Examples for secondary school students - page 38

  1. Decimal to fraction
    fractions_2 Write decimal number 8.638333333 as a fraction A/B in the basic form. Given decimal has infinite repeating figures.
  2. Parabola
    parabola_1 Find the equation of a parabola that contains the points at A[6; -5], B[14; 9], C[23; 6]. (use y = ax2+bx+c)
  3. Geometric progression 2
    exp_x There is geometric sequence with a1=5.7 and quotient q=-2.5. Calculate a17.
  4. Geometric sequence
    cralici In the geometric sequence is a4 = 20 a9 = -160. Calculate the first member a1 and quotient q.
  5. Legs
    zidle In the room are four-legged chairs, three-legged stool, and all are sitted with (one) people. I counted all the leg room and there were a total of 39. How many are there chairs, stool and people?
  6. Center of gravity
    map_1 The mass points are distributed in space as follows - specify by coordinates and weight. Find the center of gravity of the mass points system: A1 [14; -2; 5] m1 = 10.2 kg A2 [-2; -16; 7] m2 = 13.6 kg A3
  7. Scouts
    skauti_2 Scouts purchased for camp cans two types total cost 1460 CZK. First cans were for CZK 32 and second for 25 CZK. How many cans purchased each type?
  8. Profits
    podnikavec Two members will make profit 52 000, - EUR. The forst earned 8% more and the second 10% more and thus earned together 56 700, - EUR. How many will initially each earn?
  9. Traffic laws
    car_lights Under traffic regulations, car lights can illuminate the road up to a maximum of 30 m. To check the reach of the dipped-beam lights of their car, Peter stopped car at 1.5 m from the wall. The dipped-beam headlights are 60 cm high. At what height on the wa
  10. Segment in a triangle
    priecka In a triangle ABC with the side/AB/ = 24 cm is constructed middle segment/DE/ = 18 cm parallel to the side AB at a distance 1 cm from AB. Calculate the height of the triangle ABC to side AB.
  11. Trapezoid 15
    trapezoid3 Area of trapezoid is 266. What value is x if bases b1 is 2x-3, b2 is 2x+1 and height h is x+4
  12. Rectangle pool
    basen_5 Determine dimensions of open pool with a square bottom with a capacity 32 m3 to have painted/bricked walls with least amount of material.
  13. Two months
    mars with moons Mars has two months, Phobos and Deimos. Phobos orbits around Mars in 7 hours 39 minutes and Deimos in 30 h 14 min. How long will repeat the relative position of the three celestial bodies?
  14. Inscribed circle
    Su55k02_m10 Write the equation of a incircle of the triangle KLM if K [2,1], L [6,4], M [6,1].
  15. MATES
    sazka In MATES (Small Television tipping) from 35 randomly numbers drawn 5 winning numbers. How many possible combinations there is?
  16. Ratio of two unknown numbers
    numbers2_23 Two numbers are given. Their sum is 30. We calculate one-sixth of a larger number and add to both numbers. So we get new numbers whose ratio is 5:7. Which two numbers were given?
  17. Clock face
    center_angle clock face is given. Numbers 10 and 5, and 3 and 8 are connected by straight lines. Calculate the size of their angles.
  18. Power
    power Number ?. Find the value of x.
  19. Unknown number
    unknown Unknown number is divisible by exactly three different primes. When we compare these primes in ascending order, the following applies: • Difference first and second prime number is half the difference between the third and second prime numbers. • The produ
  20. Arc-sector
    vzorec arc length = 17 cm area of sector = 55 cm2 arc angle = ? the radius of the sector = ?

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