GCSE English and Maths Resits (Grade 4) · Maths

Geometry and Measures

38 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 38 questions

  1. What is the size of one interior angle of a regular octagon?
  2. What is the total surface area of a cuboid measuring cm by cm by cm?
  3. The bearing of town from town is . What is the bearing of from ?
  4. An isosceles triangle has two sides of cm and a base of cm. What is its area?
  5. A ladder m long leans against a vertical wall. Its foot is m from the wall. How high up the wall does it reach?
  6. The point is translated by the vector . What are the coordinates of its image?
  7. A cuboid measures cm by cm by cm. What is the length of the longest diagonal inside it?
  8. Which of these is not a condition that proves two triangles are congruent?
  9. In a triangle, two sides are cm and cm and the angle between them is . What is its area?
  10. Which of these is exactly equal to ?
  11. What is the midpoint of the line segment joining and ?
  12. What is the size of the angle between the hour hand and the minute hand of a clock at 4 o'clock?
  13. A rectangle has a perimeter of cm and a length of cm. What is its area?
  14. The point is reflected in the -axis. What are the coordinates of its image?
  15. Each exterior angle of a regular polygon is . How many sides does the polygon have?
  16. A cylinder has radius cm and height cm. What is its volume, to decimal place?
  17. Work out the area of a circle with radius cm. Give your answer to decimal place.
  18. A cone-shaped paper cup has a circular opening of radius cm and a vertical height of cm. What is its slant height?
  19. How many lines of symmetry does a regular hexagon have?
  20. A trapezium has parallel sides of cm and cm and a perpendicular height of cm. What is its area?
  21. A circle has diameter cm. What is its circumference, to decimal place?
  22. What is the distance between the points and ?
  23. A semicircle has a diameter of cm. What is its perimeter, to decimal place?
  24. The side length of a cube is doubled. By what factor does its volume increase?
  25. An isosceles triangle has an apex angle of . What is each base angle?
  26. Which set of side lengths forms a right-angled triangle?
  27. The point is enlarged by scale factor with centre of enlargement at the origin. What are the coordinates of its image?
  28. What is the sum of the interior angles of a hexagon?
  29. In a right-angled triangle, the hypotenuse is cm and the side opposite angle is cm. Find , to decimal place.
  30. A sector of a circle has radius cm and angle . What is its area, to decimal place?
  31. The point is rotated anticlockwise about the origin. What are the coordinates of its image?
  32. A regular polygon has an interior angle of . How many sides does it have?
  33. Triangle has a right angle at , . Point lies on a circle where is a diameter. Which is the size of ?
  34. Two co-interior (allied) angles lie between parallel lines. One is . What is the other?
  35. In a right-angled triangle, the side adjacent to a angle is cm. What is the length of the side opposite the angle, to decimal place?
  36. A parallelogram has base cm, perpendicular height cm and a slanted side of cm. What is its area?
  37. A triangular prism has a triangular cross-section with base cm and perpendicular height cm. The prism is cm long. What is its volume?
  38. How many edges does a triangular prism have?

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