Examples for secondary school students - page 108 of 213
Number of problems found: 4253
- Vertices of a right triangle
Show that the points D(2,1), E(4,0), and F(5,7) are vertices of a right triangle. - Mushrooms
Grandfather gathered fresh mushrooms. The fifth was wormwood, and we threw it away. The other dried up. He obtained 720 grams of dried mushrooms. How many kilograms did the grandfather collect, and they lost 75% of their weight by drying the mushrooms? - Two pipes
How long will the pool be filled with a double supply pipe if it takes the pool to fill the first pipe by 4 hours long and the second pipe 9 hours longer than both pipes open simultaneously? - There
There are two numbers on the screen - one in the blue and the other in the red box. In the beginning, both numbers are the same. With each beep, both numbers increase - by 1 in the blue field and by 3 in the red field. At one point, the number 49 appears - Two-digit 7607
The digit sum of a two-digit number is 11. After changing the order of the digits, I get a number 27, smaller than the intended number. What number do I think? - Together 7606
Jana and Dana have saved 220 crowns together. Jana spent a fifth of her savings, Dana a quarter. Then they had a total of CZK 150 left. How much have they saved? - Depth angle
From a cliff of 150 meters high, we can see the ship at a depth angle of 9° at sea. How far is the ship from the cliff? - Two cities
The car goes from city A to city B at an average speed of 70 km/h and back at an average speed of 50 km/h. If it goes to B and back at an average speed of 60 km/h, the whole ride will take 8 minutes less. What is the distance between cities A and B? - Temperature 7595
Colorless liquid weighing m = 200 g is heated with constant stirring on a stove with power input P0 = 600W. 80% of the supplied energy is used to heat the liquid. Selected measured values of liquid temperature as a function of time are recorded in the t - Annual pension
Calculate the amount of money generating an annual pension of EUR 1000, payable at the end of the year and for a period of 10 years, which shall be inserted into the bank to account with an annual interest rate of 2% - Infinite sum of areas
An equilateral triangle A1B1C1 is constructed above the height of the equilateral triangle ABC is constructed as. Above the height of the equilateral triangle A1B1C1 is built triangle A2B2C2, and so on. The procedure is repeated continuously. What is the - Quadrilateral 7583
For the sizes of the interior angles of the quadrilateral ABCD, the following applies: the angle alpha is 26° greater than the angle beta, twice the angle Beta is 5° less than the angle gamma, and the angle gamma is 36° greater than the angle delta. Deter - Election 4
In a certain election, there are three presidential candidates: 5 for secretory and 2 for treasurer. Find how many ways the election may (turn out/be held). - Circle described
The circle radius described in the right triangle with a 6 cm long leg is 5 cm. Calculate the circumference of this triangle. - Axial cut of a rectangle
Calculate the volume and surface of the cylinder whose axial cut is a rectangle 15 cm wide with a diagonal of 25 cm long. - Calculate 7572
At eight in the morning, a cyclist went from city K to city L. He stayed in city L for 4.25 hours and returned home at 3:00 p.m. Calculate the distance between cities K and L if the cyclist traveled to city L at a speed of 12 km/h and from city L to city - Isosceles 7566
A right isosceles triangle is inscribed in the circle with r = 8 cm. Find triangle area S. How much percent does the triangle occupy the area of the circle? - Spectators 7562
The theater has the shape of a semicircle. A podium is the diameter of a semicircle. Spectators K, L, M, N, and O, sit around the perimeter. Who sees the podium at the greatest angle? - Average 7560
The company of five people has an average age of 46 years. The average age of the first four of them is 43 years. How old is the fifth one? - A student
A student is to answer 8 out of 10 questions on the exam. a) find the number n of ways the student can choose 8 out of 10 questions b) find n if the student must answer the first three questions c) How many if he must answer at least 4 of the first five q
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