{
  "paper": {
    "school": "Catholic High",
    "year": 2022,
    "level": "P5",
    "label": "Weighted Assessment 2",
    "source_prefix": "Catholic High 2022 P5 Weighted Assessment 2",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "What is the missing number in the box?<br>\\(12 : 30 = \\square : 25\\)",
      "answer0": "5",
      "answer1": "7",
      "answer2": "10",
      "answer3": "17",
      "correct_answer": 2,
      "skill_id": 181,
      "difficulty_id": 2,
      "explanation": "Equivalent ratios. \\(12:30\\) simplifies by dividing by 6 to \\(2:5\\). Scale to make the second term 25: \\(2:5 = 10:25\\) (multiply by 5). The missing number is 10.",
      "hints": ["Simplify \\(12:30\\) first.", "Find what multiplies 5 to give 25, then apply it to the first term."],
      "source": "Catholic High 2022 P5 Weighted Assessment 2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Stem shows a ratio with a missing box; rendered with \\square. Key: option 3 = 10."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "A board game costs $63. A toy costs $45 less than the board game. Find the ratio of the cost of the toy to the cost of the board game in the simplest form.",
      "answer0": "2 : 7",
      "answer1": "5 : 7",
      "answer2": "7 : 2",
      "answer3": "7 : 5",
      "correct_answer": 0,
      "skill_id": 179,
      "difficulty_id": 2,
      "explanation": "Toy cost = $63 - $45 = $18. Ratio of toy to board game = 18 : 63. Divide both by 9: 18 : 63 = 2 : 7.",
      "hints": ["First find the cost of the toy: $63 - $45.", "Write toy : board game, then simplify by their common factor."],
      "source": "Catholic High 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": "Key: option 1 = 2:7."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "The shaded figure is drawn on a square grid. Find the area of the shaded figure.",
      "answer0": "3 cm²",
      "answer1": "6 cm²",
      "answer2": "8 cm²",
      "answer3": "10 cm²",
      "correct_answer": 1,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "Each grid square is 1 cm by 1 cm. The shaded figure on the square grid has an area of 6 cm² (counting whole and combining half squares per the answer key).",
      "hints": ["Each small square is 1 cm × 1 cm = 1 cm².", "Combine pairs of half-squares into whole squares as you count."],
      "source": "Catholic High 2022 P5 Weighted Assessment 2 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q3.png",
      "image_page": 3,
      "image_bbox": [0.40, 0.13, 0.66, 0.30],
      "image_loc": "shaded triangle/figure on a square grid, upper-right of the question, with 1 cm scale arrows",
      "notes": "Key Q3 = 2 (6 cm²)."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "The solid is made up of 1-cm cubes. What is the least number of cubes to be added to the solid to form a cuboid?",
      "answer0": "17",
      "answer1": "16",
      "answer2": "7",
      "answer3": "5",
      "correct_answer": 2,
      "skill_id": 190,
      "difficulty_id": 2,
      "explanation": "The solid is built within a smallest enclosing cuboid. The cuboid that contains the shape needs a total number of unit cubes; subtracting the cubes already present leaves 7 cubes to be added (per the answer key).",
      "hints": ["Picture the smallest cuboid that the solid fits inside.", "Subtract the cubes already present from the cuboid's total."],
      "source": "Catholic High 2022 P5 Weighted Assessment 2 Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q4.png",
      "image_page": 3,
      "image_bbox": [0.33, 0.47, 0.66, 0.63],
      "image_loc": "isometric drawing of an L-shaped arrangement of unit cubes, middle of the page below the question",
      "notes": "Key Q4 = 3 (7 cubes)."
    },
    {
      "n": 5,
      "type_id": 2,
      "question": "There were 84 children in a movie theatre. The ratio of the number of adults to the number of children in the movie theatre was \\(8 : 7\\). How many more adults than children were there in the movie theatre?<br>[?]",
      "answer0": "12",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 2,
      "explanation": "Children = 7 units = 84, so 1 unit = 84 ÷ 7 = 12. Adults are 8 units. Adults have 1 more unit than children, so the difference = 1 unit = 12 more adults.",
      "hints": ["7 units represent the 84 children.", "The difference between adults (8u) and children (7u) is just 1 unit."],
      "source": "Catholic High 2022 P5 Weighted Assessment 2 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: 84÷7=12, Ans 12."
    },
    {
      "n": 6,
      "type_id": 2,
      "question": "The figure shows a cuboid with a square base and a height of 4 cm. The side of the square base is twice its height. Find the volume of the cuboid.<br>[?] cm³",
      "answer0": "256",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 190,
      "difficulty_id": 2,
      "explanation": "Side of square base = 2 × 4 cm = 8 cm. Volume = base side × base side × height = 8 × 8 × 4 = 256 cm³.",
      "hints": ["The base side is twice the height: 2 × 4 cm.", "Volume of a cuboid = length × breadth × height."],
      "source": "Catholic High 2022 P5 Weighted Assessment 2 Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q6.png",
      "image_page": 4,
      "image_bbox": [0.30, 0.58, 0.62, 0.70],
      "image_loc": "isometric cuboid with the 4 cm height labelled on the right edge, middle-left of the question",
      "notes": "Key: 4×2=8, 8×8×4=256, Ans 256."
    },
    {
      "n": 7,
      "type_id": 2,
      "question": "The perimeter of rectangle QRST is 80 cm. The length QR is 3 times as long as its breadth RS. Find the area of the shaded triangle QST.<br>[?] cm²",
      "answer0": "150",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "Perimeter = 2(length + breadth) = 80, so length + breadth = 40. With length = 3 × breadth, 4 units = 40, 1 unit = 10. Breadth RS = 10 cm, length QR = 30 cm. Triangle QST has base QS region; area = ½ × 30 × 10 = 150 cm².",
      "hints": ["Half the perimeter is length + breadth = 40 cm.", "If length is 3 units and breadth 1 unit, the 4 units share 40 cm. Triangle area = ½ × base × height."],
      "source": "Catholic High 2022 P5 Weighted Assessment 2 Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q7.png",
      "image_page": 5,
      "image_bbox": [0.22, 0.16, 0.50, 0.25],
      "image_loc": "rectangle QRST with vertices labelled Q (top-left), R (top-right), T (bottom-left), S (bottom-right) and the shaded triangle QST, top-left of the question",
      "notes": "Key: 80÷8=10, 30×10=300, 300÷2=150, Ans 150."
    },
    {
      "n": 8,
      "type_id": 2,
      "question": "The ratio of the number of fish in Tank A to the number of fish in Tank B was \\(5 : 9\\). There were 48 fewer fish in Tank A than in Tank B. How many fish were there in Tank A and Tank B altogether?<br>[?]",
      "answer0": "168",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 2,
      "explanation": "Difference in units = 9 - 5 = 4 units = 48, so 1 unit = 48 ÷ 4 = 12. Total units = 5 + 9 = 14. Total fish = 14 × 12 = 168.",
      "hints": ["The 48 fewer fish equals the difference of 9 - 5 = 4 units.", "Find 1 unit, then multiply by the total number of units (5 + 9)."],
      "source": "Catholic High 2022 P5 Weighted Assessment 2 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: 48÷4=12, 12×14=168, Ans 168."
    },
    {
      "n": 9,
      "type_id": 0,
      "question": "The ages of three siblings, Alan, Belle and Carl, are in the ratio of \\(1 : 3 : 2\\) now. Each statement is either true, false or not possible to tell from the information given. For each statement, put a tick in the correct column. (a) The sum of Alan's and Belle's age is twice of Carl's age. (b) In two years' time, when Carl is 6 years old, Alan will be 3 years old.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 177,
      "difficulty_id": 2,
      "explanation": "Ages are 1u : 3u : 2u (Alan : Belle : Carl). (a) Alan + Belle = 1u + 3u = 4u; twice Carl = 2 × 2u = 4u, so the statement is TRUE. (b) If Carl is 6 now? In two years Carl is 6 means Carl is 4 now = 2u, so 1u = 2, Alan now = 2, in two years Alan = 4, not 3, so the statement is FALSE.",
      "hints": ["Let the units be Alan 1, Belle 3, Carl 2.", "Compare Alan + Belle against twice Carl; for (b) work out each age in two years' time."],
      "source": "Catholic High 2022 P5 Weighted Assessment 2 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Interactive tick-the-column table (true/false/not-possible) — no app question type, type_id 0, SKIPPED on insert. Answer key: (a) True, (b) False."
    },
    {
      "n": 10,
      "type_id": 0,
      "question": "The following solid is made up of 8 unit cubes. Draw the front view and the side view of the solid.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 188,
      "difficulty_id": 2,
      "explanation": "Students draw the front view and side view of the 8-unit-cube solid on the grids provided. The answer key shows the shaded front-view and side-view grids.",
      "hints": ["Look at the solid straight on from the front, then from the side.", "Shade one grid square for each cube face you can see in that view."],
      "source": "Catholic High 2022 P5 Weighted Assessment 2 Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 7,
      "image_bbox": [0.20, 0.20, 0.70, 0.45],
      "image_loc": "isometric drawing of an 8-unit-cube solid with Top/Front/Side View arrows, upper-middle of the page",
      "notes": "Interactive draw-on-grid task — no app question type, type_id 0, SKIPPED on insert. Answer key shows side-view and top/front-view shaded grids."
    },
    {
      "n": 11,
      "type_id": 2,
      "question": "QRSTU is made up of triangle QRU and square RSTU. ST = 9 cm and QT = 15 cm. Find the area of the figure QRSTU.<br>[?] cm²",
      "answer0": "108",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "Square RSTU has side 9 cm, area = 9 × 9 = 81 cm². For triangle QRU: QU = QT − UT = 15 − 9 = 6 cm (base) and height = 9 cm. Triangle area = ½ × 6 × 9 = 27 cm². Total area = 27 + 81 = 108 cm².",
      "hints": ["The square RSTU has side ST = 9 cm.", "Base QU of the triangle = QT − UT = 15 − 9 cm; add the triangle and square areas."],
      "source": "Catholic High 2022 P5 Weighted Assessment 2 Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q11.png",
      "image_page": 8,
      "image_bbox": [0.20, 0.28, 0.52, 0.42],
      "image_loc": "figure QRSTU: triangle QRU joined to square RSTU, with 9 cm (ST) and 15 cm (QT) labelled, below the question",
      "notes": "Key: 9×9=81, 15-9=6, ½×6×9=27, 27+81=108, Ans 108 cm²."
    },
    {
      "n": 12,
      "type_id": 2,
      "question": "Sam bought an oven, a pan and a toaster. The ratio of the cost of the oven to the cost of the pan to the cost of the toaster is \\(5 : 1 : 2\\). He paid $384 for all three items. How much did he pay for the oven?<br>$[?]",
      "answer0": "240",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 2,
      "explanation": "Total units = 5 + 1 + 2 = 8 units = $384, so 1 unit = $384 ÷ 8 = $48. The oven is 5 units = 5 × $48 = $240.",
      "hints": ["Add the ratio parts: 5 + 1 + 2 units make up $384.", "Find the value of 1 unit, then multiply by 5 for the oven."],
      "source": "Catholic High 2022 P5 Weighted Assessment 2 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: 384÷8=48, 48×5=240, Ans $240."
    },
    {
      "n": 13,
      "type_id": 2,
      "question": "AFCE is a rectangle and the unshaded figure is made up of three triangles ABD, BCD and ADE. AB = 4 cm, AE = 7 cm and BF = 5 cm. The area of triangle ABD is 5 cm². Find the total area of the shaded parts.<br>[?] cm²",
      "answer0": "40",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Rectangle AFCE has length AF = AB + BF = 4 + 5 = 9 cm and breadth AE = 7 cm, so its area = 9 × 7 = 63 cm². Triangle ADE (or the relevant triangle) has area ½ × 4 × 7 = 28 cm². The unshaded parts total: triangle areas 28 + 5 (triangle ABD) leave shaded = 63 − 28 − 5 = 40 cm² (using the equal-area decomposition; total area of rectangle 63 minus unshaded 28 and 5).",
      "hints": ["Rectangle length AF = AB + BF = 4 + 5 cm; area = length × breadth.", "Subtract the unshaded triangle areas (½ × 4 × 7 and the given 5 cm²) from the rectangle's area."],
      "source": "Catholic High 2022 P5 Weighted Assessment 2 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q13.png",
      "image_page": 9,
      "image_bbox": [0.28, 0.20, 0.72, 0.37],
      "image_loc": "rectangle AFCE with A,B,F across the top, E,C across the bottom and D inside; 4 cm, 5 cm and 7 cm labelled, shaded regions inside",
      "notes": "Key: 9×7=63, 2×½×4×7=28, 63-28-5=40, Ans 40 cm²."
    }
  ]
}