{
  "paper": {
    "school": "Nan Hua",
    "year": 2025,
    "level": "P4",
    "label": "Weighted Assessment 3",
    "source_prefix": "Nan Hua 2025 P4 Weighted Assessment 3",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "The value of the digit 3 in 57.43 is ____________.",
      "answer0": "0.03",
      "answer1": "0.3",
      "answer2": "3",
      "answer3": "30",
      "correct_answer": 0,
      "skill_id": 123,
      "difficulty_id": 1,
      "explanation": "The digit 3 in 57.43 is in the hundredths place. Its value is $$3 \\times 0.01 = 0.03$$.",
      "hints": ["Identify the place value of the digit 3.", "After the decimal point the places are tenths then hundredths."],
      "source": "Nan Hua 2025 P4 Weighted Assessment 3 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 1 (0.03)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Round 32.786 to the nearest hundredth.",
      "answer0": "32.70",
      "answer1": "32.78",
      "answer2": "32.79",
      "answer3": "33.00",
      "correct_answer": 2,
      "skill_id": 128,
      "difficulty_id": 1,
      "explanation": "The hundredths digit is 8; the thousandths digit is 6 (≥5), so round up. $$32.786 \\approx 32.79$$.",
      "hints": ["Look at the thousandths digit to decide rounding.", "Round up if it is 5 or more."],
      "source": "Nan Hua 2025 P4 Weighted Assessment 3 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 3 (32.79)."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Express $$8\\frac{5}{20}$$ as a decimal.",
      "answer0": "8.52",
      "answer1": "8.5",
      "answer2": "8.25",
      "answer3": "8.052",
      "correct_answer": 2,
      "skill_id": 127,
      "difficulty_id": 1,
      "explanation": "$$\\frac{5}{20} = \\frac{25}{100} = 0.25$$, so $$8\\frac{5}{20} = 8.25$$.",
      "hints": ["Convert the fraction so its denominator is 100.", "$$\\frac{5}{20} = \\frac{25}{100}$$."],
      "source": "Nan Hua 2025 P4 Weighted Assessment 3 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 3 (8.25)."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Arrange the following decimals in increasing order.<br>2.186&nbsp;&nbsp;&nbsp;2.816&nbsp;&nbsp;&nbsp;2.168&nbsp;&nbsp;&nbsp;2.681",
      "answer0": "2.186, 2.168, 2.681, 2.816",
      "answer1": "2.168, 2.186, 2.681, 2.816",
      "answer2": "2.681, 2.816, 2.186, 2.168",
      "answer3": "2.816, 2.681, 2.186, 2.168",
      "correct_answer": 1,
      "skill_id": 124,
      "difficulty_id": 2,
      "explanation": "Compare digit by digit after the units: 2.168 < 2.186 < 2.681 < 2.816. Increasing order is 2.168, 2.186, 2.681, 2.816.",
      "hints": ["Compare the tenths digit first, then the hundredths.", "Smallest goes first in increasing order."],
      "source": "Nan Hua 2025 P4 Weighted Assessment 3 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 2."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "Mary bought 3 m of ribbon. She used 1.65 m of it to tie a present. How many metres of ribbon had she left?",
      "answer0": "4.65 m",
      "answer1": "2.35 m",
      "answer2": "1.62 m",
      "answer3": "1.35 m",
      "correct_answer": 3,
      "skill_id": 131,
      "difficulty_id": 1,
      "explanation": "$$3 - 1.65 = 1.35$$. She had 1.35 m of ribbon left.",
      "hints": ["Subtract the used length from the total.", "Line up the decimal points: 3.00 − 1.65."],
      "source": "Nan Hua 2025 P4 Weighted Assessment 3 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 4 (1.35 m)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "A bag costs four times as much as a purse. Jamie paid $33 for a bag and 2 purses. How much did a bag cost?",
      "answer0": "$5.50",
      "answer1": "$11",
      "answer2": "$22",
      "answer3": "$27.50",
      "correct_answer": 2,
      "skill_id": 118,
      "difficulty_id": 2,
      "explanation": "Let a purse be 1 unit; a bag is 4 units. Bag + 2 purses = 4 + 2 = 6 units = $33, so 1 unit = $5.50. A bag = 4 units = $$4 \\times 5.50 = 22$$.",
      "hints": ["Let the purse be 1 unit and the bag be 4 units.", "Total units = 4 + 2 = 6 = $33."],
      "source": "Nan Hua 2025 P4 Weighted Assessment 3 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 3 ($22)."
    },
    {
      "n": 7,
      "type_id": 2,
      "question": "ABCD is a square. $$\\angle b$$ is twice the size of $$\\angle a$$. Find $$\\angle a$$.",
      "answer0": "13",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 2,
      "explanation": "Angle DAB of the square is 90°. So $$\\angle a + \\angle b + 51° = 90°$$. Since $$\\angle b = 2\\angle a$$, $$3\\angle a + 51° = 90°$$, giving $$3\\angle a = 39°$$ and $$\\angle a = 13°$$.",
      "hints": ["The corner angle of a square is 90°.", "Replace ∠b with 2∠a: 2a + a + 51 = 90."],
      "source": "Nan Hua 2025 P4 Weighted Assessment 3 Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q7.png",
      "image_page": 4,
      "image_bbox": [0.24, 0.25, 0.47, 0.40],
      "image_loc": "top-left of page, square ABCD with diagonal lines and angles a, b and 51° marked at corner A",
      "notes": "Answer 13 degrees (key: 13°). Answer entered as numeric value of angle a."
    },
    {
      "n": 8,
      "type_id": 0,
      "question": "Line AB is drawn for you in the square grid. Draw and label a rectangle ABCD in the square grid such that the length of Line BC is twice the length of Line AB.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 143,
      "difficulty_id": 2,
      "explanation": "AB goes 1 unit right and 2 units down. BC must be perpendicular to AB and twice its length, so BC goes 4 right and 2 down; C and D complete the rectangle. The key shows a slanted rectangle ABCD with BC twice AB.",
      "hints": [],
      "source": "Nan Hua 2025 P4 Weighted Assessment 3 Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 4,
      "image_bbox": [0.26, 0.53, 0.80, 0.80],
      "image_loc": "lower half of page, square dotted grid with line segment AB drawn",
      "notes": "type_id 0 — draw-and-label task, no value answer; SKIPPED on insert. Key shows rectangle ABCD where BC is twice AB."
    },
    {
      "n": 9,
      "type_id": 2,
      "question": "Divide 6 by 7. Correct your answer to 1 decimal place.",
      "answer0": "0.9",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 125,
      "difficulty_id": 2,
      "explanation": "$$6 \\div 7 = 0.857...$$. The second decimal digit is 5, so round up the first decimal place: $$0.857... \\approx 0.9$$.",
      "hints": ["Divide 6 by 7 to at least two decimal places.", "Round 0.85... to 1 decimal place."],
      "source": "Nan Hua 2025 P4 Weighted Assessment 3 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 0.9."
    },
    {
      "n": 10,
      "type_id": 0,
      "question": "The figure is made up of three shapes; P, Q and R. Q is a rectangle. P and R are squares. Each of the statements below is either true, false or not possible to tell from the information given. Put a tick to indicate your answer.<br>1) P has 4 equal sides and 2 pairs of perpendicular lines.<br>2) Q has 2 pairs of parallel lines.<br>3) The length of P is twice the length of R.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 143,
      "difficulty_id": 2,
      "explanation": "Statement 1 — False: a square has 4 pairs of perpendicular lines (each pair of adjacent sides), not 2. Statement 2 — True: a rectangle has 2 pairs of parallel sides. Statement 3 — Not possible to tell: no measurements for P and R are given.",
      "hints": [],
      "source": "Nan Hua 2025 P4 Weighted Assessment 3 Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 5,
      "image_bbox": [0.28, 0.47, 0.70, 0.60],
      "image_loc": "middle of page, composite figure of square P, rectangle Q and square R in a row",
      "notes": "type_id 0 — tick true/false/not-possible table, no single value answer; SKIPPED on insert. Key: 1 False, 2 True, 3 Not possible to tell."
    },
    {
      "n": 11,
      "type_id": 2,
      "question": "Pearly had $$5.4\\ell$$ of watermelon juice. Pearly had twice as much watermelon juice as May. May had three times as much watermelon juice as Amy. How much more watermelon juice does Pearly have than Amy?",
      "answer0": "4.5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 131,
      "difficulty_id": 3,
      "explanation": "May = $$5.4 \\div 2 = 2.7$$ L. Amy = $$2.7 \\div 3 = 0.9$$ L. Pearly has $$5.4 - 0.9 = 4.5$$ L more than Amy.",
      "hints": ["Work out May's amount first (half of Pearly's).", "Then Amy's amount (a third of May's), then subtract from Pearly's."],
      "source": "Nan Hua 2025 P4 Weighted Assessment 3 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 4.5 L. Answer in litres."
    },
    {
      "n": 12,
      "type_id": 2,
      "question": "Mrs Tan had 2.53 kg more flour than Mrs Sim. After Mrs Tan used 4.09 kg of flour, Mrs Sim had four times as much flour as Mrs Tan had left. How many kilograms of flour did Mrs Tan have at first?",
      "answer0": "4.61",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 131,
      "difficulty_id": 3,
      "explanation": "After using 4.09 kg, Mrs Tan's amount is (Tan first − 4.09). Mrs Sim = Tan first − 2.53. Sim = 4 × Tan's remaining: $$T - 2.53 = 4(T - 4.09)$$. So $$T - 2.53 = 4T - 16.36$$, giving $$3T = 13.83$$ and $$T = 4.61$$ kg. (Equivalently the difference 4.09 − 2.53 = 1.56 kg equals 3 units of Tan's remainder; 1 unit = 0.52 kg; Tan first = 0.52 + 4.09 = 4.61 kg.)",
      "hints": ["After using flour, let Mrs Tan's remaining amount be 1 unit; Mrs Sim is 4 units.", "The gap 4.09 − 2.53 = 1.56 kg equals 3 units."],
      "source": "Nan Hua 2025 P4 Weighted Assessment 3 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 4.61 kg. Answer in kilograms."
    },
    {
      "n": 13,
      "type_id": 2,
      "question": "Mr Tan placed 8 flags around the border of a square field. The distance between each flag and the next was equal for all the flags. The distance between the 1st flag and the 6th flag was 27 m. What was the total distance of the border around the square field?",
      "answer0": "43.2",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 131,
      "difficulty_id": 3,
      "explanation": "From the 1st flag to the 6th flag there are 5 gaps: $$27 \\div 5 = 5.4$$ m per gap. With 8 flags around a closed border there are 8 equal gaps: $$5.4 \\times 8 = 43.2$$ m.",
      "hints": ["From flag 1 to flag 6 there are 5 gaps, not 6.", "Around a closed border, the number of gaps equals the number of flags."],
      "source": "Nan Hua 2025 P4 Weighted Assessment 3 Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 43.2 m. Answer in metres."
    }
  ]
}