# Examples for secondary school students - page 65

1. Peroxide
How many ml 30% of peroxide (H2O2) should be poured into 100ml H2O to give a 20% solution?
2. The Hotel
The Holiday Hotel has the same number of rooms on each floor. Rooms are numbered with natural numbers sequentially from the first floor, no number is omitted, and each room has a different number. Three tourists arrived at the hotel. The first one was in r
3. Tetrahedron
What is the angle of the sides from the base of a three-sided pyramid where the sides are identical?
4. Utopia Island
A probability of disease A on the island of Utopia is 40%. A probability of occurrence among the men of this island, which make up 60% of all the population (the rest are women), is 50%. What is the probability of occurrence of A disease among women on Uto
5. Rate or interest
At what rate percent will Rs.2000 amount to Rs.2315.25 in 3 years at compound interest?
6. Diagonals
What x-gon has 54 diagonals?
7. Average age
The company of five people has an average age of 46 years. The average age of the first four is 43 years. How many years has the fifth member of this company?
8. Hyperbola
Find the equation of hyperbola that passes through the point M [30; 24] and has focal points at F1 [0; 4 sqrt 6], F2 [0; -4 sqrt 6].
9. Exponential equation
Determine the value of having y in the expression (3^y): (4^-1)=36.Y is a natural number greater than zero.
10. Cube edges
If the edge length of the cube increases by 50%, how does the volume of this cube increase?
11. Two diggers
Two diggers should dig a ditch. If each of them worked just one-third of the time that the other digger needs, they'd dig up a 13/18 ditch together. Find the ratio of the performance of this two diggers.
12. Boys and girls
There are 11 boys and 18 girls in the classroom. Three pupils will answer. What is the probability that two boys will be among them?
13. PIN code
PIN on Michael credit card is a four-digit number. Michael told this to his friend: • It is a prime number - that is, a number greater than 1, which is only divisible by number one and by itself. • The first digit is larger than the second. • The second.
14. Children playground
The playground has the shape of a trapezoid, the parallel sides have a length of 36 m and 21 m, the remaining two sides are 14 m long and 16 m long. Determine the size of the inner trapezoid angles.
15. Six terms
Find the first six terms of the sequence a1 = -3, an = 2 * an-1
16. Electric input power
Solve problems related to electric power: a) U = 120 V, I = 0.5 A, P =? b) P = 200 W, U = 230 V, I =? c) I = 5 A, P = 2200W, U =?
17. Vertices of a right triangle
Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle.
18. 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
19. A pizza
A pizza place offers 14 different toppings. How many different three topping pizzas can you order?
20. 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?

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