{ "Id": "527be9e9-7716-4f81-a2aa-4a582cef3419", "Title": "Advanced Problem Solving in Class 6 Mathematics", "Subject": "Mathematics", "Topic": "Place Value, Rounding, Estimation, and Multi-Step Computation", "Instructions": "Read each question carefully and answer to the best of your ability. Show all working for word problems.", "EstimatedMinutes": 35, "StudentProfileId": "", "SourceFileName": "combined_math_practice_sheets.pdf", "SessionMaterialId": "86139c68-3464-48b5-a7ec-2d15d3889839", "GeneratedAt": "2026-05-31T16:21:03.059705Z", "Questions": [ { "Id": 1, "Type": "word_problem", "Text": "Given the number 623541, determine the difference between the place value of the digit 6 and the place value of the digit 5. Then, express your answer in the Indian numbering format.", "Options": [], "Answer": "Step 1: Identify the place value of 6, which is in the hundred-thousands place (6 \u00D7 1,00,000 = 6,00,000).\nStep 2: Identify the place value of 5, which is in the hundreds place (5 \u00D7 100 = 500).\nStep 3: Compute the difference: 6,00,000 - 500 = 5,99,500.\nAnswer: 5,99,500", "Points": 10 }, { "Id": 2, "Type": "word_problem", "Text": "Using the digits 6, 0, 8, 4, and 1, form the greatest possible 6-digit number by allowing one digit to be repeated. Explain your reasoning and show each step.", "Options": [], "Answer": "Step 1: Arrange the given digits in descending order: 8, 6, 4, 1, 0.\nStep 2: Since only 5 distinct digits are available and a 6-digit number is required, repeat the highest digit (8) to maximize the number.\nStep 3: Place the repeated digit in the highest place value positions to form the number: 8, 8, 6, 4, 1, 0.\nAnswer: 886410", "Points": 10 }, { "Id": 3, "Type": "word_problem", "Text": "Determine how many unique 4-digit numbers can be formed using the digits 3, 4, 9, and 0, ensuring that the number does not start with 0. Provide a detailed explanation of your process.", "Options": [], "Answer": "Step 1: Recognize that the thousands place cannot be 0; therefore, possible digits for the thousands place are 3, 4, and 9 (3 options).\nStep 2: For each valid thousands digit, the remaining 3 digits can be arranged in 3! = 6 ways.\nStep 3: Multiply the possibilities: 3 \u00D7 6 = 18.\nAnswer: 18", "Points": 10 }, { "Id": 4, "Type": "word_problem", "Text": "Two petrol tanks contain 6325 \u2113 and 4890 \u2113 respectively. Estimate the difference in petrol between the two tanks by first rounding each volume to the nearest hundred litres. Provide all working steps.", "Options": [], "Answer": "Step 1: Round 6325 \u2113 to the nearest hundred: 6325 \u2192 6300 \u2113.\nStep 2: Round 4890 \u2113 to the nearest hundred: 4890 \u2192 4900 \u2113.\nStep 3: Compute the estimated difference: 6300 \u2113 - 4900 \u2113 = 1400 \u2113.\nAnswer: 1400 \u2113", "Points": 10 }, { "Id": 5, "Type": "word_problem", "Text": "Estimate the product of 958 and 387 by rounding each factor to the nearest hundred. Show all steps in your estimation process.", "Options": [], "Answer": "Step 1: Round 958 to the nearest hundred: 958 \u2192 1000.\nStep 2: Round 387 to the nearest hundred: 387 \u2192 400.\nStep 3: Multiply the rounded numbers: 1000 \u00D7 400 = 400000.\nAnswer: 400000", "Points": 10 }, { "Id": 6, "Type": "word_problem", "Text": "Estimate the quotient of 2838 divided by 125 by rounding both the dividend and the divisor to the nearest hundred. Provide detailed working for your estimation.", "Options": [], "Answer": "Step 1: Round 2838 to the nearest hundred: 2838 \u2192 2800.\nStep 2: Round 125 to the nearest hundred: 125 \u2192 100.\nStep 3: Perform the division with the rounded numbers: 2800 \u00F7 100 = 28.\nAnswer: 28", "Points": 10 }, { "Id": 7, "Type": "word_problem", "Text": "A school management spent $26,756 on teachers\u0027 pay, $325,378 on building construction, $5,780 on games, and $8,235 on other work. Calculate the total expenditure, showing each step and using the Indian numbering style where appropriate.", "Options": [], "Answer": "Step 1: Sum the amounts: 26756 \u002B 325378 = 352134.\nStep 2: Add the next amount: 352134 \u002B 5780 = 357914.\nStep 3: Add the final amount: 357914 \u002B 8235 = 366149.\nAnswer: 3,66,149", "Points": 10 }, { "Id": 8, "Type": "word_problem", "Text": "Madhu had $9031. After buying a TV, she was left with $1356. Determine the amount she paid for the TV, and provide each step of your calculation.", "Options": [], "Answer": "Step 1: Subtract the remaining amount from the initial amount: 9031 - 1356.\nStep 2: Perform the subtraction: 9031 - 1356 = 7675.\nAnswer: 7675", "Points": 10 }, { "Id": 9, "Type": "word_problem", "Text": "A country\u0027s population in 1990 was 906450600. In 1991, the population increased by 9889700. Calculate the population in 1991 with clear working steps.", "Options": [], "Answer": "Step 1: Write down the initial population: 906450600.\nStep 2: Add the increase: 906450600 \u002B 9889700.\nStep 3: Compute the sum: 906450600 \u002B 9889700 = 916340300.\nAnswer: 916340300", "Points": 10 }, { "Id": 10, "Type": "word_problem", "Text": "Combine two computations: First, find the sum of the predecessor of 97801 and 90526. Second, calculate the product of the successor of 147 and 389. Finally, add both results together. Provide detailed, step-by-step working.", "Options": [], "Answer": "Step 1: Find the predecessor of 97801, which is 97800.\nStep 2: Compute the sum with 90526: 97800 \u002B 90526 = 188326.\nStep 3: Find the successor of 147, which is 148.\nStep 4: Multiply 148 by 389: 148 \u00D7 389. (This can be computed as: 148 \u00D7 400 = 59200, and 148 \u00D7 11 = 1628, so 59200 - 1628 = 57572.)\nStep 5: Add the two results: 188326 \u002B 57572 = 245898.\nAnswer: 245898", "Points": 10 } ], "TotalPoints": 100 }