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1539 | [{"role": "user", "question": "The regular pentagon $P Q R S T$ in the diagram has been reflected in the line $P Q$ so that vertex $T$ is reflected to point $U$, as shown. Then the new pentagon is reflected in $P U$, so that vertex $Q$ is reflected to point $V$, as shown. This process is repeated, on each occasion refl... | 10 | numeric | 3 | transformation geometry | |
154 | [{"role": "user", "question": "Mr Beaver re-arranges the parts to build a kangaroo.\n<image1>\nWhich part is missing?\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | A | mcq | 1 | combinatorial geometry | |
1540 | [{"role": "user", "question": "<image1>\nIn the diagram above there are 11 cards, each printed with two letters. The diagram below shows a rearangement of the cards, but only the top letters are shown.\n<image2>\nWhich one of the following sequences of letters could appear on the bottom row of the second diagram?", "hi... | E | mcq | 4 | algebra | |
1541 | [{"role": "user", "question": "The robot in the diagram has been programmed to move in a straight line and, if it meets a wall (shown by bold lines), to turn right by $90^{\\circ}$ and then to continue straight on. If it cannot go straight or turn right it will stop. What will happen to this robot? <image1>", "hint": "... | E | mcq | 4 | combinatorial geometry | |
1542 | [{"role": "user", "question": "What is the least possible number of small squares that we should shade in the diagram on the right for the whole diagram to have a line of symmetry? <image1>", "hint": "", "options": {}, "choices": []}] | 3 | numeric | 4 | combinatorial geometry | |
1543 | [{"role": "user", "question": "In the diagram six circles of equal size touch adjacent circles and the sides of the large rectangle. Each of the corners of the small rectangle is the centre of one of the circles. The perimeter of the small rectangle is $60 \\mathrm{~cm}$. What is the perimeter of the large rectangle in... | 100 | numeric | 2 | metric geometry - length | |
1544 | [{"role": "user", "question": "In the diagram, each of the squares touches adjacent squares at its corners and the line $G H$ along one of its edges. The line $G H$ is $24 \\mathrm{~cm}$ long. What is the total perimeter, in centimetres, of all the squares? <image1>", "hint": "", "options": {}, "choices": []}] | 96 | numeric | 2 | metric geometry - length | |
1545 | [{"role": "user", "question": "By drawing 9 lines, 5 horizontal and 4 vertical, one can form 12 small rectangles, as shown on the right. What is the greatest possible number of small rectangles one can form by drawing 15 lines, either horizontal or vertical? <image1>", "hint": "", "options": {}, "choices": []}] | 42 | numeric | 2 | combinatorics | |
1546 | [{"role": "user", "question": "In the diagram, $V W X$ and $X Y Z$ are congruent equilateral triangles and angle $V X Y=80^{\\circ}$. What is the size of angle $V W Y$ ? <image1>", "hint": "", "options": {"A": "$25^{\\circ}$", "B": "$30^{\\circ}$", "C": "$35^{\\circ}$", "D": "$40^{\\circ}$", "E": "$45^{\\circ}$"}, "cho... | D | mcq | 5 | metric geometry - angle | |
1547 | [{"role": "user", "question": "Each object shown is made up of 7 cubes. Which of $\\mathrm{P}, \\mathrm{Q}, \\mathrm{R}$ and $\\mathrm{S}$ can be obtained by rotating $\\mathrm{T}$ ?\n<image1>", "hint": "", "options": {"A": "P and R", "B": "Q and S", "C": "only R", "D": "none of them", "E": "P, Q and R"}, "choices": []... | A | mcq | 4 | descriptive geometry | |
1548 | [{"role": "user", "question": "The diagram shows a square of side $2 \\mathrm{~m}$ with lines drawn to its sides from the centre $O$. The points $A, B, C$ and $D$ are all on different sides of the square. The lines $O A$ and $O B$ are perpendicular as are the lines $O C$ and $O D$. What is the shaded area in square met... | 2 | numeric | 3 | metric geometry - area | |
1549 | [{"role": "user", "question": "Nick and Pete each chose four numbers from the nine numbers in the diagram on the right. There was one number which neither of them chose. Nick found that the total of his numbers was three times Pete's total. Which number was not chosen? <image1>", "hint": "", "options": {}, "choices": [... | 14 | numeric | 2 | combinatorics | |
155 | [{"role": "user", "question": "Sara says: \"My boat has more than one circle. It also has 2 triangles more than squares.\" Which boat belongs to Sara?\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | E | mcq | 1 | counting | |
1550 | [{"role": "user", "question": "Marta wants to use 16 square tiles like the one shown to form a $4 \\times 4$ square design. The tiles may be turned. Each arc bisects the sides it meets and has length $p \\mathrm{~cm}$. She is trying to make the arcs connect to make a long path. What is the length, in centimetres, of th... | D | mcq | 2 | metric geometry - length | |
1551 | [{"role": "user", "question": "In the diagram, a square with sides of length $4 \\mathrm{~cm}$ and a triangle with the same perimeter as the square are joined together to form a pentagon. What is the perimeter of the pentagon? <image1>", "hint": "", "options": {"A": "$12 \\mathrm{~cm}$", "B": "$24 \\mathrm{~cm}$", "C":... | B | mcq | 2 | metric geometry - length | |
1552 | [{"role": "user", "question": "How many different squares can be drawn in total by joining the dots with line segments in the part of the square lattice as shown on the right? <image1>", "hint": "", "options": {}, "choices": []}] | 4 | numeric | 4 | combinatorial geometry | |
1553 | [{"role": "user", "question": "In the diagram, three lines intersect at one point, forming angles of $108^{\\circ}$ and $124^{\\circ}$, as shown. What is the size of the angle marked $x^{\\circ}$ ? <image1>", "hint": "", "options": {"A": "$56^{\\circ}$", "B": "$55^{\\circ}$", "C": "$54^{\\circ}$", "D": "$53^{\\circ}$",... | E | mcq | 5 | metric geometry - angle | |
1554 | [{"role": "user", "question": "A shape is made by cutting all the corners off a cube, as shown in the diagram. How many edges does the shape have? <image1>", "hint": "", "options": {}, "choices": []}] | 36 | numeric | 4 | solid geometry | |
1555 | [{"role": "user", "question": "Four tangent circles, each of radius $6 \\mathrm{~cm}$, are inscribed in a rectangle $P Q R S$ as shown in the diagram. The sides of the rectangle touch two of the circles at $T$ and $U$. What is the area of triangle RUT in $\\mathrm{cm}^{2}$ ? <image1>", "hint": "", "options": {}, "choic... | 108 | numeric | 3 | metric geometry - area | |
1556 | [{"role": "user", "question": "In the subtraction calculation on the right, each of the letters $\\mathrm{K}, \\mathrm{A}, \\mathrm{N}, \\mathrm{G}, \\mathrm{R}$ and $\\mathrm{O}$ represents a different digit.\nWhat is the largest possible value of the number 'KAN'?\n<image1>", "hint": "", "options": {}, "choices": []}... | 864 | numeric | 4 | algebra | |
1557 | [{"role": "user", "question": "Four identical dice are arranged in a row as shown in the diagram. Although each die does have 1, 2, 3, 4, 5, 6 dots, the sum of the numbers of dots on each pair of opposite faces is not necessarily 7 . What is the total number of dots on the six touching faces of the dice?\n<image1>", "h... | 20 | numeric | 5 | arithmetic | |
1558 | [{"role": "user", "question": "The star on the right is formed from 12 identical equilateral triangles. The length of the perimeter of the star is $36 \\mathrm{~cm}$. What is the length of the perimeter of the shaded hexagon? <image1>", "hint": "", "options": {"A": "$12 \\mathrm{~cm}$", "B": "$18 \\mathrm{~cm}$", "C": ... | B | mcq | 2 | metric geometry - length | |
1559 | [{"role": "user", "question": "In the diagram on the right, $Q S R$ is a straight line, $\\angle Q P S=12^{\\circ}$ and $P Q=P S=R S$.\nWhat is the size of $\\angle Q P R$ ? <image1>", "hint": "", "options": {"A": "$36^{\\circ}$", "B": "$42^{\\circ}$", "C": "$54^{\\circ}$", "D": "$60^{\\circ}$", "E": "$84^{\\circ}$"}, ... | C | mcq | 5 | metric geometry - angle | |
156 | [{"role": "user", "question": "The bee on the right has a few pieces missing. Each piece costs points (Punkte).\n<image1>\nHow many points does Maya need to complete the bee?", "hint": "", "options": {}, "choices": []}] | 13 | numeric | 2 | arithmetic | |
1560 | [{"role": "user", "question": "Which of the following knots consist of more than one loop of rope?\n<image1>", "hint": "", "options": {"A": "$P, R$ and $T$", "B": "$R, S$ and $T$", "C": "$P, R, S$ and $T$", "D": "$$ all of $P, Q, R, S$ and $T$", "E": "$$ none of $\\mathrm{A}, \\mathrm{B}, \\mathrm{C}$ or $\\mathrm{D}$"... | A | mcq | 3 | topology | |
1561 | [{"role": "user", "question": "The diagram on the right shows nine points in a square array. What is the smallest number of points that need to be removed in order that no three of the remaining points are in a straight line? <image1>", "hint": "", "options": {}, "choices": []}] | 3 | numeric | 4 | combinatorial geometry | |
1562 | [{"role": "user", "question": "The diagram shows four circles each of which touches the largest square and two adjacent circles. A second square has its vertices at the midpoints of the sides of the largest square and the central square has its vertices at the centres of the circles.\n<image1>\nWhat is the ratio of the... | B | mcq | 3 | metric geometry - area | |
1563 | [{"role": "user", "question": "The diagram shows a solid with six triangular faces. At each vertex there is a number and two of the numbers are 1 and 5, as shown. For each face the sum of the numbers at the three vertices of each face is calculated, and all the sums are the same. What is the sum of all five numbers at ... | 17 | numeric | 4 | solid geometry | |
1564 | [{"role": "user", "question": "In each of the squares in the grid, one of the letters $P, Q, R$ and $S$ must be entered in such a way that adjacent squares (whether connected by an edge or just a corner) do not contain the same letter. Some of the letters have already been entered as shown.\nWhat are the possibilities ... | D | mcq | 4 | logic | |
1565 | [{"role": "user", "question": "The diagram shows a regular 9-sided polygon (a nonagon or an enneagon) with two of the sides extended to meet at the point $X$. What is the size of the acute angle at $X$ ? <image1>", "hint": "", "options": {"A": "$40^{\\circ}$", "B": "$45^{\\circ}$", "C": "$50^{\\circ}$", "D": "$55^{\\ci... | E | mcq | 5 | metric geometry - angle | |
1566 | [{"role": "user", "question": "The diagram shows the first three patterns in a sequence in which each pattern has a square hole in the middle. How many small shaded squares are needed to build the tenth pattern in the sequence?\n<image1>", "hint": "", "options": {}, "choices": []}] | 92 | numeric | 4 | algebra | |
1567 | [{"role": "user", "question": "An ant crawls carefully around the edges of a cube, starting at point $P$ and in the direction of the arrow. At the end of the first edge he chooses to go either left or right. He then turns the other way at the end of the next edge and continues like this, turning right or left alternate... | 6 | numeric | 4 | solid geometry | |
1568 | [{"role": "user", "question": "The fractions $\\frac{1}{3}$ and $\\frac{1}{5}$ have been placed on the\n<image1>\nnumber-line shown on the right. At which position should the fraction $\\frac{1}{4}$ be placed?", "hint": "", "options": {"A": "$a$", "B": "$b$", "C": "$C$", "D": "$d$", "E": "$e$"}, "choices": []}] | A | mcq | 4 | algebra | |
1569 | [{"role": "user", "question": "Three cuts are made through a large cube to make eight smaller cuboids, as shown in the diagram on the right. What is the ratio of the total surface area of these eight cuboids to the total surface area of the original cube?\n<image1>", "hint": "", "options": {"A": "$1: 1$", "B": "$4: 3$"... | D | mcq | 4 | solid geometry | |
157 | [{"role": "user", "question": "Susi folds a piece of paper in the middle. She stamps 2 holes.\n<image1>\nWhat does the piece of paper look like when she unfolds it again?\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | B | mcq | 2 | transformation geometry | |
1570 | [{"role": "user", "question": "The diagram shows the plan of a room. Adjoining walls are perpendicular to each other and the lengths of some of the walls are shown. What is the length of the perimeter of the room? <image1>", "hint": "", "options": {"A": "$3 a+4 b$", "B": "$3 a+8 b$", "C": "$6 a+4 b$", "D": "$6 a+6 b$",... | E | mcq | 2 | metric geometry - length | |
1571 | [{"role": "user", "question": "The diagram (which is not drawn to scale) shows a box measuring $5 \\mathrm{~cm}$ by $5 \\mathrm{~cm}$. There are seven bars in the box, each measuring $1 \\mathrm{~cm}$ by $3 \\mathrm{~cm}$. Kanga wants to slide the bars in the box so there is room for one more bar. What is the minimum n... | 3 | numeric | 4 | combinatorial geometry | |
1572 | [{"role": "user", "question": "A large square is divided into 4 equal-sized smaller squares. All the smaller squares are either shaded or unshaded. How many different ways are there to colour the large square? (Two colourings are considered to be the same if one can be rotated to look exactly like the other, as in the ... | 6 | numeric | 2 | combinatorics | |
1573 | [{"role": "user", "question": "The diagram shows a quadrilateral $A B C D$, in which $A D=B C$, $\\angle C A D=50^{\\circ}, \\angle A C D=65^{\\circ}$ and $\\angle A C B=70^{\\circ}$.\n<image1>\nWhat is the size of $\\angle A B C$ ?", "hint": "", "options": {"A": "$50^{\\circ}$", "B": "$55^{\\circ}$", "C": "$60^{\\circ... | B | mcq | 5 | metric geometry - angle | |
1574 | [{"role": "user", "question": "Andrea has wound some rope around a piece of wood, as shown in the diagram on the right. She rotates the wood $180^{\\circ}$ as shown by the arrow in the diagram. What does she see after the rotation?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E... | D | mcq | 3 | transformation geometry | |
1575 | [{"role": "user", "question": "The diagram (which is not drawn to scale) shows a rectangle $A B C D$ and a square $P Q R S$, in which $P Q=B C=6 \\mathrm{~cm}$ and $C D=10 \\mathrm{~cm} . P Q$ is parallel to $A B$. The shaded area is half the area of $A B C D$.\n<image1>\nWhat is the length, in $\\mathrm{cm}$, of $P X$... | 1 | numeric | 2 | metric geometry - length | |
1576 | [{"role": "user", "question": "The diagram shows a logo made entirely from semicircular arcs, each with a radius of $2 \\mathrm{~cm}, 4 \\mathrm{~cm}$ or $8 \\mathrm{~cm}$. What fraction of the logo is shaded? <image1>", "hint": "", "options": {"A": "$\\frac{1}{3}$", "B": "$\\frac{1}{4}$", "C": "$\\frac{1}{5}$", "D": "... | B | mcq | 3 | metric geometry - area | |
1577 | [{"role": "user", "question": "In the figure there are nine regions inside the five circles. All of the numbers from 1 to 9 are written in the regions, one to each region, so that the sum of the numbers inside each circle is 11 .\nWhich number must be written in the region with the question mark?\n<image1>", "hint": ""... | 5 | numeric | 2 | combinatorics | |
1578 | [{"role": "user", "question": "Mr Gagac goes to a barter market where the items are exchanged according to the table on the right. Mr Gagac wants to take away 1 goose, 1 turkey and 1 duck. What is the minimum number of hens that he needs to bring to the barter market?\n<image1>", "hint": "", "options": {}, "choices": [... | 16 | numeric | 4 | algebra | |
1579 | [{"role": "user", "question": "The diagram shows a large equilateral triangle divided into 36 small equilateral triangles, each with area $1 \\mathrm{~cm}^{2}$. What is the area of the shaded triangle, in $\\mathrm{cm}^{2}$ ? <image1>", "hint": "", "options": {}, "choices": []}] | 11 | numeric | 4 | combinatorial geometry | |
158 | [{"role": "user", "question": "Hansi sticks 12 cubes together to make this figure. He always puts one drop of glue between two cubes. How many drops of glue does he need?\n<image1>", "hint": "", "options": {}, "choices": []}] | 11 | numeric | 1 | solid geometry | |
1580 | [{"role": "user", "question": "The diagram on the right shows an L-shape made from four small squares. Ria wants to add an extra small square in order to form a shape with a line of symmetry. In how many different ways can she do this? <image1>", "hint": "", "options": {}, "choices": []}] | 3 | numeric | 4 | combinatorial geometry | |
1581 | [{"role": "user", "question": "The diagram shows three squares. The medium square is formed by joining the midpoints of the sides of the large square. The small square is formed by joining the midpoints of the sides of the medium square. The area of the small square is $6 \\mathrm{~cm}^{2}$. What is the difference betw... | D | mcq | 3 | metric geometry - area | |
1582 | [{"role": "user", "question": "Each region in the figure is to be coloured with one of four colours: red $(\\mathrm{R})$, green $(\\mathrm{G})$, orange $(\\mathrm{O})$ or yellow $(\\mathrm{Y})$. The colours of only three regions are shown. Any two regions that touch must have different colours. <image1> The colour of t... | A | mcq | 4 | logic | |
1583 | [{"role": "user", "question": "A square piece of paper is cut into six rectangular pieces as shown in the diagram. When the lengths of the perimeters of the six rectangular pieces are added together, the result is $120 \\mathrm{~cm}$. What is the area of the square piece of paper? <image1>", "hint": "", "options": {"A"... | D | mcq | 3 | metric geometry - area | |
1584 | [{"role": "user", "question": "Lina has placed two shapes on a $5 \\times 5$ board, as shown in the picture on the right. Which of the following five shapes should she place on the empty part of the board so that none of the remaining four shapes will fit in the empty space that is left? (The shapes may be rotated or t... | D | mcq | 4 | combinatorial geometry | |
1585 | [{"role": "user", "question": "The diagram on the right shows a square with side $3 \\mathrm{~cm}$ inside a square with side $7 \\mathrm{~cm}$ and another square with side $5 \\mathrm{~cm}$ which intersects the first two squares. What is the difference between the area of the black region and the total area of the grey... | D | mcq | 3 | metric geometry - area | |
1586 | [{"role": "user", "question": "The first diagram on the right shows a shape constructed from two rectangles. The lengths of two sides are marked: 11 and 13. The shape is cut into three parts and the parts are rearranged, as shown in the second diagram on the right. What is the length marked $x$ ?\n<image1>", "hint": ""... | 37 | numeric | 2 | metric geometry - length | |
1587 | [{"role": "user", "question": "Each of the nine paths in a park is $100 \\mathrm{~m}$ long. Ann wants to go from $X$ to $Y$ without going along any path more than once. What is the length of the longest route she can choose? <image1>", "hint": "", "options": {"A": "$900 \\mathrm{~m}$", "B": "$800 \\mathrm{~m}$", "C": "... | C | mcq | 3 | graph theory | |
1588 | [{"role": "user", "question": "The diagram (which $\\underline{\\text { is }}$ drawn to scale) shows two triangles. In how many ways can you choose two vertices, one in each triangle, so that the straight line through the two vertices does not cross either triangle? <image1>", "hint": "", "options": {}, "choices": []}] | 4 | numeric | 2 | combinatorics | |
1589 | [{"role": "user", "question": "Werner folds a sheet of paper as shown in the diagram and makes two straight cuts with a pair of scissors. He then opens up the paper again. Which of the following shapes cannot be the result? <image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, ... | D | mcq | 3 | transformation geometry | |
159 | [{"role": "user", "question": "The two markers with a question mark have the same number.\n<image1>\nWhich number do you have to put instead of the question mark so that the calculation is correct?", "hint": "", "options": {}, "choices": []}] | 3 | numeric | 1 | algebra | |
1590 | [{"role": "user", "question": "Mrs Gardner has beds for peas and strawberries in her rectangular garden. This year, by moving the boundary between them, she changed her rectangular pea bed to a square by lengthening one of its sides by 3 metres. As a result of this change, the area of the strawberry bed reduced by $15 ... | C | mcq | 3 | metric geometry - area | |
1591 | [{"role": "user", "question": "Barbara wants to complete the diagram below by inserting three numbers, one into each empty cell. She wants the sum of the first three numbers to be 100 , the sum of the middle three numbers to be 200 and the sum of the last three numbers to be 300 . What number should Barbara insert into... | 60 | numeric | 4 | algebra | |
1592 | [{"role": "user", "question": "In the figure, what is the value of $x$ ? <image1>", "hint": "", "options": {}, "choices": []}] | 51 | numeric | 5 | metric geometry - angle | |
1593 | [{"role": "user", "question": "Three small equilateral triangles of the same size are cut from the corners of a larger equilateral triangle with sides $6 \\mathrm{~cm}$ as shown. The sum of the perimeters of the three small triangles is equal to the perimeter of the remaining hexagon. What is the side-length of one of ... | D | mcq | 2 | metric geometry - length | |
1594 | [{"role": "user", "question": "A cube is being rolled on a plane so it turns around its edges. Its bottom face passes through the positions $1,2,3,4,5,6$ and 7 in that order, as shown. Which of these two positions were occupied by the same face of the cube? <image1>", "hint": "", "options": {"A": "1 and 7", "B": "1 and... | B | mcq | 4 | solid geometry | |
1595 | [{"role": "user", "question": "In the diagram, $W X Y Z$ is a square, $M$ is the midpoint of $W Z$ and $M N$ is perpendicular to $W Y$. What is the ratio of the area of the shaded triangle $M N Y$ to the area of the square? <image1>", "hint": "", "options": {"A": "1:6", "B": "1:5", "C": "7:36", "D": "3:16", "E": "7:40"... | D | mcq | 3 | metric geometry - area | |
1596 | [{"role": "user", "question": "A large triangle is divided into four smaller triangles and three quadrilaterals by three straight line segments. The sum of the perimeters of the three quadrilaterals is $25 \\mathrm{~cm}$. The sum of the perimeters of the four triangles is $20 \\mathrm{~cm}$. The perimeter of the origin... | C | mcq | 2 | metric geometry - length | |
1597 | [{"role": "user", "question": "Each cell of the $3 \\times 3$ grid shown has placed in it a positive number so that: in each row and each column, the product of the three numbers is equal to 1 ; and in each $2 \\times 2$ square, the product of the four numbers is equal to 2 . What number should be placed in the central... | 16 | numeric | 4 | logic | |
1598 | [{"role": "user", "question": "Ann has the square sheet of paper shown in the left-hand diagram. By cutting along lines of the square, she produces copies of the shape shown in the right-hand diagram. What is the smallest possible number of cells she can leave unused? <image1>", "hint": "", "options": {}, "choices": []... | 4 | numeric | 4 | combinatorial geometry | |
1599 | [{"role": "user", "question": "Olivia and a friend are playing a game of 'battleships' on a $5 \\times 5$ board. Olivia has already placed two ships as shown. She still has to place a $3 \\times 1$ ship so that it covers exactly three cells. No two ships can have a boundary point in common. How many positions are there... | 8 | numeric | 4 | combinatorial geometry | |
16 | [{"role": "user", "question": "How many points are there in the three unseen sides of dice?\n<image1>", "hint": "", "options": {}, "choices": []}] | 11 | numeric | 2 | arithmetic | |
160 | [{"role": "user", "question": "Max wants to complete the jigsaw shown. He has different pieces.\n<image1>\nWhich pieces does he have to use?\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | A | mcq | 1 | combinatorial geometry | |
1600 | [{"role": "user", "question": "In the diagram, $\\alpha=55^{\\circ}, \\beta=40^{\\circ}$ and $\\gamma=35^{\\circ}$. What is the value of $\\delta$ ? <image1>", "hint": "", "options": {"A": "$100^{\\circ}$", "B": "$105^{\\circ}$", "C": "$120^{\\circ}$", "D": "$125^{\\circ}$", "E": "$130^{\\circ}$"}, "choices": []}] | E | mcq | 5 | metric geometry - angle | |
1601 | [{"role": "user", "question": "The edges of rectangle $P Q R S$ are parallel to the coordinate axes. $P Q R S$ lies below the $x$-axis and to the right of the $y$-axis as shown in the diagram. The coordinates of $P, Q, R$ and $S$ are all integers. For each point, we calculate the value $(y$-coordinate $) \\div(x$-coord... | A | mcq | 3 | analytic geometry | |
1602 | [{"role": "user", "question": "In the $6 \\times 8$ grid shown, 24 cells are not intersected by either diagonal. When the diagonals of a $6 \\times 10$ grid are drawn, how many cells are not intersected by either diagonal? <image1>", "hint": "", "options": {}, "choices": []}] | 32 | numeric | 3 | analytic geometry | |
1603 | [{"role": "user", "question": "John has made a building of unit cubes standing on a $4 \\times 4$ grid. The diagram shows the number of cubes standing on each cell. When John looks horizontally at the building from behind, what does he see? <image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D":... | C | mcq | 4 | descriptive geometry | |
1604 | [{"role": "user", "question": "The diagram shows a shaded quadrilateral $P Q R S$ drawn on a grid. Each cell of the grid has sides of length $2 \\mathrm{~cm}$. What is the area of quadrilateral $P Q R S$ ? <image1>", "hint": "", "options": {"A": "$96 \\mathrm{~cm}^{2}$", "B": "$84 \\mathrm{~cm}^{2}$", "C": "$76 \\mathr... | B | mcq | 4 | combinatorial geometry | |
1605 | [{"role": "user", "question": "One of the following nets cannot be folded along the dashed lines shown to form a cube. Which one?\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | C | mcq | 4 | solid geometry | |
1606 | [{"role": "user", "question": "Four cars enter a roundabout at the same time, each one from a different direction, as shown in the diagram. Each car drives in a clockwise direction and leaves the roundabout before making a complete circuit. No two cars leave the roundabout by the same exit. How many different ways are ... | 9 | numeric | 2 | combinatorics | |
1607 | [{"role": "user", "question": "Each of the four vertices and six edges of the tetrahedron $P Q R S$ is marked with one of the numbers $1,2,3,4,5,6,7,8,9$ and 11 ; so the number 10 is not used. Each number is used exactly once. Each edge is marked with the sum of the numbers at the two vertices connected by that edge. E... | 5 | numeric | 4 | solid geometry | |
1608 | [{"role": "user", "question": "The area of rectangle $P Q R S$ is $10 \\mathrm{~cm}^{2}$. Points $M$ and $N$ are the midpoints of the sides $P Q$ and $S R$.\nWhat is the area in $\\mathrm{cm}^{2}$ of quadrilateral MRNP? <image1>", "hint": "", "options": {}, "choices": []}] | 5 | numeric | 3 | metric geometry - area | |
1609 | [{"role": "user", "question": "Rachel has several square pieces of paper of area $4 \\mathrm{~cm}^{2}$. She cuts each of them into smaller squares and right-angled triangles in the manner shown in the first diagram. She takes some of the pieces and makes the shape shown in the second diagram.\nWhat is the area in $\\ma... | 6 | numeric | 4 | combinatorial geometry | |
161 | [{"role": "user", "question": "Elvis has 6 triangles with this pattern\n<image1>\nWhich picture can he make with them?\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | A | mcq | 1 | combinatorial geometry | |
1610 | [{"role": "user", "question": "Carl built the shape shown using seven unit cubes. How many such cubes does he have to add to make a cube with edges of length 3 ? <image1>", "hint": "", "options": {}, "choices": []}] | 20 | numeric | 4 | solid geometry | |
1611 | [{"role": "user", "question": "In the diagram, the area of each circle is $1 \\mathrm{~cm}^{2}$. The area common to any two overlapping circles is $\\frac{1}{8} \\mathrm{~cm}^{2}$. What is the area of the region covered by the five circles? <image1>", "hint": "", "options": {"A": "$4 \\mathrm{~cm}^{2}$", "B": "$\\frac{... | B | mcq | 3 | metric geometry - area | |
1612 | [{"role": "user", "question": "The heart and the arrow are in the positions shown in the figure. At the same time the heart and the arrow start moving. The arrow moves three places clockwise and then stops and the heart moves four places anticlockwise and then stops. They repeat the same routine over and over again. Af... | E | mcq | 3 | transformation geometry | |
1613 | [{"role": "user", "question": "Five equal rectangles are placed inside a square with side $24 \\mathrm{~cm}$, as shown in the diagram. What is the area in $\\mathrm{cm}^{2}$ of one rectangle? <image1>", "hint": "", "options": {}, "choices": []}] | 32 | numeric | 3 | metric geometry - area | |
1614 | [{"role": "user", "question": "The diagram shows the triangle $P Q R$ in which $R H$ is a perpendicular height and $P S$ is the angle bisector at $P$. The obtuse angle between $R H$ and $P S$ is four times angle $S P Q$. What is angle $R P Q$ ? <image1>", "hint": "", "options": {"A": "$30^{\\circ}$", "B": "$45^{\\circ}... | C | mcq | 5 | metric geometry - angle | |
1615 | [{"role": "user", "question": "Janet enters all the digits from 1 to 9 in the cells of a $3 \\times 3$ table, so that each cell contains one digit. She has already entered 1,2,3 and 4, as shown. Two numbers are considered to be 'neighbours' if their cells share an edge. After entering all the numbers, she notices that ... | 27 | numeric | 4 | logic | |
1616 | [{"role": "user", "question": "A $5 \\times 5$ square is made from $1 \\times 1$ tiles, all with the same pattern, as shown. Any two adjacent tiles have the same colour along the shared edge. The perimeter of the $5 \\times 5$ square consists of black and white segments of length 1 . What is the smallest possible numbe... | 5 | numeric | 2 | metric geometry - length | |
1617 | [{"role": "user", "question": "Quadrilateral $P Q R S$ has right angles at vertices $P$ and $Q$ only. The numbers show the areas in $\\mathrm{cm}^{2}$ of two of the triangles. What is the area in $\\mathrm{cm}^{2}$ of $P Q R S$ ? <image1>", "hint": "", "options": {}, "choices": []}] | 45 | numeric | 3 | metric geometry - area | |
1618 | [{"role": "user", "question": "My umbrella has KANGAROO written on top as shown in the diagram. Which one of the following pictures also shows my umbrella?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | E | mcq | 4 | descriptive geometry | |
1619 | [{"role": "user", "question": "Four identical small rectangles are put together to form a large rectangle as shown. The length of a shorter side of each small rectangle is $10 \\mathrm{~cm}$. What is the length of a longer side of the large rectangle? <image1>", "hint": "", "options": {"A": "$50 \\mathrm{~cm}$", "B": "... | B | mcq | 2 | metric geometry - length | |
162 | [{"role": "user", "question": "Each of the children Ali, Lea, Josef, Vittorio and Sophie get a birthday cake. The number on top of the cake shows how old the child is. Lea is two years older than Josef, but one year younger than Ali. Vittorio is the youngest. Which cake belongs to Sophie?\n<image1>", "hint": "", "optio... | C | mcq | 3 | logic | |
1620 | [{"role": "user", "question": "In the diagram, the centre of the top square is directly above the common edge of the lower two squares. Each square has sides of length $1 \\mathrm{~cm}$. What is the area of the shaded region? <image1>", "hint": "", "options": {"A": "$\\frac{3}{4} \\mathrm{~cm}^{2}$", "B": "$\\frac{7}{8... | C | mcq | 3 | metric geometry - area | |
1621 | [{"role": "user", "question": "A bush has 10 branches. Each branch has either 5 leaves only or 2 leaves and 1 flower. Which of the following could be the total number of leaves the bush has? <image1>", "hint": "", "options": {"A": "45", "B": "39", "C": "37", "D": "31", "E": "None of A to D"}, "choices": []}] | E | mcq | 4 | algebra | |
1622 | [{"role": "user", "question": "One corner of a square is folded to its centre to form an irregular pentagon as shown in the diagram. The area of the square is 1 unit greater than the area of the pentagon. What is the area of the square? <image1>", "hint": "", "options": {}, "choices": []}] | 8 | numeric | 3 | transformation geometry | |
1623 | [{"role": "user", "question": "Luis wants to make a pattern by colouring the sides of the triangles shown in the diagram. He wants each triangle to have one red side, one green side and one blue side. Luis has already coloured some of the sides as shown. What colour can he use for the side marked $x$ ? <image1>", "hint... | A | mcq | 4 | logic | |
1624 | [{"role": "user", "question": "Ria wants to write a number in each of the seven bounded regions in the diagram. Two regions are neighbours if they share part of their boundary. The number in each region is to be the sum of the numbers in all of its neighbours. Ria has already written in two of the numbers, as shown.\nW... | 6 | numeric | 4 | logic | |
1625 | [{"role": "user", "question": "A square with area $30 \\mathrm{~cm}^{2}$ is divided in two by a diagonal and then into triangles as shown. The areas of some of these triangles are given in the diagram (which is not drawn to scale). Which part of the diagonal is the longest? <image1>", "hint": "", "options": {"A": "$a$"... | D | mcq | 2 | metric geometry - length | |
1626 | [{"role": "user", "question": "Andrew has seven pieces of wire of lengths $1 \\mathrm{~cm}, 2 \\mathrm{~cm}, 3 \\mathrm{~cm}, 4 \\mathrm{~cm}$, $5 \\mathrm{~cm}, 6 \\mathrm{~cm}$ and $7 \\mathrm{~cm}$. He bends some of the pieces to form a wire frame in the shape of a cube with edges of length $1 \\mathrm{~cm}$ without... | 4 | numeric | 4 | solid geometry | |
1627 | [{"role": "user", "question": "The triangle in the diagram contains a right angle. What is the sum of the other two marked angles on the diagram? <image1>", "hint": "", "options": {"A": "$150^{\\circ}$", "B": "$180^{\\circ}$", "C": "$270^{\\circ}$", "D": "$320^{\\circ}$", "E": "$360^{\\circ}$"}, "choices": []}] | C | mcq | 5 | metric geometry - angle | |
1628 | [{"role": "user", "question": "Joanna turns over the card shown about its lower edge and then about its right-hand edge, as indicated in the diagram.\n<image1>\nWhat does she see?\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | B | mcq | 3 | transformation geometry |
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