Uzbekistan Presidential Schools Admission Test · Mathematics

Geometry, Ratio and Word Problems

53 practice questions, each with the answer and an explanation.

Practise Geometry, Ratio and Word Problems now

Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 53 questions

  1. What is the perimeter of a rectangle 12 cm long and 5 cm wide?
  2. What is the area of a triangle with base 10 cm and height 6 cm?
  3. Girls and boys in a class are in the ratio 3:5 and there are 40 students. How many boys are there?
  4. Two angles of a triangle are 50 degrees and 60 degrees. What is the third angle?
  5. A rectangle has area 48 cm squared and length 8 cm. What is its perimeter?
  6. A map has scale 1:50,000. Two towns are 4 cm apart on the map. What is the real distance?
  7. A circle has area 49 pi cm squared. What is its circumference?
  8. What is the sum of the interior angles of a hexagon?
  9. A right-angled triangle has shorter sides 9 cm and 12 cm. How long is the longest side?
  10. A recipe uses 300 g of rice for 4 people. How much rice is needed for 10 people?
  11. A cube has volume 125 cm cubed. What is its total surface area?
  12. A father is four times as old as his son. In 5 years their ages add up to 55. How old is the son now?
  13. A car travels at 60 km/h for 2.5 hours. How far does it go?
  14. Three pencils cost 4,500 soums. How much do seven pencils cost?
  15. The length of a rectangle is doubled and its width is tripled. By what factor does the area grow?
  16. How many lines of symmetry does a regular pentagon have?
  17. Six workers build a wall in 10 days. Working at the same rate, how many days do 4 workers need?
  18. What percentage of 24 students is 18 students?
  19. How many squares of all sizes are in a 3 by 3 grid of small squares?
  20. A square has a diagonal of 10 cm. What is its area?
  21. Evaluate and give the answer in standard form.
  22. On a map with scale , two towns are apart. Find the real distance in km.
  23. Expand and simplify .
  24. How many positive integers satisfy ?
  25. In an arithmetic progression the term number is and the term number is . Find the term number .
  26. Evaluate .
  27. Find the highest common factor (HCF) of and .
  28. A bus travels at for hours. How far does it travel?
  29. The angles of a triangle are in the ratio . Find the largest angle.
  30. A rectangle by has a square of side cut from one corner. Find the area of the remaining shape.
  31. The table shows the number of books read by students: book (8 students), books (7), books (2), books (3). Find the mean number of books.
  32. Find the term number of the arithmetic progression
  33. Solve .
  34. A box contains 8 red and 5 blue balls. Two balls are taken at random without replacement. Find the probability that they are of different colours.
  35. On a map with scale , two towns are apart. Find the real distance in km.
  36. Expand and simplify .
  37. How many positive integers satisfy ?
  38. Evaluate .
  39. Each exterior angle of a regular polygon is . How many sides does the polygon have?
  40. Two similar triangles have corresponding sides in the ratio . The area of the smaller triangle is . Find the area of the larger triangle.
  41. The mean of and is . Find .
  42. Solve .
  43. The length of a rectangle is more than its width. Its area is . Find the width.
  44. On a map with scale , two towns are apart. Find the real distance in km.
  45. Expand and simplify .
  46. Find the least integer value of that satisfies .
  47. Evaluate .
  48. A car travels at and then returns the same at . Find the average speed for the whole journey.
  49. The diagonal of a rectangle is and one side is . Find the area of the rectangle.
  50. A rectangle by has a square of side cut from one corner. Find the area of the remaining shape.
  51. Find the median of .
  52. A bag has 8 red and 2 blue marbles. One marble is picked at random. Find the probability that it is blue.
  53. Find the sum of the first terms of the arithmetic progression

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