Maths practice for 14 year olds - page 149 of 376

Number of problems found: 7502

Pagans
Jano and Michael ate pagans. Jano ate three more than Michael. The product of their counts (numbers) is 180. How many pagans did each of them eat?
Rectangles - integers
How many different rectangles with integer side lengths have an area S = 60 cm²?
Physics - pressure
Find the pressure exerted by a crawler tractor of mass 30 t standing on a flat road if the area of the belts' contact surface with the ground is 6 m square.
Trapezoid 25
Trapezoid PART with AR||PT has (angle P=x) and (angle A=2x) . In addition, PA = AR = RT = s. Find the length of the median of Trapezoid PART in terms of s.
One dice
Calculate the probability of one dice roll with the numbers 1, 2, 3, 4, 5, and 6 on the walls. Write the results in a notebook in the shape of a fraction in the basic form: 2/3. a, The number 1 falls on the cube. b, The number 5 falls on the cube. c, An e
Solution volume
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?
Even number writing
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?
Grandma grandchildren age
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 number creation
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.
Cone roof cost
The roof of the castle tower has the shape of a cone with a base diameter of 12 m and a height of 8 m. How many euros will we pay to cover the roof if 1m of square roofing costs 3.5 euros?
Tower room whitewash
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?

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