{
  "paper": {
    "school": "Anglo-Chinese School (Junior)",
    "year": 2022,
    "level": "P5",
    "label": "Weighted Assessment 2",
    "source_prefix": "ACS 2022 P5 Weighted Assessment 2",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "ABC is a triangle. AB = 8 cm, BC = 7 cm and AC = 13 cm. What is the area of triangle ABC?",
      "answer0": "20 cm²",
      "answer1": "28 cm²",
      "answer2": "30 cm²",
      "answer3": "42 cm²",
      "correct_answer": 0,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "Use the base AB = 8 cm and the corresponding perpendicular height = 5 cm (the vertical height shown from C). Area \\(= \\dfrac{1}{2} \\times 8 \\times 5 = 20\\) cm².",
      "hints": ["Area of a triangle \\(= \\dfrac{1}{2} \\times \\text{base} \\times \\text{height}\\).", "Use base AB = 8 cm with the perpendicular height of 5 cm; the 7 cm and 13 cm are slant sides, not the height."],
      "source": "ACS 2022 P5 Weighted Assessment 2 Q1",
      "image_needed": true,
      "image_options": false,
      "image_file": "q1.png",
      "image_page": 2,
      "image_bbox": [0.27, 0.32, 0.66, 0.46],
      "image_loc": "middle of page, below the question: right-angled triangle ABC with labels 13 cm, 7 cm, 5cm, 8 cm and 4cm",
      "notes": "Answer key: option 1 (20 cm²)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "What is the missing number in the box?<br>\\(9 : 21 = 12 : \\square\\)",
      "answer0": "24",
      "answer1": "27",
      "answer2": "28",
      "answer3": "32",
      "correct_answer": 2,
      "skill_id": 181,
      "difficulty_id": 1,
      "explanation": "9 : 21 simplifies to 3 : 7. Multiply both terms by 4 to get 12 : 28. So the missing number is 28.",
      "hints": ["Simplify \\(9 : 21\\) by dividing both terms by 3.", "9 × ? = 12, so multiply 21 by the same factor (\\(\\dfrac{12}{9} = \\dfrac{4}{3}\\))."],
      "source": "ACS 2022 P5 Weighted Assessment 2 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: option 3 (28)."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "The solid is made up of identical 1-cm cubes. The cubes are stacked on top of one another. What is the volume of the solid?",
      "answer0": "8 cm³",
      "answer1": "10 cm³",
      "answer2": "12 cm³",
      "answer3": "14 cm³",
      "correct_answer": 2,
      "skill_id": 189,
      "difficulty_id": 2,
      "explanation": "Count the unit cubes in the stacked solid: there are 12 cubes in total. Each cube has a volume of 1 cm³, so the volume is 12 cm³.",
      "hints": ["Each small cube has a volume of 1 cm³.", "Count all cubes, including the hidden ones underneath the stacks."],
      "source": "ACS 2022 P5 Weighted Assessment 2 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q3.png",
      "image_page": 3,
      "image_bbox": [0.27, 0.18, 0.66, 0.41],
      "image_loc": "upper area of page: 3D drawing of unit cubes stacked in a staircase arrangement",
      "notes": "Answer key: option 3 (12 cm³). Count of cubes = 12."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "The ratio of the perimeters of 2 squares is 3 : 8. The perimeter of the smaller square is 24 cm. What is the length of 1 side of the larger square?",
      "answer0": "8 cm",
      "answer1": "9 cm",
      "answer2": "3 cm",
      "answer3": "16 cm",
      "correct_answer": 3,
      "skill_id": 182,
      "difficulty_id": 2,
      "explanation": "3 units = 24 cm, so 1 unit = 8 cm. The larger perimeter = 8 units = 64 cm. One side of the larger square \\(= 64 \\div 4 = 16\\) cm.",
      "hints": ["Find the value of 1 unit: \\(24 \\div 3\\).", "A square has 4 equal sides, so divide the larger perimeter by 4."],
      "source": "ACS 2022 P5 Weighted Assessment 2 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: option 4 (16 cm)."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "Which of the following two triangles have the same area?",
      "answer0": "A and C",
      "answer1": "A and D",
      "answer2": "B and C",
      "answer3": "B and D",
      "correct_answer": 1,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "Counting grid squares: triangle A has base 4 and height 4, area \\(= \\dfrac{1}{2} \\times 4 \\times 4 = 8\\). Triangle D has base 2 and height 4 giving the same area of 8 square units. Hence A and D have the same area.",
      "hints": ["Area of a triangle \\(= \\dfrac{1}{2} \\times \\text{base} \\times \\text{height}\\); read base and height off the grid.", "Compare the products of base × height for each shaded triangle."],
      "source": "ACS 2022 P5 Weighted Assessment 2 Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q5.png",
      "image_page": 4,
      "image_bbox": [0.22, 0.22, 0.80, 0.44],
      "image_loc": "upper-middle of page: grid with four shaded triangles labelled A, B, C and D",
      "notes": "Answer key: option 2 (A and D)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "After spending $65 on a bag and $12 on a pack of socks, Jamie had $14 left. Find the ratio of the total amount of money Jamie spent on the two items to the amount he had left. Give your answer in its simplest form.",
      "answer0": "\\(11 : 2\\)",
      "answer1": "\\(77 : 14\\)",
      "answer2": "\\(11 : 14\\)",
      "answer3": "\\(7 : 2\\)",
      "correct_answer": 0,
      "skill_id": 179,
      "difficulty_id": 1,
      "explanation": "Total spent \\(= 65 + 12 = 77\\). Amount left = 14. Ratio spent : left \\(= 77 : 14\\). Divide both terms by 7 to get \\(11 : 2\\).",
      "hints": ["Add the two amounts spent to get the total spent.", "Simplify \\(77 : 14\\) by dividing both terms by their common factor 7."],
      "source": "ACS 2022 P5 Weighted Assessment 2 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer is a ratio so rendered as MCQ. Answer key: 77 : 14 = 11 : 2."
    },
    {
      "n": 7,
      "type_id": 2,
      "question": "Mrs Lim grouped her students for an activity. There were 3 boys and 2 girls in each group. There were 32 girls. How many boys were there? [?]",
      "answer0": "48",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 2,
      "explanation": "Number of groups \\(= 32 \\div 2 = 16\\). Each group has 3 boys, so number of boys \\(= 3 \\times 16 = 48\\).",
      "hints": ["First find the number of groups from the number of girls.", "Each group has 2 girls; divide 32 by 2 to find the groups, then multiply by 3."],
      "source": "ACS 2022 P5 Weighted Assessment 2 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: 32 ÷ 2 = 16 groups; 3u × 16 = 48 boys."
    },
    {
      "n": 8,
      "type_id": 2,
      "question": "The figure is made up of a rectangle, measuring 16 cm by 6 cm, and 2 triangles. Find the area of the shaded part. [?] cm²",
      "answer0": "48",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "The two unshaded triangles together have the same base total of 16 cm and height 6 cm, equal to the area of one rectangle of width 16 and the height. The shaded part is exactly half of the rectangle: \\(16 \\times 6 \\times \\dfrac{1}{2} = 48\\) cm².",
      "hints": ["The shaded and unshaded regions each make up half of the rectangle.", "Shaded area \\(= \\dfrac{1}{2} \\times 16 \\times 6\\)."],
      "source": "ACS 2022 P5 Weighted Assessment 2 Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 6,
      "image_bbox": [0.20, 0.20, 0.55, 0.32],
      "image_loc": "below the question: a 16 cm by 6 cm rectangle containing two shaded triangles",
      "notes": "Answer key: half of rectangle = 16 × 6 × 1/2 = 48 cm²."
    },
    {
      "n": 9,
      "type_id": 2,
      "question": "The cuboid has a square base of length 6 cm. Its height is 3 times its length. Find the volume of the cuboid. [?] cm³",
      "answer0": "648",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 190,
      "difficulty_id": 2,
      "explanation": "Height \\(= 6 \\times 3 = 18\\) cm. Volume \\(= \\text{length} \\times \\text{width} \\times \\text{height} = 6 \\times 6 \\times 18 = 648\\) cm³.",
      "hints": ["First work out the height: 3 times the base length of 6 cm.", "Volume of a cuboid \\(= \\ell \\times w \\times h\\)."],
      "source": "ACS 2022 P5 Weighted Assessment 2 Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q9.png",
      "image_page": 6,
      "image_bbox": [0.19, 0.51, 0.32, 0.66],
      "image_loc": "left side, below the question: tall shaded cuboid with base labelled 6 cm",
      "notes": "Answer key: height 6 × 3 = 18; 6 × 6 × 18 = 648 cm³."
    },
    {
      "n": 10,
      "type_id": 2,
      "question": "The figure is made up of 2 squares and a right-angled triangle. The area of square X is 49 cm² and the area of square Y is 36 cm². Find the area of triangle Z. [?] cm²",
      "answer0": "21",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "Side of square X \\(= \\sqrt{49} = 7\\) cm. Side of square Y \\(= \\sqrt{36} = 6\\) cm. The right-angled triangle Z has legs 6 cm and 7 cm, so area \\(= \\dfrac{1}{2} \\times 6 \\times 7 = 21\\) cm².",
      "hints": ["Find each square's side length by taking the square root of its area.", "Triangle Z's two perpendicular sides equal the sides of the two squares."],
      "source": "ACS 2022 P5 Weighted Assessment 2 Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 7,
      "image_bbox": [0.33, 0.24, 0.57, 0.39],
      "image_loc": "upper-middle of page: square X on the left, triangle Z to its right, square Y below Z",
      "notes": "Answer key: 7×7=49, 6×6=36, 1/2 × 6 × 7 = 21 cm²."
    },
    {
      "n": 11,
      "type_id": 2,
      "question": "Jim, Bob and Sam shared a box of stickers in the ratio 5 : 9 : 3. Jim and Sam had 128 stickers altogether. How many stickers did the three boys share altogether? [?]",
      "answer0": "272",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "Jim and Sam together \\(= 5 + 3 = 8\\) units \\(= 128\\), so 1 unit \\(= 128 \\div 8 = 16\\). Total \\(= 5 + 9 + 3 = 17\\) units \\(= 17 \\times 16 = 272\\) stickers.",
      "hints": ["Add Jim's and Sam's ratio units to match the 128 given.", "Find 1 unit, then multiply by the total number of units (17)."],
      "source": "ACS 2022 P5 Weighted Assessment 2 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: 5u+3u=8u; 128÷8=16; 17u × 16 = 272 stickers."
    },
    {
      "n": 12,
      "type_id": 2,
      "question": "In the figure, ABFG and BCDE are squares. AD and AF are straight lines. AG = 10 cm. The area of square ABFG is 4 times the area of square BCDE. Find the shaded area. [?] cm²",
      "answer0": "37.50",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Square ABFG has side AG = 10 cm, area \\(= 10 \\times 10 = 100\\) cm². Area of square BCDE \\(= 100 \\div 4 = 25\\) cm², so its side \\(= 5\\) cm. Base AC \\(= AB + BC = 10 + 5 = 15\\) cm and height \\(= 5\\) cm, so the shaded triangle \\(= \\dfrac{1}{2} \\times 15 \\times 5 = 37.50\\) cm².",
      "hints": ["Find the side of the small square from its area (a quarter of the large square).", "The shaded triangle has base AB + BC and a height equal to the small square's side."],
      "source": "ACS 2022 P5 Weighted Assessment 2 Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q12.png",
      "image_page": 9,
      "image_bbox": [0.30, 0.22, 0.60, 0.37],
      "image_loc": "upper-middle of page: large square ABFG with vertices A,B,F,G and smaller square BCDE, shaded triangle inside; AG labelled 10 cm",
      "notes": "Answer key: ABFG 10×10=100; BCDE 100÷4=25; 1/2 × 15 × 5 = 37.50 cm². Answer is a decimal so FIB is valid."
    },
    {
      "n": 13,
      "type_id": 2,
      "question": "Ronald used 13 cubes to form a solid. He wants to form a cuboid using this solid. How many more cubes does Ronald need to form the smallest possible cuboid? [?]",
      "answer0": "32",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 188,
      "difficulty_id": 3,
      "explanation": "The smallest cuboid that contains the solid has dimensions \\(3 \\times 3 \\times 5 = 45\\) cubes. The solid already uses 13 cubes, so Ronald needs \\(45 - 13 = 32\\) more cubes.",
      "hints": ["Work out the smallest cuboid that can enclose the solid (length × width × height in cubes).", "Subtract the 13 cubes already used from the cuboid's total."],
      "source": "ACS 2022 P5 Weighted Assessment 2 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q13.png",
      "image_page": 10,
      "image_bbox": [0.28, 0.20, 0.66, 0.46],
      "image_loc": "upper area of page: isometric drawing of a solid built from 13 unit cubes, with Top view, Front view and Side view arrows",
      "notes": "Only part (b) is captured (numeric answer 32). Part (a) is a draw-the-views task with no app question type and is omitted. Answer key: smallest cuboid 3×3×5=45; 45−13 = 32 more cubes."
    }
  ]
}