Examples for secondary school students - page 34
- Sum of series
Determine the 6-th member and the sum of a geometric series: 5-4/1+16/5-64/25+256/125-1024/625+....
- Miraculous tree
Miraculous tree grows so fast that the first day increases its height by half the total height of the second day by the third, the third day by a quarter, etc. How many times will increase its height after 6 days?
- Height of the arc - formula
Calculate the height of the arc if the length of the arc is 77 and chord length 40. Does exist a formula to solve this?
- Rectangle Anton
Difference between length and width of the rectangle is 8. Length is 3-times larger than the width. Calculate the dimensions of the rectangle.
Solve algebrogram for sum of three numbers: BEK KEMR SOMR ________ HERCI
Outer perimeter of silo is 32 m. Concrete wall is 35 cm thick. What is diameter and area of inside floor of silo?
Flywheel turns 450 rev/min (RPM). Determine the magnitude of the normal acceleration of the flywheel point which are at a distance of 10 cm from the rotation axis.
- Lion or virgin
We toss coin, every throw fits lion or a virgin with equal probability 1/2. Determine how much at least we have to make throws that with probability 0.9 lion fell at least once.
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?
- Swimming pool
The pool shape of cuboid is 299 m3 full of water. Determine the dimensions of its bottom if water depth is 282 cm and one bottom dimension is 4.7 m greater than the second.
- Cube corners
From cube of edge 14 cm cut off all vertices so that each cutting plane intersects the edges 1 cm from the nearest vertice. How many edges will have this body?
- Cross-sections of a cone
Cone with base radius 16 cm and height 11 cm divide by parallel planes to base into three bodies. The planes divide the height of the cone into three equal parts. Determine the volume ratio of the maximum and minimum of the resulting body.
We known heights 220, 165 and 132 of sail. It has triangular shape. What is the surface of the sail?
- 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?
How many different ways can initiate a game of chess (first pass)?
Willie got birthday 6 colour pens in different colors. How many ways he can give them side by side in pencil?
- 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.
- A three-digit numbers
Determine the total number of positive three-digit numbers that contain a digit 6.
- The city 2
Today lives 167000 citizens in city. How many citizens can we expect in 11 years if their annual increase is 1%?
- Pyramid in cube
In a cube with edge 12 dm long we have inscribed pyramid with the apex at the center of the upper wall of the cube. Calculate the volume and surface area of the pyramid.