# Examples for secondary school students - page 49

- Students

In the front row sitting three students and in every other row 11 students more than the previous row. Determine how many students are in the room when the room is 9 lines, and determine how many students are in the seventh row. - Asymptote

What is the vertical asymptote of ? - Octahedron

All walls of regular octahedron are identical equilateral triangles. ABCDEF octahedron edges have a length d = 6 cm. Calculate the surface area and volume of this octahedron. - PIN - codes

How many five-digit PIN - code can we create using the even numbers? - Owner of the company

The owner of the company with extensive administrative activity wants to sell the obsolete 3 machines at the price of CZK 1000 per 1 machine with a six-month warranty period. If the machine breaks down during this period, the owner will return the employe - Rotary bodies

The rotating cone and the rotary cylinder have the same volume 180 cm^{3}and the same height v = 15 cm. Which of these two bodies has a larger surface area? - Pears

Andrew, Lenka and Rasto have together 232 pears. Lenka has 28 more than Rasto and Rasto pears have 96 more than Andrew. Determine how much each of them has pears. - Cuboid and ratio

Cuboid has dimensions in ratio 1:2:6 and the surface area of the cuboid is 1000 dm^{2}. Calculate the volume of the cuboid. - One green

In the container are 45 white and 15 balls. We randomly select 5 balls. What is the probability that it will be a maximum one green? - Dividing money

Thomas, Honza and Vasek are to divide 1220kč. Honza got 25% more than Thomas. Vasek 20% less than Thomas. How CZK each got? - Insert into GP

Between numbers 5 and 640 insert as many numbers to form geometric progression so sum of the numbers you entered will be 630. How many numbers you must insert? - Class pairs

In a class of 34 students, including 14 boys and 20 girls. How many couples (heterosexual, boy-girl) we can create? By what formula? - Quadratic function

Write the equation of the quadratic function which includes points A (-1, 10), B (2, 19), C (1,4) - Square and rectangle

Calculate the side of a square which content area equals area of the rectangle having a length of 3 cm greater and by 2 cm smaller than the side of the square. - Sides ratio

Calculate the circumference of a triangle with area 84 cm^{2}if a:b:c = 10:17:21 - Hollow sphere

The volume of the hollow ball is 3432 cm^{3}. What is its internal radius when the wall thickness is 3 cm? - Mass

The thickness of a metallic tube is 1cm and its outer radius is 11cm. Find the mass of such 1m long tube, if the density of the metal is 7.5g per cubic cm. - Numbers

Write smallest three-digit number, which in division 5 and 7 gives the rest 2. - Cards

The player gets 8 cards of 32. What is the probability that it gets a) all 4 aces b) at least 1 ace - CuZn

Brass is an alloy of copper and zinc. The 10 centimeter brass cube has a weight of 8.6 kg. Copper density is 8930 kg/m3, the zinc density is 7130 kg/m3. Calculate how many kg of copper and zinc a cube contains.

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