Iraqi Third Intermediate Ministerial Exams · Mathematics

Algebra, Geometry and Statistics

35 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 35 questions

  1. Solve the equation 3x - 7 = 11.
  2. Simplify 2(x + 4) - 3x.
  3. Solve the simultaneous equations x + y = 10 and x - y = 4. What is the value of x?
  4. A right-angled triangle has legs of 6 cm and 8 cm. What is the length of its hypotenuse?
  5. In a right-angled triangle the hypotenuse is 13 cm and one leg is 5 cm. How long is the other leg?
  6. Share 64 sweets in the ratio 3 : 5. How many sweets does the larger share contain?
  7. Factorise x squared - 9 completely.
  8. Factorise x squared + 5x + 6.
  9. What are the solutions of x squared - 5x + 6 = 0?
  10. What is the mean of the numbers 4, 8, 6, 10 and 12?
  11. What is the median of the data set 3, 9, 5, 7, 11, 1?
  12. If A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7}, which set is A intersection B?
  13. In a group, n(A) = 12, n(B) = 9 and n(A intersection B) = 4. What is n(A union B)?
  14. What is the gradient of the straight line through the points (1, 2) and (5, 10)?
  15. Which equation represents the line with gradient 3 that cuts the y-axis at -2?
  16. Using pi = 22/7, what is the area of a circle with radius 7 cm?
  17. What is the volume of a cuboid that is 5 cm long, 4 cm wide and 3 cm high?
  18. A price rises from 80 dinars to 100 dinars. What is the percentage increase?
  19. A coat costs 250 dinars. It is reduced by 20 percent and then 10 percent tax is added to the reduced price. What is the final price?
  20. Solve (2x / 3) + 1 = 5.
  21. What is the size of one interior angle of a regular octagon?
  22. Simplify the square root of 50.
  23. A rectangle has a perimeter of 36 cm and its length is twice its width. What is its area?
  24. Solve the inequality 5 - 2x > 1.
  25. What is 2 to the power 3 multiplied by 2 to the power 4?
  26. A car travels 120 km in 2 hours and then 90 km in 1 hour. What is its average speed for the whole journey?
  27. A fair six-sided die is rolled once. What is the probability of a prime number?
  28. Two fair coins are tossed. What is the probability that both show heads?
  29. The equation x squared + kx + 9 = 0, with k greater than 0, has exactly one solution. What is k?
  30. Which set of lengths forms the sides of a right-angled triangle?
  31. Write 4 500 000 in standard form (scientific notation).
  32. Simple interest of 450 dinars is earned on 1 500 dinars at 6 percent per year. For how many years was the money invested?
  33. Expand (x + 3) squared.
  34. The sum of three consecutive whole numbers is 78. What is the largest of the three?
  35. In a class the ratio of boys to girls is 3 : 4 and there are 28 students. If 4 more boys join, what is the new ratio of boys to girls in simplest form?

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