National Benchmark Tests (NBT) · Mathematics

Geometry, sequences and counting

18 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 18 questions

  1. What is the sum of the interior angles of a polygon with 12 sides?
  2. What is the sum of the interior angles of a polygon with 8 sides?
  3. A sector of a circle has radius 9 cm and angle 120°. What is its area? (Give the answer in terms of .)
  4. A sector of a circle has radius 12 cm and angle 30°. What is its area? (Give the answer in terms of .)
  5. What is the sum of the interior angles of a polygon with 9 sides?
  6. The equation of a circle is . What is the radius?
  7. A sector of a circle has radius 4 cm and angle 90°. What is its area? (Give the answer in terms of .)
  8. Two similar triangles have corresponding sides in the ratio 1 : 4. The smaller triangle has an area of 6 cm². What is the area of the larger triangle?
  9. Two similar triangles have corresponding sides in the ratio 1 : 4. The smaller triangle has an area of 8 cm². What is the area of the larger triangle?
  10. A ladder of length 17 m leans against a vertical wall. The foot of the ladder is 8 m from the wall. How high up the wall does the ladder reach?
  11. The first three terms of an arithmetic sequence are 5; 9; 13. What is the 24th term?
  12. At a meeting, each of 12 people shakes hands once with every other person. How many handshakes take place?
  13. At a meeting, each of 10 people shakes hands once with every other person. How many handshakes take place?
  14. The sequence 4, 10, 20, 34, ... has a constant second difference. What is the next term?
  15. At a meeting, each of 8 people shakes hands once with every other person. How many handshakes take place?
  16. The first three terms of an arithmetic sequence are 3; 8; 13. What is the 28th term?
  17. The sequence 5, 17, 35, 59, ... has a constant second difference. What is the next term?
  18. The first three terms of an arithmetic sequence are 7; 10; 13. What is the 14th term?

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