data_source
stringclasses 1
value | prompt
listlengths 1
1
| ability
stringclasses 1
value | reward_model
dict | extra_info
dict |
|---|---|---|---|---|
DeepScaleR-Preview
|
[
{
"role": "user",
"content": "Find the number of real solutions of the equation\n\\[\\frac{x}{100} = \\sin x.\\]"
}
] |
math
|
{
"style": "rule",
"ground_truth": "63"
}
|
{
"index": 40310,
"original_dataset": null,
"split": "train"
}
|
DeepScaleR-Preview
|
[
{
"role": "user",
"content": "Let $A,$ $B,$ $C$ be the angles of a triangle. Evaluate\n\\[\\begin{vmatrix} \\sin^2 A & \\cot A & 1 \\\\ \\sin^2 B & \\cot B & 1 \\\\ \\sin^2 C & \\cot C & 1 \\end{vmatrix}.\\]"
}
] |
math
|
{
"style": "rule",
"ground_truth": "0"
}
|
{
"index": 40311,
"original_dataset": null,
"split": "train"
}
|
DeepScaleR-Preview
|
[
{
"role": "user",
"content": "Let $G$ be the centroid of triangle $ABC,$ and let $P$ be an arbitrary point. Then there exists a constant $k$ so that\n\\[PA^2 + PB^2 + PC^2 = k \\cdot PG^2 + GA^2 + GB^2 + GC^2.\\]Find $k.$"
}
] |
math
|
{
"style": "rule",
"ground_truth": "3"
}
|
{
"index": 40312,
"original_dataset": null,
"split": "train"
}
|
DeepScaleR-Preview
|
[
{
"role": "user",
"content": "If angle $A$ lies in the second quadrant and $\\sin A = \\frac{3}{4},$ find $\\cos A.$"
}
] |
math
|
{
"style": "rule",
"ground_truth": "-\\frac{\\sqrt{7}}{4}"
}
|
{
"index": 40313,
"original_dataset": null,
"split": "train"
}
|
DeepScaleR-Preview
|
[
{
"role": "user",
"content": "The real numbers $a$ and $b$ satisfy\n\\[\\begin{pmatrix} 2 \\\\ a \\\\ -7 \\end{pmatrix} \\times \\begin{pmatrix} 5 \\\\ 4 \\\\ b \\end{pmatrix} = \\mathbf{0}.\\]Enter the ordered pair $(a,b).$"
}
] |
math
|
{
"style": "rule",
"ground_truth": "\\left( \\frac{8}{5}, -\\frac{35}{2} \\right)"
}
|
{
"index": 40314,
"original_dataset": null,
"split": "train"
}
|
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