# Examples for secondary school students - page 33

1. Coordinate
Determine missing coordinate of the point M [x, 120] of the graph of the function f bv rule: y = 5x
2. Traffic collision
When investigating a traffic accident, it was found that the driver stopped the vehicle immediately after the accident by constant braking on a 150 m track in 15 seconds. Do you approve that the driver exceeded the permitted speed (50 km/h) in the village.
3. Mrak - cloud
It is given segment AB of length 12 cm, where one side of the square MRAK laid on it. MRAK's side length 2 cm shown. MRAK gradually flips along the line segment AB the point R leaves a paper trail. Draw the whole track of point R until square can do the.
4. Circle chord
Determine the radius of the circle in which the chord 6 cm away from the center of the circle is 12 cm longer than the radius of the circle.
5. Similarity
The area of the regular 10-gon is 563 cm2. The area of similar 10-gon is 606 dm2. What is the coefficient of similarity.
6. Three digits number
From the numbers 1, 2, 3, 4, 5 create three-digit numbers that digits not repeat and number is divisible by 2. How many numbers are there?
7. Garden
The garden has a rectangular shape and has a circumference of 130 m and area 800.25 m2. Calculate the dimensions of the garden.
8. Sequence 3
Write the first 5 members of an arithmetic sequence: a4=-35, a11=-105.
9. Vector
Determine coordinates of the vector u=CD if C[19;-7], D[-16,-5].
10. The dice
What is the probability of events that if we throw a dice is rolled less than 6?
11. Hearts
5 cards are chosen from a standard deck of 52 playing cards (13 hearts) with replacement. What is the probability of choosing 5 hearts in a row?
12. Triangle ABC
In a triangle ABC with the side BC of length 2 cm The middle point of AB. Points L and M split AC side into three equal lines. KLM is isosceles triangle with a right angle at the point K. Determine the lengths of the sides AB, AC triangle ABC.
13. Friends
Some friends had to collect the sum 72 EUR equally. If the three refused their part, others would have to give each 4 euros more. How many are friends?
14. Apples
A 2 kg of apples cost a certain sum of money. This sum is equal to the amount of kilograms for which we pay 72 CZK. How much is 1 kg of apples?
15. Algebrogram
Solve algebrogram for sum of three numbers: BEK KEMR SOMR ________ HERCI
16. Rectangular trapezoid
Calculate the content of a rectangular trapezoid with a right angle at the point A and if |AC| = 4 cm, |BC| = 3 cm and the diagonal AC is perpendicular to the side BC.
17. Car value
The car loses value 15% every year. Determine a time (in years) when the price will be halved.
18. Hexagonal pyramid
Regular hexagonal pyramid has dimensions: length edge of the base a = 1.8 dm and the height of the pyramid = 2.4 dm. Calculate the surface area and volume of a pyramid.
19. Chord - TS v2
The radius of circle k measures 87 cm. Chord GH = 22 cm. What is TS?
20. Car
At what horizontal distance reaches the car weight m = 753 kg speed v = 74 km/h when the car engine develops a tensile force F = 3061 N. (Neglect resistance of the environment.)

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