task stringlengths 16 2.65k | task_id stringlengths 6 9 | plan stringlengths 14 1.64k | task_type stringclasses 7
values | task_level stringclasses 6
values | hidden_state listlengths 135 547 |
|---|---|---|---|---|---|
"If the three lines $3y-2x=1$, $x+2y=2$ and $4x-6y=5$ are drawn in the plane, how many points will l(...TRUNCATED) | MATH_1506 | "Plan:\n1. Identify the equations of the lines:\n - Line 1: $3y - 2x = 1$\n - Line 2: $x + 2y = (...TRUNCATED) | Algebra | Level 4 | [[0.21875,0.26171875,1.15625,1.015625,0.5703125,-0.26171875,-0.546875,-0.8984375,-2.171875,-2.40625,(...TRUNCATED) |
"Find the value of $x$ between 0 and 180 such that\n\\[\\tan (120^\\circ - x^\\circ) = \\frac{\\sin (...TRUNCATED) | MATH_4562 | "Plan:\n1. Recognize the given equation involves trigonometric identities and consider the tangent s(...TRUNCATED) | Precalculus | Level 5 | [[0.3359375,0.1328125,0.7578125,0.8203125,0.3046875,-0.38671875,-0.75,-1.1875,-1.859375,-2.078125,-1(...TRUNCATED) |
Find the center of the circle with equation $9x^2-18x+9y^2+36y+44=0.$ | MATH_621 | "Plan:\n1. Recognize that the given equation is in the general form of a circle equation, $Ax^2 + Bx(...TRUNCATED) | Algebra | Level 4 | [[0.578125,0.5,0.890625,1.015625,0.4375,-0.291015625,-0.62109375,-0.984375,-2.140625,-2.171875,-1.38(...TRUNCATED) |
Find the sum of the reciprocals of the roots of $x^2-13x+4=0$. | MATH_238 | "Plan:\n1. Identify the roots of the quadratic equation $x^2-13x+4=0$ using the quadratic formula or(...TRUNCATED) | Algebra | Level 5 | [[0.6171875,0.15234375,0.9453125,1.0625,0.375,-0.298828125,-0.73828125,-0.9453125,-2.25,-2.625,-1.45(...TRUNCATED) |
"Find the angle between the vectors $\\begin{pmatrix} 2 \\\\ -1 \\\\ 1 \\end{pmatrix}$ and $\\begin{(...TRUNCATED) | MATH_4171 | "Plan:\n1. Recall the formula for the dot product of two vectors and the formula for the magnitude o(...TRUNCATED) | Precalculus | Level 2 | [[0.34765625,0.419921875,1.0078125,1.15625,0.41796875,-0.4296875,-0.6328125,-1.015625,-2.203125,-2.5(...TRUNCATED) |
"According to the chart shown, what was the average daily high temperature in Addington from Septemb(...TRUNCATED) | MATH_3765 | "Plan:\n1. Identify the daily high temperatures for September 15th through September 19th, 2008 from(...TRUNCATED) | Prealgebra | Level 3 | [[-0.23828125,-0.255859375,1.453125,0.640625,0.6328125,0.228515625,-0.142578125,-1.59375,-2.28125,-2(...TRUNCATED) |
Compute $\tan 75^\circ.$ | MATH_4527 | "Plan:\n1. Recognize that $75^\\circ$ can be expressed as the sum of two special angles: $75^\\circ (...TRUNCATED) | Precalculus | Level 1 | [[0.5625,0.22265625,0.765625,0.9140625,-0.01953125,-0.37109375,-0.83203125,-0.78515625,-1.9453125,-2(...TRUNCATED) |
"Compute the integer $k > 2$ for which\n\\[\\log_{10} (k - 2)! + \\log_{10} (k - 1)! + 2 = 2 \\log_{(...TRUNCATED) | MATH_1664 | "Plan:\n1. Recognize that the equation involves logarithms and factorials, suggesting the use of pro(...TRUNCATED) | Intermediate Algebra | Level 3 | [[0.57421875,0.259765625,1.125,1.1484375,0.35546875,-0.68359375,-0.69921875,-1.3203125,-2.046875,-2.(...TRUNCATED) |
"At Beaumont High School, there are 20 players on the basketball team. All 20 players are taking at(...TRUNCATED) | MATH_4019 | "Plan:\n1. Identify the total number of players and the given subsets.\n - Total players: 20\n -(...TRUNCATED) | Prealgebra | Level 5 | [[0.3828125,0.275390625,1.140625,0.91015625,0.1171875,-0.4140625,-0.546875,-1.03125,-1.796875,-2.390(...TRUNCATED) |
"An arithmetic sequence consists of $ 200$ numbers that are each at least $ 10$ and at most $ 100$. (...TRUNCATED) | MATH_1459 | "Plan:\n1. Identify the formula for the sum of an arithmetic sequence and apply it to the given info(...TRUNCATED) | Intermediate Algebra | Level 5 | [[0.34375,-0.078125,1.3046875,0.6875,0.73046875,-0.6015625,-0.25,-1.25,-1.8125,-3.0,-1.140625,2.3593(...TRUNCATED) |
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