{
  "paper": {
    "school": "Nanyang",
    "year": 2023,
    "level": "P5",
    "label": "Weighted Assessment 1",
    "source_prefix": "Nanyang 2023 P5 Weighted Assessment 1",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "Find the value of \\(6\\,400\\,000 \\div 400\\)",
      "answer0": "1 600 000",
      "answer1": "160 000",
      "answer2": "16 000",
      "answer3": "1600",
      "correct_answer": 2,
      "skill_id": 151,
      "difficulty_id": 1,
      "explanation": "Method: divide by tens, hundreds, thousands. \\(6\\,400\\,000 \\div 400 = 64\\,000 \\div 4 = 16\\,000\\). Final answer: 16 000 (option 3).",
      "hints": ["Cancel one zero from each of 6 400 000 and 400 first.", "64 000 ÷ 4 = 16 000."],
      "source": "Nanyang 2023 P5 Weighted Assessment 1 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 3."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Find the value of \\(2 \\times 24 - (24 - 8 \\div 2) \\div 4\\)",
      "answer0": "7",
      "answer1": "10",
      "answer2": "43",
      "answer3": "46",
      "correct_answer": 2,
      "skill_id": 155,
      "difficulty_id": 2,
      "explanation": "Method: order of operations. Inside brackets: \\(24 - 8 \\div 2 = 24 - 4 = 20\\). Then \\(2 \\times 24 - 20 \\div 4 = 48 - 5 = 43\\). Final answer: 43 (option 3).",
      "hints": ["Do division before subtraction inside the brackets.", "48 - 5 = 43."],
      "source": "Nanyang 2023 P5 Weighted Assessment 1 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 3."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Find the value of \\(6 \\times \\dfrac{4}{9}\\)",
      "answer0": "\\(\\dfrac{2}{27}\\)",
      "answer1": "\\(\\dfrac{27}{2}\\)",
      "answer2": "\\(\\dfrac{3}{8}\\)",
      "answer3": "\\(\\dfrac{8}{3}\\)",
      "correct_answer": 3,
      "skill_id": 163,
      "difficulty_id": 1,
      "explanation": "Method: multiply a whole number by a fraction. \\(6 \\times \\dfrac{4}{9} = \\dfrac{24}{9} = \\dfrac{8}{3}\\). Final answer: \\(\\dfrac{8}{3}\\) (option 4).",
      "hints": ["Multiply the numerator by 6: 6 × 4 = 24.", "Simplify 24/9 by dividing by 3."],
      "source": "Nanyang 2023 P5 Weighted Assessment 1 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 4. Fraction answer -> MCQ."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "There were \\(5\\ \\ell\\) of orange juice in the fridge. John drank \\(2\\ \\ell\\) of the orange juice. Paul drank \\(\\dfrac{2}{5}\\) as much orange juice as John. How much orange juice was left in the fridge?",
      "answer0": "\\(2\\dfrac{1}{5}\\ \\ell\\)",
      "answer1": "\\(2\\dfrac{3}{5}\\ \\ell\\)",
      "answer2": "\\(2\\dfrac{4}{5}\\ \\ell\\)",
      "answer3": "\\(4\\dfrac{1}{5}\\ \\ell\\)",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "Method: find each amount drunk, then subtract from the start. Paul drank \\(\\dfrac{2}{5} \\times 2 = \\dfrac{4}{5}\\ \\ell\\). Left \\(= 5 - 2 - \\dfrac{4}{5} = 3 - \\dfrac{4}{5} = 2\\dfrac{1}{5}\\ \\ell\\). Final answer: \\(2\\dfrac{1}{5}\\ \\ell\\) (option 1).",
      "hints": ["Paul drank 2/5 of John's 2 litres = 4/5 litre.", "5 - 2 - 4/5 = 2 1/5."],
      "source": "Nanyang 2023 P5 Weighted Assessment 1 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 1. Mixed-number answer -> MCQ."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "The first 22 numbers of a number pattern are given below.<br>5, 0, 3, 4, 5, 0, 5, 0, 3, 4, 5, 0, 5, 0, 3, 4, 5, 0, 5, 0, 3, 4, ...<br>Find the sum of the first 88 numbers.",
      "answer0": "242",
      "answer1": "250",
      "answer2": "252",
      "answer3": "264",
      "correct_answer": 1,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Method: find the repeating unit and count complete sets. The pattern repeats every 6 numbers (5, 0, 3, 4, 5, 0), each set summing to 17. \\(88 \\div 6 = 14\\) sets remainder 4. The 14 sets sum to \\(14 \\times 17 = 238\\); the next 4 numbers (5, 0, 3, 4) add 12. Total \\(= 238 + 12 = 250\\). Final answer: 250 (option 2).",
      "hints": ["The pattern repeats in groups of 6 numbers.", "Each group of 6 sums to 17; 88 = 14 groups + 4 extra."],
      "source": "Nanyang 2023 P5 Weighted Assessment 1 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 2 (14 x 17 + 12 = 250)."
    },
    {
      "n": 6,
      "type_id": 2,
      "question": "Write eight hundred and nine thousand and seven in numerals. [?]",
      "answer0": "809007",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 149,
      "difficulty_id": 1,
      "explanation": "Method: place value. Eight hundred and nine thousand = 809 000; plus seven = 809 007. Final answer: 809 007.",
      "hints": ["Eight hundred and nine thousand is 809 000.", "Add 7 to get 809 007."],
      "source": "Nanyang 2023 P5 Weighted Assessment 1 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 809 007."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "Find the value of \\(46 \\div 8\\). Express your answer as a mixed number.",
      "answer0": "\\(5\\dfrac{6}{8}\\)",
      "answer1": "\\(5\\dfrac{3}{4}\\)",
      "answer2": "\\(5\\dfrac{1}{4}\\)",
      "answer3": "\\(4\\dfrac{6}{8}\\)",
      "correct_answer": 0,
      "skill_id": 157,
      "difficulty_id": 1,
      "explanation": "Method: associate division with a fraction. \\(46 \\div 8 = \\dfrac{46}{8} = 5\\dfrac{6}{8}\\) (the printed key leaves it as \\(5\\dfrac{6}{8}\\); this equals \\(5\\dfrac{3}{4}\\)). Final answer: \\(5\\dfrac{6}{8}\\) (option 1).",
      "hints": ["8 goes into 46 five times with remainder 6.", "Write the remainder over 8 as the fraction part."],
      "source": "Nanyang 2023 P5 Weighted Assessment 1 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 5 6/8. Mixed-number answer -> MCQ; option 0 is the key's exact form, option 1 is its simplified equivalent (do not pick both)."
    },
    {
      "n": 8,
      "type_id": 2,
      "question": "Express \\(3\\dfrac{1}{200}\\) as a decimal. [?]",
      "answer0": "3.005",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 158,
      "difficulty_id": 1,
      "explanation": "Method: convert the fraction to a decimal. \\(\\dfrac{1}{200} = \\dfrac{5}{1000} = 0.005\\), so \\(3\\dfrac{1}{200} = 3.005\\). Final answer: 3.005.",
      "hints": ["Make the denominator 1000: 1/200 = 5/1000.", "5/1000 = 0.005, so the answer is 3.005."],
      "source": "Nanyang 2023 P5 Weighted Assessment 1 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 3.005."
    },
    {
      "n": 9,
      "type_id": 2,
      "question": "Mr Tan saves $1500 each month. How much does he save in 30 years? $[?]",
      "answer0": "540000",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "Method: multiply months by monthly savings. Months \\(= 30 \\times 12 = 360\\). Total \\(= 360 \\times \\$1500 = \\$540\\,000\\). Final answer: $540 000.",
      "hints": ["30 years = 30 × 12 = 360 months.", "360 × $1500 = $540 000."],
      "source": "Nanyang 2023 P5 Weighted Assessment 1 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: $540 000."
    },
    {
      "n": 10,
      "type_id": 2,
      "question": "Ali and Bob were at a carnival. Ali had 25 500 tokens. Ali had 3 times as many tokens as Bob. Ali gave some tokens to Bob. At the end, Ali and Bob had the same number of tokens. How many tokens did Ali give to Bob? [?]",
      "answer0": "8500",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Method: model with units. Ali = 3 units = 25 500, so 1 unit = 8500 (Bob). Total = 25 500 + 8500 = 34 000; each ends with 17 000. Ali gives away \\(25\\,500 - 17\\,000 = 8500\\) tokens. (Equivalently \\(25\\,500 \\div 3 = 8500\\).) Final answer: 8500.",
      "hints": ["Bob = 25 500 ÷ 3 = 8500 tokens.", "To be equal, each has half the total (17 000); Ali gives 25 500 - 17 000 = 8500."],
      "source": "Nanyang 2023 P5 Weighted Assessment 1 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 8500 (25 500 ÷ 3)."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "A room measures \\(\\dfrac{3}{4}\\) m by 6 m. Find the area of the room. Express your answer as an improper fraction in its simplest form.",
      "answer0": "\\(\\dfrac{9}{2}\\) m²",
      "answer1": "\\(\\dfrac{18}{4}\\) m²",
      "answer2": "\\(\\dfrac{4}{9}\\) m²",
      "answer3": "\\(\\dfrac{27}{4}\\) m²",
      "correct_answer": 0,
      "skill_id": 161,
      "difficulty_id": 2,
      "explanation": "Method: area = length × width. \\(\\dfrac{3}{4} \\times 6 = \\dfrac{18}{4} = \\dfrac{9}{2}\\). Final answer: \\(\\dfrac{9}{2}\\) m² (option 1).",
      "hints": ["Multiply 3/4 by 6 to get 18/4.", "Simplify 18/4 to 9/2."],
      "source": "Nanyang 2023 P5 Weighted Assessment 1 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 9/2 m². Fraction answer -> MCQ."
    },
    {
      "n": 12,
      "type_id": 2,
      "question": "Ming had some cookies at first. He sold \\(\\dfrac{6}{7}\\) of the cookies. He then baked another \\(\\dfrac{1}{2}\\) of what he originally had at first. He had 1512 cookies at the end. How many cookies did Ming have at first? [?]",
      "answer0": "2352",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Method: track the fraction of the original. After selling, \\(1 - \\dfrac{6}{7} = \\dfrac{1}{7}\\) is left. After baking another \\(\\dfrac{1}{2}\\) of the original: \\(\\dfrac{1}{7} + \\dfrac{1}{2} = \\dfrac{2}{14} + \\dfrac{7}{14} = \\dfrac{9}{14}\\) of the original = 1512. So original \\(= 1512 \\div 9 \\times 14 = 2352\\). Final answer: 2352.",
      "hints": ["After selling 6/7, only 1/7 is left.", "1/7 + 1/2 = 9/14 of the original equals 1512."],
      "source": "Nanyang 2023 P5 Weighted Assessment 1 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 2352 (9/14 of original = 1512)."
    },
    {
      "n": 13,
      "type_id": 2,
      "question": "The sum of the perimeter of two different squares is 40 cm. The difference between the area of the two squares is 40 cm². Find the length of the larger square. [?]",
      "answer0": "7",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Method: guess-and-check / reason from the totals. The perimeters sum to 40 cm, so the two side lengths sum to 10 cm. The larger square has side 7 cm and the smaller 3 cm: perimeters \\(4 \\times 7 + 4 \\times 3 = 28 + 12 = 40\\) cm, and areas \\(7^2 - 3^2 = 49 - 9 = 40\\) cm². Final answer: 7 cm.",
      "hints": ["The side lengths add up to 10 cm (since 4a + 4b = 40).", "Find two sides summing to 10 whose squares differ by 40: 7 and 3."],
      "source": "Nanyang 2023 P5 Weighted Assessment 1 Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 7 cm. Unit cm stated in answer line; FIB stores 7."
    }
  ]
}