Examples for secondary school students - page 33

  1. Traffic collision
    crash When investigating a traffic accident, it was found that the driver stopped the vehicle immediately after the accident by constant braking on a 150 m track in 15 seconds. Do you approve that the driver exceeded the permitted speed (50 km/h) in the village.
  2. Rhombus
    rhombus_5 ABCD is a rhombus, ABD is an equilateral triangle and AC is equal to 4. Find the area of the rhombus.
  3. Midpoint of segment
    midpoint-segment Point A has coordinates [-16; 23] and the midpoint of the segment AB is the point [2; 12]. What are the coordinates of point B?
  4. Semicircle
    semicircle_2 To a semicircle with diameter 10 cm inscribe square. What is the length of square sides?
  5. Garden
    garden_6 The garden has a rectangular shape and has a circumference of 130 m and area 800.25 m2. Calculate the dimensions of the garden.
  6. Vector
    vectors Determine coordinates of the vector u=CD if C[19;-7], D[-16,-5].
  7. Sequence 3
    75 Write the first 5 members of an arithmetic sequence: a4=-35, a11=-105.
  8. 10 pieces
    circle_div How to divide the circle into 10 parts (geometrically)?
  9. Triangle ABC
    lalala In a triangle ABC with the side BC of length 2 cm The middle point of AB. Points L and M split AC side into three equal lines. KLM is isosceles triangle with a right angle at the point K. Determine the lengths of the sides AB, AC triangle ABC.
  10. Rectangular trapezoid
    color_triangles Calculate the content of a rectangular trapezoid with a right angle at the point A and if |AC| = 4 cm, |BC| = 3 cm and the diagonal AC is perpendicular to the side BC.
  11. Hearts
    hearts_cards 4 cards are chosen from a standard deck of 52 playing cards (13 hearts) with replacement. What is the probability of choosing 4 hearts in a row?
  12. Friends
    friends2 Some friends had to collect the sum 72 EUR equally. If the three refused their part, others would have to give each 4 euros more. How many are friends?
  13. The dice
    hracia-kocka What is the probability of events that if we throw a dice is rolled less than 6?
  14. Chord - TS v2
    chord_TS_1 The radius of circle k measures 87 cm. Chord GH = 22 cm. What is TS?
  15. Car
    motor_cylinders_kW At what horizontal distance reaches the car weight m = 1534 kg speed v = 85 km/h when the car engine develops a tensile force F = 1691 N. (Neglect resistance of the environment.)
  16. Three digits number
    3digit From the numbers 1, 2, 3, 4, 5 create three-digit numbers that digits not repeat and number is divisible by 2. How many numbers are there?
  17. RT and circles
    r_triangle Solve right triangle if the radius of inscribed circle is r=9 and radius of circumscribed circle is R=23.
  18. Sum of series
    question Determine the 6-th member and the sum of a geometric series: 5-4/1+16/5-64/25+256/125-1024/625+....
  19. Car value
    car_old The car loses value 15% every year. Determine a time (in years) when the price will be halved.
  20. Miraculous tree
    tree Miraculous tree grows so fast that the first day increases its height by half the total height of the second day by the third, the third day by a quarter, etc. How many times will increase its height after 6 days?

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