# Examples for secondary school students

1. Population
What is the population of the city with 3% annual growth, if in 10 years the city will have 60,000 residents?
2. Tetrahedral pyramid
Calculate the volume and surface of the regular tetrahedral pyramid if content area of the base is 20 cm2 and deviation angle of the side edges from the plane of the base is 60 degrees.
3. Throw
We throw 2 times with 2 dices. What is the probability that the first roll will fall more than sum of 9 and the second throw have sum 3 or does not have the sum 4?
4. Coffee
Coffee merchant has coffee robusta and arabica species. 1 kg Robusta worth 450 CZK, Arabica 1 kg is 300 CZK more expensive. Calculate how many kilograms of Robusta and Arabica will need to produce 30 kg of the mixture so that the mixture cost is 490 CZK
5. Triangle - is RT?
Triangle has a circumference of 90 cm. Side b is 1 cm longer than c, side c is 31 cm longer than side a. Calculate the length of sides and determine whether triangle is a right triangle.
6. Cinema 4
In cinema are 1656 seats and in the last row are 105 seats , in each next row 3 seats less. How many are the total rows in cinema?
7. Mass
The thickness of a metallic tube is 1cm and its outer radius is 11cm. Find the mass of such 1m long tube, if the density of the metal is 7.5g per cubic cm.
8. Is complex
Are these numbers 2i, 4i, 2i + 1, 8i, 2i + 3, 4 + 7i, 8i, 8i + 4, 5i, 6i, 3i complex?
9. Cans
How many cans must be put in the bottom row if we want 182 cans arrange in 13 rows above so that each subsequent row has always been one tin less? How many cans will be in the top row?
10. Inclined plane
On the inclined plane with an angle of inclination of 30 ° we will put body (fixed point) with mass 2 kg. Determine the acceleration of the body motion on an inclined plane.
11. Sides of the triangle
Calculate triangle sides where its area is S = 84 cm2 and a = x, b = x + 1, xc = x + 2
Which of the points belong function f:y= 2x2- 3x + 1 : A(-2, 15) B (3,10) C (1,4)
13. Volleyball
8 girls wants to play volleyball against boys. On the field at one time can be six players per team. How many initial teams of this girls may trainer to choose?
14. Two workers
Two workers work together and perform the job in 12 hours. If one has done half the work and then second worker next half of work it will take 25 hours. How long would it take job them separately?
15. Internal angles
The ABCD is an isosceles trapezoid, which holds: |AB| = 2 |BC| = 2 |CD| = 2 |DA|: On its side BC is a K point such that |BK| = 2 |KC|, on its side CD is the point L such that |CL| = 2 |LD|, and on its side DA the point M is such that | DM | = 2 |MA|. Det
Write the equation of the quadratic function which includes points A (-1, 10), B (2, 19), C (1,4)
17. Probability
What are the chances that the lottery, in which the numbers are drawn 5 of 50 you win the first prize?
18. Probability - tickets
What is the probability when you have 25 tickets in 5000 that you not wins the first (one) prize?
19. Work at plant
Handyman has vowed to do repair work at the plant for 25 days. However, work had to be shortened and therefore gained helper. Together they made all the corrections for 13 1/3 days. How long the work would take helper himself?
20. Two masons
Two masons built the garage together - it took 18 days. If they worked independently, the other would work 15 days more than the first. For how many days would build the garage each mason himhelp?

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