DTM University Entrance Test (Uzbekistan) · Mathematics

Algebra and functions

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. Solve the equation 3x − 7 = 11.
  2. Simplify 2^5 · 2^3 / 2^6.
  3. What are the roots of x² − 5x + 6 = 0?
  4. The first term of an arithmetic progression is 3 and the common difference is 4. What is the sum of the first 10 terms?
  5. What is the value of log₂ 64?
  6. For f(x) = 2x² − 3x + 1, what is f(3)?
  7. Solve the inequality 2x − 5 > 3.
  8. What is the discriminant of x² − 4x + 5, and what does it tell you?
  9. A geometric progression begins 2, 6, 18. What is the 5th term?
  10. Solve the system x + y = 7 and x − y = 1.
  11. Simplify (x² − 9)/(x − 3) for x ≠ 3.
  12. What is the domain of f(x) = √(x − 2)?
  13. What is the x-coordinate of the vertex of y = x² − 6x + 5?
  14. Solve |2x − 1| = 5.
  15. The roots of x² + px + 12 = 0 are positive and one root is three times the other. What is p?
  16. In an infinite geometric series the second term is 2 and the common ratio is 1/3. What is the sum?
  17. Solve log₃ x + log₃ (x − 2) = 1.
  18. Two numbers have sum 14 and product 45. What is the sum of their squares?
  19. What is 3⁻² equal to?
  20. A boat travels at 12 km/h in still water in a river flowing at 3 km/h. It goes 45 km downstream and returns. How long does the round trip take?
  21. Solve x/4 = 9.
  22. Evaluate .
  23. Evaluate .
  24. Expand and simplify .
  25. Solve .
  26. Solve the simultaneous equations and . Find the value of .
  27. How many positive integers satisfy ?
  28. Given , find when , and .
  29. Find the sum of the first terms of the arithmetic progression
  30. Find the median of .
  31. A ladder long leans against a vertical wall with its foot from the wall. How high up the wall does it reach?
  32. The parallel sides of a trapezium are and and the distance between them is . Find its area.
  33. A bus travels at for hours. How far does it travel?
  34. Evaluate and give the answer in standard form.
  35. Simplify .
  36. In an arithmetic progression the term number is and the term number is . Find the term number .
  37. A box contains 8 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.
  38. A straight line passes through and . Find the value of when .
  39. Evaluate .
  40. Find the value of .
  41. Find .
  42. Evaluate .
  43. Expand and simplify .
  44. Solve and give the larger root.
  45. Solve .
  46. Solve the simultaneous equations and . Find the value of .
  47. How many positive integers satisfy ?
  48. Given , find when , and .

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