# Examples for 6th grade (the sixth graders) - page 9

1. School books
At the beginning of the school year, the teacher gave out 480 books and 220 textbooks. How many students were in the class?
2. Pairs
From the five girls and four boys teachers have to choose one pair of boy and girl. A) How many such pairs of (M + F)? B) How many pairs where only boys (M + M)? C) How many are all possible pairs?
3. Paddlers
Students of canoeists trip traveled in three days 102 km. Second day traveled 15% more than first day and at the third day 9 km over the second day. How many kilometers traveled each day?
4. 3-bracket
May be the largest angle in the triangle less than 20°?
5. Count of roots
How many solutions has equation x. y = 7757 with two unknowns on the set of natural numbers?
6. Intersections
How many intersections have circles with radius 16 mm and 15 mm, if the distance of their centers is 16 mm.
7. Company
After increasing the number of employees by 15% company has 253 employees. How many employees take?
8. Segments
Line segments 62 cm and 2.2 dm long we divide into equal parts which lengths in centimeters is expressed integer. How many ways can we divide?
9. Gardens
The garden has the square shape with circumference 124 m. Divide it into two rectangular gardens, one should circumference 10 meters more than the second. What size will have a gardens?
10. Family and age ratios
Age of father and son are in the ratio 10:3; age of father and daughter are in the ratio 5:2. How old is father and son, if daughter is 20 years old? In what ratio is age sister and brother?
11. Tiles
The room has dimensions 12 m and 5.6 m. Determine the number of square tiles and their largest possible size to cover them room's floor.
12. N-gon angles
What is the sum of interior angles 9-gon? What is the internal angle of a regular convex 9-polygon?
13. Garden
The garden has two opposite parallel fences. Their distance is 33.1 m. Lengths in these two fences are 75.5 meters and 49.4 meters. Calculate the area of this garden.
14. Quadrant II
Calculate the radius of the quadrant, which area is equal to area of circle with radius r = 15 cm.
15. Rhombus HP
Calculate area of the rhombus with height 24 dm and perimeter 12 dm.
16. Supermarket cashiers
When at the supermarket are opened only 2 cash people waiting in the front approximately 12 minutes. How many will shorten the average waiting time in a front where supermarket open another three cashiers?
17. Snow
Snow fell overnight layer of thickness 19 cm. In the morning I had to clear a path 69 m long and one meter wide. How many cubic meters of snow I clear? How many kilos was it? (1 m3 fresh snow weighs 350 kg)
18. Collective irresponsibility
At the Internet, time is very uncomfortable for the state that no more gaffe or waste is no longer possible to hush up as if people were at home with only two television channels censored. An example of the effectiveness of state can be Bridge at Komořan
19. University bubble
You'll notice that the college up slowly every other high school. In Slovakia/Czech republic a lot of people studying political science, mass media communication, social work, many sorts of management MBA. Calculate how many times more earns clever 25-year
20. Family
Martin has just as brothers as sisters. His sister Jana but has 2 times more brothers than sisters. a) How many children are in this family? b) How many boys and how many girls are in the family?

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