{
  "paper": {
    "school": "Nan Hua",
    "year": 2023,
    "level": "P5",
    "label": "Weighted Assessment 2",
    "source_prefix": "Nan Hua 2023 P5 Weighted Assessment 2",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "Find the ratio of the length of pencil to the length of eraser.",
      "answer0": "10 : 3",
      "answer1": "3 : 10",
      "answer2": "10 : 7",
      "answer3": "7 : 10",
      "correct_answer": 0,
      "skill_id": 180,
      "difficulty_id": 1,
      "explanation": "Read the lengths off the ruler. Pencil = 10 cm, eraser = 3 cm. So the ratio of pencil to eraser is 10 : 3.",
      "hints": ["Line each item up against the centimetre ruler to read its length.", "Write the ratio in the order asked: pencil first, then eraser."],
      "source": "Nan Hua 2023 P5 Weighted Assessment 2 Q1",
      "image_needed": true,
      "image_options": false,
      "image_file": "q1.png",
      "image_page": 1,
      "image_bbox": [0.22, 0.46, 0.74, 0.58],
      "notes": "Answer ratio is non-FIB, so MCQ. Pencil 10 cm : eraser 3 cm from ruler diagram. Same figure (crayon/pencil/eraser on ruler) also used for Q2."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Find the ratio of the length of crayon to the length of pencil. Give your answer in its simplest form.",
      "answer0": "3 : 5",
      "answer1": "5 : 3",
      "answer2": "6 : 10",
      "answer3": "5 : 6",
      "correct_answer": 0,
      "skill_id": 179,
      "difficulty_id": 1,
      "explanation": "From the ruler, crayon = 6 cm and pencil = 10 cm, giving 6 : 10. Divide both by 2 to simplify: 6 : 10 = 3 : 5.",
      "hints": ["Read the crayon and pencil lengths from the ruler.", "Simplify by dividing both numbers by their highest common factor (2)."],
      "source": "Nan Hua 2023 P5 Weighted Assessment 2 Q2",
      "image_needed": true,
      "image_options": false,
      "image_file": "q2.png",
      "image_page": 1,
      "image_bbox": [0.22, 0.46, 0.74, 0.58],
      "notes": "Ratio answer, so MCQ. Crayon 6 cm : pencil 10 cm = 3 : 5. Reuses the same ruler diagram as Q1 (the diagram is given before Q1)."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Find the ratio of the perimeter of Square A to the perimeter of Rectangle B. Give your answer in its simplest form.",
      "answer0": "8 : 11",
      "answer1": "11 : 8",
      "answer2": "16 : 22",
      "answer3": "2 : 3",
      "correct_answer": 0,
      "skill_id": 179,
      "difficulty_id": 2,
      "explanation": "Square A has side 4 cm, so perimeter = 4 × 4 = 16 cm. Rectangle B is 6 cm by 5 cm, so perimeter = 5 + 5 + 6 + 6 = 22 cm. Ratio = 16 : 22 = 8 : 11 (divide both by 2).",
      "hints": ["Perimeter of a square = 4 × side; perimeter of a rectangle = 2 × (length + breadth).", "Simplify 16 : 22 by dividing both numbers by 2."],
      "source": "Nan Hua 2023 P5 Weighted Assessment 2 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q3.png",
      "image_page": 2,
      "image_bbox": [0.27, 0.16, 0.72, 0.32],
      "notes": "Ratio answer, so MCQ. Square A side 4 cm (perimeter 16); Rectangle B 6 cm by 5 cm (perimeter 22). 16:22 = 8:11."
    },
    {
      "n": 4,
      "type_id": 2,
      "question": "Find the missing number in the pair of ratios.<br>\\(6 : 8 = 27 : \\) [?]",
      "answer0": "36",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 181,
      "difficulty_id": 1,
      "explanation": "First simplify 6 : 8 = 3 : 4. To go from 3 to 27, multiply by 9, so multiply 4 by 9 as well: 4 × 9 = 36. The missing number is 36.",
      "hints": ["Simplify 6 : 8 to 3 : 4 first.", "Find what 3 was multiplied by to get 27, then apply the same to 4."],
      "source": "Nan Hua 2023 P5 Weighted Assessment 2 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "notes": "Missing term in equivalent ratios. Answer 36 is an integer, so FIB."
    },
    {
      "n": 5,
      "type_id": 2,
      "question": "The ratio of the amount of water in Beaker A to the amount of water in Beaker B is 16 : 9. What is the amount of water in Beaker B? [?]",
      "answer0": "450",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 182,
      "difficulty_id": 2,
      "explanation": "Beaker A shows 800 ml of water, which is 16 units. 1 unit = 800 ÷ 16 = 50 ml. Beaker B is 9 units = 50 × 9 = 450 ml.",
      "hints": ["Read the water level in Beaker A from the scale (800 ml = 16 units).", "Find the value of 1 unit, then multiply by 9 for Beaker B."],
      "source": "Nan Hua 2023 P5 Weighted Assessment 2 Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q5.png",
      "image_page": 2,
      "image_bbox": [0.30, 0.62, 0.62, 0.80],
      "notes": "Answer 450 (ml) is an integer, so FIB. Beaker A reads 800 ml from the scale (=16 units); 1u=50; Beaker B = 9u = 450 ml. Units = ml."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "Find the ratio of the number of oranges to the number of apples to the number of mangoes. Give your answer in its simplest form.",
      "answer0": "2 : 4 : 3",
      "answer1": "4 : 2 : 3",
      "answer2": "300 : 600 : 450",
      "answer3": "3 : 4 : 2",
      "correct_answer": 0,
      "skill_id": 180,
      "difficulty_id": 2,
      "explanation": "From the bar graph: oranges = 300, apples = 600, mangoes = 450. Ratio oranges : apples : mangoes = 300 : 600 : 450. Divide each by 150: = 2 : 4 : 3.",
      "hints": ["Read each bar's height: oranges 300, apples 600, mangoes 450.", "Divide all three numbers by their highest common factor (150)."],
      "source": "Nan Hua 2023 P5 Weighted Assessment 2 Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q6.png",
      "image_page": 3,
      "image_bbox": [0.18, 0.24, 0.72, 0.47],
      "notes": "Three-term ratio answer, so MCQ. Bar graph: oranges 300, apples 600, mangoes 450 -> 2:4:3."
    },
    {
      "n": 7,
      "type_id": 2,
      "question": "The table shows the number of girls and boys who wear and do not wear spectacles in Class 5A. 8 girls wear spectacles, 7 girls do not wear spectacles, and 11 boys do not wear spectacles. The ratio of the number of girls to the number of boys in 5A is 3 : 5. Find the number of boys who wear spectacles in 5A. [?]",
      "answer0": "14",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 182,
      "difficulty_id": 3,
      "explanation": "Total girls = 8 + 7 = 15, which is 3 units, so 1 unit = 15 ÷ 3 = 5. Boys = 5 units = 5 × 5 = 25. Boys who do not wear spectacles = 11, so boys who wear spectacles = 25 − 11 = 14.",
      "hints": ["Find the total number of girls first, then use the 3 : 5 ratio to find the total number of boys.", "Subtract the boys who do not wear spectacles from the total number of boys."],
      "source": "Nan Hua 2023 P5 Weighted Assessment 2 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "notes": "Table data folded into stem (girls wear 8, girls do not wear 7, boys do not wear 11). Answer 14 (boys) is integer, so FIB."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "Percy is 11 years old. Bala is 15 years old. Find the ratio of Percy's age to Bala's age in 5 years' time. Give your answer in its simplest form.",
      "answer0": "4 : 5",
      "answer1": "11 : 15",
      "answer2": "16 : 20",
      "answer3": "5 : 4",
      "correct_answer": 0,
      "skill_id": 179,
      "difficulty_id": 2,
      "explanation": "In 5 years' time: Percy = 11 + 5 = 16, Bala = 15 + 5 = 20. Ratio = 16 : 20 = 4 : 5 (divide both by 4).",
      "hints": ["Add 5 years to each person's age first.", "Simplify 16 : 20 by dividing both numbers by 4."],
      "source": "Nan Hua 2023 P5 Weighted Assessment 2 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "notes": "Ratio answer, so MCQ. 16:20 = 4:5."
    },
    {
      "n": 9,
      "type_id": 0,
      "question": "The total number of pens that Alice, Peter and John have is between 45 and 50. The ratio of the number of Alice's pens to the number of Peter's pens to the number of John's pens is 1 : 2 : 5. Each statement below is either true or false. For each statement, put a tick in the correct column. Statement 1: The total number of pens that Alice and Peter have is less than the number of pens that John has. Statement 2: Alice has 6 pens.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "Total units = 1 + 2 + 5 = 8 units. The total is between 45 and 50, and must be a multiple of 8, so total = 48; 1 unit = 6. Alice = 6, Peter = 12, John = 30. Statement 1: Alice + Peter = 6 + 12 = 18, which is less than John's 30 -> TRUE. Statement 2: Alice has 1 unit = 6 pens -> TRUE. Both statements are true.",
      "hints": ["The total must be a multiple of (1 + 2 + 5) = 8 units, and lie between 45 and 50.", "Find the value of 1 unit, then check each statement."],
      "source": "Nan Hua 2023 P5 Weighted Assessment 2 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "notes": "Interactive true/false tick-the-column task; no app question type, set type_id 0 (skipped on insert). Answer key: both statements are TRUE (total = 48, 1u = 6; Alice=6, Peter=12, John=30)."
    },
    {
      "n": 10,
      "type_id": 2,
      "question": "The ratio of the number of boys to the number of girls to the number of teachers in a school is 8 : 9 : 2. There are 588 more girls than teachers.<br>a) How many girls are there in the school? [?]<br>b) How many more students than teachers are there in the school? [?]",
      "answer0": "756",
      "answer1": "1260",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "Boys : Girls : Teachers = 8 : 9 : 2. Girls − Teachers = 9u − 2u = 7u = 588, so 1u = 588 ÷ 7 = 84. a) Girls = 9u = 84 × 9 = 756. b) Students = boys + girls = 8u + 9u = 17u; boys = 84 × 8 = 672, so students = 672 + 756 = 1428. Teachers = 2u = 84 × 2 = 168. More students than teachers = 1428 − 168 = 1260.",
      "hints": ["The difference 9 units − 2 units = 7 units equals 588; find 1 unit.", "Part b: students = boys + girls; subtract the number of teachers."],
      "source": "Nan Hua 2023 P5 Weighted Assessment 2 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "notes": "Two-part FIB, both integers. a) 756 girls, b) 1260 more students than teachers. 1u = 84."
    },
    {
      "n": 11,
      "type_id": 2,
      "question": "Jie Min and her brother had some marbles. The ratio of the number of marbles that Jie Min had to the number of marbles that her brother had was 1 : 4 at first. After their mother gave Jie Min 54 more marbles, Jie Min and her brother had the same number of marbles. How many marbles did Jie Min's brother have at first? [?]",
      "answer0": "72",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "Jie Min : Brother = 1 : 4. The brother's marbles do not change. After Jie Min gets 54 more, they are equal, so the 54 marbles fill the gap of 4u − 1u = 3u. So 3u = 54, 1u = 54 ÷ 3 = 18. Brother had 4u = 18 × 4 = 72 marbles at first.",
      "hints": ["The brother's number of marbles stays the same throughout.", "The 54 marbles make up the difference between the two original amounts (4 units − 1 unit)."],
      "source": "Nan Hua 2023 P5 Weighted Assessment 2 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "notes": "Answer 72 (marbles) is integer, so FIB. 3u = 54, 1u = 18, brother = 4u = 72."
    }
  ]
}