# Examples for secondary school students

- Population growth

How many people will be on Earth from two people for 5,000 years, if every couple has always 4 children, (2 boys and 2 girls) at the age of 25-35, and every man will live 75 years? - Two people

Two straight lines cross at right angles. Two people start simultaneously at the point of intersection. John walking at the rate of 4 kph in one road, Jenelyn walking at the rate of 8 kph on the other road. How long will it take for them to be 20√5 km apa - Last digit

What is the last number of 2016 power of 2017 - Peaches

There are 20 peaches in the pocket. 3 peaches are rotten. What is the probability that one of the randomly picked two peaches will be just one rotten? - Right triangle from axes

A line segment has its ends on the coordinate axes and forms with them a triangle of area equal to 36 square units. The segment passes through the point ( 5,2). What is the slope of the line segment? - Three sides

Side b is 2 cm longer than side c, side a is 9 cm shorter than side b. The triangle circumference is 40 cm. Find the length of sides a, b, c . .. . - Tropical, mild and arctic

How many percents of the Earth's surface lies in the tropical, mild and arctic range? The border between the ranges is the parallel 23°27 'and 66°33'. - Geometric progression 4

8,4√2,4,2√2 - Hemispherical hollow

The vessel hemispherical hollow is filled with water to a height of 10 cm =. How many liters of water are inside if the inside diameter of the hollow is d = 28cm? - Sum of inner angles

Prove that the sum of all inner angles of any convex n-angle equals (n-2) . 180 degrees. - Lunch

Seven classmates go every day for lunch. If they always come to the front in a different order, will be enough school year to take of all the possibilities? - Algebra

X+y=5, find xy (find the product of x and y if x+y = 5) - Prove

Prove that k1 and k2 is the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x^{2}+y^{2}+2x+4y+1=0 k2: x^{2}+y^{2}-8x+6y+9=0 - Digits

Show that if x, y, z are 3 consecutive nonzero digits, zyx-xyz = 198, where zyx and xyz are three-digit numbers created from x, y, z. - The big clock

The big clock hands stopped at a random moment. What is the probability that: a) a small hand showed the time between 1:00 and 3:00? b) the big hand was in the same area as a small hand in the role of a)? c) did the hours just show the time between 21:00 - 75th percentile (quartille Q3)

Find 75th percentile for 30,42,42,46,46,46,50,50,54 - Utopia Island

A probability of disease A on the island of Utopia is 40%. A probability of occurrence among the men of this island, which make up 60% of all the population (the rest are women), is 50%. What is the probability of occurrence of A disease among women on Ut - The perimeter

The perimeter of equilateral △PQR is 12. The perimeter of regular hexagon STUVWX is also 12. What is the ratio of the area of △PQR to the area of STUVWX? - Performance

Two masons with the same performance would have made of plaster for 6 days. One of them, however, has increased its daily performance by 50%. How long would take they now to make plaster together? - Angle of diagonal

Angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume.

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