Basic Education Certificate Examination · Mathematics

Geometry, Measurement and Mensuration

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

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All 35 questions

  1. The interior angles of a triangle are in the ratio 2 : 3 : 5. Find the size of the largest angle.
  2. Find the sum of the interior angles of a regular hexagon (six-sided polygon).
  3. Each interior angle of a regular polygon is 140°. How many sides does the polygon have?
  4. In a right-angled triangle, the two shorter sides measure 6 cm and 8 cm. Find the length of the hypotenuse.
  5. Find the perimeter of a rectangle whose length is 14 cm and breadth is 9 cm.
  6. Calculate the area of a circle of radius 7 cm (take π = 22/7).
  7. Find the circumference of a circular wheel with a diameter of 28 cm (take π = 22/7).
  8. A trapezium has parallel sides of lengths 8 cm and 12 cm, and a perpendicular height of 6 cm. Find its area.
  9. Calculate the total surface area of a closed cube of side length 5 cm.
  10. Find the volume of a rectangular cuboid of length 10 cm, width 6 cm, and height 4 cm.
  11. Calculate the volume of a solid cylinder of radius 7 cm and height 10 cm (take π = 22/7).
  12. Find the curved surface area of a cylinder of radius 7 cm and height 12 cm (take π = 22/7).
  13. In a triangle ABC, angle A = 65° and angle B = 45°. Find the size of exterior angle at vertex C.
  14. Two parallel lines are cut by a transversal. If one interior alternate angle is 58°, what is the other alternate angle?
  15. A ladder 13 m long leans against a vertical wall with its foot 5 m from the base of the wall. How high up the wall does it reach?
  16. Point P(3, -2) is reflected in the x-axis. What are the coordinates of the image point P'?
  17. Point Q(-4, 5) is reflected in the y-axis. What are the coordinates of the image point Q'?
  18. Point A(2, 3) is translated by the vector v = (4, -5). Find the coordinates of image point A'.
  19. If vector u = (3, 4), what is the magnitude (length) of vector u?
  20. Find the bearing of a point that lies directly South-East from an observer.
  21. The bearing of town B from town A is 070°. What is the back bearing of town A from town B?
  22. The perimeter of a square plot is 64 metres. What is the area of the plot?
  23. A sector of a circle of radius 6 cm has a central angle of 60°. Calculate the area of the sector (take π = 3.14).
  24. Calculate the length of the arc of a circle of radius 14 cm that subtends an angle of 90° at the centre (π = 22/7).
  25. The scale of a district map is 1 : 50,000. If two school buildings are 4 cm apart on the map, what is their real distance?
  26. Find the gradient (slope) of the straight line passing through points A(2, 3) and B(6, 11).
  27. What is the equation of a straight line with gradient 3 that passes through the point (0, -4)?
  28. Find the midpoint of the line segment joining the points P(-2, 5) and Q(4, 1).
  29. How many lines of symmetry does an equilateral triangle have?
  30. How many lines of symmetry does a non-square rectangle have?
  31. The diameter of a spherical football is 21 cm. What is its radius?
  32. A triangular prism has a cross-sectional area of 24 cm² and a length of 15 cm. Find its volume.
  33. Find the area of a right-angled triangle whose base is 12 cm and height is 9 cm.
  34. What is the order of rotational symmetry of a regular pentagon about its centre?
  35. Convert an area of 5 square metres (m²) to square centimetres (cm²).

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