# Examples for secondary school students

- Bottles

The must is sold in 5-liter and 2-liter bottles. Mr Kucera bought a total of 216 liters in 60 bottles. How many liters did Mr. Kucera buy in five-liter bottles? - Bridge cards

How many bridge hands are possible containing 4 spades,6 diamonds, 1 club, and 2 hearts? - Area of garden

If the width of the rectangular garden is decreased by 2 meters and its length is increased by 5 meters, the area of the rectangle will be 0.2 ares larger. If the width and the length of the garden will increase by 3 meters, its original size will increa - Cube, cuboid, and sphere

Volumes of a cube and a cuboid are in ratio 3: 2. Volumes of sphere and cuboid are in ratio 1: 3. In what ratio are the volumes of cube, cuboid, and sphere? - Evaluation of expressions

If a^{2}-3a+1=0, find (i)a^{2}+1/a^{2}(ii) a^{3}+1/a^{3} - Expression with powers

If x-1/x=5, find the value of x^{4}+1/x^{4} - Cancel fractions

Compress the expression of factorial: (n+6)!/(n+4)!-n!/(n-2)! - Speed of car

The car went to a city that was 240 km away. If his speed increased by 8 km/h, it would reach the finish one hour earlier. Determine its original speed. - Candy and boxes

We have some number of candy and empty boxes. When we put candies in boxes of ten, there will be 2 candies and 8 empty boxes left, when of eight, there will be 6 candies and 3 boxes left. How many candy and empty boxes left when we put candies in boxes of - Normal distribution GPA

The average GPA is 2.78 with a standard deviation of 4.5. What are students in the bottom the 20% having what GPA? - Merchant

The merchant lower cost by 10% in December when it was not sold. Again in January lower cost by 20% and now costs 576 €. A. How much the goods stood originally? B, how much cost the goods after the first lowering? C, How many percents totally merchant l - Young mathematician

One young mathematician was bored again. He found that the average age of people in the room where the seminar is equal to its count. Then his 29-year-old brother entered this room. Even then, the average age of all present was the same as the count of pe - Ratio of sides

The triangle has a circumference of 21 cm and the length of its sides is in a ratio of 6: 5: 3. Find the length of the longest side of the triangle in cm. - Overload

What overload in g (g-force) has passed the pilot if he accelerated from 0 to 600 km/h in 3 seconds? - A triangle

A triangle has an angle that is 63.1 other 2 are in ratio of 2:5 What are the measurements of the two angles? - Employees

The company employs 1 440 employees (men and women). For over-average results, the premiums were 18.75% of all men and 22.5% of all women. 20% of employees were rewarded with premiums. How many men and how many women are employed in the company? - Hypotenuse - RT

A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle? - Geometric progression

In geometric progression, a1 = 7, q = 5. Find the condition for n to sum first n members is: sn≤217. - Alice

Alice spent 5/11 of her money on a back pack. She has $42 dollars left. How much was her back pack? - Hexagon ABCDEF

In the regular hexagon ABCDEF, the diagonal AE has a length 8cm. Calculate the circumference and the hexagon area.

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