{
  "paper": {
    "school": "Nan Hua",
    "year": 2023,
    "level": "P5",
    "label": "Weighted Assessment 1",
    "source_prefix": "Nan Hua 2023 P5 Weighted Assessment 1",
    "has_answer_key": true,
    "notes": "PDF bundles Paper 1 (8 MCQ Section A + Q9-14 Section B) and Paper 2 (Q1-4). Question numbers restart per paper; the source field disambiguates with a P1/P2 prefix. Cover says 'Term 1 Weighted Assessment 2023'; folder/url label is WA1."
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "Which of the following is the base of the triangle ACD given that the height is BD?",
      "answer0": "AB",
      "answer1": "BC",
      "answer2": "AC",
      "answer3": "AD",
      "correct_answer": 2,
      "skill_id": 186,
      "difficulty_id": 1,
      "explanation": "The height BD is drawn perpendicular to AC (the foot B lies on AC, with the right angle at B). The base is the side perpendicular to the height, so the base of triangle ACD is AC. Answer: AC.",
      "hints": ["The base is the side that the height meets at a right angle.", "BD drops perpendicularly onto the line AC."],
      "source": "Nan Hua 2023 P5 Weighted Assessment 1 P1 Q1",
      "image_needed": true,
      "image_options": false,
      "image_file": "q1.png",
      "image_page": 1,
      "image_bbox": [0.18, 0.46, 0.62, 0.62],
      "image_loc": "triangle ACD with vertices A (bottom-left), B (foot on base), C (right), D (top), height BD shown; below Q1 on page 1"
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "6 : 8 = ____ : 72",
      "answer0": "9",
      "answer1": "12",
      "answer2": "54",
      "answer3": "96",
      "correct_answer": 2,
      "skill_id": 181,
      "difficulty_id": 1,
      "explanation": "Equivalent ratios: 8 is multiplied by 9 to give 72, so 6 is also multiplied by 9. 6 × 9 = 54. The missing number is 54. Answer: 54.",
      "hints": ["8 × ? = 72, find the multiplier.", "72 ÷ 8 = 9, then multiply 6 by the same factor."],
      "source": "Nan Hua 2023 P5 Weighted Assessment 1 P1 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "John uses unit cubes to form the solids. What is the ratio of the volume of Solid A to the volume of Solid B to the volume of Solid C?",
      "answer0": "1 : 2 : 3",
      "answer1": "2 : 3 : 1",
      "answer2": "1 : 2 : 6",
      "answer3": "2 : 3 : 6",
      "correct_answer": 1,
      "skill_id": 188,
      "difficulty_id": 2,
      "explanation": "Count the unit cubes in each solid and compare. The volumes are in the ratio 2 : 3 : 1 (Solid A : Solid B : Solid C). Answer: 2 : 3 : 1.",
      "hints": ["Count the number of unit cubes making up each solid.", "Then write the three counts as a ratio in the order A : B : C."],
      "source": "Nan Hua 2023 P5 Weighted Assessment 1 P1 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q3.png",
      "image_page": 2,
      "image_bbox": [0.17, 0.18, 0.66, 0.32],
      "image_loc": "three unit-cube solids labelled A, B, C side by side near the top of page 2",
      "notes": "Counting question — cubes hidden behind front faces must be inferred; key answer is 2:3:1, so A=2 units, B=3 units, C=1 unit relative."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "The following solid is made up of 1-cm cubes. What is the volume of the solid?",
      "answer0": "9 cm³",
      "answer1": "10 cm³",
      "answer2": "14 cm³",
      "answer3": "15 cm³",
      "correct_answer": 2,
      "skill_id": 189,
      "difficulty_id": 2,
      "explanation": "The stepped pyramid is built in layers: bottom layer 3×3 = 9 cubes, middle layer 2×2 = 4 cubes, top layer 1 cube. Total = 9 + 4 + 1 = 14 cubes, so volume = 14 cm³. Answer: 14 cm³.",
      "hints": ["Count the cubes layer by layer from the bottom up.", "9 + 4 + 1 = ?"],
      "source": "Nan Hua 2023 P5 Weighted Assessment 1 P1 Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q4.png",
      "image_page": 2,
      "image_bbox": [0.28, 0.52, 0.55, 0.76],
      "image_loc": "stepped 3-layer cube pyramid in the middle-lower half of page 2",
      "notes": "Counting question; required count = 14 cubes (9+4+1)."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "A roll of ribbon is cut into three pieces in the ratio 2 : 3 : 7. The shortest piece is 24 cm. Find the original length of the roll of ribbon.",
      "answer0": "8 cm",
      "answer1": "12 cm",
      "answer2": "96 cm",
      "answer3": "144 cm",
      "correct_answer": 3,
      "skill_id": 182,
      "difficulty_id": 2,
      "explanation": "The shortest piece is 2 units = 24 cm, so 1 unit = 24 ÷ 2 = 12 cm. The whole roll is 2 + 3 + 7 = 12 units = 12 × 12 = 144 cm. Answer: 144 cm.",
      "hints": ["The shortest piece corresponds to the smallest ratio term, 2 units.", "Find 1 unit, then multiply by the total number of units (2+3+7)."],
      "source": "Nan Hua 2023 P5 Weighted Assessment 1 P1 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Printed answer key marks option (2)=12 cm, but that is the value of 1 unit, not the total length asked for. The mathematically correct original length is 144 cm = option (4). Using the correct value; key has a typo."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "A rectangular container 8 cm long, 2 cm wide and 6 cm high is filled with water to a depth of 5 cm. Find the volume of water in the container.",
      "answer0": "60 cm³",
      "answer1": "80 cm³",
      "answer2": "96 cm³",
      "answer3": "240 cm³",
      "correct_answer": 1,
      "skill_id": 191,
      "difficulty_id": 2,
      "explanation": "Volume of water = length × width × water depth = 8 × 2 × 5 = 80 cm³. The container height of 6 cm is not used because the water only reaches 5 cm. Answer: 80 cm³.",
      "hints": ["Use the water depth (5 cm), not the container height (6 cm).", "Volume of water = 8 × 2 × 5."],
      "source": "Nan Hua 2023 P5 Weighted Assessment 1 P1 Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q6.png",
      "image_page": 3,
      "image_bbox": [0.42, 0.39, 0.74, 0.55],
      "image_loc": "rectangular tank diagram with water shaded inside, dimensions 8 cm, 2 cm, 6 cm and water level 5 cm; middle of page 3"
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "The ratio of the number of Mary's stickers to the number of Nancy's stickers was 1 : 5. They have a total of 102 stickers. How many more stickers does Nancy have than Mary?",
      "answer0": "17",
      "answer1": "51",
      "answer2": "68",
      "answer3": "85",
      "correct_answer": 2,
      "skill_id": 182,
      "difficulty_id": 2,
      "explanation": "Total units = 1 + 5 = 6 units = 102 stickers, so 1 unit = 102 ÷ 6 = 17 stickers. Nancy has more by 5 − 1 = 4 units = 4 × 17 = 68 stickers. Answer: 68.",
      "hints": ["Add the ratio terms to find how many units make up 102.", "The difference is (5 − 1) = 4 units."],
      "source": "Nan Hua 2023 P5 Weighted Assessment 1 P1 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "DCB is a straight line and DC = CB. What is the area of the shaded triangle?",
      "answer0": "11 cm²",
      "answer1": "44 cm²",
      "answer2": "88 cm²",
      "answer3": "176 cm²",
      "correct_answer": 1,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "DB = 22 cm and DC = CB, so CB = 22 ÷ 2 = 11 cm. The shaded triangle ACB has base CB = 11 cm and height AD = 8 cm. Area = ½ × 11 × 8 = 44 cm². Answer: 44 cm².",
      "hints": ["DC = CB means each is half of DB = 22 cm.", "Shaded triangle base = CB, height = 8 cm; area = ½ × base × height."],
      "source": "Nan Hua 2023 P5 Weighted Assessment 1 P1 Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 4,
      "image_bbox": [0.20, 0.37, 0.58, 0.50],
      "image_loc": "right triangle with A top-left, D bottom-left (right angle), C and B along base; shaded portion ACB; height 8 cm, base 22 cm; upper-middle of page 4",
      "notes": "Figure not drawn to scale (stated in original)."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "200 people went to a carnival. 46 of them are female. What is the ratio of the number of males to the number of females in the simplest form?",
      "answer0": "77 : 23",
      "answer1": "100 : 23",
      "answer2": "23 : 77",
      "answer3": "154 : 46",
      "correct_answer": 0,
      "skill_id": 179,
      "difficulty_id": 2,
      "explanation": "Number of males = 200 − 46 = 154. Ratio males : females = 154 : 46. Divide both by the common factor 2: 154 ÷ 2 = 77, 46 ÷ 2 = 23. Simplest form = 77 : 23. Answer: 77 : 23.",
      "hints": ["Males = total − females = 200 − 46.", "Simplify 154 : 46 by dividing both parts by 2."],
      "source": "Nan Hua 2023 P5 Weighted Assessment 1 P1 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Originally a free-response ratio (simplest form 77:23). Converted to MCQ because a ratio answer is not a single integer/decimal FIB value. Distractors: 154:46 = unsimplified, 23:77 = reversed, 100:23 = wrong male count."
    },
    {
      "n": 10,
      "type_id": 2,
      "question": "Find the area of the triangle.<br>Area = [?] cm²",
      "answer0": "27",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 1,
      "explanation": "Area of a triangle = ½ × base × height. The base is 9 cm and the perpendicular height is 6 cm (the 7 cm and 8 cm are the slanted sides, not used). Area = ½ × 9 × 6 = 27 cm². Answer: 27 cm².",
      "hints": ["Use the perpendicular height (6 cm), not the slanted sides 7 cm or 8 cm.", "Area = ½ × 9 × 6."],
      "source": "Nan Hua 2023 P5 Weighted Assessment 1 P1 Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 5,
      "image_bbox": [0.26, 0.46, 0.64, 0.68],
      "image_loc": "triangle with slant sides 7 cm and 8 cm, base 9 cm, dashed perpendicular height 6 cm; lower half of page 5"
    },
    {
      "n": 11,
      "type_id": 0,
      "question": "The figure shows Cuboid A. Draw another cuboid such that the volume is thrice that of Cuboid A on the isometric grid provided.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 190,
      "difficulty_id": 2,
      "explanation": "Cuboid A is 3 units × 3 units × 1 unit = 9 cubic units. Three times that is 27 cubic units. Any cuboid with volume 27 cubic units drawn on the isometric grid is acceptable, e.g. 3 × 3 × 3, or 9 × 3 × 1.",
      "hints": ["Volume of Cuboid A = 3 × 3 × 1 = 9 cubic units.", "Draw any cuboid whose dimensions multiply to 9 × 3 = 27 cubic units."],
      "source": "Nan Hua 2023 P5 Weighted Assessment 1 P1 Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q11.png",
      "image_page": 6,
      "image_bbox": [0.16, 0.18, 0.50, 0.34],
      "image_loc": "Cuboid A (3 units x 3 units x 1 unit) above an empty isometric dot grid; upper half of page 6",
      "notes": "Draw-on-grid construction task with no single value/sequence answer → type_id 0 (skipped on insert). Required volume = 27 cubic units (thrice 9)."
    },
    {
      "n": 12,
      "type_id": 2,
      "question": "Triangle ABD is made up of triangles ABE, BEC and CED. AE = ED and BC = CD. The area of triangle BEC is 16 cm². What is the area of triangle ABD?<br>Area = [?] cm²",
      "answer0": "64",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "AE = ED and BC = CD split the figure into equal-area triangles. The printed working gives area of triangle ABD = 16 × 4 = 64 cm². Answer: 64 cm².",
      "hints": ["Equal bases (AE = ED, BC = CD) give equal-area sub-triangles.", "Triangle ABD is 4 times triangle BEC: 16 × 4."],
      "source": "Nan Hua 2023 P5 Weighted Assessment 1 P1 Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q12.png",
      "image_page": 7,
      "image_bbox": [0.28, 0.16, 0.56, 0.32],
      "image_loc": "right triangle with B at top, C on the right side, A bottom-left, E and D along the base (right angle at D); upper half of page 7"
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "Mrs Chew had 256 nuggets and hashbrowns. The ratio of the number of nuggets to the number of hashbrowns was 3 : 1. She sold 130 nuggets and 22 hashbrowns. Find the ratio of the number of nuggets left to the number of hashbrowns left. Give your answer in the simplest form.",
      "answer0": "31 : 21",
      "answer1": "62 : 42",
      "answer2": "21 : 31",
      "answer3": "3 : 1",
      "correct_answer": 0,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "Total = 256 in ratio 3 : 1, so 4 units = 256, 1 unit = 64. Nuggets = 3 × 64 = 192, hashbrowns = 1 × 64 = 64. After selling: nuggets left = 192 − 130 = 62; hashbrowns left = 64 − 22 = 42. Ratio = 62 : 42 = 31 : 21 (divide both by 2). Answer: 31 : 21.",
      "hints": ["Split 256 in the ratio 3 : 1 to find the starting amounts.", "Subtract what was sold, then simplify 62 : 42."],
      "source": "Nan Hua 2023 P5 Weighted Assessment 1 P1 Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Originally free-response ratio (simplest form 31:21). Converted to MCQ because a ratio is not a single FIB value. Distractors: 62:42 = unsimplified, 21:31 = reversed, 3:1 = original ratio."
    },
    {
      "n": 14,
      "type_id": 2,
      "question": "Tank A measuring 40 cm long, 20 cm wide and 30 cm high was \\(\\dfrac{1}{2}\\)-filled with water. How many buckets of capacity 4 ℓ are needed to fill the tank to the brim?<br>[?]",
      "answer0": "3",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 193,
      "difficulty_id": 3,
      "explanation": "Tank volume = 40 × 20 × 30 = 24 000 cm³. It is half-filled, so the empty space to fill = ½ × 24 000 = 12 000 cm³ = 12 000 ml = 12 ℓ. Each bucket holds 4 ℓ, so buckets needed = 12 ÷ 4 = 3. Answer: 3 buckets.",
      "hints": ["Find the tank volume, then the volume still empty (half of it).", "Convert cm³ to litres (1000 cm³ = 1 ℓ), then divide by 4."],
      "source": "Nan Hua 2023 P5 Weighted Assessment 1 P1 Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer is a whole-number count (3 buckets) → FIB. Key working: (30×40×20)÷2 = 12000 cm³; 12000÷4000 = 3."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "At a party, there were 24 adults. The number of children was twice the number of adults. There were 18 more boys than girls. Find the ratio of the number of girls to the number of boys to the number of adults in the simplest form.",
      "answer0": "5 : 11 : 8",
      "answer1": "15 : 33 : 24",
      "answer2": "8 : 11 : 5",
      "answer3": "11 : 5 : 8",
      "correct_answer": 0,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "Adults = 24. Children = 2 × 24 = 48 = boys + girls. With 18 more boys than girls: girls = (48 − 18) ÷ 2 = 15, boys = 15 + 18 = 33. Ratio girls : boys : adults = 15 : 33 : 24. Divide all by 3: 5 : 11 : 8. Answer: 5 : 11 : 8.",
      "hints": ["Children = twice the 24 adults; split into boys and girls using the 18 difference.", "Write girls : boys : adults then divide every term by 3."],
      "source": "Nan Hua 2023 P5 Weighted Assessment 1 P2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q1. Originally free-response ratio (simplest form 5:11:8). Converted to MCQ because a 3-term ratio is not a single FIB value. Distractors: 15:33:24 = unsimplified, 8:11:5 and 11:5:8 = wrong order."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Container X is a cubical tank of edge 11 cm. It was completely filled with water. The water was then poured into Container Y. How much more water was needed to fill Container Y to the brim? Give your answer in milliliters.<br>[?] ml",
      "answer0": "397",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 193,
      "difficulty_id": 3,
      "explanation": "Volume of water from X = 11 × 11 × 11 = 1331 cm³. Capacity of Container Y = 24 × 6 × 12 = 1728 cm³. Extra water needed = 1728 − 1331 = 397 cm³ = 397 ml. Answer: 397 ml.",
      "hints": ["Volume of the cube X = edge × edge × edge.", "Subtract X's volume from Y's capacity (24 × 6 × 12)."],
      "source": "Nan Hua 2023 P5 Weighted Assessment 1 P2 Q2",
      "image_needed": true,
      "image_options": false,
      "image_file": "q16.png",
      "image_page": 10,
      "image_bbox": [0.14, 0.18, 0.74, 0.36],
      "image_loc": "two tanks side by side: cube X (edge 11 cm) on the left, cuboid Y (24 cm x 6 cm x 12 cm) on the right; upper third of page 10",
      "notes": "Paper 2 Q2. Answer is a whole-number millilitre count (397 ml) → FIB."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "ABCD is a rectangle and DEFG is a square with an area of 64 cm². Find the total area of the shaded part.<br>Area = [?] cm²",
      "answer0": "236",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Square DEFG has area 64 cm², so its side = 8 cm. Rectangle ABCD = 20 × 22 = 440 cm². The unshaded triangle ABE has AE = 22 − 8 = 14 cm, so its area = ½ × 20 × 14 = 140 cm². Shaded part = rectangle − triangle ABE − square = 440 − 140 − 64 = 236 cm². Answer: 236 cm².",
      "hints": ["Side of square = \\(\\sqrt{64}\\) = 8 cm; rectangle area = 20 × 22.", "Shaded = rectangle − unshaded triangle ABE − square DEFG."],
      "source": "Nan Hua 2023 P5 Weighted Assessment 1 P2 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q17.png",
      "image_page": 11,
      "image_bbox": [0.28, 0.13, 0.56, 0.30],
      "image_loc": "rectangle ABCD with A top-left, B top-right, C bottom-right, D bottom-left; square DEFG sits in the lower-left; shaded region is the large triangle plus square area; width 20 cm, height 22 cm; upper half of page 11"
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "ABCD is a square with sides 14 cm and DE = EC. Triangle AFD and triangle BEF have a total area of 66 cm². Find the area of the shaded triangle DEF.<br>Area = [?] cm²",
      "answer0": "16",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Square area = 14 × 14 = 196 cm². With DE = EC = 7 cm: area of triangle ABD = ½ × 14 × 14 = 98 cm², area of triangle ABE = ½ × 14 × 14 = 98 cm², area of triangle BCE = ½ × 14 × 7 = 49 cm². The printed working gives shaded triangle DEF = 196 − 65 − 49 − 66 = 16 cm². Answer: 16 cm².",
      "hints": ["Square area = 14 × 14; DE = EC = 7 cm.", "Subtract the surrounding triangles and the given 66 cm² total from the square."],
      "source": "Nan Hua 2023 P5 Weighted Assessment 1 P2 Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q18.png",
      "image_page": 12,
      "image_bbox": [0.24, 0.20, 0.58, 0.42],
      "image_loc": "square ABCD with A top-left, B top-right, C bottom-right, D bottom-left; E on base DC, F inside; shaded triangle DEF at the bottom-left; side 14 cm; upper-middle of page 12",
      "notes": "Paper 2 Q4. Printed key shows the chain of working leading to 16 cm² (square 196 − 65 − 49 − 66). Final answer 16 cm² used."
    }
  ]
}