# Examples for secondary school students

- Center of gravity

In the isosceles triangle ABC is the ratio of the lengths of AB and the height to AB 10:12. The arm has a length of 26 cm. If the center of gravity T of triangle ABC find area of triangle ABT. - Cards

From a set of 32 cards we randomly pull out three cards. What is the probability that it will be seven king and ace? - Sun rays

If the sun's rays are at an angle 60° then famous Great Pyramid of Egypt (which is now high 137.3 meters) has 79.3 m long shadow. Calculate current height of neighboring chefren pyramid whose shadow is measured at the same time 78.8 m and the current hei - Quadratic inequation

If 5x + x² > 100, then x is not - Trapezoid 15

Area of trapezoid is 266. What value is x if bases b1 is 2x-3, b2 is 2x+1 and height h is x+4 - 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 € 88000 to the stock market. After six months he invested July 5 stock markets fell by 56%. Fortunately for Simon from July 5 5 to October 5 his shares have risen by 39%. Simon is then: ? - 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? ? - 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. - Logic

A man drinks a barrel of water for 31 days, woman for 58 days, for how many days they drink barrel together?

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