Sultan Qaboos University Foundation & Aptitude Test · Mathematics 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. In a right triangle, the hypotenuse is 13 cm and one leg is 5 cm. What is the length of the other leg and the area of the triangle?
  2. Two parallel lines are intersected by a transversal. If one interior angle is (3x + 15) degrees and its consecutive interior angle is (2x + 25) degrees, find x.
  3. A circle has a radius of 6 cm. What is the length of an arc intercepted by a central angle of 60 degrees?
  4. Find the area of a circular sector with a radius of 10 cm and a central angle of 72 degrees.
  5. What is the exact value of cos(150 degrees)?
  6. Given that sin(theta) = 3/5 and theta is in Quadrant II, what is the value of tan(theta)?
  7. A closed right circular cylinder has a base radius of 3 cm and a height of 7 cm. What is its total surface area?
  8. What is the volume of a right circular cone with radius 6 cm and height 10 cm?
  9. A car travels 180 km from Muscat to Nizwa at an average speed of 90 km/h, and returns along the same route at 60 km/h. What is the average speed for the entire round trip?
  10. A store discounts an item by 20%, and then applies an additional 10% discount on the discounted price during a promotion. What is the total single percentage discount from the original price?
  11. Pipe A can fill a water tank in 4 hours, and Pipe B can fill it in 6 hours. If both pipes operate simultaneously, how many hours will it take to fill the tank?
  12. In a group of 60 students, the ratio of boys to girls is 3:2. If 10 additional girls join the group, what is the new ratio of boys to girls?
  13. Find the distance between the two points A(-2, 5) and B(4, -3) in the Cartesian coordinate plane.
  14. What is the slope of a line that is perpendicular to the line 3x - 6y = 12?
  15. A data set consists of seven values: 4, 8, 3, 9, 12, 8, 5. What are the median and mode of this data set?
  16. What is the sum of the interior angles of a regular convex octagon (8-sided polygon)?
  17. In a triangle ABC, angle A = 30 degrees, angle B = 45 degrees, and side a = 8 cm. What is the length of side b using the Law of Sines?
  18. How many liters of pure water must be added to 30 liters of a 40% acid solution to dilute it to a 25% acid solution?
  19. What is the total number of diagonals in a convex hexagon (6-sided polygon)?
  20. A spherical metal ball has a diameter of 12 cm. What is its volume in terms of pi?
  21. If a fair coin is tossed 4 times, what is the probability of getting exactly 3 heads?
  22. Find the equation of the line passing through points (1, 3) and (4, -3).
  23. A ladder 10 meters long leans against a vertical wall, making an angle of 60 degrees with the horizontal ground. How high up the wall does the ladder reach?
  24. What is the perimeter of a rhombus whose diagonals measure 12 cm and 16 cm?
  25. A student scored 78, 85, 92, and 81 on four tests. What score must they achieve on the fifth test to have an overall mean of 86?
  26. What is the simplified value of the trigonometric expression: [sin^2(x) + cos^2(x)] / [1 + tan^2(x)]?
  27. In how many ways can a delegation of 3 teachers and 4 students be selected from a pool of 6 teachers and 8 students?
  28. A motorboat travels 36 km downstream along a river in 3 hours, and returns upstream the same distance in 6 hours. What is the speed of the river current?
  29. Two fair six-sided dice are tossed. What is the probability that the product of the two numbers obtained is an odd number?
  30. What is the length of the diagonal of a rectangular prism with dimensions 6 cm, 8 cm, and 24 cm?
  31. If , what is the positive real solution for ?

Keep practising

More Sultan Qaboos University Foundation & Aptitude Test topics

All Sultan Qaboos University Foundation & Aptitude Test practice →

Ready for the full Sultan Qaboos University Foundation & Aptitude Test test?

Take a mock testSultan Qaboos University Foundation & Aptitude Test hub
Geometry, Trigonometry and Quantitative Problem Solving | GetMyMockTest