# Examples for secondary school students

1. 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?
2. Bridge cards
How many bridge hands are possible containing 4 spades,6 diamonds, 1 club, and 2 hearts?
3. 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
4. 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?
5. Evaluation of expressions
If a2-3a+1=0, find (i)a2+1/a2 (ii) a3+1/a3
6. Expression with powers
If x-1/x=5, find the value of x4+1/x4
7. Cancel fractions
Compress the expression of factorial: (n+6)!/(n+4)!-n!/(n-2)!
8. 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.
9. 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
10. 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?
11. 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
12. 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
13. 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.
What overload in g (g-force) has passed the pilot if he accelerated from 0 to 600 km/h in 3 seconds?
15. 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?
16. 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?
17. Hypotenuse - RT
A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle?
18. Geometric progression
In geometric progression, a1 = 7, q = 5. Find the condition for n to sum first n members is: sn≤217.
19. Alice
Alice spent 5/11 of her money on a back pack. She has \$42 dollars left. How much was her back pack?
20. 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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