{
  "title": "Division of Algebraic Expressions - Grade 8 ICSE",
  "total_questions": 60,
  "questions": [
    {
      "id": 1,
      "difficulty": "easy",
      "question": "Divide: 12x² by 3x ➗",
      "options": { "A": "4x", "B": "4x²", "C": "9x", "D": "15x³" },
      "correct_answer": "A"
    },
    {
      "id": 2,
      "difficulty": "easy",
      "question": "What is 15y ÷ 5? ✨",
      "options": { "A": "3y", "B": "3", "C": "10y", "D": "75y" },
      "correct_answer": "A"
    },
    {
      "id": 3,
      "difficulty": "easy",
      "question": "Simplify: (8m⁴) / (2m²) 🧮",
      "options": { "A": "4m²", "B": "6m²", "C": "4m⁶", "D": "16m²" },
      "correct_answer": "A"
    },
    {
      "id": 4,
      "difficulty": "easy",
      "question": "Divide 24p³q by 6pq. 🔍",
      "options": { "A": "4p²", "B": "4p³q", "C": "18p²", "D": "4pq" },
      "correct_answer": "A"
    },
    {
      "id": 5,
      "difficulty": "easy",
      "question": "What is the result of 10 ÷ 10a? (Assume a≠0) 🤔",
      "options": { "A": "1/a", "B": "1", "C": "a", "D": "10/a" },
      "correct_answer": "A"
    },
    {
      "id": 6,
      "difficulty": "easy",
      "question": "Simplify: (-18k) ÷ 3 ➖",
      "options": { "A": "-6k", "B": "6k", "C": "-15k", "D": "-21k" },
      "correct_answer": "A"
    },
    {
      "id": 7,
      "difficulty": "easy",
      "question": "Divide: a⁵ by a² 📚",
      "options": { "A": "a³", "B": "a⁷", "C": "a¹⁰", "D": "a².⁵" },
      "correct_answer": "A"
    },
    {
      "id": 8,
      "difficulty": "easy",
      "question": "What is (14xy) ÷ (7x)? 🎯",
      "options": { "A": "2y", "B": "2xy", "C": "7y", "D": "21xy" },
      "correct_answer": "A"
    },
    {
      "id": 9,
      "difficulty": "easy",
      "question": "Simplify: (21b³) / (3b) ➗",
      "options": { "A": "7b²", "B": "7b³", "C": "18b²", "D": "7b⁴" },
      "correct_answer": "A"
    },
    {
      "id": 10,
      "difficulty": "easy",
      "question": "Divide 100r²s by 25rs. 🧲",
      "options": { "A": "4r", "B": "4rs", "C": "75r", "D": "4r²s" },
      "correct_answer": "A"
    },
    {
      "id": 11,
      "difficulty": "easy",
      "question": "What is 1 ÷ (1/x)? (x≠0) 🔄",
      "options": { "A": "x", "B": "1/x", "C": "1", "D": "0" },
      "correct_answer": "A"
    },
    {
      "id": 12,
      "difficulty": "easy",
      "question": "Simplify: (0.5z⁴) ÷ (0.1z²) 📐",
      "options": { "A": "5z²", "B": "0.5z²", "C": "5z⁶", "D": "0.4z²" },
      "correct_answer": "A"
    },
    {
      "id": 13,
      "difficulty": "easy",
      "question": "Divide: -32t⁴ by 8t². ❄️",
      "options": { "A": "-4t²", "B": "4t²", "C": "-24t²", "D": "-4t⁶" },
      "correct_answer": "A"
    },
    {
      "id": 14,
      "difficulty": "easy",
      "question": "What is (9u⁶v²) / (3u²v²)? ✂️",
      "options": { "A": "3u⁴", "B": "3u⁶", "C": "6u⁴", "D": "3u⁸v⁴" },
      "correct_answer": "A"
    },
    {
      "id": 15,
      "difficulty": "easy",
      "question": "Simplify: (50) ÷ (50mn) 🎪",
      "options": { "A": "1/(mn)", "B": "mn", "C": "1", "D": "50mn" },
      "correct_answer": "A"
    },
    {
      "id": 16,
      "difficulty": "easy",
      "question": "Divide: x¹⁰ by x⁷. ⬆️",
      "options": { "A": "x³", "B": "x¹⁷", "C": "x⁻³", "D": "3" },
      "correct_answer": "A"
    },
    {
      "id": 17,
      "difficulty": "easy",
      "question": "What is (16a²b⁴) ÷ (4ab²)? 🪀",
      "options": { "A": "4ab²", "B": "12ab²", "C": "4a²b²", "D": "20a³b⁶" },
      "correct_answer": "A"
    },
    {
      "id": 18,
      "difficulty": "easy",
      "question": "Simplify: (-1/2 w) ÷ (1/4) 🍰",
      "options": { "A": "-2w", "B": "-1/8 w", "C": "2w", "D": "-2" },
      "correct_answer": "A"
    },
    {
      "id": 19,
      "difficulty": "easy",
      "question": "Divide 1 by c⁵. (c≠0) 🧩",
      "options": {
        "A": "1/c⁵",
        "B": "c⁵",
        "C": "5/c",
        "D": "1/c⁴"
      },
      "correct_answer": "A"
    },
    {
      "id": 20,
      "difficulty": "easy",
      "question": "What is (0 ÷ 5xy)? ✅",
      "options": { "A": "0", "B": "1", "C": "5xy", "D": "Undefined" },
      "correct_answer": "A"
    },
    {
      "id": 21,
      "difficulty": "medium",
      "question": "Divide: (15x³ - 10x²) by 5x² 🚧",
      "options": {
        "A": "3x - 2",
        "B": "3x² - 2x",
        "C": "10x - 5",
        "D": "3x³ - 2"
      },
      "correct_answer": "A"
    },
    {
      "id": 22,
      "difficulty": "medium",
      "question": "Simplify: (24p⁴q² - 16p³q³) ÷ (8p²q²) ⚡",
      "options": {
        "A": "3p² - 2pq",
        "B": "3p²q² - 2pq",
        "C": "16p² - 8pq",
        "D": "3p - 2q"
      },
      "correct_answer": "A"
    },
    {
      "id": 23,
      "difficulty": "medium",
      "question": "Divide 9y⁵ - 6y⁴ + 3y³ by 3y³. 🔢",
      "options": {
        "A": "3y² - 2y + 1",
        "B": "3y⁸ - 2y⁷ + y⁶",
        "C": "6y² - 3y + 0",
        "D": "y² - 2y + 3"
      },
      "correct_answer": "A"
    },
    {
      "id": 24,
      "difficulty": "medium",
      "question": "Find quotient: (14a²b - 21ab²) ÷ 7ab 🏗️",
      "options": {
        "A": "2a - 3b",
        "B": "2ab - 3ab",
        "C": "7a - 14b",
        "D": "2 - 3b"
      },
      "correct_answer": "A"
    },
    {
      "id": 25,
      "difficulty": "medium",
      "question": "Simplify: (x⁶ - x⁴) / x⁴ (x≠0) 📦",
      "options": { "A": "x² - 1", "B": "x²", "C": "x¹⁰ - x⁸", "D": "1 - x²" },
      "correct_answer": "A"
    },
    {
      "id": 26,
      "difficulty": "medium",
      "question": "Divide: (8m⁷n² + 12m⁵n⁴ - 4m³n⁶) by 4m³n² 🌱",
      "options": {
        "A": "2m⁴ + 3m²n² - n⁴",
        "B": "2m⁴n² + 3m²n⁴ - n⁶",
        "C": "12m⁴ + 8m²n² - 0",
        "D": "m⁴ + 3m² - n⁴"
      },
      "correct_answer": "A"
    },
    {
      "id": 27,
      "difficulty": "medium",
      "question": "What is (0.5z³ + 1.5z²) ÷ 0.5z²? 🧮",
      "options": {
        "A": "z + 3",
        "B": "z³ + 3z²",
        "C": "1 + 3z",
        "D": "z + 1.5"
      },
      "correct_answer": "A"
    },
    {
      "id": 28,
      "difficulty": "medium",
      "question": "Divide the polynomial 25t⁴ - 15t² by 5t². 🚀",
      "options": {
        "A": "5t² - 3",
        "B": "5t² - 15",
        "C": "20t² - 10",
        "D": "t² - 3"
      },
      "correct_answer": "A"
    },
    {
      "id": 29,
      "difficulty": "medium",
      "question": "Simplify: (1/4 p⁴q - 1/2 p²q³) ÷ (1/2 p²q) 🍕",
      "options": {
        "A": "(1/2)p² - q²",
        "B": "p² - q²",
        "C": "(1/2)p²q - q³",
        "D": "p²/2 - q"
      },
      "correct_answer": "A"
    },
    {
      "id": 30,
      "difficulty": "medium",
      "question": "Find quotient: (-18u³v + 27u²v²) ÷ (-9u²v) ➖",
      "options": {
        "A": "2u - 3v",
        "B": "-2u + 3v",
        "C": "-2u - 3v",
        "D": "2u + 3v"
      },
      "correct_answer": "A"
    },
    {
      "id": 31,
      "difficulty": "medium",
      "question": "Divide: (a⁵b² - a³b⁴ + a²b⁵) by a²b² 🧩",
      "options": {
        "A": "a³ - ab² + b³",
        "B": "a⁷b⁴ - a⁵b⁶ + a⁴b⁷",
        "C": "a³b² - ab⁴ + b⁵",
        "D": "a³ + b³"
      },
      "correct_answer": "A"
    },
    {
      "id": 32,
      "difficulty": "medium",
      "question": "Simplify: (12x⁴y⁶ - 8x³y⁷) ÷ 4x³y⁶ ✂️",
      "options": {
        "A": "3x - 2y",
        "B": "3xy - 2y",
        "C": "8x - 4y",
        "D": "3x⁴ - 2y⁷"
      },
      "correct_answer": "A"
    },
    {
      "id": 33,
      "difficulty": "medium",
      "question": "What is (100r⁵s³ - 50r⁴s⁴) ÷ 25r⁴s³? 💡",
      "options": {
        "A": "4r - 2s",
        "B": "4rs - 2s",
        "C": "75r - 25s",
        "D": "4r⁵ - 2s⁴"
      },
      "correct_answer": "A"
    },
    {
      "id": 34,
      "difficulty": "medium",
      "question": "Divide: (0.6m⁸ - 0.9m⁶) by 0.3m⁶ 📐",
      "options": {
        "A": "2m² - 3",
        "B": "0.3m² - 0.6",
        "C": "m² - 3",
        "D": "2m² - 0.3"
      },
      "correct_answer": "A"
    },
    {
      "id": 35,
      "difficulty": "medium",
      "question": "Simplify: (√4 x⁶ - √9 x⁴) ÷ x⁴ 🌳",
      "options": {
        "A": "2x² - 3",
        "B": "4x² - 9",
        "C": "x² - 3",
        "D": "2x⁶ - 3x⁴"
      },
      "correct_answer": "A"
    },
    {
      "id": 36,
      "difficulty": "medium",
      "question": "Find quotient: (p⁷q⁵ + p⁵q⁷ - p⁴q⁸) ÷ p⁴q⁵ 🎲",
      "options": {
        "A": "p³ + pq² - q³",
        "B": "p³q⁵ + pq⁷ - q⁸",
        "C": "p¹¹q¹⁰ - p⁹q¹²",
        "D": "p³ + q² - q³"
      },
      "correct_answer": "A"
    },
    {
      "id": 37,
      "difficulty": "medium",
      "question": "Divide: (48a¹⁰b⁸ - 36a⁹b⁹) by 12a⁹b⁸ ⚖️",
      "options": {
        "A": "4a - 3b",
        "B": "36a - 24b",
        "C": "a - 3b",
        "D": "4a¹⁰ - 3b⁹"
      },
      "correct_answer": "A"
    },
    {
      "id": 38,
      "difficulty": "medium",
      "question": "Simplify: (x¹²y¹⁰ - x¹⁰y¹²) ÷ x¹⁰y¹⁰ 🚀",
      "options": {
        "A": "x² - y²",
        "B": "x²²y²⁰ - x²⁰y²²",
        "C": "2xy",
        "D": "x²y¹⁰ - y¹²"
      },
      "correct_answer": "A"
    },
    {
      "id": 39,
      "difficulty": "medium",
      "question": "What is (1.2c⁹d⁶ - 0.6c⁸d⁷) ÷ 0.6c⁸d⁶? 🛒",
      "options": {
        "A": "2c - d",
        "B": "0.6c - 0.6d",
        "C": "c - d",
        "D": "1.2c⁹ - 0.6d⁷"
      },
      "correct_answer": "A"
    },
    {
      "id": 40,
      "difficulty": "medium",
      "question": "Divide: (3/5 f⁶g⁴ - 9/10 f⁵g⁵) ÷ (3/10 f⁵g⁴) 🍰",
      "options": {
        "A": "2f - 3g",
        "B": "f - g",
        "C": "(6/5)f - (9/10)g",
        "D": "2f⁶ - 3g⁵"
      },
      "correct_answer": "A"
    },
    {
      "id": 41,
      "difficulty": "hard",
      "question": "Divide: (x³ - 8) by (x - 2). Hint: Use identity a³-b³. 🎯",
      "options": {
        "A": "x² + 2x + 4",
        "B": "x² - 2x + 4",
        "C": "x² + 4",
        "D": "x - 4"
      },
      "correct_answer": "A"
    },
    {
      "id": 42,
      "difficulty": "hard",
      "question": "Simplify: (4p⁴ - 9q⁴) ÷ (2p² - 3q²) 🔥",
      "options": {
        "A": "2p² + 3q²",
        "B": "2p² - 3q²",
        "C": "4p⁴ - 9q⁴",
        "D": "(2p²-3q²)²"
      },
      "correct_answer": "A"
    },
    {
      "id": 43,
      "difficulty": "hard",
      "question": "Divide: (8m³ + 27n³) by (2m + 3n). Use a³+b³ identity. 🧠",
      "options": {
        "A": "4m² - 6mn + 9n²",
        "B": "4m² + 6mn + 9n²",
        "C": "2m² - 3mn + 3n²",
        "D": "(2m+3n)²"
      },
      "correct_answer": "A"
    },
    {
      "id": 44,
      "difficulty": "hard",
      "question": "Find quotient: (x⁴ - 16) ÷ (x² + 4) ✨",
      "options": {
        "A": "x² - 4",
        "B": "x² + 4",
        "C": "x⁴ - 4",
        "D": "x² - 16"
      },
      "correct_answer": "A"
    },
    {
      "id": 45,
      "difficulty": "hard",
      "question": "Simplify: (a⁶ - b⁶) ÷ (a³ - b³) 🧩",
      "options": {
        "A": "a³ + b³",
        "B": "a³ - b³",
        "C": "a⁶ - b⁶",
        "D": "a² + ab + b²"
      },
      "correct_answer": "A"
    },
    {
      "id": 46,
      "difficulty": "hard",
      "question": "Divide: (9x² - 24xy + 16y²) by (3x - 4y) 📏",
      "options": {
        "A": "3x - 4y",
        "B": "3x + 4y",
        "C": "9x - 16y",
        "D": "x - y"
      },
      "correct_answer": "A"
    },
    {
      "id": 47,
      "difficulty": "hard",
      "question": "Find quotient: (27p³ - 8q³) ÷ (3p - 2q) ⚡",
      "options": {
        "A": "9p² + 6pq + 4q²",
        "B": "9p² - 6pq + 4q²",
        "C": "3p² + 2pq + 2q²",
        "D": "(3p-2q)²"
      },
      "correct_answer": "A"
    },
    {
      "id": 48,
      "difficulty": "hard",
      "question": "Simplify: (x⁵ - 32) ÷ (x - 2). Hint: 32=2⁵. 🚀",
      "options": {
        "A": "x⁴+2x³+4x²+8x+16",
        "B": "x⁴-2x³+4x²-8x+16",
        "C": "x⁴+16",
        "D": "x⁵+32"
      },
      "correct_answer": "A"
    },
    {
      "id": 49,
      "difficulty": "hard",
      "question": "Divide: (a⁴ - (b-c)⁴) by (a² - (b-c)²) 🌪️",
      "options": {
        "A": "a² + (b-c)²",
        "B": "a² - (b-c)²",
        "C": "a⁴ - (b-c)²",
        "D": "a + (b-c)"
      },
      "correct_answer": "A"
    },
    {
      "id": 50,
      "difficulty": "hard",
      "question": "Find quotient: (m⁸ - n⁸) ÷ (m⁴ - n⁴) ➗",
      "options": {
        "A": "m⁴ + n⁴",
        "B": "m⁴ - n⁴",
        "C": "m² + n²",
        "D": "(m⁴-n⁴)²"
      },
      "correct_answer": "A"
    },
    {
      "id": 51,
      "difficulty": "hard",
      "question": "Simplify: (125r³ - 64s³) ÷ (5r - 4s) 🔑",
      "options": {
        "A": "25r² + 20rs + 16s²",
        "B": "25r² - 20rs + 16s²",
        "C": "5r² + 4rs + 4s²",
        "D": "125r² - 64s²"
      },
      "correct_answer": "A"
    },
    {
      "id": 52,
      "difficulty": "hard",
      "question": "Divide: (x³ + 3x²y + 3xy² + y³) by (x+y). Use (x+y)³. 📚",
      "options": {
        "A": "(x+y)²",
        "B": "x² + y²",
        "C": "x² + 2xy + y²",
        "D": "x³ + y³"
      },
      "correct_answer": "C"
    },
    {
      "id": 53,
      "difficulty": "hard",
      "question": "Find quotient: (16a⁴ - 81b⁴) ÷ (4a² + 9b²) 🏗️",
      "options": {
        "A": "4a² - 9b²",
        "B": "4a² + 9b²",
        "C": "2a - 3b",
        "D": "16a⁴ - 81b⁴"
      },
      "correct_answer": "A"
    },
    {
      "id": 54,
      "difficulty": "hard",
      "question": "Simplify: (p¹⁰ - q¹⁰) ÷ (p⁵ - q⁵) 🎲",
      "options": {
        "A": "p⁵ + q⁵",
        "B": "p⁵ - q⁵",
        "C": "p² + q²",
        "D": "(p⁵-q⁵)²"
      },
      "correct_answer": "A"
    },
    {
      "id": 55,
      "difficulty": "hard",
      "question": "Divide: (x⁶ - y⁶) by (x³ + y³) 🧲",
      "options": {
        "A": "x³ - y³",
        "B": "x³ + y³",
        "C": "x² - y²",
        "D": "x⁶ - y⁶"
      },
      "correct_answer": "A"
    },
    {
      "id": 56,
      "difficulty": "hard",
      "question": "Find quotient: (49m² - 84mn + 36n²) ÷ (7m - 6n) ✅",
      "options": {
        "A": "7m - 6n",
        "B": "7m + 6n",
        "C": "49m - 36n",
        "D": "m - n"
      },
      "correct_answer": "A"
    },
    {
      "id": 57,
      "difficulty": "hard",
      "question": "Simplify: (a³ + 3a²b + 3ab² + b³) ÷ (a+b) 🌟",
      "options": {
        "A": "a² + 2ab + b²",
        "B": "a² + ab + b²",
        "C": "a³ + b³",
        "D": "a + b"
      },
      "correct_answer": "A"
    },
    {
      "id": 58,
      "difficulty": "hard",
      "question": "Divide: (8x³ - 125y³) by (2x - 5y) 🎪",
      "options": {
        "A": "4x² + 10xy + 25y²",
        "B": "4x² - 10xy + 25y²",
        "C": "2x² + 5xy + 5y²",
        "D": "8x² - 125y²"
      },
      "correct_answer": "A"
    },
    {
      "id": 59,
      "difficulty": "hard",
      "question": "Find quotient: (x⁴ + 4x² + 16) ÷ (x² + 2x + 4)? Hint: Use (a²+ab+b²) pattern. 🔍",
      "options": {
        "A": "x² - 2x + 4",
        "B": "x² + 2x + 4",
        "C": "x² + 4",
        "D": "x⁴ - 4"
      },
      "correct_answer": "A"
    },
    {
      "id": 60,
      "difficulty": "hard",
      "question": "Simplify: (27 + 64c³) ÷ (3 + 4c) 🚅",
      "options": {
        "A": "9 - 12c + 16c²",
        "B": "9 + 12c + 16c²",
        "C": "3 + 4c",
        "D": "27 - 64c³"
      },
      "correct_answer": "A"
    }
  ]
}