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Answers and Feedback for the High School Math Question Paper:

Question 1: Solve the equation
2𝑥² − 5𝑥 + 2 = 0

• Student's Response: Correctly applied the quadratic formula to find 𝑥 = 2 and 𝑥 = 0.5.
• Feedback: Excellent use of the quadratic formula. All steps are clearly shown and the calculations are accurate.

Question 2: Factorize
4𝑥² − 9

• Student's Response: Correctly identified as a difference of squares and factored to (2𝑥 − 3)(2𝑥 + 3).
• Feedback: Well done on recognizing the pattern and applying the difference of squares formula correctly.

Question 3: Simplify
3𝑥² + 4𝑥 − 1𝑥 + 1

• Student's Response: Performed polynomial division correctly to simplify to 3𝑥 − 1.
• Feedback: Good job on the polynomial division. The final expression is correctly simplified.

Question 4: Find 𝑥 such that log₁₀(𝑥 + 2) + log₁₀𝑥 = 1

• Student's Response: Successfully combined the logarithmic expressions and applied the quadratic formula to find 𝑥 = 11 − 1.
• Feedback: Excellent work in handling logarithmic properties and solving the quadratic equation. Remember to check that the solution fits the domain of the logarithm.

Question 5: Check if the triangle with sides 𝑎 = 5, 𝑏 = 8, and 𝑐 = 10 is a right triangle:

• Student's Response: Correctly used Pythagoras' theorem to determine that the triangle is not a right triangle.
• Feedback: Correct approach using Pythagoras' theorem. Your conclusion is accurate based on the calculations.

Overall Performance:

• Accuracy: All answers are correct and well-supported by mathematical procedures.
• Presentation: Clear and organized responses with all necessary steps shown.
• Critical Thinking: Demonstrated good problem-solving skills across various types of mathematical problems.

Final Grade: 100%

Additional Comments:
You've shown excellent mathematical skills and a clear understanding of the topics covered. Keep up the great work and continue practicing to further enhance your problem-solving abilities!

Grading Summary

Question 1: String Manipulation

• Score: 10/10
• Feedback: The function reverse_string correctly reverses the input string using Python slicing, which is an efficient and concise method. The example usage demonstrates the correct output.

Question 2: Array Operations

• Score: 10/10
• Feedback: The function sum_positive_numbers accurately computes the sum of all positive numbers in the array. The logic is clear and correctly implemented, iterating through the array and summing positive values.

Question 3: Sorting

• Score: 10/10
• Feedback: The bubble_sort function correctly implements the bubble sort algorithm to sort an array in ascending order. The example demonstrates that the array is sorted correctly after the function execution.

Question 4: Recursion

• Score: 10/10
• Feedback: The recursive function factorial is implemented correctly to compute the factorial of a number. The base case and recursive call are appropriately used, and the example output is correct.

Question 5: Linked Lists

• Score: 10/10
• Feedback: The implementation of the singly linked list with methods for insertion at the beginning, deletion from the beginning, and printing all elements is correct. The operations perform as expected, and the example usage effectively demonstrates these operations.

Overall Feedback

• Total Score: 50/50
• General Comments: Excellent work! All functions are implemented correctly with clear and efficient code. The examples provided demonstrate the functionality effectively. Continue exploring additional data structures and algorithms to further enhance your understanding and skills in Python programming.

Keep up the great work!