# Examples for secondary school students - page 57

1. Two aces
From a 32 card box we randomly pick 1 card and then 2 more cards. What is the probability that last two drawn cards are aces?
2. Trapezoid - central median
The central median divides the trapezoid into two smaller trapezoids. Determines the ratio of their contents.
3. Prize
How many ways can be rewarded 9 participants with the first, second and third prize in a sports competition?
4. Ravens
On two trees sitting 17 ravens. If 3 ravens flew from first to second tree and 5 ravens took off from second tree then the first tree has 2 times more ravens than second tree. How many ravens was originally on every tree?
5. 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.
6. Kerosine and petrol
if 4 litres of petrol containing 15% kerosine are added to another 7 litres of petrol containing 10% kerosine, what percentage of the petrol is kerosine?
7. The rectangle
Determine the area of the rectangle where the length and width are in the ratio 5:2 and its length is 7.5 cm longer than its width. Determine also its length and its width.
On a straight stretch of road is marked 12 percent drop. What angle makes the direction of the road with the horizontal plane?
9. One percent
One percent of all the lights in the city are LED, the remaining 99% are conventional. Other types are not there. John counted them honestly but he had counted only conventional. After a good dinner he registered numbers and he have notice that from all t
10. Is complex
Are these numbers 2i, 4i, 2i + 1, 8i, 2i + 3, 4 + 7i, 8i, 8i + 4, 5i, 6i, 3i complex?
11. Boys and money
270 USD boys divided so that Peter got three times more than Paul and Ivan has 120 USD more than than Paul. How much each received?
12. Medians of isosceles triangle
The isosceles triangle has a base ABC |AB| = 16 cm and 10 cm long arm. What are the length of medians?
13. Regular n-gon
In a regular n-angle polygon the internal angle is 144 degrees. Find the number n indicating the number of sides of this polygon.
14. Arithmetic progression
In some AP applies: 5a2 + 7a5 = 90 s3 = 12 Find the first member a =? and difference d = ?
15. Tricolors
From the colors - red, blue, green, black and white, create all possible tricolors.
16. AS - sequence
What are the first ten members of the sequence if a11=22, d=2.