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92 lines
3.1 KiB
Python
92 lines
3.1 KiB
Python
from opencompass.openicl.icl_prompt_template import PromptTemplate
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from opencompass.openicl.icl_retriever import ZeroRetriever
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from opencompass.openicl.icl_inferencer import GenInferencer
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from opencompass.openicl.icl_evaluator import AccEvaluator
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from opencompass.datasets import HungarianExamMathDataset
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hungarianmath_reader_cfg = dict(input_columns=['question'], output_column=None)
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template = """Problem:
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Find the domain of the expression $\frac{\sqrt{x-2}}{\sqrt{5-x}}$.
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Solution:
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To determine the domain, we must ensure that:
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1. The expressions inside each square root are non-negative.
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2. The denominator is not equal to zero.
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For the numerator, $x-2 \ge 0$ gives $x \ge 2$.
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For the denominator, $5-x \ge 0$ gives $x \le 5$. And since the denominator cannot be zero, $5-x > 0$ which further narrows it to $x < 5$.
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Combining these results, the domain of the expression is $[2,5)$.
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Final Answer: The final answer is $[2,5)$.
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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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Solution:
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Using the property of determinants, we can say that:
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$\det (\mathbf{A} \mathbf{B}) = (\det \mathbf{A})(\det \mathbf{B})$.
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Plugging in the given values:
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$\det (\mathbf{A} \mathbf{B}) = 2 \times 12 = 24$.
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Final Answer: The final answer is $24$.
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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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Solution:
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First, calculate the total weight Terrell lifts with the 20-pound weights:
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$2 \times 12 \times 20 = 480$ pounds.
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If he uses 15-pound weights and lifts them $n$ times:
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$2 \times 15 \times n = 30n$ pounds.
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To find $n$, set these two equal:
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\begin{align*}
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30n &= 480 \\
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n &= \frac{480}{30} \\
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n &= 16
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\end{align*}
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Final Answer: The final answer is $16$.
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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*}
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has a solution $(x, y)$ where $x$ and $y$ are both nonzero, find $\frac{a}{b}$, assuming $b$ is nonzero.
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Solution:
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Multiply the first equation by $-\frac{3}{2}$ to obtain:
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$6y-9x = -\frac{3}{2}a$.
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Since we also know that $6y-9x = b$, equating them gives:
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$-\frac{3}{2}a = b$ which implies $\frac{a}{b} = -\frac{2}{3}$.
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Final Answer: The final answer is $-\frac{2}{3}$."""
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hungarianmath_infer_cfg = dict(
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prompt_template=dict(
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type=PromptTemplate,
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template=dict(
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round=[
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dict(role='HUMAN', prompt=template+'\n\nProblem:\n{question}\n\nSolution:\n'),
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],
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)),
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retriever=dict(type=ZeroRetriever),
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inferencer=dict(type=GenInferencer, max_out_len=1024))
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# Attention: this math dataset needs human to evaluate the generated answer, so the AccEvaluator is just a placeholder.
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hungarianmath_eval_cfg = dict(evaluator=dict(type=AccEvaluator))
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hungarianmath_datasets = [
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dict(
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abbr='HungarianExamMath',
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type=HungarianExamMathDataset,
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path='./data/HungarianExamMath/test.csv',
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reader_cfg=hungarianmath_reader_cfg,
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infer_cfg=hungarianmath_infer_cfg,
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eval_cfg=hungarianmath_eval_cfg)
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]
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