University of Bahrain Aptitude Test (UOB Aptitude) · Mathematics Reasoning

Functions, Trigonometry and Statistics

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

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All 31 questions

  1. Given f(x) = 2x + 3 and g(x) = x^2 - 1, find the composite function value (f o g)(3).
  2. Find the inverse function f^(-1)(x) for f(x) = (3x - 5) / 2.
  3. If sin(theta) = 3/5 and theta is in the second quadrant (90 degrees < theta < 180 degrees), what is the value of cos(theta)?
  4. Simplify the trigonometric expression: (1 - cos^2(theta)) / sin(theta).
  5. Evaluate the exact value of tan(45 degrees) + 2 * cos(60 degrees) - sin(30 degrees).
  6. A right-angled triangle has an angle of 30 degrees and an adjacent side of length 12 cm. What is the length of the opposite side?
  7. What is the radian equivalent of an angle measuring 150 degrees?
  8. Find the mean of the dataset: 14, 18, 22, 26, 30, 34, 38.
  9. A dataset has values: 5, 8, 12, 14, 17, 21, 25, 29. What is the median of this dataset?
  10. A fair six-sided die is rolled twice. What is the probability of rolling a sum of 8?
  11. If a bag contains 4 red marbles, 5 blue marbles, and 3 green marbles, what is the probability of drawing a blue marble at random?
  12. Two events A and B are independent with P(A) = 0.4 and P(B) = 0.5. What is the probability that both events occur, P(A and B)?
  13. Find the amplitude and period of the trigonometric function: y = -4 * sin(2x).
  14. What is the variance of the numbers: 2, 4, 6, 8, 10?
  15. Evaluate the exact value of cos(2*theta) given that sin(theta) = 0.6.
  16. In a standard normal distribution, approximately what percentage of data falls within 2 standard deviations of the mean?
  17. Find the domain of the rational function: g(x) = (2x + 1) / (x^2 - 9).
  18. What is the range of the quadratic function: f(x) = -2(x - 3)^2 + 8?
  19. If tan(theta) = 4/3 and theta lies in the first quadrant, find sin(2*theta).
  20. A student takes 5 exams and scores 78, 85, 92, 88, and 82. What score must they achieve on the 6th exam to earn an overall average of 86?
  21. Solve for x in the interval [0, 2pi): 2sin(x) - sqrt(3) = 0.
  22. If a box contains 3 red pens and 7 black pens, two pens are drawn one after another without replacement. What is the probability that both pens drawn are red?
  23. Find the vertical and horizontal asymptotes of the rational function: f(x) = (3x + 6) / (x - 4).
  24. Which of the following functions is an even function, satisfying f(-x) = f(x) for all x in its domain?
  25. A line segment connects points A(-3, 5) and B(5, -1). Find the coordinates of the midpoint of segment AB.
  26. In a circle of radius 6 cm, what is the length of an arc subtended by a central angle of 60 degrees? (Leave in terms of pi).
  27. What is the probability of selecting 2 red cards and 1 black card when 3 cards are drawn without replacement from a standard 52-card deck?
  28. A sum of…
  29. The diagonal of a square is . What is the area of a circle inscribed inside this square?
  30. If , what is the value of ?
  31. How many numbers between 100 and 500 are divisible by both 4 and 6?

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