yobro4619/DynaMath_sample · Datasets at Hugging Face

id stringlengths 1 3	question stringlengths 23 422	ground_truth stringlengths 1 19	subject stringclasses 9 values
101	The derivative of f(x) at x=1 is ____ that at x=5 choice: (A) larger than (B) smaller than (C) equal to	B	analytic geometry
102	What is the function value when x = 1?	-1	analytic geometry
103	The polar coordinates of a point are (3,3.53). Determine the Cartesian coordinates for the point.	(-2.777, -1.136)	analytic geometry
104	The clock shows the time. What time is it? Answer in the form of __:__.	17:06	arithmetic
105	Which of the following numbers is the closest to the value of f(x) at x=1? choice: (A) 5 (B) 3 (C) 1	B	analytic geometry
106	Is the function f:R\{0}->R injective, surjective, or bijective? choice: (A) Injective (B) Surjective (C) Bijective (D) Neither	C	analytic geometry
107	Two identical circles are placed into a square in such a way that they are tangent to each other at a single point, and each circle is tangent to the square at two points, as shown. If the radius of each circle is 5 , what is the area of the square?	291.4214	plane geometry
108	The function f(x) is a cubic function. What is the value of f(x) when x = 4?	563	algebra
109	The image shows the derivative of f(x). Where is the local min or max of f(x) at?	-1.0	analytic geometry
110	The image shows the derivative of f(x). Where is the local min of f(x) at?	-5	analytic geometry
111	The image shows the derivative of f(x). Where is the local max of f(x) at?	-1	analytic geometry
112	Find the area of azure part.	25.1327	plane geometry
113	The angle of the sector is 30 degree. What is the area of the blue part?	61.7847	plane geometry
114	What is on the north side of home? choice: (A) university (B) restaurant (C) park (D) library	B	scientific figure
115	The sum of the three numbers on each of the two lines of the cross is 83. Find the number in the center.	8	puzzle test
116	Squares ACDE and CBFG are constructed on the outside of △ABC with AC and BC as one side, respectively. Point P is the midpoint of EF. AC = 10, BC = 8, AB = 9, find the length of PQ.	4.5	plane geometry
117	Is this function bounded in interval [-8, 8]? choice: (A) Yes (B) No	A	analytic geometry
118	What is the least upper bound of this function?	1.5708	analytic geometry
119	Find the area of the shaded part.	-1.0	analytic geometry
120	Is this graph a cyclic graph? choice: (A) Yes (B) No	B	graph theory
121	Which of the following fact is true about set A and set B in image? choice: (A) A ⊂ B (B) A ⊃ B (C) A ∪ B (D) A ∩ B = ∅	C	algebra
122	In the diagram, there are three semi-circles. D is the diameter of left white semi-circle, and d is the diameter of the right white semi-circle. Find the area of azure part.	35.3429	plane geometry
123	Find the perimeter of the sector of the circle with radius r.	40.944	plane geometry
124	What is the purple curve? choice: (A) sigmoid function (B) tanh function (C) LeakyRelu function	A	analytic geometry
125	Which quadrant this function lies? choice: (A) first quadrant (B) second quadrant (C) third quadrant (D) fourth quadrant	B	analytic geometry
126	The truncated right circular cone below has a large base radius 10 cm and a small base radius of 4 cm. The height of the truncated cone is 5 cm. What is the volume of this solid?	816.8141	solid geometry
127	The ♠ is drawn on the sheet. We turn the sheet clockwise through 90° and then turn counter-clockwise 180°. Which figure can we now see? choice: (A) (B) (C) (D)	D	plane geometry
128	The image shows the second derivative of cubic function f(x). Is f(x) concave or convex at x = -1? choice: (A) convex (B) concave (C) inflection point	B	analytic geometry
129	What is the volume of this azure right square pyramid?	149.3333	solid geometry
130	What is the surface area of this pink right square pyramid?	192.9961	solid geometry
131	f(z) = 72, C is the purple circle shown in the image. Find ∫cf(z)dz.	0	analytic geometry
132	If the black point is reflected in x-axis, what are the coordinates of its image? Please answer in the form (_, _)	(0, 6)	analytic geometry
133	If the red point is reflected in y-axis, what are the coordinates of its image? Please answer in the form (_, _)	(2, 4)	analytic geometry
134	If the blue point is reflected about the origin, what are the coordinates of its image? Please answer in the form (_, _)	(3, 2)	analytic geometry
135	Find the distance between point A and point B.	12.8062	analytic geometry
136	What is the shortest distance from node S to node G in this directed graph?	29	graph theory
137	what is the first edge added to the MST when running Kruskal's Algorithm? In the case of a tie, choose the edge which comes first in alphabetical order i.e. if you had to choose between AS and AE, then you would choose AE first.	BS	graph theory
138	The figure shows graphs of functions $f$ and $g$ defined on real numbers. Each graph consists of two perpendicular halflines. Which equality is satisfied for every real number $x$? choice: (A) f(x)=g(x)-5 (B) f(x)=-g(x - 5) (C) f(x)=g(x - 5) (D) f(x)=-g(x)-5	B	analytic geometry
139	For each of the points A, B, C, D of the rectangle ABCD, the quotient (y-coordinate):(x-coordinate) is calculated. For which point will you obtain the smallest quotient? choice: (A) A (B) B (C) C (D)	B	analytic geometry
140	For each of the points A, B, C, D of the rectangle ABCD, the quotient (x-coordinate):(y-coordinate) is calculated. For which point will you obtain the smallest quotient? choice: (A) A (B) B (C) C (D)	D	analytic geometry
141	The length of the diameter of this spherical ball is equal to the height of the box in which it is placed. The box is a cube and has an edge length of 20 cm. How many cubic centimeters of the box are not occupied by the solid sphere?	3811.2098	solid geometry
142	Is this graph a bipartite? Choice: (A) Yes (B) No	A	graph theory
143	Determine for which values of x=a the function is continuous but not differentiable at x=a.	1	analytic geometry
144	Find the area of shaded part.	0.8284	analytic geometry
145	P is a point inside the square ABCD, and PA = 8, PB = 16, PC = 24. Find the side length of the square.	22.3835	solid geometry
146	Find the missing number.	87	puzzle test
147	Is this function differentiable? choice: (A) Yes (B) No	B	analytic geometry
148	Is this function uniformly continuous on [-8, 8]? choice: (A) Yes (B) No	B	analytic geometry
149	The function value f(1) is ____ f(-1) choice: (A) smaller than (B) larger than (C) equal to	A	analytic geometry
150	The function value f(1) is ____ 0 choice: (A) smaller than (B) larger than (C) equal to	A	analytic geometry
151	what is the first edge added to the MST when running Kruskal's Algorithm? In the case of a tie, choose the edge which comes first in alphabetical order i.e. if you had to choose between AG and AD, then you would choose AD first.	CE	graph theory
152	what is the first edge added to the MST when running Prim's Algorithm from node A? In the case of a tie, choose the edge which comes first in alphabetical order i.e. if you had to choose between AG and AD, then you would choose AD first.	AG	graph theory
153	The azure area in the figure is composed of 4 identical sectors, which can be combined to form a complete circle. What is the area of the azure part	63.6173	plane geometry
154	The white area in the figure is composed of 4 identical sectors, which can be combined to form a complete circle. What is the area of the azure part	25.9668	plane geometry
155	Find the missing number in the last node.	233	puzzle test
156	Find the missing number in the last node.	160	puzzle test
157	As shown in the figure, quadrilateral ABCD is a square, with DE parallel to AC, and CE equal to CA. Line EC intersects the extended line of DA at point F. AE = 18, find the length of AF	18	plane geometry
158	What are the coordinates of the vector between two blue points?	(-5, 5)	plane geometry
159	Find the area of the region bounded by the curves y = x^1/6, y = 1, and x = 5.	0.7471	analytic geometry
160	The blue curve is the function transformed from black curve. What transformation is applied to the original function? choice: (A) shift up (B) shift down (C) shift left (D) shift right	B	analytic geometry
161	On which number is the spinner more likely to land?	5	statistics
162	On which color is the spinner more likely to land?	White	statistics
163	The blue and green curves are f(x) and g(x). What is the monotonicity of f(x) + g(x)? choice: (A) monotone increasing (B) monotone decreasing (C) undefined	C	analytic geometry
164	The red and green curves are f(x) and g(x). What is the monotonicity of -f(x)? choice: (A) monotone increasing (B) monotone decreasing (C) undefined	B	analytic geometry
165	The purple and orange curves are f(x) and g(x). What is the monotonicity of 1/f(x)? choice: (A) monotone increasing (B) monotone decreasing (C) undefined	B	analytic geometry
166	The brown and black curves are f(x) and g(x). What is the monotonicity of f[g(x)]? choice: (A) monotone increasing (B) monotone decreasing (C) undefined	B	analytic geometry
167	quadrilateral ABCD is a square, with DE parallel to AC, AE=AC, and AE intersects CD at point F. The length of the side of ABCD is 14 amd CE = 12. Find the length of CF.	12	plane geometry
168	The blue and green curves are f(x) and g(x). Is f(x) + g(x) even or odd? choice: (A) odd (B) even (C) neither	C	analytic geometry
169	The purple and orange curves are f(x) and g(x). Is f(x)g(x) even or odd? choice: (A) odd (B) even (C) neither	B	analytic geometry
170	The red and green curves are f(x) and g(x). Is f[g(x)] even or odd? choice: (A) odd (B) even (C) neither	A	analytic geometry
171	What is the sum of interior angles in this polygon?	900	plane geometry
172	What is the sum of external angles in this polygon?	360	plane geometry
173	Find the ∠A in this regular polygon.	120.0	plane geometry
174	In the diagram below, both squares have a equal side length. What is the area of the azure region?	49	plane geometry
175	The equation of this ellipse is x^2/20.25 + y^2/9.0 = 1. Find the length of A1A2.	9	analytic geometry
176	The equation of this ellipse is x^2/12.25 + y^2/1.0 = 1. Find the length of B1B2.	2	analytic geometry
177	The equation of this ellipse is x^2/16.0 + y^2/2.25 = 1. Find the eccentricity of this ellipse.	0.927	analytic geometry
178	In the diagram, triangle ABC is right-angled at C. Also, points M, N and P are the midpoints of sides BC, AC and AB, respectively. If the area of triangle APN is 2, then what is the area of triangle ABC?	8	plane geometry
179	Find the missing number in the last node.	37	puzzle test
180	Find the missing number in the last node.	38	puzzle test
181	The line L1 and L2 are parallel to each other. Is ∠A the same as ∠B? choice: (A) Yes (B) No	A	plane geometry
182	The line L1 and L2 are parallel to each other. Is ∠A the same as ∠B? choice: (A) Yes (B) No	A	plane geometry
183	The line L1 and L2 are parallel to each other. Is ∠A the same as ∠B? choice: (A) Yes (B) No	A	plane geometry
184	The line L1 and L2 are parallel to each other. Is ∠A the same as ∠B? choice: (A) Yes (B) No	A	plane geometry
185	Based on the measurement results shown in the diagram, this blue angle is ( )°.	110	scientific figure
186	Based on the measurement results shown in the diagram, this blue angle is ( )°.	100	scientific figure
187	A sphere is inscribed in a cone with height 5 and base radius 4. What is the volume of the sphere ?	29.7637	solid geometry
188	Are two planes parallel? choice: (A) Yes (B) No	A	solid geometry
189	What is the area of the azure part?	174.2843	plane geometry
190	In the diagram, there are two semi-circles. D is the diameter of left azure semi-circle, and d is the diameter of the right white semi-circle. Find the area of azure part.	87.9646	plane geometry
191	Part of the graph of f(x) = x^3 + bx^2 + cx + d is shown. What is b?	-6	analytic geometry
192	Part of the graph of f(x) = x^3 + bx^2 + cx + d is shown. What is c?	-13	analytic geometry
193	Part of the graph of f(x) = x^3 + bx^2 + cx + d is shown. What is d?	-3	analytic geometry
194	Find the area of the azure part in two square.	4.5	plane geometry
195	Let P be a point on side BC of the square ABCD, PF⊥AP, and CF bisects ∠DCE. PA = 15,find the length of PF	15	plane geometry
196	The sum of the numbers at the two vertices at the ends of each edge is equal to the number written on that edge. What number should he write on the edge marked with the question mark?	3	puzzle test
197	As shown in the figure, points A, O, and B are collinear, and DE is perpendicular to CO. If ∠BOC = 25°, what is the measure of ∠BOE?	65	plane geometry
198	Is the function differentiable at x = 0? choice: (A) Yes (B) No	A	analytic geometry
199	Is the function continuous on x = 0? choice: (A) Yes (B) No	A	analytic geometry
200	As shown in the figure, BC is parallel to DE, with BC = 6 and DE = 7. Given AB = 7, find the length of BD.	1.1667	plane geometry

101

The derivative of f(x) at x=1 is ____ that at x=5 choice: (A) larger than (B) smaller than (C) equal to

B

analytic geometry

102

What is the function value when x = 1?

-1

analytic geometry

103

The polar coordinates of a point are (3,3.53). Determine the Cartesian coordinates for the point.

(-2.777, -1.136)

analytic geometry

104

The clock shows the time. What time is it? Answer in the form of __:__.

17:06

arithmetic

105

Which of the following numbers is the closest to the value of f(x) at x=1? choice: (A) 5 (B) 3 (C) 1

B

analytic geometry

106

Is the function f:R\{0}->R injective, surjective, or bijective? choice: (A) Injective (B) Surjective (C) Bijective (D) Neither

C

analytic geometry

107

Two identical circles are placed into a square in such a way that they are tangent to each other at a single point, and each circle is tangent to the square at two points, as shown. If the radius of each circle is 5 , what is the area of the square?

291.4214

plane geometry

108

The function f(x) is a cubic function. What is the value of f(x) when x = 4?

563

algebra

109

The image shows the derivative of f(x). Where is the local min or max of f(x) at?

-1.0

analytic geometry

110

The image shows the derivative of f(x). Where is the local min of f(x) at?

-5

analytic geometry

111

The image shows the derivative of f(x). Where is the local max of f(x) at?

-1

analytic geometry

112

Find the area of azure part.

25.1327

plane geometry

113

The angle of the sector is 30 degree. What is the area of the blue part?

61.7847

plane geometry

114

What is on the north side of home? choice: (A) university (B) restaurant (C) park (D) library

B

scientific figure

115

The sum of the three numbers on each of the two lines of the cross is 83. Find the number in the center.

8

puzzle test

116

Squares ACDE and CBFG are constructed on the outside of △ABC with AC and BC as one side, respectively. Point P is the midpoint of EF. AC = 10, BC = 8, AB = 9, find the length of PQ.

4.5

plane geometry

117

Is this function bounded in interval [-8, 8]? choice: (A) Yes (B) No

A

analytic geometry

118

What is the least upper bound of this function?

1.5708

analytic geometry

119

Find the area of the shaded part.

-1.0

analytic geometry

120

Is this graph a cyclic graph? choice: (A) Yes (B) No

B

graph theory

121

Which of the following fact is true about set A and set B in image? choice: (A) A ⊂ B (B) A ⊃ B (C) A ∪ B (D) A ∩ B = ∅

C

algebra

122

In the diagram, there are three semi-circles. D is the diameter of left white semi-circle, and d is the diameter of the right white semi-circle. Find the area of azure part.

35.3429

plane geometry

123

Find the perimeter of the sector of the circle with radius r.

40.944

plane geometry

124

What is the purple curve? choice: (A) sigmoid function (B) tanh function (C) LeakyRelu function

A

analytic geometry

125

Which quadrant this function lies? choice: (A) first quadrant (B) second quadrant (C) third quadrant (D) fourth quadrant

B

analytic geometry

126

The truncated right circular cone below has a large base radius 10 cm and a small base radius of 4 cm. The height of the truncated cone is 5 cm. What is the volume of this solid?

816.8141

solid geometry

127

The ♠ is drawn on the sheet. We turn the sheet clockwise through 90° and then turn counter-clockwise 180°. Which figure can we now see? choice: (A) (B) (C) (D)

D

plane geometry

128

The image shows the second derivative of cubic function f(x). Is f(x) concave or convex at x = -1? choice: (A) convex (B) concave (C) inflection point

B

analytic geometry

129

What is the volume of this azure right square pyramid?

149.3333

solid geometry

130

What is the surface area of this pink right square pyramid?

192.9961

solid geometry

131

f(z) = 72, C is the purple circle shown in the image. Find ∫cf(z)dz.

0

analytic geometry

132

If the black point is reflected in x-axis, what are the coordinates of its image? Please answer in the form (_, _)

(0, 6)

analytic geometry

133

If the red point is reflected in y-axis, what are the coordinates of its image? Please answer in the form (_, _)

(2, 4)

analytic geometry

134

If the blue point is reflected about the origin, what are the coordinates of its image? Please answer in the form (_, _)

(3, 2)

analytic geometry

135

Find the distance between point A and point B.

12.8062

analytic geometry

136

What is the shortest distance from node S to node G in this directed graph?

29

graph theory

137

what is the first edge added to the MST when running Kruskal's Algorithm? In the case of a tie, choose the edge which comes first in alphabetical order i.e. if you had to choose between AS and AE, then you would choose AE first.

BS

graph theory

138

The figure shows graphs of functions $f$ and $g$ defined on real numbers. Each graph consists of two perpendicular halflines. Which equality is satisfied for every real number $x$? choice: (A) f(x)=g(x)-5 (B) f(x)=-g(x - 5) (C) f(x)=g(x - 5) (D) f(x)=-g(x)-5

B

analytic geometry

139

For each of the points A, B, C, D of the rectangle ABCD, the quotient (y-coordinate):(x-coordinate) is calculated. For which point will you obtain the smallest quotient? choice: (A) A (B) B (C) C (D)

B

analytic geometry

140

For each of the points A, B, C, D of the rectangle ABCD, the quotient (x-coordinate):(y-coordinate) is calculated. For which point will you obtain the smallest quotient? choice: (A) A (B) B (C) C (D)

D

analytic geometry

141

The length of the diameter of this spherical ball is equal to the height of the box in which it is placed. The box is a cube and has an edge length of 20 cm. How many cubic centimeters of the box are not occupied by the solid sphere?

3811.2098

solid geometry

142

Is this graph a bipartite? Choice: (A) Yes (B) No

A

graph theory

143

Determine for which values of x=a the function is continuous but not differentiable at x=a.

1

analytic geometry

144

Find the area of shaded part.

0.8284

analytic geometry

145

P is a point inside the square ABCD, and PA = 8, PB = 16, PC = 24. Find the side length of the square.

22.3835

solid geometry

146

Find the missing number.

87

puzzle test

147

Is this function differentiable? choice: (A) Yes (B) No

B

analytic geometry

148

Is this function uniformly continuous on [-8, 8]? choice: (A) Yes (B) No

B

analytic geometry

149

The function value f(1) is ____ f(-1) choice: (A) smaller than (B) larger than (C) equal to

A

analytic geometry

150

The function value f(1) is ____ 0 choice: (A) smaller than (B) larger than (C) equal to

A

analytic geometry

151

what is the first edge added to the MST when running Kruskal's Algorithm? In the case of a tie, choose the edge which comes first in alphabetical order i.e. if you had to choose between AG and AD, then you would choose AD first.

CE

graph theory

152

what is the first edge added to the MST when running Prim's Algorithm from node A? In the case of a tie, choose the edge which comes first in alphabetical order i.e. if you had to choose between AG and AD, then you would choose AD first.

AG

graph theory

153

The azure area in the figure is composed of 4 identical sectors, which can be combined to form a complete circle. What is the area of the azure part

63.6173

plane geometry

154

The white area in the figure is composed of 4 identical sectors, which can be combined to form a complete circle. What is the area of the azure part

25.9668

plane geometry

155

Find the missing number in the last node.

233

puzzle test

156

Find the missing number in the last node.

160

puzzle test

157

As shown in the figure, quadrilateral ABCD is a square, with DE parallel to AC, and CE equal to CA. Line EC intersects the extended line of DA at point F. AE = 18, find the length of AF

18

plane geometry

158

What are the coordinates of the vector between two blue points?

(-5, 5)

plane geometry

159

Find the area of the region bounded by the curves y = x^1/6, y = 1, and x = 5.

0.7471

analytic geometry

160

The blue curve is the function transformed from black curve. What transformation is applied to the original function? choice: (A) shift up (B) shift down (C) shift left (D) shift right

B

analytic geometry

161

On which number is the spinner more likely to land?

5

statistics

162

On which color is the spinner more likely to land?

White

statistics

163

The blue and green curves are f(x) and g(x). What is the monotonicity of f(x) + g(x)? choice: (A) monotone increasing (B) monotone decreasing (C) undefined

C

analytic geometry

164

The red and green curves are f(x) and g(x). What is the monotonicity of -f(x)? choice: (A) monotone increasing (B) monotone decreasing (C) undefined

B

analytic geometry

165

The purple and orange curves are f(x) and g(x). What is the monotonicity of 1/f(x)? choice: (A) monotone increasing (B) monotone decreasing (C) undefined

B

analytic geometry

166

The brown and black curves are f(x) and g(x). What is the monotonicity of f[g(x)]? choice: (A) monotone increasing (B) monotone decreasing (C) undefined

B

analytic geometry

167

quadrilateral ABCD is a square, with DE parallel to AC, AE=AC, and AE intersects CD at point F. The length of the side of ABCD is 14 amd CE = 12. Find the length of CF.

12

plane geometry

168

The blue and green curves are f(x) and g(x). Is f(x) + g(x) even or odd? choice: (A) odd (B) even (C) neither

C

analytic geometry

169

The purple and orange curves are f(x) and g(x). Is f(x)g(x) even or odd? choice: (A) odd (B) even (C) neither

B

analytic geometry

170

The red and green curves are f(x) and g(x). Is f[g(x)] even or odd? choice: (A) odd (B) even (C) neither

A

analytic geometry

171

What is the sum of interior angles in this polygon?

900

plane geometry

172

What is the sum of external angles in this polygon?

360

plane geometry

173

Find the ∠A in this regular polygon.

120.0

plane geometry

174

In the diagram below, both squares have a equal side length. What is the area of the azure region?

49

plane geometry

175

The equation of this ellipse is x^2/20.25 + y^2/9.0 = 1. Find the length of A1A2.

9

analytic geometry

176

The equation of this ellipse is x^2/12.25 + y^2/1.0 = 1. Find the length of B1B2.

2

analytic geometry

177

The equation of this ellipse is x^2/16.0 + y^2/2.25 = 1. Find the eccentricity of this ellipse.

0.927

analytic geometry

178

In the diagram, triangle ABC is right-angled at C. Also, points M, N and P are the midpoints of sides BC, AC and AB, respectively. If the area of triangle APN is 2, then what is the area of triangle ABC?

8

plane geometry

179

Find the missing number in the last node.

37

puzzle test

180

Find the missing number in the last node.

38

puzzle test

181

The line L1 and L2 are parallel to each other. Is ∠A the same as ∠B? choice: (A) Yes (B) No

A

plane geometry

182

The line L1 and L2 are parallel to each other. Is ∠A the same as ∠B? choice: (A) Yes (B) No

A

plane geometry

183

The line L1 and L2 are parallel to each other. Is ∠A the same as ∠B? choice: (A) Yes (B) No

A

plane geometry

184

The line L1 and L2 are parallel to each other. Is ∠A the same as ∠B? choice: (A) Yes (B) No

A

plane geometry

185

Based on the measurement results shown in the diagram, this blue angle is ( )°.

110

scientific figure

186

Based on the measurement results shown in the diagram, this blue angle is ( )°.

100

scientific figure

187

A sphere is inscribed in a cone with height 5 and base radius 4. What is the volume of the sphere ?

29.7637

solid geometry

188

Are two planes parallel? choice: (A) Yes (B) No

A

solid geometry

189

What is the area of the azure part?

174.2843

plane geometry

190

In the diagram, there are two semi-circles. D is the diameter of left azure semi-circle, and d is the diameter of the right white semi-circle. Find the area of azure part.

87.9646

plane geometry

191

Part of the graph of f(x) = x^3 + bx^2 + cx + d is shown. What is b?

-6

analytic geometry

192

Part of the graph of f(x) = x^3 + bx^2 + cx + d is shown. What is c?

-13

analytic geometry

193

Part of the graph of f(x) = x^3 + bx^2 + cx + d is shown. What is d?

-3

analytic geometry

194

Find the area of the azure part in two square.

4.5

plane geometry

195

Let P be a point on side BC of the square ABCD, PF⊥AP, and CF bisects ∠DCE. PA = 15,find the length of PF

15

plane geometry

196

The sum of the numbers at the two vertices at the ends of each edge is equal to the number written on that edge. What number should he write on the edge marked with the question mark?

3

puzzle test

197