and 84, what score do you need to get on the final exam to get an A? 

3. Your manager asks you to set up a display of 10 wrenches that are on sale this week. The wrenches will be 1/3 off of the regular price, $57.00 ($19.00). After the sale is over, your manager asks for the sales figures. If 150 sets were sold this week, what amount of revenue will you report? 

4. To reach a destination, a pilot is plotting a course that will result in a velocity of 450 miles per hour at an angle of 30 degrees north of west. The wind is blowing 50 miles per hour to the north. Find the direction and speed the pilot should set to achieve the desired resultant.

5. Between 15000yd cubed and 16000 yd cubed of earth must be trucked away from a construction site . The trucks can remove 1000 yard cubed per day and 10500 yd cubed has already been removed. How many days are needed?

6. An executive in an engineering firm earns a monthly salary plus a Christmas bonus of 6900 dollars. If she earns a total of 95700 dollars per year, what is her monthly salary in dollars?

7. The sum of three numbers is -2. The sum of three times the first number, twice the second and third numbers is 9. The difference between the second number and half the third number is 10. Find the numbers and equations.

8. Anita and Nick are playing tug-of-war near a mud puddle. They are each holding on to an end of a taut rope that has a knot exactly in the middle. Anita's position is 5.6 meters east of the center of the puddle and Nick's position is 3.0 meters west of the center of the puddle. What is the location of the knot relative to the center of the puddle? Treat east as positive and west as negative.

9. Clara has a bag of 60 coins with a value of $2.00. The coins are all pennies and nickels. How many of each coin are in the bag?

10. Two cars on a highway passed one another going in opposite directions at 10:30 am. The southbound car was traveling 10mi/hr faster than the northbound car, At 1:00pm, they were 225 miles apart. At what speed was each car traveling?

11. The width of a rectangle is 13 centimeters. Find all possible values for the length of the the rectangle if the perimeter is at least 228 cm.

12. Susan bought a 6 month $1,400 certificate of deposit. At the end of 6 months, she received $126 simple interest. What annual rate of interest did the certificate pay?

13. A Chemist needs 120 milliliters of a 21% solution but only has 3% and 27% solutions available. Find how many milliliters of 27% solution should be used to the desired solution.

14. A window in an apartment is 32m above the ground. From this window, the angle of elevation of the top of the taller building across the street is 36degress and the angle of depression of the bottom of the taller bulding is 47degrees. Calculate the height of the taller building to one decimal place.

15. A steel bar is 96 inches long. It is sawn up into 2 1/4 inches long. Assuming each saw cut wastes 1/8th of an inch, how much scrap is left at the end of the bar?

16. You sell electronics online. Last month, your business had 22 credit card transactions that totaled $47,456. The credit card company charged you $0.25 per transaction and 2 percent of the total transactions. How much did it cost you last month to provide this service to your customers?

17. Mr. de long travels to state a to purchase coming equipment she must pay the prevailing sales tax of 8 percent on what she buy the store will ship her purchase to her home in state b without charging at but with a fixed shipping fee of 3.20 what is the least number of dollar she can spend so that having the purchase shipped will not be more expensive than paying the sales tax.

18. At the cable car museum you can see the four cables lines that are used to pull cable cars up and down the hills of San Francisco. Each cable travels at a speed of 9.55 miles per hour , caused by a rotating wheel whose diameter is 8.5 feet. How fast is the wheel rotating? Express your answer in revolutions per minute.

19. How fast would you have to travel on the surface of earth at the equator to keep up with the sun that is so that the sun would appear to remain in the same position in the sky.

20. Helene is building a garage on her farm near stavley. She knows that the angle of elevation on the roof must be 23 degrees for the peak of the roof to be 3.2 metres above the end of the rafters. how long is each rafter?

21. Jospeh can eat 15 hotdog in 36 second. how long will take him to eat 66 hotdog?

22. A five foot man can cast a 6 foot shadow. if a certain tree castsa a 27 foot shadow,. hoe tall is the tree?

23. A boat can travel 114 miles upstream in the same time it can travel 186 miles downstream. If the speed of the current is 6 miles per hour, find the speed of the boat without a current.

24. A research department of a company that manufactures children’s fruit drinks is experimenting with a new flavor. A 17.5% fructose solution is needed, but only 10% and 20% solutions are available. How many gallons of each solution should be mixed in order to obtain 20 gallons of the 17.5% fructose solution?

25. A bag has 15 different cards. What is the probability of pulling a red, blue, green in any order?

26. Find the annual percentage yield for an account earning 6.7% annual interest compounded quarterly. Round your percentage to two places after the decimal point(so an answer of 12.9763% would be entered as 12.98).

27. Solve with elimination: A plan traveled 416 miles to Des Moines and back. The trip there was with the wind. It took 4 hours. The trip back was into the wind. The trip back took 8 hours. Find the speed of the plane in still air and the speed of the wind.

28. 3 singers are each looking for a piano player to accompany them. There are 4 piano players available. How many different pairs of singer and piano player are possible?

29. A string quartet has members that play these instruments: cello, bass, violin and viola. In how many different ways can these 4 musicians arrange themselves in a row onstage?

30. After the first term 2, ea. term of the sequence, 2, 6, 18, .. is obtained by multiplying the preceding term by 3. Which of the terms in the sequence is divisible by 3^4?

31. Simplify: (2x + 5)(3x - 7)

32. The following graph shows data for a particular SUV driven on city streets. Suppose a compact car can travel twice as far as the SUV on the same amount of gas. Answer the following questions. Please show all of your work. At what rate does the SUV consume gas? At what rate does the compact car consume gas? What is the amount of gasoline used by the compact car after 120 miles?

33. In the year 2000, Texas' population was about 20.85 million. In 2006, the population had increased by 12.7%.

a. Assuming this growth continued what should Texas population today be?

b. In what year will the population reach about 30 million?

34. Triangle ABC has sides measuring 10cm. If ABC undergoes a size transformation of magnitude 4...what would the new lengths of the sides be?

35. On a map, Elmwood Drive passes through R (4, -11) and S(0, -9), and Taylor Road passes through J(6, -2) and K(4, -5). If they are straight lines, are the two streets perpendicular? Explain. 

   36. Fcator completely: 3x⁴ - 3w⁴x⁴

37. You are standing (at sea level) a certain distance from a hill, and measure the angle to the top of the hill as 3°. You walk directly away from the top of the hill 500 feet, and now measure the angle to the top of the hill to be 2°. How high is hill?

38. You have invested 34,000 in bonds and stocks. Bonds account paid you interest according the interest rate of 12%, stocks account does it with interest rate of 5%. What are the portions invested in each account if the total interest received in one year from both accounts was 2,950?

39. Jenna ordered 28 t shirts for her soccer team. Seventy five percent of those shirts were size large. How many large shirts did Jenna ordered?

40. Samuel has run for 45 minutes. If he has completed 60% of his run, how many minutes will Samuel run in all? 3. Sum of two numbers is 44. One number is 3 times as large as the other. What are the numbers?

41. Douglas sold 125 sandwiches to raise money for his boy scout troop eighty percent of those sandwiches were sold in his neighborhood how many sandwiches did Douglas sell in his neighborhood

42. Line 1_  y = 1/3 - 1 line 2_ - x + 3y = - 3, if the line is inconsistent, consistent independent, consistent dependent.

43. A rock band has 3 members: a guitarist, a drummer and a bass guitarist. They are taking publicity photos. In how many different ways can these 3 musician’s stands together in a row? Describe the order.

44. The musicians are choosing a costume to wear on stage. How many different outfits can be made with a white shirt, a striped, a blue shirt, black pants and gray pants?

45. Ria is making a poster to advertise a concert. She can use any 2 of these colors; red, blue, yellow or green. List all the possible color combinations she could use.

   46. Find the x and y values for the item below;

a^x ∙ a^y = a¹⁷³; x and y differ by 85



   47. Find the x and y values for the item below;

a^x ∙ a^y= a⁸²; x and y differ by 62



   48. Find the x and y values for the item below;

a^x ∙ a^y = a¹⁶²; x and y differ by 84



   49. Find the x and y values for the item below;

a^x ∙ a^y = a¹⁷⁸; x and y differ by 60.

50. The Sugar Sweet Company is going to transport its sugar to market. It will cost $ 5800 to rent trucks, and it will cost an additional $ 200 for each ton of sugar transported. Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported. Write an equation relating to C ,to S.

51. The first term of geometric sequence is 1 and the common ratio is 10.What is the 10th term of the sequence?

52. What is the 11th term of the geometric sequence 3,6,,12,24?

53. Write an equation of the line with slope 5 that passes through the point (-1,-8).

54. Write an equation of the line with the slope -4/3 that passes through the point (6,2).

55. Write an equation of the line that passes through the origin and has a slope of 5.

56. Create your own polynomial with a degree of 3 that when divided by x + 2 has a remainder of -4.

57. A cylindrical container must be constructed to contain 250 cubic inches of liquid.

A. Express the entire surface area of the container as a function of its radius r and height h. Don’t forget the top and bottom.

B. Express the volume as a function of r and h, and set this expression equal to 250.

C. Use your work from part b to solve for h in terms of r. Then substitute this expression for h into your area expression from part a.

D. Using a graphing technique, find the value of r that makes the surface area a minimum.

E. What dimensions of the container should the manufacturer use if his goal is to minimize the amount of material used in its manufacture?

58. A rectangular box with a square base of length s and height y is to have a volume of 16 cubic feet. The cost of top and bottom material for the box is 25 cents per square foot, and the cost for the sides is 10 cents per square foot.

A. Find an expression for the volume of the box in terms of s and y, and set this equal to 16.

B. Find an expression for the cost of the material used to make the box in terms of s and y.

C. Use your work from part a to express the cost of the box in terms of s only.

D. Find the dimensions of the box that will minimize the cost of materials used to make it.

59. A box without a lid is formed by taking a piece of cardboard that is 40 inches by 20 inches, cutting out square pieces from the four corners, and then bending up the sides to form a box.

A. Find an expression for the volume of the box in terms of the side length x of the cut-out squares.

B. Find the value of x that yields maximum volume.

60. Jeff has been saving his change. If he puts his coins in jars of 50 each there is one coin left over. If instead he puts them in boxes of 37 each there is one coin left over. If he puts them in containers of 11 each then there are none left over. What is the smallest number of coins that Jeff has?

61. The temp of a six pack of pop is 90 degrees it is put in a cooler at 2:00 pm at a constant temp of 40 degrees. It cools to 60 degrees in one hour. When will it reach 45 degrees?

62. Julie Burgmeire receives twice the profit in a business venture than Peter Ancona does. If the profit for the year was $120,000, how much will each receive?

63. One number is 12 less than 5 times the other. Find the two numbers if their sum is 42.

64. The sum of two integers is 158. Find the two integers if the larger is 10 less than twice the smaller.

65. William Echols is going to hire a snow plowing service. Elizabeth Suco charges an annual fees of $80, plus $5 each time she plows. Jon Wilkins charges an annual fee of $50, plus $10 each time he plows. How many times would the snow need to be plowed for the cost of both plans to be the same?

66. Alice and Bonnie start running at the same time from the same point and run in the same direction. Alice runs at 8mph while Bonnie runs at slower pace. After 2 hours they are 4 miles apart. determine the speed at which Bonnie is running?

67. A Hair Salon rents booths for $200 per month plus a 5% commission on receipts. How much rent does Qiana owe for one month when her receipts total $4500?

68. The smith family decided to go on a road trip last summer. Their family car can hold up to 16 gallon of gas. over the course of their trip they had to fill up the car 3 times each way. If their trip was 2568 miles in total. At what rate did their car consume gas?

   69.Write the equation of the line that passes through(1,1) and throught the center of the circle (x - 2)² + (y - 4)² = 20. Write in Ax + By = C form.

70. Lisa is looking up to the top of a giant elephant. The angle of elevation to the giant elephant is 38 degrees and the height of the giant elephant is 21 feet. What is the distance from Lisa to the giant elephant?
a) 0.04 feet b) 16.65 feet c) 16.41 feet d) 26.88 feet

Answer: d) 26.88 feet

71. A 37.54 meter line is used to tether a hot air balloon. Because of a breeze the makes an angle of 50 degrees with the ground. What is the height of the hot air balloon.
a) 49 meters b) 24.13 meters c) 0.02 meters d) 28.76 meters

Answer: d) 28.76 meters

72. A 13 Feet tall lamppost casts a shadow. If the angle of depression looking down from the top of the lamppost to the tip of the shadow is 7 degrees what is the length of the shadow.
a) 105.88 feet b) 0.01 feet C) 12.9 Feet D) 1.6 feet

Answer: a) 105.88 feet

73. The population of 6th grade students at Success Academy last year was 1,500. It was expected to rise to 1,575 this year, but in fact it rose to 1,750. What was the percent error?

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