Examples for secondary school students - page 14

  1. Coin and die
    die Flip a coin and then roll a six-sided die. How many possible combinations are there?
  2. Spherical segment
    circular_segment_1 Spherical segment with height h=6 has a volume V=134. Calculate the radius of the sphere of which is cut this segment.
  3. Geometric progression
    fractal Fill 4 numbers between 4 and -12500 to form geometric progression.
  4. Slope of the pool
    swimming_pool Calculate slope (rise:run) of the bottom of swimming pool long 10 m. Water depth at beginning of pool is 1.16 m (for children) and depth at end is 1.89 m (for swimmers). Slope express as percentage and as angle in degrees.
  5. Shooter
    terc_1 The shooter fired to a target from distance 11 m The individual concentric circle of targets have a radius increments 1 cm (25 points) by 1 point. Shot was shifted by 8'(angle degree minutes). How many points should win his shot?
  6. Wiring
    install_pipes Conduit has a cross section 482 mm. Maybe put it into 6 conductors with a cross section S2 $mm2?
  7. Divisibility
    dots Determine the smallest integer which divided 11 gives remainder 4 when divided 15 gives remainder 10 and when divided by 19 gives remainder 16.
  8. Mystery of stereometrie
    Tetrahedron Two regular tetrahedrons have surfaces 88 cm2 and 198 cm2. In what ratio is their volumes? Write as a fraction and as a decimal rounded to 4 decimal places.
  9. Nine-gon
    9gon_1 Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 13 cm.
  10. 3y inflation
    bread Price of the roll rise in the first year by 9%, the second year fell by 5% and in the third year increased by 3%. Calculate the average annual increase in price of the roll.
  11. Sphere and cone
    cone_in_sphere Within the sphere of radius G = 33 cm inscribe cone with largest volume. What is that volume and what are the dimensions of the cone?
  12. Side c
    trig-cos-law In △ABC a=2, b=4 and ∠C=100°. Calculate length of the side c.
  13. Black building
    talapka_cierna_stavba Keith built building with a rectangular shape 6.5 m × 3.9 m. Calculate how much percent exceeded the limit 25 m2 for small building. Building not built in accordance with the law is called "black building". Calculate the angle that the walls were clenchin
  14. Pit
    truncated_pyramid Pit has shape of a truncated pyramid with rectangular bases and is 0.8 m deep. The length and width of the pit is the top 3 × 1.5 m bottom 1 m × 0.5 m. To paint one square meter of pit we use 0.6 l of green colour. How many liters of paint is needed when w
  15. Road
    route-66 Average climb of the road is given by ratio 1:15. By what angle road average climb?
  16. Lock
    combination-lock Combination lock will open when the right choice of 3 numbers (from 1 to 25 inclusive) is selected. A. How many different lock combinations are possible? B. Is he combination lock named appropriately?
  17. Circle
    circles From the equation of a circle: ? Calculate the coordinates of the center of the circle S[x0, y0] and radius of the circle r.
  18. AVG of INT
    seq_moon What is the average of the integers from 9 throuht 52 inclusive?
  19. Height difference
    road What height difference overcome if we pass road 1 km long with a pitch21 per mille?
  20. Elevation
    horizon_diagram What must be the elevation of an observer in order that he may be able to see an object on the earth 782 km away? Assume the earth to be a smooth sphere with radius 6378.1 km.

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