# Examples for secondary school students

- Cuboid and eq2

Calculate the volume of cuboid with square base and height 6 cm if the surface area is 48 cm^{2.} - Pharmacy

The pharmacy add to 3 liters of 95-percent alcohol 5 liters of 38.04 percent alcohol. How many percent pharmacy got? - Right triangle eq2

Hypotenuse of a right triangle is 9 cm longer than one leg and 8 cm longer than the second leg. Determine the circumference and area of a triangle. - Cuboids

Two separate cuboids with different orientation in space. Determine the angle between them, knowing the direction cosine matrix for each separate cuboid. u1=(0.62149553, 0.11709336, 0.77461762) u2=(0.046501848, 0.66652649, 0.74402958) - Rhombus and diagonals

The a rhombus area is 150 cm2 and the ratio of the diagonals is 3:4. Calculate the length of its height. - Points in plane

The plane is given 12 points, 5 of which is located on a straight line. How many different lines could by draw from this points? - One half

One half of ? is: ? - Laws

From which law follows directly the validity of Pythagoras' theorem in the right triangle? ? - 7 heroes

5 heroes galloping on 5 horses behind. How many ways can sort them behind? - Proof PT

Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it. - Vans

In how many ways can 7 shuttle vans line up at the airport? - Flags

How many different flags can be made from colors red, white, blue, black, yellow, green, purple, gray, orange so that each flag consisted of three different colors? - Seating

How many ways can 7 people sit on 3 numbered chairs (eg seat reservation on the train)? - Football league

In the 2nd football league is 19 teams. How many ways can be filled first, second and third place? - Guests

How many ways can 7 guests sit down on 9 seats standing in a row? - Stock market

Simon one day decided to invest € 48000 to the stock market. After six months he invested July 11 stock markets fell by 43%. Fortunately for Simon from July 11 5 to October 11 his shares have risen by 13%. Simon is then: ? - Playing cards

How many possible ways are to shuffle 7 playing cards? - Shelf

How many ways are there to arrange 9 books on a shelf? - Sequence

Write the first 7 members of an arithmetic sequence: a_{1}=8, d=-9. - Candies

In the box are 12 candies that look the same. Three of them are filled with nougat, five by nuts, four by cream. At least how many candies must Ivan choose to satisfy itself that the selection of two with the same filling? ?

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