Math practice for 13 year olds - page 299 of 423
Number of problems found: 8457
- Horizontally 5480
Let's have a 4x6 grid, i.e., with 5x7 grid points. Can each grid point be colored white or blue so that each point has an even number of white neighbors? At the same time, those points that are connected by one line of the grid are considered to be neighb - Natural 5474
How many natural numbers can we create less than 301 from the number 0,1,2,3,6,7? - Competitors
In the first round of the slalom, 15% of all competitors dropped out, and in the second round, another 10 competitors dropped out. In total, 40% of all competitors dropped out. What was the total number of competitors? - Corresponding 5468
On the straight line representing the number axis, tie together the various points corresponding to the numbers a, 2a, 3a+1 in all possible orders. For each option, decide whether such an arrangement is possible. If yes, give a specific example; if not, e - Three cubes
The body was created by gluing three identical cubes. Its volume is 192 cm³. What is its surface in dm²? - Tournament 5463
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 - Specify 5462
P (x) = 15x- (5x + 10,000) specify x so that P (x) = 0 - Occupies 5461
What is the land area in reality if 1 cm² occupies a 1:20000 scale map? - Tracksuit 5460
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? - 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? - Parallelogram perimeter
The ABC triangle with sides a = 5cm, b = 3cm, c = 40mm has the center of the sides of the K,L,M. How many cm have the KBLM parallelogram perimeter? - 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. - Perpendicular 5424
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. - triangle 5420
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 triangl - Intersection of the altitudes
In the acute triangle KLM, the angle KLM is 68°. Point V is the intersection of the altitudes, and P is the foot of the altitude on the side LM. The angle P V M axis is parallel to the side KM. Compare the sizes of angles MKL and LMK. - Iron collecting
Class 7A collected 3.2 tonnes of iron, more than class 7B. Together they collected 6.4 tonnes of iron for the secondary raw material collection. How much did each class collect? - Cyclo trip
Eighth-graders took a full-day trip on a cycling course. They took 1/7 of the route to the first break and added another 3/7 of the route to lunch. They had 18 km left to the finish. How many kilometers was the trip route measured?
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