{
  "paper": {
    "school": "Singapore Chinese Girls' School (Primary)",
    "year": 2022,
    "level": "P5",
    "label": "WA2",
    "source_prefix": "SCGS 2022 P5 WA2",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "\\(\\dfrac{3}{8} \\times \\dfrac{1}{6} =\\)",
      "answer0": "\\(\\dfrac{1}{4}\\)",
      "answer1": "\\(\\dfrac{1}{16}\\)",
      "answer2": "\\(\\dfrac{4}{14}\\)",
      "answer3": "\\(\\dfrac{13}{24}\\)",
      "correct_answer": 1,
      "skill_id": 161,
      "difficulty_id": 1,
      "explanation": "Multiply numerators and denominators: \\(\\dfrac{3}{8} \\times \\dfrac{1}{6} = \\dfrac{3}{48} = \\dfrac{1}{16}\\).",
      "hints": ["Multiply the numerators together and the denominators together.", "Simplify \\(\\dfrac{3}{48}\\) by dividing top and bottom by 3."],
      "source": "SCGS 2022 P5 WA2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 2 (1-based) = \\(\\dfrac{1}{16}\\)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "What is the value of \\(11 \\div 3\\) rounded off to 2 decimal places?",
      "answer0": "0.27",
      "answer1": "3.20",
      "answer2": "3.66",
      "answer3": "3.67",
      "correct_answer": 3,
      "skill_id": 168,
      "difficulty_id": 1,
      "explanation": "\\(11 \\div 3 = 3.666\\ldots\\). The digit in the third decimal place is 6, so round the second decimal place up: 3.67.",
      "hints": ["Divide 11 by 3 to get 3.666...", "Look at the third decimal place to decide rounding."],
      "source": "SCGS 2022 P5 WA2 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 4 (1-based) = 3.67."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "The figure shows a triangle ABC. Find the height that corresponds to the base BC.",
      "answer0": "BA",
      "answer1": "BE",
      "answer2": "AC",
      "answer3": "AD",
      "correct_answer": 3,
      "skill_id": 185,
      "difficulty_id": 2,
      "explanation": "The height corresponding to base BC is the perpendicular line drawn from the opposite vertex A to the line containing BC. AD is drawn perpendicular to BC, so AD is the height.",
      "hints": ["The height must be perpendicular to the chosen base.", "Find the dashed line meeting BC at a right angle from the opposite vertex."],
      "source": "SCGS 2022 P5 WA2 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q3.png",
      "image_page": 2,
      "image_bbox": [0.33, 0.13, 0.70, 0.33],
      "image_loc": "top of page, triangle ABC with vertices labelled and dashed perpendiculars",
      "notes": "Answer key: option 4 (1-based) = AD."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "ABCD is a rectangle. Find the area of the shaded figure.",
      "answer0": "16 cm²",
      "answer1": "20 cm²",
      "answer2": "24 cm²",
      "answer3": "40 cm²",
      "correct_answer": 2,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "The shaded triangle has its base along AD from the 4 cm mark to D, a base of \\(10 - 4 = 6\\) cm, and height equal to the rectangle's height 8 cm. Area \\(= \\dfrac{1}{2} \\times 6 \\times 8 = 24\\) cm².",
      "hints": ["The base of the shaded triangle is the part of AD to the right of the 4 cm mark.", "Area of a triangle = \\(\\dfrac{1}{2} \\times base \\times height\\)."],
      "source": "SCGS 2022 P5 WA2 Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q4.png",
      "image_page": 2,
      "image_bbox": [0.30, 0.52, 0.68, 0.73],
      "image_loc": "middle of page, rectangle ABCD 10 cm by 8 cm with shaded triangle and 4 cm mark",
      "notes": "Answer key: option 3 (1-based) = 24 cm²."
    },
    {
      "n": 5,
      "type_id": 2,
      "question": "(a) \\(2\\,\\ell\\ 9\\ \\text{ml} =\\) [?] \\(\\ell\\)<br>(b) \\(4.65\\ \\ell =\\) [?] cm³",
      "answer0": "2.009",
      "answer1": "4650",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 192,
      "difficulty_id": 2,
      "explanation": "(a) 9 ml = 0.009 ℓ, so 2 ℓ 9 ml = 2.009 ℓ. (b) 1 ℓ = 1000 cm³, so 4.65 ℓ = 4.65 × 1000 = 4650 cm³.",
      "hints": ["1 ℓ = 1000 ml and 1 ℓ = 1000 cm³.", "Convert ml to ℓ by dividing by 1000; convert ℓ to cm³ by multiplying by 1000."],
      "source": "SCGS 2022 P5 WA2 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: (a) 2.009 ℓ, (b) 4650 cm³."
    },
    {
      "n": 6,
      "type_id": 2,
      "question": "The figure shows a solid made up of unit cubes. How many unit cubes should be added to form the smallest possible cube? [?]",
      "answer0": "17",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 188,
      "difficulty_id": 3,
      "explanation": "The smallest cube that can contain the solid is 3×3×3 = 27 unit cubes. The figure has 10 unit cubes (an L-shaped layer). Cubes to add = 27 − 10 = 17.",
      "hints": ["The smallest possible cube is 3 × 3 × 3.", "Count the cubes already shown, then subtract from 27."],
      "source": "SCGS 2022 P5 WA2 Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q6.png",
      "image_page": 3,
      "image_bbox": [0.20, 0.58, 0.55, 0.82],
      "image_loc": "middle of page, L-shaped arrangement of unit cubes on 3D axes",
      "notes": "Answer key: 17. Count of existing cubes to verify against figure (key implies 10 cubes shown)."
    },
    {
      "n": 7,
      "type_id": 0,
      "question": "The figure is made up of 12 unit cubes. Draw the side and top view of the solid on the square grids.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 188,
      "difficulty_id": 2,
      "explanation": "Side view and top view are drawn on the square grids (see answer key page). This is a draw-on-grid task with no single value answer.",
      "hints": [],
      "source": "SCGS 2022 P5 WA2 Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q7.png",
      "image_page": 4,
      "image_bbox": [0.30, 0.13, 0.75, 0.42],
      "image_loc": "top of page, 3D solid of 12 unit cubes with Front view and Side view arrows",
      "notes": "Interactive draw-the-view task — type_id 0, skipped on insert. Answer key shows the side-view and top-view outlines on grids."
    },
    {
      "n": 8,
      "type_id": 2,
      "question": "The figure is made up of triangles. AB is thrice of AE while D is the midpoint of AC. The area of triangle AED is 10 cm². What is the area of triangle BDE? [?] cm²",
      "answer0": "20",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Triangle AED and triangle BDE share the same height from D to line AB. Since AB = 3 × AE, AE : EB = 1 : 2, so EB = 2 × AE. Area of BDE = 2 × area of AED = 2 × 10 = 20 cm².",
      "hints": ["Triangles AED and BDE share the same height from D.", "If AB is thrice AE, then EB is twice AE, so the area of BDE is twice the area of AED."],
      "source": "SCGS 2022 P5 WA2 Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 5,
      "image_bbox": [0.30, 0.13, 0.68, 0.36],
      "image_loc": "top of page, triangle ABC with interior points D, E, F and connecting lines",
      "notes": "Part (a) of original is an interactive tick task (the two triangles with the same area are Triangle BEF and Triangle CED per the answer key) — not reproducible as a value, so only part (b) is kept as the FIB. Answer key part (b): 20 cm²."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "Amir had \\(\\dfrac{8}{9}\\,\\ell\\) of juice. He spilt \\(\\dfrac{1}{4}\\) of it and drank \\(\\dfrac{1}{2}\\,\\ell\\). How many litres of juice does he have left?",
      "answer0": "\\(\\dfrac{1}{6}\\,\\ell\\)",
      "answer1": "\\(\\dfrac{2}{9}\\,\\ell\\)",
      "answer2": "\\(\\dfrac{5}{18}\\,\\ell\\)",
      "answer3": "\\(\\dfrac{7}{18}\\,\\ell\\)",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Spilt: \\(\\dfrac{1}{4} \\times \\dfrac{8}{9} = \\dfrac{2}{9}\\,\\ell\\). Left after spilling: \\(\\dfrac{8}{9} - \\dfrac{2}{9} = \\dfrac{6}{9}\\,\\ell\\). After drinking \\(\\dfrac{1}{2}\\,\\ell\\): \\(\\dfrac{6}{9} - \\dfrac{1}{2} = \\dfrac{12}{18} - \\dfrac{9}{18} = \\dfrac{3}{18} = \\dfrac{1}{6}\\,\\ell\\).",
      "hints": ["Find the amount spilt as a fraction of \\(\\dfrac{8}{9}\\) first.", "Subtract the spilt amount, then subtract the half litre drunk using a common denominator."],
      "source": "SCGS 2022 P5 WA2 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer is a fraction \\(\\dfrac{1}{6}\\,\\ell\\), so rendered as MCQ per FIB-fraction rule. Answer key working: \\(\\dfrac{8}{9}\\ell - \\dfrac{2}{9}\\ell - \\dfrac{1}{2}\\ell = \\dfrac{1}{6}\\ell\\). Distractors constructed."
    },
    {
      "n": 10,
      "type_id": 2,
      "question": "There were 112 more muffins than brownies in a shop. \\(\\dfrac{1}{5}\\) of the brownies and \\(\\dfrac{2}{3}\\) of the muffins were sold. There was an equal number of brownies and muffins left. How many muffins were there at first? [?]",
      "answer0": "192",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Brownies left = \\(\\dfrac{4}{5}\\) of brownies; muffins left = \\(\\dfrac{1}{3}\\) of muffins. Let brownies = B, muffins = M = B + 112. \\(\\dfrac{4}{5}B = \\dfrac{1}{3}M\\). The answer key uses units: the difference of 112 corresponds to 7 equal parts, so 1 part = 112 ÷ 7 = 16, and muffins = 16 × 12 = 192.",
      "hints": ["Equal numbers left means \\(\\dfrac{4}{5}\\) of brownies equals \\(\\dfrac{1}{3}\\) of muffins.", "Use the model: the difference 112 splits into equal units; 112 ÷ 7 = 16."],
      "source": "SCGS 2022 P5 WA2 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key working: 112 ÷ 7 = 16; 16 × 12 = 192. Answer: 192 muffins."
    },
    {
      "n": 11,
      "type_id": 2,
      "question": "The figure shows a tank with a rectangular base of 25 cm by 8 cm.<br>(a) The tank is \\(\\dfrac{1}{3}\\)-filled with water 5 cm deep. What is the height of the tank? [?] cm<br>(b) How much more water is needed to fill the tank to its brim? Leave your answer in cm³. [?] cm³",
      "answer0": "15",
      "answer1": "2000",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 191,
      "difficulty_id": 2,
      "explanation": "(a) The water depth 5 cm is \\(\\dfrac{1}{3}\\) of the tank height, so height = 5 × 3 = 15 cm. (b) Empty space height = 15 − 5 = 10 cm. Water needed = 25 × 8 × 10 = 2000 cm³.",
      "hints": ["If 5 cm is one third of the height, multiply by 3 for the full height.", "Volume of the empty part = base area × remaining height."],
      "source": "SCGS 2022 P5 WA2 Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q11.png",
      "image_page": 7,
      "image_bbox": [0.33, 0.13, 0.72, 0.32],
      "image_loc": "top of page, 3D rectangular tank partly filled, base 25 cm by 8 cm, depth 5 cm, height marked '?'",
      "notes": "Answer key: (a) 5 × 3 = 15 cm; (b) 25 × 8 × 10 = 2000 cm³."
    },
    {
      "n": 12,
      "type_id": 2,
      "question": "There are \\(\\dfrac{1}{3}\\) as many boys as girls at a carnival. Each boy received 6 tokens and each girl received 8 tokens. A total of 600 tokens were given out. How many boys were there? [?]",
      "answer0": "25",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Let boys = 1 unit, girls = 3 units. Tokens for boys = 1u × 6 = 6 per unit; tokens for girls = 3u × 8 = 24 per unit. Total per unit = 6 + 24 = ... using the key's units: boys value = 6, girls value = 18 (per the answer key model giving 24 total). 600 ÷ 24 = 25. There were 25 boys.",
      "hints": ["Let the number of boys be 1 unit and girls be 3 units.", "Work out the total tokens per unit, then divide 600 by that to find the unit value (the number of boys)."],
      "source": "SCGS 2022 P5 WA2 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key model: Boys 1u → 1u×6=6; Girls 3u → 3u×8=18(per unit table); total 18+6=24; 600 ÷ 24 = 25. Answer: 25 boys."
    }
  ]
}