{
  "paper": {
    "school": "Nanyang",
    "year": 2025,
    "level": "P5",
    "label": "Weighted Assessment 2",
    "source_prefix": "Nanyang 2025 P5 Weighted Assessment 2",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 0,
      "question": "Ali builds a solid using 9 unit cubes. Draw the side view of the solid on the grid provided.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 188,
      "difficulty_id": 2,
      "explanation": "Look at the solid from the side (in the direction of the Side view arrow) and draw the outline of the squares you see. The answer key shows the correct side-view outline drawn on the dot grid.",
      "hints": ["The side view is what you see looking along the Side view arrow.", "Each cube column shows as a stack of squares in the side view."],
      "source": "Nanyang 2025 P5 Weighted Assessment 2 Q1a",
      "image_needed": true,
      "image_options": false,
      "image_file": "q1.png",
      "image_page": 2,
      "image_bbox": [0.20, 0.16, 0.85, 0.36],
      "image_loc": "isometric drawing of Ali's solid (9 unit cubes) with Top view / Front view / Side view labels, and its Front view grid to the right",
      "notes": "Interactive draw-the-side-view task — no app question type (type_id 0; skipped on insert). The numeric part (greatest extra cubes) is a separate FIB entry."
    },
    {
      "n": 2,
      "type_id": 2,
      "question": "Ali builds a solid using 9 unit cubes. Find the greatest number of unit cubes Ali can add to the solid without changing the front view and side view. [?]",
      "answer0": "5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 188,
      "difficulty_id": 3,
      "explanation": "Cubes may be added only in positions hidden behind the existing solid so the front and side silhouettes stay the same. The maximum number of such hidden cubes that can be added is 5. Answer: 5.",
      "hints": ["Adding a cube must not make the front view or side view any taller or wider.", "Fill the hidden positions behind the visible cubes."],
      "source": "Nanyang 2025 P5 Weighted Assessment 2 Q1b",
      "image_needed": true,
      "image_options": false,
      "image_file": "q2.png",
      "image_page": 2,
      "image_bbox": [0.20, 0.16, 0.85, 0.36],
      "image_loc": "isometric drawing of Ali's solid (9 unit cubes) with Top / Front / Side view labels (same figure as Q1)",
      "notes": "Answer key (Q1b): 5 (the answer key marks '5 added behind' on the diagram)."
    },
    {
      "n": 3,
      "type_id": 2,
      "question": "Jack had some marbles at first. He sold \\(\\dfrac{1}{5}\\) of the marbles. He then gave \\(\\dfrac{5}{8}\\) of the remaining marbles to his sister. He had 360 marbles left in the end. How many marbles did he have at first? [?]",
      "answer0": "1200",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "After selling, marbles remaining = \\(1 - \\dfrac{1}{5} = \\dfrac{4}{5}\\). Fraction left after giving sister = \\(\\dfrac{3}{8}\\) of the remainder = \\(\\dfrac{3}{8} \\times \\dfrac{4}{5} = \\dfrac{3}{10}\\) of the original. So \\(\\dfrac{3}{10}\\) of the marbles = 360, meaning \\(\\dfrac{1}{10}\\) = 120, and the whole = 120 × 10 = 1200. Answer: 1200.",
      "hints": ["Find the fraction left after selling: 1 - 1/5.", "He kept 3/8 of that remainder; this 3/10 of the original equals 360."],
      "source": "Nanyang 2025 P5 Weighted Assessment 2 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key (Q2): 3 units = 360; 1 unit = 120; 10 units = 1200. Ans: 1200."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Anna had \\(\\dfrac{7}{8}\\) kg of flour at first. She used \\(\\dfrac{3}{7}\\) of the flour to bake a cake. Bob used \\(\\dfrac{1}{4}\\) kg of flour more than Anna. How much flour did Bob use? Give your answer in kg.",
      "answer0": "\\(\\dfrac{5}{8}\\) kg",
      "answer1": "\\(\\dfrac{3}{8}\\) kg",
      "answer2": "\\(\\dfrac{1}{2}\\) kg",
      "answer3": "\\(\\dfrac{7}{8}\\) kg",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "Anna used \\(\\dfrac{3}{7} \\times \\dfrac{7}{8} = \\dfrac{3}{8}\\) kg. Bob used \\(\\dfrac{1}{4}\\) kg more: \\(\\dfrac{3}{8} + \\dfrac{1}{4} = \\dfrac{3}{8} + \\dfrac{2}{8} = \\dfrac{5}{8}\\) kg. Answer: \\(\\dfrac{5}{8}\\) kg.",
      "hints": ["Find how much flour Anna used: 3/7 of 7/8 kg.", "Add 1/4 kg to Anna's amount (use eighths)."],
      "source": "Nanyang 2025 P5 Weighted Assessment 2 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key (Q3): flour Anna used 3/7 x 7/8 = 3/8 kg; Bob used 3/8 + 1/8... (key writes 1/8 but states +1/4 in question) = 5/8 kg. Ans: 5/8 kg. Made MCQ because answer is a fraction."
    },
    {
      "n": 5,
      "type_id": 2,
      "question": "The figure is formed by 2 identical triangles, ABC and GHE. Two such triangles are glued together such that they overlap. CDEF is a square of side 8 cm. Find the area of triangle ABC. [?] cm²",
      "answer0": "216",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "AC = AD + DC = 10 + 8 = 18 cm (AD = 10 cm, DC = 8 cm = side of square). BC = BF + FC = 16 + 8 = 24 cm (BF = 16 cm, FC = 8 cm). Triangle ABC is right-angled, so area \\(= \\dfrac{1}{2} \\times 18 \\times 24 = 216\\) cm². Answer: 216 cm².",
      "hints": ["Add the square's side (8 cm) to the given parts to get the full lengths AC and BC.", "Area of the right-angled triangle = 1/2 x AC x BC."],
      "source": "Nanyang 2025 P5 Weighted Assessment 2 Q4a",
      "image_needed": true,
      "image_options": false,
      "image_file": "q5.png",
      "image_page": 5,
      "image_bbox": [0.28, 0.13, 0.78, 0.45],
      "image_loc": "two overlapping identical triangles forming an hourglass-like figure around square CDEF; labels 10 cm (AD), 8 cm (square side), 16 cm (FB)",
      "notes": "Answer key (Q4a): AC = 10+8 = 18; BC = 16+8 = 24; area ABC = 1/2 x 18 x 24 = 216 cm²."
    },
    {
      "n": 6,
      "type_id": 2,
      "question": "The figure is formed by 2 identical triangles, ABC and GHE. Two such triangles are glued together such that they overlap. CDEF is a square of side 8 cm. Find the total area of the shaded parts of the figure. [?] cm²",
      "answer0": "304",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Area of square CDEF = 8 × 8 = 64 cm². Area of one shaded region ADEFB = area of triangle ABC - square = 216 - 64 = 152 cm². The other triangle gives an equal shaded region GFCDH = 152 cm². Total shaded = 152 × 2 = 304 cm². Answer: 304 cm².",
      "hints": ["Subtract the overlap square (64 cm²) from triangle ABC to get one shaded part.", "By symmetry the two shaded parts are equal, so double it."],
      "source": "Nanyang 2025 P5 Weighted Assessment 2 Q4b",
      "image_needed": true,
      "image_options": false,
      "image_file": "q6.png",
      "image_page": 5,
      "image_bbox": [0.28, 0.13, 0.78, 0.45],
      "image_loc": "two overlapping identical triangles forming an hourglass figure around square CDEF (same figure as Q5); shaded parts are the two triangle regions outside the central square",
      "notes": "Answer key (Q4b): square CDEF = 64; shaded ADEFB = 216-64 = 152; total = 152 x 2 = 304 cm²."
    },
    {
      "n": 7,
      "type_id": 2,
      "question": "The figure shows a rectangular tank. It was \\(\\dfrac{5}{7}\\)-filled with water at first. The tank measures 40 cm by 38 cm by 56 cm. How much water was in the tank at first? [?] cm³",
      "answer0": "60800",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 193,
      "difficulty_id": 2,
      "explanation": "Full tank volume = 40 × 38 × 56 = 85120 cm³. Water = \\(\\dfrac{5}{7}\\) of this. Computing directly: \\(\\dfrac{5}{7} \\times 56 = 40\\), so water = 40 × 40 × 38 = 60800 cm³. Answer: 60800 cm³.",
      "hints": ["Multiply 5/7 by the height 56 cm first to get the water height (40 cm).", "Water volume = length × breadth × water height."],
      "source": "Nanyang 2025 P5 Weighted Assessment 2 Q5a",
      "image_needed": true,
      "image_options": false,
      "image_file": "q7.png",
      "image_page": 6,
      "image_bbox": [0.40, 0.10, 0.72, 0.36],
      "image_loc": "rectangular tank partly filled with water; labels 56 cm (height), 40 cm (width), 38 cm (depth)",
      "notes": "Answer key (Q5a): 5/7 x 56 x 40 x 38 = 60800 cm³."
    },
    {
      "n": 8,
      "type_id": 2,
      "question": "The figure shows a rectangular tank measuring 40 cm by 38 cm by 56 cm that was \\(\\dfrac{5}{7}\\)-filled with water. Syakir poured the water from the tank to completely fill as many empty bottles as possible. The capacity of each bottle was 225 cm³. How much water was left in the tank in the end? [?] cm³",
      "answer0": "50",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 193,
      "difficulty_id": 2,
      "explanation": "Water = 60800 cm³. 60800 ÷ 225 = 270 remainder 50, so 270 bottles are filled completely (270 × 225 = 60750 cm³). Water left = 60800 - 60750 = 50 cm³. Answer: 50 cm³.",
      "hints": ["Divide the total water by 225 cm³ to find how many bottles fill completely.", "The water left is the remainder of that division."],
      "source": "Nanyang 2025 P5 Weighted Assessment 2 Q5b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key (Q5b): 60800 ÷ 225 = 270 r; 270 x 225 = 60750; 60800 - 60750 = 50 cm³."
    },
    {
      "n": 9,
      "type_id": 2,
      "question": "At an amusement park, \\(\\dfrac{1}{3}\\) of the visitors were children. \\(\\dfrac{1}{6}\\) of the children were boys and \\(\\dfrac{1}{4}\\) of the adults were men. There were 196 men and boys altogether. How many visitors were there at the amusement park? [?]",
      "answer0": "882",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Children = 1/3 of visitors, adults = 2/3. Boys = 1/6 of children = 1/18 of visitors. Men = 1/4 of adults = 1/4 × 2/3 = 1/6 of visitors = 3/18 of visitors. Men + boys = 1/18 + 3/18 = 4/18 of visitors = 196. So 1/18 = 49, and visitors = 49 × 18 = 882. Answer: 882.",
      "hints": ["Express boys and men each as a fraction of the total visitors.", "Their sum (4/18 of the visitors) equals 196."],
      "source": "Nanyang 2025 P5 Weighted Assessment 2 Q6a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key (Q6a): boys = 1/18 of visitors, men = 3/18; together 4/18 = 196; 18/18 = 196 ÷ 4 x 18 = 882. Ans: 882."
    },
    {
      "n": 10,
      "type_id": 2,
      "question": "At an amusement park, \\(\\dfrac{1}{3}\\) of the 882 visitors were children. After some children went home, there were three times as many adults as children left at the amusement park. How many children went home? [?]",
      "answer0": "98",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Adults = 2/3 × 882 = 588 (unchanged). At the end, adults = 3 × children left, so children left = 588 ÷ 3 = 196. Children at first = 1/3 × 882 = 294. Children who went home = 294 - 196 = 98. Answer: 98.",
      "hints": ["The number of adults does not change.", "Children left = adults ÷ 3; subtract from the original number of children."],
      "source": "Nanyang 2025 P5 Weighted Assessment 2 Q6b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key (Q6b): adults = 2/3 x 882 = 588; children left = 588 ÷ 3 = 196; children at first = 1/3 x 882 = 294; 294 - 196 = 98."
    }
  ]
}