# Examples for secondary school students

- A three-digit numbers

Determine the total number of positive three-digit numbers that contain a digit 6. - Square roots

What is equal to the product of the square roots of 295936? - Goat and circles

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 - 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? - Line

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. - Water reservoir

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. - ISO Triangle V2

Perimeter of RR triangle (isosceles) is 474 m and the base is 48 m longer than the arms. Calculate the area of this triangle. - Tree

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. - Sphere - parts

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. - Triangular prism

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. - 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 - The body

The body on the figure consists of cubes with an edge length 10 cm. What surface has this body? - Three dice

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? - Tourist Jirka

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? - Square ABCD

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]. - Angle

A straight line p given by the equation ?. Calculate the size of angle in degrees between line p and y-axis. - Pit

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 - 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. - Tourists

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? - Sinus

Determine the smallest integer p for which the equation 4 sin x = p has no solution.

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