# Examples for secondary school students - page 33

1. Rhombus ABCD is a rhombus, ABD is an equilateral triangle and AC is equal to 4. Find the area of the rhombus.
2. Two wine In 2:1 mix wine solution cost 4.1 USD. In 1:2 mix wine solution cost 4.5 USD. How much cost liter of each wine?
3. 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?
4. Exponential equation Solve exponential equation (in real numbers): 98x-2=9
5. 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.
6. Coordinate Determine missing coordinate of the point M [x, 120] of the graph of the function f bv rule: y = 5x
7. 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.
8. 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.
9. 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.
10. 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.
11. Sequence 3 Write the first 5 members of an arithmetic sequence: a4=-35, a11=-105.
12. The dice What is the probability of events that if we throw a dice is rolled less than 6?
13. Vector Determine coordinates of the vector u=CD if C[19;-7], D[-16,-5].
14. 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?
15. 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?
16. 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.
17. 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.
18. 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?
19. Algebrogram Solve algebrogram for sum of three numbers: BEK KEMR SOMR ________ HERCI
20. 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.

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