# Examples for secondary school students

#### Number of problems found: 2186

• Coordinates
Determine the coordinates of the vertices and the content of the parallelogram, the two sides of which lie on the lines 8x + 3y + 1 = 0, 2x + y-1 = 0 and the diagonal on the line 3x + 2y + 3 = 0
• Bonuses
Five employees of the company were paid bonuses so that each successor received 550 USD less than the previous employee. How much did everyone get if a total of USD 11,000 has paid?
• Ice cream
Annie likes much ice cream. In the shop are six kinds of ice cream. In how many ways she can buy ice cream to three scoop if each have a different flavor mound and the order of scoops doesn't matter?
• Hockey game
In the hockey game was made six goals. Czech played against Finland. Czechs won 4:2. In what order to fall goals? How many game sequences were possible during the game?
• Shot
Shot with a mass 43 g flying at 256 m/s penetrates into the wood to a depth 25 cm. What is the average force of resistance of wood?
• Prism
The lenght, width and height of a right prism are 17, 11 and 11 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism?
• Lines
How many lines can be draw with 8 points, if three points lie on one line and the other any three points do not lie on the same line?
• Angles in triangle
The triangle is ratio of the angles β:γ = 6:8. Angle α is 40° greater than β. What are the size of angles of the triangle?
• Circle
From the equation of a circle: ? Calculate the coordinates of the center of the circle S[x0, y0] and radius of the circle r.
• Cubes
Surfaces of cubes, one of which has an edge of 48 cm shorter than the other, differ by 36288 dm2. Determine the length of the edges of this cubes.
• Vertex points
Given the following points of a triangle: P(-12,6), Q(4,0), R(-8,-6). Graph the triangle. Find the triangle area.
• Center of line segment
Calculate the distance of the point X [1,3] from the center of the line segment x = 2-6t, y = 1-4t ; t is .
• Hiking trail
The newly built hiking trail leads 25% through the field, 3/8 of the trail leads through the forest and the remaining 9 km along the river. How long is the train?
• The body
The body on the figure consists of cubes with an edge length 10 cm. What surface has this body?
• Chairs
Determine the number of seats in the seventh row and ninth row, if 3rd row has 14 seats and in every next row of seats has five more than the previous row.
• Jane and Miro
Jane's brother Miro is 42 years. And he is three times old as it was Jane when Miro was for so many years as there are now Jane. How old is Jane?
• Kostka
Kostka je vepsána do koule o poloměru r = 6 cm. Kolik procent tvoří objem kostky z objemu koule?
• Compound interest 3
After 8 years, what is the total amount of a compound interest investment of \$25,000 at 3% interest, compounded quarterly? (interest is now dream - in the year 2019)
• Brakes
The braking efficiency of a passenger car is required to stop at 12.5 m at an initial speed of 40 km/h. What is the acceleration braking by brakes?
• Three points 2
The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB, and DC is parallel to AB. Calculate the coordinates of D.

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