task large_stringlengths 16 4.31k | task_id large_stringlengths 6 9 | plan large_stringclasses 3 values | task_type large_stringclasses 2 values | task_level large_stringclasses 6 values | hidden_state listlengths 3 3 |
|---|---|---|---|---|---|
Let \[f(x) = \left\{
\begin{array}{cl} ax+3, &\text{ if }x>2, \\
x-5 &\text{ if } -2 \le x \le 2, \\
2x-b &\text{ if } x <-2.
\end{array}
\right.\]Find $a+b$ if the piecewise function is continuous (which means that its graph can be drawn without lifting your pencil from the paper). | MATH_1 | Plan:
1 | Algebra | Level 5 | [
[
0.65234375,
0.10986328125,
1.4296875,
-1.171875,
-0.1650390625,
2.03125,
-0.84765625,
-0.53515625,
4.03125,
3.984375,
-2.640625,
8.8125,
-1.84375,
1.890625,
-5.375,
-2.453125,
0.703125,
2.515625,
-0.01141357421875,
-0.71875,
3.359... |
A rectangular band formation is a formation with $m$ band members in each of $r$ rows, where $m$ and $r$ are integers. A particular band has less than 100 band members. The director arranges them in a rectangular formation and finds that he has two members left over. If he increases the number of members in each row by 1 and reduces the number of rows by 2, there are exactly enough places in the new formation for each band member. What is the largest number of members the band could have? | MATH_2 | Plan:
1 | Algebra | Level 5 | [
[
1.9921875,
0.7265625,
1.6953125,
-0.59375,
2.078125,
1.4921875,
-2.390625,
-0.703125,
4.53125,
4.9375,
-3.671875,
7.9375,
-2.078125,
2.71875,
-6.78125,
-2.046875,
0.14453125,
1.703125,
1.1796875,
-0.058837890625,
3.515625,
4.9... |
What is the degree of the polynomial $(4 +5x^3 +100 +2\pi x^4 + \sqrt{10}x^4 +9)$? | MATH_3 | Plan:
| Algebra | Level 3 | [[1.03125,-0.953125,0.66015625,-2.234375,-0.056640625,0.72265625,-0.173828125,1.125,3.328125,4.53125(...TRUNCATED) |
Evaluate $\left\lceil3\left(6-\frac12\right)\right\rceil$. | MATH_4 | Plan:
1 | Algebra | Level 3 | [[0.67578125,-0.06591796875,0.1181640625,-0.9609375,1.078125,0.486328125,-0.087890625,1.5234375,3.25(...TRUNCATED) |
"Sam is hired for a 20-day period. On days that he works, he earns $\\$$60. For each day that he doe(...TRUNCATED) | MATH_5 | Plan:
1 | Algebra | Level 3 | [[1.9375,-0.53515625,-0.2470703125,-1.0703125,1.3203125,1.1484375,-1.46875,-0.94140625,4.03125,2.859(...TRUNCATED) |
Find the center of the circle with equation $x^2 - 6x + y^2 + 2y = 9$. | MATH_6 | Plan:
1 | Algebra | Level 4 | [[1.703125,-0.359375,-0.66796875,-0.8046875,-0.07373046875,2.296875,-2.171875,0.8046875,2.671875,6.0(...TRUNCATED) |
"What are all values of $p$ such that for every $q>0$, we have $$\\frac{3(pq^2+p^2q+3q^2+3pq)}{p+q(...TRUNCATED) | MATH_7 | Plan:
1 | Algebra | Level 5 | [[0.984375,1.4296875,-0.0712890625,-1.9375,0.291015625,1.4921875,-1.3515625,0.671875,4.53125,6.25,-2(...TRUNCATED) |
If $x = 2$ and $y = 5$, then what is the value of $\frac{x^4+2y^2}{6}$ ? | MATH_8 | Plan:
1 | Algebra | Level 1 | [[1.703125,0.3671875,0.291015625,-1.03125,-0.64453125,0.66015625,-1.1171875,0.89453125,3.609375,5.03(...TRUNCATED) |
"The sequence of integers in the row of squares and in each of the two columns of squares form three(...TRUNCATED) | MATH_9 | Plan:
1 | Algebra | Level 2 | [[0.8515625,1.953125,2.484375,-2.078125,-1.7421875,-0.9609375,-1.0078125,1.046875,3.34375,4.8125,-4.(...TRUNCATED) |
"Tim wants to invest some money in a bank which compounds quarterly with an annual interest rate of (...TRUNCATED) | MATH_10 | Plan:
1 | Algebra | Level 5 | [[0.546875,-0.7109375,1.1484375,0.12109375,1.0546875,1.3984375,-2.265625,0.33984375,4.09375,2.5,-3.6(...TRUNCATED) |
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