Državna Matura (Bosnia & Herzegovina) · Mathematics

Algebra, Functions, Geometry and Probability

118 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 118 questions

  1. Solve the equation .
  2. What is the value of ?
  3. What is the value of ?
  4. What is the slope of the line ?
  5. What is the sum of the interior angles of a hexagon?
  6. What is the area of a circle with radius ?
  7. What is the value of ?
  8. A fair six-sided die is rolled once. What is the probability of an even number?
  9. What are the solutions of ?
  10. An arithmetic sequence has first term and common difference . What is the tenth term?
  11. What is the value of ?
  12. What is the mean of the numbers ?
  13. Solve the inequality .
  14. How many real roots does have?
  15. What is the vertex of the parabola ?
  16. What is the domain of ?
  17. Evaluate .
  18. The legs of a right triangle are and . What is the length of the hypotenuse?
  19. What is the slope of the line through and ?
  20. What is the derivative of ?
  21. In how many ways can a committee of people be chosen from people?
  22. A geometric sequence begins . What is its sixth term?
  23. In the first quadrant . What is ?
  24. A cylinder has base radius and height . What is its volume?
  25. Solve .
  26. What is the value of ?
  27. The quadratic has one root equal to twice the other. What is ?
  28. Solve .
  29. A rectangular garden is fenced with metres of wire. What is the largest possible area?
  30. Find the sum of the infinite geometric series
  31. What is the equation of the tangent to at the point where ?
  32. Two cards are drawn without replacement from a standard -card deck. What is the probability that both are aces?
  33. Two sides of a triangle are and and the angle between them is . What is the third side?
  34. The mean of five numbers is . When a sixth number is added the mean becomes . What is the sixth number?
  35. Solve the inequality .
  36. Find f'(3) for f(x) = x^3-2x^2+4x.
  37. Find f'(2) for f(x) = 2x^3-x^2+5x.
  38. Find f'(3) for f(x) = x^3+x^2-4x.
  39. Evaluate the integral of (3x^2+4x) dx from x = 0 to x = 3.
  40. Evaluate the integral of (6x^2+6x) dx from x = 0 to x = 2.
  41. Evaluate the integral of (9x^2+2x) dx from x = 0 to x = 2.
  42. Evaluate the integral of (3x^2+8x) dx from x = 0 to x = 2.
  43. Evaluate the integral of (6x^2+4x) dx from x = 0 to x = 3.
  44. Differentiate y = (3x + 1)^3 and evaluate dy/dx at x = 1.
  45. Differentiate y = (2x - 1)^4 and evaluate dy/dx at x = 1.
  46. Differentiate y = (5x + 1)^2 and evaluate dy/dx at x = 0.
  47. Differentiate y = (1x + 3)^3 and evaluate dy/dx at x = -1.
  48. Differentiate y = (4x - 2)^3 and evaluate dy/dx at x = 1.
  49. Differentiate y = (2x + 2)^2 and evaluate dy/dx at x = 2.
  50. Find the distance from the point (2, 3) to the line 3x+4y-6 = 0.
  51. Find the distance from the point (-1, 2) to the line 5x+12y+1 = 0.
  52. Find the distance from the point (3, 3) to the line 8x+15y-4 = 0.
  53. Find the distance from the point (0, 1) to the line 4x+3y+2 = 0.
  54. Find the distance from the point (1, -2) to the line 5x+12y = 0.
  55. Find the distance from the point (2, 2) to the line 6x+8y-3 = 0.
  56. Find the radius of the circle x^2+y^2-4x-6y-12 = 0.
  57. Find the radius of the circle x^2+y^2+2x-8y+8 = 0.
  58. Find the radius of the circle x^2+y^2-6x+4y-23 = 0.
  59. Find the radius of the circle x^2+y^2-2x-2y-47 = 0.
  60. Find the radius of the circle x^2+y^2+6x+4y+9 = 0.
  61. An arithmetic sequence has first term 4 and common difference 3. Find the sum of its first 12 terms.
  62. An arithmetic sequence has first term 6 and common difference 5. Find the sum of its first 10 terms.
  63. An arithmetic sequence has first term -2 and common difference 4. Find the sum of its first 9 terms.
  64. An arithmetic sequence has first term 9 and common difference 2. Find the sum of its first 15 terms.
  65. An arithmetic sequence has first term 1 and common difference 7. Find the sum of its first 8 terms.
  66. An arithmetic sequence has first term 8 and common difference -3. Find the sum of its first 10 terms.
  67. A geometric sequence has first term 2 and common ratio 4. Find the sum of its first 4 terms.
  68. A geometric sequence has first term 5 and common ratio 3. Find the sum of its first 3 terms.
  69. A geometric sequence has first term 1 and common ratio 5. Find the sum of its first 4 terms.
  70. A geometric sequence has first term 2 and common ratio 3. Find the sum of its first 6 terms.
  71. Find the sum to infinity of the geometric series 10 + 5 + 5/2 + ...
  72. Find the sum to infinity of the geometric series 9 + 3 + 1 + ...
  73. Find the sum to infinity of the geometric series 12 + 3 + 3/4 + ...
  74. Find the sum to infinity of the geometric series 15 + 10 + 20/3 + ...
  75. Find the sum to infinity of the geometric series 20 + 4 + 4/5 + ...
  76. Find the sum to infinity of the geometric series 18 + 27/2 + 81/8 + ...
  77. Solve log_2(x) = 6.
  78. Solve log_3(x) = 2.
  79. Solve log_5(x) = 3.
  80. Solve log_2(x) = 8.
  81. Solve log_4(x) = 2.
  82. Solve log_10(x) = 3.
  83. Write (1 - i)(2 + 2i) in the form x + yi.
  84. Write (4 + i)(3 - i) in the form x + yi.
  85. Write (3 + 2i)(2 - 3i) in the form x + yi.
  86. Write (1 + 5i)(1 + i) in the form x + yi.
  87. In how many ways can a committee of 2 be chosen from 8 people?
  88. In how many ways can a committee of 3 be chosen from 9 people?
  89. In how many ways can a committee of 2 be chosen from 12 people?
  90. Events A and B satisfy P(B) = 1/2 and P(A and B) = 1/8. Find P(A | B).
  91. Events A and B satisfy P(B) = 1/2 and P(A and B) = 1/3. Find P(A | B).
  92. Events A and B satisfy P(B) = 1/2 and P(A and B) = 2/5. Find P(A | B).
  93. Events A and B satisfy P(B) = 3/4 and P(A and B) = 1/4. Find P(A | B).
  94. Events A and B satisfy P(B) = 3/5 and P(A and B) = 1/2. Find P(A | B).
  95. A basketball player scores with probability 1/4 on each independent shot. Find the probability of exactly 2 scores in 3 shots.
  96. A basketball player scores with probability 1/5 on each independent shot. Find the probability of exactly 2 scores in 3 shots.
  97. A basketball player scores with probability 2/5 on each independent shot. Find the probability of exactly 2 scores in 3 shots.
  98. A basketball player scores with probability 1/3 on each independent shot. Find the probability of exactly 2 scores in 4 shots.
  99. A basketball player scores with probability 2/3 on each independent shot. Find the probability of exactly 3 scores in 4 shots.
  100. A basketball player scores with probability 1/2 on each independent shot. Find the probability of exactly 2 scores in 5 shots.

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