ENEM Brazil · Mathematics and its Technologies

Geometry, Functions and Probability

21 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 21 questions

  1. A wall 12 m long and 5 m high is painted with a paint that covers 6 square metres per litre. How many litres are needed for one coat?
  2. A circular garden has radius 7 m. Using pi = 3.14, what is its circumference?
  3. A cylindrical tank has radius 1 m and height 2 m. Using pi = 3, how many litres does it hold when full?
  4. A taxi charges a fixed fee of 5 reais plus 2.50 reais per kilometre. How much does a 14 km ride cost?
  5. A bag has 3 red, 5 blue and 2 green balls. One ball is drawn at random. What is the probability that it is NOT red?
  6. Two fair six-sided dice are rolled. What is the probability that the sum is 7?
  7. A 5 m ladder leans against a wall with its foot 3 m from the wall. How high up the wall does it reach?
  8. A ball's height in metres is h = -t^2 + 4t, where t is in seconds. What is its maximum height?
  9. A 1.8 m tall person casts a 2.4 m shadow. At the same moment a tree casts an 8 m shadow. What is the height of the tree?
  10. A culture starts with 500 bacteria, and the number doubles every hour. How many bacteria are there after 4 hours?
  11. A shop sells 3 shirt models and 4 trouser models. How many different shirt-and-trousers outfits can be made?
  12. In how many different orders can four friends stand in a line for a photo?
  13. An urn holds 4 white and 6 black balls. Two balls are drawn one after the other, without replacement. What is the probability that both are black?
  14. The water filling a cube of edge 10 cm is poured into a cylinder of radius 5 cm. Using pi = 3.14, what is the height of the water in the cylinder?
  15. A small factory has monthly cost C = 300 + 5x (in reais) and sells each unit for 8 reais. How many units must be sold in a month to break even?
  16. A straight line passes through (0, 2) and (4, 10). What is its equation?
  17. Two angles of a triangle measure 50 and 60 degrees. What is the third angle?
  18. A cube has edge 3 cm. What is its total surface area?
  19. A ramp of length 6 m makes an angle of 30 degrees with the ground (sin 30 = 0.5). How high does it rise?
  20. Savings start at 50 reais in month 1 and rise by 30 reais each month (50, 80, 110, ...). What is the total saved over 12 months?
  21. A circle's radius is doubled. By what factor does its area change?

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