Examples for 7th grade (seventh)

1. Ratio of volumes
If the heights of two cylindrical drums are in the ratio 7:8 and their base radii are in the ratio 4:3. What is the ratio of their volumes?
2. Temperature difference 2
The temperature in London on new year’s day is -2 degree Celsius. The temperature in Moscow on the same day is -14 degree Celsius, what is the temperature difference between the two cities?
3. Temperature difference
The highest temperature of Libya was recorded 58 degree Celsius and the lowest was recorded -88 degree Celsius, what is the temperature difference?
4. Simplify
Simplify powers multiplication: (3+22)(5-42)
5. Sphere VS
Find the surface and volume of a sphere that has a radius of 2 dm.
6. A sculptor
A sculptor is duplicating a statue based on an original statue. If the scale factor of the replication is 3.2, will the new statue be larger or smaller than the original statue (enter 1 = larger, 0= smaller)
7. Metal tube
Calculate the metal tube mass 8dm long with the outer radius 5cm and the inner radius 4.5cm and 1cm3 of this metal is 9.5g.
8. Winch
The steel rope has a diameter of 6mm and a length of 20m. We are winding on drum width 60mm, starting diameter 50mm. What is the final diameter after winding?
9. Delayed clock
Michael put a new battery into his watch at midnight. However, they are 5 seconds late each minute. How many hours does the watch show in 24 hours?
10. Iceberg
What is the surface area of 50 cm iceberg (in the shape of a cuboid) that can carry a man with luggage with a total weight of 120 kg?
11. Holidays with grandmam
We have packed three T-shirts - white, red, orange and five pants - blue, green, black, pink and yellow. How many days can we spend with the old mother if we put on a different combination of clothes every day?
12. Geometric plan
At what scale the building plan if one side of the building is 45m long and 12mm long on a plan?
13. Tourist
A tourist walked an average speed of 3.5 km/h route in 6 hours. Calculate how many hours he would have passed at an average speed of 5.5 km/h.
14. Down syndrome
Down syndrome is one of the serious diseases caused by a gene mutation. Down syndrome occurs in approximately every 550-born child. Express the incidence of Down's syndrome in newborns at per mille.
15. Triangular prism
Calculate a triangular prism if it has a rectangular triangle base with a = 4cm and hypotenuse c = 50mm and height of the prism is 0.12 dm.
16. Cube into cylinder
If we dip a wooden cube into a barrel with a 40cm radius, the water will rise 10 cm. What is the size of the cube edge?
17. Iron pole
The iron pole is in the ground 2/5 of its length, partly above the ground 1/3 is yellow, and the unpainted section is 6 m long. How long is the entire column?
18. Cook on gas
The gas cylinder will last for 30 weekends for 2 hours of daily cooking. How many days will we be able to cook on a new cylinder when we cook 3 hours a day?
19. Dance group
The dance group formed groups of 4, 5, and 6 members. Always one dancer remains. How many dancers were there in the whole group?
20. Barter
There is exchange trade on the market. We know that for two sheepskins we get three goat skins. We also know that for six rabbits skins we get four goat skins. How many rabbit's skins we get for four sheepskins?

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