Examples for secondary school students

  1. A three-digit numbers
    clocks_1 Determine the total number of positive three-digit numbers that contain a digit 6.
  2. Square roots
    roots What is equal to the product of the square roots of 295936?
  3. Goat and circles
    equation_nonlinear What is the radius of a circle centered on the other circle and the intersection of the two circles is equal to half the area of the first circle? This task is the mathematical expression of the role of agriculture. The farmer has circular land on which
  4. Building
    building The building I focused at an angle 30°. When I moved 5 m building I focused at an angle 45°. What is the height of the building?
  5. Line
    lines_1 Write an equation of a line parallel to To 9x + 3y = 8 That Passes Through The Point (-1, -4). Write in form ax+by=c.
  6. Water reservoir
    water_tower The cuboid reservoir contains 1900 hectoliters of water and the water height is 2.5 m. Determine the dimensions of the bottom where one dimension is 3.2 m longer than the second one.
  7. ISO Triangle V2
    triangle_3 Perimeter of RR triangle (isosceles) is 474 m and the base is 48 m longer than the arms. Calculate the area of this triangle.
  8. Tree
    strom How tall is the tree that observed in the visual angle of 52°? If I stand 5 m from the tree and eyes are two meters above the ground.
  9. Sphere - parts
    odsek_vusek Calculate the area of a spherical cap, which is part of an area with base radius ρ = 9 cm and a height v = 3.1 cm.
  10. Triangular prism
    hranol_3sides The base perpendicular triangular prism is a right triangle whose hypotenuse measures 5 cm and one cathetus 2 cm. Height of the prism is equal to 7/9 of the perimeter of the base. Calculate the surface area of prism.
  11. Tickets
    tickets Tickets to the zoo cost $4 for children, $5 for teenagers and $6 for adults. In the high season, 1200 people come to the zoo every day. On a certain day, the total revenue at the zoo was $5300. For every 3 teenagers, 8 children went to the zoo. How many t
  12. The body
    body_cubes The body on the figure consists of cubes with an edge length 10 cm. What surface has this body?
  13. Three dice
    3_cubes When you throw three dice was the sum total of the dice 10. The yellow dice fell one eye more than on the red and brown fell 3 eyes less than red. How many eyes fell on every dice?
  14. Tourist Jirka
    turisti Distance between the points A and B is 13.5 km. Jirka went from point A to point B unknown speed and for an unknown period of time. Back to the point A went slower by 3 km/h which means that went 20 minutes more. How long Jirka took the return journey?
  15. Square ABCD
    squares_5 Construct a square ABCD with cente S [3,2] and the side a = 4 cm. Point A lies on the x-axis. Construct square image in the displacement given by oriented segment SS'; S` [-1 - 4].
  16. Angle
    atan A straight line p given by the equation ?. Calculate the size of angle in degrees between line p and y-axis.
  17. 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
  18. Loan
    loan Apply for a $ 59000 loan, the loan repayment period is 8 years, the interest rate 7%. How much should I pay for every month (or every year if paid yearly). Example is for practise geometric progression and/or periodic payment for an annuity.
  19. Tourists
    hiking From the cottage started first group of tourists at 10:00 AM at speed 4 km/h. The second started after them 47 minutes later at speed 6 km/h. How long and how many kilometers from the cottage will catch the first group?
  20. Sinus
    sine_cosine Determine the smallest integer p for which the equation 4 sin x = p has no solution.

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