Math practice for 13 year olds - page 295 of 420
Number of problems found: 8400
- 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. - Prism height
A regular perpendicular quadrilateral prism with a base edge of 10 cm has a volume of 10 dm³. What is the height of this prism? - Surface area of the top
A cylinder is three times as high as it is wide. The length of the cylinder diagonal is 20 cm. Find the exact surface area of the top of the cylinder. - Area of triangle
Two pairs of parallel lines, AB to CD and AC to BD, are given. Point E lies on the line BD, point F is the midpoint of the segment BD, point G is the midpoint of the segment CD, and the area of the triangle ACE is 20 cm². Determine the area of triangle DF - 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 - Unadjusted clock
Matej was finding out how precisely the tower clock measures time. He came to the conclusion that if no one adjusted it on an ongoing basis, it would show completely exact time once every 200 days. a) Calculate by how many seconds the time measured by the - 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
- 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 - Target probability
Viktor shot darts into a circular target with a radius of 5 cm. Inside the circle is a smaller circle with a radius of 2 cm. Calculate Viktor's chance of hitting a smaller circle in percent. - Holiday trip
Paul is saving for the holiday trip. He received 1100 CZK from his father. He saved a fifth and received the rest 500 CZK from his mother. How much did his holiday trip cost? - The ladder
A ladder is 10 m long and reaches a height of 8 m on a wall. How far is the base of the ladder from the wall? - Walkers
Walker, which makes 120 steps per minute, makes the distance from point A to point B 55 minutes. The length of his step is 75cm. How long does this distance go, a boy who will do 110 steps 60 cm long in a minute? - Football field area
A football field for an interstate match must be between 100 m and 110 m long and between 64 m and 75 m wide. Calculate the area of the smallest and largest fields corresponding to the conditions. - Functions f,g
Find g(1) if g(x) = 3x - x² Find f(5) if f(x) = x + 1/2 - Weekend percentage
What percentage in a non-transferable year are Saturday and Sunday? - Container
The container has a cylindrical shape, the base diameter is 0.8 m, and the area of the base is equal to the area of the wall. How many liters of water can we pour into the container? - MO8-Z8-I-5 2017
Identical rectangles ABCD and EFGH are positioned such that their sides are parallel to the same. The points I, J, K, L, M, and N are the intersections of the extended sides, as shown. The area of the BNHM rectangle is 12 cm², the rectangle MBCK area is 6
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