task large_stringlengths 16 4.31k | task_id large_stringlengths 6 9 | plan large_stringclasses 3
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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... | 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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