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298 | [{"role": "user", "question": "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?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": [... | A | mcq | 5 | combinatorial geometry | |
2980 | [{"role": "user", "question": "In right triangle $XYZ$, shown below, what is $\\sin{X}$?\n\n<image1>", "hint": "", "options": {}, "choices": []}] | \frac{3}{5} | open | 1 | metric geometry - angle | |
2981 | [{"role": "user", "question": "The right pyramid shown has a square base and all eight of its edges are the same length. What is the degree measure of angle $ABD$?<image1>", "hint": "", "options": {}, "choices": []}] | 45 | numeric | 2 | solid geometry | |
2982 | [{"role": "user", "question": "A rectangular box is 4 cm thick, and its square bases measure 16 cm by 16 cm. What is the distance, in centimeters, from the center point $P$ of one square base to corner $Q$ of the opposite base? Express your answer in simplest terms.\n\n<image1>", "hint": "", "options": {}, "choices": [... | 12 | numeric | 1 | solid geometry | |
2983 | [{"role": "user", "question": "In $\\triangle{RST}$, shown, $\\sin{R}=\\frac{2}{5}$. What is $\\sin{T}$?\n\n<image1>", "hint": "", "options": {}, "choices": []}] | \frac{\sqrt{21}}{5} | open | 1 | metric geometry - angle | |
2984 | [{"role": "user", "question": "The lines $y = -2x + 8$ and $y = \\frac{1}{2} x - 2$ meet at $(4,0),$ as shown. What is the area of the triangle formed by these two lines and the line $x = -2?$ <image1>", "hint": "", "options": {}, "choices": []}] | 45 | numeric | 5 | analytic geometry | |
2985 | [{"role": "user", "question": "In the diagram, $PRT$ and $QRS$ are straight lines. What is the value of $x$? <image1>", "hint": "", "options": {}, "choices": []}] | 55 | numeric | 1 | metric geometry - angle | |
2986 | [{"role": "user", "question": "In the triangle, $\\angle A=\\angle B$. What is $x$? <image1>", "hint": "", "options": {}, "choices": []}] | 3 | numeric | 1 | metric geometry - length | |
2987 | [{"role": "user", "question": "Four circles of radius 1 are each tangent to two sides of a square and externally tangent to a circle of radius 2, as shown. What is the area of the square?\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 22+12\sqrt{2} | open | 4 | metric geometry - area | |
2988 | [{"role": "user", "question": "In the diagram, square $ABCD$ has sides of length 4, and $\\triangle ABE$ is equilateral. Line segments $BE$ and $AC$ intersect at $P$. Point $Q$ is on $BC$ so that $PQ$ is perpendicular to $BC$ and $PQ=x$. <image1>\n\nFind the value of $x$ in simplest radical form.", "hint": "", "option... | 2\sqrt{3}-2 | open | 4 | metric geometry - length | |
2989 | [{"role": "user", "question": "The following diagonal is drawn in a regular heptagon, creating a pentagon and a quadrilateral. What is the measure of $x$, in degrees? \n\n<image1>", "hint": "", "options": {}, "choices": []}] | \frac{360}7 | open | 2 | metric geometry - angle | |
299 | [{"role": "user", "question": "Which quadrant contains no points of the graph of the linear function $f(x)=-3.5 x+7$?\n<image1>", "hint": "", "options": {"A": "I", "B": "II", "C": "III", "D": "IV", "E": "Every quadrant contains at least one point of the graph."}, "choices": []}] | C | mcq | 4 | analytic geometry | |
2990 | [{"role": "user", "question": "A semicircle is constructed along each side of a right triangle with legs 6 inches and 8 inches. The semicircle placed along the hypotenuse is shaded, as shown. What is the total area of the two non-shaded crescent-shaped regions? Express your answer in simplest form.\n\n<image1>", "hint"... | 24 | numeric | 4 | metric geometry - area | |
2991 | [{"role": "user", "question": "A unit circle has its center at $(5,0)$ and a second circle with a radius of $2$ units has its center at $(11,0)$ as shown. A common internal tangent to the circles intersects the $x$-axis at $Q(a,0)$. What is the value of $a$? <image1>", "hint": "", "options": {}, "choices": []}] | 7 | numeric | 2 | analytic geometry | |
2992 | [{"role": "user", "question": "In the diagram, $K$, $O$ and $M$ are the centers of the three semi-circles. Also, $OC = 32$ and $CB = 36$. <image1> What is the area of the shaded region?", "hint": "", "options": {}, "choices": []}] | 900\pi | open | 4 | metric geometry - area | |
2993 | [{"role": "user", "question": "In triangle $ABC$, $AB = 13$, $AC = 15$, and $BC = 14$. Let $I$ be the incenter. The incircle of triangle $ABC$ touches sides $BC$, $AC$, and $AB$ at $D$, $E$, and $F$, respectively. Find the area of quadrilateral $AEIF$.\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 28 | numeric | 4 | metric geometry - area | |
2994 | [{"role": "user", "question": "What is the angle of rotation in degrees about point $C$ that maps the darker figure to the lighter image? <image1>", "hint": "", "options": {}, "choices": []}] | 180 | numeric | 2 | transformation geometry | |
2995 | [{"role": "user", "question": "$ABCDEFGH$ shown below is a right rectangular prism. If the volume of pyramid $ABCH$ is 20, then what is the volume of $ABCDEFGH$?\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 120 | numeric | 2 | solid geometry | |
2996 | [{"role": "user", "question": "Segment $AB$ measures 4 cm and is a diameter of circle $P$. In triangle $ABC$, point $C$ is on circle $P$ and $BC = 2$ cm. What is the area of the shaded region?\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 4\pi-2\sqrt{3} | open | 4 | metric geometry - area | |
2997 | [{"role": "user", "question": "What is the number of square centimeters in the shaded area? (The 10 represents the hypotenuse of the white triangle only.) <image1>", "hint": "", "options": {}, "choices": []}] | 30 | numeric | 1 | metric geometry - area | |
2998 | [{"role": "user", "question": "Four semi-circles are shown with $AB:BC:CD = 1:2:3$. What is the ratio of the shaded area to the unshaded area in the semi circle with diameter $AD$? <image1>", "hint": "", "options": {}, "choices": []}] | \frac{11}{7} | open | 4 | metric geometry - area | |
2999 | [{"role": "user", "question": "Rectangle $WXYZ$ is drawn on $\\triangle ABC$, such that point $W$ lies on segment $AB$, point $X$ lies on segment $AC$, and points $Y$ and $Z$ lies on segment $BC$, as shown. If $m\\angle BWZ=26^{\\circ}$ and $m\\angle CXY=64^{\\circ}$, what is $m\\angle BAC$, in degrees? <image1>", "hin... | 90 | numeric | 1 | metric geometry - angle | |
3 | [{"role": "user", "question": "Which kite has the longest string?\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | C | mcq | 1 | metric geometry - length | |
30 | [{"role": "user", "question": "Put the animals in order of size. Begin with the smallest. Which animal will be in the middle?\n<image1>", "hint": "", "options": {}, "choices": []}] | 2 | numeric | 1 | metric geometry - area | |
300 | [{"role": "user", "question": "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 $A B C$?\n<image1>", "hint": "", "options": {}, "choices": []}] | 6 | numeric | 5 | metric geometry - area | |
3000 | [{"role": "user", "question": "$ABCD$ is a square with $AB = 8$cm. Arcs $BC$ and $CD$ are semicircles. Express the area of the shaded region, in square centimeters, and in terms of $\\pi$. (As always, do not include units in your submitted answer.) <image1>", "hint": "", "options": {}, "choices": []}] | 8\pi-16 | open | 4 | metric geometry - area | |
3001 | [{"role": "user", "question": "A decorative arrangement of floor tiles forms concentric circles, as shown in the figure to the right. The smallest circle has a radius of 2 feet, and each successive circle has a radius 2 feet longer. All the lines shown intersect at the center and form 12 congruent central angles. What ... | \pi | open | 1 | metric geometry - area | |
3002 | [{"role": "user", "question": "Given that $\\overline{MN}\\parallel\\overline{AB}$, how many units long is $\\overline{BN}$?\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 4 | numeric | 1 | metric geometry - length | |
3003 | [{"role": "user", "question": "All of the triangles in the figure and the central hexagon are equilateral. Given that $\\overline{AC}$ is 3 units long, how many square units, expressed in simplest radical form, are in the area of the entire star? <image1>", "hint": "", "options": {}, "choices": []}] | 3\sqrt{3} | open | 4 | metric geometry - area | |
3004 | [{"role": "user", "question": "The lateral surface area of the frustum of a solid right cone is the product of one-half the slant height ($L$) and the sum of the circumferences of the two circular faces. What is the number of square centimeters in the total surface area of the frustum shown here? Express your answer in... | 256\pi | open | 2 | solid geometry | |
3005 | [{"role": "user", "question": "What is the area in square units of the quadrilateral XYZW shown below? <image1>", "hint": "", "options": {}, "choices": []}] | 2304 | numeric | 4 | metric geometry - area | |
3006 | [{"role": "user", "question": "A hexagon is inscribed in a circle: <image1> What is the measure of $\\alpha$, in degrees?", "hint": "", "options": {}, "choices": []}] | 145 | numeric | 2 | metric geometry - angle | |
3007 | [{"role": "user", "question": "By joining alternate vertices of a regular hexagon with edges $4$ inches long, two equilateral triangles are formed, as shown. What is the area, in square inches, of the region that is common to the two triangles? Express your answer in simplest radical form. <image1>", "hint": "", "optio... | 8\sqrt{3}{squareinches} | open | 4 | metric geometry - area | |
3008 | [{"role": "user", "question": "A greeting card is 6 inches wide and 8 inches tall. Point A is 3 inches from the fold, as shown. As the card is opened to an angle of 45 degrees, through how many more inches than point A does point B travel? Express your answer as a common fraction in terms of $\\pi$. <image1>", "hint": ... | \frac{3}{4}\pi{inches} | open | 2 | solid geometry | |
3009 | [{"role": "user", "question": "A right circular cone is inscribed in a right circular cylinder. The volume of the cylinder is $72\\pi$ cubic centimeters. What is the number of cubic centimeters in the space inside the cylinder but outside the cone? Express your answer in terms of $\\pi$.\n\n<image1>", "hint": "", "opti... | 48\pi | open | 1 | solid geometry | |
301 | [{"role": "user", "question": "Each face of the polyhedron shown is either a triangle or a square. Each square borders 4 triangles, and each triangle borders 3 squares. The polyhedron has 6 squares. How many triangles does it have?\n<image1>", "hint": "", "options": {}, "choices": []}] | 8 | numeric | 3 | solid geometry | |
3010 | [{"role": "user", "question": "In right triangle $ABC$, $M$ and $N$ are midpoints of legs $\\overline{AB}$ and $\\overline{BC}$, respectively. Leg $\\overline{AB}$ is 6 units long, and leg $\\overline{BC}$ is 8 units long. How many square units are in the area of $\\triangle APC$? <image1>", "hint": "", "options": {}, ... | 8 | numeric | 4 | metric geometry - area | |
3011 | [{"role": "user", "question": "A solid right prism $ABCDEF$ has a height of $16$ and equilateral triangles bases with side length $12,$ as shown. $ABCDEF$ is sliced with a straight cut through points $M,$ $N,$ $P,$ and $Q$ on edges $DE,$ $DF,$ $CB,$ and $CA,$ respectively. If $DM=4,$ $DN=2,$ and $CQ=8,$ determine the v... | \frac{224\sqrt{3}}{3} | open | 2 | solid geometry | |
3012 | [{"role": "user", "question": "Triangles $BDC$ and $ACD$ are coplanar and isosceles. If we have $m\\angle ABC = 70^\\circ$, what is $m\\angle BAC$, in degrees?\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 35 | numeric | 1 | metric geometry - angle | |
3013 | [{"role": "user", "question": "What is the volume of a pyramid whose base is one face of a cube of side length $2$, and whose apex is the center of the cube? Give your answer in simplest form.\n\n<image1>", "hint": "", "options": {}, "choices": []}] | \frac{4}{3} | open | 1 | solid geometry | |
3014 | [{"role": "user", "question": "A rectangular piece of paper $ABCD$ is folded so that edge $CD$ lies along edge $AD,$ making a crease $DP.$ It is unfolded, and then folded again so that edge $AB$ lies along edge $AD,$ making a second crease $AQ.$ The two creases meet at $R,$ forming triangles $PQR$ and $ADR$. If $AB=5\\... | 11.5 | numeric | 4 | transformation geometry | |
3015 | [{"role": "user", "question": "$ABCD$ is a rectangle that is four times as long as it is wide. Point $E$ is the midpoint of $\\overline{BC}$. What percent of the rectangle is shaded?\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 75 | numeric | 1 | metric geometry - area | |
3016 | [{"role": "user", "question": "An isosceles trapezoid is inscribed in a semicircle as shown below, such that the three shaded regions are congruent. The radius of the semicircle is one meter. How many square meters are in the area of the trapezoid? Express your answer as a decimal to the nearest tenth.\n\n<image1>", "h... | 1.3 | numeric | 4 | metric geometry - area | |
3017 | [{"role": "user", "question": "Five points $A$, $B$, $C$, $D$, and $O$ lie on a flat field. $A$ is directly north of $O$, $B$ is directly west of $O$, $C$ is directly south of $O$, and $D$ is directly east of $O$. The distance between $C$ and $D$ is 140 m. A hot-air balloon is positioned in the air at $H$ directly a... | 160 | numeric | 2 | solid geometry | |
3018 | [{"role": "user", "question": "In the figure, point $A$ is the center of the circle, the measure of angle $RAS$ is 74 degrees, and the measure of angle $RTB$ is 28 degrees. What is the measure of minor arc $BR$, in degrees? <image1>", "hint": "", "options": {}, "choices": []}] | 81 | numeric | 2 | metric geometry - angle | |
3019 | [{"role": "user", "question": "In the diagram, $AD=BD=CD$ and $\\angle BCA = 40^\\circ.$ What is the measure of $\\angle BAC?$\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 90 | numeric | 1 | metric geometry - angle | |
302 | [{"role": "user", "question": "Julia has 2017 round discs available: 1009 black ones and 1008 white ones. Using them, she wants to lay the biggest square pattern (as shown) possible and starts by using a black disc in the left upper corner. Subsequently she lays the discs in such a way that the colours alternate in eac... | E | mcq | 5 | algebra | |
3020 | [{"role": "user", "question": "In the diagram, what is the area of $\\triangle ABC$? <image1>", "hint": "", "options": {}, "choices": []}] | 54 | numeric | 2 | analytic geometry | |
3021 | [{"role": "user", "question": "Two circles are centered at the origin, as shown. The point $P(8,6)$ is on the larger circle and the point $S(0,k)$ is on the smaller circle. If $QR=3$, what is the value of $k$? <image1>", "hint": "", "options": {}, "choices": []}] | 7 | numeric | 2 | analytic geometry | |
3022 | [{"role": "user", "question": "In the diagram shown here (which is not drawn to scale), suppose that $\\triangle ABC \\sim \\triangle PAQ$ and $\\triangle ABQ \\sim \\triangle QCP$. If $m\\angle BAC = 70^\\circ$, then compute $m\\angle PQC$. <image1>", "hint": "", "options": {}, "choices": []}] | 15 | numeric | 2 | metric geometry - angle | |
3023 | [{"role": "user", "question": "What is the ratio of the area of triangle $BDC$ to the area of triangle $ADC$?\n\n<image1>", "hint": "", "options": {}, "choices": []}] | \frac{1}{3} | open | 1 | metric geometry - area | |
3024 | [{"role": "user", "question": "In triangle $ABC$, $AB = AC = 5$ and $BC = 6$. Let $O$ be the circumcenter of triangle $ABC$. Find the area of triangle $OBC$.\n\n<image1>", "hint": "", "options": {}, "choices": []}] | \frac{21}{8} | open | 4 | metric geometry - area | |
3025 | [{"role": "user", "question": "Triangle $ABC$ and triangle $DEF$ are congruent, isosceles right triangles. The square inscribed in triangle $ABC$ has an area of 15 square centimeters. What is the area of the square inscribed in triangle $DEF$?\n\n<image1>", "hint": "", "options": {}, "choices": []}] | \frac{40}{3} | open | 4 | metric geometry - area | |
3026 | [{"role": "user", "question": "In the diagram below, $\\triangle ABC$ is isosceles and its area is 240. What is the $y$-coordinate of $A?$\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 24 | numeric | 2 | analytic geometry | |
3027 | [{"role": "user", "question": "Assume that the length of Earth's equator is exactly 25,100 miles and that the Earth is a perfect sphere. The town of Lena, Wisconsin, is at $45^{\\circ}$ North Latitude, exactly halfway between the equator and the North Pole. What is the number of miles in the circumference of the circle... | 17700 | numeric | 4 | metric geometry - length | |
3028 | [{"role": "user", "question": "In right triangle $ABC$, shown below, $\\cos{B}=\\frac{6}{10}$. What is $\\tan{C}$?\n\n<image1>", "hint": "", "options": {}, "choices": []}] | \frac{3}{4} | open | 1 | metric geometry - angle | |
3029 | [{"role": "user", "question": "Square $ABCD$ and equilateral triangle $AED$ are coplanar and share $\\overline{AD}$, as shown. What is the measure, in degrees, of angle $BAE$? <image1>", "hint": "", "options": {}, "choices": []}] | 30 | numeric | 1 | metric geometry - angle | |
303 | [{"role": "user", "question": "The diagram shows a regular hexagon with side length 1. The grey flower is outlined by circular arcs with radius 1 whose centre's lie in the vertices of the hexagon. How big is the area of the grey flower?\n<image1>", "hint": "", "options": {"A": "$\\frac{\\pi}{2}$", "B": "$\\frac{2 \\pi}... | E | mcq | 5 | metric geometry - area | |
3030 | [{"role": "user", "question": "In the figure, square $WXYZ$ has a diagonal of 12 units. Point $A$ is a midpoint of segment $WX$, segment $AB$ is perpendicular to segment $AC$ and $AB = AC.$ What is the length of segment $BC$? <image1>", "hint": "", "options": {}, "choices": []}] | 18 | numeric | 1 | metric geometry - length | |
3031 | [{"role": "user", "question": "In triangle $ABC$, point $D$ is on segment $BC$, the measure of angle $BAC$ is 40 degrees, and triangle $ABD$ is a reflection of triangle $ACD$ over segment $AD$. What is the measure of angle $B$?\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 70 | numeric | 1 | metric geometry - angle | |
3032 | [{"role": "user", "question": "A particular right square-based pyramid has a volume of 63,960 cubic meters and a height of 30 meters. What is the number of meters in the length of the lateral height ($\\overline{AB}$) of the pyramid? Express your answer to the nearest whole number.\n\n<image1>", "hint": "", "options": ... | 50 | numeric | 2 | solid geometry | |
3033 | [{"role": "user", "question": "In triangle $ABC$, $\\angle BAC = 72^\\circ$. The incircle of triangle $ABC$ touches sides $BC$, $AC$, and $AB$ at $D$, $E$, and $F$, respectively. Find $\\angle EDF$, in degrees.\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 54 | numeric | 2 | metric geometry - angle | |
3034 | [{"role": "user", "question": "In isosceles triangle $ABC$, angle $BAC$ and angle $BCA$ measure 35 degrees. What is the measure of angle $CDA$? <image1>", "hint": "", "options": {}, "choices": []}] | 70 | numeric | 2 | metric geometry - angle | |
3035 | [{"role": "user", "question": "In $\\triangle ABC$, $AC=BC$, and $m\\angle BAC=40^\\circ$. What is the number of degrees in angle $x$? <image1>", "hint": "", "options": {}, "choices": []}] | 140 | numeric | 1 | metric geometry - angle | |
3036 | [{"role": "user", "question": "The two externally tangent circles each have a radius of 1 unit. Each circle is tangent to three sides of the rectangle. What is the area of the shaded region? Express your answer in terms of $\\pi$.\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 8-2\pi | open | 1 | metric geometry - area | |
3037 | [{"role": "user", "question": "The area of $\\triangle ABC$ is 6 square centimeters. $\\overline{AB}\\|\\overline{DE}$. $BD=4BC$. What is the number of square centimeters in the area of $\\triangle CDE$? <image1>", "hint": "", "options": {}, "choices": []}] | 54 | numeric | 4 | metric geometry - area | |
3038 | [{"role": "user", "question": "In the diagram, $K$, $O$ and $M$ are the centers of the three semi-circles. Also, $OC = 32$ and $CB = 36$.\n\n<image1>\n\nWhat is the area of the semi-circle with center $K$?", "hint": "", "options": {}, "choices": []}] | 1250\pi | open | 4 | metric geometry - area | |
3039 | [{"role": "user", "question": "The volume of the cylinder shown is $45\\pi$ cubic cm. What is the height in centimeters of the cylinder? <image1>", "hint": "", "options": {}, "choices": []}] | 5 | numeric | 1 | solid geometry | |
304 | [{"role": "user", "question": "We look at a regular tetrahedron with volume 1. Its four vertices are cut off by planes that go through the midpoints of the respective edges (see diagram). How big is the volume of the remaining solid?\n<image1>", "hint": "", "options": {"A": "$\\frac{4}{5}$", "B": "$\\frac{3}{4}$", "C":... | D | mcq | 3 | solid geometry | |
3040 | [{"role": "user", "question": "A semi-circle of radius 8 cm, rocks back and forth along a line. The distance between the line on which the semi-circle sits and the line above is 12 cm. As it rocks without slipping, the semi-circle touches the line above at two points. (When the semi-circle hits the line above, it im... | 55 | numeric | 4 | metric geometry - length | |
305 | [{"role": "user", "question": "Nine whole numbers were written into the cells of a $3 \\times 3$-table. The sum of these nine numbers is 500. We know that the numbers in two adjacent cells (with a common sideline) differ by exactly 1. Which number is in the middle cell?\n<image1>", "hint": "", "options": {}, "choices":... | 56 | numeric | 1 | logic | |
306 | [{"role": "user", "question": "In the diagram you can see the calendar page of a certain month. Unfortunately ink has run across parts of the page. Which day of the week does the 27th of that month fall on?\n<image1>", "hint": "", "options": {"A": "Monday", "B": "Wednesday", "C": "Thursday", "D": "Saturday", "E": "Sund... | A | mcq | 1 | arithmetic | |
307 | [{"role": "user", "question": "The diagram shows the floor plan of Renate's house. Renate enters her house from the terrace (Terrasse) and walks through every door of the house exactly once. Which room does she end up in?\n<image1>", "hint": "", "options": {}, "choices": []}] | 2 | numeric | 5 | graph theory | |
308 | [{"role": "user", "question": "The diagram shows an object made up of 12 dice glued-together. The object is dipped into some colour so that the entire outside is coloured in this new colour. How many of the small dice will have exactly four faces coloured in?\n<image1>", "hint": "", "options": {}, "choices": []}] | 10 | numeric | 3 | solid geometry | |
309 | [{"role": "user", "question": "Four identical rhombuses (diamonds) and two squares are fitted together to form a regular octagon as shown. How big are the obtuse interior angles in the rhombuses?\n<image1>", "hint": "", "options": {"A": "$135^{\\circ}$", "B": "$140^{\\circ}$", "C": "$144^{\\circ}$", "D": "$145^{\\circ}... | A | mcq | 3 | solid geometry | |
31 | [{"role": "user", "question": "How many ducks weigh the same as a crocodile?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | B | mcq | 2 | arithmetic | |
310 | [{"role": "user", "question": "The faces of the brick have the areas A, B and C as shown. How big is the volume of the brick?\n<image1>", "hint": "", "options": {"A": "$A B C$", "B": "$\\sqrt{A B C}$", "C": "$\\sqrt{A B+B C+C A}$", "D": "$\\sqrt[3]{A B C}$", "E": "$2(A+B+C)$"}, "choices": []}] | B | mcq | 3 | solid geometry | |
311 | [{"role": "user", "question": "Two dice with volumes $V$ and $W$ intersect each other as shown. $90 \\%$ of the volume of the die with volume $V$ does not belong to both dice. $85 \\%$ of the volume of the die with volume $W$ does not belong to both dice. What is the relationship between the volumes of the two dice?\n<... | B | mcq | 3 | solid geometry | |
312 | [{"role": "user", "question": "The five vases shown are filled with water. The filling rate is constant. For which of the five vases does the graph shown describe the height of the water $h$ as a function of the time t?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "ch... | D | mcq | 3 | statistics | |
313 | [{"role": "user", "question": "An octahedron is inscribed into a die with side length 1. The vertices of the octahedron are the midpoints of the faces of the die. How big is the volume of the octahedron?\n<image1>", "hint": "", "options": {"A": "$\\frac{1}{3}$", "B": "$\\frac{1}{4}$", "C": "$\\frac{1}{5}$", "D": "$\\fr... | D | mcq | 3 | solid geometry | |
314 | [{"role": "user", "question": "The vertices of a triangle have the co-ordinates $A(p \\mid q), B(r \\mid s)$ and $C(t \\mid u)$ as shown. The midpoints of the sides of the triangle are the points $\\mathrm{M}(-2 \\mid 1), \\mathrm{N}(2 \\mid-1)$ and $\\mathrm{P}(3 \\mid 2)$. Determine the value of the expression $p+q+r... | 5 | numeric | 4 | analytic geometry | |
315 | [{"role": "user", "question": "A regular pentagon is cut out of a page of lined paper. Step by step this pentagon is then rotated $21^{\\circ}$ counter clockwise about its midpoint. The result after step one is shown in the diagram. Which of the diagrams shows the situation when the pentagon fills the hole entirely aga... | B | mcq | 5 | transformation geometry | |
316 | [{"role": "user", "question": "Three of the cards shown will be dealt to Nadia, the rest to Riny. Nadia multiplies the three values of her cards and Riny multiplies the two values of his cards. It turns out that the sum of those two products is a prime number. Determine the sum of the values of Nadia's cards.\n<image1>... | 13 | numeric | 5 | algebra | |
317 | [{"role": "user", "question": "Two rectangles form the angles $40^{\\circ}$ and $30^{\\circ}$ respectively, with a straight line (see diagram). How big is angle $\\alpha$?\n<image1>", "hint": "", "options": {"A": "$105^{\\circ}$", "B": "$120^{\\circ}$", "C": "$130^{\\circ}$", "D": "$135^{\\circ}$", "E": "another value"... | E | mcq | 4 | metric geometry - angle | |
318 | [{"role": "user", "question": "The faces of the prism shown, are made up of two triangles and three squares. The six vertices are labelled using the numbers 1 to 6. The sum of the four numbers around each square is always the same. The numbers 1 and 5 are given in the diagram. Which number is written at vertex $X$?\n<i... | 2 | numeric | 5 | algebra | |
319 | [{"role": "user", "question": "On an idealised rectangular billiard table with side lengths $3 \\mathrm{~m}$ and $2 \\mathrm{m}$ a ball (point-shaped) is pushed away from point $M$ on the long side $A B$. It is reflected exactly once on each of the other sides as shown. at which distance from the vertex $A$ will the ba... | E | mcq | 5 | metric geometry - length | |
32 | [{"role": "user", "question": "The kangaroo is inside how many circles?\n<image1>", "hint": "", "options": {}, "choices": []}] | 3 | numeric | 1 | counting | |
320 | [{"role": "user", "question": "$A B C D E F$ is a regular hexagon, as shown in the diagram. $G$ is the midpoint of $A B. H$ and I are the intercepts of the line segments GD and GE respectively, with the line segment FC. How big is the ratio of the areas of the triangle GIF and the trapezium IHDE?\n<image1>", "hint": ""... | A | mcq | 5 | metric geometry - area | |
321 | [{"role": "user", "question": "Archimedes has calculated 15!. The result is on the board. Unfortunately two of the digits, the second and the tenth, cannot be read. What are the two missing digits? (Remark: $15 !=15 \\cdot 14 \\cdot 13 \\cdot \\ldots \\cdot 2 \\cdot 1$ )\n<image1>", "hint": "", "options": {"A": "2 and ... | E | mcq | 1 | arithmetic | |
322 | [{"role": "user", "question": "The flag of Kangoraland is a rectangle which is split into three equal rectangles as shown. How big is the ratio of the side lengths of the white rectangle?\n<image1>", "hint": "", "options": {"A": "$1: 2$", "B": "$2: 3$", "C": "$2: 5$", "D": "$3: 7$", "E": "$4: 9$"}, "choices": []}] | A | mcq | 5 | metric geometry - length | |
323 | [{"role": "user", "question": "The numbers $1,2,3$ and 4 are inserted into different cells of the $2 \\times 2$ table shown. Then the sums of the numbers in each row and column are determined. Two of these sums are 4 and 5. How big are the two remaining sums?\n<image1>", "hint": "", "options": {"A": "6 and 6", "B": "3 ... | E | mcq | 5 | algebra | |
324 | [{"role": "user", "question": "A rectangle is coloured in five different ways as shown. In which picture is the grey area biggest?\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | E | mcq | 5 | metric geometry - area | |
325 | [{"role": "user", "question": "Three triangles are connected to each other as shown. In which of the following pictures are the three triangles connected in the same way?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | D | mcq | 1 | topology | |
326 | [{"role": "user", "question": "Three four-digit numbers are written onto three separate pieces of paper as shown. The sum of the three numbers is 11126. Three of the digits in the picture are hidden. Which are the three hidden digits?\n<image1>", "hint": "", "options": {"A": "1,4 and 7", "B": "1,5 and 7", "C": "3,3 and... | B | mcq | 5 | algebra | |
327 | [{"role": "user", "question": "Each side of a die is marked with either 1,2 or 3 dots so that the probability of rolling a 1 is equal to $\\frac{1}{2}$, the probability of rolling a 2 is equal to $\\frac{1}{3}$ and the probability of rolling a 3 is equal to $\\frac{1}{6}$. Which of these pictures cannot be a picture of... | C | mcq | 3 | solid geometry | |
328 | [{"role": "user", "question": "A cuboid-shaped container that is not filled completely contains $120 \\mathrm{~m}^{3}$ of water. The depth of the water is either $2 \\mathrm{~m}$ or $3 \\mathrm{~m}$ or $5 \\mathrm{~m}$, depending on which side the container is actually standing on (drawings not to scale). How big is th... | E | mcq | 3 | solid geometry | |
329 | [{"role": "user", "question": "The system shown consists of three pulleys that are connected to each other via two ropes. $P$, the end of one rope, is pulled down by $24 \\mathrm{~cm}$. By how many centimeters does point $Q$ move upwards?\n<image1>", "hint": "", "options": {}, "choices": []}] | 6 | numeric | 5 | metric geometry - length | |
33 | [{"role": "user", "question": "When the ant <image1> walks from home <image2> along the arrows $\\rightarrow 3, \\uparrow 3, \\rightarrow 3, \\uparrow 1$, he gets to the ladybird <image3>.\nWhich animal does the ant <image1> get to when he walks from home <image2> along the following arrows: $\\rightarrow 2, \\downarro... | A | mcq | 2 | analytic geometry | |
330 | [{"role": "user", "question": "The diagram shows two adjoining squares with side lengths $a$ and $b$ (with $a<b$). How big is the area of the grey triangle?\n<image1>", "hint": "", "options": {"A": "$\\sqrt{a b}$", "B": "$\\frac{1}{2} a^{2}$", "C": "$\\frac{1}{2} b^{2}$", "D": "$\\frac{1}{4}\\left(a^{2}+b^{2}\\right)$"... | B | mcq | 5 | metric geometry - area | |
331 | [{"role": "user", "question": "The points of intersection of the network of bars shown are labelled with the numbers 1 to 10. The sums $S$ of the four numbers on the vertices of each square are\nall the same. What is the minimum value of $S$?\n<image1>", "hint": "", "options": {}, "choices": []}] | 20 | numeric | 5 | algebra |
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