Kuwait University Aptitude Tests (KUAT) · Mathematics and Quantitative Reasoning

Geometry, Trigonometry, and Quantitative Problem Solving

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

Practise Geometry, Trigonometry, and Quantitative Problem Solving now

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

All 31 questions

  1. What is the exact value of sin(75 degrees)?
  2. Find all solutions for theta in the interval [0, 2pi) that satisfy: 2 cos^2(theta) - cos(theta) - 1 = 0.
  3. In triangle ABC, side a = 7 cm, side b = 5 cm, and the included angle C = 60 degrees. Find the exact length of side c using the Law of Cosines.
  4. Find the center and radius of the circle defined by the equation: x^2 + y^2 - 6x + 8y - 11 = 0.
  5. What is the equation of the line passing through point (4, -2) that is perpendicular to the line 3x + 2y = 8?
  6. A right circular cylinder has a height of 12 cm and a total surface area of 110pi cm^2. What is the radius of its base?
  7. Find the area of a regular hexagon with a side length of 8 cm.
  8. What is the distance between the two parallel lines: 3x - 4y + 7 = 0 and 3x - 4y - 18 = 0?
  9. If tan(theta) = -3/4 and theta lies in the second quadrant (pi/2 < theta < pi), what is the value of cos(theta)?
  10. A circular sector has a central angle of 120 degrees and a radius of 9 cm. What is the perimeter of the sector?
  11. In a standard deck of 52 cards, two cards are drawn consecutively without replacement. What is the probability that both cards drawn are Aces?
  12. A student takes 5 exams and scores 82, 88, 91, 79, and 85. What must the student score on the 6th exam to achieve an overall arithmetic mean of exactly 86?
  13. How many distinct 4-digit codes can be formed using the digits 0 through 9 if repetition of digits is strictly prohibited and the first digit cannot be 0?
  14. Evaluate the limit: lim_{x -> 3} (x^2 - 9) / (2x^2 - 5x - 3).
  15. Find the derivative dy/dx of the function y = (3x^2 + 1)^4.
  16. Evaluate the definite integral: Integral from 1 to 4 of (3x^2 - 4x + 5) dx.
  17. A ladder 10 meters long leans against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1.5 m/s, how fast is the top of the ladder sliding down the wall when the bott…
  18. In a right triangle ABC with right angle at C, if sin(A) = 5/13, what is the value of cot(A)?
  19. What is the period of the trigonometric function: f(x) = 4 sin(3x - pi/2) + 7?
  20. What is the magnitude and direction angle theta (in degrees, 0 <= theta < 360) of the vector v = <-3, 3 sqrt(3)>?
  21. Two fair six-sided dice are rolled simultaneously. What is the probability that the sum of the numbers rolled is at least 10?
  22. A shopkeeper marks up the cost price of an item by 40% and then offers a 20% discount on the marked price during a promotional sale. What is the net profit percentage realized on the cost price?
  23. An investment of 5,000 USD is placed into an account earning 6% annual interest compounded semi-annually. What is the total account balance at the end of 2 years?
  24. A spherical water tank has a diameter of 6 meters. What is the volume of water the tank can hold when completely filled?
  25. If a line has an angle of inclination of 135 degrees with the positive x-axis, what is its slope?
  26. The coordinates of the vertices of a triangle are A(0, 0), B(6, 0), and C(2, 4). What is the area of triangle ABC?
  27. In a class of 60 students, 35 study Physics, 30 study Chemistry, and 15 study both subjects. How many students study neither Physics nor Chemistry?
  28. A sum of $8,000 invested at compound interest compounded annually amounts to $9,261 in 3 years. What is the annual interest rate?
  29. What is the probability of obtaining a sum of 8 when rolling two fair standard six-sided dice simultaneously?
  30. If the roots of the quadratic equation are real and equal, what is the value of ?
  31. A cylinder of radius 3 cm has a volume of . What is its total surface area including both circular bases?

Keep practising

More Kuwait University Aptitude Tests (KUAT) topics

All Kuwait University Aptitude Tests (KUAT) practice →

Ready for the full Kuwait University Aptitude Tests (KUAT) test?

Take a mock testKuwait University Aptitude Tests (KUAT) hub