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stringlengths 36
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|---|---|---|---|---|---|
b9e03b03-01a1-4536-800f-eb436496f2c3
|
201
|
As shown in <image>,Two semicircles are drawn as shown in the figure. The chord $C D$, of length 4 , is parallel to the diameter $A B$ of the greater semicircle and touches the smaller semicircle. Then the area of the shaded region equals
<image1>
|
MathVision
|
C
| |
2accc919-2101-4210-af8b-d63ee637fca1
|
202
|
As shown in <image>,Which is the graph of the function $y=\sqrt{|(1+x)(1-|x|)|}$?
<image1>
|
MathVision
|
D
| |
251c26c3-23d7-403f-8a9f-eb4ec43455cb
|
203
|
As shown in <image>,We see in the diagram at the right a piece of the graphic of the function
$$
f(x)=a x^{3}+b x^{2}+c x+d.
$$
What is the value of $b$?
<image1>
|
MathVision
|
-2
| |
8a1088b5-3e8c-4c4f-9187-7b7571625436
|
204
|
As shown in <image>,The digits of the sequence $123451234512345 \ldots$ fill the cells on a sheet of paper in a spiral-like manner beginning with the marked cell (see the figure). Which digit is written in the cell being 100 cells above the marked one?
<image1>
|
MathVision
|
1
| |
7145b8c2-9b70-4d21-b1bd-020d8bb3271d
|
205
|
As shown in <image>,Numbers 3,4 and two other unknown numbers are written in the cells of the $2 \times 2$ table. It is known that the sums of numbers in the rows are equal to 5 and 10, and the sum of numbers in one of the columns is equal to 9. The larger number of the two unknown ones is
<image1>
|
MathVision
|
6
| |
f75a6d74-92d0-4038-8206-f5a8cfb18dca
|
206
|
As shown in <image>,A river starts at point $A$. As it flows the river splits into two. The first branch takes $\frac{2}{3}$ of the water and the second takes the rest. Later the first branch splits into three, one taking $\frac{1}{8}$ of the branch's water, the second $\frac{5}{8}$ and the third one the rest. Further down this last branch meets again a branch of the river. The map below shows the situation. What part of the original water flows at point $B$?
<image1>
|
MathVision
|
D
| |
e0263a6a-b72d-4ef0-a90b-bd92f4d061c3
|
207
|
As shown in <image>,Given an isosceles triangle $A B C, C A=C B, A D=$ $=A C, D B=D C$ (see the fig.). Find the value of the angle $A C B$.
<image1>
|
MathVision
|
D
| |
047262a5-a4e3-4e86-8f9b-f23e033d1d4e
|
208
|
As shown in <image>,The figure shows a circle with the diameter $A B$ and point $D$ on it. Find $d$.
<image1>
|
MathVision
|
4
| |
0e595c84-4375-4da2-b2e5-3b868824da5c
|
209
|
As shown in <image>,Each of the cubes in the figure has the length of an edge equal to 1. What is the length of the segment $A B$?
<image1>
|
MathVision
|
A
| |
83e69af2-0d4f-4ff1-9afe-cad9fa6599bc
|
210
|
As shown in <image>,We take three points from the grid so that they were collinear. How many possibilities do we have?
<image1>
|
MathVision
|
20
| |
39e8ed27-b199-49c7-b5b9-dafe9153d877
|
211
|
As shown in <image>,In the figure each asterisk stands for one digit. The sum of the digits of the product is equal to
<image1>
|
MathVision
|
16
| |
63669eab-8f1c-488e-b17c-7fbf102aae39
|
212
|
As shown in <image>,A circle is inscribed in the triangle $A B C$ (see the figure), $A C=5, A B=6, B C=3$. The segment $E D$ is tangent to the circle. The perimeter of the triangle $A D E$ is
<image1>
|
MathVision
|
8
| |
96e298dd-c7b9-484e-915f-67a55bb03d6f
|
213
|
As shown in <image>,The square $A B C D$ has a side of length 1 and $M$ is the midpoint of $A B$. The area of the shaded region is
<image1>
|
MathVision
|
D
| |
f153ea2d-fae4-4f43-ba30-3dec68a8455b
|
214
|
As shown in <image>,We used metal rods to build this nice ensemble. We know there are 61 octagons. How many rods are there?
<image1>
|
MathVision
|
446
| |
9995c617-f714-4021-8c57-b776207e0bdf
|
215
|
As shown in <image>,The suare in the diagram has side length 1. The radius of the small circle would
then be of the length
<image1>
|
MathVision
|
E
| |
6d005348-123a-4124-8311-83c5150167b3
|
216
|
As shown in <image>,Each side of a triangle $A B C$ is being extended to the points $\mathrm{P}, \mathrm{Q}, \mathrm{R}, \mathrm{S}, \mathrm{T}$ and $\mathrm{U}$, so that $\mathrm{PA}=\mathrm{AB}=\mathrm{BS}, \mathrm{TC}=\mathrm{CA}$ $=\mathrm{AQ}$ and $\mathrm{UC}=\mathrm{CB}=\mathrm{BR}$. The area of $\mathrm{ABC}$ is 1. How big is the area of the hexagon PQRSTU?
<image1>
|
MathVision
|
13
| |
6a9ff9a0-82b5-4909-b1f1-6abb1e67b718
|
217
|
As shown in <image>,In the diagram on the right we want to colour the fields with the colours A, B, C and D so that adjacent fields are always in different colours. (Even fields that share only one corner, count as adjacent.) Some fields have already been coloured in. In which colour can the grey field be coloured in?
<image1>
|
MathVision
|
D
| |
3cdfe566-c71b-4f30-8159-8e12b5085ee1
|
218
|
As shown in <image>,A (very small) ball is kicked off from point A on a square billiard table with side length $2 \mathrm{~m}$. After moving along the shown path and touching the sides three times as indicated, the path ends in point $B$. How long is the path that the bal travels from A to B? (As indicated on the right: incident angle = emergent angle.)
<image1>
|
MathVision
|
B
| |
a7bcd272-692c-4833-aae3-0c7e11919a6a
|
219
|
As shown in <image>,In the diagram to the right a $2 \times 2 \times 2$ cube is made up of four transparent $1 \times 1 \times 1$ cubes and four non-transparent black $1 \times 1 \times 1$ cubes. They are placed in a way so that the entire big cube is nontransparent; i.e. looking at it from the front to the back, the right to the left, the top to the bottom, at no point you can look through the cube. What is the minimum number of black $1 \times 1 \times 1$ cubes needed to make a $3 \times 3 \times 3$ cube non-transparent in the same way?
<image1>
|
MathVision
|
9
| |
3bba9255-c786-4dcd-9160-be0704f19e86
|
220
|
As shown in <image>,An equilateral triangle with side length 3 and a circle with radius 1 have the same centre. What is the perimeter of the figure that is created when the two are being put together?
<image1>
|
MathVision
|
A
| |
f6cf5ace-d4c6-4878-bab8-6992d84dcbd7
|
221
|
As shown in <image>,The adjacent diagram illustrates the graphs of the two functions f and g. How can we describe the relationship between f and g?
<image1>
|
MathVision
|
A
| |
e973f98d-675e-468f-9c81-1e4cd68db4b5
|
222
|
As shown in <image>,In the diagram on the right we see the birdô-eye view and front elevation of a solid that is defined by flat surfaces (i.e. view from obove and the front respectively). Bird' s-Eye View (view from above): <image1>. Front Elevation (view from the front): <image2>.
Which of the outlines I to IV can be the side elevation (i.e. view from the left) of the same object?
<image3>
|
MathVision
|
D
| |
16d065eb-c12e-468b-8888-acd1ecdf38a2
|
223
|
As shown in <image>,The sum of the number in each line, column and diagonal in the Ămagic squareñon the right is always constant. Only two numbers are visible. Which number is missing in field $a$?
<image1>
|
MathVision
|
D
| |
8fb532d8-fbbf-4c69-9a17-697b7b418629
|
224
|
As shown in <image>,In a rectangle JKLM the angle bisector in $\mathrm{J}$ intersects the diagonal KM in $\mathrm{N}$. The distance of $\mathrm{N}$ to $\mathrm{LM}$ is 1 and the distance of $\mathrm{N}$ to $\mathrm{KL}$ is 8. How long is LM?
<image1>
|
MathVision
|
A
| |
1922a1c1-2b3c-4b19-b03a-f39726d26b12
|
225
|
As shown in <image>,In the box are seven blockss. You want to rearrange the blocks so that another block can placed. What is the minimum number of blocks that have to be moved?
<image1>
|
MathVision
|
3
| |
62e09723-8a5f-4376-a23b-c6da10347df4
|
226
|
As shown in <image>,The triangle pictured is right-angled. $M$ is the midoint of the hypotenuse $\mathrm{AB}$ and $\angle \mathrm{BCA}=90^{\circ}$. How big is $\angle \mathrm{BMC}$?
<image1>
|
MathVision
|
D
| |
0933a690-10c2-4292-b991-f510c20ed200
|
227
|
As shown in <image>,In the figure the square has side length 2. The semi-circles pass through the midpoint of the square and have their centres on the corners of the square. The grey circles have their centres on the sides of the square and touch the semi-circles. How big is the total area of the grey parts?
<image1>
|
MathVision
|
A
| |
65ad0898-f887-4316-b552-8095a155c0d3
|
228
|
As shown in <image>,The chord $A B$ touches the smaller of the two concentric circles. The length $A B=$ 16. How big is the area of the grey part?
<image1>
|
MathVision
|
C
| |
d1c9fff4-e2c5-419d-91fa-d7f18a25bee1
|
229
|
As shown in <image>,The big equilateral triangle consists of 36 small equilateral triangles which each have an area of $1 \mathrm{~cm}^{2}$. Determine the area of $A B C$.
<image1>
|
MathVision
|
A
| |
9f0a84a3-b46b-4c90-8d96-64ef88eb6a9e
|
230
|
As shown in <image>,Which of the following graphs represents the solution set of $(x-|x|)^{2}+(y-|y|)^{2}=4$?
<image1>
|
MathVision
|
A
| |
7b6a761a-02df-4004-af1e-6284a7044195
|
231
|
As shown in <image>,A strip of paper is folded three times as shown. Determine $\beta$ if $\alpha=70^{\circ}$.
<image1>
|
MathVision
|
C
| |
0369bf38-6e3a-4f73-8a47-9c4d1029262f
|
232
|
As shown in <image>,A barcode as pictured is made up of alternate black and white stripes. The code always starts and ends with a black stripee. Each strip (black or white) has the width 1 or 2 and the total width of the barcode is 12. How many different barcodes if this kind are there if one reads from left to right?
<image1>
|
MathVision
|
116
| |
57484547-a855-4704-8c66-5cda252d2167
|
233
|
As shown in <image>,The picture on the right shows a tile pattern. The side length of the bigger tiles is a and of the smaller ones b. The dotted lines (horizontal and tilted) include an angle of $30^{\circ}$. How big is the ratio a:b?
<image1>
|
MathVision
|
B
| |
c5ae1ab1-ac65-490f-bac7-c359ecb7baf9
|
234
|
As shown in <image>,In the picture on the right a number should be written next to each point. The sum of the numbers on the corners of each side of the hexagon should be equal. Two numbers have already been inserted. Which number should be in the place marked '$x$'?
<image1>
|
MathVision
|
1
| |
ed2244d7-f392-499d-abdb-e2f2ca5b8640
|
235
|
As shown in <image>,Jan cannot draw very accurately but nevertheless he tried to produce a roadmap of his village. The relative position of the houses and the street crossings are all correct but three of the roads are actually straight and only Qurwik street is not. Who lives in Qurwik street?
<image1>
|
MathVision
|
C
| |
966aa141-e2b9-42f3-bd52-0abf0ca8e464
|
236
|
As shown in <image>,A rectangular piece of paper is wrapped around a cylinder. Then an angled straight cut is made through the points $\mathrm{X}$ and $\mathrm{Y}$ of the cylinder as shown on the left. The lower part of the piece of paper is then unrolled. Which of the following pictures could show the result?
<image1>
<image2>
|
MathVision
|
C
| |
3a58ed26-6515-4fb4-825e-3f4cd260e241
|
237
|
As shown in <image>,Determine the area of the quadrilateral PQRS pictured on the right, where $\mathrm{PS}=\mathrm{RS}$, $\angle \mathrm{PSR}=\angle \mathrm{PQR}=90^{\circ}, \mathrm{ST} \perp \mathrm{PQ}$, and $\mathrm{ST}=5$.
<image1>
|
MathVision
|
25
| |
16c15c3e-38ac-4fbe-996a-a4cebc60e8d3
|
238
|
As shown in <image>,Michael wants to write whole numbers into the empty fields of the $3 \times 3$ table on the right so that the sum of the numbers in each $2 \times 2$ square equals 10. Four numbers have already been written down. Which of the following values could be the sum of the remaining five numbers?
<image1>
|
MathVision
|
E
| |
8a74c6db-c4e1-4dcd-bf8f-7a479728fee5
|
239
|
As shown in <image>,How many graphs of the functions $y=x^{2}, y=-x^{2}, y=+\sqrt{x}, y=-\sqrt{x}$, $y=+\sqrt{-x}, y=-\sqrt{-x}, y=+\sqrt{|x|}, y=-\sqrt{|x|}$ are included in the sketch on the right?
<image1>
|
MathVision
|
6
| |
d49d8542-be86-4a53-a0f6-d195471fadc4
|
240
|
As shown in <image>,The rear window wiper of a car is made in a way so that the rod $r$ and the wiper blade $\mathrm{w}$ are equally long and are connected at an angle $\alpha$. The wiper rotates around the centre of rotation $\mathrm{O}$ and wipes over the area shown on the right. Calculate the angle $\beta$ between the right edge of the cleaned area and the tangent of the curved upper edge.
<image1>
|
MathVision
|
B
| |
65a859cf-45e4-4735-90c5-ecbc1b7feaf7
|
241
|
As shown in <image>,We have three horizontal lines and three parallel, sloped lines. Both of the circles shown touch four of the lines. X, Y and Z are the areas of the grey regions. $\mathrm{D}$ is the area of the parallelogram PQRS. At least how many of the areas $\mathrm{X}, \mathrm{Y}, \mathrm{Z}$ and $\mathrm{D}$ does one have to know in order to be able to determine the area of the parallelogram $\mathrm{T}$ ?
<image1>
|
MathVision
|
1
| |
f558a3f6-85fb-443e-a836-bc98ebe5f498
|
242
|
As shown in <image>,In the (x,y)-plane the co-ordinate axes are positioned as usual. Point $A(1,-10)$ which is on the parabola $y=a x^{2}+b x+c$ was marked. Afterwards the co-ordinate axis and the majority of the parabola were deleted. Which of the following statements could be false?
<image1>
|
MathVision
|
E
| |
ffa2741f-f2ea-4092-bf10-6a7f7c1540be
|
243
|
As shown in <image>,An archer tries his art on the target shown below on the right. With each of his three arrows he always hits the target. How many different scores could he total with three arrows?
<image1>
|
MathVision
|
19
| |
6a51f561-fc69-4310-8a5f-9d2cc5fc3a1a
|
244
|
As shown in <image>,A clock has three hands in different lengths (for seconds, minutes and hours). We don't know the length of each hand but we know that the clock shows the correct time. At 12:55:30 the hands are in the positions shown on the right. What does the clockface look like at 8:10:00?
<image1>
<image2>
|
MathVision
|
A
| |
3016b6a1-2325-4e06-a39c-28775ef6cb92
|
245
|
As shown in <image>,The water level in a port rises and falls on a certain day as shown in the diagram. How many hours on that day was the water level over $30 \mathrm{~cm}$?
<image1>
|
MathVision
|
13
| |
2cd42751-5319-4766-b137-3216b73b868d
|
246
|
As shown in <image>,In a list of five numbers the first number is 2 and the last one is 12. The product of the first three numbers is 30 , of the middle three 90 and of the last three 360. What is the middle number in that list?
<image1>
|
MathVision
|
5
| |
cb1b4729-d041-4dbe-aa7b-35ad9f6b6e91
|
247
|
As shown in <image>,A rectangular piece of paper $A B C D$ with the measurements $4 \mathrm{~cm} \times 16 \mathrm{~cm}$ is folded along the line $\mathrm{MN}$ so that point $C$ coincides with point $A$ as shown. How big is the area of the quadrilateral ANMD'?
<image1>
|
MathVision
|
C
| |
4610446a-b11a-400e-aba8-10978013a305
|
248
|
As shown in <image>,How big is the angle $\alpha$ in the regular five-sided star shown?
<image1>
|
MathVision
|
C
| |
d0490ea2-7696-47fa-a148-e4bf62f120bb
|
249
|
As shown in <image>,In the diagram we see a rose bed. White roses are growing in the squares that are equally big, red ones are in the big square and yellow ones in the right-angled triangle. The bed has width and height $16 \mathrm{~m}$. How big is the area of the bed?
<image1>
|
MathVision
|
C
| |
3f4fa048-63d5-48fd-8e31-f0b5f92c362d
|
250
|
As shown in <image>,A right-angled triangle with side lengths $a=8, b=15$ and $c=17$ is given. How big is the radius $r$ of the inscribed semicircle shown?
<image1>
|
MathVision
|
4.8
| |
076311d0-f5b0-4d04-b321-9a26b7f9684b
|
251
|
As shown in <image>,The clock shown has a rectangular clock face, the hands however move as usual in a constant circular pattern. How big is the distance $x$ of the digits 1 and 2 (in $\mathrm{cm}$ ), if the distance between the numbers 8 and 10 is given as $12 \mathrm{~cm}$?
<image1>
|
MathVision
|
C
| |
aea0971f-e9f8-4997-813f-e203ba6a60de
|
252
|
As shown in <image>,Renate wants to glue together a number of ordinary dice (whose number of points on opposite sides always adds up to 7) to form a "dicebar" as shown. Doing this she only wants to glue sides together with an equal number of points. She wants to make sure that the sum of all points on the non-glued sides equals 2012. How many dice does she have to glue together?
<image1>
|
MathVision
|
E
| |
72842a21-df5b-4fe5-9737-d0cfc5dee9a0
|
253
|
As shown in <image>,Let $a>b$. If the ellipse shown rotates about the $x$-axis an ellipsoid $E_{x}$ with volume $\operatorname{Vol}\left(E_{x}\right)$ is obtained. If it rotates about the $y$-axis an ellipsoid $E_{y}$ with volume $\operatorname{Vol}\left(E_{y}\right)$ is obtained. Which of the following statements is true?
<image1>
|
MathVision
|
C
| |
3fca6f8d-b587-4a0d-b76a-3d6acc194815
|
254
|
As shown in <image>,An equilateral triangle is being rolled around a unit square as shown. How long is the path that the point shown covers, if the point and the triangle are both back at the start for the first time?
<image1>
|
MathVision
|
B
| |
bcb15a70-c95c-4cc1-aeb8-8cc3662d4ee2
|
255
|
As shown in <image>,The regular eight-sided shape on the right has sides of length 10. A circle touches all inscribed diagonals of this eight-sided shape. What is the radius of this circle?
<image1>
|
MathVision
|
5
| |
79523348-468a-42eb-9589-ed0b21191fbd
|
256
|
As shown in <image>,Inside the cube lattice pictured on the side one can see a solid, non-seethrough pyramid $A B C D S$ with square base $A B C D$, whose top $S$ is exactly in the middle of one edge of the cube. If you look at the pyramid from above, from below, from the front, from the back, from the right and from the left - which of the following views cannot be possible?
<image1>
<image2>
|
MathVision
|
E
| |
4d7616f3-2165-4dd4-ba3e-f5701636c436
|
257
|
As shown in <image>,Ralf has a number of equally big plastic plates each in the form of a regular five sided shape. He glues them together along the sides to form a complete ring (see picture). Out of how many of these plates is the ring made up?
<image1>
|
MathVision
|
10
| |
dace7b8a-5257-4589-a982-d275ac37ac90
|
258
|
As shown in <image>,A circular carpet is placed on a floor which is covered by equally big, square tiles. All tiles that have at least one point in common with the carpet are coloured in grey. Which of the following cannot be a result of this?
<image1>
|
MathVision
|
E
| |
328a2f29-855e-461a-bebb-68d01e8f32c0
|
259
|
As shown in <image>,Amongst the graphs shown below there is the graph of the function $f(x)=(a-x)(b-x)^{2}$ with $a<b$. Which is it?
<image1>
|
MathVision
|
A
| |
7a3c494c-0506-46cd-b8ad-ded5d4a69632
|
260
|
As shown in <image>,Peter has drawn the graph of a function $f: R \rightarrow R$ which consists of two rays and a line segment as indicated on the right. How many solutions has the equation $f(f(f(x)))=0$ ?
<image1>
|
MathVision
|
4
| |
ad34062c-5fb0-4e48-b4d4-8c7c6d7439eb
|
261
|
As shown in <image>,In a triangle $A B C$ the points $M$ and $N$ are placed on side $A B$ so that $A N=A C$ and $B M=$ $B C$. Determine $\angle A C B$ if $\angle M C N=43^{\circ}$
<image1>
|
MathVision
|
E
| |
575124e4-8783-4dd4-ade4-b801c04a41c8
|
262
|
As shown in <image>,The cube pictured on the side is intersected by a plane that passes through the three points adjacent to $A$, that is $D, E$ and $B$. In a similar way the cube is also intersected by those planes that go through the three points adjacent to each of the other seven vertices. These planes dissect the cube into several pieces. What does the piece that contains the centre of the cube look like?
<image1>
<image2>
|
MathVision
|
A
| |
9ea47c9e-939e-4603-b944-f772fbf47527
|
263
|
As shown in <image>,If one removes some $1 \times 1 \times 1$ cubes from a $5 \times 5 \times 5$ cube, you obtain the solid shown. It consists of several equally high pillars that are built upon a common base. How many little cubes have been removed?
<image1>
|
MathVision
|
64
| |
7cfea2f7-389c-4708-8e88-f19d7d6ea32c
|
264
|
As shown in <image>,The curved surfaces of two identical cylinders are cut open along the vertical dotted line, as shown and then stuck together to create the curved surface of one big cylinder. What can be said about the volume of the resulting cylinder compared to the volume of one of the small cylinders?
<image1>
|
MathVision
|
D
| |
5de6298f-972f-4803-8a52-475a689b81e1
|
265
|
As shown in <image>,The ratio of the radii of two concentric circles is $1: 3$. The line $A C$ a diameter of the biggest circle. A chord $B C$ of the big circle touches the small circle (see diagram). The line $A B$ has length 12. How big is the radius of the big circle?
<image1>
|
MathVision
|
18
| |
f73e7737-3542-45d6-ab91-222b9b0c9742
|
266
|
As shown in <image>,The vertices of a die are numbered 1 to 8, so that the sum of the four numbers on the vertices of each face are the same. The numbers 1, 4 and 6 are already indicated in the picture. Which number is in position $x$?
<image1>
|
MathVision
|
2
| |
29aeeecb-a858-427e-9136-6d64a982e167
|
267
|
As shown in <image>,PQRS is a rectangle. $T$ is the midpoint of $R S. Q T$ is normal to the diagonal $P R$. What is the ratio of the lengths $P Q: Q R$?
<image1>
|
MathVision
|
D
| |
a307ce91-ba56-4fc7-8e60-4ccb64f02b96
|
268
|
As shown in <image>,The straight line $g$ runs through the vertex $A$ of the rectangle $A B C D$ shown. The perpendicular distance from $C$ to $g$ is 2 and from $D$ to $g$ is $6. A D$ is twice as long as $A B$. Determine the length of $A D$.
<image1>
|
MathVision
|
10
| |
dcb0e9f4-2408-4454-93f8-9f429459f108
|
269
|
As shown in <image>,In the diagram on the right the following can be seen: a straight line, which is the common tangent of two touching circles with radius 1, and a square with one edge on the straight line and the other vertices one on each of the two circles. How big is the side length of the square?
<image1>
|
MathVision
|
A
| |
3f300e2c-cdbe-4a12-9160-a91fe7335a4b
|
270
|
As shown in <image>,In the diagram a closed polygon can be seen whose vertices are the midpoints of the edges of the die. The interior angles are as usual defined as the angle that two sides of the polygon describe in a common vertex. How big is the sum of all interior angles of the polygon?
<image1>
|
MathVision
|
B
| |
e852b1de-e0c6-45f3-866e-68ee8f39b2ea
|
271
|
As shown in <image>,Diana produces a bar chart which shows the number of four different types of trees which she has counted on a biology trip. Heinz believes that a pie chart would represent the ratio of the different types of trees in a better way. What would the pie chart look like?
<image1>
<image2>
|
MathVision
|
A
| |
15841657-7d4f-4ba3-8586-a82aa6800b4e
|
272
|
As shown in <image>,How many of the following shapes can be drawn using one continuous line (i.e. without lifting the pencil) and without going over a line twice?
<image1>
|
MathVision
|
3
| |
e52a7bef-6c9c-4725-aad1-06a0e9e5a0d6
|
273
|
As shown in <image>,A drinking glass is made in the shape of a truncated cone. The outside of the glass (without the upper or lower circle) should be covered with coloured paper. How do you need to cut the paper to completely cover the glass without an overlap?
<image1>
<image2>
|
MathVision
|
E
| |
a6cd78c9-ec2d-45cd-8975-1c1fbb78f489
|
274
|
As shown in <image>,The diameters of three semi-circles form the sides of a right-angled triangle. Their areas are $X \mathrm{~cm}^{2}, Y \mathrm{~cm}^{2}$ and $Z \mathrm{~cm}^{2}$ as pictured. Which of the following expressions is definitely correct?
<image1>
|
MathVision
|
C
| |
6ba5452a-aa37-473a-a8bf-31e52a130d38
|
275
|
As shown in <image>,A square bit of paper is folded along the dashed lines in some order and direction. One of the corners of the resulting small square is cut off. The piece of paper is then unfolded. How many holes are on the inner area of the piece of paper?
<image1>
|
MathVision
|
1
| |
33239ea8-5ea6-4c05-b6ef-760290a2aa7f
|
276
|
As shown in <image>,Ella wants to write a number into each circle in the diagram on the right, in such a way that each number is equal to the sum, of its two direct neighbours. Which number does Ella need to write into the circle marked with "?".
<image1>
|
MathVision
|
E
| |
b6d2b274-57b2-4c10-9bdb-9265086ae8ae
|
277
|
As shown in <image>,The diagram shows three concentric circles and two perpendicular, common diameters of the three circles. The three grey sections are of equal area, the small circle has radius 1. What is the product of the radii of the three circles?
<image1>
|
MathVision
|
A
| |
e4ce58ea-8784-4448-a7da-6893818b912d
|
278
|
As shown in <image>,On a standard die the sum of the numbers on opposite faces is always 7. Two identical standard dice are shown in the figure. How many dots could there be on the non-visible right-hand face (marked with "?")?
<image1>
|
MathVision
|
A
| |
c122d515-22ff-4856-a016-3f51006a414f
|
279
|
As shown in <image>,The curve in the diagram is defined by the equation
$$
\left(x^{2}+y^{2}-2 x\right)^{2}=2\left(x^{2}+y^{2}\right)
$$
Which of the lines $a, b, c, d$ is the $y$-axis?
<image1>
|
MathVision
|
A
| |
69aebd89-5816-4baa-ac7c-d02df3cfd650
|
280
|
As shown in <image>,The following table is the multiplication table of the numbers 1 to 10. What is the sum of all 100 products in the complete table?
<image1>
|
MathVision
|
3025
| |
cec2dbae-ddc1-4124-a69f-517fc51e4255
|
281
|
As shown in <image>,In the rectangle $A B C D$ pictured, $M_{1}$ is the midpoint of $D C, M_{2}$ the midpoint of $A M_{1}, M_{3}$ the midpoint of $B M_{2}$ and $M_{4}$ the midpoint of $C M_{3}$. Determine the ratio of the area of the quadrilateral $M_{1} M_{2} M_{3} M_{4}$ to the area of the rectangle $A B C D$.
<image1>
|
MathVision
|
C
| |
218cffdb-28b9-4a72-b084-67142d72074a
|
282
|
As shown in <image>,Maria wants to build a bridge across a river. This river has the special feature that from each point along one shore the shortest possible bridge to the other shore has always got the same length. Which of the following diagrams is definitely not a sketch of this river?
<image1>
|
MathVision
|
B
| |
9a07431c-8349-40c1-ae63-f34306b4c327
|
283
|
As shown in <image>,A scatter diagram on the $x y$-plane gives the picture of a kangaroo as shown on the right. Now the $x$- and the $y$-coordinate are swapped around for every point. What does the resulting picture look like?
<image1>
<image2>
|
MathVision
|
A
| |
4e87fd45-99f5-4f14-8c98-b0cbadc12b8d
|
284
|
As shown in <image>,Diana wants to write whole numbers into each circle in the diagram, so that for all eight small triangles the sum of the three numbers in the corners is always the same. What is the maximum amount of different numbers she can use?
<image1>
|
MathVision
|
3
| |
282bc0fc-2540-477d-b5e6-d4ea82956181
|
285
|
As shown in <image>,The rectangles $S_{1}$ and $S_{2}$ shown in the picture have the same area. Determine the ratio $x: y$.
<image1>
|
MathVision
|
E
| |
ec82cb3f-55c3-4c8d-99cf-0ff8564d0a1f
|
286
|
As shown in <image>,The diagram shows a circle with centre $O$ as well as a tangent that touches the circle in point $P$. The arc $A P$ has length 20, the arc $B P$ has length 16. What is the size of the angle $\angle A X P$?
<image1>
|
MathVision
|
E
| |
fae8680b-6904-463b-8157-d94de2b7850c
|
287
|
As shown in <image>,In this number pyramid each number in a higher cell is equal to the product of the two numbers in the cells immediately underneath that number. Which of the following numbers cannot appear in the topmost cell, if the cells on the bottom row hold natural numbers greater than 1 only?
<image1>
|
MathVision
|
D
| |
f490b405-4302-4dae-a9bf-16e52638ba82
|
288
|
As shown in <image>,The square shown in the diagram has a perimeter of 4. The perimeter of the equilateral triangle is
<image1>
|
MathVision
|
B
| |
db480ffc-17bf-4fbc-b6c2-dda87d63a198
|
289
|
As shown in <image>,Each of the ten points in the diagram is labelled with one of the numbers 0,1 or 2. It is known that the sum of the numbers in the corner points of each white triangle is divisible by 3, while the sum of the numbers in the corner points of each black triangle is not divisible by 3. Three of the points are already labeled as shown in the diagram. With which numbers can the inner point be labeled?
<image1>
|
MathVision
|
A
| |
e430193d-8fb3-47dd-8359-70bad22f241b
|
290
|
As shown in <image>,Bettina chooses five points $A, B, C, D$ and $E$ on a circle and draws the tangent to the circle at point $A$. She realizes that the five angles marked $x$ are all equally big. (Note that the diagram is not drawn to scale!) How big is the angle $\angle A B D$?
<image1>
|
MathVision
|
C
| |
718e9c60-03b2-44f7-ba25-944edb39f96d
|
291
|
As shown in <image>,How many quadratic functions $y=a x^{2}+b x+c$ (with $a \neq 0$ ) have graphs that go through at least 3 of the marked points?
<image1>
|
MathVision
|
22
| |
07d48e74-f00f-4e32-aef5-3a47fcac8ce4
|
292
|
As shown in <image>,A rectangular piece of paper $A B C D$ is $5 \mathrm{~cm}$ wide and $50 \mathrm{~cm}$ long. The paper is white on one side and grey on the other. Christina folds the strip as shown so that the vertex $B$ coincides with $M$ the midpoint of the edge $C D$. Then she folds it so that the vertex $D$ coincides with $N$ the midpoint of the edge $A B$. How big is the area of the visible white part in the diagram?
<image1>
<image2>
<image3>
|
MathVision
|
B
| |
53a9d189-d466-4137-9f8f-05ce2cba87ce
|
293
|
As shown in <image>,We consider a $5 \times 5$ square that is split up into 25 fields. Initially all fields are white. In each move it is allowed to change the colour of three fields that are adjacent in a horizontal or vertical line (i.e. white fields turn black and black ones turn white). What is the smallest number of moves needed to obtain the chessboard colouring shown in the diagram?
<image1>
|
MathVision
|
A
| |
d8daa97e-e219-4844-8960-50a96055a8ed
|
294
|
As shown in <image>,On the number wall shown the number on each tile is equal to the sum of the numbers on the two tiles directly below it. Which number is on the tile marked with "?"?
<image1>
|
MathVision
|
16
| |
5d888689-f2cd-4f1f-82c8-a26b0d705f6a
|
295
|
As shown in <image>,In the diagram we see 10 islands that are connected by 15 bridges. What is the minimum number of bridges that need to be closed off so that there is no connection from $A$ to $B$ anymore?
<image1>
|
MathVision
|
3
| |
63d89fcc-d0fe-4d77-a363-ac12be868b7f
|
296
|
As shown in <image>,Four of the following five pictures show pieces of the graph of the same quadratic function. Which piece does not belong?
<image1>
|
MathVision
|
C
| |
4e47744e-f66d-4f37-8e5b-d13bb356f377
|
297
|
As shown in <image>,The diagram shows a circle with centre $O$ and the diameters $A B$ and $C X$. Let $O B=$ $B C$. Which fraction of the circle area is shaded?
<image1>
|
MathVision
|
B
| |
10faa125-1b3d-4dc3-888c-7abd65d24865
|
298
|
As shown in <image>,A $4 \times 1 \times 1$ cuboid is made up of 2 white and 2 grey cubes as shown. Which of the following cuboids can be build entirely out of such $4 \times 1 \times 1$ cuboids?
<image1>
<image2>
|
MathVision
|
A
| |
79a5b6d5-474e-4ddf-b400-457fb87c45c7
|
299
|
As shown in <image>,Which quadrant contains no points of the graph of the linear function $f(x)=-3.5 x+7$?
<image1>
|
MathVision
|
C
| |
2df666b2-a6e2-46c7-9e8c-d41eb90318a3
|
300
|
As shown in <image>,Three circles with centres $A, B, C$ touch each other in pairs from the outside (see diagram). Their radii are 3,2 and 1. How big is the area of the triangle $A B C$?
<image1>
|
MathVision
|
6
|
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