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values | question_type stringclasses 1
value | knowledge_concept stringlengths 8 177 | problem_id stringlengths 8 10 | step_key stringclasses 7
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|---|---|---|---|---|---|---|---|
1359 | [{"role": "user", "question": "As shown in the figure, triangle ABC is folded along the straight line DE so that point B coincides with point A. Given that AD + CD = 12 cm, what are the lengths of BC and AB in cm, respectively?", "hint": "", "options": {"A": "10, 8", "B": "12, 8", "C": "15, 9", "D": "17, 10", "E": "No ... | B | mcq | Folding Problems of Figures | 3stpes_114 | 3steps_2 | |
136 | [{"role": "user", "question": "In the diagram, the line segment that is perpendicular to OA is ( )", "hint": "", "options": {"A": "OB", "B": "OC", "C": "OD", "D": "No correct answer"}, "choices": []}] | B | mcq | perpendicularity | 2steps_136 | 2steps_1 | |
1360 | [{"role": "user", "question": "A rectangular cuboid of wood is shown in the figure. After cutting it into 5 segments, the surface area increased by 40 dm². What is the area of the rectangular side ABCD of this prism in dm²?", "hint": "", "options": {"A": "10", "B": "5", "C": "15", "D": "17", "E": "No correct answer"}, ... | B | mcq | Combining and Dividing Solids | 3stpes_115 | 3steps_2 | |
1361 | [{"role": "user", "question": "As shown in the figure, the three-dimensional shape is composed of a rectangular cuboid and a cube. What is the surface area of the cube on the right in cm²?", "hint": "", "options": {"A": "144", "B": "208", "C": "96", "D": "224", "E": "No correct answer"}, "choices": []}] | C | mcq | Surface Area of Cubes | 3stpes_116 | 3steps_2 | |
1362 | [{"role": "user", "question": "As shown in the figure, the radius of the sector coincides with the diameter of the circle. The area of the sector is half of the area of the circle. What is the central angle of the sector? ( )°", "hint": "", "options": {"A": "30", "B": "45", "C": "60", "D": "90", "E": "No correct answer... | B | mcq | Area of Sectors | 3stpes_117 | 3steps_2 | |
1363 | [{"role": "user", "question": "As shown in the figure, the sector is symmetrical about the line l1. What is the measure of ∠AOB?", "hint": "", "options": {"A": "90°", "B": "100°", "C": "120°", "D": "135°", "E": "No correct answer"}, "choices": []}] | C | mcq | Calculation and Comparison of Angles | 3stpes_118 | 3steps_2 | |
1364 | [{"role": "user", "question": "As shown in the figure, in the rectangle ABGH, fold along DC. What is the measure of ∠BCD and ∠DCF?", "hint": "", "options": {"A": "60°", "B": "45°", "C": "65°", "D": "75°", "E": "No correct answer"}, "choices": []}] | D | mcq | Calculation and Comparison of Angles | 3stpes_119 | 3steps_2 | |
1365 | [{"role": "user", "question": "In the quadrilateral ABCD shown in the figure, what is the area of triangle ABD in cm²?", "hint": "", "options": {"A": "12", "B": "24", "C": "6", "D": "9", "E": "No correct answer"}, "choices": []}] | C | mcq | Area of Triangles | 3stpes_120 | 3steps_2 | |
1366 | [{"role": "user", "question": "In the square BEFG shown in the figure, what is the degree measure of ∠CBG? ", "hint": "", "options": {"A": "30°", "B": "60°", "C": "45°", "D": "90°", "E": "No correct answer"}, "choices": []}] | B | mcq | Properties and Understanding of Squares | 3stpes_121 | 3steps_2 | |
1367 | [{"role": "user", "question": "As shown in the figure, the area of parallelogram ABCD is 240 cm². What is the length of CP in centimeters?", "hint": "", "options": {"A": "12", "B": "13", "C": "15", "D": "20", "E": "No correct answer"}, "choices": []}] | A | mcq | Area of Parallelograms | 3stpes_122 | 3steps_2 | |
1368 | [{"role": "user", "question": "In the parallelogram ABCD shown in the figure, point D and point D' are symmetric with respect to the axis CP, and CD = CD'. The perimeter of triangle CDD' is 26 cm. What is the length of CD in cm?", "hint": "", "options": {"A": "8", "B": "10", "C": "5", "D": "12", "E": "No correct answer... | A | mcq | Perimeter of Triangles | 3stpes_123 | 3steps_2 | |
1369 | [{"role": "user", "question": "In the parallelogram ABCD shown in the figure, what is the positional relationship between AB and CD?", "hint": "", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Cannot be determined", "D": "No correct answer"}, "choices": []}] | A | mcq | Properties and Understanding of Parallelograms | 3stpes_124 | 3steps_2 | |
137 | [{"role": "user", "question": "To draw the shortest line segment from point E to side b, the relationship between this line segment and side b is ( )", "hint": "", "options": {"A": "Perpendicular", "B": "Parallel", "C": "Cannot be determined", "D": "No correct answer"}, "choices": []}] | A | mcq | perpendicularity | 2steps_137 | 2steps_1 | |
1370 | [{"role": "user", "question": "In the right triangle ABC shown in the figure, there is a triangle ABE. What is the height of triangle ABE from the base BE in cm?", "hint": "", "options": {"A": "2", "B": "3", "C": "4", "D": "Cannot be determined", "E": "No correct answer"}, "choices": []}] | C | mcq | perpendicularity | 3stpes_125 | 3steps_2 | |
1371 | [{"role": "user", "question": "As shown in the figure, BD is parallel to EG. What is the relationship between the areas of triangle EDG and triangle BEG?", "hint": "", "options": {"A": "Equal", "B": "The area of triangle EDG is twice the area of triangle BEG", "C": "The area of triangle EDG is twice the area of triangl... | A | mcq | Parallel | 3stpes_126 | 3steps_2 | |
1372 | [{"role": "user", "question": "For the rectangular cuboid shown in the figure, the left side is its expanded view. To travel the shortest distance from point A to point F in this rectangular cuboid, which of the following routes should be taken?", "hint": "", "options": {"A": "A->B->E->F", "B": "A->B->D->F", "C": "A->C... | D | mcq | Distance Between Two Points | 3stpes_127 | 3steps_2 | |
1373 | [{"role": "user", "question": "As shown in the figure, the right trapezoid ABCD has a base AB, and the area of the trapezoid is 9 cm². What is the length of AB in cm?", "hint": "", "options": {"A": "2", "B": "3", "C": "4", "D": "5", "E": "No correct answer"}, "choices": []}] | D | mcq | Area of Trapezoids | 3stpes_128 | 3steps_2 | |
1374 | [{"role": "user", "question": "A point A (4, 0) on a square moves along with the square. If the square is translated two units to the right and two units up, which new square is obtained? Which point corresponds to A' in the new square?", "hint": "", "options": {"A": "⑤,A", "B": "④,B", "C": "②,D", "D": "①,D", "E": "Can... | D | mcq | Translation | 3stpes_129 | 3steps_2 | |
1375 | [{"role": "user", "question": "The expanded view of a rectangular cuboid is shown in the figure. What are the length, width, and height of this rectangular cuboid? (Unit: cm)", "hint": "", "options": {"A": "5, 4, 3", "B": "4, 4, 4", "C": "4, 4, 3", "D": "7, 4, 3", "E": "No correct answer"}, "choices": []}] | C | mcq | Expanded View of Rectangular Cuboids | 3stpes_130 | 3steps_2 | |
1376 | [{"role": "user", "question": "As shown in the figure, the equilateral triangle ABC is composed of 16 smaller equilateral triangles tiled together. What is the side length of triangle ABC in cm?", "hint": "", "options": {"A": "12", "B": "16", "C": "18", "D": "9", "E": "No correct answer"}, "choices": []}] | A | mcq | Tessellation of Figures | 3stpes_131 | 3steps_2 | |
1377 | [{"role": "user", "question": "As shown in the figure, triangle ABC and triangle ACD are joined together, with point B and point D being symmetric with respect to the axis AC. What is the positional relationship between BD and AC?", "hint": "", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Cannot be determin... | B | mcq | Axial Symmetry | 3stpes_132 | 3steps_2 | |
1378 | [{"role": "user", "question": "As shown in the figure, triangle ABC and triangle ACD are identical equilateral triangles. After joining the two triangles, the perimeter of the resulting shape is 4 cm less than twice the perimeter of triangle ABC. What is the side length of these equilateral triangles in cm?", "hint": "... | D | mcq | Combining Plane Figures | 3stpes_133 | 3steps_2 | |
1379 | [{"role": "user", "question": "In the rectangular cuboid's unfolded diagram shown, the perimeter of rectangle ABCD is 36 cm. What are the length, width, and height of this rectangular cuboid in cm?", "hint": "", "options": {"A": "10, 8, 4", "B": "14, 8, 4", "C": "18, 8, 4", "D": "10, 6, 4", "E": "No correct answer"}, "... | A | mcq | Expanded View of Rectangular Cuboids | 3stpes_134 | 3steps_2 | |
138 | [{"role": "user", "question": "From point E to side b, the shortest line segment drawn has what relationship to side B? ", "hint": "", "options": {"A": "Perpendicular", "B": "Parallel", "C": "Cannot be determined", "D": "No correct answer"}, "choices": []}] | A | mcq | perpendicularity | 2steps_138 | 2steps_1 | |
1380 | [{"role": "user", "question": "As shown in the figure, the parallelogram ABCD is formed by joining two identical isosceles trapezoids. What is the length of AB? ( ) cm", "hint": "", "options": {"A": "8", "B": "4", "C": "2", "D": "Cannot be determined", "E": "No correct answer"}, "choices": []}] | C | mcq | Properties and Understanding of Trapezoids | 3stpes_135 | 3steps_2 | |
1381 | [{"role": "user", "question": "The perimeter of rectangle ABCD is 12 cm. The shaded area shown in the figure consists of two identical circles. What is the radius of a single circle ( ) cm?", "hint": "", "options": {"A": "3", "B": "2", "C": "1", "D": "Cannot be determined", "E": "No correct answer"}, "choices": []}] | C | mcq | Perimeter of Rectangles | 3stpes_136 | 3steps_2 | |
1382 | [{"role": "user", "question": "As shown in the figure, triangle ABC in rectangle ABCD is translated to the right to the position of triangle DCE, forming quadrilateral ACED. The perimeter of quadrilateral ACED is 2 cm more than the perimeter of rectangle ABCD. What is the length of AC in cm?", "hint": "", "options": {"... | B | mcq | Combining Plane Figures | 3stpes_137 | 3steps_2 | |
1383 | [{"role": "user", "question": "As shown in the diagram, there are multiple paths from point A to point C. Which is the shortest path?", "hint": "", "options": {"A": "A->D->C", "B": "A->B->C", "C": "A->C", "D": "A->F->C", "E": "No correct answer"}, "choices": []}] | C | mcq | Distance Between Two Points | 3stpes_138 | 3steps_2 | |
1384 | [{"role": "user", "question": "Given that Jack travels from point A to point B along a 1/4 circle arc, what is the radius of the circle in units?", "hint": "", "options": {"A": "4", "B": "3", "C": "2", "D": "1", "E": "No correct answer"}, "choices": []}] | C | mcq | Circumference of Circles | 3stpes_139 | 3steps_2 | |
1385 | [{"role": "user", "question": "As shown in the figure, the triangle formed by points A, B, and C is an equilateral triangle. What is the length of route ② from point A to point B? ( ) m", "hint": "", "options": {"A": "10", "B": "20", "C": "15.7", "D": "Cannot be determined", "E": "No correct answer"}, "choices": []}] | B | mcq | Properties and Understanding of Triangles | 3stpes_140 | 3steps_2 | |
1386 | [{"role": "user", "question": "In right triangle ABC, AC = 5 cm. When it is rotated counterclockwise around point A to form triangle ADE, points B and C trace out arcs BD and CE, respectively. What are the central angles of these arcs, and what is the length of DE?", "hint": "", "options": {"A": "90°, 3 cm", "B": "90°,... | A | mcq | Rotation | 3stpes_141 | 3steps_2 | |
1387 | [{"role": "user", "question": "In the unfolded diagram of the rectangular cuboid shown, which face among a, b, c, and d has the most circles drawn on it? ( )", "hint": "", "options": {"A": "a", "B": "b", "C": "c", "D": "d", "E": "No correct answer"}, "choices": []}] | D | mcq | Observing Figures | 3stpes_142 | 3steps_2 | |
1388 | [{"role": "user", "question": "As shown in the figure, the isosceles trapezoid ABCD has two base angles of 45°. Now extend BA and CD to meet at point O. From point O, draw OF perpendicular to BC at point F, and perpendicular to AD at point E. Given OE = 2 cm, OF = 4 cm, AE = 2 cm, and BF = 4 cm. This trapezoid is the f... | C | mcq | Observing Figures | 3stpes_143 | 3steps_2 | |
1389 | [{"role": "user", "question": "As shown in the figure, a cylindrical container holds 37.68 cm³ of water. The base area of a small rectangular iron block is 3.14 cm². When these small rectangular blocks are vertically stacked and submerged in the water one by one as shown, the top surface of the fourth block is just lev... | A | mcq | Volume and Capacity of Rectangular Cuboids | 3stpes_144 | 3steps_2 | |
139 | [{"role": "user", "question": "As shown in the diagram, two triangular boards are arranged to form a shape. ∠1 + ∠2 = （ ）", "hint": "", "options": {"A": "120°", "B": "160°", "C": "145°", "D": "90°", "E": "No correct answer"}, "choices": []}] | D | mcq | perpendicularity | 2steps_139 | 2steps_1 | |
1390 | [{"role": "user", "question": "If you want to use the rectangular cuboid tiles shown in the figure to pave the floor, what is the area of the largest face of the rectangular cuboid tile in cm²?", "hint": "", "options": {"A": "48", "B": "16", "C": "64", "D": "68", "E": "No correct answer"}, "choices": []}] | A | mcq | Properties and Understanding of Rectangular Cuboids | 3stpes_145 | 3steps_2 | |
1391 | [{"role": "user", "question": "To use the water container shaped like a cone as shown in the figure to fetch water, what is its volume in cm³?(Use π = 3.14)", "hint": "", "options": {"A": "3140", "B": "2056", "C": "6280", "D": "2093.33", "E": "No correct answer"}, "choices": []}] | D | mcq | Volume and Capacity of Cones | 3stpes_146 | 3steps_2 | |
1392 | [{"role": "user", "question": "As shown in the figure, the shape can be used as a tessellation. What is the degree measure of one of its interior angles? ", "hint": "", "options": {"A": "90°", "B": "30°", "C": "60°", "D": "45°", "E": "No correct answer"}, "choices": []}] | C | mcq | Properties and Understanding of Triangles | 3stpes_147 | 3steps_2 | |
1393 | [{"role": "user", "question": "As shown in the figure, the shape can be used as a tessellation. What is the degree measure of one of its interior angles?", "hint": "", "options": {"A": "90°", "B": "30°", "C": "60°", "D": "45°", "E": "No correct answer"}, "choices": []}] | A | mcq | Properties and Understanding of Triangles | 3stpes_148 | 3steps_2 | |
1394 | [{"role": "user", "question": "As shown in the figure, A, B, and C are three points on the straight line l. There are three line segments in the figure. Using each of these line segments as the side length, squares are drawn. What is the sum of the areas of all the squares? ( ) cm²", "hint": "", "options": {"A": "900",... | C | mcq | Area of Squares | 3stpes_149 | 3steps_2 | |
1395 | [{"role": "user", "question": "As shown in the figure, A, B, and C are three points on the straight line l. There are three line segments in the figure. Using each line segment as the diameter, draw a circle. What is the sum of the areas of all the circles? (π is taken as 3.14)", "hint": "", "options": {"A": "706.5", "... | D | mcq | Area of Circles | 3stpes_150 | 3steps_2 | |
1396 | [{"role": "user", "question": "As shown in the figure, A, B, and C are three points on the straight line l. Using the lengths of the three line segments in the figure as the length, width, and height of a rectangular cuboid, what is the volume of the rectangular cuboid in cm³?", "hint": "", "options": {"A": "210000", "... | A | mcq | Volume and Capacity of Rectangular Cuboids | 3stpes_151 | 3steps_2 | |
1397 | [{"role": "user", "question": "As shown in the figure, point A is to the northeast of point B, point C is to the south by west 15° of point A, and point A is to the north by west 15° of point D. What are the degrees of ∠CAE and ∠DAE respectively?", "hint": "", "options": {"A": "15°, 75°", "B": "15°, 45°", "C": "45°, 1... | A | mcq | Describing Simple Routes Based on Direction and Distance | 3stpes_152 | 3steps_2 | |
1398 | [{"role": "user", "question": "In the diagram, one unit of length represents 1 meter. Point A is to the northeast of point O, and point O is to the northwest of point B. The distances OA and OB are equal. Given that the area of the sector with ∠AOB as the central angle and OA as the radius is 3.14 m², what is the radiu... | B | mcq | Area of Sectors | 3stpes_153 | 3steps_2 | |
1399 | [{"role": "user", "question": "Below is a top view of a cylindrical pool with a depth of 1m. In the diagram, one unit length represents 1m. What is the volume of this cylindrical pool in cubic meters?(π = 3.14)", "hint": "", "options": {"A": "6.28", "B": "12.56", "C": "20.56", "D": "Cannot be determined", "E": "No corr... | B | mcq | Volume and Capacity of Cylinders | 3stpes_154 | 3steps_2 | |
14 | [{"role": "user", "question": "As shown in the diagram, A, B, C, D are four cubes. From the front view, the object to the right of A is ( )", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "No correct answer"}, "choices": []}] | C | mcq | Left-Right Position | 2steps_14 | 2steps_1 | |
140 | [{"role": "user", "question": "As shown in the diagram, there is a right angle turn located at ( )", "hint": "", "options": {"A": "Point A", "B": "Point B", "C": "Point C", "D": "Point D", "E": "No correct answer"}, "choices": []}] | C | mcq | perpendicularity | 2steps_140 | 2steps_1 | |
1400 | [{"role": "user", "question": "Below is a top-down view of a circular water surface. In the diagram, one unit length represents 1 meter. What is the value of OA·OB = ()?", "hint": "", "options": {"A": "1", "B": "2", "C": "4", "D": "Cannot be determined", "E": "No correct answer"}, "choices": []}] | B | mcq | Area of Triangles | 3stpes_155 | 3steps_2 | |
1401 | [{"role": "user", "question": "The points below can be represented by the coordinates shown in the figure. Point A is southwest of point B, and point E is southeast of point B. What is the measure of ∠ABE?", "hint": "", "options": {"A": "45°", "B": "60°", "C": "75°", "D": "90°", "E": "No correct answer"}, "choices": []... | D | mcq | Determining the Positions of Objects Based on Direction, Angle, and Distance | 3stpes_156 | 3steps_2 | |
1402 | [{"role": "user", "question": "As shown in the figure, the area of the rectangular iron sheet is 48 cm². A expanded view of a cube is cut out from it, with face A removed and folded into an open-top square iron box. It is found that there is a hole in face ⑤. If this iron box is used to hold water, the maximum height o... | C | mcq | Expanded View of Cubes | 3stpes_157 | 3steps_2 | |
1403 | [{"role": "user", "question": "As shown in the figure, it is known that points A, B, and C are collinear, AB = BC = 3m, point D is directly east of A, point D is directly south of B, and AD = BD. What is the measure of ∠BAD?", "hint": "", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°", "E": "No correct answ... | B | mcq | Properties and Understanding of Triangles | 3stpes_158 | 3steps_2 | |
1404 | [{"role": "user", "question": "As shown in the figure, point A is directly north of point O, point B is southeast of point A, and the distance between A and B is 6 meters. Point B is directly east of point O. Translate triangle ABO such that the translated point O' is directly east of point A and directly north of poin... | A | mcq | Describing Simple Routes Based on Direction and Distance | 3stpes_159 | 3steps_2 | |
1405 | [{"role": "user", "question": "As shown in the figure, if the line segment AB is rotated 90 degrees clockwise around point A, what will be the resulting line segment?", "hint": "", "options": {"A": "⑤", "B": "④", "C": "③", "D": "②", "E": "①; F. Cannot be determined; G. No correct answer"}, "choices": []}] | A | mcq | Rotation | 3stpes_160 | 3steps_2 | |
1406 | [{"role": "user", "question": "As shown in the figure, if the right angle with vertex B is translated upward by three units, what will it become?", "hint": "", "options": {"A": "B1", "B": "B2", "C": "B3", "D": "Cannot be determined", "E": "No correct answer"}, "choices": []}] | B | mcq | Translation | 3stpes_161 | 3steps_2 | |
1407 | [{"role": "user", "question": "As shown in the figure, ABCD are four points on a map. It is known that C is directly south of B, and A is directly west of C. AB = 6m. The line segment BD can be obtained by rotating line segment AB counterclockwise around point B by 130°. Then BD = () cm, and ∠ABD = ()°?", "hint": "", "... | D | mcq | Rotation | 3stpes_162 | 3steps_2 | |
1408 | [{"role": "user", "question": "As shown in the figure, the diagram is the unfolded view of a cube. It is known that when the cube is assembled, face C is on top, and from a top-down perspective, face A is facing north. Face B can be seen in the right-side view. What is the orientation of face B?", "hint": "", "options"... | A | mcq | Cardinal Directions (East, South, West, North) | 3stpes_163 | 3steps_2 | |
1409 | [{"role": "user", "question": "As shown in the figure, point C is in the northeast direction from point A, and point C is in the north by west 50° direction from point B. What is ∠2 equal to in degrees?", "hint": "", "options": {"A": "50°", "B": "45°", "C": "60°", "D": "90°", "E": "No correct answer"}, "choices": []}] | A | mcq | Determining the Positions of Objects Based on Direction, Angle, and Distance | 3stpes_164 | 3steps_2 | |
141 | [{"role": "user", "question": "How many line segments are there in total on line segment AD? ", "hint": "", "options": {"A": "1", "B": "6", "C": "7", "D": "8", "E": "No correct answer"}, "choices": []}] | B | mcq | Understanding Line Segments, Lines, and Rays | 2steps_141 | 2steps_1 | |
1410 | [{"role": "user", "question": "As shown in the figure, there is a circular flower bed. Mary walked from the northernmost point of the flower bed along the edge to the easternmost point, taking a total of 80 steps. Given that Mary's average step length is 0.628m, what is the radius of the circle in meters?(π = 3.14)", "... | B | mcq | Circumference of Circles | 3stpes_165 | 3steps_2 | |
1411 | [{"role": "user", "question": "As shown in the figure, a circle is drawn with the vertex C of a square as the center. The circumference of the circle is 25.12 cm. The length of the arc EF corresponding to the central angle ∠ECF is () cm.", "hint": "", "options": {"A": "50.24", "B": "25.12", "C": "12.56", "D": "6.28", "... | D | mcq | Understanding Sectors | 3stpes_1 | 3steps_3 | |
1412 | [{"role": "user", "question": "The height of the cylindrical water storage container is as shown in the figure. Its height is equivalent to ( ) meters.", "hint": "", "options": {"A": "0.8", "B": "0.08", "C": "16", "D": "8", "E": "No correct answer"}, "choices": []}] | B | mcq | Conversion Rates and Calculations Between Length Units | 3stpes_2 | 3steps_3 | |
1413 | [{"role": "user", "question": "As shown in the figure, the perimeter of the isosceles trapezoid ABCD is () cm.", "hint": "", "options": {"A": "4", "B": "6", "C": "8", "D": "10", "E": "No correct answer"}, "choices": []}] | D | mcq | Perimeter of Trapezoids | 3stpes_3 | 3steps_3 | |
1414 | [{"role": "user", "question": "As shown in the figure, the diagonals of square DFEO are OD and EF. What is the area of square DFEO? ( ) cm²", "hint": "", "options": {"A": "0.5", "B": "3", "C": "2", "D": "1", "E": "No correct answer"}, "choices": []}] | A | mcq | Area of Squares | 3stpes_4 | 3steps_3 | |
1415 | [{"role": "user", "question": "As shown in the figure, the area of triangle BCE is () cm².", "hint": "", "options": {"A": "6", "B": "3", "C": "2", "D": "1", "E": "No correct answer"}, "choices": []}] | A | mcq | Area of Triangles | 3stpes_5 | 3steps_3 | |
1416 | [{"role": "user", "question": "As shown in the figure, Mike's initial position is at point A. He walks 5 meters north to reach point B, then walks 5 meters east to reach point C. In which direction is point C from point A?", "hint": "", "options": {"A": "North by west 45°", "B": "South by east 45°", "C": "North by east... | C | mcq | Southeast, Southwest, Northeast, Northwest Directions | 3stpes_6 | 3steps_3 | |
1417 | [{"role": "user", "question": "As shown in the figure, the height of the cone is OA, and the diameter of the base is BC. What is the volume of the cone? ( ) cm³", "hint": "", "options": {"A": "3π", "B": "1π", "C": "2π", "D": "No correct answer"}, "choices": []}] | B | mcq | Volume and Capacity of Cones | 3stpes_7 | 3steps_3 | |
1418 | [{"role": "user", "question": "In parallelogram ABCE, the lengths of AF and AE are as shown in the figure. What is the area of parallelogram ABCE? ( ) cm²", "hint": "", "options": {"A": "45", "B": "60", "C": "72", "D": "90", "E": "No correct answer"}, "choices": []}] | C | mcq | Area of Parallelograms | 3stpes_8 | 3steps_3 | |
1419 | [{"role": "user", "question": "As shown in the figure, the radius of circle B is marked, and point A is on circle B. A and B are the centers of two circles, and point P is the intersection point of the two circles. At this time, the arc length of segment PA is ( ) cm.", "hint": "", "options": {"A": "3π", "B": "1π", "C"... | B | mcq | Understanding Sectors | 3stpes_9 | 3steps_3 | |
142 | [{"role": "user", "question": "How many line segments are contained within line segment BF? ", "hint": "", "options": {"A": "7", "B": "9", "C": "8", "D": "10", "E": "No correct answer"}, "choices": []}] | D | mcq | Understanding Line Segments, Lines, and Rays | 2steps_142 | 2steps_1 | |
1420 | [{"role": "user", "question": "As shown in the figure, a circle is drawn with center C, and points A and B are exactly on the circle. The lengths of BC, AC, and CD are as shown in the figure, and AB = CD. What is the measure of ∠ABC?", "hint": "", "options": {"A": "45°", "B": "60°", "C": "72°", "D": "90°", "E": "No cor... | B | mcq | Properties and Understanding of Triangles | 3stpes_10 | 3steps_3 | |
1421 | [{"role": "user", "question": "Given the length of the diagonal BG of square FBHG, what is the area of square FBHG? ( ) cm² ", "hint": "", "options": {"A": "16", "B": "8", "C": "6", "D": "4", "E": "No correct answer"}, "choices": []}] | B | mcq | Area of Squares | 3stpes_11 | 3steps_3 | |
1422 | [{"role": "user", "question": "As shown in the figure, the surface area of the following cylinder is () cm².", "hint": "", "options": {"A": "24π", "B": "16π", "C": "32π", "D": "No correct answer"}, "choices": []}] | C | mcq | Surface Area of Cylinders | 3stpes_12 | 3steps_3 | |
1423 | [{"role": "user", "question": "The lateral view of the cylinder is a rectangle ABCD as shown in the figure. Therefore, the front view of this cylinder is a ().", "hint": "", "options": {"A": "Cannot be determined", "B": "Circle", "C": "Rectangle", "D": "Square", "E": "No correct answer"}, "choices": []}] | D | mcq | Properties of Cylinders | 3stpes_13 | 3steps_3 | |
1424 | [{"role": "user", "question": "As shown in the figure, the rectangular cuboid has a square base. What is the surface area of the rectangular cuboid? ( ) cm²", "hint": "", "options": {"A": "16", "B": "12", "C": "6", "D": "4", "E": "No correct answer"}, "choices": []}] | A | mcq | Surface Area of Rectangular Cuboids | 3stpes_14 | 3steps_3 | |
1425 | [{"role": "user", "question": "As shown in the figure, the rectangular cuboid can be split into two identical cubes. What is the surface area of the rectangular cuboid? ( ) cm²", "hint": "", "options": {"A": "48", "B": "40", "C": "32", "D": "20", "E": "No correct answer"}, "choices": []}] | B | mcq | Surface Area of Rectangular Cuboids | 3stpes_15 | 3steps_3 | |
1426 | [{"role": "user", "question": "As shown in the figure, the front view of the cone is the isosceles triangle below. The area of this triangle is () cm².", "hint": "", "options": {"A": "4", "B": "3", "C": "2", "D": "1", "E": "No correct answer"}, "choices": []}] | B | mcq | Area of Triangles | 3stpes_16 | 3steps_3 | |
1427 | [{"role": "user", "question": "The height and the radius of the base of a cone are shown in the diagram. What is the volume of this cone in cm³?", "hint": "", "options": {"A": "24π", "B": "16π", "C": "32π", "D": "64π", "E": "No correct answer"}, "choices": []}] | D | mcq | Volume and Capacity of Cones | 3stpes_17 | 3steps_3 | |
1428 | [{"role": "user", "question": "The radius of the sector is shown in the figure, and the central angle is 90°. What is the area of triangle ABC? ( ) cm²", "hint": "", "options": {"A": "4", "B": "3", "C": "2", "D": "1", "E": "No correct answer"}, "choices": []}] | C | mcq | Area of Triangles | 3stpes_18 | 3steps_3 | |
1429 | [{"role": "user", "question": "As shown in the figure, quadrilateral ABCD is a parallelogram. What is the perimeter of this parallelogram in cm? ", "hint": "", "options": {"A": "48", "B": "40", "C": "32", "D": "20", "E": "No correct answer"}, "choices": []}] | A | mcq | Perimeter of Parallelograms | 3stpes_19 | 3steps_3 | |
143 | [{"role": "user", "question": "As shown in the diagram, only one of the following is a line segment. Which one is it?", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "No correct answer"}, "choices": []}] | B | mcq | Understanding Line Segments, Lines, and Rays | 2steps_143 | 2steps_1 | |
1430 | [{"role": "user", "question": "As shown in the figure, DC = AD = AB, and quadrilateral ABED is a parallelogram. What is the relationship between the lengths of DE and AD? ", "hint": "", "options": {"A": "DE=AD", "B": "DE>AD", "C": "DE<AD", "D": "No correct answer"}, "choices": []}] | A | mcq | Properties and Understanding of Parallelograms | 3stpes_20 | 3steps_3 | |
1431 | [{"role": "user", "question": "A rectangular steel plate is shown in the figure. The shaded part obtained by cutting can be used to make a cylinder. The area of the circular shaded part is 12.56 cm². What is the volume of this cylinder in cm³?(Use π = 3.14)", "hint": "", "options": {"A": "50.24", "B": "25.12", "C": "12... | A | mcq | Volume and Capacity of Cylinders | 3stpes_21 | 3steps_3 | |
1432 | [{"role": "user", "question": "As shown in the figure, triangle ABC is the front view of a cone. The base area of the cone is 28.26 cm². What is the volume of the cone ( ) cm³?", "hint": "", "options": {"A": "50.24", "B": "37.68", "C": "125.6", "D": "62.8", "E": "No correct answer"}, "choices": []}] | B | mcq | Volume and Capacity of Cones | 3stpes_22 | 3steps_3 | |
1433 | [{"role": "user", "question": "As shown in the figure, two identical largest circles can be cut out from the rectangular paper. What is the perimeter of the rectangle ABCD? (Use π = 3.14) ( ) cm", "hint": "", "options": {"A": "48", "B": "40", "C": "32", "D": "24", "E": "No correct answer"}, "choices": []}] | D | mcq | Perimeter of Rectangles | 3stpes_23 | 3steps_3 | |
1434 | [{"role": "user", "question": "As shown in the figure, the area of square ABCD is 16 cm². A circle with a radius of 2 cm is drawn inside the square. The area of the shaded region S1 in the figure is 0.86 cm². Then, using point A as the center and AB as the radius, a sector ABD is drawn, forming another irregular shaded... | D | mcq | Area of Sectors | 3stpes_24 | 3steps_3 | |
1435 | [{"role": "user", "question": "As shown in the figure, triangle ABC is an isosceles triangle, ∠B = ( )°", "hint": "", "options": {"A": "30", "B": "60", "C": "120", "D": "150", "E": "No correct answer"}, "choices": []}] | C | mcq | Sum of Interior Angles of Triangles | 3stpes_25 | 3steps_3 | |
1436 | [{"role": "user", "question": "As shown in the figure, quadrilateral ABDE is a rectangle. What is the length of CD in cm?", "hint": "", "options": {"A": "5", "B": "4", "C": "3", "D": "2", "E": "No correct answer"}, "choices": []}] | A | mcq | Properties and Understanding of Rectangles | 3stpes_26 | 3steps_3 | |
1437 | [{"role": "user", "question": "As shown in the figure, DAE and CBE are two sectors with radii AD and BC, respectively. What is the perimeter of rectangle ABCD? ( ) cm", "hint": "", "options": {"A": "16", "B": "12", "C": "6", "D": "4", "E": "No correct answer"}, "choices": []}] | B | mcq | Perimeter of Rectangles | 3stpes_27 | 3steps_3 | |
1438 | [{"role": "user", "question": "A rectangular cuboid with a square base, if its height is increased by 4 cm, it becomes a cube. What is the original surface area of the rectangular cuboid in cm²?", "hint": "", "options": {"A": "512", "B": "64", "C": "128", "D": "256", "E": "No correct answer"}, "choices": []}] | D | mcq | Surface Area of Cubes | 3stpes_28 | 3steps_3 | |
1439 | [{"role": "user", "question": "As shown in the figure, the length of the rectangle is 12.56 cm. What is the area of the rectangle in cm²?(Use π = 3.14)", "hint": "", "options": {"A": "50.24", "B": "25.12", "C": "12.56", "D": "75.36", "E": "No correct answer"}, "choices": []}] | D | mcq | Area of Rectangles | 3stpes_29 | 3steps_3 | |
144 | [{"role": "user", "question": "In the diagram, which line segment cannot be extended indefinitely? ", "hint": "", "options": {"A": "①", "B": "②", "C": "③", "D": "Cannot be determined", "E": "No correct answer"}, "choices": []}] | B | mcq | Understanding Line Segments, Lines, and Rays | 2steps_144 | 2steps_1 | |
1440 | [{"role": "user", "question": "As shown in the figure, the circumference of the base of a cylinder is equal to its height. The circumference of the base is 12.56 cm. What is the surface area of the cylinder? (Use π = 3.14)", "hint": "", "options": {"A": "502.4", "B": "251.2", "C": "125.6", "D": "182.8", "E": "No correc... | D | mcq | Surface Area of Cylinders | 3stpes_30 | 3steps_3 | |
1441 | [{"role": "user", "question": "As shown in the figure, a wire is used to form the circle on the left. The same wire, with a length of 10π, can also be used to form the isosceles trapezoid on the right. What is the length of the legs of this trapezoid in π? (Unit: cm)", "hint": "", "options": {"A": "4", "B": "5", "C": "... | C | mcq | Perimeter of Trapezoids | 3stpes_31 | 3steps_3 | |
1442 | [{"role": "user", "question": "As shown in the figure, a right-angled triangle and three circular paper pieces are stacked. The lengths of the two legs of the right-angled triangle are equal. The radius of circle 2 is as shown in the figure. What is the area of circle 2? ( ) cm²", "hint": "", "options": {"A": "24π", "B... | C | mcq | Area of Circles | 3stpes_32 | 3steps_3 | |
1443 | [{"role": "user", "question": "As shown in the figure, a 12 cm long wire is bent into an isosceles trapezoid. What is the length of the legs of the trapezoid in cm?", "hint": "", "options": {"A": "4", "B": "5", "C": "2", "D": "No correct answer"}, "choices": []}] | C | mcq | Perimeter of Trapezoids | 3stpes_33 | 3steps_3 | |
1444 | [{"role": "user", "question": "There are two iron wires, each 60 cm long, which are respectively formed into the following cube frame and rectangular cuboid frame. What is the volume of the rectangular cuboid in cm³?", "hint": "", "options": {"A": "114", "B": "125", "C": "105", "D": "No correct answer"}, "choices": []}... | C | mcq | Volume and Capacity of Rectangular Cuboids | 3stpes_34 | 3steps_3 | |
1445 | [{"role": "user", "question": "As shown in the figure, rectangle ABCD is formed by a piece of wire. If the side CD is cut off and used to form a cube on the right, what is the volume of the cube? ( ) cm³", "hint": "", "options": {"A": "24", "B": "52", "C": "27", "D": "No correct answer"}, "choices": []}] | C | mcq | Volume and Capacity of Cubes | 3stpes_35 | 3steps_3 | |
1446 | [{"role": "user", "question": "As shown in the figure, a circular wire frame is cut at segment CD and formed into a cube. What is the volume of the cube? ( ) cm³", "hint": "", "options": {"A": "4", "B": "5", "C": "1", "D": "No correct answer"}, "choices": []}] | C | mcq | Volume and Capacity of Cubes | 3stpes_36 | 3steps_3 | |
1447 | [{"role": "user", "question": "As shown in the figure, quadrilateral GBCD is an isosceles trapezoid. The lengths of AB and GH are given in the figure. What is the area of triangle GAB in cm²?", "hint": "", "options": {"A": "24", "B": "50", "C": "40", "D": "No correct answer"}, "choices": []}] | C | mcq | Area of Triangles | 3stpes_37 | 3steps_3 | |
1448 | [{"role": "user", "question": "In the triangle shown in the figure, the degrees of each angle are marked in the diagram. What is the value of ∠2 + ∠3 = ()°?", "hint": "", "options": {"A": "200", "B": "250", "C": "260", "D": "No correct answer"}, "choices": []}] | C | mcq | Sum of Interior Angles of Other Polygons | 3stpes_38 | 3steps_3 |
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