# Examples for secondary school students

1. Three points
Three points A (-3;-5) B (9;-10) and C (2;k) . AB=AC What is value of k?
2. Center of line segment
Calculate the distance of the point X [1,3] from the center of the line segment x = 2-6t, y = 1-4t ; t is .
3. On line
On line p: x = 4 + t, y = 3 + 2t, t is R, find point C, which has the same distance from points A [1,2] and B [-1,0].
4. Coordinates of vector
Determine the coordinate of a vector u=CD if C(19;-7) and D(-16;-5)
5. Left handed
It is known that 25% of the population is left-handed. What is the probability that there is a maximum of three left-handers at a seminar where there are 30 participants?
6. Construct
Construct a triangle ABC inscribed circle has a radius r = 2 cm, the angle alpha = 50 degrees = 8 cm. Make a sketch, analysis, construction and description.
7. Powers 3
2 to the power of n divided by 4 to the power of -3 equal 4. What is the vaule of n?
8. Component fail
There is a 90 percent chance that a particular type of component will perform adequately under high temperature conditions. If the device involved has four such components, determine the probability that the device is inoperable because exactly one of the
9. Distance problem 2
A=(x,2x) B=(2x,1) Distance AB=√2, find value of x
10. Distance problem
A=(x, x) B=(1,4) Distance AB=√5, find x;
11. Driver
The driver of the car at a speed of 100 km/h faced the obstacle and began to brake with a slowing of 5 m/s². What is the path to stopping the car when the driver has registered the obstacle with a delay of 0.7 s?
12. Brakes of a car
For the brakes of a passenger car to be effective, it is prescribed that a car moving on a horizontal road at a speed of 40 km. A car must stop on the track 15.4 m. What is the deceleration of the car?
13. Age
In 1960 my age was equal to the digits sum of the year of my birth. What is my age now?
14. Microorganisms
The first generation of micro-organisms has a population of 13500 members. Each next generation is 11/10 times the previous one. Find out how many generations will reach at least three times members of the first generation.
15. Brakes
The braking efficiency of a passenger car is required to stop at 12.5 m at an initial speed of 40 km/h. What is the acceleration braking by brakes?
16. The crime
The crime rate of a certain city is increasing by exactly 7% each year. If there were 600 crimes in the year 1990 and the crime rate remains constant each year, determine the approximate number of crimes in the year 2025.
17. Boys and girls
There are eight boys and nine girls in the class. There were six children on the trip from this class. What is the probability that left a) only boys b) just two boys
18. Collision
The two bodies, whose initial distance is 240 m, move evenly against each other consistently. The first body has an initial velocity of 4 m/s and an acceleration of 3 m/s2, the second body has an initial speed of 6 m/s and an acceleration of 2 m/s2. Fin
19. Sss triangle
Calculate the area and heights in the triangle ABC by sides a = 8cm, b = 11cm, c = 12cm
20. AP RT triangle
The length of the sides of a right triangle form an arithmetic progression, longer leg is 24 cm long. What are the perimeter and area?

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