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https://github.com/deepseek-ai/DeepSeek-Math
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60 lines
2.6 KiB
Python
60 lines
2.6 KiB
Python
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from .few_shot_prompting import FewShotPrompting
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few_shot_prompt = """
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Problem:
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Find the domain of the expression $\\frac{\\sqrt{x-2}}{\\sqrt{5-x}}$.
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What of the following is the right choice? Explain your answer.
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(A) [-5,-2), (B) [2,5), (C) [-2,-5), (D) [5,2)
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Solution:
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The expressions inside each square root must be non-negative. Therefore, $x-2 \\ge 0$, so $x\\ge2$, and $5 - x \\ge 0$, so $x \\le 5$. Also, the denominator cannot be equal to zero, so $5-x>0$, which gives $x<5$.
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Therefore, the domain of the expression is $\\boxed{[2,5)}$.
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Final Answer: The final answer is (B). I hope it is correct.
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Problem:
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If $\\det \\mathbf{A} = 2$ and $\\det \\mathbf{B} = 12,$ then find $\\det (\\mathbf{A} \\mathbf{B}).$
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What of the following is the right choice? Explain your answer.
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(A) 14, (B) 4, (C) 2, (D) 24
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Solution:
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We have that $\\det (\\mathbf{A} \\mathbf{B}) = (\\det \\mathbf{A})(\\det \\mathbf{B}) = (2)(12) = \\boxed{24}.$
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Final Answer: The final answer is (D). I hope it is correct.
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Problem:
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Terrell usually lifts two 20-pound weights 12 times. If he uses two 15-pound weights instead, how many times must Terrell lift them in order to lift the same total weight?
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What of the following is the right choice? Explain your answer.
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(A) 12, (B) 20, (C) 16, (D) 15
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Solution:
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If Terrell lifts two 20-pound weights 12 times, he lifts a total of $2\\cdot 12\\cdot20=480$ pounds of weight. If he lifts two 15-pound weights instead for $n$ times, he will lift a total of $2\\cdot15\\cdot n=30n$ pounds of weight. Equating this to 480 pounds, we can solve for $n$: \\begin{align*}
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30n&=480\\\\
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\\Rightarrow\\qquad n&=480/30=\\boxed{16}
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\\end{align*}
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Final Answer: The final answer is (C). I hope it is correct.
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Problem:
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If the system of equations
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\\begin{align*}
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6x-4y&=a,\\\\
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6y-9x &=b.
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\\end{align*}has a solution $(x, y)$ where $x$ and $y$ are both nonzero, find $\\frac{a}{b},$ assuming $b$ is
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nonzero.
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What of the following is the right choice? Explain your answer.
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(A) $-\\frac{2}{3}$, (B) $\\frac{2}{3}$, (C) $\\frac{1}{3}$, (D) $\\frac{4}{9}$
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Solution:
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If we multiply the first equation by $-\\frac{3}{2}$, we obtain
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$$6y-9x=-\\frac{3}{2}a.$$Since we also know that $6y-9x=b$, we have
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$$-\\frac{3}{2}a=b\\Rightarrow\\frac{a}{b}=\\boxed{-\\frac{2}{3}}.$$
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Final Answer: The final answer is (A). I hope it is correct.
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""".strip()
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class CoTSATPrompt(FewShotPrompting):
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def __init__(self):
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super().__init__()
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def format_prompt(self, task_input, task_output):
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prompt = f"{few_shot_prompt}\n\nProblem:\n{task_input}\nSolution:\n{task_output}"
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return prompt.rstrip()
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def stop_words(self):
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return ["\nProblem:"]
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