Examples for secondary school students
- Float boya
A 0.5 meter spherical float is used as a location mark for a fishing boat anchor. It floats in salt water. Find the depth to which the float sinks if the material of which the float is made weighs 8 kilograms per cubic meter and salt water weighs 1027 kg/
A domed stadium is in the shape of spherical segment with a base radius of 150 m. The dome must contain a volume of 3500000 m³. Determine the height of the dome at its centre to the nearest tenth of a meter.
- Area and two angles
Calculate the size of all sides and internal angles of a triangle ABC, if it is given by area S = 501.9; and two internal angles α = 15°28' and β = 45°.
- Disinfecting solution
How much distilled water is necessary to pour into 500 ml of 33% hydrogen peroxide solution to obtain 3% disinfecting solution?
arc length = 17 cm area of sector = 55 cm2 arc angle = ? the radius of the sector = ?
- Forth and back
Car goes from point A to point B at speed 78 km/h and back at 82 km/h. If went there and back at speed 81 km/h journey would take five minutes less. What is the distance between points A and B?
- Two pipes
One pipe fill one-fifth volume 20 minutes before by second one. The two pipes together will fill the tank in two hours. How long is will fill tank each pipe separately?
- Combinations of sweaters
I have 4 sweaters two are white, 1 red and 1 green. How many ways can this done?
- Inscribed circle
Write the equation of a incircle of the triangle KLM if K [2,1], L [6,4], M [6,1].
ABCD is a rhombus, ABD is an equilateral triangle and AC is equal to 4. Find the area of the rhombus.
$ 1390 was collected. How much was in $20 notes and how many in $50 notes in that order? How many solutions exists?
Cyclist rode two-fifths of the way the first day. The second day drove 5 km less while traveled three-eighths of route. How many kilometers does he have to finish target?
If the length of the sides of the square we decrease by 25% decrease the content area of 28 cm2. Determine the side length of the original square.
- Three ints
The sum of three consecutive integers is 2016. What numbers are they?
- Bus stop
Determine at what time the bus leaves from the bus stop outside the village, if you know that when you leave home at 8:00 and go at speed 3 km/h, you come to a stop 9 minutes after the departure of the bus, and when you go speed at 4 km/h, you come to th
- Road drop
On a straight stretch of road is marked 12 percent drop. What angle makes the direction of the road with the horizontal plane?
- Dices throws
What is the probability that the two throws of the dice: a) Six falls even once b) Six will fall at least once
- AS - sequence
What are the first ten members of the sequence if a11=22, d=2.
- Cube - wall
V kocke ABCDEFGH je ?. Aký je povrch kocky?
- Consecutive numbers
Sum of ten consecutive numbers is 105. Determine these numbers (write first and last).