# Grade - examples - page 2

1. 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?
2. Annular area The square with side a = 1 is inscribed and circumscribed by circles. Find the annular area.
3. Life expectancy The life expectancy of batteries has a normal distribution with a mean of 350 minutes and standard deviation of 10 minutes. What the range in minutes 68% of the batteries will last? What is the range in minutes approximately 99.7% of batteries will last?
4. 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?
5. Lateral surface area The ratio of the area of the base of the rotary cone to its lateral surface area is 3: 5. Calculate the surface and volume of the cone, if its height v = 4 cm.
6. A kite ABCD is a kite. Angle OBC = 20° and angle OCD = 35°. O is the intersection of diagonals. Find angle ABC, angle ADC and angle BAD.
7. Today in school There are 9 girls and 11 boys in the class today. What is the probability that Suzan will go to the board today?
8. A rectangular patio A rectangular patio measures 20 ft by 30 ft. By adding x feet to the width and x feet to the length, the area is doubled. Find the new dimensions of the patio.
9. Two cubes The surfaces of two cubes, one of which has an edge of 22 cm longer than the second are differ by 19272 cm2. Calculate the edge length of both cubes.
10. Rectangular trapezoid In a rectangular trapezoid ABCD with right angles at vertices A and D with sides a = 12cm, b = 13cm, c = 7cm. Find the angles beta and gamma and height v.
11. The temperature 2 The temperature of Siberia fell13 degrees below 2/3 degrees centigrad. What is the temperature there now?
12. Sphere VS Find the surface and volume of a sphere that has a radius of 2 dm.
13. A photograph A photograph will stick to a white square letter with a x cm length. The photo is 3/4 x cm long and 20 cm wide than the width of the paper. The surface of the remaining paper surrounding the photograph is 990 cm2. Find the size of paper and photo. The radius of the sphere we reduce by 1/3 of the original radius. How much percent does the volume and surface of the sphere change?
15. A fisherman A fisherman buys carnivores to fish. He could buy either 6 larvae and 4 worms for \$ 132 or 4 larvae and 7 worms per \$ 127. What is the price of larvae and worms? Argue the answer.
16. Simplify Simplify powers multiplication: (3+22)(5-42)
17. Rectangular garden 2 A farmer bought 600 m of wire for the fence. He wants to use it to besiege a rectangular garden with a surface of 16875 m2. Calculate the size of the garden.
18. 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)
19. RT sides Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm.
20. Six workers Six workers planned to repair the roof in 5 days. After two days, two workers get sick. How long will the remaining workers complete the roof at the same rate of work?

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