{
  "Id": "8e654dcf-f004-4e78-baf5-f44ea19cdb7c",
  "Title": "Playing with Numbers Worksheet",
  "Subject": "Mathematics",
  "Topic": "Operations, BODMAS, Multiples, Factors and Divisibility",
  "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": "Math-Ch02.pdf",
  "SessionMaterialId": "bf837b4c-03f6-4a6f-b091-a407c50c931a",
  "GeneratedAt": "2026-05-31T13:04:47.776171Z",
  "Questions": [
    {
      "Id": 1,
      "Type": "true_false",
      "Text": "The rabbit takes one step forward for each correct answer.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 2,
      "Type": "true_false",
      "Text": "The result of 4 \u00D7 100 \u002B 7 \u00D7 10 \u002B 3 is 473.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 3,
      "Type": "true_false",
      "Text": "According to the BODMAS rule, operations inside brackets are performed first.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 4,
      "Type": "true_false",
      "Text": "In a multi-operation problem, subtraction is always carried out first.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 5,
      "Type": "true_false",
      "Text": "The property LCM \u00D7 HCF = Product of two numbers holds true for any pair of numbers.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 6,
      "Type": "true_false",
      "Text": "Prime factorization involves breaking down a number into its prime factors.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 7,
      "Type": "true_false",
      "Text": "A prime number has more than two distinct factors.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 8,
      "Type": "true_false",
      "Text": "Multiples of a number are obtained by repeatedly adding the number to itself.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 9,
      "Type": "true_false",
      "Text": "If a number is divisible by both 9 and 11, it is always divisible by 90.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 10,
      "Type": "true_false",
      "Text": "A perfect number is one that is equal to the sum of its proper divisors.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 11,
      "Type": "multiple_choice",
      "Text": "What is 4 \u00D7 100 \u002B 7 \u00D7 10 \u002B 3?",
      "Options": [
        "A. 473",
        "B. 4730",
        "C. 470",
        "D. 4733"
      ],
      "Answer": "A. 473",
      "Points": 2
    },
    {
      "Id": 12,
      "Type": "multiple_choice",
      "Text": "What is 10 less than 10 times 51?",
      "Options": [
        "A. 500",
        "B. 510",
        "C. 520",
        "D. 490"
      ],
      "Answer": "A. 500",
      "Points": 2
    },
    {
      "Id": 13,
      "Type": "multiple_choice",
      "Text": "What is the simplified form of 5 \u00D7 10,000 \u002B 9 \u00D7 10 \u002B 1?",
      "Options": [
        "A. 50091",
        "B. 50100",
        "C. 50090",
        "D. 50081"
      ],
      "Answer": "A. 50091",
      "Points": 2
    },
    {
      "Id": 14,
      "Type": "multiple_choice",
      "Text": "According to the BODMAS rule, which operation should be performed first?",
      "Options": [
        "A. Addition",
        "B. Multiplication",
        "C. Brackets",
        "D. Subtraction"
      ],
      "Answer": "C. Brackets",
      "Points": 2
    },
    {
      "Id": 15,
      "Type": "multiple_choice",
      "Text": "The HCF of two coprime numbers is:",
      "Options": [
        "A. 0",
        "B. 1",
        "C. The smaller number",
        "D. The larger number"
      ],
      "Answer": "B. 1",
      "Points": 2
    },
    {
      "Id": 16,
      "Type": "multiple_choice",
      "Text": "In prime factorization, which number is considered the smallest prime?",
      "Options": [
        "A. 1",
        "B. 2",
        "C. 4",
        "D. 6"
      ],
      "Answer": "B. 2",
      "Points": 2
    },
    {
      "Id": 17,
      "Type": "multiple_choice",
      "Text": "Which of the following numbers is divisible by 3?",
      "Options": [
        "A. 73",
        "B. 54",
        "C. 137",
        "D. 277"
      ],
      "Answer": "B. 54",
      "Points": 2
    },
    {
      "Id": 18,
      "Type": "multiple_choice",
      "Text": "What does LCM stand for?",
      "Options": [
        "A. Least Common Multiple",
        "B. Lowest Common Measure",
        "C. Largest Common Multiple",
        "D. Least Common Factor"
      ],
      "Answer": "A. Least Common Multiple",
      "Points": 2
    },
    {
      "Id": 19,
      "Type": "multiple_choice",
      "Text": "What is the key concept behind the factor tree method?",
      "Options": [
        "A. Division into prime factors",
        "B. Multiplication only",
        "C. Addition of factors",
        "D. Subtraction of numbers"
      ],
      "Answer": "A. Division into prime factors",
      "Points": 2
    },
    {
      "Id": 20,
      "Type": "multiple_choice",
      "Text": "Which statement is true about prime numbers?",
      "Options": [
        "A. All even numbers are prime",
        "B. 2 is the only even prime number",
        "C. 1 is a prime number",
        "D. Prime numbers are divisible by 2"
      ],
      "Answer": "B. 2 is the only even prime number",
      "Points": 2
    },
    {
      "Id": 21,
      "Type": "fill_blank",
      "Text": "In the number 4 \u00D7 100 \u002B 7 \u00D7 10 \u002B 3, the digit in the tens place is _____ .",
      "Options": [],
      "Answer": "7",
      "Points": 2
    },
    {
      "Id": 22,
      "Type": "fill_blank",
      "Text": "The result of 10 times 51 minus 10 is _____ .",
      "Options": [],
      "Answer": "500",
      "Points": 2
    },
    {
      "Id": 23,
      "Type": "fill_blank",
      "Text": "The simplified expression for 5 \u00D7 10,000 \u002B 9 \u00D7 10 \u002B 1 is _____ .",
      "Options": [],
      "Answer": "50091",
      "Points": 2
    },
    {
      "Id": 24,
      "Type": "fill_blank",
      "Text": "According to the BODMAS rule, operations inside _____ are performed first.",
      "Options": [],
      "Answer": "brackets",
      "Points": 2
    },
    {
      "Id": 25,
      "Type": "fill_blank",
      "Text": "The smallest factor of every number is _____ .",
      "Options": [],
      "Answer": "1",
      "Points": 2
    },
    {
      "Id": 26,
      "Type": "fill_blank",
      "Text": "Prime factorization breaks a number into its _____ factors.",
      "Options": [],
      "Answer": "prime",
      "Points": 2
    },
    {
      "Id": 27,
      "Type": "fill_blank",
      "Text": "LCM stands for Least Common _____ .",
      "Options": [],
      "Answer": "Multiple",
      "Points": 2
    },
    {
      "Id": 28,
      "Type": "fill_blank",
      "Text": "The property LCM \u00D7 HCF = Product of two numbers shows the relation between _____.",
      "Options": [],
      "Answer": "multiples and factors",
      "Points": 2
    },
    {
      "Id": 29,
      "Type": "fill_blank",
      "Text": "Divisibility by 3 is determined by the sum of the _____ of a number.",
      "Options": [],
      "Answer": "digits",
      "Points": 2
    },
    {
      "Id": 30,
      "Type": "fill_blank",
      "Text": "A perfect number is one that is equal to the sum of its _____ divisors.",
      "Options": [],
      "Answer": "proper",
      "Points": 2
    },
    {
      "Id": 31,
      "Type": "word_problem",
      "Text": "A rabbit hops forward each time a correct answer is given. If it takes 473 steps to reach a carrot, and each correct answer moves it 1 step, how many correct answers did it get? Show your working.",
      "Options": [],
      "Answer": "Step 1: Recognize each correct answer equals 1 step\nStep 2: Total steps = 473\nAnswer: 473",
      "Points": 5
    },
    {
      "Id": 32,
      "Type": "word_problem",
      "Text": "Solve: 10 less than 10 times 51. Show your working.",
      "Options": [],
      "Answer": "Step 1: Calculate 10 \u00D7 51 = 510\nStep 2: Subtract 10: 510 - 10\nAnswer: 500",
      "Points": 5
    },
    {
      "Id": 33,
      "Type": "word_problem",
      "Text": "Evaluate: 5 \u00D7 10,000 \u002B 9 \u00D7 10 \u002B 1 \u00D7 1. Show your working.",
      "Options": [],
      "Answer": "Step 1: Calculate 5 \u00D7 10,000 = 50000\nStep 2: Calculate 9 \u00D7 10 = 90\nStep 3: Add 50000 \u002B 90 \u002B 1\nAnswer: 50091",
      "Points": 5
    },
    {
      "Id": 34,
      "Type": "word_problem",
      "Text": "Calculate 36,000 \u002B 400 - 100 \u002B 10. Show your working.",
      "Options": [],
      "Answer": "Step 1: Add 36,000 \u002B 400 = 36400\nStep 2: Subtract 100: 36400 - 100 = 36300\nStep 3: Add 10: 36300 \u002B 10\nAnswer: 36310",
      "Points": 5
    },
    {
      "Id": 35,
      "Type": "word_problem",
      "Text": "Find the least common multiple (LCM) of 15 and 20. Show your working.",
      "Options": [],
      "Answer": "Step 1: Prime factors: 15 = 3 \u00D7 5, 20 = 2\u00B2 \u00D7 5\nStep 2: LCM = 2\u00B2 \u00D7 3 \u00D7 5\nAnswer: 60",
      "Points": 5
    },
    {
      "Id": 36,
      "Type": "word_problem",
      "Text": "Determine the highest common factor (HCF) of 36 and 60. Show your working.",
      "Options": [],
      "Answer": "Step 1: Prime factors: 36 = 2\u00B2 \u00D7 3\u00B2, 60 = 2\u00B2 \u00D7 3 \u00D7 5\nStep 2: HCF = 2\u00B2 \u00D7 3\nAnswer: 12",
      "Points": 5
    },
    {
      "Id": 37,
      "Type": "word_problem",
      "Text": "A six-digit number has digits that sum to 27. Explain why this number is divisible by 9. Show your working.",
      "Options": [],
      "Answer": "Step 1: Sum of digits = 27\nStep 2: Since 27 \u00F7 9 = 3 exactly\nAnswer: The number is divisible by 9",
      "Points": 5
    },
    {
      "Id": 38,
      "Type": "word_problem",
      "Text": "In a colony with 62 blocks, a bus stops every 10th block and a van every 6th block. What is the first block where both vehicles stop? Show your working.",
      "Options": [],
      "Answer": "Step 1: Find LCM of 6 and 10 = 30\nStep 2: First common stop is block 30\nAnswer: 30",
      "Points": 5
    },
    {
      "Id": 39,
      "Type": "word_problem",
      "Text": "If the property LCM \u00D7 HCF = Product of two numbers holds, and the LCM of two numbers is 60 while the HCF is 12, find the product of the two numbers. Show your working.",
      "Options": [],
      "Answer": "Step 1: Multiply LCM and HCF: 60 \u00D7 12\nStep 2: Compute the product\nAnswer: 720",
      "Points": 5
    },
    {
      "Id": 40,
      "Type": "word_problem",
      "Text": "Three water tankers have capacities of 5000, 8000, and 10,000 litres. What is the maximum capacity of a container that can measure all three tanks exactly? Show your working.",
      "Options": [],
      "Answer": "Step 1: Find HCF of 5000, 8000, and 10000\nStep 2: HCF = 1000\nAnswer: 1000",
      "Points": 5
    }
  ],
  "TotalPoints": 100
}