{
  "paper": {
    "school": "Nan Hua",
    "year": 2024,
    "level": "P5",
    "label": "Weighted Assessment 3",
    "source_prefix": "Nan Hua 2024 P5 Weighted Assessment 3",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "What is the product of 0.007 and 800?",
      "answer0": "0.56",
      "answer1": "5.6",
      "answer2": "56",
      "answer3": "560",
      "correct_answer": 1,
      "skill_id": 166,
      "difficulty_id": 1,
      "explanation": "0.007 × 800 = 0.007 × 8 × 100 = 0.056 × 100 = 5.6.",
      "hints": ["0.007 × 8 = 0.056.", "Then multiply by 100 by shifting the decimal point 2 places."],
      "source": "Nan Hua 2024 P5 Weighted Assessment 3 Paper 1 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Paper 1: option 2."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Which of the following is the same as 5002 cm?",
      "answer0": "5.2 m",
      "answer1": "5.02 m",
      "answer2": "50.2 m",
      "answer3": "50.02 m",
      "correct_answer": 3,
      "skill_id": 184,
      "difficulty_id": 1,
      "explanation": "100 cm = 1 m, so 5002 cm = 5002 ÷ 100 = 50.02 m.",
      "hints": ["100 cm = 1 m.", "Divide 5002 by 100."],
      "source": "Nan Hua 2024 P5 Weighted Assessment 3 Paper 1 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Paper 1: option 4."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "The usual price for a watch was $140. David bought it at a discount of 20%. How much was the discount?",
      "answer0": "$20",
      "answer1": "$28",
      "answer2": "$112",
      "answer3": "$120",
      "correct_answer": 1,
      "skill_id": 176,
      "difficulty_id": 1,
      "explanation": "Discount = 20% of $140 = \\(\\dfrac{20}{100}\\) × 140 = $28.",
      "hints": ["The discount is 20% of the usual price.", "\\(\\dfrac{20}{100}\\) × 140."],
      "source": "Nan Hua 2024 P5 Weighted Assessment 3 Paper 1 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Paper 1: option 2."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "In the number line, what is the value of A?",
      "answer0": "5",
      "answer1": "5.25",
      "answer2": "5.75",
      "answer3": "5.9",
      "correct_answer": 2,
      "skill_id": 124,
      "difficulty_id": 2,
      "explanation": "From 6 to 7 there are 4 equal intervals, so each interval = 0.25. A is 1 interval to the left of 6, so A = 6 - 0.25 = 5.75.",
      "hints": ["Find the size of one interval between two labelled marks (6 to 7).", "A sits one interval before 6."],
      "source": "Nan Hua 2024 P5 Weighted Assessment 3 Paper 1 Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q4.png",
      "image_page": 4,
      "image_bbox": [0.18, 0.18, 0.94, 0.29],
      "image_loc": "horizontal number line marked A, 6, 7, 8 with tick marks, top of page",
      "notes": "Answer key Paper 1: option 3."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "A rectangular tank measures 40 cm by 30 cm by 20 cm. It is filled with water to a height of 8 cm. How much water is needed to fill the tank completely?",
      "answer0": "9600 cm³",
      "answer1": "14 400 cm³",
      "answer2": "24 000 cm³",
      "answer3": "192 000 cm³",
      "correct_answer": 1,
      "skill_id": 191,
      "difficulty_id": 2,
      "explanation": "Empty height to fill = 20 - 8 = 12 cm. Volume needed = 40 × 30 × 12 = 14 400 cm³.",
      "hints": ["Find the remaining height of empty space: 20 - 8.", "Volume = length × breadth × remaining height."],
      "source": "Nan Hua 2024 P5 Weighted Assessment 3 Paper 1 Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q5.png",
      "image_page": 4,
      "image_bbox": [0.30, 0.55, 0.72, 0.73],
      "image_loc": "rectangular tank diagram showing 40 cm, 30 cm, 20 cm and 8 cm water level, middle of page",
      "notes": "Answer key Paper 1: option 2."
    },
    {
      "n": 6,
      "type_id": 2,
      "question": "What is the value of 3 tens, 12 tenths and 8 hundredths? [?]",
      "answer0": "31.28",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 149,
      "difficulty_id": 2,
      "explanation": "3 tens = 30; 12 tenths = 12 × 0.1 = 1.2; 8 hundredths = 8 × 0.01 = 0.08. Total = 30 + 1.2 + 0.08 = 31.28.",
      "hints": ["Tenths are 0.1 each; hundredths are 0.01 each.", "30 + 1.2 + 0.08."],
      "source": "Nan Hua 2024 P5 Weighted Assessment 3 Paper 1 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Paper 1: 30 + 1.2 = 31.2; 31.2 + 0.08 = 31.28."
    },
    {
      "n": 7,
      "type_id": 2,
      "question": "In a class, \\(\\dfrac{2}{5}\\) of the students are boys. What percentage of the students are girls? [?] %",
      "answer0": "60",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 173,
      "difficulty_id": 2,
      "explanation": "Girls = \\(\\dfrac{10}{10} - \\dfrac{4}{10} = \\dfrac{6}{10}\\) of the class (since \\(\\dfrac{2}{5} = \\dfrac{4}{10}\\)). As a percentage that is \\(\\dfrac{6}{10}\\) = 60%.",
      "hints": ["Fraction of girls = 1 - \\(\\dfrac{2}{5}\\) = \\(\\dfrac{3}{5}\\).", "Convert \\(\\dfrac{3}{5}\\) to a percentage."],
      "source": "Nan Hua 2024 P5 Weighted Assessment 3 Paper 1 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Paper 1: 10/10 - 4/10 = 6/10 = 60%. Answer is the integer 60 (percent), FIB ok."
    },
    {
      "n": 8,
      "type_id": 2,
      "question": "The price for 30 mangoes is $48. What is the price of 2 such mangoes? $[?]",
      "answer0": "3.20",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 2,
      "explanation": "Price of 1 mango = $48 ÷ 30 = $1.60. Price of 2 mangoes = $1.60 × 2 = $3.20. (Key: 30 ÷ 2 = 15, then 48 ÷ 15 = $3.20.)",
      "hints": ["Find the price of 1 mango first, or group the 30 into 15 pairs.", "48 ÷ 15 = price of one pair."],
      "source": "Nan Hua 2024 P5 Weighted Assessment 3 Paper 1 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Paper 1: 30 ÷ 2 = 15; 48 ÷ 15 = $3.20."
    },
    {
      "n": 9,
      "type_id": 2,
      "question": "The price of a camera is $1200 excluding 9% GST. How much is the price of the camera including GST? $[?]",
      "answer0": "1308",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 2,
      "explanation": "Price including GST = 109% of $1200 = \\(\\dfrac{109}{100}\\) × 1200 = $1308.",
      "hints": ["Including 9% GST means 100% + 9% = 109% of the price.", "\\(\\dfrac{109}{100}\\) × 1200."],
      "source": "Nan Hua 2024 P5 Weighted Assessment 3 Paper 1 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Paper 1: 109/100 × 1200 = $1308."
    },
    {
      "n": 10,
      "type_id": 2,
      "question": "Mrs Raju has $8000 in her savings account. She earns 2% interest each year. How much money will Mrs Raju have in her account at the end of 1 year? $[?]",
      "answer0": "8160",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 2,
      "explanation": "Total at end of 1 year = 102% of $8000 = \\(\\dfrac{102}{100}\\) × 8000 = $8160.",
      "hints": ["After 1 year she has the original 100% plus 2% interest = 102%.", "\\(\\dfrac{102}{100}\\) × 8000."],
      "source": "Nan Hua 2024 P5 Weighted Assessment 3 Paper 1 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Paper 1: 102/100 × 8000 = $8160."
    },
    {
      "n": 11,
      "type_id": 2,
      "question": "Pails of water are poured into a cubical container of edge 40 cm. Each pail has a capacity of 2 ℓ. How many full pails of water are needed to fill the container completely? [?]",
      "answer0": "32",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 192,
      "difficulty_id": 2,
      "explanation": "Volume of cube = 40 × 40 × 40 = 64 000 cm³ = 64 ℓ (1000 cm³ = 1 ℓ). Number of pails = 64 ℓ ÷ 2 ℓ = 32. (Key: 64000 ÷ 2000 = 32.)",
      "hints": ["Find the cube's volume in cm³, then convert to litres (1000 cm³ = 1 ℓ).", "Divide the total volume by the pail capacity of 2 ℓ."],
      "source": "Nan Hua 2024 P5 Weighted Assessment 3 Paper 1 Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q11.png",
      "image_page": 7,
      "image_bbox": [0.27, 0.25, 0.74, 0.42],
      "image_loc": "cube of edge 40 cm and a pail labelled 2 ℓ, upper-middle of page",
      "notes": "Answer key Paper 1: 40×40×40 = 64000; 64000 ÷ 2000 = 32 pails."
    },
    {
      "n": 12,
      "type_id": 2,
      "question": "A dress was sold at a discount at a store. Usual Price: $190; 40% off. How much was the discounted price of the dress? $[?]",
      "answer0": "114",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 2,
      "explanation": "Discounted price = 100% - 40% = 60% of $190 = \\(\\dfrac{60}{100}\\) × 190 = $114. (Key: 100 - 40 = 60; 60/100 × 190 = $114.)",
      "hints": ["40% off means you pay 60% of the usual price.", "\\(\\dfrac{60}{100}\\) × 190."],
      "source": "Nan Hua 2024 P5 Weighted Assessment 3 Paper 1 Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q12.png",
      "image_page": 7,
      "image_bbox": [0.16, 0.58, 0.42, 0.78],
      "image_loc": "dress price tag showing 'Usual Price: $190' and '40% off', lower-left of page",
      "notes": "Answer key Paper 1: 100 - 40 = 60; 60/100 × 190 = $114. Price tag detail (Usual Price/40% off) also stated in stem text."
    },
    {
      "n": 13,
      "type_id": 2,
      "question": "Mrs Tay bought 80 apples and 120 oranges. 10% of the apples and 5% of the oranges were rotten. What percentage of the fruits were not rotten? [?] %",
      "answer0": "93",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 175,
      "difficulty_id": 3,
      "explanation": "Good apples = 90% of 80 = 72. Good oranges = 95% of 120 = 114. Good fruit = 72 + 114 = 186. Total fruit = 80 + 120 = 200. Percentage not rotten = \\(\\dfrac{186}{200} = \\dfrac{93}{100}\\) = 93%.",
      "hints": ["Find the number of good apples (90% of 80) and good oranges (95% of 120).", "Good fruit ÷ total fruit, then convert to a percentage."],
      "source": "Nan Hua 2024 P5 Weighted Assessment 3 Paper 2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Paper 2 Q1: 72 good apples + 114 good oranges = 186; 186/200 = 93/100 = 93%."
    },
    {
      "n": 14,
      "type_id": 2,
      "question": "Caili had a rectangular piece of paper measuring 31 cm by 21 cm. She cut out a square of 4 cm at each corner. She then folded up the sides and taped the corners to form an open box. What was the volume of the open box? [?] cm³",
      "answer0": "1196",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 190,
      "difficulty_id": 3,
      "explanation": "After cutting 4 cm squares from each corner, the base length = 31 - 4 - 4 = 23 cm, base breadth = 21 - 4 - 4 = 13 cm, and the box height = 4 cm. Volume = 23 × 13 × 4 = 1196 cm³.",
      "hints": ["Each side loses 4 cm at both ends: new length = 31 - 8, new breadth = 21 - 8.", "The cut size (4 cm) becomes the height; Volume = length × breadth × height."],
      "source": "Nan Hua 2024 P5 Weighted Assessment 3 Paper 2 Q2",
      "image_needed": true,
      "image_options": false,
      "image_file": "q14.png",
      "image_page": 10,
      "image_bbox": [0.16, 0.18, 0.70, 0.43],
      "image_loc": "31 cm by 21 cm rectangle with 4 cm corner squares and the folded open box, upper part of page",
      "notes": "Answer key Paper 2 Q2: 31 - 8 = 23, 21 - 8 = 13; 23 × 13 × 4 = 1196 cm³."
    },
    {
      "n": 15,
      "type_id": 2,
      "question": "A piggy bank contains 45 coins with a total value of $17.10. There are only 20-cent coins and 50-cent coins in the piggy bank. How many 50-cent coins are there? [?]",
      "answer0": "27",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "If all 45 coins were 20-cent coins, total = 45 × $0.20 = $9.00. Actual total = $17.10, so extra = $17.10 - $9.00 = $8.10. Each 20-cent coin replaced by a 50-cent coin adds $0.30. Number of 50-cent coins = $8.10 ÷ $0.30 = 27. (Key: 20×45 = 900; 1710 - 900 = 810; 50 - 20 = 30; 810 ÷ 30 = 27.)",
      "hints": ["Assume all 45 coins are 20-cent coins and find the shortfall in value.", "Each swap to a 50-cent coin adds 30 cents; divide the shortfall by 30 cents."],
      "source": "Nan Hua 2024 P5 Weighted Assessment 3 Paper 2 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Paper 2 Q3: 20×45 = 900; 1710 - 900 = 810; 810 ÷ 30 = 27 fifty-cent coins."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Tom was given $4 pocket money every day of the week. He spent $3.20 per day from Monday to Friday and saved the rest. He saved all his pocket money on Saturday and Sunday. Starting on a Monday, how many days did it take for him to save $52? [?]",
      "answer0": "33",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "Mon-Fri he saves $4 - $3.20 = $0.80 per day; over 5 weekdays that is $0.80 × 5 = $4. Sat & Sun he saves all $4 each, i.e. $4 × 2 = $8. So each full week he saves $4 + $8 = $12. After 4 weeks (28 days) he has saved $48. He needs $52 - $48 = $4 more. Days 29-33 (Mon-Fri of week 5) each add $0.80: after 5 weekdays he reaches another $4, total $52 on day 33.",
      "hints": ["Find the weekly savings: weekday savings (5 × $0.80) plus weekend savings (2 × $4).", "Work out how many whole weeks reach close to $52, then count the remaining weekdays."],
      "source": "Nan Hua 2024 P5 Weighted Assessment 3 Paper 2 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Paper 2 Q4: weekday saving 4 - 3.20 = 0.80; weekly saving 0.80×5 + 4×2 = $12; reaches $52 on day 33."
    }
  ]
}