{
  "paper": {
    "school": "Ai Tong",
    "year": 2023,
    "level": "P5",
    "label": "Weighted Assessment 2",
    "source_prefix": "Ai Tong 2023 P5 Weighted Assessment 2",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 2,
      "question": "9 : 5 is equivalent to [?] : 40.",
      "answer0": "72",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 181,
      "difficulty_id": 1,
      "explanation": "5 is multiplied by 8 to get 40 (40 ÷ 5 = 8). Multiply the first term the same way: 9 × 8 = 72. So 9 : 5 = 72 : 40. Missing number = 72.",
      "hints": ["Find what 5 was multiplied by to give 40.", "Multiply 9 by that same factor."],
      "source": "Ai Tong 2023 P5 Weighted Assessment 2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 72."
    },
    {
      "n": 2,
      "type_id": 2,
      "question": "The cubical container shown has a height of 12 cm. What is its volume? [?]",
      "answer0": "1728",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 190,
      "difficulty_id": 1,
      "explanation": "A cube has equal edges, so each side = 12 cm. Volume = 12 × 12 × 12 = 1728 cm³.",
      "hints": ["All edges of a cube are equal.", "Volume of a cube = side × side × side."],
      "source": "Ai Tong 2023 P5 Weighted Assessment 2 Q2",
      "image_needed": true,
      "image_options": false,
      "image_file": "q2.png",
      "image_page": 1,
      "image_bbox": [0.13, 0.66, 0.40, 0.82],
      "image_loc": "cube drawing with '12 cm' label, lower-left of page 1",
      "notes": "Answer in cm³. Answer key: 12 x 12 x 12 = 1728 cm3."
    },
    {
      "n": 3,
      "type_id": 2,
      "question": "Two identical squares are joined together to form figure ABCD. Find the area of the shaded part. [?]",
      "answer0": "32",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "DC = 16 cm is made of two identical squares, so each square has side 16 ÷ 2 = 8 cm. The shaded triangle has base 8 cm (one square's width) and height 8 cm (the square's side). Area = \\(\\dfrac{1}{2}\\) × 8 × 8 = 32 cm².",
      "hints": ["Two equal squares make up the 16 cm length, so each side is 8 cm.", "Area of a triangle = \\(\\dfrac{1}{2}\\) × base × height."],
      "source": "Ai Tong 2023 P5 Weighted Assessment 2 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q3.png",
      "image_page": 2,
      "image_bbox": [0.38, 0.13, 0.66, 0.27],
      "image_loc": "rectangle ABCD with shaded triangle, '16 cm' base label, top of page 2",
      "notes": "Answer in cm². Answer key: 1/2 x 8 x 8 = 32 cm2."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "The figure shows triangle EFG. EG is the base of the triangle. Which of the following lines is its corresponding height?",
      "answer0": "FX",
      "answer1": "GY",
      "answer2": "EH",
      "answer3": "FG",
      "correct_answer": 0,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "The height corresponding to base EG must be perpendicular to EG (or to EG extended) and pass through the opposite vertex F. The line FX meets EG extended at a right angle (shown by the right-angle mark at X), so FX is the corresponding height of base EG.",
      "hints": ["The height must be perpendicular to the chosen base EG.", "It runs from the opposite vertex F to the line EG (extended), meeting it at a right angle."],
      "source": "Ai Tong 2023 P5 Weighted Assessment 2 Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q4.png",
      "image_page": 2,
      "image_bbox": [0.10, 0.50, 0.72, 0.68],
      "image_loc": "triangle EFG with dashed lines to X and Y and EH, middle of page 2",
      "notes": "Answer key: FX. Options label the candidate lines drawn in the figure."
    },
    {
      "n": 5,
      "type_id": 2,
      "question": "The figure shows some 1-cm cubes glued together at the corner of a room. How many 1-cm cubes are there in the figure? [?]",
      "answer0": "6",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 188,
      "difficulty_id": 1,
      "explanation": "Count the unit cubes shown in the figure: there are 6 one-centimetre cubes glued together.",
      "hints": ["Count every individual 1-cm cube, including any hidden behind others.", "Use the top, front and side views to check none are missed."],
      "source": "Ai Tong 2023 P5 Weighted Assessment 2 Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q5.png",
      "image_page": 3,
      "image_bbox": [0.10, 0.16, 0.50, 0.34],
      "image_loc": "isometric drawing of glued 1-cm cubes with Top/Front/Side view labels, upper part of page 3",
      "notes": "Answer key (a): 6 cubes. Required count = 6. Part (b) 'Draw the side view' is a drawing task with no value answer and is omitted (interactive)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "Square ABCD is made up of 4 identical small squares, 1 rectangle and 1 large square. Express the ratio of the area of 1 small square to the total area of the figure.",
      "answer0": "1 : 16",
      "answer1": "1 : 4",
      "answer2": "1 : 8",
      "answer3": "1 : 12",
      "correct_answer": 0,
      "skill_id": 180,
      "difficulty_id": 2,
      "explanation": "Let each small square have side 1 unit and area 1 unit². The large square ABCD has side 4 units (the small squares run 4 along an edge), so its total area = 4 × 4 = 16 unit². Ratio of 1 small square to the whole figure = 1 : 16.",
      "hints": ["Take the side of one small square as 1 unit.", "The whole square is 4 units by 4 units, so its area is 16 small-square units."],
      "source": "Ai Tong 2023 P5 Weighted Assessment 2 Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q6.png",
      "image_page": 4,
      "image_bbox": [0.33, 0.12, 0.62, 0.32],
      "image_loc": "square ABCD subdivided into small squares, rectangle and large square with shaded strip, upper-middle of page 4",
      "notes": "Answer key (a): 1 : 16. Ratio answer -> MCQ."
    },
    {
      "n": 7,
      "type_id": 2,
      "question": "Square ABCD is made up of 4 identical small squares, 1 rectangle and 1 large square. The area of the large square is 144 cm². What is the area of the shaded parts? [?]",
      "answer0": "64",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 138,
      "difficulty_id": 2,
      "explanation": "The large square has area 144 cm², so its side = 12 cm and one small square (a quarter of the large square's side per unit) has side 12 ÷ 3 = 4 cm... Using the answer key: each small square area = 144 ÷ 9 = 16 cm²; the shaded part covers 4 such small-square units, so shaded area = 16 × 4 = 64 cm².",
      "hints": ["Find the area of one small square from the large square's area.", "Multiply by the number of small-square units in the shaded region."],
      "source": "Ai Tong 2023 P5 Weighted Assessment 2 Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q7.png",
      "image_page": 4,
      "image_bbox": [0.33, 0.12, 0.62, 0.32],
      "image_loc": "same square ABCD figure as Q6 (shaded strip on the right), upper-middle of page 4",
      "notes": "Answer in cm². This is part (b) of the paper's Q6. Answer key: 16 x 4 = 64 cm2 (one small square = 16 cm2). Reuses the Q6 figure on page 4."
    },
    {
      "n": 8,
      "type_id": 2,
      "question": "The box is 18 cm long, 10.5 cm wide and 20 cm tall. John fills the box with as many 1-cm cubes as possible. How many such cubes does he fit into the box? [?]",
      "answer0": "3600",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 188,
      "difficulty_id": 2,
      "explanation": "Along the width only 10 whole cubes fit (the 0.5 cm cannot hold another cube). So cubes = 18 × 20 × 10 = 3600.",
      "hints": ["The 10.5 cm width only holds 10 whole 1-cm cubes (round down).", "Multiply the whole-cube counts along each dimension."],
      "source": "Ai Tong 2023 P5 Weighted Assessment 2 Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 5,
      "image_bbox": [0.36, 0.13, 0.70, 0.36],
      "image_loc": "open box with 18 cm / 10.5 cm / 20 cm labels and a 1-cm cube, top of page 5",
      "notes": "This is the paper's Q7. Answer key: 18 x 20 x 10 = 3600 (width rounds down to 10)."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "Jenny had a bottle of juice. She drank 525 ml on Monday and \\(\\dfrac{1}{5}\\) of the remaining juice on Tuesday. After that, there was \\(\\dfrac{1}{2}\\) a bottle of juice left. How much juice was there in the bottle at first?",
      "answer0": "1400 ml",
      "answer1": "1050 ml",
      "answer2": "700 ml",
      "answer3": "875 ml",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "After Tuesday, \\(\\dfrac{4}{5}\\) of the Monday-remainder equals \\(\\dfrac{1}{2}\\) of the bottle. So the remaining after Monday = \\(\\dfrac{1}{2} \\div \\dfrac{4}{5} = \\dfrac{5}{8}\\) of the bottle. The 525 ml drunk on Monday is therefore \\(\\dfrac{3}{8}\\) of the bottle: 525 ÷ 3 = 175 ml per \\(\\dfrac{1}{8}\\); whole bottle = 175 × 8 = 1400 ml.",
      "hints": ["525 ml is what fraction of the whole bottle? Work backwards from the half left.", "525 ÷ 3 = 175 gives one-eighth; multiply by 8."],
      "source": "Ai Tong 2023 P5 Weighted Assessment 2 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "This is the paper's Q8. Answer key: 525 ÷ 3 = 175; 175 x 8 = 1400 ml. Made MCQ because the working involves fractions; answer itself is 1400 ml."
    },
    {
      "n": 10,
      "type_id": 2,
      "question": "ABC is a piece of paper in the shape of a triangle. AB is perpendicular to BC. AB is of the same length as BC. It is then folded as shown, giving AD = 9 cm and DB = 6 cm. Find the length of BC of the triangular paper. [?]",
      "answer0": "21",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "After folding, AD = 9 cm and the folded part DB = 6 cm; the fold brings B onto the line so BC = AD + DB + (the 6 cm fold again) along the base. From the answer key: BC = 15 + 6 = 21 cm (AB = AD + DB = 9 + 6 = 15, then BC = 15 + 6 = 21).",
      "hints": ["Use the fold: the 6 cm segment is duplicated.", "Add the segments along the base: 15 + 6 = 21."],
      "source": "Ai Tong 2023 P5 Weighted Assessment 2 Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 6,
      "image_bbox": [0.30, 0.10, 0.66, 0.58],
      "image_loc": "two triangle diagrams 'Before folding' (ABC) and 'After folding' (9 cm, 6 cm labels) on page 6",
      "notes": "Answer in cm. This is the paper's Q9 part (a). Answer key: 15 + 6 = 21 cm."
    },
    {
      "n": 11,
      "type_id": 2,
      "question": "ABC is a right-angled triangular paper with AB perpendicular to BC and AB equal to BC, where BC = 21 cm. Find the area of the piece of triangular paper when it is not folded. [?]",
      "answer0": "220.5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "AB = BC = 21 cm and AB is perpendicular to BC, so the triangle is right-angled at B with base 21 cm and height 21 cm. Area = \\(\\dfrac{1}{2}\\) × 21 × 21 = 220.5 cm².",
      "hints": ["The right angle is at B, so AB and BC are the base and height.", "Area = \\(\\dfrac{1}{2}\\) × 21 × 21."],
      "source": "Ai Tong 2023 P5 Weighted Assessment 2 Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q11.png",
      "image_page": 6,
      "image_bbox": [0.30, 0.10, 0.66, 0.34],
      "image_loc": "'Before folding' right-angled triangle ABC on page 6 (same figure as Q10)",
      "notes": "Answer in cm². This is the paper's Q9 part (b). Answer key: 1/2 x 21 x 21 = 220.5 cm2."
    },
    {
      "n": 12,
      "type_id": 2,
      "question": "Triangle ABC and triangle DEF are identical right-angled triangles that overlap with each other. The ratio of BC to FC is 5 : 2 and FC is 7 cm. How long is BC? [?]",
      "answer0": "17.5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 182,
      "difficulty_id": 2,
      "explanation": "BC : FC = 5 : 2 and FC = 7 cm corresponds to 2 units, so 1 unit = 7 ÷ 2 = 3.5 cm. BC = 5 units = 3.5 × 5 = 17.5 cm.",
      "hints": ["FC = 7 cm is the 2-unit part; find 1 unit.", "BC is 5 units: multiply 3.5 by 5."],
      "source": "Ai Tong 2023 P5 Weighted Assessment 2 Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q12.png",
      "image_page": 7,
      "image_bbox": [0.22, 0.11, 0.78, 0.42],
      "image_loc": "two overlapping right-angled triangles with 10 cm, 2 cm, 7 cm labels (vertices A,B,C,D,E,F), top of page 7",
      "notes": "Answer in cm. This is the paper's Q10 part (a). Answer key: 7 ÷ 2 = 3.5; 3.5 x 5 = 17.5 cm."
    },
    {
      "n": 13,
      "type_id": 2,
      "question": "Triangle ABC and triangle DEF are identical right-angled triangles that overlap with each other. AB = 10 cm, the small triangle's height is 2 cm, FC = 7 cm and BC = 17.5 cm. Find the area of the shaded parts. [?]",
      "answer0": "161",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Area of one whole triangle = \\(\\dfrac{1}{2}\\) × 10 × 17.5 = 87.5 cm². The two identical triangles together (without overlap counted once) = 87.5 × 2 = 175 cm². The small overlap triangle = \\(\\dfrac{1}{2}\\) × 7 × 2 = 7 cm². Shaded = 175 − 7 − 7 = 161 cm².",
      "hints": ["Find the area of one large triangle, then both.", "Subtract the overlapping region (twice, as the key shows): 175 − 7 − 7 = 161."],
      "source": "Ai Tong 2023 P5 Weighted Assessment 2 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q13.png",
      "image_page": 7,
      "image_bbox": [0.22, 0.11, 0.78, 0.42],
      "image_loc": "same overlapping-triangles figure as Q12 (shaded parts), top of page 7",
      "notes": "Answer in cm². This is the paper's Q10 part (b). Answer key: 1/2 x 10 x 17.5 = 87.5; 87.5 x 2 = 175; 1/2 x 7 x 2 = 7; 175 − 7 = 168; 168 − 7 = 161 cm2."
    },
    {
      "n": 14,
      "type_id": 2,
      "question": "Joseph and Daniel shared $884 in the ratio of 6 : 11. How much does Daniel have? [?]",
      "answer0": "572",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 182,
      "difficulty_id": 2,
      "explanation": "Total units = 6 + 11 = 17. Value per unit = 884 ÷ 17 = $52. Daniel has 11 units = 52 × 11 = $572.",
      "hints": ["Add the ratio parts to get the total number of units.", "Find one unit, then multiply by Daniel's 11 units."],
      "source": "Ai Tong 2023 P5 Weighted Assessment 2 Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer in dollars. This is the paper's Q11 part (a). Answer key: 11 + 6 = 17; 884 ÷ 17 = 52; 52 x 11 = $572."
    },
    {
      "n": 15,
      "type_id": 2,
      "question": "Joseph and Daniel shared $884 in the ratio of 6 : 11. How much must Daniel give to Joseph so that both of them have an equal amount of money? [?]",
      "answer0": "130",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "Equal share = 884 ÷ 2 = $442 each. Daniel had $572, so he must give 572 − 442 = $130 to Joseph (key form: 442 − 312 ... Joseph had $312, 442 − 312 = $130).",
      "hints": ["Each should end with half of $884.", "Daniel gives away the amount above his fair share: 572 − 442."],
      "source": "Ai Tong 2023 P5 Weighted Assessment 2 Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer in dollars. This is the paper's Q11 part (b). Answer key: 884 ÷ 2 = 442; 442 − 312 = $130 (Joseph had 6 units = $312)."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "A tank measuring 40 cm by 12 cm by 32 cm was \\(\\dfrac{5}{8}\\) filled with water. The water in the tank was then poured into as many pails as possible. Each pail can hold 1.5 \\(\\ell\\) of water. What was the volume of the water in the tank at first? [?]",
      "answer0": "9600",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 191,
      "difficulty_id": 2,
      "explanation": "Full tank volume = 40 × 12 × 32 = 15360 cm³. Water = \\(\\dfrac{5}{8}\\) × 15360 = 9600 cm³ (which equals 9600 ml).",
      "hints": ["Find the full volume first: 40 × 12 × 32.", "Take \\(\\dfrac{5}{8}\\) of it."],
      "source": "Ai Tong 2023 P5 Weighted Assessment 2 Q16",
      "image_needed": true,
      "image_options": false,
      "image_file": "q16.png",
      "image_page": 9,
      "image_bbox": [0.18, 0.16, 0.78, 0.40],
      "image_loc": "rectangular water tank (32 cm / 12 cm / 40 cm) and a 1.5 l pail, top of page 9",
      "notes": "Answer in cm³ (= ml). This is the paper's Q12 part (a). Answer key: 40 x 12 x 32 = 15360; 15360 x 5/8 = 9600 ml."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "A tank measuring 40 cm by 12 cm by 32 cm was \\(\\dfrac{5}{8}\\) filled with water. The water in the tank (9600 ml) was then poured into as many pails as possible, each holding 1.5 \\(\\ell\\). What was the volume of water left in the tank after filling the pails with water? [?]",
      "answer0": "600",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 193,
      "difficulty_id": 3,
      "explanation": "Each pail holds 1.5 \\(\\ell\\) = 1500 ml. Number of full pails = 9600 ÷ 1500 = 6 pails (using 9000 ml), with 9600 − 9000 = 600 ml left over in the tank.",
      "hints": ["Convert 1.5 litres to 1500 ml.", "Find how many whole pails fill (round down), then the leftover: 9600 − 6 × 1500."],
      "source": "Ai Tong 2023 P5 Weighted Assessment 2 Q17",
      "image_needed": true,
      "image_options": false,
      "image_file": "q17.png",
      "image_page": 9,
      "image_bbox": [0.18, 0.16, 0.78, 0.40],
      "image_loc": "same tank-and-pail figure as Q16, top of page 9",
      "notes": "Answer in ml. This is the paper's Q12 part (b). Answer key: 600 ml (6 pails of 1500 ml = 9000 ml; 9600 − 9000 = 600 ml)."
    }
  ]
}