Jubilee Institute Admission Test Β· Mathematics and Analytical Logic

Quantitative Problem Solving and Geometry

82 practice questions, each with the answer and an explanation.

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All 82 questions

  1. If a right circular cylinder has a base radius of 3 cm and a height of 10 cm, what is its total surface area in square centimeters (in terms of pi)?
  2. Solve the quadratic equation 2x^2 - 7x + 3 = 0 for all real values of x.
  3. In a triangle ABC, angle A = 60Β°, side b = AC = 5 cm, and side c = AB = 8 cm. What is the length of side a = BC according to the Law of Cosines?
  4. What is the sum of the infinite geometric series: 12 + 6 + 3 + 1.5 + ... ?
  5. A merchant marks up the cost price of an item by 40% and subsequently offers a 20% discount on the marked price. What is the merchant's net percentage profit on the cost price?
  6. What is the slope of the line perpendicular to the line given by the linear equation 3x - 6y = 15?
  7. If log_2(x) + log_2(x - 2) = 3, what is the value of x in the real number domain?
  8. Two fair six-sided dice are rolled simultaneously. What is the probability that the sum of the two uppermost numbers is a prime number?
  9. A circle is inscribed in a square of side length 14 cm. Taking pi = 22/7, what is the area of the region inside the square but outside the inscribed circle?
  10. How many distinct 4-letter permutations can be formed using the letters of the word 'JORDAN' without repeating any letter?
  11. A car travels from Amman to Irbid (80 km) at an average speed of 60 km/h, and immediately returns along the same route at an average speed of 100 km/h. What is the average speed of the car for the ent…
  12. If 3^(2x - 1) = 27^(x - 2), what is the value of x?
  13. In a right triangle with legs of length a = 9 cm and b = 12 cm, what is the length of the altitude drawn from the right angle to the hypotenuse?
  14. What is the remainder when the polynomial P(x) = 2x^3 - 5x^2 + 4x - 7 is divided by (x - 2) according to the Polynomial Remainder Theorem?
  15. A bag contains 5 red balls, 4 green balls, and 3 blue balls. If two balls are drawn at random one after another without replacement, what is the probability that both balls are red?
  16. What is the solution set of the absolute value inequality |2x - 5| <= 7?
  17. Find the value of x that satisfies the system of linear equations:
    3x + 2y = 16
    5x - 2y = 8
  18. The interior angle of a regular polygon measures 144Β°. How many sides does this regular polygon have?
  19. A worker can complete a construction project in 12 days, while an apprentice takes 24 days to complete the same project. If they work together at their constant rates, how many days will it take them…
  20. If f(x) = 2x^2 - 3x + 1, what is the value of the difference quotient [f(x + h) - f(x)] / h as h approaches 0 (the derivative f'(x))?
  21. What is the radius of the circle defined by the equation x^2 + y^2 - 6x + 8y = 0?
  22. In how many ways can a committee of 3 members be selected from a group of 8 eligible candidates?
  23. A ladder 10 m long leans against a vertical wall. If the foot of the ladder is 6 m away from the wall on level ground, how high up the wall does the top of the ladder reach?
  24. Simplify the algebraic fraction expression: (x^2 - 9) / (2x^2 + 5x - 3).
  25. What is the value of the trigonometric expression: sin^2(25Β°) + sin^2(65Β°)?
  26. A sequence is defined recursively by a_1 = 3 and a_(n+1) = 2*a_n - 1 for n >= 1. What is the value of the 5th term (a_5)?
  27. Pipe A fills an empty tank in 6 hours and pipe B fills it in 9 hours, while drain C empties a full tank in 18 hours. If all three are open together, how long does the empty tank take to fill?
  28. In an arithmetic sequence the 5th term is 17 and the 12th term is 45. What is the sum of the first 20 terms?
  29. A right-angled triangle has a hypotenuse of 13 cm and an area of 30 square centimetres. What is its perimeter?
  30. A shop raised the price of a jacket by 20 percent, then offered a 25 percent discount on the new price. The customer paid JD 1,080. What was the original price?
  31. Point P lies on the segment from A(1, 2) to B(5, 10) so that AP : PB = 3 : 1. What is the distance from P to the origin?
  32. Three consecutive terms of a geometric sequence have a sum of 39 and a product of 729. What is the largest of the three terms?
  33. Solve for : .
  34. After a 10% increase a price is 66 pounds. What was the original price?
  35. If and , what is the value of ?
  36. 20 litres of a 10% solution are mixed with 40 litres of a 60% solution. What is the concentration of the mixture?
  37. A price of 40 pounds is increased by 30% and then reduced by 25%. What is the final price?
  38. Solve for : .
  39. What is the sum of the roots of ?
  40. From a point 40 m from the foot of a building on level ground, the angle of elevation of the top is . How high is the building, in metres (eye height ignored)?
  41. In triangle , , and . Find .
  42. If and , what is the value of ?
  43. A coat costing 60 pounds is sold with a 30% discount. What is the sale price?
  44. What is the sum of the roots of ?
  45. The graph of is moved 1 units to the right and 6 units up. What is the equation of the new graph?
  46. Group A has 14 students with mean score 43; group B has 16 students with mean score 53. What is the combined mean, rounded to two decimals?
  47. Group A has 18 students with mean score 55; group B has 11 students with mean score 48. What is the combined mean, rounded to two decimals?
  48. Solve for : .
  49. A line has slope 2 and passes through . What is its -intercept?
  50. What is the slope of the line through and ?
  51. The graph of is moved 6 units to the right and 5 units up. What is the equation of the new graph?
  52. A data set has mean 17. Each value is multiplied by 2 and then 3 is added. What is the new mean?
  53. Evaluate .
  54. A car drives to a town at 40 km/h and returns by the same road at 60 km/h. What is its average speed for the round trip?
  55. What is the total surface area of a cuboid measuring 3 cm by 9 cm by 9 cm?
  56. A coat costing 800 pounds is sold with a 20% discount. What is the sale price?
  57. What is the sum of the roots of ?
  58. A price of 60 pounds is increased by 25% and then reduced by 25%. What is the final price?
  59. A value changes from 400 to 500. What is the percentage increase?
  60. Machine A finishes a job in 6 hours and machine B in 3 hours. Working together, how long do they take?
  61. A car drives to a town at 50 km/h and returns by the same road at 75 km/h. What is its average speed for the round trip?
  62. The graph of is moved 4 units to the right and 2 units up. What is the equation of the new graph?
  63. Two fair dice are rolled. What is the probability that the sum is 7?
  64. What is the volume of a cylinder of radius 14 cm and height 13 cm? (Use .)
  65. A circle has radius 9 cm. What is its circumference, in terms of ?
  66. What is the sum of the roots of ?
  67. A price of 120 pounds is increased by 20% and then reduced by 30%. What is the final price?
  68. What is the sum of the roots of ?
  69. After a 40% increase a price is 168 pounds. What was the original price?
  70. What is the sum of the roots of ?
  71. How many distinct arrangements are there of the letters of the word STATISTICS?
  72. Solve for : .
  73. A plumber charges a fixed fee of 21 pounds plus 6 pounds per hour. What is the cost of a 8-hour job?
  74. A data set has standard deviation 5. Each value is multiplied by 4 and then 1 is added. What is the new standard deviation?
  75. If and , what is the value of ?
  76. A fair coin is tossed 6 times. What is the probability of exactly 4 heads?
  77. The ratio of boys to girls in a class is 3 : 5. If there are 40 students in the class, how many girls are there?
  78. What is the area of a trapezium with parallel sides of 8 cm and 12 cm and a perpendicular height of 5 cm?
  79. JD 2,000 is invested at 5% per year compound interest. What is the total value of the investment after 2 years?
  80. If x + 1/x = 5, what is the value of x^2 + 1/x^2?
  81. The mean of four numbers is 15. Three of the numbers are 10, 12 and 20. What is the fourth number?
  82. How many whole numbers from 1 to 100 inclusive are divisible by 3 or by 5?

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