Splošna Matura (Slovenia) · Mathematics

Algebra, Functions, Geometry and Probability

95 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 95 questions

  1. Solve the equation .
  2. What is the value of ?
  3. What is the area of a triangle with base and height ?
  4. What is ?
  5. Where does the line cross the -axis?
  6. What is the range of the data ?
  7. What is the value of ?
  8. What is equal to?
  9. What is the circumference of a circle with radius ?
  10. A bag contains red and blue balls. One ball is drawn at random. What is the probability that it is red?
  11. What is ?
  12. Two angles of a triangle are and . What is the third angle?
  13. Solve .
  14. What is the minimum value of ?
  15. What is the derivative of ?
  16. Find .
  17. Solve .
  18. The first term of an arithmetic sequence is and the common difference is . What is the sum of the first terms?
  19. In a triangle , and . What is side ?
  20. What is the length of the vector ?
  21. In how many ways can people be chosen from a group of ?
  22. Which line passes through and ?
  23. Solve .
  24. What is the inverse function of ?
  25. A cone has base radius and height . What is its volume?
  26. Events and are independent with and . What is ?
  27. What is the largest value of on the interval ?
  28. What is the area enclosed by the parabola and the -axis?
  29. In a geometric sequence and . What is the sum of the first four terms?
  30. What is ?
  31. What is the distance from the point to the line ?
  32. How many solutions does have in the interval ?
  33. In a class of students, study French, study German and study both. What is the probability that a student who studies German also studies French?
  34. What is ?
  35. For which values of does have no real solutions?
  36. What is the simplified value of the numerical expression ?
  37. What are the real roots of the quadratic equation ?
  38. What is the solution to the linear equation ?
  39. In a right-angled triangle with hypotenuse of length and one leg of length , what is the length of the other leg?
  40. In an arithmetic sequence with first term and common difference , what is the value of the sixth term ?
  41. What is the area of a circle whose diameter measures ?
  42. For the function , what is the value of ?
  43. What is the solution to the logarithmic equation ?
  44. What is the first derivative of the polynomial function ?
  45. Given two vectors and in , what is ?
  46. What is the slope of the straight line passing through the points and ?
  47. A book price decreases from to . What is the percentage decrease?
  48. What is the Euclidean distance between the points and in the coordinate plane?
  49. What is the arithmetic mean of the five numbers ?
  50. What is the solution set of the equation ?
  51. What is the definite integral ?
  52. What is the median of the data set ?
  53. In an isosceles triangle, the vertex angle measures . What is the measure of each base angle?
  54. In a geometric sequence, the first term is and the fourth term is . What is the common ratio ?
  55. What are the coordinates of the center and the radius of the circle ?
  56. What are the coordinates of the vertex of the parabola defined by ?
  57. What is the remainder when the polynomial is divided by ?
  58. What is the single simplified number equal to ?
  59. For the real functions and , what is the composite value ?
  60. What is the formula for the inverse function of the bijection where ?
  61. What is the slope of the tangent line to the curve at the point where ?
  62. What is the area of the region bounded by the curve and the line ?
  63. For which real value of are the vectors and orthogonal in ?
  64. If and the angle lies in the second quadrant, what is the value of ?
  65. In how many distinct ways can a committee of students be chosen from a group of candidates?
  66. What is the real solution to the exponential equation ?
  67. What is the sum of all positive integers less than that are divisible by ?
  68. In a triangle with side lengths , , and included angle , what is the length of side ?
  69. Two cards are drawn successively without replacement from a standard deck of cards. What is the probability that both cards are Aces?
  70. What is the product of the complex numbers and ?
  71. What is the derivative of the rational function for ?
  72. How many intersection points do the circle and the straight line have?
  73. What are all solutions to the trigonometric equation in the interval ?
  74. A right circular cylinder has base radius and height . What is its total surface area?
  75. What is the solution set of the quadratic inequality ?
  76. What is the real solution to the equation ?
  77. A fair coin is tossed times. What is the probability of obtaining exactly heads?
  78. What is the population variance of the five numbers ?
  79. What is the length of the major axis of the ellipse given by the equation ?
  80. A principal of is invested at an annual compound interest rate of , compounded once a year. What is the total accumulated amount after years?
  81. What is the limit ?
  82. At which point does the cubic function have its point of inflection?
  83. What is the definite integral ?
  84. An infinite geometric series has first term and sum . What is the common ratio ?
  85. How many distinct solutions does the trigonometric equation have in the open interval ?
  86. An open-top rectangular box is made from a square sheet of metal of side by cutting equal squares of side from each corner and turning up the sides. What value of maximizes the…
  87. In a triangle, side and its opposite angle is . What is the radius of the circumscribed circle?
  88. In a student group, study Spanish, study German, and study both languages. Given that a randomly chosen student studies German, what is the probability that the student also studi…
  89. What is the area of the parallelogram spanned by the vectors and in three-dimensional space?
  90. What is the equation of the tangent line to the circle at the point ?
  91. What is the area of the region in the first quadrant bounded by the curve and the line ?
  92. What is the sum of all third roots of unity, which are the solutions of in the complex plane?
  93. A regular four-sided pyramid has a square base with edge length and lateral edge length . What is the volume of the pyramid?
  94. For which real value of parameter does the linear system and have infinitely many solutions?
  95. The exam scores in a national assessment follow a normal distribution with mean and standard deviation . What percentage of candidates score between and ?

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