id stringlengths 36 36 | dataset_id stringlengths 1 36 | problem stringlengths 13 1.52k | source stringclasses 5
values | answer stringclasses 993
values | image imagewidth (px) 41 7.36k |
|---|---|---|---|---|---|
f351f810-b76d-45b5-bbe8-c3188f0ef969 | 301 | As shown in <image>,Each face of the polyhedron shown is either a triangle or a square. Each square borders 4 triangles, and each triangle borders 3 squares. The polyhedron has 6 squares. How many triangles does it have?
<image1> | MathVision | 8 | |
f51be939-dea0-40d8-b105-768f2c5895bf | 302 | As shown in <image>,Julia has 2017 round discs available: 1009 black ones and 1008 white ones. Using them, she wants to lay the biggest square pattern (as shown) possible and starts by using a black disc in the left upper corner. Subsequently she lays the discs in such a way that the colours alternate in each row and c... | MathVision | E | |
1f8eb7a4-f912-453c-81b4-db0c29c6fca4 | 303 | As shown in <image>,The diagram shows a regular hexagon with side length 1. The grey flower is outlined by circular arcs with radius 1 whose centre's lie in the vertices of the hexagon. How big is the area of the grey flower?
<image1> | MathVision | E | |
d1af099a-d7ab-4c3d-8ff3-c6ae1e568145 | 304 | As shown in <image>,We look at a regular tetrahedron with volume 1. Its four vertices are cut off by planes that go through the midpoints of the respective edges (see diagram). How big is the volume of the remaining solid?
<image1> | MathVision | D | |
1d2dbb17-607b-46b1-a039-9f015ef06567 | 305 | As shown in <image>,Nine whole numbers were written into the cells of a $3 \times 3$-table. The sum of these nine numbers is 500. We know that the numbers in two adjacent cells (with a common sideline) differ by exactly 1. Which number is in the middle cell?
<image1> | MathVision | 56 | |
ed7bccd4-cae0-4d95-ac77-95cca7b7c7fc | 306 | As shown in <image>,In the diagram you can see the calendar page of a certain month. Unfortunately ink has run across parts of the page. Which day of the week does the 27th of that month fall on?
<image1> | MathVision | A | |
f410c35d-0fc5-4f41-9227-4fab17be3a73 | 307 | As shown in <image>,The diagram shows the floor plan of Renate's house. Renate enters her house from the terrace (Terrasse) and walks through every door of the house exactly once. Which room does she end up in?
<image1> | MathVision | 2 | |
befee4d7-08d0-4d73-9e6c-4c832949b700 | 308 | As shown in <image>,The diagram shows an object made up of 12 dice glued-together. The object is dipped into some colour so that the entire outside is coloured in this new colour. How many of the small dice will have exactly four faces coloured in?
<image1> | MathVision | 10 | |
50a313e9-b0ec-4409-bdbb-f8fcfe01ebc0 | 309 | As shown in <image>,Four identical rhombuses (diamonds) and two squares are fitted together to form a regular octagon as shown. How big are the obtuse interior angles in the rhombuses?
<image1> | MathVision | A | |
4cadcea0-f05d-4649-8eda-8ba568ee5a6b | 310 | As shown in <image>,The faces of the brick have the areas A, B and C as shown. How big is the volume of the brick?
<image1> | MathVision | B | |
82558a93-7566-4da9-97d4-593643648b6b | 311 | As shown in <image>,Two dice with volumes $V$ and $W$ intersect each other as shown. $90 \%$ of the volume of the die with volume $V$ does not belong to both dice. $85 \%$ of the volume of the die with volume $W$ does not belong to both dice. What is the relationship between the volumes of the two dice?
<image1> | MathVision | B | |
a073911d-c702-4664-8161-86ec19ff073c | 312 | As shown in <image>,The five vases shown are filled with water. The filling rate is constant. For which of the five vases does the graph shown describe the height of the water $h$ as a function of the time t?
<image1>
<image2> | MathVision | D | |
b52ff007-9185-47da-a017-2bca131bf16f | 313 | As shown in <image>,An octahedron is inscribed into a die with side length 1. The vertices of the octahedron are the midpoints of the faces of the die. How big is the volume of the octahedron?
<image1> | MathVision | D | |
6bde1185-52d1-4025-b041-56fcfa467a71 | 314 | As shown in <image>,The vertices of a triangle have the co-ordinates $A(p \mid q), B(r \mid s)$ and $C(t \mid u)$ as shown. The midpoints of the sides of the triangle are the points $\mathrm{M}(-2 \mid 1), \mathrm{N}(2 \mid-1)$ and $\mathrm{P}(3 \mid 2)$. Determine the value of the expression $p+q+r+s+t+u$
<image1> | MathVision | 5 | |
3cd275f4-0b5e-490b-94be-40b439e58346 | 315 | As shown in <image>,A regular pentagon is cut out of a page of lined paper. Step by step this pentagon is then rotated $21^{\circ}$ counter clockwise about its midpoint. The result after step one is shown in the diagram. Which of the diagrams shows the situation when the pentagon fills the hole entirely again for the f... | MathVision | B | |
81158291-d7d8-4b12-8195-0e809becd787 | 316 | As shown in <image>,Three of the cards shown will be dealt to Nadia, the rest to Riny. Nadia multiplies the three values of her cards and Riny multiplies the two values of his cards. It turns out that the sum of those two products is a prime number. Determine the sum of the values of Nadia's cards.
<image1> | MathVision | 13 | |
fc54ec37-61ae-40a3-8eba-d90471faf2ab | 317 | As shown in <image>,Two rectangles form the angles $40^{\circ}$ and $30^{\circ}$ respectively, with a straight line (see diagram). How big is angle $\alpha$?
<image1> | MathVision | E | |
f4641bcf-4f1b-4f6f-a058-1a3e56146b00 | 318 | As shown in <image>,The faces of the prism shown, are made up of two triangles and three squares. The six vertices are labelled using the numbers 1 to 6. The sum of the four numbers around each square is always the same. The numbers 1 and 5 are given in the diagram. Which number is written at vertex $X$?
<image1> | MathVision | 2 | |
36ae9b5e-1cbc-4500-ad1a-2c207a709807 | 319 | As shown in <image>,On an idealised rectangular billiard table with side lengths $3 \mathrm{~m}$ and $2 \mathrm{m}$ a ball (point-shaped) is pushed away from point $M$ on the long side $A B$. It is reflected exactly once on each of the other sides as shown. at which distance from the vertex $A$ will the ball hit this s... | MathVision | E | |
c60c4e00-4573-4270-a94b-afa080a69b31 | 320 | As shown in <image>,$A B C D E F$ is a regular hexagon, as shown in the diagram. $G$ is the midpoint of $A B. H$ and I are the intercepts of the line segments GD and GE respectively, with the line segment FC. How big is the ratio of the areas of the triangle GIF and the trapezium IHDE?
<image1> | MathVision | A | |
7046b9a0-98c0-4b1c-a834-31a395ffe782 | 321 | As shown in <image>,Archimedes has calculated 15!. The result is on the board. Unfortunately two of the digits, the second and the tenth, cannot be read. What are the two missing digits? (Remark: $15 !=15 \cdot 14 \cdot 13 \cdot \ldots \cdot 2 \cdot 1$ )
<image1> | MathVision | E | |
8f7342a2-aff1-4fec-b37c-5f241890898f | 322 | As shown in <image>,The flag of Kangoraland is a rectangle which is split into three equal rectangles as shown. How big is the ratio of the side lengths of the white rectangle?
<image1> | MathVision | A | |
e31f0428-4f22-42d8-85fd-12c147e52c21 | 323 | As shown in <image>,The numbers $1,2,3$ and 4 are inserted into different cells of the $2 \times 2$ table shown. Then the sums of the numbers in each row and column are determined. Two of these sums are 4 and 5. How big are the two remaining sums?
<image1> | MathVision | E | |
8c9b008d-8c38-4687-bc88-185786454b5b | 324 | As shown in <image>,A rectangle is coloured in five different ways as shown. In which picture is the grey area biggest?
<image1> | MathVision | E | |
86de4344-3795-459d-a9d8-3cec51796432 | 325 | As shown in <image>,Three triangles are connected to each other as shown. In which of the following pictures are the three triangles connected in the same way?
<image1>
<image2> | MathVision | D | |
cc82130a-367b-411b-9b05-6bd4c765e9c2 | 326 | As shown in <image>,Three four-digit numbers are written onto three separate pieces of paper as shown. The sum of the three numbers is 11126. Three of the digits in the picture are hidden. Which are the three hidden digits?
<image1> | MathVision | B | |
7184c0e2-a4fe-4e73-abb7-a797aaff9217 | 327 | As shown in <image>,Each side of a die is marked with either 1,2 or 3 dots so that the probability of rolling a 1 is equal to $\frac{1}{2}$, the probability of rolling a 2 is equal to $\frac{1}{3}$ and the probability of rolling a 3 is equal to $\frac{1}{6}$. Which of these pictures cannot be a picture of this particul... | MathVision | C | |
8c8c5efc-24a6-4cc3-8e5f-5a9c0e5f684a | 328 | As shown in <image>,A cuboid-shaped container that is not filled completely contains $120 \mathrm{~m}^{3}$ of water. The depth of the water is either $2 \mathrm{~m}$ or $3 \mathrm{~m}$ or $5 \mathrm{~m}$, depending on which side the container is actually standing on (drawings not to scale). How big is the volume of the... | MathVision | E | |
901ba241-dbba-49ad-a35f-fd1f887b923b | 329 | As shown in <image>,The system shown consists of three pulleys that are connected to each other via two ropes. $P$, the end of one rope, is pulled down by $24 \mathrm{~cm}$. By how many centimeters does point $Q$ move upwards?
<image1> | MathVision | 6 | |
5dfb77c5-197e-4e05-b0f4-7018ebc96b00 | 330 | As shown in <image>,The diagram shows two adjoining squares with side lengths $a$ and $b$ (with $a<b$). How big is the area of the grey triangle?
<image1> | MathVision | B | |
900c1f2e-51f3-49f1-8b69-03dc0e60be3d | 331 | As shown in <image>,The points of intersection of the network of bars shown are labelled with the numbers 1 to 10. The sums $S$ of the four numbers on the vertices of each square are
all the same. What is the minimum value of $S$?
<image1> | MathVision | 20 | |
38ea3f17-03d5-429d-8d61-390ecf9319bd | 332 | As shown in <image>,A path $D E F B$ with $D E \perp E F$ and $E F \perp F B$ lies within the square $A B C D$ as shown. We know that $D E=5, E F=1$ and $F B=2$. What is the side length of the square?
<image1> | MathVision | E | |
3091d672-9cf8-4baa-98b7-334ed607b16d | 333 | As shown in <image>,Three circles with radius 2 are drawn in such a way that each time one of the points of intersection of two circles is identical with the centre of the third circle. How big is the area of the grey zone?
<image1> | MathVision | D | |
e38bcd6d-e1c6-4b8e-87a1-748e804f8be3 | 334 | As shown in <image>,Numbers are to be placed into the square grid shown, so that each of the numbers $1,2,3,4$ and 5 appears exactly once in each row and in each column. Furthermore sthe sum of all numbers in the three black-bordered sections should always be the same. Which number has to be written into the top right ... | MathVision | 3 | |
a47fb265-098f-441d-b6e3-cfa818c9aa55 | 335 | As shown in <image>,An ant walked $6 \mathrm{~m}$ every day to go from point $A$ to point $B$ in a straight line. One day Johnny put a straight cylinder of one meter high in that way. Now the ant walks on the same straight line or above it, having to go up and down the cylinder, as shown in the picture. How much does s... | MathVision | A | |
34e4b135-4491-43a6-93a9-c697639d5ee6 | 336 | As shown in <image>,The pie chart beside refers to the number of inhabitants of the five zones of a city. The central zone has the same population as the north, west and east zones together and the south zone has half of the inhabitants of the west zone. What is the percentage difference between the inhabitants of the ... | MathVision | D | |
2ead1da5-38ed-4dcb-b318-2fd1003b7d27 | 337 | As shown in <image>,In the addition on the right, different letters represent different numbers. Assuming the account is correct, what is the highest possible value for the sum $\mathrm{C}+\mathrm{A}+\mathrm{N}$?
<image1> | MathVision | 21 | |
01079245-2de4-496d-8f8a-ecd55a2a425a | 338 | As shown in <image>,A gray square with an area of $36 \mathrm{~cm}^{2}$ and a black square with an area of $25 \mathrm{~cm}^{2}$ are superimposed, as shown beside. What is the perimeter of the overlapping region, represented by the white quadrilateral, which has a vertex on the side of the gray square?
<image1> | MathVision | B | |
901aff3e-d17e-4045-95c4-436d037372bb | 339 | As shown in <image>,Zilda will use six equal cubes and two different rectangular blocks to form the structure beside with eight faces. Before gluing the pieces, she will paint each one entirely and calculated that she will need 18 liters of paint (the color does not matter). How many liters of paint would she use if sh... | MathVision | 11.5 | |
d17b4151-9ea9-43af-97f5-fa84d0fe4aad | 340 | As shown in <image>,The last two digits of a 2020 number are 9 and 9. At most, how many digits does the square of that number have?
<image1> | MathVision | 4040 | |
7110fc8b-0388-49f8-8024-8b4a4ca4c047 | 341 | As shown in <image>,Matias wrote 15 numbers on the wheel represented beside. Only one of them is visible, the 10 on top of the wheel. The sum of the numbers in any seven consecutive positions, such as the gray positions in the figure, does not vary. When seven numbers in consecutive positions are summed up, which of th... | MathVision | B | |
23859c8a-2db3-4cfe-a4af-4a4e0c217323 | 342 | As shown in <image>,A large square touches another two squares, as shown in the picture. The numbers inside the smaller squares indicate their areas. What is the area of the largest square?
<image1> | MathVision | 13 | |
a1aacba9-42d6-4948-8d1c-eff2c5f6a735 | 343 | As shown in <image>,A circle is tangent to one side of a rectangle and passes through two of its vertices, as shown beside. A square of $20 \mathrm{~cm}^{2}$ area has one side over the side of the rectangle and two vertices over the circle, as shown in the figure. What is the area of the rectangle?
<image1> | MathVision | C | |
ff5ad414-b4ca-4ef9-a1fd-af7f8be940f9 | 344 | As shown in <image>,Two rectangular blocks and a cube are joined to form a larger rectangular block, which volume is $280 \mathrm{~cm}^{3}$. The cube, in dark gray in the picture, has volume equal to $125 \mathrm{~cm}^{3}$ and the smaller rectangular block has volume equal to $75 \mathrm{~cm}^{3}$. What is the area of ... | MathVision | A | |
ebb42d5e-bd2f-4f4c-a721-e761d45c8709 | 345 | As shown in <image>,The figure shows the lines $r$ and $s$, which equations are, respectively, $y=a x
+b$ e $y=c x+d$. Which of the following statements is true?
<image1> | MathVision | A | |
5677b25f-e9c4-49f3-a42e-069c0914ac69 | 346 | As shown in <image>,A little kangaroo draws a line passing through point $P$ of the grid and then paints three triangles in black as shown in the picture. The areas of these triangles are proportional to which numbers?
<image1> | MathVision | A | |
22858e1a-f26d-4e99-9166-9933ac882788 | 347 | As shown in <image>,A rectangular garden was $50 \mathrm{~m}$ long and $40 \mathrm{~m}$ wide. An artificial lake was built next to it, so that the whole set forms a $60 \mathrm{~m}$ square. Then a fence was stretched, separating both the garden and the lake in two parts with equal areas, as shown in the picture. How lo... | MathVision | B | |
f9070140-f643-4098-b44e-082d7b7145ee | 348 | As shown in <image>,Vilma took a sheet of paper measuring $10 \mathrm{~cm} \times 20 \mathrm{~cm}$ and made two folds, taking the two smaller sides of the sheet to a diagonal of it. She gets a parallelogram, as shown in the picture. What is the area of this quadrilateral, in $\mathrm{cm}^{2}$?
<image1> | MathVision | D | |
d15d57d9-609e-4746-80cc-2373df1e9980 | 349 | As shown in <image>,There are $n$ different prime numbers $p_{1}, p_{2}, \ldots, p_{n}$ written from left to right on the last line below the table shown beside. The product of two neighboring numbers in the same line is written in the upper two boxes. The number $K=p_{1}^{\alpha_{1}} \cdot p_{2}^{\alpha_{2}} \ldots p_... | MathVision | 28 | |
5e4a404b-3dc5-45d9-aba8-0be85e2d3a00 | 350 | As shown in <image>,Adam and Bruna try to find out which is Carla's favorite figure, amongst the figures beside. Adam knows that Carla told Bruna what the shape of the figure was. Bruna knows that Carla told Adam what color the figure was. The following conversation takes place. Adam: "I don't know what Carla's favorit... | MathVision | E | |
0ba1d232-b891-4352-a00c-973aeebc6415 | 351 | As shown in <image>,Paula's weather app shows a diagram of the predicted weather and maximum temperatures for the next seven days, as shown. Which of the following represents the corresponding graph of maximum temperatures?
<image1>
<image2> | MathVision | E | |
04f29d4f-dbf5-4450-bf83-b7ee7fb16ac2 | 352 | As shown in <image>,A large square is divided into smaller squares, as shown. A shaded circle is inscribed inside each of the smaller squares. What proportion of the area of the large square is shaded?
<image1> | MathVision | E | |
2997889b-7af6-4cce-94c6-10c34f667711 | 353 | As shown in <image>,After the storm last night, the flagpole on our school building is leaning over. Looking from northwest, its tip is to the right of its bottom point. Looking from the east, its tip is also to the right of its bottom point. In which direction could the flagpole be leaning over?
<image1> | MathVision | A | |
affc6f71-adf4-4acf-87c3-dff16caa1a79 | 354 | As shown in <image>,The parabola in the figure has an equation of the form $y=a x^{2}+b x+c$ for some distinct real numbers $a, b$ and $c$. Which of the following equations could be an equation of the line in the figure?
<image1> | MathVision | D | |
1d38d475-8f65-438b-9692-e662903a9079 | 355 | As shown in <image>,A large triangle is divided into smaller triangles as shown. The number inside each small triangle indicates its perimeter. What is the perimeter of the large
triangle?
<image1> | MathVision | 34 | |
bf455bfc-6fca-44c7-8f3c-bb6ef52f53d7 | 356 | As shown in <image>,In the $5 \times 5$ square shown the sum of the numbers in each row and in each column is the same. There is a number in every cell, but some of the numbers are not shown. What is the number in the cell marked with a question mark?
<image1> | MathVision | 10 | |
21dcc70a-b928-4b3e-923e-b05e9e86691f | 357 | As shown in <image>,A piece of string is lying on the table. It is partially covered by three coins as seen in the figure. Under each coin the string is equally likely to pass over itself like this: <image1>
or like this: <image2>. What is the probability that the string is knotted after its ends are pulled?
<image3> | MathVision | B | |
1cd2e2c3-7428-41ca-90ca-f07f8716bc21 | 358 | As shown in <image>,A naughty pup grabs the end of a roll of toilet paper and walks away at a constant speed. Which of the functions below best describes the thickness $y$ of the roll as a function of the unrolled part $x$?
<image1>
<image2> | MathVision | E | |
dcf1d860-4b82-41b2-b17b-05da3410ecee | 359 | As shown in <image>,The diagram shows three squares, $P Q R S, T U V R$ and $U W X Y$. They are placed together, edge to edge. Points $P, T$ and $X$ lie on the same straight line. The area of $P Q R S$ is 36 and the area of TUVR is 16. What is the area of triangle PXV?
<image1> | MathVision | 16 | |
aca00d31-5333-4dd5-a9fe-724116ddc53f | 360 | As shown in <image>,The figure shows the graph of a function $f:[-5,5] \rightarrow R$. How many distinct solutions does the equation $f(f(x))=0$ have?
<image1> | MathVision | 8 | |
a2f09daa-eefd-4cfb-8258-6a9934ff171d | 361 | As shown in <image>,Five kangaroos named A, B, C, D and E have one child each, named a, b, c, d and e, not necessarily in that order. In the first group photo shown exactly 2 of the children are standing next to their mothers. In the second group photo exactly 3 of the children are standing next to their mothers. Whose... | MathVision | D | |
a1bb3514-848a-428b-91cb-bd428dd32695 | 362 | As shown in <image>,The solid shown in the diagram has 12 regular pentagonal faces, the other faces being either equilateral triangles or squares. Each pentagonal face is surrounded by 5 square faces and each triangular face is surrounded by 3 square faces. John writes 1 on each triangular face, 5 on each pentagonal fa... | MathVision | 50 | |
b2a4c703-0c2b-44c2-baf4-c4135a21f5d6 | 363 | As shown in <image>,On a circle 15 points are equally spaced. We can form triangles by joining any 3 of these. Congruent triangles, by rotation or reflection, are counted as only one triangle. How many different triangles can be drawn?
<image1> | MathVision | 19 | |
bf66b53b-e514-4446-b630-2d6e47290f73 | 364 | As shown in <image>,A triangle $A B C$ is divided into four parts by two straight lines, as shown. The areas of the smaller triangles are 1,3 and 3. What is the area of the original triangle?
<image1> | MathVision | 12 | |
de16b965-6739-4fbb-a27c-646bc04541e0 | 365 | As shown in <image>,Two plane mirrors $O P$ and $O Q$ are inclined at an acute angle (diagram is not to scale). A ray of light $X Y$ parallel to $O Q$ strikes mirror $O P$ at $Y$. The ray is reflected and hits mirror $O Q$, is reflected again and hits mirror $O P$ and is reflected for a third time and strikes mirror $O... | MathVision | C | |
d9846fb5-5cc0-42d9-9964-3fa14c816ef3 | 366 | As shown in <image>,Martin's smartphone displays the diagram on the right. It shows how long he has worked with four different apps in the previous week. The apps are sorted from top to bottom according to the amount of time they have been used. This week he has spent only half the amount of time using two of the apps ... | MathVision | E | |
6ed9566d-9533-4bc1-8785-3cac9481c320 | 367 | As shown in <image>,Four circles with radius 1 intersect each other as seen in the diagram. What is the perimeter of the grey area?
<image1> | MathVision | D | |
dfd2273a-bad5-4ce2-9d3b-50ea0057e06f | 368 | As shown in <image>,The points $A, B, C$ and $D$ are marked on a straight line in this order as shown in the diagram. We know that $A$ is $12 \mathrm{~cm}$ from $C$ and that $B$ is $18 \mathrm{~cm}$ from $D$. How far apart from each other are the midpoints of the line segments $A B$ and $C D$?
<image1> | MathVision | E | |
b62d1d78-7f27-423e-9009-307516ebea94 | 369 | As shown in <image>,Four straight lines that intersect in one single point form eight equal angles (see diagram). Which one of the black arcs has the same length as the circumference of the little (grey) circle?
<image1> | MathVision | D | |
d026e67c-42a4-4c88-9a2b-044ca959819b | 370 | As shown in <image>,We check the water meter and see that all digits on the display are different. What is the minimum amount of water that has to be used before this happens again?
<image1> | MathVision | D | |
db63d327-5447-4b41-9e9e-e2191a6ac4f2 | 371 | As shown in <image>,The square pictured, is split into two squares and two rectangles. The vertices of the shaded quadrilateral with area 3 are the midpoints of the sides of the smaller squares. What is the area of the non-shaded part of the big square?
<image1> | MathVision | 21 | |
eff72447-c482-4ad3-bf71-4cf24dc5e7a0 | 372 | As shown in <image>,The diagram shows a map with 16 towns which are connected via roads. The government is planning to build power plants in some towns. Each power plant can generate enough electricity for the town in which it stands as well as for its immediate neighbouring towns (i.e. towns that can be reached via a ... | MathVision | 4 | |
18afb8c7-17ef-425b-8c78-7d9b336db6d2 | 373 | As shown in <image>,A cuboid with surface area $X$ is cut up along six planes parallel to the sides (see diagram). What is the total surface area of all 27 thus created solids?
<image1> | MathVision | C | |
21d1396c-907f-4918-b1a3-30f27d7b7e45 | 374 | As shown in <image>,A circle with midpoint $(0 \mid 0)$ has a radius of 5. How many points are there on the circumference where both co-ordinates are integers?
<image1> | MathVision | 12 | |
6ef5603f-0c15-4cfc-a0f6-eb71fc3d2a72 | 375 | As shown in <image>,Which two building blocks can be joined together so that the object shown is created?
<image1>
<image2> | MathVision | A | |
e24655db-808b-44eb-83ab-f1f67b60e21c | 376 | As shown in <image>,A rectangle is split into 11 smaller rectangles as shown. All 11 small rectangles are similar to the initial rectangle. The smallest rectangles are aligned like the original rectangle (see diagram). The lower sides of the smallest rectangles have length 1. How big is the perimeter of the big rectang... | MathVision | 30 | |
b33be8ca-5299-4373-81eb-3a57c50590de | 377 | As shown in <image>,Two rectangles are inscribed into a triangle as shown in the diagram. The dimensions of the rectangles are $1 \times 5$ and $2 \times 3$ respectively. How big is the height of the triangle in $A$?
<image1> | MathVision | B | |
acbff3a3-d331-4a38-89c7-6aba03d63d4c | 378 | As shown in <image>,The numbers 1 to 10 were written into the ten circles in the pattern shown in the picture. The sum of the four numbers in the left and the right column is 24 each and the sum of the three numbers in the bottom row is 25. Which number is in the circle with the question mark?
<image1> | MathVision | E | |
5bc69854-78a0-42be-856b-a7a31aa15a06 | 379 | As shown in <image>,A square is placed in a co-ordinate system as shown. Each point $(x \mid y)$ of the square is deleted and replaced by the point $\left(\frac{1}{x} \mid \frac{1}{y}\right)$. Which diagram shows the resulting shape?
<image1>
<image2> | MathVision | C | |
0f9a8b24-ef0a-4c8f-a00f-a767ecac33d4 | 380 | As shown in <image>,Two circles intersect a rectangle AFMG as shown in the diagram. The line segments along the long side of the rectangle that are outside the circles have length $A B=8, C D=26, E F=22, G H=12$ and $J K=24$. How long is the length $x$ of the line segment $L M$?
<image1> | MathVision | 16 | |
094baf69-8c80-401a-9c86-479efe7bbd42 | 381 | As shown in <image>,A cylindrical tin is $15 \mathrm{~cm}$ high. The circumference of the base circle is $30 \mathrm{~cm}$. An ant walks from point $A$ at the base to point $B$ at the top. Its path is partly vertically upwards and partly along horizontal circular arcs. Its path is drawn in bold on the diagram (with a s... | MathVision | E | |
f64a0120-cf02-438a-9e3b-eb1120e89ef8 | 382 | As shown in <image>,Emma should colour in the three strips of the flag shown. She has four colours available. She can only use one colour for each strip and immediately adjacent strips are not to be of the same colour. How many different ways are there for her to colour in the flag? <image1> | MathVision | 36 | |
52b7af41-9b93-498d-a0cf-74b372405739 | 383 | As shown in <image>,What is the value of the following sum? <image1> | MathVision | 12 | |
df930b9d-4060-43fe-8e5f-7aa201bf25c1 | 384 | As shown in <image>,A square with area 84 is split into four squares. The upper left square is coloured in black. The lower right square is again split into four squares and so on. The process is repeated infinitely many times. How big is the area coloured in black? <image1> | MathVision | 28 | |
3a00214c-6273-4ced-bf21-905b006ef72f | 385 | As shown in <image>,The numbers from 1 to 9 are to be distributed to the nine squares in the diagram according to the following rules: There is to be one number in each square. The sum of three adjacent numbers is always a multiple of 3 . The numbers 7 and 9 are already written in. How many ways are there to insert the... | MathVision | 24 | |
fb9cca8c-79b5-446d-940f-2a832f6904c5 | 386 | As shown in <image>,Two equilateral triangles of different sizes are placed on top of each other so that a hexagon is formed on the inside whose opposite sides are parallel. Four of the side lengths of the hexagon are stated in the diagram. How big is the perimeter of the hexagon? <image1> | MathVision | 70 | |
7a82f370-e049-43e2-a17a-3ba455a68993 | 387 | As shown in <image>,In a three-sided pyramid all side lengths are integers. Four of the side lengths can be seen in the diagram. What is the sum of the two remaining side lengths? <image1> | MathVision | 11 | |
09bf10e3-ec79-40d1-a739-1919d2a12e76 | 388 | As shown in <image>,Leon has drawn a closed path on the surface of a cuboid. Which net can represent his path?
<image1> | MathVision | D | |
f98353ea-8917-4293-a733-f2d7b4737a8a | 389 | As shown in <image>,A pentagon is cut into smaller parts as shown in the diagram. The numbers in the triangles state the area of the according triangle. How big is the area $P$ of the grey quadrilateral? <image1> | MathVision | 16 | |
e0606ada-c18d-4a49-a5b1-281a88951ad8 | 390 | As shown in <image>,The diagram shows a spiral of consecutive numbers starting with 1. In which order will the numbers 625, 626 and 627 appear in the spiral? <image1> | MathVision | B | |
105f01d6-f704-4987-9dda-a5a1097995c5 | 391 | As shown in <image>,A game marker in the shape of a regular tetrahedron has one marked area. That side is placed on the triangle marked START. The marker is then moved within the diagram always to the next adjacent triangle by rolling it around an edge. On which triangle is the marker when it is on the marked side agai... | MathVision | E | |
818b4fd2-fc3a-4365-9802-d31f32aa9843 | 392 | As shown in <image>,A part of a polynomial of degree five is illegible due to an ink stain. It is known that all zeros of the polynomial are integers. What is the highest power of $x-1$ that divides this polynomial? <image1> | MathVision | D | |
d1fd5c2b-b45c-4c32-b956-14ea8deadf78 | 393 | As shown in <image>,The big square shown is split into four small squares. The circle touches the right side of the square in its midpoint. How big is the side length of the big square? (Hint: The diagram is not drawn to scale.) <image1> | MathVision | A | |
62005adc-90e1-418e-a856-db15ab2e9775 | 394 | As shown in <image>,The numbers from 1 to 11 are written in the empty hexagons. The sums of the three numbers in three hexagons with a common bold point are always equal. Three of the eleven numbers are already written in (see diagram). Which number is written in the hexagon with the question mark? <image1> | MathVision | 9 | |
d6d1c1b5-2124-4ea9-8731-cadff0b2d587 | 395 | As shown in <image>,Two identical cylindrical glasses contain the same amount of water. The left glass is upright, while the right one rests against the other one at a slant. The water level in both glasses is at the same height. The water level in the leaning glass touches its bottom in exactly one point (see diagram)... | MathVision | A | |
46a90d32-a81c-45f7-9df3-10a7c83cd47e | 396 | As shown in <image>,There are 10 boxes in the first van. Every further van contains twice as many boxes as the previous one. How many boxes are there in the fifth van?
<image1> | MathVision | 160 | |
8ba7d102-1df8-455f-84b9-8c93b1d0f076 | 397 | As shown in <image>,In the picture the distance $KM=10, LN=15, KN=22$. Find the distance $LM$.
<image1> | MathVision | 3 | |
f98fdcc8-e523-444e-8369-8ff9ee58db1d | 398 | As shown in <image>,Chris constructed the brick on the picture using red and blue cubes of the same size. The outside of the brick is completely red, but all cubes used inside are blue. How many blue cubes did Chris use?
<image1> | MathVision | 12 | |
76ef03c2-7c77-4222-97fb-d6e5ce99f055 | 399 | As shown in <image>,This table shows the quantity of different types of flowers in the botanical garden. Ted was told by the gardener that there were 35 azaleas, 50 irises and 85 roses in the garden. What is the number of gerberas growing in the garden?
<image1> | MathVision | 110 | |
208f746f-ae3d-4068-a702-7463a4263bd4 | 400 | As shown in <image>,The construction in the picture is built of cubes of the same size and weighs 189 grams. How many grams does one cube weigh?
<image1> | MathVision | 21 |
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