Go through the following stringent guidelines again and then using the sample json formulate 4 similar questions in context. Use single dollar signs for latex formatting. Start with id 194:

Guidelines for Creating High-Quality SAT Math Questions

When crafting SAT Math questions for college-bound students, it's essential to ensure each question is educational, fair, and reflective of the actual exam standards. The following updated guidelines incorporate specific considerations for charts questions and are designed to help you develop high-quality SAT Math questions that meet the expectations of students preparing for the SAT.

1. Align with SAT Content Areas
Heart of Algebra: Include linear equations and inequalities, systems of equations, and linear functions.
Problem Solving and Data Analysis: Focus on ratios, percentages, proportional relationships, data interpretation, and statistics.
Passport to Advanced Math: Incorporate quadratic equations, higher-order equations, functions, and their manipulations.
Additional Topics in Math: Cover geometry, trigonometry, complex numbers, and the coordinate plane.
2. Ensure Appropriate Difficulty Level
Balance Difficulty: Provide a mix of easy, medium, and challenging questions to cater to a range of skill levels.
Reflect Exam Standards: Questions should mimic the complexity found in actual SAT questions.
3. Use Clear and Concise Language
Avoid Ambiguity: Write questions with precise language to prevent misunderstandings.
Standard Terminology: Use mathematical terms consistent with high school curricula.
Direct Questions: Clearly state what is being asked without unnecessary information.
4. Focus on Mathematical Accuracy
Correct Solutions: Verify that all calculations and solutions are accurate.
Logical Reasoning: Ensure the reasoning in explanations is sound and follows logical mathematical principles.
Appropriate Significance: Use numbers and results that are realistic and appropriately scaled for the context.
5. Create High-Quality Multiple-Choice Options
Plausible Distractors: Develop incorrect answer choices that are common mistakes or misconceptions to test students' understanding.
Answer Variety: Avoid patterns in correct answer choices (e.g., don't make the same option (A, B, C, or D) the correct answer too frequently).
Randomization Consideration: Do not reference specific answer labels (e.g., "Answer choice D") in explanations, as options may be randomized.
6. Provide Detailed Explanations
Step-by-Step Solutions: Offer comprehensive explanations that walk through the problem-solving process.
Educational Value: Use explanations to reinforce concepts and address why incorrect options are wrong.
Omit Answer Labels in Explanations: Do not mention specific option labels in explanations to maintain clarity when options are randomized.
7. Incorporate Diverse Question Formats
Variety in Presentation: Use different formats such as equations, word problems, graphs, and tables.
Real-World Scenarios: Include context-based questions that apply mathematical concepts to real-life situations.
Charts Questions: For charts questions, provide clear and accurate charts, tables, or graphs with sufficient detail.
8. Guidelines Specific to Charts Questions
Data Clarity: Ensure that all charts, tables, or graphs are clearly labeled with appropriate titles, headers, and units of measurement.
Sufficient Data: Include enough data points or categories to make the question meaningful and appropriately challenging (e.g., tables should have at least 4-5 columns or rows).
Variety of Data Types: Use different types of data presentations, such as bar graphs, line charts, pie charts, or complex tables.
Interpretation Skills: Design questions that require students to interpret data accurately, perform calculations based on the data, or draw conclusions.
Consistency with Question: Make sure the data provided directly relates to the question being asked and contains all necessary information to answer it.
Double Newline Characters: When formatting data in the chartData key/value pair, use double newline characters (\n\n) as needed to enhance readability, especially when LaTeX rendering is involved.
9. Maintain Fairness and Accessibility
Cultural Sensitivity: Avoid content that may disadvantage any group of students.
Inclusivity: Use diverse names and contexts that reflect a wide range of experiences.
Avoid Bias: Ensure that questions are free from stereotypes and do not require outside knowledge beyond common experience.
10. Use Proper Formatting and Notation
Consistency: Follow standard mathematical notation and formatting.
Clarity: Use clear fonts and layouts that are easy to read.
Units and Labels: Include appropriate units of measurement and labels where necessary.
Formatting for LaTeX Rendering: Use LaTeX syntax for mathematical expressions and ensure proper spacing using double newline characters where appropriate.
11. Adhere to Timing Considerations
Reasonable Completion Time: Design questions that can be answered within the average time allocated per question on the SAT.
Avoid Overly Complex Calculations: Ensure computations are manageable without a calculator if applicable.
12. Originality and Plagiarism
Create Original Content: Develop unique questions and avoid copying existing material.
Cite Sources: If using inspiration from existing problems, modify them sufficiently and give appropriate credit if necessary.
13. Review and Edit Thoroughly
Proofreading: Check for grammatical errors, typos, and mathematical inaccuracies.
Peer Review: Have questions reviewed by other educators or subject matter experts.
Pilot Testing: If possible, test questions on a sample of students to gauge clarity and difficulty.
14. Ethical and Legal Compliance
Respect Privacy: Do not include personal information or scenarios that could violate privacy.
Age Appropriateness: Ensure content is suitable for high school students.
Examples and Best Practices

Charts Questions
Example Guideline: When creating a charts question, provide a table or graph with sufficient data, including at least 4-5 columns or categories to offer complexity and depth.
Data Presentation: Ensure that the data is presented in a clear and organized manner, with appropriate titles and labels for each column and row.
Question Development: Formulate questions that require students to analyze the data, perform calculations (such as finding probabilities, percentages, or averages), or interpret trends.
Sample Scenario:
Context: A table showing the distribution of sales across different regions and product categories.
Question: "Based on the data in the table, what is the probability that a randomly selected sale was for Product X in Region Y?"
Explanation: Provide a step-by-step calculation showing how to use the data to find the correct probability.
Algebraic Equations: Design problems that require solving for variables, interpreting linear functions, or manipulating expressions.
Example Guideline: When creating an equation-solving problem, ensure the equation is solvable using methods taught at the high school level, such as factoring or using the quadratic formula.
Geometry and Trigonometry: Include questions involving angles, lengths, areas, volumes, and trigonometric ratios.
Example Guideline: For geometry problems, provide diagrams when necessary and ensure all figures are drawn to scale unless specified otherwise.
Data Interpretation: Develop questions that require analyzing graphs, tables, and charts.
Example Guideline: Use clear and accurately scaled graphs or charts, and ask questions that test the ability to extract and interpret data.
Word Problems: Craft real-life scenarios requiring mathematical solutions, such as calculating interest, distances, or rates.
Example Guideline: Ensure word problems are relatable and the required information is all contained within the question.
Additional Tips

Avoid Tricky Questions: The goal is to assess mathematical understanding, not the ability to decipher confusing wording.
Calculator Policy: Be mindful of whether the question falls into the calculator or no-calculator section of the SAT and design accordingly.
Consistent Units: Use consistent units throughout a question and specify units in the answer choices if applicable.
Label Diagrams: Clearly label all parts of any diagrams or figures used in questions.
Formatting for LaTeX Rendering: When writing mathematical expressions or equations that will be rendered in LaTeX, use double newline characters where appropriate to ensure adequate vertical spacing. This enhances readability and prevents overlapping or cramped formatting.
Omit Answer Labels in Explanations: When writing explanations, do not reference specific answer choices by their labels (e.g., "Answer choice A"). Instead, focus on the correct equation or method to avoid confusion when options are randomized.
By incorporating these updated guidelines, including specific considerations for charts questions, you will contribute to a comprehensive and effective SAT Math module. High-quality questions not only assess students' knowledge but also enhance their understanding and problem-solving skills.

Sample Json:

{
"text": "For the equations a^x/a^y=a^10 and a^y^3 = a^x, if a > 1, what is the value of x?",
"type": "multiple-choice-single-answer",
"id": 1,
"correctAnswer": "d",
"quiztype": "satmath",
"explanation": "The question asks for the value of x, but it looks pretty intimidating with all those variables. In fact, you might be about to cry 'POOD' and go on to the next question. That might not be a bad idea, but before you skip the question, pull out those MADSPM rules. For the first equation, you can use the Divide-Subtract Rule: a^x/a^y = a^x-y = a^10. In other words, the first equation tells you that x – y = 10. For the second equation, you can use the Power-Multiply Rule: (a^y)^3 = a^3y = a^x. So, that means that 3y = x. Now, it’s time to substitute: x − y = 3y − y = 10. So, 2y = 10 and y = 5. Be careful, though! Don’t choose 5. That’s the value of y, but the question wants to know the value of x. Since x = 3y, x = 3(5) = 15. The correct answer is 15.",
"options": [
{
"text": "$5$",
"id": "a"
},
{
"text": "$10$",
"id": "b"
},
{
"text": "$15$",
"id": "c"
},
{
"text": "$20$",
"id": "d"
}
]
}