# Examples for secondary school students

1. Hexagon rotation
A regular hexagon of side 6 cm is rotated through 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated?
2. Fifth member
Determine the fifth member of the arithmetic progression, if the sum of the second and fifth members equal to 73, and difference d = 7.
3. Blueberries
Miko and Anton have a total of 1,580 blueberries. Miko and Anton have them in the ratio 2: 3. Determine how much each of them has.
4. Unknown number
I think number. If subtract from the twelfth square the ninth square I get a number 27 times greater than the intended number. What is this unknown number?
5. Circle - AG
Find the coordinates of circle and its diameter if its equation is: ?
6. Harmonic and arithmetic means
The local Utah Department of Child Service office wants to project staffing needs based on current social worker assignments. They have the number of cases per social worker for the following staff: Mary: 25 John: 35 Ted: 15 Lisa: 45 Anna: 20 Calcula
7. Linear imaginary equation
Given that ? "this is z star" Find the value of the complex number z.
8. Unknown number 7
Calculate unknown number whose 12th power when divided by the 9th power get a number 27 times greater than the unknown number. Determine the unknown number.
9. Chocholate pyramid
How many chocolates are in the third shelf when at the 8th shelf are 41 chocolates in any other shelf is 7 chocolates more the previous shelf.
10. Equation of circle
find an equation of the circle with indicated properties: a. center at (-3,5), diameter 20. b. center at origin and diameter 16.
11. Chairs
Determine the number of seats in the seventh row and ninth row, if 3rd row has 14 seats and in every next row of seats has five more than the previous row.
12. Ball game
Richard, Denis and Denise together scored 932 goals. Denis scored 4 goals over Denise but Denis scored 24 goals less than Richard. Determine the number of goals for each player.
13. EQ2
14. 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 th
15. Variance and average
Of the 40 values were calculated average mx = 7.5 and variance sx = 2.25. After the control was found to lack the two items of the values of x41 = 3.8 and x42=7. Correct the above characteristics (mx and sx).
16. Solve equation
solve equation: ?
17. Infinite decimal
Imagine the infinite decimal number 0.99999999 .. ... ... ... That is a decimal and her endless serie of nines. Determine how much this number is less than the number 1. Thank you in advance.
18. Bonbons
Create a mixture of 50 kg of candy on price 700Kč. Candies has prices: 820Kč, 660Kč and 580Kč. Use cross rule.
19. Bookshelve
Bookshelve with an original price of € 200 twice become cheaper. After the second discounted by 15% the price was € 149.60. Determine how much % become cheaper for the first time.
20. Trapezoid
trapezoid ABCD a = 35 m, b=28 m c = 11 m and d = 14 m. How to calculate its area?

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