Maths practice for 14 year olds - page 265 of 382
Number of problems found: 7625
- Chess reward
A reward of 1200 CZK is prepared for the 4 best champions in the chess tournament. It will be divided so that the second gets half of the first, the third half of the second's reward, and the fourth half of the third. How many CZK will each person receive - Finding x for Profit
P (x) = 15x- (5x + 10,000) specify x so that P (x) = 0 - Tracksuit savings
The tracksuit became cheaper by 15% later on sale and later by 10%. How many euros did Janka save if she bought this set after the second discount and paid € 45.9? - Car acceleration
A driver traveling at 72 km/h decides to overtake another car traveling at the same speed. Over a period of 4.0 seconds, he increases his speed to 90 km/h. Calculate his acceleration and the distance he covered while accelerating. - Mother and daughter
The mother is four times older than her daughter. Five years ago, her daughter was seven times younger than her mother. How many years do they have now? - Digit equations
The digit sum of a two-digit number is 8. If we change the order of the digits, we get a number 18 smaller than the original. Identify these numbers. We are using linear equations of two unknowns. - Z9–I–4 MO 2017
Numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 were prepared for a train journey with three wagons. They wanted to sit out so that three numbers were seated in each carriage, and the largest of the three was equal to the sum of the remaining two. The conductor sai - Big number
What is the remainder when dividing 10 by 9 to 47 - 111? - Remainder A is an arbitrary integer that gives remainder 1 in the division with 6. B is a random integer that provides the remainder with division by two. What makes remainder in a division by three products of numbers A x B?
- Inscribed circle
The circle inscribed in a triangle has a radius of 3 cm. Express the area of the triangle using a, b, and c. - Chord
It is given to a circle k(r=6 cm), and the points A and B such that |AB| = 8 cm lie on k. Calculate the distance of the center of circle S to the midpoint C of segment AB. - MO Z8–I–4 2017
Robots Robert and Hubert assemble and disassemble coffee grinders. Each of them, however, assembles a grinder four times faster than the other one disassembles it. When they came to the workshop in the morning, several grinders were already assembled ther - Iron collecting
Class 7 A collected 3.2 tonnes more iron than class 7B. Together they collected 6.4 tonnes of iron for the scrap metal drive. How much did each class collect? - Smallest Asymmetric Power
Find the smallest natural number k for which the number 11 on k is asymmetric. (e.g. 11² = 121) - Cake duration
Four children eat ten cakes in 30 minutes. How many minutes will it take nine children to eat 27 cakes? - Adela number Adela had two numbers written on the paper. When she added their greatest common divisor and least common multiple, she was given four different numbers less than 100. She was amazed that if she divided the largest of these four numbers by the least, she
- MO Z9–I–3 - 2017 Robots Robert and Hubert assemble and disassemble coffee grinders. Each of them assembles a grinder four times faster than he disassembles one himself. When they came to the workshop in the morning, several grinders were already assembled there. At 7:00 H
- MO Z9–I–2 - 2017
In trapezoid VODY, VO is the longer base. The diagonal intersection K divides segment VD in the ratio 3:2. The area of triangle KOV is 13.5 cm². Find the area of the entire trapezoid. - Average age
The average age of all people at the celebration was equal to the number of people present. After the departure of one person who was 29 years old, the average age was again equal to the number present. How many people were originally at the celebration? - Gear train
A gear train is assembled from three gear wheels. The first has 165 teeth, the second 132 teeth, and the third 231, where the second engages with the first and the third with the second. The first and third do not touch. How many times per minute will all
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