id stringlengths 1 4 | question stringlengths 31 709 | options listlengths 6 6 | image_path stringlengths 12 15 | image imagewidth (px) 56 2.52k | answer stringclasses 5
values | solution stringclasses 259
values | level int64 1 5 | subject stringclasses 16
values | Answer(Option) stringclasses 5
values |
|---|---|---|---|---|---|---|---|---|---|
1068 | In the figure we see semicircles with radii $2 \mathrm{~cm}, 4 \mathrm{~cm}$ or $8 \mathrm{~cm}$. What fraction of the area is grey?
<image1> | [
"$\\frac{1}{3}$",
"$\\frac{1}{4}$",
"$\\frac{1}{5}$",
"$\\frac{3}{4}$",
"$\\frac{2}{3}$",
"I don't know"
] | images/1068.jpg | B | null | 3 | metric geometry - area | B | |
1070 | A paperstrip is folded three times in the middle. It is then opened again and looked at from the side so that one can see all 7 folds from the side at the same time. Which of the following views is not a possible result?
<image1> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1070.jpg | D | null | 3 | transformation geometry | D | |
1072 | In the picture on the right we can see three squares. The corners of the middle square are on the midpoints of the sides of the larger square, and the corners of the smaller square are on the midpoints of the sides of the middle square. The area of the small square is $6 \mathrm{~cm}^{2}$. What is the area of the big s... | [
"$24 \\mathrm{~cm}^{2}$",
"$18 \\mathrm{~cm}^{2}$",
"$15 \\mathrm{~cm}^{2}$",
"$12 \\mathrm{~cm}^{2}$",
"$9 \\mathrm{~cm}^{2}$",
"I don't know"
] | images/1072.jpg | A | null | 3 | metric geometry - area | A | |
1075 | Each area in the picture on the right should be coloured using one of the colours, red (R), green (G), blue (B) or orange (O). Areas which touch must be different colours. Which colour is the area marked $X$?
<image1> | [
"red",
"blue",
"green",
"orange",
"The colour cannot definitely be determined.",
"I don't know"
] | images/1075.jpg | A | null | 4 | logic | A | |
1076 | A square piece of paper is cut into six rectangular pieces as shown on the right. The sum of the perimeters of the six pieces is $120 \mathrm{~cm}$. How big is the area of the square?
<image1> | [
"$48 \\mathrm{~cm}^{2}$",
"$64 \\mathrm{~cm}^{2}$",
"$110.25 \\mathrm{~cm}^{2}$",
"$144 \\mathrm{~cm}^{2}$",
"$256 \\mathrm{~cm}^{2}$",
"I don't know"
] | images/1076.jpg | D | null | 3 | metric geometry - area | D | |
1077 | The dark line halves the surface area of the dice shown on the right. Which drawing could represent the net of the die?
<image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1077.jpg | A | null | 4 | descriptive geometry | A | |
1078 | Lina has placed two tiles on a square game board. Which one of the 5 counters shown, can she add, so that none of the remaining four counters can be placed anymore?
<image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1078.jpg | D | null | 4 | descriptive geometry | D | |
1079 | On the inside of a square with side length $7 \mathrm{~cm}$ another square is drawn with side length $3 \mathrm{~cm}$. Then a third square with side length $5 \mathrm{~cm}$ is drawn so that it cuts the first two as shown in the picture on the right. How big is the difference between the black area and the grey area?
<i... | [
"$0 \\mathrm{~cm}^{2}$",
"$10 \\mathrm{~cm}^{2}$",
"$11 \\mathrm{~cm}^{2}$",
"$15 \\mathrm{~cm}^{2}$",
"It can not be decided from the information given.",
"I don't know"
] | images/1079.jpg | D | null | 3 | metric geometry - area | D | |
1082 | Eva has a pair a scissors and five letters made from cardboard. She cuts up each letter with a single straight cut so that as many pieces as possible are obtained. For which letter does she obtain the most pieces?
<image1> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1082.jpg | E | null | 3 | transformation geometry | E | |
1083 | Each of the nine paths in a park are $100 \mathrm{~m}$ long. Anna wants to walk from $A$ to $B$ without using the same path twice. How long the longest path she can choose?
<image1> | [
"$900 \\mathrm{~m}$",
"$800 \\mathrm{~m}$",
"$700 \\mathrm{~m}$",
"$500 \\mathrm{~m}$",
"$400 \\mathrm{~m}$",
"I don't know"
] | images/1083.jpg | C | null | 4 | combinatorial geometry | C | |
1085 | Werner folds a piece of paper as shown in the diagram. With a pair of scissors he makes two straight cuts into the paper. Then is unfolds it again. Which on the following shapes are not possible for the piece of paper to show afterwards?
<image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1085.jpg | D | null | 3 | transformation geometry | D | |
1086 | A cuboid consists of three building blocks. Each building block has a different colour and is made up of 4 cubes. What does the white building block look like?
<image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1086.jpg | D | null | 4 | solid geometry | D | |
1087 | Ms. Green plants peas ("Erbsen") and strawberries ("Erdbeeren") only in her garden. This year she has changed her pea-bed into a square-shaped bed by increasing one side by $3 \mathrm{~m}$. By doing this her strawberry-bed became $15 \mathrm{~m}^{2}$ smaller. What area did the pea-bed have before?
<image1> | [
"$5 \\mathrm{~m}^{2}$",
"$9 \\mathrm{~m}^{2}$",
"$10 \\mathrm{~m}^{2}$",
"$15 \\mathrm{~m}^{2}$",
"$18 \\mathrm{~m}^{2}$",
"I don't know"
] | images/1087.jpg | C | null | 3 | metric geometry - area | C | |
1089 | The diagram shows a five-pointed star. How big is the angle $A$?
<image1> | [
"$35^{\\circ}$",
"$42^{\\circ}$",
"$51^{\\circ}$",
"$65^{\\circ}$",
"$109^{\\circ}$",
"I don't know"
] | images/1089.jpg | C | null | 5 | metric geometry - angle | C | |
1090 | Three equally sized equilateral triangles are cut from the vertices of a large equilateral triangle of side length $6 \mathrm{~cm}$. The three little triangles together have the same perimeter as the remaining grey hexagon. What is the side-length of one side of one small triangle?
<image1> | [
"$1 \\mathrm{~cm}$",
"$1.2 \\mathrm{~cm}$",
"$1.25 \\mathrm{~cm}$",
"$1.5 \\mathrm{~cm}$",
"$2 \\mathrm{~cm}$",
"I don't know"
] | images/1090.jpg | D | null | 2 | metric geometry - length | D | |
1091 | The diagram shows the 7 positions $1,2,3,4,5,6,7$ of the bottom side of a die which is rolled around its edge in this order. Which two of these positions were taken up by the same face of the die?
<image1> | [
"1 and 7",
"1 and 6",
"1 and 5",
"2 and 7",
"2 and 6",
"I don't know"
] | images/1091.jpg | B | null | 4 | solid geometry | B | |
1092 | In a square $A B C D M$ is the midpoint of $A B$. $M N$ is perpenticular to $A C$. Determine the ratio of the area of the grey triangle to the area of the square $A B C D$.
<image1> | [
"$1: 6$",
"$1: 5$",
"$7: 36$",
"$3: 16$",
"$7: 40$",
"I don't know"
] | images/1092.jpg | D | null | 3 | metric geometry - area | D | |
1093 | A piece of string is folded as shown in the diagram by folding it in the middle, then folding it in the middle again und finally folding it in the middle once more. Then this folded piece of string is cut so that several pieces emerge. Amongst the resulting pieces there are some with length $4 \mathrm{~m}$ and some wit... | [
"$52 \\mathrm{~m}$",
"$68 \\mathrm{~m}$",
"$72 \\mathrm{~m}$",
"$88 \\mathrm{~m}$",
"All answers are possible.",
"I don't know"
] | images/1093.jpg | C | null | 4 | algebra | C | |
1094 | Three lines disect a big triangle into four triangles and three quadrilaterals. The sum of the perimeters of the three quadrialterals is $25 \mathrm{~cm}$. The sum of the perimeters of the four triangles is $20 \mathrm{~cm}$. The perimeter of the big triangle is $19 \mathrm{~cm}$. How big is the sum of the lengths of t... | [
"$11 \\mathrm{~cm}$",
"$12 \\mathrm{~cm}$",
"$13 \\mathrm{~cm}$",
"$15 \\mathrm{~cm}$",
"$16 \\mathrm{~cm}$",
"I don't know"
] | images/1094.jpg | C | null | 2 | metric geometry - length | C | |
1098 | The five shapes pictured were cut out of paper. Four of them can be folded to form a cube. For which shape is this not possible.
<image1> | [
"Shape 1",
"Shape 2",
"Shape 3",
"Shape 4",
"Shape 5",
"I don't know"
] | images/1098.jpg | C | null | 4 | descriptive geometry | C | |
1100 | Johann stacked $1 \times 1$ cubes on the squares of a $4 \times 4$ grid. The diagram on the right shows the number of cubes that were stacked on top of each other above each square. What will Johann see if he looks from the back (hinten) at the tower?
<image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1100.jpg | C | null | 4 | descriptive geometry | C | |
1101 | The sides of the rectangle $A B C D$ are parallel to the co-ordinate axes. The rectangle is positioned below the $x$-axis and to the right of the $y$-axis, as shown in the picture. The co-ordinates of the points $A, B, C, D$ are whole numbers. For each of the points we calculate the value of ( $y$ co-ordinate) $\div$(x... | [
"A",
"B",
"C",
"D",
"It depends on the rectangle.",
"I don't know"
] | images/1101.jpg | A | null | 3 | analytic geometry | A | |
1102 | On a sheet of paper a grid is drawn such that each of the squares has sides $2 \mathrm{~cm}$ long. How big is the area of the grey shaded quadrilateral $A B C D$?
<image1> | [
"$96 \\mathrm{~cm}^{2}$",
"$84 \\mathrm{~cm}^{2}$",
"$76 \\mathrm{~cm}^{2}$",
"$88 \\mathrm{~cm}^{2}$",
"$104 \\mathrm{~cm}^{2}$",
"I don't know"
] | images/1102.jpg | B | null | 4 | combinatorial geometry | B | |
1110 | Five circles each with an area of $1 \mathrm{~cm}^{2}$ overlap each other to form the figure in the diagram. The sections where two circles overlap, each have an area of $\frac{1}{8} \mathrm{~cm}^{2}$. How big is the area, which is completely covered by the figure in the diagram?
<image1> | [
"$4 \\mathrm{~cm}^{2}$",
"$\\frac{9}{2} \\mathrm{~cm}^{2}$",
"$\\frac{35}{8} \\mathrm{~cm}^{2}$",
"$\\frac{39}{8} \\mathrm{~cm}^{2}$",
"$\\frac{19}{4} \\mathrm{~cm}^{2}$",
"I don't know"
] | images/1110.jpg | B | null | 3 | metric geometry - area | B | |
1111 | 5 congruent rectangles are positioned in a square with side length 24 as shown in the diagram. How big is the area of one of these rectangles?
<image1> | [
"$12 \\mathrm{~cm}^{2}$",
"$16 \\mathrm{~cm}^{2}$",
"$18 \\mathrm{~cm}^{2}$",
"$24 \\mathrm{~cm}^{2}$",
"$32 \\mathrm{~cm}^{2}$",
"I don't know"
] | images/1111.jpg | E | null | 3 | metric geometry - area | E | |
1112 | In the following figure, the heart and the arrow are arranged as pictured. At the same moment the heart and the arrow begin to move. The arrow moves around the figure 3 spaces clockwise and the heart 4 spaces anticlockwise and then they stop. This process repeats itself over and over again. After how many repetitions d... | [
"7",
"8",
"9",
"10",
"That will never happen",
"I don't know"
] | images/1112.jpg | E | null | 4 | algebra | E | |
1113 | In triangle $A B C$ (see sketch) $A D$ is the angle bisector of the angle at $A$ and $B H$ is the height from side $A C$. The obtuse angle between $B H$ and $A D$ is four times the size of angle $\angle D A B$. How big is the angle $\angle C A B$?
<image1> | [
"$30^{\\circ}$",
"$45^{\\circ}$",
"$60^{\\circ}$",
"$75^{\\circ}$",
"$90^{\\circ}$",
"I don't know"
] | images/1113.jpg | C | null | 5 | metric geometry - angle | C | |
1116 | Four identical cubes (see diagram) were fitted together. If the resulting shape is viewed from the front you see a black circle (picture on the right). What will you see on the back of the shape?
<image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1116.jpg | A | null | 4 | descriptive geometry | A | |
1119 | The word KANGAROO is written on the top of my umbrella. Which of the following pictures shows my umbrella?
<image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1119.jpg | E | null | 4 | descriptive geometry | E | |
1120 | The diagram shows the net of a cube whose faces are numbered. Sascha adds the numbers that are on opposite faces of the cube. Which three results does he get?
<image1> | [
"$4,6,11$",
"$4,5,12$",
"$5,6,10$",
"$5,7,9$",
"$5,8,8$",
"I don't know"
] | images/1120.jpg | A | null | 4 | descriptive geometry | A | |
1121 | The diagram shows the net of a three-sided prism. Which line of the diagram forms an edge of the prism together with line UV when the net is folded up?
<image1> | [
"WV",
"XW",
"XY",
"QR",
"RS",
"I don't know"
] | images/1121.jpg | C | null | 4 | descriptive geometry | C | |
1122 | When simon the squirrel comes down from his tree onto the floor, he never moves further than $5 \mathrm{~m}$ away from the trunk of his tree. Furthermore, he stays at least $5 \mathrm{~m}$ away from the dog kennel. Which picture shows most accurately the area in which Simon can be found?
<image1> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1122.jpg | C | null | 3 | metric geometry - area | C | |
1125 | A bush has 10 twigs. Each twig has exactly 5 leaves or exactly 2 leaves and a flower. Which of the following numbers could be the total number of leaves on the bush?
<image1> | [
"45",
"39",
"37",
"31",
"None of the numbers from (A) to (D)",
"I don't know"
] | images/1125.jpg | E | null | 4 | algebra | E | |
1126 | Each side of each triangle in the diagram is painted either blue, green or red. Four of the sides are already painted. Which colour can the line marked "x" have, if each triangle must have all sides in different colours?
<image1> | [
"only green",
"only red",
"only blue",
"either red or blue",
"The question cannot be solved.",
"I don't know"
] | images/1126.jpg | A | null | 4 | logic | A | |
1127 | A square with area 30 is split into two by its diagonal and then Split into triangles as shown in the diagram. Some of the areas of the triangles are given in the diagram. Which of the line segments $a, b, c, d, e$ of the diagonal is the longest?
<image1> | [
"a",
"b",
"c",
"d",
"e",
"I don't know"
] | images/1127.jpg | D | null | 2 | metric geometry - length | D | |
1130 | In the trapezium $P Q R S$ the sides $P Q$ and $S R$ are parallel. Also $\angle \mathrm{RSP}=120^{\circ}$ and $\overline{R S}=\overline{S P}=\frac{1}{3} \overline{P Q}$. What is the size of angle $\angle \mathrm{PQR}$ ?
<image1> | [
"$15^{\\circ}$",
"$22.5^{\\circ}$",
"$25^{\\circ}$",
"$30^{\\circ}$",
"$45^{\\circ}$",
"I don't know"
] | images/1130.jpg | D | null | 5 | metric geometry - angle | D | |
1131 | Which of the road signs has the most axes of symmetry?
<image1> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1131.jpg | A | null | 3 | transformation geometry | A | |
1132 | What is the sum of the two marked angles?
<image1> | [
"$150^{\\circ}$",
"$180^{\\circ}$",
"$270^{\\circ}$",
"$320^{\\circ}$",
"$360^{\\circ}$",
"I don't know"
] | images/1132.jpg | C | null | 5 | metric geometry - angle | C | |
1133 | A card has a diagram printed on one side and the other side is plain white. The card is first flipped over downwards and then to the right (see diagram). Which picture is obtained?
<image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1133.jpg | B | null | 3 | transformation geometry | B | |
1134 | In the rectangle $A B C D$ the side $A D$ is $10 \mathrm{~cm}$ long. $M$ and $N$ are the midpoints of the sides $A B$ and $C D$ respectively. How big is the grey area?
<image1> | [
"$50 \\mathrm{~cm}^{2}$",
"$80 \\mathrm{~cm}^{2}$",
"$100 \\mathrm{~cm}^{2}$",
"$120 \\mathrm{~cm}^{2}$",
"$150 \\mathrm{~cm}^{2}$",
"I don't know"
] | images/1134.jpg | C | null | 3 | metric geometry - area | C | |
1136 | Within the square $A B C D$ there are four identical rectangles (see diagram). The perimeter of each rectangle is $16 \mathrm{~cm}$. What is the perimeter of this
square?
<image1>square? | [
"$16 \\mathrm{~cm}$",
"$20 \\mathrm{~cm}$",
"$24 \\mathrm{~cm}$",
"$28 \\mathrm{~cm}$",
"$32 \\mathrm{~cm}$",
"I don't know"
] | images/1136.jpg | E | null | 2 | metric geometry - length | E | |
1137 | Anne has glued together some cubes and has obtained the solid shown on the right. She turns it around to check it out from different sides. Which view can she not obtain?
<image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1137.jpg | A | null | 4 | solid geometry | A | |
1138 | A $3 \mathrm{~cm}$ wide strip of paper is dark on one side and light on the other. The folded strip of paper lies exactly within a rectangle with length $27 \mathrm{~cm}$ and width $9 \mathrm{~cm}$ (see diagram). How long is the strip of paper?
<image1> | [
"$36 \\mathrm{~cm}$",
"$48 \\mathrm{~cm}$",
"$54 \\mathrm{~cm}$",
"$57 \\mathrm{~cm}$",
"$81 \\mathrm{~cm}$",
"I don't know"
] | images/1138.jpg | D | null | 2 | metric geometry - length | D | |
1142 | The diagram shows a pentagon and indicates the length of each side. Five circles are drawn with centres A, B, C, D and E. On each side of the pentagon the two circles that are drawn around the ends of that side touch each other. Which point is the centre of the biggest circle?
<image1> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1142.jpg | A | null | 4 | combinatorial geometry | A | |
1144 | A cube of side length 3 consists of 15 black and 12 white unit cubes. In the diagram five of the six faces of the big cube can be seen. Which of the regions shown below is the 6th face of the big cube?
<image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1144.jpg | A | null | 4 | solid geometry | A | |
1145 | The diagram shows an isosceles triangle, where the height is marked and its area is split up into equally wide white and grey stripes. Which fraction of the area of the triangle is white?
<image1> | [
"$\\frac{1}{2}$",
"$\\frac{1}{3}$",
"$\\frac{2}{3}$",
"$\\frac{3}{4}$",
"$\\frac{2}{5}$",
"I don't know"
] | images/1145.jpg | A | null | 3 | metric geometry - area | A | |
1146 | The diagram shows two rectangles whose sides are parallel to each other. By how much is the perimeter of the bigger rectangle greater than the perimeter of the smaller rectangle?
<image1> | [
"$12 \\mathrm{~m}$",
"$16 \\mathrm{~m}$",
"$20 \\mathrm{~m}$",
"$21 \\mathrm{~m}$",
"$24 \\mathrm{~m}$",
"I don't know"
] | images/1146.jpg | E | null | 2 | metric geometry - length | E | |
1147 | Paul folds a piece of paper, then punches a hole into the paper and unfolds it again. The unfolded paper then looks like the picture on the right. Along which dotted line can Paul have folded the paper beforehand?
<image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1147.jpg | D | null | 3 | transformation geometry | D | |
1148 | Petra crafts a piece of jewellery out of two black and two white hearts. The hearts have areas of $1 \mathrm{~cm}^{2}, 4 \mathrm{~cm}^{2}, 9 \mathrm{~cm}^{2}$ and $16 \mathrm{~cm}^{2}$ respectively. She places the hearts on top of each other as shown in the diagram and glues them together. How big is the total area of ... | [
"$9 \\mathrm{~cm}^{2}$",
"$10 \\mathrm{~cm}^{2}$",
"$11 \\mathrm{~cm}^{2}$",
"$12 \\mathrm{~cm}^{2}$",
"$13 \\mathrm{~cm}^{2}$",
"I don't know"
] | images/1148.jpg | B | null | 3 | metric geometry - area | B | |
1149 | Ant Annie starts at the left end of the stick and crawls $\frac{2}{3}$ of the length of the stick. Ladybird Bob starts at the right end of the stick und crawls $\frac{3}{4}$ of the length of the stick. Which fraction of the length of the stick are they then apart from each other?
<image1> | [
"$\\frac{3}{8}$",
"$\\frac{1}{12}$",
"$\\frac{5}{7}$",
"$\\frac{5}{12}$",
"$\\frac{7}{12}$",
"I don't know"
] | images/1149.jpg | D | null | 5 | arithmetic | D | |
1150 | The black and the dashed line together form seven equilateral triangles. The dashed line is $20 \mathrm{~cm}$ long. How long is the black line?
<image1> | [
"$25 \\mathrm{~cm}$",
"$30 \\mathrm{~cm}$",
"$35 \\mathrm{~cm}$",
"$40 \\mathrm{~cm}$",
"$45 \\mathrm{~cm}$",
"I don't know"
] | images/1150.jpg | D | null | 2 | metric geometry - length | D | |
1152 | Two $1 \mathrm{~cm}$ long segments are marked on opposite sides of a square with side length 8 $\mathrm{cm}$. The end points of the segments are connected with each other as shown in the diagram. How big is the area of the grey part?
<image1> | [
"$2 \\mathrm{~cm}^{2}$",
"$4 \\mathrm{~cm}^{2}$",
"$6.4 \\mathrm{~cm}^{2}$",
"$8 \\mathrm{~cm}^{2}$",
"$10 \\mathrm{~cm}^{2}$",
"I don't know"
] | images/1152.jpg | B | null | 3 | metric geometry - area | B | |
1155 | The diagram shows Maria's square tablecloth to scale. All small light squares are equally big and their diagonals are parallel to the sides of the table cloth. Which part of the whole table cloth is black?
<image1> | [
"$16 \\%$",
"$24 \\%$",
"$25 \\%$",
"$32 \\%$",
"$36 \\%$",
"I don't know"
] | images/1155.jpg | D | null | 2 | metric geometry - length | D | |
1158 | The parallelogram has area 1. The two diagonals intersect each other at point M. Another point $P$ lies on the side DC. $E$ is the point of intersection of the segments $A P$ and $B D$, and $F$ is the point of intersection of the segments $B P$ and $A C$. What is the area of the quadrilateral EMFP, if the sum of the ar... | [
"$\\frac{1}{6}$",
"$\\frac{1}{8}$",
"$\\frac{1}{10}$",
"$\\frac{1}{12}$",
"$\\frac{1}{14}$",
"I don't know"
] | images/1158.jpg | D | null | 3 | metric geometry - area | D | |
1159 | If the letters of the Word MAMA are written underneath each other then the word has a vertical axis of symmetry. For which of these words does that also hold true?
<image1> | [
"ADAM",
"BAUM",
"BOOT",
"LOGO",
"TOTO",
"I don't know"
] | images/1159.jpg | E | null | 3 | transformation geometry | E | |
1160 | The fence on the right has many holes. One morning the fence falls over and lies on the floor. Which of the following pictures shows the fallen down fence?
<image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1160.jpg | C | null | 4 | descriptive geometry | C | |
1163 | A large rectangle is made up of 9 equally big rectangles. The longer side of each small rectangle is $10 \mathrm{~cm}$ long. What is the perimeter of the large rectangle?
<image1> | [
"$40 \\mathrm{~cm}$",
"$48 \\mathrm{~cm}$",
"$76 \\mathrm{~cm}$",
"$81 \\mathrm{~cm}$",
"$90 \\mathrm{~cm}$",
"I don't know"
] | images/1163.jpg | C | null | 4 | combinatorial geometry | C | |
1164 | Two circles are inscribed into an $11 \mathrm{~cm}$ long and $7 \mathrm{~cm}$ wide rectangle so that they each touch three sides of the rectangle. How big is the distance between the centres of the two circles?
<image1> | [
"$1 \\mathrm{~cm}$",
"$2 \\mathrm{~cm}$",
"$3 \\mathrm{~cm}$",
"$4 \\mathrm{~cm}$",
"$5 \\mathrm{~cm}$",
"I don't know"
] | images/1164.jpg | D | null | 2 | metric geometry - length | D | |
1165 | The square $A B C D$ has side length $3 \mathrm{~cm}$. The points $M$ and $N$, which lie on the sides $A D$ and $A B$ respectively, are joined to the corner $C$. That way the square is split up into three parts with equal area. How long is the line segment DM?
<image1> | [
"$0.5 \\mathrm{~cm}$",
"$1 \\mathrm{~cm}$",
"$1.5 \\mathrm{~cm}$",
"$2 \\mathrm{~cm}$",
"$2.5 \\mathrm{~cm}$",
"I don't know"
] | images/1165.jpg | D | null | 2 | metric geometry - length | D | |
1167 | Valentin draws a zig-zag line inside a rectangle as shown in the diagram. For that he uses the angles $10^{\circ}, 14^{\circ}, 33^{\circ}$ and $26^{\circ}$. How big is angle $\varphi$?
<image1> | [
"$11^{\\circ}$",
"$12^{\\circ}$",
"$16^{\\circ}$",
"$17^{\\circ}$",
"$33^{\\circ}$",
"I don't know"
] | images/1167.jpg | A | null | 5 | metric geometry - angle | A | |
1168 | The diagram shows a rectangle and a straight line $x$, which is parallel to one of the sides of the rectangle. There are two points $A$ and $B$ on $x$ inside the rectangle. The sum of the areas of the two triangles shaded in grey is $10 \mathrm{~cm}^{2}$. How big is the area of the rectangle?
<image1> | [
"$18 \\mathrm{~cm}^{2}$",
"$20 \\mathrm{~cm}^{2}$",
"$22 \\mathrm{~cm}^{2}$",
"$24 \\mathrm{~cm}^{2}$",
"It depends on the position of the points A and B.",
"I don't know"
] | images/1168.jpg | B | null | 3 | metric geometry - area | B | |
1170 | The diagram shows the net of a box consisting only of rectangles. How big is the volume of the box?
<image1> | [
"$43 \\mathrm{~cm}^{3}$",
"$70 \\mathrm{~cm}^{3}$",
"$80 \\mathrm{~cm}^{3}$",
"$100 \\mathrm{~cm}^{3}$",
"$1820 \\mathrm{~cm}^{3}$",
"I don't know"
] | images/1170.jpg | C | null | 4 | solid geometry | C | |
1172 | Simon runs along the edge round a $50 \mathrm{~m}$ long rectangular swimming pool, while at the same time Jan swims lengths in the pool. Simon runs three times as fast as Jan swims. While Jan swims 6 lengths, Simon manages 5 rounds around the pool. How wide is the swimming pool?
<image1> | [
"$25 \\mathrm{~m}$",
"$40 \\mathrm{~m}$",
"$50 \\mathrm{~m}$",
"$80 \\mathrm{~m}$",
"$180 \\mathrm{~m}$",
"I don't know"
] | images/1172.jpg | B | null | 2 | metric geometry - length | B | |
1173 | Lisas aviation club designs a flag with a flying "dove" on a $4 \times 6$-grid. The area of the "dove" is $192 \mathrm{~cm}^{2}$. The perimeter of the "dove" is made up of straight lines and circular arcs. What measurements does the flag have?
<image1> | [
"$6 \\mathrm{~cm} \\times 4 \\mathrm{~cm}$",
"$12 \\mathrm{~cm} \\times 8 \\mathrm{~cm}$",
"$20 \\mathrm{~cm} \\times 12 \\mathrm{~cm}$",
"$24 \\mathrm{~cm} \\times 16 \\mathrm{~cm}$",
"$30 \\mathrm{~cm} \\times 20 \\mathrm{~cm}$",
"I don't know"
] | images/1173.jpg | D | null | 4 | combinatorial geometry | D | |
1174 | The points $N, M$ and $L$ lie on the sides of an equilateral triangle $A B C$ so that $\mathrm{NM} \perp \mathrm{BC}, \mathrm{ML} \perp \mathrm{AB}$ and $\mathrm{LN} \perp \mathrm{AC}$ holds true. The area of the triangle $\mathrm{ABC}$ is $36 \mathrm{~cm}^{2}$. What is the area of the triangle LMN?
<image1> | [
"$9 \\mathrm{~cm}^{2}$",
"$12 \\mathrm{~cm}^{2}$",
"$15 \\mathrm{~cm}^{2}$",
"$16 \\mathrm{~cm}^{2}$",
"$18 \\mathrm{~cm}^{2}$",
"I don't know"
] | images/1174.jpg | B | null | 3 | metric geometry - area | B | |
1175 | In the isosceles triangle $A B C$ (with base $A C$ ) the points $K$ and $L$ are added on the sides $A B$ and $B C$ respectively so that $A K=K L=\angle B$ and $K B=A C$. How big is the angle $\angle A B C$?
<image1> | [
"$30^{\\circ}$",
"$35^{\\circ}$",
"$36^{\\circ}$",
"$40^{\\circ}$",
"$44^{\\circ}$",
"I don't know"
] | images/1175.jpg | C | null | 5 | metric geometry - angle | C | |
1177 | Which cloud contains even numbers only?
<image1> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1177.jpg | E | null | 5 | arithmetic | E | |
1179 | Three rings are connected to each other as shown. Which of the following pictures also shows three rings connected in the same way?
<image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1179.jpg | D | null | 4 | descriptive geometry | D | |
1180 | Four of the following five diagrams can be drawn without lifting the pencil and without going over a line twice. For one diagram this is not true. Which one is it?
<image1> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1180.jpg | D | null | 3 | graph theory | D | |
1181 | A big square is divided up into smaller squares of different sizes as shown. Some of the smaller squares are shaded in grey. Which fraction of the big square is shaded in grey?
<image1> | [
"$\\frac{2}{3}$",
"$\\frac{2}{5}$",
"$\\frac{4}{7}$",
"$\\frac{4}{9}$",
"$\\frac{5}{12}$",
"I don't know"
] | images/1181.jpg | D | null | 3 | metric geometry - area | D | |
1182 | Three four-digit numbers are written onto three separate pieces of paper as shown. The sum of the three numbers is 10126. Three of the digits in the picture are hidden. Which are the hidden digits?
<image1> | [
"5,6 and 7",
"4,5 and 7",
"4,6 and 7",
"4,5 and 6",
"3,5 and 6",
"I don't know"
] | images/1182.jpg | A | null | 4 | algebra | A | |
1183 | The following information is known about triangle PSQ: $\angle Q P S=20^{\circ}$. The triangle PSQ has been split up into two smaller triangles by the line $Q R$ as shown. It is known that $P Q=P R=Q S$. How big is the angle RQS?
<image1> | [
"$50^{\\circ}$",
"$60^{\\circ}$",
"$65^{\\circ}$",
"$70^{\\circ}$",
"$75^{\\circ}$",
"I don't know"
] | images/1183.jpg | B | null | 5 | metric geometry - angle | B | |
1184 | A $4 \times 4$ square is made up of the two pieces shown. Which of the following $4 \times 4$ squares cannot be made this way?
<image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1184.jpg | E | null | 4 | combinatorial geometry | E | |
1186 | Mia draws some congruent rectangles and one triangle. She then shades in grey those parts of the rectangles that lie outside the triangle (see diagram). How big is the resulting grey area?
<image1> | [
"$10 \\mathrm{~cm}^{2}$",
"$12 \\mathrm{~cm}^{2}$",
"$14 \\mathrm{~cm}^{2}$",
"$15 \\mathrm{~cm}^{2}$",
"$21 \\mathrm{~cm}^{2}$",
"I don't know"
] | images/1186.jpg | B | null | 4 | combinatorial geometry | B | |
1190 | An ant crawls along a closed line on the surface of a cube until it reaches its starting point. Which of the following nets of a cube belongs to the cube that the ant is crawling on?
<image1> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1190.jpg | E | null | 3 | analytic geometry | E | |
1191 | Peter colours in each of the eight circles in one of the colours red, yellow or blue. Two circles that are directly connected by a line, are not allowed to be of the same colour. Which two circles does Peter definitely have to colour in the same colour?
<image1> | [
"5 and 8",
"1 and 6",
"2 and 7",
"4 and 5",
"3 and 6",
"I don't know"
] | images/1191.jpg | A | null | 3 | graph theory | A | |
1192 | In square $A B C D, P, Q$ and $R$ are the midpoints of the edges $D A, B C$ and $C D$. Which fraction of the square $A B C D$ is shaded in the diagram?
<image1> | [
"$\\frac{3}{4}$",
"$\\frac{5}{8}$",
"$\\frac{1}{2}$",
"$\\frac{7}{16}$",
"$\\frac{3}{8}$",
"I don't know"
] | images/1192.jpg | E | null | 3 | metric geometry - area | E | |
1193 | One square was divided into four equal squares, containing other equal colored squares and equal colored triangles, as shown in the picture. What fraction of the original square does the colored part represent?
<image1> | [
"$\\frac{1}{3}$",
"$\\frac{1}{2}$",
"$\\frac{4}{9}$",
"$\\frac{5}{8}$",
"$\\frac{3}{4}$",
"I don't know"
] | images/1193.jpg | B | null | 4 | combinatorial geometry | B | |
1196 | In the figure, formed by a square and an equilateral triangle, the letters indicate the measurements of the angles. Which of the following equality is true?
<image1> | [
"$a=d$",
"$b+c=d$",
"$a+c=d+e$",
"$a+b=d+e$",
"$e+d=a$",
"I don't know"
] | images/1196.jpg | E | null | 5 | metric geometry - angle | E | |
1197 | As soon as he left his city towards Caecá, Charles saw the sign on the left. When he came back from Caecá, he saw the sign on the right. At that point, how far was it to get to his city?
<image1> | [
"$12 \\mathrm{~km}$",
"$21 \\mathrm{~km}$",
"$29 \\mathrm{~km}$",
"$41 \\mathrm{~km}$",
"$52 \\mathrm{~km}$",
"I don't know"
] | images/1197.jpg | D | null | 4 | logic | D | |
1198 | Which of the pictures below shows what you will see if you look from above the piece represented on the right?
<image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1198.jpg | C | null | 4 | descriptive geometry | C | |
1201 | A square is formed by four identical rectangles and a central square, as in the figure. The area of the square is $81 \mathrm{~cm}^{2}$ and the square formed by the diagonals of these rectangles has an area equal to $64 \mathrm{~cm}^{2}$. What is the area of the central square?
<image1> | [
"$25 \\mathrm{~cm}^{2}$",
"$27 \\mathrm{~cm}^{2}$",
"$36 \\mathrm{~cm}^{2}$",
"$47 \\mathrm{~cm}^{2}$",
"$49 \\mathrm{~cm}^{2}$",
"I don't know"
] | images/1201.jpg | D | null | 5 | arithmetic | D | |
1203 | Amelia has a paper strip with five equal cells containing different drawings, according to the figure. She folds the strip in such a way that the cells overlap in five layers. Which of the sequences of layers, from top to bottom, is not possible to obtain?
<image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1203.jpg | A | null | 3 | topology | A | |
1204 | Zilda took a square sheet of paper of side 1 and made two folds taking two consecutive sides of the sheet to a diagonal of it, as shown in the picture, obtaining a quadrilateral (highlighted outline). What is the area of this quadrilateral?
<image1> | [
"$\\frac{7}{10}$",
"$2-\\sqrt{2}$",
"$\\frac{3}{5}$",
"$\\sqrt{2}-1$",
"$\\frac{\\sqrt{2}}{2}$",
"I don't know"
] | images/1204.jpg | B | null | 3 | transformation geometry | B | |
1206 | Which of the following symbols for signs of the Zodiac has an axis of symmetry?
<image1> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1206.jpg | A | null | 3 | transformation geometry | A | |
1207 | The figure shows three concentric circles with four lines passing through their common centre. What percentage of the figure is shaded?
<image1> | [
"$30 \\%$",
"$35 \\%$",
"$40 \\%$",
"$45 \\%$",
"$50 \\%$",
"I don't know"
] | images/1207.jpg | E | null | 3 | metric geometry - area | E | |
1209 | Each of the five vases shown has the same height and each has a volume of 1 litre. Half a litre of water is poured into each vase. In which vase would the level of the water be the highest?
<image1> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1209.jpg | A | null | 4 | solid geometry | A | |
1210 | A cube $3 \times 3 \times 3$ is made from $1 \times 1 \times 1$ white, grey and black cubes, as shown in the first diagram. The other two diagrams show the white part and the black part of the cube. Which of the following diagrams shows the grey part?
<image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1210.jpg | E | null | 4 | descriptive geometry | E | |
1211 | A bike lock has four wheels numbered with the digits 0 to 9 in order. Each of the four wheels is rotated by $180^{\circ}$ from the code shown in the first diagram to get the correct code. What is the correct code for the bike lock?
<image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1211.jpg | B | null | 3 | transformation geometry | B | |
1215 | Five squares are positioned as shown. The small square indicated has area 1. What is the value of $h$?
<image1> | [
"$3 \\mathrm{~m}$",
"$3.5 \\mathrm{~m}$",
"$4 \\mathrm{~m}$",
"$4.2 \\mathrm{~m}$",
"$4.5 \\mathrm{~m}$",
"I don't know"
] | images/1215.jpg | C | null | 2 | metric geometry - length | C | |
1216 | A rectangular strip of paper of dimensions $4 \mathrm{~cm} \times 13 \mathrm{~cm}$ is folded as shown in the diagram. 2 rectangles are formed with areas $P$ and $Q$ where $P=2 Q$. What is the value of $x$?
<image1> | [
"$5 \\mathrm{~cm}$",
"$5.5 \\mathrm{~cm}$",
"$6 \\mathrm{~cm}$",
"$6.5 \\mathrm{~cm}$",
"$4 \\sqrt{2} \\mathrm{~cm}$",
"I don't know"
] | images/1216.jpg | C | null | 3 | transformation geometry | C | |
1217 | 5 friends talk about their collected <image1>. Xenia says: "I have an even number of pins", Zach: "Half of my pins are planets, Sue: "I don't have any moons", Paul: "I have more moons than stars" and Yvonne: "I have more stars than planets". Below are the collections of the 5 friends. Which set of pins belongs to Yvonn... | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1217.jpg | E | null | 4 | logic | E | |
1218 | A triangular pyramid is built with 20 cannon balls, as shown. Each cannon ball is labelled with one of $A, B, C, D$ or $E$. There are 4 cannon balls with each type of label. The picture shows the labels on the cannon balls on 3 of the faces of the pyramid. What is the label on the hidden cannon ball in the middle of th... | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1218.jpg | D | null | 4 | solid geometry | D | |
1222 | Meike paddles around five buoys with her boat (see diagram). Which of the buoys does she paddle around in a clockwise direction?
<image1> | [
"2, 3 and 4",
"1, 2 and 3",
"1, 3 and 5",
"2, 4 and 5",
"2, 3 and 5",
"I don't know"
] | images/1222.jpg | E | null | 3 | topology | E | |
1224 | Kengu likes to jump on the number line. He starts at 0 , then always starts with two big jumps and then three small jumps (see diagram). He keeps repeating this in the same way, over and over again. On which of the following numbers will he land in the course of his jumps?
<image1> | [
"82",
"83",
"84",
"85",
"86",
"I don't know"
] | images/1224.jpg | C | null | 4 | algebra | C | |
1225 | Sonja builds the cube shown, out of equally sized bricks. The shortest side of one brick is $4 \mathrm{~cm}$ long. What dimensions in $\mathrm{cm}$ does one brick have?
<image1> | [
"$4 \\times 6 \\times 12$",
"$4 \\times 6 \\times 16$",
"$4 \\times 8 \\times 12$",
"$4 \\times 8 \\times 16$",
"$4 \\times 12 \\times 16$",
"I don't know"
] | images/1225.jpg | C | null | 4 | solid geometry | C | |
1226 | The black-white caterpillar shown, rolls up to go to sleep. Which diagram could show the rolled-up caterpillar?
<image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1226.jpg | A | null | 3 | topology | A | |
1228 | There are five gaps in the following calculation. Adriana wants to write a "+" into four of the gaps and a "−" into one of the gaps so that the equation is correct. Where does she have to insert the "-"?
<image1> | [
"between 6 and 9",
"between 9 and 12",
"between 12 and 15",
"between 15 and 18",
"between 18 and 21",
"I don't know"
] | images/1228.jpg | D | null | 4 | algebra | D | |
1229 | There are 5 trees and 3 paths in a park as shown on the map. Another tree is planted so that there is an equal number of trees on both sides of each path. In
which section of the park will the new tree be planted?
<image1> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1229.jpg | B | null | 4 | logic | B | |
1232 | Gardener Toni plants tulips <image1> and sunflowers <image2> in a square flowerbed with side length $12 \mathrm{~m}$, as shown in the diagram. How big is the entire area where sunflowers are planted?
<image3> | [
"$36 \\mathrm{~m}^{2}$",
"$40 \\mathrm{~m}^{2}$",
"$44 \\mathrm{~m}^{2}$",
"$46 \\mathrm{~m}^{2}$",
"$48 \\mathrm{~m}^{2}$",
"I don't know"
] | images/1232.jpg | E | null | 3 | metric geometry - area | E |
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