data_source stringclasses 1 value | prompt listlengths 2 2 | ability stringclasses 1 value | reward_model dict | extra_info dict | answer stringclasses 10 values |
|---|---|---|---|---|---|
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "(1) Given that $0 < x < \\dfrac{4}{3}$, find the maximum value of $x(4-3x)$.\n\n(2) Point $(x,y)$ moves along the line $x+2y=3$. Find the minimum value of $2^{x}+4^{y}$.\nPlease ... | math | {
"ground_truth": "4 \\sqrt{2}",
"style": "rule"
} | {
"cluster_id": 1,
"difficulty": 37.5,
"index": 11953,
"split": "train"
} | 4 \sqrt{2} |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the asymptote equation of the hyperbola $y^{2}+\\frac{x^2}{m}=1$ is $y=\\pm \\frac{\\sqrt{3}}{3}x$, find the value of $m$.\nPlease reason step by step, and put your fi... | math | {
"ground_truth": "-3",
"style": "rule"
} | {
"cluster_id": 1,
"difficulty": 40.625,
"index": 9152,
"split": "train"
} | -3 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given points $A(-2,0)$ and $B(2,0)$, the slope of line $PA$ is $k_1$, and the slope of line $PB$ is $k_2$, with the product $k_1k_2=-\\frac{3}{4}$.\n$(1)$ Find the equation of th... | math | {
"ground_truth": "\\frac{3}{2}",
"style": "rule"
} | {
"cluster_id": 1,
"difficulty": 98.4375,
"index": 1230,
"split": "train"
} | \frac{3}{2} |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x)=x^{3}+3ax^{2}+bx+a^{2}$ has an extreme value of $0$ at $x=-1$, find the value of $a-b$.\nPlease reason step by step, and put your final answer within \\b... | math | {
"ground_truth": "-7",
"style": "rule"
} | {
"cluster_id": 1,
"difficulty": 51.5625,
"index": 8597,
"split": "train"
} | -7 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the circle $x^{2}-2x+y^{2}-2y+1=0$, find the cosine value of the angle between the two tangents drawn from the point $P(3,2)$.\nPlease reason step by step, and put your fin... | math | {
"ground_truth": "\\frac{3}{5}",
"style": "rule"
} | {
"cluster_id": 1,
"difficulty": 53.90625,
"index": 8476,
"split": "train"
} | \frac{3}{5} |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the minimum value of the discriminant of a quadratic trinomial whose graph does not intersect the regions below the x-axis and above the graph of the function \\( y = \\frac... | math | {
"ground_truth": "-4",
"style": "rule"
} | {
"cluster_id": 1,
"difficulty": 78.90625,
"index": 4778,
"split": "train"
} | -4 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the line \\(x=\\frac{\\pi}{4}\\) intersects the curve \\(C: (x-\\arcsin a)(x-\\arccos a) + (y-\\arcsin a)(y+\\arccos a)=0\\), determine the minimum value of the chord length a... | math | {
"ground_truth": "\\frac{\\pi}{2}",
"style": "rule"
} | {
"cluster_id": 1,
"difficulty": 60.9375,
"index": 7086,
"split": "train"
} | \frac{\pi}{2} |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $f\\left(x\\right)=ax^{2}-1$ and $g\\left(x\\right)=\\ln \\left(ax\\right)$ have an \"$S$ point\", then find the value of $a$.\nPlease reason step by step, and put your final... | math | {
"ground_truth": "\\frac{2}{e}",
"style": "rule"
} | {
"cluster_id": 1,
"difficulty": 30.46875,
"index": 10931,
"split": "train"
} | \frac{2}{e} |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function \\( f(x)=\\sqrt{3} \\sin 2x + 2 \\cos^2 x + a \\), if the minimum value of \\( f(x) \\) on the interval \\(\\left[ 0, \\frac{\\pi}{2} \\right] \\) is \\(-1\\),... | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"cluster_id": 1,
"difficulty": 46.09375,
"index": 10260,
"split": "train"
} | -1 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the coordinate plane, let $A = (-8, 0)$ , $B = (8, 0)$ , and $C = (t, 6)$ . What is the maximum value of $\\sin m\\angle CAB \\cdot \\sin m\\angle CBA$ , over all real nu... | math | {
"ground_truth": "3/8",
"style": "rule"
} | {
"cluster_id": 1,
"difficulty": 75.78125,
"index": 3752,
"split": "train"
} | 3/8 |
README.md exists but content is empty.
- Downloads last month
- 79