# Examples for secondary school students - page 44

1. Tent Pyramid-shaped tent has a base square with a side length of 2 m and a height 1.7 m. How many meters of canvas is nneded to make it if for a waste should be added 10%?
2. Acceleration 2 if a car traveling at a velocity of 80 m/s/south accelerated to a velocity of 100 m/s east in 5 seconds, what is the cars acceleration? using Pythagorean theorem
3. Probability - tickets What is the probability when you have 25 tickets in 5000 that you not wins the first (one) prize?
4. Pyramid 4sides Calculate the volume and the surface of a regular quadrangular pyramid when the edge of the base is 4 cm long and the height of the pyramid is 7 cm.
5. Neighborhood I have 7 cups: 1 2 3 4 5 6 7. How many opportunities of standings cups are there if 1 and 2 are always neighborhood?
6. 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?
7. Vectors For vector w is true: w = 2u-5v. Determine coordinates of vector w if u=(3, -1), v=(12, -10)
8. Rectangle Perimeter of rectangle is 48 cm. Calculate its dimensions if they are in the ratio 5:3 (width:height)
9. Three numbers Find three numbers so that the second number is 4 times greater than the first and the third is lower by 5 than the second number. Their sum is 67.
10. Cube diagonals Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm.
11. 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?
12. Line It is true that the lines that do not intersect are parallel?
13. Sequence Write the first 6 members of these sequence: a1 = 5 a2 = 7 an+2 = an+1 +2 an Show that the quadrilateral with vertices P1(0,1), P2(4,2) P3(3,6) P4(-5,4) has two right triangles.
15. Target Peter, Martin and Jirka were fire in a special target, which had only three fields with values of 12, 18 and 30 points. All boys were firing with the same number of arrows and all the arrows hit the target, and the results of every two boys differed in one
16. Sinus Determine the smallest integer p for which the equation 4 sin x = p has no solution.
17. Coffee shop To the coffee shop brought 2 types of coffee totally 50 kg. The first type was CZK 220 per kilogram, coffee second type 300 CZK per 1 kg. For all the coffee trader earned CZK 12,000. How many kilograms of coffee of first type and how many kilograms of cof
18. Vector - basic operations There are given points A [-9; -2] B [2; 16] C [16; -2] and D [12; 18] a. Determine the coordinates of the vectors u=AB v=CD s=DB b. Calculate the sum of the vectors u + v c. Calculate difference of vectors u-v d. Determine the coordinates of the vector w.
19. Right angled triangle Hypotenuse of a right triangle is 17 cm long. When we decrease length of legs by 3 cm then decrease its hypotenuse by 4 cm. Determine the size of legs.
20. Sines In ▵ ABC, if sin(α)=0.5 and sin(β)=0.6 calculate sin(γ)

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