Examples for secondary school students - page 17
Line segments 67 cm and 3.1 dm long we divide into equal parts which lengths in centimeters is expressed integer. How many ways can we divide?
At party overyone clink with everyone. Together, they clink 171 times. How many people were at the party?
- Similarity n-gon
9-gones ABCDEFGHI and A'B'C'D'E'F'G'H'I' are similar. The area of 9-gon ABCDEFGHI is S1=190 dm2 and the diagonal length GD is 32 dm. Calculate area of the 9-gon A'B'C'D'E'F'G'H'I' if G'D' = 13 dm.
A school survey found that 12 out of 15 students like pizza. If 6 students are chosen at random, what is the probability that all 6 students like pizza?
Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine angle between body diagonal and the base plane (round to degrees).
- 2nd class combinations
From how many elements you can create 4560 combinations of the second class?
- Tetrahedral prism
Calculate surface and volume tetrahedral prism, which has a rhomboid-shaped base, and its dimensions are: a = 12 cm, b = 7 cm, ha = 6 cm and prism height h = 10 cm.
- Geometric mean
Calculate the geometric mean of numbers a=15.2 and b=25.6. Determine the mean by construction where a and b are the length of the lines.
The perimeter of the rectangle is 22 cm and content area 30 cm2. Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers.
- Two runners
Two runners ran simultaneously towards each other from locations distant 34.6 km. The average speed of the first runner was 1/5 higher than the average speed of the second runner. How long should each ran a 34.6 km, if you know that they meet after 67 mi
Rectangular rink with dimensions of 68.7 m and 561 dm must be covered with a layer of ice 4.2 cm thick. How many liters of water is necessary for the formation of ice when the volume of ice is 9.7% greater than the volume of water.
From how many tiles 20 cm by 30 cm we can build a square of maximum dimensions, if we have maximum 881 tiles.
The plane flies at altitude 6500 m. At the time of first measurement was to see the elevation angle of 21° and second measurement of the elevation angle of 46°. Calculate the distance the plane flew between the two measurements.
What is the slope of the perpendicular bisector of line segment AB if A[-4,-5] and B[1,-1]?
How many different ways can sit 8 boys and 3 girls in line, if girls want to sit on the edge?
- Triangle TBC
TBC is isosceles triangle with base TB with base angle 63° and legs length |TC| = |BC| = 25. How long is the base TB?
- ISO trapezium
Calculate area of isosceles trapezoid with base 95 long, leg 27 long and with the angle between the base and leg 70 degrees.
The body was thrown vertically upward at speed v0 = 79 m/s. Body height versus time describe equation ?. What is the maximum height body reach?
In how many points will intersect 14 different lines, where no two are parallel?
- Rhombus base
Calculate the volume and surface area of prisms whose base is a rhombus with diagonals u1 = 12 cm and u2 = 10 cm. Prism height is twice base edge length.