DTM University Entrance Test (Uzbekistan) · Mathematics

Geometry, trigonometry and probability

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

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 48 questions

  1. A triangle has base 10 and height 6. What is its area?
  2. What is the sum of the interior angles of a hexagon?
  3. Using π = 22/7, what is the circumference of a circle with radius 7?
  4. The legs of a right triangle are 9 and 12. What is the hypotenuse?
  5. What is the value of sin 30°?
  6. What is the area of a circle with radius 5?
  7. A cylinder has radius 3 and height 5. What is its volume?
  8. Each interior angle of a regular polygon is 135°. How many sides does it have?
  9. What is the distance between the points (1, 2) and (4, 6)?
  10. What is the diagonal of a square with side 8?
  11. An inscribed angle in a circle subtends a diameter. What is its measure?
  12. What is the total surface area of a cube with edge 4?
  13. What is the value of tan 45°?
  14. Which line passes through (0, 3) with slope 2?
  15. In triangle ABC, AB = 7, AC = 8 and angle A = 60°. What is BC?
  16. A right triangle has sides 6, 8 and 10. What is the radius of its inscribed circle?
  17. The radius of a sphere is doubled. By what factor does its volume increase?
  18. A cone has radius 5 and slant height 13. What is its volume?
  19. If sin α = 3/5 and α is an acute angle, what is cos α?
  20. Two fair dice are rolled. What is the probability that the sum is 8?
  21. In how many ways can a committee of 2 be chosen from 5 people?
  22. A right-angled triangle has perpendicular sides of and . Find the hypotenuse.
  23. In a right-angled triangle, the sides adjacent and opposite to angle are and . Find .
  24. Evaluate and give the answer in standard form.
  25. The length of a rectangle is more than its width. Its area is . Find the width.
  26. A box contains 6 red and 3 blue balls. Two balls are taken one after the other without putting the first back. Find the probability that both are red.
  27. A straight line passes through and . Find the value of when .
  28. Find the lowest common multiple (LCM) of and .
  29. Evaluate .
  30. Find if .
  31. Find .
  32. Expand and simplify .
  33. Expand and simplify .
  34. Solve .
  35. Solve the simultaneous equations and . Find the value of .
  36. How many positive integers satisfy ?
  37. If , find when and .
  38. Find the sum of the first terms of the arithmetic progression
  39. A bag has 5 red and 6 blue marbles. One marble is picked at random. Find the probability that it is blue.
  40. Find the size of each interior angle of a regular polygon with sides.
  41. A ladder long leans against a vertical wall with its foot from the wall. How high up the wall does it reach?
  42. From a point from the foot of a tower on level ground, the angle of elevation of the top is . Find the height of the tower.
  43. Find the gradient of the line through and .
  44. The parallel sides of a trapezium are and and the distance between them is . Find its area.
  45. A train covers in hours. Find its average speed.
  46. Evaluate and give the answer in standard form.
  47. The length of a rectangle is more than its width. Its area is . Find the width.
  48. In an arithmetic progression the term number is and the term number is . Find the term number .

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