id
string
setting_key
string
difficulty
string
level
int32
messages
dict
ground_truth
string
dataset
string
omega_split
string
math_algebra_func_derivative_sign_level_2_2_300
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = -1(2|(1sin(1πx - 3) - 1) - 1| - 2) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
11
math
train
math_algebra_func_derivative_sign_level_2_2_301
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3cos(2π(3((1x - 3)/(-2x + 3))^2 + 4((1x - 3)/(-2x + 3)) + 5) - 1) + 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
10
math
train
math_algebra_func_derivative_sign_level_2_2_302
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2sin(3π(1|(2|x + 1| - 1) - 3| - 3)) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
62
math
train
math_algebra_func_derivative_sign_level_2_2_303
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(1|(1cos(3πx - 3) + 1) + 2| - 3) + 5 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
30
math
train
math_algebra_func_derivative_sign_level_2_2_304
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = -2|(2cos(2π(4x^2 - 1x - 5) + 2)) - 2| + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
38
math
train
math_algebra_func_derivative_sign_level_2_2_305
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 4(3|(-3cos(2πx) + 1) - 2| - 3)^2 + 2(3|(-3cos(2πx) + 1) - 2| - 3) - 4 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
23
math
train
math_algebra_func_derivative_sign_level_2_2_306
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1|(1|(2sin(2πx - 1) - 3) - 1| - 1) - 3| + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
40
math
train
math_algebra_func_derivative_sign_level_2_2_307
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3cos(3π(-2|((1x - 1)/(-1x + 2)) + 1| + 2) - 1) + 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
11
math
train
math_algebra_func_derivative_sign_level_2_2_308
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (3(2sin(3π(-1x + 4) - 2) + 1) - 2)/(-2(2sin(3π(-1x + 4) - 2) + 1) + 3) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
30
math
train
math_algebra_func_derivative_sign_level_2_2_309
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1cos(2π(-3((2x - 2)/(-2x + 3))^2 - 2((2x - 2)/(-2x + 3)) - 3) - 3) - 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
8
math
train
math_algebra_func_derivative_sign_level_2_2_310
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -5(-1sin(2π(3|x + 2| - 1) + 1) + 3) + 4 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
60
math
train
math_algebra_func_derivative_sign_level_2_2_311
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = (-1(-1sin(2π(-5x - 2) - 3) - 1))/(-2(-1sin(2π(-5x - 2) - 3) - 1) - 1), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
89
math
train
math_algebra_func_derivative_sign_level_2_2_312
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3(3cos(1π(2|x - 3|) - 2) - 1)^2 + 4(3cos(1π(2|x - 3|) - 2) - 1) + 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
41
math
train
math_algebra_func_derivative_sign_level_2_2_313
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -5(2(-2cos(3πx + 3) + 1) + 1)^2 + 2(2(-2cos(3πx + 3) + 1) + 1) - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
40
math
train
math_algebra_func_derivative_sign_level_2_2_314
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = -2|(-1cos(2π(-1|x - 2| + 2)) - 3) - 2| - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
20
math
train
math_algebra_func_derivative_sign_level_2_2_315
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (2(3|(-1sin(3πx + 1) + 1) - 3| - 2) + 3)/(-3(3|(-1sin(3πx + 1) + 1) - 3| - 2) - 1) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
30
math
train
math_algebra_func_derivative_sign_level_2_2_316
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1cos(1π(-3(1x + 5)^2 - 1(1x + 5) - 1) - 2) - 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
62
math
train
math_algebra_func_derivative_sign_level_2_2_317
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -4(1(-2cos(2πx + 1) - 2) + 4)^2 - 4(1(-2cos(2πx + 1) - 2) + 4) + 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
20
math
train
math_algebra_func_derivative_sign_level_2_2_318
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2|(-2|(-1sin(3πx + 1)) - 3| - 2) - 3| + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
31
math
train
math_algebra_func_derivative_sign_level_2_2_319
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3(2cos(3π(-3|x - 2| - 3)) + 3) + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
90
math
train
math_algebra_func_derivative_sign_level_2_2_320
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = 1sin(3π(-1|(-3x^2 + 4x - 5) + 1| + 2) + 3) + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
55
math
train
math_algebra_func_derivative_sign_level_2_2_321
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2(-1cos(3π(4x + 3) - 1)) + 5 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
80
math
train
math_algebra_func_derivative_sign_level_2_2_322
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1(1cos(3π(-5x + 2) - 2) - 2)^2 - 3(1cos(3π(-5x + 2) - 2) - 2) + 5 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
67
math
train
math_algebra_func_derivative_sign_level_2_2_323
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = 2sin(1π(-3|(-2|x - 1| + 3) + 1| + 3) - 2), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
61
math
train
math_algebra_func_derivative_sign_level_2_2_324
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1cos(3π(-2|(3x + 4) - 1|) - 3) + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
20
math
train
math_algebra_func_derivative_sign_level_2_2_325
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2(-1|(1cos(2πx + 2) - 1) - 3| + 1)^2 - 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
21
math
train
math_algebra_func_derivative_sign_level_2_2_326
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1sin(2π(-1|(-2|x + 1| + 1) + 1| + 3) - 3) + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
42
math
train
math_algebra_func_derivative_sign_level_2_2_327
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = 3|(2cos(3π(-2x - 2) - 1) - 1) + 1| - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
79
math
train
math_algebra_func_derivative_sign_level_2_2_328
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-1((3(2cos(3πx) - 3) + 2)/(2(2cos(3πx) - 3) - 1)) + 1)/(1((3(2cos(3πx) - 3) + 2)/(2(2cos(3πx) - 3) - 1))) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
30
math
train
math_algebra_func_derivative_sign_level_2_2_329
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2|(1sin(1π((-2x + 2)/(-2x - 3)) + 3) + 2) + 1| - 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
8
math
train
math_algebra_func_derivative_sign_level_2_2_330
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = (-1(-3|(3cos(2πx + 1) - 1) - 3| - 3) - 3)/(-2(-3|(3cos(2πx + 1) - 1) - 3| - 3) + 3), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
21
math
train
math_algebra_func_derivative_sign_level_2_2_331
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1|(-2sin(2π(3|x - 3| - 2) - 1) - 3)| negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
61
math
train
math_algebra_func_derivative_sign_level_2_2_332
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1cos(2π(-3(3x - 1))) + 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
18
math
train
math_algebra_func_derivative_sign_level_2_2_333
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (2(-2cos(1π(-2|x - 3| + 2) - 2) + 2) - 1)/(1(-2cos(1π(-2|x - 3| + 2) - 2) + 2) + 1) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
21
math
train
math_algebra_func_derivative_sign_level_2_2_334
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3|(3(3cos(2πx + 1) + 3)^2 - 5(3cos(2πx + 1) + 3) + 1) - 3| + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
50
math
train
math_algebra_func_derivative_sign_level_2_2_335
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = -5(-3sin(2π(-3|x - 2| - 1)) + 3) + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
61
math
train
math_algebra_func_derivative_sign_level_2_2_336
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = (-1(1cos(3π((-2x - 3)/(-3x + 2))) + 3) - 2)/(2(1cos(3π((-2x - 3)/(-3x + 2))) + 3) - 1), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
10
math
train
math_algebra_func_derivative_sign_level_2_2_337
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2cos(3π(-1(4x^2 + 4x - 4)^2 + 2(4x^2 + 4x - 4) - 5) - 2) + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
9
math
train
math_algebra_func_derivative_sign_level_2_2_338
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|(5(1x^2 - 3x - 4)^2 - 4) + 1| + 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
4
math
train
math_algebra_func_derivative_sign_level_2_2_339
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2cos(1π(2((2x + 3)/(2x + 2))^2 - 3((2x + 3)/(2x + 2))) - 1) - 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
4
math
train
math_algebra_func_derivative_sign_level_2_2_340
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2|(4(-1sin(1πx + 3) + 1)^2 - 4) + 2| + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
21
math
train
math_algebra_func_derivative_sign_level_2_2_341
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1cos(3π(4(4x) - 3) - 2) + 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
84
math
train
math_algebra_func_derivative_sign_level_2_2_342
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = -1(-2sin(3π((2x - 3)/(-1x - 3)) + 3) + 3)^2 + 1(-2sin(3π((2x - 3)/(-1x - 3)) + 3) + 3) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
17
math
train
math_algebra_func_derivative_sign_level_2_2_343
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1sin(3π(1(1|x - 2| - 1) + 5) + 3) + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
31
math
train
math_algebra_func_derivative_sign_level_2_2_344
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1sin(2π(-2(-3x^2 - 4x - 4)^2 + 1(-3x^2 - 4x - 4) + 4) + 2) - 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
7
math
train
math_algebra_func_derivative_sign_level_2_2_345
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 5(-1cos(1π(4x^2 - 3x) - 2) - 3)^2 - 2(-1cos(1π(4x^2 - 3x) - 2) - 3) - 5 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
18
math
train
math_algebra_func_derivative_sign_level_2_2_346
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -4(2cos(1π(3|x + 2| + 3) + 1) + 1)^2 - 5(2cos(1π(3|x + 2| + 3) + 1) + 1) + 5 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
39
math
train
math_algebra_func_derivative_sign_level_2_2_347
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = -1|((2(-2cos(1πx - 1) + 2) - 2)/(1(-2cos(1πx - 1) + 2) - 2)) - 2| - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
20
math
train
math_algebra_func_derivative_sign_level_2_2_348
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = (3(1(2sin(3πx + 3) - 2) - 3) + 2)/(-1(1(2sin(3πx + 3) - 2) - 3) - 2), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
30
math
train
math_algebra_func_derivative_sign_level_2_2_349
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = 2sin(2π((2((1x - 2)/(3x + 2)) + 3)/(1((1x - 2)/(3x + 2)))) + 2) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
27
math
train
math_algebra_func_derivative_sign_level_2_2_350
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3cos(1π(4((-1x + 3)/(3x + 3)) + 1) - 2) - 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
9
math
train
math_algebra_func_derivative_sign_level_2_2_351
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2sin(3π(-1((-3x + 3)/(3x - 2))^2) - 2) - 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
6
math
train
math_algebra_func_derivative_sign_level_2_2_352
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2cos(1π(1|((-2x + 1)/(1x + 2)) - 2| + 3) + 2) - 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
12
math
train
math_algebra_func_derivative_sign_level_2_2_353
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = 1(1|(2sin(1πx + 3) - 3) - 2| + 3) + 4, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
11
math
train
math_algebra_func_derivative_sign_level_2_2_354
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 4(-3(-1cos(1πx - 1) - 3) - 3) - 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
10
math
train
math_algebra_func_derivative_sign_level_2_2_355
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = 4(-5(2cos(1πx - 1) + 1) - 3) - 5, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
10
math
train
math_algebra_func_derivative_sign_level_2_2_356
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3sin(1π(4((-2x - 1)/(-3x - 2)) - 2) + 3) - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
4
math
train
math_algebra_func_derivative_sign_level_2_2_357
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = -1|(-3sin(3π((-2x + 2)/(-3x - 2)) - 3) - 3) + 2| - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
10
math
train
math_algebra_func_derivative_sign_level_2_2_358
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2sin(1π(-2((-1x - 2)/(1x + 1)) - 4) - 2) - 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
5
math
train
math_algebra_func_derivative_sign_level_2_2_359
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|(-1(1cos(2πx + 1) + 2) - 2) - 3| - 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
20
math
train
math_algebra_func_derivative_sign_level_2_2_360
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = -4(-2cos(3π(1x^2 + 5x - 3) - 2) - 2) - 5, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
36
math
train
math_algebra_func_derivative_sign_level_2_2_361
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3(-2cos(2π(-3|x|) + 3) + 3) - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
61
math
train
math_algebra_func_derivative_sign_level_2_2_362
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (3(3cos(3π(-2x + 3) - 1) - 2))/(-2(3cos(3π(-2x + 3) - 1) - 2) - 1) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
60
math
train
math_algebra_func_derivative_sign_level_2_2_363
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1cos(2π(1(5x + 5) - 4) + 3) - 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
100
math
train
math_algebra_func_derivative_sign_level_2_2_364
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = -3cos(2π(3(-2|x + 2| - 3)^2 - 3(-2|x + 2| - 3) - 2) - 1) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
11
math
train
math_algebra_func_derivative_sign_level_2_2_365
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1sin(2π(2|((-1x)/(3x + 2))| - 3)) - 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
4
math
train
math_algebra_func_derivative_sign_level_2_2_366
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = -3sin(3π(-2|(-2|x + 2| + 1) + 1| + 2) - 1) + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
80
math
train
math_algebra_func_derivative_sign_level_2_2_367
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (1(-1sin(2π(5x + 4) + 1) - 1))/(-2(-1sin(2π(5x + 4) + 1) - 1) + 3) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
100
math
train
math_algebra_func_derivative_sign_level_2_2_368
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2|(2(-1cos(1πx + 2) + 1) - 4) - 2| - 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
10
math
train
math_algebra_func_derivative_sign_level_2_2_369
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 5(-1(2cos(2πx - 2) + 3) - 5) - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
20
math
train
math_algebra_func_derivative_sign_level_2_2_370
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = 1((-2(-3sin(2πx - 1) + 2) + 2)/(1(-3sin(2πx - 1) + 2))), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
21
math
train
math_algebra_func_derivative_sign_level_2_2_371
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = 2|((-3(3cos(3πx + 2) + 2) - 1)/(1(3cos(3πx + 2) + 2) - 3)) - 1|, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
68
math
train
math_algebra_func_derivative_sign_level_2_2_372
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = -2|(1(-1x^2 + 4x)^2 - 4(-1x^2 + 4x) + 5) - 3| - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
4
math
train
math_algebra_func_derivative_sign_level_2_2_373
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = -3(-2|(2sin(1πx - 3) - 2) + 2| + 2)^2 + 3(-2|(2sin(1πx - 3) - 2) + 2| + 2) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
41
math
train
math_algebra_func_derivative_sign_level_2_2_374
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1(3|(2sin(1πx - 2) + 1) - 2| + 3)^2 + 5(3|(2sin(1πx - 2) + 1) - 2| + 3) + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
21
math
train
math_algebra_func_derivative_sign_level_2_2_375
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2cos(1π(2|(-2|x - 2| - 1)| - 2) + 3) - 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
40
math
train
math_algebra_func_derivative_sign_level_2_2_376
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = 4(-3(-3sin(1πx - 3) + 2) - 4) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
10
math
train
math_algebra_func_derivative_sign_level_2_2_377
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3sin(1π(-4(4x^2 - 4x - 4) - 1) + 1) - 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
34
math
train
math_algebra_func_derivative_sign_level_2_2_378
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = 3cos(3π(-3((-3x)/(-2x + 3)) - 2) + 3) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
16
math
train
math_algebra_func_derivative_sign_level_2_2_379
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = -3cos(1π(2|(-2x - 3) - 1| + 3)) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
40
math
train
math_algebra_func_derivative_sign_level_2_2_380
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = 2(-1cos(1π(2|x - 3| - 1) - 3) - 2) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
21
math
train
math_algebra_func_derivative_sign_level_2_2_381
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1|((-1(2cos(2πx - 3) + 1) - 1)/(3(2cos(2πx - 3) + 1) + 1))| - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
40
math
train
math_algebra_func_derivative_sign_level_2_2_382
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2|(3|(3cos(3πx - 3) + 2) - 1| + 2) - 1| + 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
60
math
train
math_algebra_func_derivative_sign_level_2_2_383
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2cos(2π((-2(-2|x| + 1))/(3(-2|x| + 1) + 3)) + 1) + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
6
math
train
math_algebra_func_derivative_sign_level_2_2_384
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2sin(3π((3(-1|x - 2|) - 3)/(-2(-1|x - 2|)))) - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
10
math
train
math_algebra_func_derivative_sign_level_2_2_385
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = -2|(-1|(2sin(2πx + 1) - 1) + 3| - 2) - 1|, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
20
math
train
math_algebra_func_derivative_sign_level_2_2_386
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = -2(1(-2cos(2πx) - 3)^2 - 4(-2cos(2πx) - 3) - 1) + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
20
math
train
math_algebra_func_derivative_sign_level_2_2_387
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1|(3cos(1π(-1x^2 - 2x + 4) - 1) - 2) + 1| + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
43
math
train
math_algebra_func_derivative_sign_level_2_2_388
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -5((-2(2cos(3πx - 3) - 3) - 1)/(-1(2cos(3πx - 3) - 3) - 3)) + 4 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
30
math
train
math_algebra_func_derivative_sign_level_2_2_389
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3sin(3π(1|(2x^2 - 4x - 1) + 1| + 1) - 3) + 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
52
math
train
math_algebra_func_derivative_sign_level_2_2_390
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 4(3(-2cos(3πx + 3) + 2)^2 - 4(-2cos(3πx + 3) + 2) + 2) - 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
53
math
train
math_algebra_func_derivative_sign_level_2_2_391
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1sin(3π((2(-3x - 3) - 3)/(-1(-3x - 3) + 3)) - 1) + 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
7
math
train
math_algebra_func_derivative_sign_level_2_2_392
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = 3cos(2π(-3|(-2x) + 3| - 3)) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
80
math
train
math_algebra_func_derivative_sign_level_2_2_393
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -5((1(1cos(2πx + 1) + 1) + 1)/(-2(1cos(2πx + 1) + 1))) + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
20
math
train
math_algebra_func_derivative_sign_level_2_2_394
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1cos(3π((-1(-1|x + 3| + 3) - 1)/(1(-1|x + 3| + 3) + 2)) - 3) - 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
18
math
train
math_algebra_func_derivative_sign_level_2_2_395
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = 3sin(3π(1|(-2|x + 3| + 3) + 3| + 1)) + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
62
math
train
math_algebra_func_derivative_sign_level_2_2_396
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = (-1(-2sin(2π((1x + 3)/(2x + 1)) + 3) + 2) - 3)/(-1(-2sin(2π((1x + 3)/(2x + 1)) + 3) + 2) + 3), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
6
math
train
math_algebra_func_derivative_sign_level_2_2_397
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "For the function f(x) = (-2((3(-3cos(3πx + 3) - 3) + 3)/(2(-3cos(3πx + 3) - 3) - 1)) - 1)/(1((3(-3cos(3πx + 3) - 3) + 3)/(2(-3cos(3πx + 3) - 3) - 1)) + 3), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
30
math
train
math_algebra_func_derivative_sign_level_2_2_398
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1sin(2π(-1(2|x + 2| + 2)^2 + 1(2|x + 2| + 2) - 3) + 3) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
49
math
train
math_algebra_func_derivative_sign_level_2_2_399
algebra_func_derivative_sign2
medium (level 2,3)
2
{ "role": [ "user" ], "content": [ "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3(-1sin(2π(-1|x + 3| - 3) - 1) - 3)^2 + 4(-1sin(2π(-1|x + 3| - 3) - 1) - 3) - 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}" ] }
21
math
train