General Education Diploma (GED Oman) Β· Pure Mathematics

Coordinate Geometry, Vectors and Probability

31 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 31 questions

  1. Find the center and radius of the circle given by x^2 + y^2 - 6x + 8y = 0.
  2. What is the eccentricity of the ellipse given by (x^2 / 25) + (y^2 / 16) = 1?
  3. Find the focus of the parabola y^2 = 12x.
  4. Find the dot product of two vectors u = <3, -2, 4> and v = <5, 1, -2>.
  5. Calculate the cross product u x v for u = <1, 0, 0> and v = <0, 1, 0> in standard basis.
  6. Determine the angle theta between vectors a = <1, 1> and b = <0, 2>.
  7. What is the magnitude of the 3D vector v = <2, -3, 6>?
  8. Find the perpendicular distance from point P(1, 2, 3) to the plane 2x - 2y + z + 5 = 0.
  9. Find the number of distinct permutations of the letters in the word 'OMAN'.
  10. In how many ways can a committee of 3 students be selected from a class of 8 students?
  11. Find the coefficient of x^3 in the binomial expansion of (2x + 1)^5.
  12. Two fair six-sided dice are rolled. What is the probability that the sum of the numbers is 8?
  13. If P(A) = 0.4, P(B) = 0.5, and events A and B are independent, find P(A union B).
  14. A random variable X follows a binomial distribution B(n = 20, p = 0.3). Find the expected value E(X) and variance Var(X).
  15. Find the asymptotes of the hyperbola (x^2 / 9) - (y^2 / 16) = 1.
  16. Find the coordinates of the midpoint of the segment connecting A(4, -2, 7) and B(-2, 6, 1).
  17. Given vectors u and v such that ||u|| = 4, ||v|| = 5, and u . v = 10, find ||u - v||.
  18. Find the equation of the plane passing through (2, 1, -1) with normal vector n = <3, -1, 4>.
  19. In a bag containing 5 red, 4 blue, and 3 green marbles, what is the probability of drawing 2 red marbles without replacement?
  20. Find the directrix of the parabola x^2 = -8y.
  21. What is the vertex of the parabola (y - 3)^2 = 8(x + 2)?
  22. A box has 10 components, 2 of which are defective. If 2 are selected at random, what is the probability that at least one is defective?
  23. Find the unit vector in the direction of v = <6, -8>.
  24. Determine the angle between the planes 2x - y + 2z = 5 and 3x + 4y = 1.
  25. If events A and B are mutually exclusive with P(A) = 0.35 and P(B) = 0.45, find P(A intersect B).
  26. Find the length of the major axis of the ellipse 4x^2 + 9y^2 = 36.
  27. Evaluate the integral: .
  28. What is the sum of the infinite geometric series: ?
  29. If the line is tangent to the parabola , what is the value of ?
  30. How many 5-card hands containing exactly 3 aces can be dealt from a standard 52-card deck?
  31. What is the center and radius of the sphere defined by the equation ?

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