# Examples for secondary school students - page 45

1. Cubes - diff Second cubes edge is 2 cm longer than the edge of the first cube. Volume difference blocks is 728 cm3. Calculate the sizes of the edges of the two dice.
2. Three dice When you throw three dice was the sum total of the dice 10. The yellow dice fell one eye more than on the red and brown fell 3 eyes less than red. How many eyes fell on every dice?
3. Log Calculate value of expression log |3 +7i +5i2| .
4. Book Alena read a book at speed 15 pages per day. If she read twice as fast she should read a book four days earlier. How many pages have a book?
5. Bearing A plane flew 50 km on a bearing 63°20' and the flew on a bearing 153°20' for 140km. Find the distance between the starting point and the ending point.
6. Debt Joe and Caryl have a debt of \$100,500. Joe makes \$90,000 per year, and Caryl makes \$35,000 per year. How much should both pay to zero out the debt fairly, based on their salaries?
7. Class - boys and girls In the class are 60% boys and 40% girls. Long hair has 10% boys and 80% girls. a) What is the probability that a randomly chosen person has long hair? b) The selected person has long hair. What is the probability that it is a girl?
8. The city At the end of 2010 the city had 248000 residents. The population increased by 2.5% each year. What is the population at the end of 2013?
9. Water reservoir The cuboid reservoir contains 1900 hectoliters of water and the water height is 2.5 m. Determine the dimensions of the bottom where one dimension is 3.2 m longer than the second one.
10. Diamond Calculate the length of the two diagonals of the diamond if: a = 13 cm v = 12 cm
11. Car and cyclist Cyclist started from town at speed 18 km/h. After 1 hour 30 min started the car from town and caught up with the cyclist in 50 minutes. How fast was a car?
12. Scalar dot product Calculate u.v if |u| = 5, |v| = 2 and when angle between the vectors u, v is: a) 60° b) 45° c) 120°
13. Enterprise The value of annual production enterprise is 7.1 million USD. The average annual growth rate is 1.5%. What will be value of production at the end of the fifth year?
14. Medians and sides Determine the size of a triangle KLM and the size of the medians in the triangle. K=(-5; -6), L=(7; -2), M=(5; 6).
15. Wavelength Calculate the wavelength of the tone frequency 11 kHz if the sound travels at speeds of 343 m/s.
16. Bank Paul put 10000 in the bank for 6 years. Calculate how much you will have in the bank if he not pick earned interest or change deposit conditions. The annual interest rate is 3.5%, and the tax on interest is 10%.
17. Triangle KLM In the rectangular triangle KLM, where is hypotenuse m (sketch it!) find the length of the leg k and the height of triangle h if hypotenuse's segments are known mk = 5cm and ml = 15cm
18. Confectionery The village markets have 5 kinds of sweets, one weighs 31 grams. How many different ways a customer can buy 1.519 kg sweets.
19. Interesting property Plot a rectangular shape has the interesting property that circumference in meters and the area in square meters are the same numbers. What are the dimensions of the rectangle?
20. Average mark Calculate average mark in English, if a student got a couple of 3's, 20% less 2 than 3, and 50% more 1's than the 2's.

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