# Examples for secondary school students - page 35

- Cuboid - volume and areas

The cuboid has a volume of 250 cm^{3}, a surface of 250 cm^{2}and one side 5 cm long. How do I calculate the remaining sides? - Triangle ABC

Triangle ABC has side lengths m-1, m-2, m-3. What has to be m to be triangle a) rectangular b) acute-angled? - Chess

How many different ways can initiate a game of chess (first pass)? - Medians in triangle

Median of isosceles triangle has a length 3 cm. Determine the length of its sides if its perimeter is 16 cm. - Colors

Willie got birthday 6 colour pens in different colors. How many ways he can give them side by side in pencil? - The city 2

Today lives 167000 citizens in city. How many citizens can we expect in 11 years if their annual increase is 1%? - Candies

In the box are 12 candies that look the same. Three of them are filled with nougat, five by nuts, four by cream. At least how many candies must Ivan choose to satisfy itself that the selection of two with the same filling? ? - A three-digit numbers

Determine the total number of positive three-digit numbers that contain a digit 6. - Water reservoir

The water reservoir is filled through one inlet 4 hours later than both together, then another inlet 9 hours later than both together. For how long is filled by each separately? - Right angled triangle 2

LMN is a right angled triangle with vertices at L(1,3), M(3,5) and N(6,n). Given angle LMN is 90° find n - Water

In the garden with an area of 8 ares rain 40hl of water. To what heights leveled water? - Direct route

From two different places A and B connected by a direct route, Adam (from city A) and Bohus (from city B) started at a constant speed. As Adam continued to go from A to B, Bohus turned around at the time of their meeting and at the same speed he returned t - Probabilities

If probabilities of A, B and A ∩ B are P (A) = 0.62 P (B) = 0.78 and P (A ∩ B) = 0.26 calculate the following probability (of union. intersect and opposite and its combinations): - Rings groups

27 pupils attend some group; dance group attends 14 pupils, 21 pupils sporty group and dramatic group 16 pupils. Dance and sporting attend 9 pupils, dance and drama 6 pupil, sporty and dramatic 11 pupils. How many pupils attend all three groups? - Shot

Shot with a mass 43 g flying at 256 m/s penetrates into the wood to a depth 25 cm. What is the average force of resistance of wood? - Center of gravity

In the isosceles triangle ABC is the ratio of the lengths of AB and the height to AB 10:12. The arm has a length of 26 cm. If the center of gravity T of triangle ABC find area of triangle ABT. - Harvesters

The first harvester reaps the grain from land for 24 hours, the second harvester for 16 hours. For how many hours will take harvest by two harvesters, but the second harvester started working four hours later than the first? - Znojmo

From Znojmo to Brno started truck with a trailer at an average speed 53 km per hour. Against him 14 minutes later from Brno started car with an average speed of 1.2-times greater than the truck. How long and how far from Znojmo, they meet if the distanc - Weekly service

In the class are 20 pupils. How many opportunities have the teacher if he wants choose two pupils randomly who will weeklies? - Equation

Eequation f(x) = 0 has roots x_{1}= 64, x_{2}= 100, x_{3}= 25, x_{4}= 49. How many roots have equation f(x^{2}) = 0 ?

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