id
stringlengths 31
70
| setting_key
stringclasses 31
values | difficulty
stringclasses 1
value | level
int64 1
1
| messages
listlengths 1
1
| ground_truth
stringlengths 1
19
| dataset
stringclasses 1
value | omega_split
stringclasses 1
value | __index_level_0__
int64 0
160k
|
|---|---|---|---|---|---|---|---|---|
math_algebra_func_derivative_sign_level_1_1_0
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -4(-2sin(1πx - 2) + 2) + 5 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
10
|
math
|
train
| 1,000 |
math_algebra_func_derivative_sign_level_1_1_1
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1|(-1sin(2πx + 2) + 3) + 2| - 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
21
|
math
|
train
| 1,001 |
math_algebra_func_derivative_sign_level_1_1_2
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = -1(-1cos(1πx - 2) + 1) + 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}",
"role": "user"
}
] |
10
|
math
|
train
| 1,002 |
math_algebra_func_derivative_sign_level_1_1_3
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = -2(-2cos(3πx + 3) + 2)^2 - 1(-2cos(3πx + 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}",
"role": "user"
}
] |
31
|
math
|
train
| 1,003 |
math_algebra_func_derivative_sign_level_1_1_4
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2(-3sin(2πx - 1) + 3)^2 - 1(-3sin(2πx - 1) + 3) + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
27
|
math
|
train
| 1,004 |
math_algebra_func_derivative_sign_level_1_1_5
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1cos(1π(-3|x - 1| + 2) + 2) - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
31
|
math
|
train
| 1,005 |
math_algebra_func_derivative_sign_level_1_1_6
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-1(-1cos(1πx + 2) + 2) - 2)/(-1(-1cos(1πx + 2) + 2)) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
10
|
math
|
train
| 1,006 |
math_algebra_func_derivative_sign_level_1_1_7
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1|(3sin(2πx - 3) - 3) - 3| - 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
21
|
math
|
train
| 1,007 |
math_algebra_func_derivative_sign_level_1_1_8
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3cos(1π(-3|x + 1| - 1) - 1) - 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
31
|
math
|
train
| 1,008 |
math_algebra_func_derivative_sign_level_1_1_9
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = 3|(1cos(3πx - 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}",
"role": "user"
}
] |
60
|
math
|
train
| 1,009 |
math_algebra_func_derivative_sign_level_1_1_10
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2(3sin(2πx + 3) + 2) - 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
21
|
math
|
train
| 1,010 |
math_algebra_func_derivative_sign_level_1_1_11
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3cos(2π((3x)/(-2x - 2)) - 1) - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
10
|
math
|
train
| 1,011 |
math_algebra_func_derivative_sign_level_1_1_12
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = 3cos(3π(1x^2 - 5x + 3) + 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}",
"role": "user"
}
] |
46
|
math
|
train
| 1,012 |
math_algebra_func_derivative_sign_level_1_1_13
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3sin(1π(2x + 4)) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
21
|
math
|
train
| 1,013 |
math_algebra_func_derivative_sign_level_1_1_14
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = 2sin(1π(-2x + 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}",
"role": "user"
}
] |
20
|
math
|
train
| 1,014 |
math_algebra_func_derivative_sign_level_1_1_15
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = (-1(3cos(2πx + 3) + 3))/(-2(3cos(2πx + 3) + 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}",
"role": "user"
}
] |
21
|
math
|
train
| 1,015 |
math_algebra_func_derivative_sign_level_1_1_16
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = -3(2cos(3πx + 3))^2 + 2(2cos(3πx + 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}",
"role": "user"
}
] |
60
|
math
|
train
| 1,016 |
math_algebra_func_derivative_sign_level_1_1_17
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1(-2sin(2πx - 2) - 3) + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
21
|
math
|
train
| 1,017 |
math_algebra_func_derivative_sign_level_1_1_18
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3cos(3π(5x - 4) - 3) + 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
48
|
math
|
train
| 1,018 |
math_algebra_func_derivative_sign_level_1_1_19
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = -2sin(3π(-2x - 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}",
"role": "user"
}
] |
60
|
math
|
train
| 1,019 |
math_algebra_func_derivative_sign_level_1_1_20
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3sin(3π(2x^2 - 1x + 4) + 1) - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
38
|
math
|
train
| 1,020 |
math_algebra_func_derivative_sign_level_1_1_21
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = -2(1sin(3πx + 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}",
"role": "user"
}
] |
30
|
math
|
train
| 1,021 |
math_algebra_func_derivative_sign_level_1_1_22
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2sin(1π(-1|x - 2| - 3) - 2) + 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
11
|
math
|
train
| 1,022 |
math_algebra_func_derivative_sign_level_1_1_23
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3|(2cos(3πx) - 1) + 2| - 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
60
|
math
|
train
| 1,023 |
math_algebra_func_derivative_sign_level_1_1_24
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = -1sin(3π(3|x - 2| + 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}",
"role": "user"
}
] |
89
|
math
|
train
| 1,024 |
math_algebra_func_derivative_sign_level_1_1_25
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = 3|(2sin(2πx + 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}",
"role": "user"
}
] |
21
|
math
|
train
| 1,025 |
math_algebra_func_derivative_sign_level_1_1_26
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = 3(-1cos(1πx + 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}",
"role": "user"
}
] |
10
|
math
|
train
| 1,026 |
math_algebra_func_derivative_sign_level_1_1_27
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -5(1sin(2πx + 2)) - 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
20
|
math
|
train
| 1,027 |
math_algebra_func_derivative_sign_level_1_1_28
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = (2(2cos(2πx - 3) - 3) + 1)/(3(2cos(2πx - 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}",
"role": "user"
}
] |
20
|
math
|
train
| 1,028 |
math_algebra_func_derivative_sign_level_1_1_29
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 5(2cos(2πx) + 2)^2 - 3(2cos(2πx) + 2) + 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
36
|
math
|
train
| 1,029 |
math_algebra_func_derivative_sign_level_1_1_30
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = 1(3sin(2πx - 1) + 1) + 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}",
"role": "user"
}
] |
21
|
math
|
train
| 1,030 |
math_algebra_func_derivative_sign_level_1_1_31
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = -3|(-2sin(3πx - 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}",
"role": "user"
}
] |
31
|
math
|
train
| 1,031 |
math_algebra_func_derivative_sign_level_1_1_32
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|(1sin(3πx + 3) - 2) + 2| - 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
61
|
math
|
train
| 1,032 |
math_algebra_func_derivative_sign_level_1_1_33
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = -1cos(2π(-2|x| + 2) - 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}",
"role": "user"
}
] |
41
|
math
|
train
| 1,033 |
math_algebra_func_derivative_sign_level_1_1_34
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = 1(3sin(3πx - 1) - 3)^2 - 5(3sin(3πx - 1) - 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}",
"role": "user"
}
] |
30
|
math
|
train
| 1,034 |
math_algebra_func_derivative_sign_level_1_1_35
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2(-1cos(1πx + 2) - 1) + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
11
|
math
|
train
| 1,035 |
math_algebra_func_derivative_sign_level_1_1_36
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1cos(1π((2x - 2)/(2x + 2)) - 3) + 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
9
|
math
|
train
| 1,036 |
math_algebra_func_derivative_sign_level_1_1_37
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1sin(1π(-1x + 4) - 2) - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
10
|
math
|
train
| 1,037 |
math_algebra_func_derivative_sign_level_1_1_38
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = 1sin(3π((-1x + 1)/(2x + 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}",
"role": "user"
}
] |
9
|
math
|
train
| 1,038 |
math_algebra_func_derivative_sign_level_1_1_39
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = (3(3cos(3πx + 3)) + 2)/(-3(3cos(3πx + 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}",
"role": "user"
}
] |
31
|
math
|
train
| 1,039 |
math_algebra_func_derivative_sign_level_1_1_40
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = 3cos(3π(4x + 5) - 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}",
"role": "user"
}
] |
79
|
math
|
train
| 1,040 |
math_algebra_func_derivative_sign_level_1_1_41
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (1(2cos(2πx + 3) + 1) - 3)/(-3(2cos(2πx + 3) + 1) - 2) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
21
|
math
|
train
| 1,041 |
math_algebra_func_derivative_sign_level_1_1_42
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = 3cos(1π((-3x - 2)/(-1x - 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}",
"role": "user"
}
] |
8
|
math
|
train
| 1,042 |
math_algebra_func_derivative_sign_level_1_1_43
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-1(2sin(2πx - 2) - 2) + 1)/(1(2sin(2πx - 2) - 2) + 3) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
20
|
math
|
train
| 1,043 |
math_algebra_func_derivative_sign_level_1_1_44
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 5(2sin(3πx + 1) + 2) + 4 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
30
|
math
|
train
| 1,044 |
math_algebra_func_derivative_sign_level_1_1_45
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(-2cos(1πx - 1) + 3)^2 - 4(-2cos(1πx - 1) + 3) + 5 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
11
|
math
|
train
| 1,045 |
math_algebra_func_derivative_sign_level_1_1_46
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1sin(3π(-4x^2 - 1x - 4) + 3) + 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
51
|
math
|
train
| 1,046 |
math_algebra_func_derivative_sign_level_1_1_47
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-3(1cos(1πx + 3)) - 2)/(3(1cos(1πx + 3))) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
11
|
math
|
train
| 1,047 |
math_algebra_func_derivative_sign_level_1_1_48
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = -3(-3sin(3πx + 2) - 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}",
"role": "user"
}
] |
30
|
math
|
train
| 1,048 |
math_algebra_func_derivative_sign_level_1_1_49
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2cos(1π((2x + 1)/(1x - 2)) - 1) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
10
|
math
|
train
| 1,049 |
math_algebra_func_derivative_sign_level_1_1_50
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1|(-3cos(3πx) - 1) - 2| - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
30
|
math
|
train
| 1,050 |
math_algebra_func_derivative_sign_level_1_1_51
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 5(3cos(3πx - 2) + 3) + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
30
|
math
|
train
| 1,051 |
math_algebra_func_derivative_sign_level_1_1_52
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3sin(2π(2|x - 3|) - 2) - 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
40
|
math
|
train
| 1,052 |
math_algebra_func_derivative_sign_level_1_1_53
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3sin(2π(3|x - 1| + 2) - 3) - 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
61
|
math
|
train
| 1,053 |
math_algebra_func_derivative_sign_level_1_1_54
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1|(2cos(2πx - 2) + 1) - 2| positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
41
|
math
|
train
| 1,054 |
math_algebra_func_derivative_sign_level_1_1_55
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 5(-2sin(3πx) - 3)^2 + 5 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
30
|
math
|
train
| 1,055 |
math_algebra_func_derivative_sign_level_1_1_56
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = -3sin(2π(-3x^2 - 2x + 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}",
"role": "user"
}
] |
46
|
math
|
train
| 1,056 |
math_algebra_func_derivative_sign_level_1_1_57
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 5(2sin(1πx))^2 + 3(2sin(1πx)) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
21
|
math
|
train
| 1,057 |
math_algebra_func_derivative_sign_level_1_1_58
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1|(1sin(1πx + 3) - 3) + 2| - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
11
|
math
|
train
| 1,058 |
math_algebra_func_derivative_sign_level_1_1_59
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3cos(2π(-1|x + 2|)) - 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
20
|
math
|
train
| 1,059 |
math_algebra_func_derivative_sign_level_1_1_60
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (3(3cos(3πx) - 2) - 2)/(3(3cos(3πx) - 2) - 1) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
30
|
math
|
train
| 1,060 |
math_algebra_func_derivative_sign_level_1_1_61
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1(1cos(2πx - 3) - 3) + 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
20
|
math
|
train
| 1,061 |
math_algebra_func_derivative_sign_level_1_1_62
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = 3|(-2sin(2πx + 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}",
"role": "user"
}
] |
40
|
math
|
train
| 1,062 |
math_algebra_func_derivative_sign_level_1_1_63
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(2cos(1πx) + 1) + 5 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
10
|
math
|
train
| 1,063 |
math_algebra_func_derivative_sign_level_1_1_64
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = 1sin(2π(-2x - 5) - 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}",
"role": "user"
}
] |
41
|
math
|
train
| 1,064 |
math_algebra_func_derivative_sign_level_1_1_65
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2sin(2π(1x) - 3) + 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
20
|
math
|
train
| 1,065 |
math_algebra_func_derivative_sign_level_1_1_66
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (2(-1cos(2πx - 1) - 1) - 3)/(3(-1cos(2πx - 1) - 1) - 2) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
20
|
math
|
train
| 1,066 |
math_algebra_func_derivative_sign_level_1_1_67
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(3sin(1πx - 3) + 3) + 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
10
|
math
|
train
| 1,067 |
math_algebra_func_derivative_sign_level_1_1_68
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3|(3sin(2πx + 1) - 1)| + 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
40
|
math
|
train
| 1,068 |
math_algebra_func_derivative_sign_level_1_1_69
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = -2(-2cos(1πx - 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}",
"role": "user"
}
] |
10
|
math
|
train
| 1,069 |
math_algebra_func_derivative_sign_level_1_1_70
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 5(3sin(3πx) - 3)^2 - 2(3sin(3πx) - 3) + 4 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
31
|
math
|
train
| 1,070 |
math_algebra_func_derivative_sign_level_1_1_71
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3sin(2π(-4x^2 - 4x + 4) + 1) + 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
40
|
math
|
train
| 1,071 |
math_algebra_func_derivative_sign_level_1_1_72
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3|(-2cos(3πx - 2) + 3) - 3| - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
60
|
math
|
train
| 1,072 |
math_algebra_func_derivative_sign_level_1_1_73
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1cos(1π(-1|x - 2| - 3) + 1) + 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
11
|
math
|
train
| 1,073 |
math_algebra_func_derivative_sign_level_1_1_74
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2cos(1π(1x - 5) + 2) - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
11
|
math
|
train
| 1,074 |
math_algebra_func_derivative_sign_level_1_1_75
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = 3cos(2π(3x)), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
60
|
math
|
train
| 1,075 |
math_algebra_func_derivative_sign_level_1_1_76
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3sin(2π(1|x - 1| - 1) - 1) + 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
21
|
math
|
train
| 1,076 |
math_algebra_func_derivative_sign_level_1_1_77
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-1(3sin(2πx + 2) + 3) + 1)/(3(3sin(2πx + 2) + 3) - 2) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
21
|
math
|
train
| 1,077 |
math_algebra_func_derivative_sign_level_1_1_78
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = -1cos(1π(2|x| - 1) - 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}",
"role": "user"
}
] |
21
|
math
|
train
| 1,078 |
math_algebra_func_derivative_sign_level_1_1_79
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3|(1sin(1πx + 1) + 1) + 1| + 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
10
|
math
|
train
| 1,079 |
math_algebra_func_derivative_sign_level_1_1_80
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(1cos(2πx + 3) - 3)^2 - 2(1cos(2πx + 3) - 3) + 5 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
20
|
math
|
train
| 1,080 |
math_algebra_func_derivative_sign_level_1_1_81
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = -3cos(2π(-3x - 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}",
"role": "user"
}
] |
60
|
math
|
train
| 1,081 |
math_algebra_func_derivative_sign_level_1_1_82
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2cos(2π(-4x^2 - 2x + 5) - 2) + 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
59
|
math
|
train
| 1,082 |
math_algebra_func_derivative_sign_level_1_1_83
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3cos(2π(3|x - 2| - 3) + 2) - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
61
|
math
|
train
| 1,083 |
math_algebra_func_derivative_sign_level_1_1_84
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 5(-2cos(2πx - 3) - 1)^2 + 2(-2cos(2πx - 3) - 1) + 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
41
|
math
|
train
| 1,084 |
math_algebra_func_derivative_sign_level_1_1_85
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = 1cos(3π(-2x^2 + 1x + 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}",
"role": "user"
}
] |
50
|
math
|
train
| 1,085 |
math_algebra_func_derivative_sign_level_1_1_86
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3cos(1π(5x^2 - 2x - 1)) - 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
57
|
math
|
train
| 1,086 |
math_algebra_func_derivative_sign_level_1_1_87
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = -3(-2sin(2πx - 2) + 2)^2 + 5(-2sin(2πx - 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}",
"role": "user"
}
] |
40
|
math
|
train
| 1,087 |
math_algebra_func_derivative_sign_level_1_1_88
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = -3sin(1π(3x^2 + 5x + 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}",
"role": "user"
}
] |
52
|
math
|
train
| 1,088 |
math_algebra_func_derivative_sign_level_1_1_89
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = -3cos(3π(-2x + 1) + 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}",
"role": "user"
}
] |
61
|
math
|
train
| 1,089 |
math_algebra_func_derivative_sign_level_1_1_90
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = 1sin(3π(1|x - 2| - 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}",
"role": "user"
}
] |
30
|
math
|
train
| 1,090 |
math_algebra_func_derivative_sign_level_1_1_91
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2(-1cos(3πx + 2) - 2)^2 - 4(-1cos(3πx + 2) - 2) - 5 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
30
|
math
|
train
| 1,091 |
math_algebra_func_derivative_sign_level_1_1_92
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2(-2sin(2πx + 2)) - 5 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
20
|
math
|
train
| 1,092 |
math_algebra_func_derivative_sign_level_1_1_93
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1cos(2π((2x + 1)/(-1x - 3)) - 2) - 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12
|
math
|
train
| 1,093 |
math_algebra_func_derivative_sign_level_1_1_94
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2sin(1π(-5x - 5)) - 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
51
|
math
|
train
| 1,094 |
math_algebra_func_derivative_sign_level_1_1_95
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1(-2sin(2πx - 2))^2 - 4(-2sin(2πx - 2)) + 4 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
21
|
math
|
train
| 1,095 |
math_algebra_func_derivative_sign_level_1_1_96
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = -2sin(2π(3x - 5) + 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}",
"role": "user"
}
] |
60
|
math
|
train
| 1,096 |
math_algebra_func_derivative_sign_level_1_1_97
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = -1cos(2π(-2x - 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}",
"role": "user"
}
] |
41
|
math
|
train
| 1,097 |
math_algebra_func_derivative_sign_level_1_1_98
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "For the function f(x) = -1(-1cos(2πx - 3) + 1)^2 + 2(-1cos(2πx - 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}",
"role": "user"
}
] |
40
|
math
|
train
| 1,098 |
math_algebra_func_derivative_sign_level_1_1_99
|
algebra_func_derivative_sign1
|
easy (level 1)
| 1 |
[
{
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3sin(3π(5x - 1) + 2) + 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
52
|
math
|
train
| 1,099 |
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