Iraqi Third Intermediate Ministerial Exams · Mathematics

Problem solving

30 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 30 questions

  1. After a discount of 20% a coat costs 72 dinars. What was its price before the discount?
  2. After a discount of 40% a coat costs 90 dinars. What was its price before the discount?
  3. After a discount of 30% a coat costs 63 dinars. What was its price before the discount?
  4. After a discount of 25% a coat costs 84 dinars. What was its price before the discount?
  5. After a discount of 10% a coat costs 45 dinars. What was its price before the discount?
  6. After a discount of 20% a coat costs 120 dinars. What was its price before the discount?
  7. Solve the simultaneous equations 2x + 1y = 11 and 1x - 1y = 1. What is x + y?
  8. Solve the simultaneous equations 1x + 1y = 9 and 3x - 1y = 3. What is x + y?
  9. A car drives the first half of a journey at 60 km/h and the second half (the same distance) at 40 km/h. What is its average speed for the whole journey?
  10. A car drives the first half of a journey at 30 km/h and the second half (the same distance) at 60 km/h. What is its average speed for the whole journey?
  11. A car drives the first half of a journey at 80 km/h and the second half (the same distance) at 120 km/h. What is its average speed for the whole journey?
  12. A car drives the first half of a journey at 20 km/h and the second half (the same distance) at 30 km/h. What is its average speed for the whole journey?
  13. A car drives the first half of a journey at 90 km/h and the second half (the same distance) at 45 km/h. What is its average speed for the whole journey?
  14. A sum of 1000 dinars is invested at 10% compound interest per year. What is the total after 2 years?
  15. A sum of 2000 dinars is invested at 5% compound interest per year. What is the total after 2 years?
  16. A sum of 500 dinars is invested at 10% compound interest per year. What is the total after 3 years?
  17. A sum of 4000 dinars is invested at 25% compound interest per year. What is the total after 2 years?
  18. A ladder 13 m long leans against a vertical wall with its foot 5 m from the wall. How high up the wall does it reach?
  19. A ladder 17 m long leans against a vertical wall with its foot 8 m from the wall. How high up the wall does it reach?
  20. A ladder 25 m long leans against a vertical wall with its foot 7 m from the wall. How high up the wall does it reach?
  21. A ladder 29 m long leans against a vertical wall with its foot 20 m from the wall. How high up the wall does it reach?
  22. A bag holds 3 red and 2 blue marbles. Two marbles are drawn without replacement. What is the probability that both are red?
  23. A bag holds 4 red and 3 blue marbles. Two marbles are drawn without replacement. What is the probability that both are red?
  24. A bag holds 5 red and 3 blue marbles. Two marbles are drawn without replacement. What is the probability that both are red?
  25. A bag holds 6 red and 4 blue marbles. Two marbles are drawn without replacement. What is the probability that both are red?
  26. A bag holds 7 red and 3 blue marbles. Two marbles are drawn without replacement. What is the probability that both are red?
  27. A circle has radius 2 cm and a second circle has radius 3 cm. By what factor is the area of the second circle larger than the first?
  28. A circle has radius 3 cm and a second circle has radius 4 cm. By what factor is the area of the second circle larger than the first?
  29. A circle has radius 1 cm and a second circle has radius 2 cm. By what factor is the area of the second circle larger than the first?
  30. A circle has radius 2 cm and a second circle has radius 5 cm. By what factor is the area of the second circle larger than the first?

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