# Examples for secondary school students - page 66

1. Prism diagonal The body diagonal of a regular square prism has an angle of 60 degrees with the base, the edge length is 10 cm. What is the volume of the prism?
2. Vertices of a right triangle Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle. Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
4. A pizza A pizza place offers 14 different toppings. How many different three topping pizzas can you order?
5. Variability In the table bellow the number of wrong produced goods in two shifts: morning shift: 2; 0; 6; 10; 2; 2; 4; 2; 5; 2; afternoon shift: 4; 4; 0; 2; 10; 2; 6; 2; 3; 10; Compare the variability in both shifts, compare the average number of wrong goods on both
6. Pupils There are 32 pupils in the classroom, and girls are two-thirds more than boys. a) How many percents are more girls than boys? Round the result to a whole percentage. b) How many are boys in the class? c) Find the ratio of boys and girls in the class. Wr
7. Functions f,g Find g(1) if g(x) = 3x - x2 Find f(5) if f(x) = x + 1/2
8. Pravoúhly trojúhelník Určete obsah pravoúhlého trojúhelníku, jehož délky stran tvoří po sobě jdoucí členy aritmetické posloupnosti a poloměr kružnice opsané tomuto trojúhelníku je 5 cm.
9. Population growth How many people will be on Earth from two people for 5,000 years, if every couple has always 4 children, (2 boys and 2 girls) at the age of 25-35, and every man will live 75 years?
10. One three We throw two dice. What is the probability that max one three falls?
11. Isosceles triangle The leg of the isosceles triangle is 5 dm, its height is 20 cm longer than the base. Calculate base length z.
12. Uphill and downhill The cyclist moves uphill at a constant speed of v1 = 10 km/h. When he reaches the top of the hill, he turns and passes the same track downhill at a speed of v2 = 40 km/h. What is the average speed of a cyclist?
13. Sixty Sixty percent of one-fifteen of the total is equal to thirty. What are two percent of the total?
14. Right angled triangle 3 Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees. Find its unknown sides length.
15. Rectangle There is a rectangle with a length of 12 cm and a diagonal 8 cm longer than the width. Calculate the area of rectangle.
16. Overtaking On the direct road, the passenger car overtakes the slower bus by starting to overtake 20 meters from the bus and after passing it ahead of it again 20 meters away. The car overtakes at a steady speed of 72 km/h, the bus goes at a steady speed of 54 km/h..
17. Bookshelf and books How many can we place 7 books in a bookshelf?
18. Family 94 boys are born per 100 girls. Determine the probability that there are two boys in a randomly selected family with three children.
19. Vinegar mixing We mix 70g water and 50g 8% vinegar. How many percents of the solution of vinegar we produce?
20. RT sides Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm.

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