{
  "Id": "6c57ec21-976c-45cf-918e-138b1909bec7",
  "Title": "Grade 6 Mathematics Comprehensive Practice Worksheet",
  "Subject": "Mathematics",
  "Topic": "Arithmetic and Problem Solving",
  "Instructions": "Read each question carefully and answer to the best of your ability. Show all working for word problems.",
  "EstimatedMinutes": 35,
  "StudentProfileId": "dd186faa-f489-46ee-84e4-26e2d01e2691",
  "SourceFileName": "combined_math_practice_sheets.pdf",
  "SessionMaterialId": "86139c68-3464-48b5-a7ec-2d15d3889839",
  "GeneratedAt": "2026-05-31T16:18:12.363676Z",
  "Questions": [
    {
      "Id": 1,
      "Type": "true_false",
      "Text": "In the number 623541, the place value of 6 is always greater than that of 5.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 2,
      "Type": "true_false",
      "Text": "The sum of an odd number and an even number is always an odd number.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 3,
      "Type": "true_false",
      "Text": "A number formed by rearranging the digits 6, 0, 8, 4, 1 can begin with 0 to be considered a six-digit number.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 4,
      "Type": "true_false",
      "Text": "Rounding off numbers to the nearest hundred can sometimes significantly change the result of an arithmetic operation.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 5,
      "Type": "true_false",
      "Text": "Prime factorisation is used to determine the LCM of 210 and 186.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 6,
      "Type": "true_false",
      "Text": "The additive identity for whole numbers is 1.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 7,
      "Type": "true_false",
      "Text": "To find the difference between the place values of 6 and 5 in 623541, you simply subtract 5 from 6.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 8,
      "Type": "true_false",
      "Text": "The sum of rounded numbers is always equal to the rounded sum of the original numbers.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 9,
      "Type": "true_false",
      "Text": "Estimating a product by rounding each factor usually leads to a close approximation of the actual product.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 10,
      "Type": "true_false",
      "Text": "The prime numbers between 30 and 50 include 37 and 41.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 11,
      "Type": "multiple_choice",
      "Text": "Which of the following is the additive identity for whole numbers?",
      "Options": [
        "A. 0",
        "B. 1",
        "C. 6",
        "D. None"
      ],
      "Answer": "A. 0",
      "Points": 2
    },
    {
      "Id": 12,
      "Type": "multiple_choice",
      "Text": "How many 4-digit numbers can be formed using the digits 3, 4, 9, and 0 without repeating any digit?",
      "Options": [
        "A. 6",
        "B. 12",
        "C. 18",
        "D. 24"
      ],
      "Answer": "C. 18",
      "Points": 2
    },
    {
      "Id": 13,
      "Type": "multiple_choice",
      "Text": "In Roman numerals, what number completes the equation LXX \u002B _____ = LXXVI?",
      "Options": [
        "A. VI",
        "B. V",
        "C. IV",
        "D. VII"
      ],
      "Answer": "A. VI",
      "Points": 2
    },
    {
      "Id": 14,
      "Type": "multiple_choice",
      "Text": "What is the approximate product of 958 and 387 when each factor is rounded to the nearest hundred?",
      "Options": [
        "A. 380,000",
        "B. 400,000",
        "C. 420,000",
        "D. 450,000"
      ],
      "Answer": "B. 400,000",
      "Points": 2
    },
    {
      "Id": 15,
      "Type": "multiple_choice",
      "Text": "Which method is used to find the LCM of 210 and 186 as shown in the worksheet?",
      "Options": [
        "A. Addition",
        "B. Prime Factorisation",
        "C. Subtraction",
        "D. Estimation"
      ],
      "Answer": "B. Prime Factorisation",
      "Points": 2
    },
    {
      "Id": 16,
      "Type": "multiple_choice",
      "Text": "If a country\u0027s population was 906450600 in 1990 and increased by 9889700 the next year, which option best describes the population in 1991?",
      "Options": [
        "A. The original population",
        "B. The increased amount",
        "C. The population of 1991",
        "D. The quotient of the two numbers"
      ],
      "Answer": "C. The population of 1991",
      "Points": 2
    },
    {
      "Id": 17,
      "Type": "multiple_choice",
      "Text": "Which expression correctly approximates 2838 \u00F7 125 by rounding to the nearest hundreds?",
      "Options": [
        "A. 2800 \u00F7 100",
        "B. 2900 \u00F7 100",
        "C. 2800 \u00F7 130",
        "D. 3000 \u00F7 100"
      ],
      "Answer": "A. 2800 \u00F7 100",
      "Points": 2
    },
    {
      "Id": 18,
      "Type": "multiple_choice",
      "Text": "Which of the following pairs are examples of twin primes as suggested by the worksheet?",
      "Options": [
        "A. (3, 5)",
        "B. (11, 13)",
        "C. (17, 19)",
        "D. All of the above"
      ],
      "Answer": "D. All of the above",
      "Points": 2
    },
    {
      "Id": 19,
      "Type": "multiple_choice",
      "Text": "What is the correct interpretation of \u0027successor\u0027 in the context of finding the product with 147 and 389?",
      "Options": [
        "A. 148 \u00D7 389",
        "B. 147 \u00D7 390",
        "C. 148 \u00D7 390",
        "D. 147 \u00D7 389"
      ],
      "Answer": "A. 148 \u00D7 389",
      "Points": 2
    },
    {
      "Id": 20,
      "Type": "multiple_choice",
      "Text": "Which method is used to find the HCF of 420 and 430 in the worksheet?",
      "Options": [
        "A. Division Algorithm",
        "B. Distributive Property",
        "C. Prime Factorisation",
        "D. Estimation"
      ],
      "Answer": "C. Prime Factorisation",
      "Points": 2
    },
    {
      "Id": 21,
      "Type": "fill_blank",
      "Text": "_____ is called additive identity for whole number.",
      "Options": [],
      "Answer": "0",
      "Points": 2
    },
    {
      "Id": 22,
      "Type": "fill_blank",
      "Text": "The sum of an odd number and an even number is always a(n) _____ number.",
      "Options": [],
      "Answer": "odd",
      "Points": 2
    },
    {
      "Id": 23,
      "Type": "fill_blank",
      "Text": "In the number 623541, the difference between the place values of 6 and 5 is _____.",
      "Options": [],
      "Answer": "599500",
      "Points": 2
    },
    {
      "Id": 24,
      "Type": "fill_blank",
      "Text": "The estimated quotient of 2838 divided by 125 by rounding off to the nearest hundreds is _____.",
      "Options": [],
      "Answer": "28",
      "Points": 2
    },
    {
      "Id": 25,
      "Type": "fill_blank",
      "Text": "The rounded product of 958 and 387 by rounding each to the nearest 100\u0027s is _____.",
      "Options": [],
      "Answer": "400000",
      "Points": 2
    },
    {
      "Id": 26,
      "Type": "fill_blank",
      "Text": "The number of 4-digit numbers that can be formed with digits 3, 4, 9, and 0 without repeating any digit is _____.",
      "Options": [],
      "Answer": "18",
      "Points": 2
    },
    {
      "Id": 27,
      "Type": "fill_blank",
      "Text": "The sum of 1086, 2117, 3543, and 1284 is _____.",
      "Options": [],
      "Answer": "8030",
      "Points": 2
    },
    {
      "Id": 28,
      "Type": "fill_blank",
      "Text": "The population of a country in 1991, after an increase of 9889700 from 906450600 in 1990, is _____.",
      "Options": [],
      "Answer": "916340300",
      "Points": 2
    },
    {
      "Id": 29,
      "Type": "fill_blank",
      "Text": "LXX \u002B _____ = LXXVI",
      "Options": [],
      "Answer": "VI",
      "Points": 2
    },
    {
      "Id": 30,
      "Type": "fill_blank",
      "Text": "LIX = _____ \u002B IX",
      "Options": [],
      "Answer": "L",
      "Points": 2
    },
    {
      "Id": 31,
      "Type": "word_problem",
      "Text": "Find the difference between the place values of 6 and 5 in the number 623541. Show your working.",
      "Options": [],
      "Answer": "Step 1: Place value of 6 = 600000, place value of 5 = 500\nStep 2: Difference = 600000 - 500\nAnswer: 599500",
      "Points": 5
    },
    {
      "Id": 32,
      "Type": "word_problem",
      "Text": "Madhu had $9031 and bought a TV, leaving her with $1356. How much did she pay for the TV? Show your working.",
      "Options": [],
      "Answer": "Step 1: Subtract the remaining amount from the initial amount: 9031 - 1356\nStep 2: Price paid = 7675\nAnswer: 7675",
      "Points": 5
    },
    {
      "Id": 33,
      "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. Find the total amount spent. Show your working.",
      "Options": [],
      "Answer": "Step 1: Add teachers\u0027 pay and building construction: 26756 \u002B 325378\nStep 2: Add games cost: Result \u002B 5780\nStep 3: Add other work cost: Result \u002B 8235\nAnswer: 366149",
      "Points": 5
    },
    {
      "Id": 34,
      "Type": "word_problem",
      "Text": "Find the sum of the predecessor of 97801 and 90526. Show your working.",
      "Options": [],
      "Answer": "Step 1: Predecessor of 97801 is 97800\nStep 2: Sum = 97800 \u002B 90526\nAnswer: 188326",
      "Points": 5
    },
    {
      "Id": 35,
      "Type": "word_problem",
      "Text": "Find the product of the successor of 147 and 389. Show your working.",
      "Options": [],
      "Answer": "Step 1: Successor of 147 is 148\nStep 2: Product = 148 \u00D7 389\nAnswer: 57572",
      "Points": 5
    },
    {
      "Id": 36,
      "Type": "word_problem",
      "Text": "Solve using the distributive property: 632 \u00D7 1001. Show your working.",
      "Options": [],
      "Answer": "Step 1: Express 1001 as 1000 \u002B 1\nStep 2: Calculate 632\u00D71000 \u002B 632\u00D71\nAnswer: 632632",
      "Points": 5
    },
    {
      "Id": 37,
      "Type": "word_problem",
      "Text": "Simplify the expression: 34 - [32 - {31 - (18 - 15 - 1)}]. Show your working.",
      "Options": [],
      "Answer": "Step 1: Compute inner parentheses: 18 - 15 - 1 = 2\nStep 2: Compute {31 - 2} = 29\nStep 3: Compute [32 - 29] = 3\nStep 4: Compute 34 - 3\nAnswer: 31",
      "Points": 5
    },
    {
      "Id": 38,
      "Type": "word_problem",
      "Text": "Find three different whole numbers whose sum and product are equal. Show your working.",
      "Options": [],
      "Answer": "Step 1: Consider numbers 1, 2, and 3\nStep 2: Sum = 1 \u002B 2 \u002B 3 = 6 and Product = 1 \u00D7 2 \u00D7 3 = 6\nAnswer: 1, 2, 3",
      "Points": 5
    },
    {
      "Id": 39,
      "Type": "word_problem",
      "Text": "Find the HCF of 420 and 430 by prime factorisation. Show your working.",
      "Options": [],
      "Answer": "Step 1: Prime factors of 420 are 2^2, 3, 5, 7 and of 430 are 2, 5, 43\nStep 2: Common factors: 2 and 5\nAnswer: 10",
      "Points": 5
    },
    {
      "Id": 40,
      "Type": "word_problem",
      "Text": "Find the LCM of 210 and 186 by prime factorisation. Show your working.",
      "Options": [],
      "Answer": "Step 1: Prime factors of 210: 2, 3, 5, 7\nStep 2: Prime factors of 186: 2, 3, 31\nStep 3: LCM = 2 \u00D7 3 \u00D7 5 \u00D7 7 \u00D7 31\nAnswer: 6510",
      "Points": 5
    }
  ],
  "TotalPoints": 100
}