Examples for secondary school students - page 17
- Isosceles III
The base of the isosceles triangle is 17 cm area 416 cm2. Calculate the perimeter of this triangle.
Area of rectangle is 3002. Its length is 41 larger than the width. What are the dimensions of the rectangle?
Line segments 62 cm and 2.2 dm long we divide into equal parts which lengths in centimeters is expressed integer. How many ways can we divide?
- Bits, bytes
Calculate how many different numbers can be encoded in 16-bit binary word?
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).
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?
A force of 300 kg (3000 N) is required to pull a boat up a ramp inclined at 14° with horizontal. How much does the boat weight?
The top of a lighthouse is 17 m above the sea. How far away is an object which is just “on the horizon”? [Assume the earth is a sphere of radius 6378.1 km.]
At party overyone clink with everyone. Together, they clink 171 times. How many people were at the party?
- 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.
- 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.
- 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.
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?
- 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
From how many tiles 20 cm by 30 cm we can build a square of maximum dimensions, if we have maximum 881 tiles.
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.
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.