Maths practice for 14 year olds - page 145 of 370
Number of problems found: 7400
- Calculate 33911
Calculate the volume of 50% KI solution and the volume of 20% KI solution needed to prepare 180g of 30% KI solution. The solution densities are known: ρ50% = 1.54575 g / cm3, ρ20% = 1.16597 g / cm³. - Three dice
The player throwing the three dice asked G. Galilei: "Should I bet on the sum of 11 or the sum of 12?" What did Galilei answer him? Hint: write down all three triples of numbers that can be thrown, have a total of 11, have a total of 12, and compare proba - Three roads
The three boys moved from start to finish on three different routes, A, B, and C, always simultaneously. Adam drove road A 1500 m long on a scooter. Blake walked route B 600 m long on foot. Cyril got on a scooter on route C after a 90 m walk, then he left - Acute triangle
In the acute triangle KLM, V is the intersection of its heights, and X is the heel of height to the side KL. The axis of the angle XVL is parallel to the side LM, and the angle MKL is 70°. What size are the KLM and KML angles? - Roads
There are four roads from city A to city B and five roads from city B to city C. How many different routes can we take from city A to city C via city B? - Repeated 33571
Use the digits 3, 4, 5, and 6 to write all even numbers. How many such numbers can you write when you can repeat the numbers? - Construction
Construct the triangle ABC if you know: the size of the side AC is 6 cm, the size of the angle ACB is 60°, and the distance of the center of gravity T from the vertex A is 4 cm. (Sketch, analysis, notation of construction, construction) - Number 4 Kamila wrote all-natural numbers from 1 to 400 inclusive. How many times did she write the number 4?
- Grandchildren 33491
Grandma is 72 years old. It's four times the sum of the ages of her two grandchildren. The age of the older of them is twice of a younger grandson. How old is your younger grandson? - Double-digit 33471 How many double-digit numbers greater than 60 can we make from digits 0,5,6,7,8,9? The numerals must not be repeated.
- The staircase
The staircase has a total height of 3.6 m and forms an angle of 26° with the horizontal. Calculate the length of the whole staircase. - Whitewash 33351
The castle tower room has the shape of a cylinder with a diameter of 4.6m and a height of 2.9m. Calculate how much it will cost to whitewash the ceiling and walls of this room if €23 is paid for 1 square meter, while windows and doors account for 15℅ of t - Sphere cut
A sphere segment is cut off from a sphere k with radius r = 1. The volume of the sphere inscribed in this segment is equal to 1/6 of the segment's volume. What is the distance of the cutting plane from the center of the sphere? - Deceleration of car
The car has a speed of 60 km/h and, after a 100 m journey speed of 40 km/h. What is the deceleration of a car if we assume that its movement is constantly slowed down? - Two-element combinations
Write all two-element combinations from elements a, b, c, and d. - Fresh juice
The seller offers fresh-squeezed juice, which the customer either pours into his own containers or sells in liter plastic bottles, which the customer buys from him. A liter of juice costs 40 CZK more than a bottle. There is no charge for turning the juice - Ladder
How long is a ladder that touches a wall 4 meters high and has a lower part 3 meters away from the wall? - Quadrilateral pyramid
Find the height and surface of a regular quadrilateral pyramid with a base edge a = 8cm and a wall height w = 10cm. Sketch a picture. - Triangular pyramid
Calculate the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height v = 20cm. - Quadrilateral 33143
The roof of the prefabricated holiday cottage has the shape of a regular quadrilateral pyramid with a length of the base edge of 8 meters and a height of 9 m. How many square meters of cardboard are needed to cover the roof?
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