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 |
|---|---|---|---|---|---|---|---|---|---|
1233 | The big rectangle $A B C D$ is made up of 7 congruent smaller rectangles (see diagram). What is the ratio $\frac{A B}{B C}$?
<image1> | [
"$\\frac{1}{2}$",
"$\\frac{4}{3}$",
"$\\frac{8}{5}$",
"$\\frac{12}{7}$",
"$\\frac{7}{3}$",
"I don't know"
] | images/1233.jpg | D | null | 2 | metric geometry - length | D | |
1236 | A shape is made up of a triangle and a circle that partially overlap. The grey area is $45 \%$ of the entire area of the shape. The white part of the triangle is $40 \%$ of the total area of the shape. What percent of the area of the circle is the white part, outside the triangle?
<image1> | [
"$20 \\%$",
"$25 \\%$",
"$30 \\%$",
"$35 \\%$",
"$50 \\%$",
"I don't know"
] | images/1236.jpg | B | null | 3 | metric geometry - area | B | |
1239 | The diagram shows a grid made of vertical and horizontal lines. Which part was cut from the grid? <image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1239.jpg | E | null | 4 | combinatorial geometry | E | |
1240 | Which of the following shapes cannot be cut into two trapeziums with one single straight line? <image1> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1240.jpg | A | null | 4 | combinatorial geometry | A | |
1241 | A dark disc with two holes is placed on top of a dial of a watch as shown. The dark disc is now rotated so that the number 8 can be seen through one of the holes. Which of the numbers could one see through the other hole now? <image1> | [
"4 and 12",
"1 and 5",
"1 and 4",
"7 and 11",
"5 and 12",
"I don't know"
] | images/1241.jpg | A | null | 3 | transformation geometry | A | |
1242 | Kristina has a piece of see-through foil on which some points and lines are drawn. She folds the foil along the dotted line. <image1> What can she see now? | [
"$2\\vdots6\\vdots9$",
"$2\\vdots6\\vdots6$",
"$5\\vdots6\\vdots6$",
"$2\\vdots8\\vdots6$",
"$5\\vdots8\\vdots9$",
"I don't know"
] | images/1242.jpg | C | null | 3 | transformation geometry | C | |
1243 | A $4\times 6$ grid should be cut along the black lines into several identical shapes. No piece is to be left over. Into which of the following shapes is it not possible to cut this grid in this way? <image1> <image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1243.jpg | D | null | 4 | combinatorial geometry | D | |
1244 | The diagram shows the starting position, the direction and the distance covered within 5 seconds by four bumper cars. Which two cars will first crash into each other? <image1> | [
"A and B",
"A and C",
"A and D",
"B and C",
"C and D",
"I don't know"
] | images/1244.jpg | B | null | 3 | analytic geometry | B | |
1254 | The shown triangle $A B C$ is isosceles with $\measuredangle A B C=40^{\circ}$. The two angles indicated $\measuredangle E A B$ and $\measuredangle D C A$ are equally big. How big is the angle $\measuredangle C F E$ ? <image1> | [
"$55^{\\circ}$",
"$60^{\\circ}$",
"$65^{\\circ}$",
"$70^{\\circ}$",
"$75^{\\circ}$",
"I don't know"
] | images/1254.jpg | D | null | 5 | metric geometry - angle | D | |
1255 | An ant walks along the sides of an equilateral triangle (see diagram). Its velocity is $5 \mathrm{~cm} / \mathrm{min}$ along the first side, $15 \mathrm{~cm} / \mathrm{min}$ along the second and $20 \mathrm{~cm} / \mathrm{min}$ along the third. With which average velocity in $\mathrm{cm} / \mathrm{min}$ does the ant wa... | [
"$10$",
"$\\frac{80}{11}$",
"$\\frac{180}{19}$",
"$15$",
"$\\frac{40}{3}$",
"I don't know"
] | images/1255.jpg | C | null | 4 | algebra | C | |
1259 | A regular hexagon is split into four quadrilaterals and a smaller regular hexagon. The ratio $\frac{\text { Area of the dark sections }}{\text { Area of the small hexagon }}=\frac{4}{3}$. How big is the ratio $\frac{\text { Area of the small hexagon }}{\text { Area of the big hexagon }}$ ? <image1> | [
"$\\frac{3}{11}$",
"$\\frac{1}{3}$",
"$\\frac{2}{3}$",
"$\\frac{3}{4}$",
"$\\frac{3}{5}$",
"I don't know"
] | images/1259.jpg | A | null | 3 | metric geometry - area | A | |
1261 | $15 \%$ of a round cake is cut as shown in the figure. How many degrees is the angle denoted by the question mark?
<image1> | [
"$30^{\\circ}$",
"$45^{\\circ}$",
"$54^{\\circ}$",
"$15^{\\circ}$",
"$20^{\\circ}$",
"I don't know"
] | images/1261.jpg | C | null | 2 | metric geometry - angle | C | |
1262 | In the picture, three strips of the same horizontal width $a$ are marked 1,2,3. These strips connect the two parallel lines. Which strip has the biggest area?
<image1> | [
"All three strips have the same area",
"Strip 1",
"Strip 2",
"Strip 3",
"Impossible to answer without knowing $a$",
"I don't know"
] | images/1262.jpg | A | null | 4 | metric geometry - area | A | |
1263 | The area of the wooden square equals $a$. The area of each wooden circle equals $b$. Three circles are lined up as shown in the picture. If we tie together the three circles with a thread as short as possible, without moving them, what is the area inside the thread?
<image1> | [
"3b",
"2a + b",
"a + 2b",
"3a",
"a + b",
"I don't know"
] | images/1263.jpg | C | null | 4 | metric geometry - area | C | |
1265 | A rectangular parallelepiped was composed of 4 pieces, each consisting of 4 little cubes. Then one piece was removed (see picture) Which one?
<image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1265.jpg | C | null | 3 | combinatorial geometry | C | |
1267 | The diagram shows four semicircles with radius 1. The centres of the semicircles are at the mid-points of the sides of a square. What is the radius of the circle which touches all four semicircles?
<image1> | [
"$\\sqrt{2}-1$",
"$\\frac{\\pi}{2}-1$",
"$\\sqrt{3}-1$",
"$\\sqrt{5}-2$",
"$\\sqrt{7}-2$",
"I don't know"
] | images/1267.jpg | A | null | 4 | metric geometry - length | A | |
1268 | The graph of the function $f(x)$, defined for all real numbers, is formed by two half-lines and one segment, as illustrated in the picture. Clearly, -8 is a solution of the equation $f(f(x))=0$, because $f(f(-8))=f(-4)=0$. Find all the solutions of the equation $f(f(f(x)))=0$.
<image1> | [
"-4 ; 0",
"-8 ;-4 ; 0",
"-12 ;-8 ;-4 ; 0",
"-16 ;-12 ;-8 ;-4 ; 0",
"No solutions",
"I don't know"
] | images/1268.jpg | C | null | 5 | analytic geometry | C | |
1272 | Some angles in the quadrilateral $A B C D$ are shown in the figure. If $B C=A D$, then what is the angle $A D C$?
<image1> | [
"$30^{\\circ}$",
"$50^{\\circ}$",
"$55^{\\circ}$",
"$65^{\\circ}$",
"$70^{\\circ}$",
"I don't know"
] | images/1272.jpg | D | null | 2 | metric geometry - angle | D | |
1273 | In a square $2003 \times 2003$, the squares $1 \times 1$ on the diagonals are colored (like in the picture, where the square is $7 \times 7$). How many white squares are there?
<image1> | [
"$2002^{2}$",
"$2002 \\times 2001$",
"$2001^{2}$",
"$2003 \\times 2002$",
"$2003^{2}-2004$",
"I don't know"
] | images/1273.jpg | A | null | 4 | arithmetic | A | |
1275 | The circles with centers $C$ and $D$ meet at the points $A$ and $B$, as shown. Angle $A C B=60^{\circ}$ and angle $A D B=90^{\circ}$. How many times longer is the radius of the larger circle than the radius of the smaller circle?
<image1> | [
"$\\frac{4}{3}$",
"$\\sqrt{2}$",
"$\\frac{3}{2}$",
"$\\sqrt{3}$",
"2",
"I don't know"
] | images/1275.jpg | B | null | 4 | metric geometry - length | B | |
1276 | In tank I, whose base has an area of $2 \mathrm{dm}^{2}$ and whose height is $10 \mathrm{~cm}$, the water is $5 \mathrm{~cm}$ high. An empty tank II with a base of area $1 \mathrm{dm}^{2}$ and a height of $7 \mathrm{~cm}$ is placed in tank I. The water of tank I rises, of course, and spills over into tank II. What leve... | [
"$1 \\mathrm{~cm}$",
"$2 \\mathrm{~cm}$",
"$3 \\mathrm{~cm}$",
"$4 \\mathrm{~cm}$",
"$5 \\mathrm{~cm}$",
"I don't know"
] | images/1276.jpg | C | null | 2 | solid geometry | C | |
1277 | Three semi-circles, the diameters of two of which are equal to 4 and of the third to 8, are arranged as seen in the picture. What is the distance from the center $S$ of the bigger semi-circle to the tangent point $T$ of the smaller semi-circles?
<image1> | [
"$6.$",
"$\\sqrt{32}$",
"5.7",
"$\\sqrt{40}$",
"5",
"I don't know"
] | images/1277.jpg | B | null | 4 | metric geometry - length | B | |
1279 | The diagram shows two tangential circles with radii in the ratio 1:2. The smaller circle rolls around the inside of the large circle. Which of the following is the path traced out by the point $P$ of the smaller circle?
<image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1279.jpg | A | null | 4 | transformation geometry | A | |
1282 | A rectangle is divided into 4 triangles as shown in the figure. Of the following possibilities for the areas of the triangles at most one can be true. Which one is it?
<image1> | [
"$4,5,8,9$",
"$3,5,6,7$",
"$5,6,7,12$",
"$10,11,12,19$",
"$5,6,8,10$",
"I don't know"
] | images/1282.jpg | A | null | 4 | metric geometry - length | A | |
1284 | What is the sum of the 10 angles marked in the picture?
<image1> | [
"$720^{\\circ}$",
"$600^{\\circ}$",
"$450^{\\circ}$",
"$360^{\\circ}$",
"$300^{\\circ}$",
"I don't know"
] | images/1284.jpg | A | null | 2 | metric geometry - angle | A | |
1285 | A rectangle with length $24 \mathrm{~m}$ and width $1 \mathrm{~m}$ is cut into smaller rectangles, each with width $1 \mathrm{~m}$. There are four pieces with length $4 \mathrm{~m}$, two pieces with length $3 \mathrm{~m}$ and one piece with length $2 \mathrm{~m}$. These smaller rectangles are put together to form anoth... | [
"$14 \\mathrm{~m}$",
"$20 \\mathrm{~m}$",
"$22 \\mathrm{~m}$",
"$25 \\mathrm{~m}$",
"$28 \\mathrm{~m}$",
"I don't know"
] | images/1285.jpg | B | null | 4 | metric geometry - area | B | |
1288 | Two pieces of land are separated by the borderline $A B C D$, as shown in the figure. The line segments $A B, B C$ and $C D$ are parallel to the sides of the rectangle and have lengths $30 \mathrm{~m}, 24 \mathrm{~m}$ and $10 \mathrm{~m}$, respectively. We want to straighten the borderline by replacing it with a line $... | [
"$8 \\mathrm{~m}$",
"$10 \\mathrm{~m}$",
"$12 \\mathrm{~m}$",
"$14 \\mathrm{~m}$",
"$16 \\mathrm{~m}$",
"I don't know"
] | images/1288.jpg | C | null | 4 | metric geometry - length | C | |
1291 | Three squares are placed together as shown. The lines $A E$ and $C H$ intersect at point $P$. What is the angle $\angle C P E$?
<image1> | [
"$30^{\\circ}$",
"$45^{\\circ}$",
"$60^{\\circ}$",
"$50^{\\circ}$",
"$40^{\\circ}$",
"I don't know"
] | images/1291.jpg | B | null | 2 | metric geometry - angle | B | |
1292 | A flag consists of three stripes of equal width, which are divided into two, three and four equal parts, respectively. What fraction of the area of the flag is coloured grey?
<image1> | [
"$\\frac{1}{2}$",
"$\\frac{2}{3}$",
"$\\frac{3}{5}$",
"$\\frac{4}{7}$",
"$\\frac{5}{9}$",
"I don't know"
] | images/1292.jpg | E | null | 4 | arithmetic | E | |
1296 | A square of area $125 \mathrm{~cm}^{2}$ was divided into five parts of equal area - four squares and one L-shaped figure as shown in the picture. Find the length of the shortest side of the L-shaped figure.
<image1> | [
"1",
"1.2",
"$2(\\sqrt{5}-2)$",
"$3(\\sqrt{5}-1)$",
"$5(\\sqrt{5}-2)$",
"I don't know"
] | images/1296.jpg | E | null | 4 | metric geometry - length | E | |
1297 | Two squares have side 1. What is the area of the black quadrangle?
<image1> | [
"$\\sqrt{2}-1$",
"$\\frac{\\sqrt{2}}{2}$",
"$\\frac{\\sqrt{2}+1}{2}$",
"$\\sqrt{2}+1$",
"$\\sqrt{3}-\\sqrt{2}$",
"I don't know"
] | images/1297.jpg | A | null | 4 | metric geometry - area | A | |
1299 | A square with sides of length 10 is rolled without slipping along a line. The rolling stops when $P$ first returns to the line. What is the length of the curve that $P$ has travelled?
<image1> | [
"$10 \\pi$",
"$5 \\pi+5 \\pi \\sqrt{2}$",
"$10 \\pi+5 \\pi \\sqrt{2}$",
"$5 \\pi+10 \\pi \\sqrt{2}$",
"$10 \\pi+10 \\pi \\sqrt{2}$",
"I don't know"
] | images/1299.jpg | C | null | 4 | transformation geometry | C | |
1300 | Points $M$ and $N$ are arbitrarily chosen on the sides $A D$ and $D C$, respectively, of a square $A B C D$. Then the square is divided into eight parts of areas $S_{1}, S_{2}, \ldots, S_{8}$ as shown in the diagram. Which of the following expressions is always equal to $S_{8}$?
<image1> | [
"$S_{2}+S_{4}+S_{6}$",
"$S_{1}+S_{3}+S_{5}+S_{7}$",
"$S_{1}+S_{4}+S_{7}$",
"$S_{2}+S_{5}+S_{7}$",
"$S_{3}+S_{4}+S_{5}$",
"I don't know"
] | images/1300.jpg | A | null | 4 | metric geometry - area | A | |
1302 | The cells of the table are being coloured red (R) and green (G). In each row and in each column there must be two red and two green cells. What will the lowest row look like after colouring the table?
<image1> | [
"GRGR",
"RGRG",
"GRRG",
"RGGR",
"GGRR",
"I don't know"
] | images/1302.jpg | A | null | 5 | logic | A | |
1304 | An $8 \mathrm{~m}$ long rope is fastened to the corner of the house. A dog is fastened to the rope. Find the perimeter of the area, where the dog can be found.
<image1> | [
"$15 \\pi+16$",
"$15 \\pi+20$",
"$15 \\pi$",
"$15 \\pi+18$",
"$30 \\pi+16$",
"I don't know"
] | images/1304.jpg | A | null | 4 | metric geometry - length | A | |
1306 | A coin with diameter $1 \mathrm{~cm}$ rolls around the contour outside of a regular hexagon with sides $1 \mathrm{~cm}$ long, as shown. How long is the path traced by the centre of the coin (in $\mathrm{cm}$ )?
<image1> | [
"$6+\\frac{\\pi}{2}$",
"$6+\\pi$",
"$12+\\pi$",
"$6+2 \\pi$",
"$12+2 \\pi$",
"I don't know"
] | images/1306.jpg | B | null | 4 | transformation geometry | B | |
1307 | An equilateral triangle and a regular hexagon are inscribed in a circle, the latter beeing inscribed in an equilateral triangle (see the picture). $S$ is the area of the big triangle, $s$ the area of the little one and $Q$ is the area of the hexagon. What is true?
<image1> | [
"$Q=\\sqrt{S \\cdot s}$",
"$Q=\\frac{S+s}{2}$",
"$S=s+Q$",
"$Q=\\sqrt{S^{2}+s^{2}}$",
"$S=Q+3 s$",
"I don't know"
] | images/1307.jpg | A | null | 4 | metric geometry - area | A | |
1308 | Two circles have their centres on the same diagonal of a square. They touch each other and the sides of the square as shown. The side of the square is $1 \mathrm{~cm}$ long. What is the sum of the lengths of the radii of the circles in centimetres?
<image1> | [
"$\\frac{1}{2}$",
"$\\frac{1}{\\sqrt{2}}$",
"$\\sqrt{2}-1$",
"$2-\\sqrt{2}$",
"It depends on sizes of the circles",
"I don't know"
] | images/1308.jpg | D | null | 4 | metric geometry - length | D | |
1310 | To meet the New Year day 2008, Basil put on a T-shirt with <image1> on it, and stood in front of a mirror on his hands, with his feet up. What number did Nick standing on his feet behind Basil see in the mirror?
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1310.jpg | B | null | 4 | transformation geometry | B | |
1311 | What is the length of line $A B$ if the side of each of the four squares shown is 1?
<image1> | [
"5",
"$\\sqrt{13}$",
"$\\sqrt{5}+\\sqrt{2}$",
"$\\sqrt{5}$",
"None of the previous",
"I don't know"
] | images/1311.jpg | B | null | 4 | metric geometry - length | B | |
1313 | Rectangle $A B C D$ intersects the circle at points $E, F$, $G, H$. If $A E=4 \mathrm{~cm}, E F=5 \mathrm{~cm}, D H=3 \mathrm{~cm}$, then the length of $H B$ is
<image1> | [
"$6 \\mathrm{~cm}$",
"$7 \\mathrm{~cm}$",
"$\\frac{20}{3} \\mathrm{~cm}$",
"$8 \\mathrm{~cm}$",
"$9 \\mathrm{~cm}$",
"I don't know"
] | images/1313.jpg | B | null | 4 | metric geometry - length | B | |
1314 | In the figure, two regular hexagons are equal to each other. What part of the parallelogram's area is shaded?
<image1> | [
"$\\frac{1}{2}$",
"$\\frac{1}{3}$",
"$\\frac{1}{4}$",
"$\\frac{1}{5}$",
"$\\frac{1}{6}$",
"I don't know"
] | images/1314.jpg | A | null | 4 | metric geometry - area | A | |
1315 | Six integers are marked on the real line (see the fig.). It is known that at least two of them are divisible by 3, and at least two of them are divisible by 5. Which numbers are divisible by 15?
<image1> | [
"$A$ and $F$",
"$B$ and $D$",
"$C$ and $E$",
"All the six numbers",
"Only one of them",
"I don't know"
] | images/1315.jpg | A | null | 3 | algebra | A | |
1316 | The picture shows an isosceles triangle with $A B=A C$. If $\angle B P C=120^{\circ}, \angle A B P=50^{\circ}$, then what is angle $P B C$?
<image1> | [
"$5^{\\circ}$",
"$10^{\\circ}$",
"$15^{\\circ}$",
"$20^{\\circ}$",
"$25^{\\circ}$",
"I don't know"
] | images/1316.jpg | A | null | 2 | metric geometry - angle | A | |
1317 | Find the length of the arc denoted by the interrogation sign.
<image1> | [
"$\\frac{5 \\pi}{4}$",
"$\\frac{5 \\pi}{3}$",
"$\\frac{\\pi}{2}$",
"$\\frac{3 \\pi}{2}$",
"$\\frac{2 \\pi}{3}$",
"I don't know"
] | images/1317.jpg | D | null | 4 | metric geometry - length | D | |
1319 | A 3-pyramid is a stack of the following 3 layers of balls. In the same way we have a 4-pyramid, a 5-pyramid, etc. All the outside balls of an 8-pyramid are removed. What kind of figure form the rest balls?
<image1> | [
"3-pyramid",
"4-pyramid",
"5-pyramid",
"6-pyramid",
"7-pyramid",
"I don't know"
] | images/1319.jpg | B | null | 2 | solid geometry | B | |
1321 | In the picture $A B C D$ is a square of side 1 and the semicircles have centers on $A, B, C$ and $D$. What is the length of $P Q$?
<image1> | [
"$2-\\sqrt{2}$",
"$\\frac{3}{4}$",
"$\\sqrt{5}-\\sqrt{2}$",
"$\\frac{\\sqrt{3}}{3}$",
"$\\sqrt{3}-1$",
"I don't know"
] | images/1321.jpg | E | null | 4 | metric geometry - length | E | |
1324 | The area of the shown triangle equals $80 \mathrm{~m}^{2}$. Each circle has a radius of $2 \mathrm{~m}$ and itôs centre is in one of the vertices of the triangles. What is the area of the grey shaded region (in $\mathrm{m}^{2}$)?
<image1> | [
"76",
"$80-2 \\pi$",
"$40-4 \\pi$",
"$80-\\pi$",
"$78 \\pi$",
"I don't know"
] | images/1324.jpg | B | null | 4 | metric geometry - area | B | |
1325 | In the triangle illustrated one internal angle measures $68^{\circ}$. The three angle bisectors of the triangle are shown. What is the size of the angle indicated with a question mark?
<image1> | [
"$120^{\\circ}$",
"$124^{\\circ}$",
"$128^{\\circ}$",
"$132^{\\circ}$",
"$136^{\\circ}$",
"I don't know"
] | images/1325.jpg | B | null | 2 | metric geometry - angle | B | |
1326 | The "Borromaic Rings" have an extraordinary property. Although no two are interlocked, they are strongly connected within each other. If one ring is cut through, the other two fall apart. Which of the following diagrams shows the picture of "Borromaic Rings"?
<image1> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1326.jpg | B | null | 2 | topology | B | |
1327 | The centres of the four illustrated circles are in the corners of the square. The two big circles touch each other and also the two little circles. With which factor do you have to multiply the radii of the little circles to obtain the radius of the big circles?
<image1> | [
"$\\frac{2}{9}$",
"$\\sqrt{5}$",
"$0.8 \\cdot \\pi$",
"2.5",
"$1+\\sqrt{2}$",
"I don't know"
] | images/1327.jpg | E | null | 4 | metric geometry - length | E | |
1330 | The object pictured is made up of four equally sized cubes. Each cube has a surface area of $24 \mathrm{~cm}^{2}$. What is the surface area of the object pictured?
<image1> | [
"$80 \\mathrm{~cm}^{2}$",
"$64 \\mathrm{~cm}^{2}$",
"$40 \\mathrm{~cm}^{2}$",
"$32 \\mathrm{~cm}^{2}$",
"$24 \\mathrm{~cm}^{2}$",
"I don't know"
] | images/1330.jpg | B | null | 2 | solid geometry | B | |
1331 | Six points are marked on a square grid as pictured. Which geometric figure cannot be drawn if only the marked points are allowed to be used as cornerpoints of the figure?
<image1> | [
"square",
"parallelogram with different long sides",
"acute triangle",
"obtuse triangle",
"all figures are possible",
"I don't know"
] | images/1331.jpg | E | null | 3 | combinatorial geometry | E | |
1332 | In the picture opposite we see that $1+3+5+7=4 \times 4$. How big is $1+3+5+7+\ldots+17+19$?
<image1> | [
"$10 \\times 10$",
"$11 \\times 11$",
"$12 \\times 12$",
"$13 \\times 13$",
"$14 \\times 14$",
"I don't know"
] | images/1332.jpg | A | null | 3 | algebra | A | |
1333 | In the figure, $\mathrm{ABCE}$ is a square. $\mathrm{CDE}$ and $\mathrm{BCF}$ are equilateral triangles. The length of $\mathrm{AB}$ is 1. How long is $\mathrm{FD}$?
<image1> | [
"$\\sqrt{2}$",
"$\\frac{\\sqrt{3}}{2}$",
"$\\sqrt{3}$",
"$\\sqrt{5}-1$",
"$\\sqrt{6}-1$",
"I don't know"
] | images/1333.jpg | A | null | 4 | metric geometry - length | A | |
1334 | How big is the angle indicated with a question mark?
<image1> | [
"$10^{\\circ}$",
"$20^{\\circ}$",
"$30^{\\circ}$",
"$40^{\\circ}$",
"$50^{\\circ}$",
"I don't know"
] | images/1334.jpg | D | null | 2 | metric geometry - angle | D | |
1336 | A circle of radius $4 \mathrm{~cm}$ is divided, as shown, by four semicircles with radius $2 \mathrm{~cm}$ into four congruent parts. What is the perimeter of one of these parts?
<image1> | [
"$2 \\pi$",
"$4 \\pi$",
"$6 \\pi$",
"$8 \\pi$",
"$12 \\pi$",
"I don't know"
] | images/1336.jpg | C | null | 4 | metric geometry - length | C | |
1337 | Five students carry out a run. Their results are recorded in the graph opposite, according to the time taken (Zeit) and the distance covered (Strecke). Who had the greatest average speed?
<image1> | [
"Anja",
"Bernd",
"Chris",
"Doris",
"Ernst",
"I don't know"
] | images/1337.jpg | D | null | 5 | analytic geometry | D | |
1339 | In front of a supermarket there are two rows of interconnected trolleys.The first one is $2.9 \mathrm{~m}$ long and consists of 10 trolleys. The second one is $4.9 \mathrm{~m}$ long and consists of twenty trolleys. How long is one trolley?
<image1> | [
"$0.8 \\mathrm{~m}$",
"$1 \\mathrm{~m}$",
"$1.1 \\mathrm{~m}$",
"$1.2 \\mathrm{~m}$",
"$1.4 \\mathrm{~m}$",
"I don't know"
] | images/1339.jpg | C | null | 3 | algebra | C | |
1340 | Lines drawn parallel to the base of the triangle pictured, separate the other two sides into 10 equally large parts. What percentage of the triangle is grey?
<image1> | [
"$41.75 \\%$",
"$42.5 \\%$",
"$45 \\%$",
"$46 \\%$",
"$47.5 \\%$",
"I don't know"
] | images/1340.jpg | C | null | 4 | metric geometry - area | C | |
1343 | The area of the grey rectangle shown on the right is $13 \mathrm{~cm}^{2}. X$ and $Y$ are the midpoints of the sides of the trapezium. How big is the area of the trapezium?
<image1> | [
"$24 \\mathrm{~cm}^{2}$",
"$25 \\mathrm{~cm}^{2}$",
"$26 \\mathrm{~cm}^{2}$",
"$27 \\mathrm{~cm}^{2}$",
"$28 \\mathrm{~cm}^{2}$",
"I don't know"
] | images/1343.jpg | C | null | 4 | metric geometry - area | C | |
1345 | The two bold lines on the right are rotations of each other. Which of the given points could be the centre of this rotation?
<image1> | [
"only $X$",
"$X$ and $Z$",
"$X$ and $T$",
"only $T$",
"$X, Y, Z$ and $T$",
"I don't know"
] | images/1345.jpg | C | null | 4 | transformation geometry | C | |
1353 | Three big boxes $P, Q$ and $R$ are stored in a warehouse. The upper picture on the right shows their placements from above. The boxes are so heavy that they can only be rotated $90^{\circ}$ around a vertical edge as indicated in the pictures below. Now the boxes should be rotated to stand against the wall in a certain ... | [
"A",
"B",
"C",
"D",
"All four arrangements are possible.",
"I don't know"
] | images/1353.jpg | B | null | 4 | transformation geometry | B | |
1354 | The two circles shown on the right intersect each other at $X$ and $Y$. Thereby $X Y$ is the diameter of the small circle. The centre $S$ of the large circle (with radius $r$ ) is on the small circle. How big is the area of the grey region?
<image1> | [
"$\\frac{\\pi}{6} r^{2}$",
"$\\frac{\\sqrt{3} \\pi}{12} r^{2}$",
"$\\frac{1}{2} r^{2}$",
"$\\frac{\\sqrt{3}}{4} r^{2}$",
"another number",
"I don't know"
] | images/1354.jpg | C | null | 4 | metric geometry - area | C | |
1355 | Which of the shapes to the right has the largest area?
<image1> | [
"A",
"B",
"C",
"D",
"All shapes have the same area.",
"I don't know"
] | images/1355.jpg | E | null | 3 | combinatorial geometry | E | |
1357 | A cuboid is formed from 3 pieces (see picture). Each piece is made from 4 cubes of the same colour. What shape does the white piece have?
<image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1357.jpg | D | null | 3 | combinatorial geometry | D | |
1358 | The quadrilateral $A B C D$ with side length $4 \mathrm{~cm}$ has the same area as triangle $E C D$. What is the perpendicular distance from point $E$ to the line $g$?
<image1> | [
"$8 \\mathrm{~cm}$",
"$(4+2 \\sqrt{3}) \\mathrm{cm}$",
"$12 \\mathrm{~cm}$",
"$10 \\times \\sqrt{2} \\mathrm{~cm}$",
"It depends on the position of $\\mathrm{E}$.",
"I don't know"
] | images/1358.jpg | C | null | 4 | metric geometry - length | C | |
1359 | One of the two sides of a rectangle has length $6 \mathrm{~cm}$. In the rectangle circles are drawn next to each other in such a way that their centres form an equilateral triangle. What is the shortest distance between the two grey circles (in $\mathrm{cm}$ )?
<image1> | [
"1",
"$\\sqrt{2}$",
"$2 \\sqrt{3}-2$",
"$\\frac{\\pi}{2}$",
"2",
"I don't know"
] | images/1359.jpg | C | null | 4 | metric geometry - length | C | |
1360 | The diagram shows a right-angled triangle with side lengths 5,12 and 13. What is the length of the radius of the inscribed semi-circle?
<image1> | [
"$7 / 3$",
"$10 / 3$",
"$12 / 3$",
"$13 / 3$",
"$17 / 3$",
"I don't know"
] | images/1360.jpg | B | null | 4 | metric geometry - length | B | |
1363 | A rectangle $A B C D$ with dimensions $16 \mathrm{~cm}$ by $4 \mathrm{~cm}$ was folded along the line MN so that corner C meets corner A. What is the area of the Pentagon ABNMD'?
<image1> | [
"$17 \\mathrm{~cm}^{2}$",
"$27 \\mathrm{~cm}^{2}$",
"$37 \\mathrm{~cm}^{2}$",
"$47 \\mathrm{~cm}^{2}$",
"$57 \\mathrm{~cm}^{2}$",
"I don't know"
] | images/1363.jpg | D | null | 4 | transformation geometry | D | |
1364 | The shape pictured, is made out of two squares with side lengths $4 \mathrm{~cm}$ and $5 \mathrm{~cm}$ respectively, a triangle with area $8 \mathrm{~cm}^{2}$ and the grey parallelogram. What is the area of the parallelogram?
<image1> | [
"$15 \\mathrm{~cm}^{2}$",
"$16 \\mathrm{~cm}^{2}$",
"$18 \\mathrm{~cm}^{2}$",
"$20 \\mathrm{~cm}^{2}$",
"$21 \\mathrm{~cm}^{2}$",
"I don't know"
] | images/1364.jpg | B | null | 4 | metric geometry - area | B | |
1367 | Mrs. Maisl buys four pieces of corn-on-the-cob for each of the four members of her family and get the discount offered. How much does she end up paying?
<image1> | [
"$0.80 €$",
"$1.20 €$",
"$2.80 €$",
"$3.20 €$",
"$80 €$",
"I don't know"
] | images/1367.jpg | C | null | 4 | arithmetic | C | |
1368 | On a square grid made up of unit squares, six points are marked as shown on the right. Three of which form a triangle with the least area. How big is this smallest area?
<image1> | [
"$1 / 2$",
"$1 / 3$",
"$1 / 4$",
"1",
"2",
"I don't know"
] | images/1368.jpg | A | null | 3 | combinatorial geometry | A | |
1369 | A cube is coloured on the outside as if it was made up of four white and four black cubes where no cubes of the same colour are next to each other (see picture). Which of the following figures represents a possible net of the coloured cube?
<image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1369.jpg | E | null | 3 | descriptive geometry | E | |
1370 | In a drawing we can see a three quarter circle with centre M and an indicated orientation arrow. This three-quarter circle is first turned $90^{\circ}$ anti-clockwise about M and then reflected in the x - axis. Which is the resulting picture?
<image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1370.jpg | D | null | 5 | analytic geometry | D | |
1371 | Triangle RZT is generated by rotating the equilateral triangle AZC about point Z. Angle $\beta=\angle \mathrm{CZR}=70^{\circ}$. Determine angle $\alpha=\angle \mathrm{CAR}$.
<image1> | [
"$20^{\\circ}$",
"$25^{\\circ}$",
"$30^{\\circ}$",
"$35^{\\circ}$",
"$40^{\\circ}$",
"I don't know"
] | images/1371.jpg | D | null | 2 | metric geometry - angle | D | |
1374 | The sides of the rectangle $A B C D$ are parallel to the co-ordinate axis. The rectangle lies below the $\mathrm{x}$-axis and to the right of the $\mathrm{y}$-axis, as shown in the diagram. For each of the points A, B, C, D the quotient (y-coordinate):(x-coordinate) is calculated. For which point will you obtain the sm... | [
"A",
"B",
"C",
"D",
"It depends on the position of the rectangle and its side lengths.",
"I don't know"
] | images/1374.jpg | D | null | 5 | analytic geometry | D | |
1375 | Tarzan wanted to draw a rhombus made up of two equilateral triangles. He drew the line segments inaccurately. When Jane checked the measurements of the four angles shown, she sees that they are not equally big (see diagram). Which of the five line segments in this diagram is the longest?
<image1> | [
"AD",
"AC",
"AB",
"BC",
"BD",
"I don't know"
] | images/1375.jpg | A | null | 4 | metric geometry - length | A | |
1377 | $a, b$ and $c$ show the lengths of the different of pieces of wire pictured. Which of the following inequalities is correct?
<image1> | [
"$a<b<c$",
"$a<c<b$",
"$b<a<c$",
"$b<c<a$",
"$c<b<a$",
"I don't know"
] | images/1377.jpg | E | null | 3 | combinatorial geometry | E | |
1378 | The side lengths of the large regular hexagon are twice the length of those of the small regular hexagon. What is the area of the large hexagon if the small hexagon has an area of $4 \mathrm{~cm}^{2}$?
<image1> | [
"$16 \\mathrm{~cm}^{2}$",
"$14 \\mathrm{~cm}^{2}$",
"$12 \\mathrm{~cm}^{2}$",
"$10 \\mathrm{~cm}^{2}$",
"$8 \\mathrm{~cm}^{2}$",
"I don't know"
] | images/1378.jpg | A | null | 4 | metric geometry - area | A | |
1379 | The circumference of the large wheel measures $4.2 \mathrm{~m}$, and that of the small wheel $0.9 \mathrm{~m}$. To begin with the valves on both wheels are at the lowest point, and then the bicycle moves to the left. After a few metres both valves are again at the lowest point at the same time. After how many metres do... | [
"$4.2 \\mathrm{~m}$",
"$6.3 \\mathrm{~m}$",
"$12.6 \\mathrm{~m}$",
"$25.2 \\mathrm{~m}$",
"$37.8 \\mathrm{~m}$",
"I don't know"
] | images/1379.jpg | C | null | 4 | transformation geometry | C | |
1380 | Paul hangs rectangular pictures on a wall. For each picture he hammers a nail into the wall $2.5 \mathrm{~m}$ above the floor. He ties a $2 \mathrm{~m}$ long string to the upper corners of each picture (see diagram). which picture size (width in $\mathrm{cm} \times$ height in $\mathrm{cm}$ ) has its lower edge nearest ... | [
"$60 \\times 40$",
"$120 \\times 50$",
"$120 \\times 90$",
"$160 \\times 60$",
"$160 \\times 100$",
"I don't know"
] | images/1380.jpg | C | null | 4 | metric geometry - length | C | |
1381 | The shaded part of the regular octagon has an area of $3 \mathrm{~cm}^{2}$. How big is the area of the octagon?
<image1> | [
"$8+4 \\sqrt{2} \\mathrm{~cm}^{2}$",
"$9 \\mathrm{~cm}^{2}$",
"$8 \\sqrt{2} \\mathrm{~cm}^{2}$",
"$12 \\mathrm{~cm}^{2}$",
"$14 \\mathrm{~cm}^{2}$",
"I don't know"
] | images/1381.jpg | D | null | 4 | metric geometry - area | D | |
1385 | $P T$ is the tangent to a circle $O$, and $P B$ is the angle bisector of the angle TPA (see diagram). How big is the angle TBP?
<image1> | [
"$30^{\\circ}$",
"$45^{\\circ}$",
"$50^{\\circ}$",
"$75^{\\circ}$",
"It depends on the location of point $P$",
"I don't know"
] | images/1385.jpg | B | null | 2 | metric geometry - angle | B | |
1386 | In triangle $A B C, A B=6 \mathrm{~cm}, A C=8 \mathrm{~cm}$ and $B C=10 \mathrm{~cm}$. $M$ is the midpoint of the side $B C$. $A M D E$ is a square and $M D$ intersects $A C$ at point $F$. What is the area of the quadrilateral $A F D E$ in $\mathrm{cm}^{2}$?
<image1> | [
"$\\frac{124}{8}$",
"$\\frac{125}{8}$",
"$\\frac{126}{8}$",
"$\\frac{127}{8}$",
"$\\frac{128}{8}$",
"I don't know"
] | images/1386.jpg | B | null | 4 | metric geometry - area | B | |
1387 | The grey areas of the square with side length $a$ are bounded by a semi-circle and two quarter-circles respectively. What is their total area?
<image1> | [
"$\\frac{\\pi a^{2}}{8}$",
"$\\frac{a^{2}}{2}$",
"$\\frac{\\pi a^{2}}{2}$",
"$\\frac{a^{2}}{4}$",
"$\\frac{\\pi a^{2}}{4}$",
"I don't know"
] | images/1387.jpg | B | null | 4 | metric geometry - area | B | |
1388 | Mr. Hide wants to find a treasure that he buried years before. He can only remember that he buried the treasure at least $5 \mathrm{~m}$ away from the hedge and no more than $5 \mathrm{~m}$ away from the old pear tree. Which picture shows best the area where Mr. Hide has to look for the treasure?
<image1> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1388.jpg | B | null | 4 | metric geometry - area | B | |
1389 | In the diagram one can see my decision-die in three different positions. What is the probability I get a "YES", when rolling this die once.
<image1> | [
"$\\frac{1}{3}$",
"$\\frac{1}{2}$",
"$\\frac{5}{9}$",
"$\\frac{2}{3}$",
"$\\frac{5}{6}$",
"I don't know"
] | images/1389.jpg | B | null | 2 | solid geometry | B | |
1390 | The side lengths of each of the small squares in the diagram are 1. How long is the shortest path from "Start" to "Ziel", if you are only allowed to move along the sides and the diagonals of the squares?
<image1> | [
"$2 \\sqrt{5}$",
"$\\sqrt{10}+\\sqrt{2}$",
"$2+2 \\sqrt{2}$",
"$4 \\sqrt{2}$",
"6",
"I don't know"
] | images/1390.jpg | C | null | 3 | combinatorial geometry | C | |
1392 | Four objects $a, b, c, d$ are placed on a double balance as shown. Then two of the objects are exchanged, which results in the change of position of the balance as shown. Which two objects were exchanged?
<image1> | [
"$a$ and $b$",
"$b$ and $d$",
"$b$ and $c$",
"$a$ and $d$",
"$a$ and $c$",
"I don't know"
] | images/1392.jpg | D | null | 3 | algebra | D | |
1394 | Lines parallel to the base $A C$ of triangle $A B C$ are drawn through $X$ and $Y$. In each case, the areas of the grey parts are equal in siz. The ratio $B X: X A=4: 1$ is known. What is the ratio $B Y: Y A$?
<image1> | [
"$1: 1$",
"$2: 1$",
"$3: 1$",
"$3: 2$",
"$4: 3$",
"I don't know"
] | images/1394.jpg | D | null | 4 | metric geometry - length | D | |
1395 | A $3 \times 3$ field is made up of 9 unit squares. In two of these squares, circles are inscribed as shown in the diagram. How big is the shortest distance between these circles?
<image1> | [
"$2 \\sqrt{2}-1$",
"$\\sqrt{2+1}$",
"$2 \\sqrt{2}$",
"2",
"3",
"I don't know"
] | images/1395.jpg | A | null | 4 | metric geometry - length | A | |
1396 | What percentage of the area of the triangle is coloured in grey in the adjacent diagram?
<image1> | [
"$80 \\%$",
"$85 \\%$",
"$88 \\%$",
"$90 \\%$",
"It cannot be calculated.",
"I don't know"
] | images/1396.jpg | C | null | 4 | metric geometry - area | C | |
1398 | Jack wants to keep six tubes each of diameter $2 \mathrm{~cm}$ together using a rubber band. He chooses between the two possible variations shown. How are the lengths of the rubber bands related to each other?
<image1> | [
"In the left picture the band is $\\pi \\mathrm{cm}$ shorter.",
"In the left picture the band is $4 \\mathrm{~cm}$ shorter.",
"In the right picture the band is $\\pi \\mathrm{cm}$ shorter.",
"In the right picture the band is $4 \\mathrm{~cm}$ shorter.",
"Both bands are equally long.",
"I don't know"
] | images/1398.jpg | E | null | 4 | metric geometry - length | E | |
1400 | In the diagram we see a cube and four marked angles. How big is the sum of those angles?
<image1> | [
"$315^{\\circ}$",
"$330^{\\circ}$",
"$345^{\\circ}$",
"$360^{\\circ}$",
"$375^{\\circ}$",
"I don't know"
] | images/1400.jpg | B | null | 2 | solid geometry | B | |
1401 | A creeping plant twists exactly 5 times around a post with circumference $15 \mathrm{~cm}$ (as shown in the diagram) and thus reaches a height of $1 \mathrm{~m}$. While the plant grows the height of the plant also grows with constant speed. How long is the creeping plant?
<image1> | [
"$0.75 \\mathrm{~m}$",
"$1.0 \\mathrm{~m}$",
"$1.25 \\mathrm{~m}$",
"$1.5 \\mathrm{~m}$",
"$1.75 \\mathrm{~m}$",
"I don't know"
] | images/1401.jpg | C | null | 2 | solid geometry | C | |
1403 | Peter writes the word KANGAROO on a see-through piece of glass, as seen on the right. What can he see when he first flips over the glass onto its back along the right-hand side edge and then turns it about $180^{\circ}$ while it is lying on the table?
<image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1403.jpg | E | null | 4 | transformation geometry | E | |
1404 | A wheel rolls along a zigzag curve as can be seen below. Which of the following pictures shows the curve that is described by the centre of the wheel?
<image1> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1404.jpg | E | null | 4 | transformation geometry | E | |
1405 | A circle with radius 1 rolls along a straight line from point $K$ to point $L$, as shown, with $K L=11 \pi$. In which position is the circle when it has arrived in $L$?
<image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/1405.jpg | E | null | 4 | transformation geometry | E | |
1407 | In an equilateral triangle with area 1, we draw the six perpendicular lines from the midpoints of each side to the other two sides as seen in the diagram. How big is the area of the grey hexagon that has been created this way?
<image1> | [
"$\\frac{1}{3}$",
"$\\frac{2}{5}$",
"$\\frac{4}{9}$",
"$\\frac{1}{2}$",
"$\\frac{2}{3}$",
"I don't know"
] | images/1407.jpg | D | null | 4 | metric geometry - area | D |
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