Please analyze the following stringent guidelines:

Guidelines for Creating SAT Math Quiz Questions Using the Provided JSON Structure

Creating high-quality math quiz questions requires careful attention to both content and structure. The following guidelines outline how to construct quiz questions using the provided JSON format, ensuring they are appropriate for college-bound students preparing for standardized tests like the SAT.

JSON Structure Breakdown
Each quiz question should adhere to the following JSON structure:

"text": (String)
Description: The main content of the question.
Guidelines:
Clearly state the problem or question.
Use LaTeX formatting for mathematical expressions, enclosed within $ symbols for inline math or $$` for display math. - Ensure all necessary information is included for the student to answer the question. 2. **"type"**: *(String)* - **Description**: Indicates the type of question. - **Expected Value**: `"multiple-choice-single-answer"` - **Guidelines**: - Use this exact string for consistency, as the quiz focuses on single-answer multiple-choice questions. 3. **"id"**: *(Integer or Unique String)* - **Description**: A unique identifier for the question. - **Guidelines**: - Assign a unique ID to each question to differentiate it from others. - IDs can be sequential numbers or unique strings. 4. **"correctAnswer"**: *(String)* - **Description**: The identifier of the correct option. - **Guidelines**: - Match this value to the `"id"` of the correct option in the `"options"` array. - Use lowercase letters (e.g., `"a"`, `"b"`, `"c"`, `"d"`). 5. **"quiztype"**: *(String)* - **Description**: Specifies the category of the quiz. - **Expected Value**: `"satmath"` - **Guidelines**: - Use this exact string to categorize the question under SAT Math. 6. **"explanation"**: *(String)* - **Description**: Provides a detailed solution or explanation for the correct answer. - **Guidelines**: - Offer step-by-step reasoning. - Use LaTeX formatting for mathematical expressions. - Aim to enhance understanding by explaining concepts, not just providing the answer. - Avoid mentioning option labels; focus on the solution process. 7. **"options"**: *(Array of Objects)* - **Description**: Contains the answer choices. - **Guidelines**: - Include at least four options. - Each option is an object with `"text"` and `"id"` fields. - Ensure one and only one option is correct. - **Within each option object**: a. **"text"**: *(String)* - **Description**: The content of the answer choice. - **Guidelines**: - Clearly state the answer choice. - **Do not use LaTeX formatting in the options**; write mathematical expressions in plain text. - Ensure numbers and expressions are clearly understandable without LaTeX. b. **"id"**: *(String)* - **Description**: Identifier for the option. - **Guidelines**: - Use lowercase letters starting from `"a"` (e.g., `"a"`, `"b"`, `"c"`, `"d"`). - Each option must have a unique `"id"`. **Additional Guidelines:** 8. **LaTeX Rendering in Question and Explanation** - **Guidelines**: - LaTeX formatting is required for mathematical expressions in the question text and explanation. - Do **not** use LaTeX formatting in the answer options; present options in plain text. 9. **JSON Formatting** - **Guidelines**: - When providing multiple questions, include all question objects within a single continuous JSON structure. - This may be an array of question objects without any breaks or separators. --- ### **Content Guidelines for SAT Math Questions** 1. **Relevance to SAT Curriculum** - Focus on topics commonly tested in the SAT Math sections: - **Heart of Algebra**: Linear equations, inequalities, systems of equations. - **Problem Solving and Data Analysis**: Ratios, percentages, proportional relationships. - **Passport to Advanced Math**: Quadratic equations, functions, polynomials. - **Additional Topics**: Geometry, trigonometry, complex numbers. 2. **Difficulty Level** - Tailor questions to reflect a range of difficulties found on the SAT: - **Easy**: Fundamental concepts and straightforward calculations. - **Medium**: Multi-step problems requiring critical thinking. - **Hard**: Complex problems involving abstract reasoning or advanced applications. 3. **Clarity and Precision** - Write questions clearly and concisely. - Avoid ambiguous language or overly complicated wording. - Ensure all necessary information is provided. 4. **Mathematical Accuracy** - Verify all mathematical expressions, calculations, and solutions. - Double-check the correct answer and ensure distractors are plausible but incorrect. 5. **Use of LaTeX Formatting** - Enclose all mathematical expressions in `$` or `$$ within the question text and explanation only.
Do not use LaTeX formatting in the options; present options in plain text.
Creating Effective Distractors
Design incorrect options that reflect common misconceptions or calculation errors.
Distractors should be reasonable to prevent students from easily eliminating them.
Explanation Quality
Provide comprehensive explanations that teach the underlying concepts.
Break down the solution into clear, logical steps.
Use proper mathematical notation and terminology.
Avoid mentioning option labels in the explanation; focus on the solution process.


{
  "text": "If $\\frac{3}{4}x - 2 = 7$, what is the value of $x$?",
  "type": "multiple-choice-single-answer",
  "id": 101,
  "correctAnswer": "c",
  "quiztype": "satmath",
  "explanation": "Start by adding 2 to both sides: $\\frac{3}{4}x = 9$. Then, multiply both sides by $\\frac{4}{3}$ to solve for $x$: $x = 9 \\times \\frac{4}{3} = 12$.",
  "options": [
    {
      "text": "9",
      "id": "a"
    },
    {
      "text": "10",
      "id": "b"
    },
    {
      "text": "12",
      "id": "c"
    },
    {
      "text": "15",
      "id": "d"
    }
  ]
}
Explanation:

Question Content: Solving a linear equation involving fractions.
Options: Include common errors, such as miscalculating when solving the equation.
Correct Answer: The correct answer is "12," which corresponds to option "c".
LaTeX Formatting: Mathematical expressions are properly formatted in the question text and explanation.
Options Formatting: Options are presented in plain text without LaTeX.
Explanation: Provides a step-by-step solution without mentioning option labels.
Best Practices
Consistency: Use consistent formatting and style across all questions.
Proofreading: Review questions for grammatical errors and mathematical accuracy.
Inclusivity: Ensure content is free from bias and accessible to all students.
Feedback Incorporation: If possible, use student feedback to improve question quality.
Final Notes
By following these guidelines, you will create high-quality, effective SAT Math practice questions that help students prepare for the exam. Remember to focus on clarity, accuracy, and educational value in each question and explanation.