prompt4extract = """You are an educational AI designed to help students improve their math skills. Your task is categorizing the math problem based on the primary knowledge points it assesses. Please keep the following requirements in mind:

### Requirements:

1. The knowledge points should be as independent as possible, without overlapping.

2. The knowledge points should not be too granular; maintain a reasonable level of generalization.

3. Each problem should be labeled with no more than 4 primary knowledge points.

4. Use simple noun phrases to summarize the knowledge points.

5. The format for returning the knowledge points should be in the form of a list, e.g., [Addition, Multiplication].

### Example Knowledge Points:

- Addition

- Subtraction

- Multiplication

- Division

- Mixed Operations

- Algebraic Expressions

- Linear Equations

- Inequalities

- Area

- Perimeter

- Volume

- Angles

- Properties of Shapes

- Prime and Composite Numbers

- Factors and Multiples

- Mean, Median, Mode

- Probability

- Data Analysis

- Permutations and Combinations

- Length Units

- Volume Units

- Weight Units

- Time Units

- Ratios and Proportions

### Math Problem

{QUESTION}

{ANSWER}

Please categorize the math problem according to these requirements."""

template4tagging = Template(

    """You are an educational AI designed to help students improve their math skills. Your task is categorizing the math problem based on the primary knowledge points it assesses. Please keep the following requirements in mind:

### Requirements:

1. Select the appropriate knowledge points from the list provided under ### Knowledge Points.

2. Label each problem with no more than 4 primary knowledge points.

3. Return the knowledge points in a list format, e.g., [Addition, Multiplication].

### Knowledge Points:

{% for KNOWLEDGE_POINT in KNOWLEDGE_POINTS %}- {{ KNOWLEDGE_POINT }}

{% endfor %}

### Math Problem

{{ QUESTION }}

{{ ANSWER }}

Please categorize the math problem according to these requirements.""")

prompt4kps = """Based on the given knowledge points, create new, more challenging math questions that emphasize understanding and applying these knowledge points.

### Given Knowledge Points

{kps}

### Requirements:

- Create clear and high-quality questions.

- Ensure that the new questions comprehensively cover all the given knowledge points.

- Provide accurate mathematical calculations and detailed steps in your samples.

- Ensure that the difficulty level of the new questions is appropriate for {DIFFICULTY} mathematics.

- Ensure the final answer is explicitly presented with "So, the final answer is [NUMBER]".

### Return Format:

Return your samples in the following format:

**Question**: [QUESTION]

**Answer**:

>>

[ANSWER]

<<

Please follow the requirements and generate {X} samples."""

template4cognitive = Template(

    """You are an educational AI designed to help students improve their math skills by performing cognitive diagnosis on their incorrect answers and identifying their knowledge mastery levels.

### Knowledge Points:

{% for KNOWLEDGE_POINT in KNOWLEDGE_POINTS %}- {{ KNOWLEDGE_POINT }}

{% endfor %}

### Return Format:

Return your cognitive diagnosis results in the following format:

- Unmastered Knowledge Points: [UNMASTERED_KNOWLEDGE_POINTS]

- Mastered Knowledge Points: [MASTERED_KNOWLEDGE_POINTS]

e.g.:

- Unmastered Knowledge Points: [Equations, Unit Conversion]

- Mastered Knowledge Points: [Addition, Multiplication]

### Question given to the student:

{{ QUESTION }}

### Student's incorrect answer:

{{ WRONG_ANSWER }}

### Requirements:

- Perform a clear and detailed cognitive diagnosis.

- Diagnose the student's incorrect answer step-by-step.

- Ensure the identified knowledge points are from those provided in the ### Knowledge Points.

- Do not include knowledge points that are not involved in the question in the Unmastered Knowledge Points.

Please follow the requirements and generate your cognitive diagnosis.""")

template4cogsynthesis = Template("""Based on the results of the previous cognitive diagnosis, create new, more challenging questions focusing on the student's unmastered knowledge points to reinforce their understanding.

### Requirements:

- Create clear and high-quality questions.

- Provide accurate mathematical calculations and detailed steps in your samples.

- Ensure that the new questions have a greater focus on the unmastered knowledge points.

- Ensure that the difficulty level of the new questions is appropriate for {{ DIFFICULTY }} mathematics.

{% if UNMASTERED %}

### Unmastered Knowledge Points:

{{ UNMASTERED }}

{% endif %}

### Return Format:

Return your samples in the following format:

**Question**: [QUESTION]

**Answer**:

>>

[ANSWER]

<<

Please follow the requirements and generate {{ X }} samples.""")

prompt4kps = """Based on the given knowledge points, create new, more challenging math questions that emphasize understanding and applying these knowledge points.

### Given Knowledge Points

{kps}

### Requirements:

- Create clear and high-quality questions.

- Ensure that the new questions comprehensively cover all the given knowledge points.

- Provide accurate mathematical calculations and detailed steps in your samples.

- Ensure that the difficulty level of the new questions is appropriate for {DIFFICULTY} mathematics.

- Ensure the final answer is explicitly presented with "So, the final answer is [NUMBER]".

### Return Format:

Return your samples in the following format:

**Question**: [QUESTION]

**Answer**:

>>

[ANSWER]

<<

Please follow the requirements and generate {X} samples."""

prompt4more = """Based on the provided math question example, create new, more challenging math questions.

### Requirements:

- Create clear and high-quality questions.

- Provide accurate mathematical calculations and detailed steps in your samples.

- Generate questions with varying difficulty levels (e.g., junior high, senior high).

- Ensure that the generated question examine the same knowledge points as the example math question, but avoid simple variable replacement.

### Example:

**Question**: {question}

**Answer**: {answer}

**Knowledge Points**: {label}

### Return Format:

Return your samples in the following format:

**Question**: [QUESTION]

**Answer**:

>>

[ANSWER]

<<

Please follow the requirements and generate {X} samples."""

prompt4filter = """Here are the math problem and the answer in a question-answer format.

**Question**: {question}

**Answer**: {answer}

**Knowledge Points**: {label}

As a strict evaluator, please follow these steps when scoring:

## Correctness of the Answer (Top Priority 1):

If the answer is incorrect, assign a score of 0 and briefly explain. No further evaluation is needed.

If the answer is correct, proceed to the next step.

## Relevance to Knowledge Points (Top Priority 2):

Does the problem assess the specified knowledge points?

If no, assign a score of 0 with an explanation. If yes, continue.

## Evaluation of Other Dimensions:

### Clarity: Is the reasoning clear and easy to follow?

### Conciseness: Is the explanation succinct without unnecessary details?

### Format and Structure: Is the response well-structured and correctly formatted?

After considering these factors, provide a single score (0-10) for the overall quality, with correctness and knowledge point relevance as the highest priorities. Use the format:

Score: <score>||<explanation>."""

Coding 

Basic Data Types, Bitwise Operations, Boolean Logic, Class Definitions, Comparison Operators, Conditional Statements, Copying and Deep Copying, Dictionary Operations, Dynamic Programming, Exception Handling, Finding Min and Max, Heap Operations, Importing Libraries and Modules, Indexing and Slicing, Lambda Functions, List and Array Operations, Looping, Map Function, Recursion, Regular Expressions, Search Algorithms, Sorting Algorithms, Stacks and Queues, String Operations, Summation, Tree Structures, Tuple Operations, Type Checking and Conversion

Math 

Basic Arithmetic Operations, Decimal and Fraction Operations, Mixed Operations, Prime and Composite Numbers, Factors and Multiples, GCD and LCM, Algebraic Expressions, Equations, Inequalities, Basic Geometry, Area, Perimeter, Volume, Angles, Coordinates, Mean, Median, Mode, Probability, Permutations, Combinations, Financial Calculations, Unit Conversion, Time and Date Calculations, Speed, Distance, and Time, Measurement, Money, Ratio and Proportion, Bar Graphs, Line Graphs, Number Sequences, Word Problems, Linear Equations, Simple Algebra, Pattern Recognition, Mathematical Logic, Shapes and Spatial Understanding, Symmetry, Congruence, Units of Measurement, Temperature, Length, Mass, Capacity

Exams 

Biology: Protein and Nucleic Acid Structure, Sugar and Lipid Types and Functions, Water and Inorganic Salts, Cell Theory, Prokaryotic and Eukaryotic Cells, Cell Membrane Structure, Organelles Structure and Function, Nucleus Structure and Function, Substance Transport Across Cell Membrane, Enzyme Role in Metabolism, ATP Metabolism, Photosynthesis Process, Environmental Impact on Photosynthesis, Cellular Respiration, Cell Growth and Division, Cell Differentiation, Cell Aging and Apoptosis, Cancer Cells and Prevention, Meiotic Division, DNA Structure and Replication, Gene Transcription and Translation, Mendel’s Laws, Sex-linked Inheritance, Gene Mutation, Transgenic Food Safety, Human Genetic Diseases, Evolution Theory, Plant Hormones, Nervous and Hormonal Regulation, Nerve Impulse Transmission, Homeostasis, Immune System Role, Population and Community, Ecosystem Structure and Function, Ecosystem Stability, Biodiversity Conservation, Plant Growth Regulators, Yeast Respiration.Chemistry: Physical vs Chemical Changes, Acids, Bases, Salts and Oxides, Element Symbols, Valency and Formulas, Atomic and Molecular Masses, Law of Mass Conservation, Chemical Reactions, Molar Mass and Volume Calculations, Solubility and Concentration, Colloids and Solutions, Periodic Table Structure, Element Trends, Chemical Bonds, Oxidation-Reduction Reactions, Heat of Reactions, Electrochemistry, Reaction Rate and Activation Energy, Chemical Equilibrium, Electrolytes and Conductivity, pH Calculation, Ionization and Hydrolysis, Organic Compounds, Polymer Chemistry, Laboratory Safety, Gas Production and Separation, Chemical Analysis, Concentration Calculations.Geography: Earth’s Position in Space, Solar Influence, Earth’s Movements and Seasons, Earth’s Layers, Earth Material Cycles, Surface Changes, Atmospheric Heating, Wind and Pressure Systems, Climate and Weather Systems, Water Cycle, Ocean Currents, Geography and Environment, Climate Change, Natural Resources, Natural Disasters, Population Growth, Migration, Urbanization, Agricultural and Industrial Location, Environmental Impact, Geography of Resources, Transportation Systems, Human-Earth Relationships, Sustainability, Green Development, Remote Sensing, Geographic Information Systems, GPS and Navigation, Digital Earth.History: Ancient Chinese Political Systems, Shang and Zhou Dynasties, Qin Centralization, Han to Yuan Political Evolution, Ming and Qing Monarchy, Ancient Chinese Economy, Agricultural Systems, Handicraft and Commerce, Capitalism Emergence, Cultural Evolution, Hundred Schools of Thought, Confucianism, Neo-Confucianism, Chinese Scientific and Technological Achievements, Ancient Greek and Roman Political Systems, Athenian Democracy, Roman Law, Renaissance, Enlightenment, Industrial Revolution, World War Effects, Cold War and Bipolarity, Globalization, WTO and China’s Role, Modern Chinese Politics, Reform and Opening-up, Scientific and Technological Development in China, Modern Chinese Education and Culture. Math: Basic Arithmetic Operations, Decimal and Fraction Operations, Prime and Composite Numbers, Factors and Multiples, GCD and LCM, Algebraic Expressions, Equations, Inequalities, Geometry, Area, Perimeter, Volume, Angles, Coordinates, Mean, Median, Mode, Probability, Permutations, Combinations, Financial Calculations, Unit Conversion, Time and Date Calculations, Speed, Distance, Time, Measurement, Fractions, Decimals, Ratio, Proportion, Bar Graphs, Line Graphs, Probability Theory, Number Sequences, Word Problems, Time Tables, Integer Operations, Linear Equations, Simple Algebra, Pattern Recognition, Mathematical Logic, Shapes and Spatial Understanding, Symmetry, Congruence, Binomial Theorem, Conic Sections.Physics: Motion of Particles, Newton’s Laws, Mechanical Energy, Projectile and Circular Motion, Law of Gravitation, Electric Field, Circuits, Magnetic Field, Electromagnetic Induction, AC, Kinetic Theory of Gases, States of Matter, Thermodynamics, Vibration and Waves, Electromagnetic Waves, Light, Relativity, Reference Frames, Linear Motion, Friction, Hooke’s Law, Scalars and Vectors, Force Composition, Equilibrium, Energy Conservation, Momentum, Collision Theory, Universal Gravitation, Satellite Motion, Electric Potential, Capacitors, Ohm’s Law, Electric Resistance, Magnetic Forces, Lorentz Force, Spectroscopy, Nuclear Physics, Radiation, Energy Loss, Fission and Fusion Reactions, Photoelectric Effect, Einstein’s Equation.

问题：<br>(问题内容)<br>解题方案：<br>[解题方案内容]<br>以上是一个数学问题及其解题方案。请使用代码验证上述解题方案。

Prompt 

**Question**:{question}**Solution**:{solution}Above is a math problem and its solution. Please use code to verify the solution above. 

Input: 

*Question**: 

Express 0.54 as a fraction in lowest terms. 

将 0.54‾ 化为最简分数。(其中‾表示循环小数)

*Solution**: 

To express the repeating decimal 0.54 as a fraction in lowest terms, we can use algebraic manipulation. 

要将循环小数 0.54（即 0.54‾0.\overline{54}0.54）表示为最简分数，可以使用代数变形。

Let x=0.54. 

Step 1: Multiply x by 100 to shift the decimal point. 

…… 

Therefore, 0.54¯ can be expressed as 611 in lowest terms. 

Above is a math problem and its solution. Please use code to verify the solution above. 

Output: 

Now, let’s verify the answer by converting 6/11 back to a decimal.

# Convert the fraction 6/11 to a decimal

decimal_value = float(simplified_fraction)

decimal_value

Result: 

0.5454545454545454 

The decimal representation of 611 is approximately 0.5454545454545454, which matches the repeating decimal 0.54¯ 

Thus, our answer is verified and correct. 

Input: 

*Question**: 

What is 2121_3−212_3? Express your answer in base 3. 

*Solution**: 

Alright, let’s solve this step by step. 

To subtract these numbers, we’ll start from the rightmost digit (least significant) and move to the left, just like we do in base 10 subtraction. 

…… 

The result of 21213−2123 is 2223. 

Above is a math problem and its solution. Please use code to verify the solution above. 

Output: 

Now, let’s verify our answer by converting both numbers to base 10, performing the subtraction, and then converting the result back to base 3 to see if it matches our answer.

Result: 

1202 

It seems there was an error in our calculations. The correct result for 21213−2123 is 12023, not 2223. I apologize for the oversight. 

增强方法

GSM8K

MATH

SVAMP

Simuleq

Mathematics

平均

MetaMath

79.5

44.6

78.4

79.6

67.9

70.0

直接问题增强 (无解题方案) Direct question augmentation (w/o sol.)

78.8

43.0

84.0

77.0

70.2

70.6

直接问题增强 (有解题方案) Direct question augmentation (w/ sol.)

79.2

44.2

83.6

72.0

68.6

69.5

MathGenie (本文方法)

80.5

45.1

83.3

79.4

71.8

72.0