# Examples for secondary school students

1. 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?
2. 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
3. Last digit
What is the last number of 2016 power of 2017
4. 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?
5. 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?
6. 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 . .. .
7. 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'.
8. Geometric progression 4
8,4√2,4,2√2
9. 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?
10. Sum of inner angles
Prove that the sum of all inner angles of any convex n-angle equals (n-2) . 180 degrees.
11. 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?
12. Algebra
X+y=5, find xy (find the product of x and y if x+y = 5)
13. 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: x2+y2+2x+4y+1=0 k2: x2+y2-8x+6y+9=0
14. 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.
15. 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
16. 75th percentile (quartille Q3)
Find 75th percentile for 30,42,42,46,46,46,50,50,54
17. 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
18. 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?
19. 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?
20. 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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