{
  "paper": {
    "school": "Ai Tong",
    "year": 2022,
    "level": "P5",
    "label": "Weighted Assessment 2",
    "source_prefix": "Ai Tong 2022 P5 Weighted Assessment 2",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "There are 28 blue marbles and 22 yellow marbles in a box. Find the ratio of the number of blue marbles to the total number of marbles in the box. Give your answer in its simplest form.",
      "answer0": "14 : 25",
      "answer1": "14 : 11",
      "answer2": "28 : 22",
      "answer3": "25 : 14",
      "correct_answer": 0,
      "skill_id": 179,
      "difficulty_id": 1,
      "explanation": "Total marbles = 28 + 22 = 50. Ratio of blue to total = 28 : 50. Simplify by dividing both by 2: 14 : 25.",
      "hints": ["Find the total number of marbles first.", "Write blue : total, then divide both parts by their common factor."],
      "source": "Ai Tong 2022 P5 Weighted Assessment 2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Ratio answer -> MCQ. Key: 14 : 25."
    },
    {
      "n": 2,
      "type_id": 2,
      "question": "How many cubes are there in the solid? [?]",
      "answer0": "11",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 187,
      "difficulty_id": 1,
      "explanation": "Count all the unit cubes in the solid, including the hidden ones supporting the structure. There are 11 cubes.",
      "hints": ["Count layer by layer.", "Remember cubes hidden behind or beneath others still count."],
      "source": "Ai Tong 2022 P5 Weighted Assessment 2 Q2",
      "image_needed": true,
      "image_options": false,
      "image_file": "q2.png",
      "image_page": 1,
      "image_bbox": [0.18, 0.62, 0.45, 0.82],
      "image_loc": "left side of page, below the question - isometric drawing of stacked unit cubes",
      "notes": "Count answer = 11 (matches key). Crop must show whole solid so hidden cubes can be inferred."
    },
    {
      "n": 3,
      "type_id": 2,
      "question": "Find the area of triangle ABC. [?]",
      "answer0": "10",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 1,
      "explanation": "From the grid, the base AB = 4 cm and the height (horizontal distance to C) = 5 cm. Area of triangle = \\(\\dfrac{1}{2}\\times 5\\times 4 = 10\\) cm².",
      "hints": ["Use the grid (each square is 1 cm) to read off the base and height.", "Area of a triangle = \\(\\dfrac{1}{2}\\times\\text{base}\\times\\text{height}\\)."],
      "source": "Ai Tong 2022 P5 Weighted Assessment 2 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q3.png",
      "image_page": 2,
      "image_bbox": [0.30, 0.14, 0.66, 0.33],
      "image_loc": "top-centre of page, below the question - shaded triangle ABC on a 1 cm square grid",
      "notes": "Answer in cm². Key: 1/2 x 5 x 4 = 10 cm². Answer is an integer so FIB is fine."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Name a pair of base and height that can be used to find the area of triangle DEF.",
      "answer0": "DF and EH",
      "answer1": "DE and FH",
      "answer2": "EF and DG",
      "answer3": "DF and FG",
      "correct_answer": 0,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "A base and its corresponding height must be perpendicular. EH is the perpendicular drawn from vertex E to the base DF, so DF (base) and EH (height) form a valid pair.",
      "hints": ["The height must be perpendicular to the chosen base and drawn from the opposite vertex.", "Look at which dashed line forms a right angle with which side."],
      "source": "Ai Tong 2022 P5 Weighted Assessment 2 Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q4.png",
      "image_page": 2,
      "image_bbox": [0.17, 0.55, 0.55, 0.76],
      "image_loc": "centre-left of page, below the question - triangle DEF with perpendiculars EH and DG marked",
      "notes": "Word answer (names a base/height pair) -> MCQ. Key: DF and EH."
    },
    {
      "n": 5,
      "type_id": 2,
      "question": "A cuboid has a height of 14 cm and a square base of 8 cm. What is the volume of the cuboid? [?]",
      "answer0": "896",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 190,
      "difficulty_id": 1,
      "explanation": "Square base means length = breadth = 8 cm. Volume = length × breadth × height = 8 × 8 × 14 = 896 cm³.",
      "hints": ["A square base means two sides are both 8 cm.", "Volume of a cuboid = length × breadth × height."],
      "source": "Ai Tong 2022 P5 Weighted Assessment 2 Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q5.png",
      "image_page": 3,
      "image_bbox": [0.22, 0.18, 0.46, 0.34],
      "image_loc": "upper-left of page, below the question - tall cuboid labelled 8 cm and 14 cm",
      "notes": "Answer in cm³. Key: 8 x 8 x 14 = 896 cm³."
    },
    {
      "n": 6,
      "type_id": 2,
      "question": "Two pieces of wood, X and Y, are glued together. The ratio of the length of X to the length of Y is 3 : 5. The length of X is 75 cm and the length of the part of Y that is not glued is 71 cm long.<br>(a) What is the length of Y? [?] cm<br>(b) What is the length of the part of X that is glued to Y? [?] cm",
      "answer0": "125",
      "answer1": "54",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 182,
      "difficulty_id": 2,
      "explanation": "(a) X : Y = 3 : 5 and X = 75 cm, so 1 unit = 75 ÷ 3 = 25 cm. Y = 5 units = 25 × 5 = 125 cm. (b) The glued part of X = total Y minus the un-glued part of Y = 125 − 71 = 54 cm.",
      "hints": ["Find the value of 1 ratio unit using X = 75 cm and its 3 units.", "The glued part equals the whole of Y minus the part of Y that is not glued."],
      "source": "Ai Tong 2022 P5 Weighted Assessment 2 Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q6.png",
      "image_page": 4,
      "image_bbox": [0.24, 0.28, 0.70, 0.42],
      "image_loc": "centre of page, below the question - two overlapping rectangular bars X (75 cm) and Y, glued region marked",
      "notes": "Two integer answers -> two [?] blanks. Key: (a) 125 cm; (b) 125 - 71 = 54 cm."
    },
    {
      "n": 7,
      "type_id": 2,
      "question": "The box is 11 cm long, 10.5 cm wide and 4 cm tall. There are 4 cubes in the box. The volume of each cube is 1 cm³. John wants to fill the box with as many cubes as possible. How many more of such cubes can fit into the box? [?]",
      "answer0": "436",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 193,
      "difficulty_id": 2,
      "explanation": "Each 1 cm³ cube has 1 cm edges. Along the width only 10 whole cubes fit (10.5 cm), so the box holds 11 × 10 × 4 = 440 cubes. There are already 4 cubes inside, so 440 − 4 = 436 more cubes can fit.",
      "hints": ["A 1 cm cube cannot use the extra 0.5 cm of width, so round the width down to 10.", "Find the total cubes that fit, then subtract the 4 already there."],
      "source": "Ai Tong 2022 P5 Weighted Assessment 2 Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q7.png",
      "image_page": 5,
      "image_bbox": [0.33, 0.21, 0.62, 0.32],
      "image_loc": "top-centre of page, below the question - open rectangular box labelled 11 cm, 10.5 cm, 4 cm with a few small cubes inside",
      "notes": "Key: 11 x 10 x 4 = 440; 440 - 4 = 436. Width 10.5 rounds down to 10 because only whole 1 cm cubes fit."
    },
    {
      "n": 8,
      "type_id": 2,
      "question": "The figure SXWU is made up of a rectangle and two triangles. STU is a straight line. ST = 16 cm and ST is twice as long as TU. XS = TU and WT = 19 cm. Find the area of the figure. [?]",
      "answer0": "292",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "TU = 16 ÷ 2 = 8 cm, and XS = TU = 8 cm. Triangle SXW: \\(\\dfrac{1}{2}\\times 8\\times 19 = 76\\) cm² (base XS = 8, height = WT = 19). Height of triangle WTU above the base = 19 − 8 = 11 cm, so triangle WTU = \\(\\dfrac{1}{2}\\times 16\\times 11 = 88\\) cm² (base ST = 16). Rectangle XSTV = 16 × 8 = 128 cm². Total area = 76 + 88 + 128 = 292 cm².",
      "hints": ["Find TU first: it is half of ST.", "Split the figure into the rectangle and the two triangles, find each area, then add."],
      "source": "Ai Tong 2022 P5 Weighted Assessment 2 Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 6,
      "image_bbox": [0.27, 0.18, 0.66, 0.37],
      "image_loc": "centre of page, below the question - figure SXWU with vertices S, X, W, U, V, T and 19 cm and 16 cm marked",
      "notes": "Answer in cm². Key working: 16/2=8; 1/2*8*19=76; 19-8=11; 1/2*16*11=88; 16*8=128; 76+88+128=292 cm²."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "There were 120 000 spectators at a stadium. 91 200 were men. There were 4 times as many men as women. The remaining spectators were children. Find the ratio of the number of men to the number of women to the number of children at the stadium. Give your answer in its simplest form.",
      "answer0": "76 : 19 : 5",
      "answer1": "91200 : 22800 : 6000",
      "answer2": "4 : 1 : 5",
      "answer3": "76 : 19 : 6",
      "correct_answer": 0,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "Women = 91 200 ÷ 4 = 22 800. Men + women = 91 200 + 22 800 = 114 000. Children = 120 000 − 114 000 = 6 000. Ratio M : W : C = 91 200 : 22 800 : 6 000. Dividing through (÷100 then ÷12, i.e. ÷1200) gives 76 : 19 : 5.",
      "hints": ["Find the number of women from '4 times as many men as women'.", "Children = total − (men + women); then simplify the three-part ratio."],
      "source": "Ai Tong 2022 P5 Weighted Assessment 2 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Three-part ratio answer -> MCQ. Key: 91200:22800:6000 = 76:19:5."
    },
    {
      "n": 10,
      "type_id": 2,
      "question": "The figure is made up of a rectangle JKLM and triangle PQR. JK = 16 cm, KQ = QL and the total area of the shaded part is 216 cm². Find the length of KQ. [?] cm",
      "answer0": "9",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Let KQ = QL = h. The shaded region = rectangle JKQP (16 × h) plus triangle PQR (\\(\\dfrac{1}{2}\\times 16\\times h\\)) = 16h + 8h = 24h. Set 24h = 216, so h = 216 ÷ 24 = 9 cm. (Equivalently, from the key: 216 ÷ 3 = 72 and \\(\\dfrac{1}{2}\\times 16\\times 9 = 72\\), giving KQ = 9 cm.)",
      "hints": ["Since KQ = QL, the rectangle JKQP and the triangle below it share the same height KQ.", "Add the shaded rectangle and triangle areas in terms of KQ, then solve for KQ."],
      "source": "Ai Tong 2022 P5 Weighted Assessment 2 Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 8,
      "image_bbox": [0.36, 0.20, 0.62, 0.40],
      "image_loc": "top-centre of page, below the question - rectangle JKLM with shaded region and triangle PQR, JK = 16 cm marked",
      "notes": "Answer in cm. Key: 216 / 3 = 72; 1/2 x 16 x 9 = 72; Ans: 9 cm."
    },
    {
      "n": 11,
      "type_id": 0,
      "question": "The figure shows Triangle A overlapping Triangle B. The ratio of the area of Triangle A to the area of Triangle B is 8 : 5. The ratio of the shaded area to the area of Triangle B is 1 : 3. The area of Triangle A is 168 cm². (a) What is the area of Triangle B? (b) Find the ratio of the shaded area to the area of Triangle A.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "(a) A : B = 8 : 5 and A = 168 cm², so 1 unit = 168 ÷ 8 = 21 cm²; B = 5 × 21 = 105 cm². (b) Shaded : B = 1 : 3, so shaded = 105 ÷ 3 = 35 cm². Shaded : A = 35 : 168 = 5 : 24.",
      "hints": ["Use A : B = 8 : 5 with A = 168 to find the value of one unit.", "Shaded = one-third of B; then write shaded : A and simplify."],
      "source": "Ai Tong 2022 P5 Weighted Assessment 2 Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q11.png",
      "image_page": 9,
      "image_bbox": [0.33, 0.19, 0.62, 0.37],
      "image_loc": "top-centre of page, below the question - two overlapping triangles A and B with the overlap shaded",
      "notes": "type_id 0: part (a) area = 105 cm2 is FIB-able but part (b) answer 5:24 is a ratio (must be MCQ), so this two-part item cannot be a single FIB. Key: (a) 168/8=21, 21x5=105 cm2; (b) 105/3=35, shaded:A = 35:168 = 5:24. SKIPPED on insert. Recommend splitting downstream into 11a (FIB, ans 105) and 11b (MCQ, options 5:24 / 5:21 / 1:3 / 35:168)."
    },
    {
      "n": 12,
      "type_id": 2,
      "question": "A container measuring 50 cm by 30 cm by 40 cm was \\(\\dfrac{5}{6}\\) filled with water. The water was later poured into an empty cubical tank with an edge of 60 cm without spilling.<br>(a) What was the volume of the water in the container? Give your answer in litres. [?] ℓ<br>(b) How much more water was needed to fill the cubical tank completely? Give your answer in litres. [?] ℓ",
      "answer0": "50",
      "answer1": "166",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 193,
      "difficulty_id": 3,
      "explanation": "(a) Container volume = 50 × 30 × 40 = 60 000 cm³. Water = \\(\\dfrac{5}{6}\\times 60000 = 50000\\) cm³ = 50 ℓ (since 1000 cm³ = 1 ℓ). (b) Cubical tank volume = 60 × 60 × 60 = 216 000 cm³ = 216 ℓ. More water needed = 216 − 50 = 166 ℓ.",
      "hints": ["Find the container's full volume, then take \\(\\dfrac{5}{6}\\) of it; convert 1000 cm³ to 1 ℓ.", "Find the tank's full volume in litres, then subtract the water already poured in."],
      "source": "Ai Tong 2022 P5 Weighted Assessment 2 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Two integer (litre) answers -> two [?] blanks. Key: (a) 60000 x 5/6 = 50000 cm3 = 50 L; (b) 60x60x60 = 216000 cm3 = 216 L, 216 - 50 = 166 L."
    }
  ]
}