# Examples for secondary school students - page 54

1. Average If the average(arithmetic mean) of three numbers x,y,z is 50. What is the average of there numbers (3x +10), (3y +10), (3z+10) ?
2. Five members Write first 5 members geometric sequence and determine whether it is increasing or decreasing: a1 = 3 q = -2
3. Threesome Dana, Dalibor and Michael have a combined 57 years. Dana is five years older than Dalibor, but Dana is five years younger than Michael. Determine how old is Dana, Dalibor and Michael.
4. Four integers Fnd four consecutive integers so that the product of the first two is 70 times smaller than the product of the next two.
5. Internal angles Find the internal angles of the triangle ABC if the angle at the vertex C is twice the angle at the B and the angle at the vertex B is 4 degrees smaller than the angle at the vertex A.
6. Banknotes \$ 1390 was collected. How much was in \$20 notes and how many in \$50 notes in that order? How many solutions exists?
7. Repair company The company repairs cars. The first day repair half of the contract second day, the half of the rest and third day 8 residue cars. How many total cars company repaired?
8. The swing To swing the two girls. Aneta weight 45 kg and Simon 35 kg weight. How far should sit Simon from the middle of swing so it is balanced, if we know that Aneta is sitting at distance 1,5m? How far are girls sitting apart?
9. Tenth member Calculate the tenth member of geometric sequence when given: a1=1/2 and q=2
10. Probability What are the chances that the lottery, in which the numbers are drawn 5 of 50 you win the first prize?
11. Variable Find variable P: PP plus P x P plus P = 160
12. Daily temperature The average of daily temperature measurements in one week every day at the same hour was -2.8 °C. All temperatures were measured in different days are different. The highest daily maximum temperature was 2.4 °C, the lowest -6 °C. Determine the options tha
13. Candy - MO Gretel deploys to the vertex of a regular octagon different numbers from one to eight candy. Peter can then choose which three piles of candy give Gretel others retain. The only requirement is that the three piles lie at the vertices of an isosceles triang
14. Cylinder horizontally The cylinder with a diameter of 3 m and a height/length of 15 m is laid horizontally. Water is poured into it, reaching a height of 60 cm below the axis of the cylinder. How many hectoliters of water is in the cylinder?
15. Electricity consumption cost Last year Karol family reduced its electricity consumption by 31% compared to the previous year and paid CZK 2883 less. How many CZK is electricity last year and how many two year ago?
16. Difference of two number The difference of two numbers is 20. They are positive integers greater than zero. The first number raised to one-half equals the second number. Determine the two numbers.
17. AP - simple Find the first ten members of the sequence if a11 = 132, d = 3.
18. Inscribed sphere How many % of the volume of the cube whose edge is 6 meters long is a volume of a sphere inscribed in that cube?
19. Sawmill factory Peter works in the factory. The bus stop is 10 km from the factory. Therefore, always when the bus arrives for Peter, the driver leaves factory and takes him to work. They are coming at the saw exactly at 8:00. Today the bus arrived 11 minutes earlier and.
20. EQ2 Solve quadratic equation: ?

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