{
  "paper": {
    "school": "Ai Tong",
    "year": 2024,
    "level": "P5",
    "label": "Term 2 Review",
    "source_prefix": "Ai Tong 2024 P5 Term 2 Review",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 2,
      "question": "What is the missing number in the box?<br>\\(9 : 8 = [?] : 56\\)",
      "answer0": "63",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 181,
      "difficulty_id": 1,
      "explanation": "8 \\times 7 = 56, so multiply both terms of 9 : 8 by 7. The missing term is 9 \\times 7 = 63.",
      "hints": ["What do you multiply 8 by to get 56?", "Multiply 9 by the same factor."],
      "source": "Ai Tong 2024 P5 Term 2 Review Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 63. Single integer answer, FIB is fine."
    },
    {
      "n": 2,
      "type_id": 2,
      "question": "Jenny, Siti and Ali shared the cost of a present in the ratio \\(3 : 7 : 4\\). Jenny and Ali paid a total of $210. What was the cost of the present? $[?]",
      "answer0": "420",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 2,
      "explanation": "Jenny + Ali = 3 + 4 = 7 units = $210, so 1 unit = 210 \\div 7 = $30. Total units = 3 + 7 + 4 = 14, so the present cost 14 \\times 30 = $420.",
      "hints": ["Jenny and Ali together are 3 + 4 = 7 units.", "Find 1 unit, then multiply by the total 14 units."],
      "source": "Ai Tong 2024 P5 Term 2 Review Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: $420. Answer in dollars, integer, FIB is fine."
    },
    {
      "n": 3,
      "type_id": 2,
      "question": "The solid is made of 1-cm cubes glued together at the corner of a room. How many 1-cm cubes are there in the solid? [?]",
      "answer0": "12",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 188,
      "difficulty_id": 2,
      "explanation": "Counting the unit cubes in the stacked solid (including the hidden cubes against the two walls of the corner) gives 12 cubes.",
      "hints": ["Count layer by layer; do not forget the cubes hidden behind others.", "The printed answer is 12 cubes."],
      "source": "Ai Tong 2024 P5 Term 2 Review Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "fig-q3.png",
      "image_page": 2,
      "image_bbox": [0.18, 0.18, 0.6, 0.46],
      "image_loc": "isometric drawing of a solid of 1-cm cubes in a corner, with Top view / Side view / Front view arrows",
      "notes": "Key: 3a) 12 cubes. Part (b) 'Draw the top view in the square grid' is a draw task with no value answer and is omitted (interactive). Counting answer = 12."
    },
    {
      "n": 4,
      "type_id": 0,
      "question": "Draw the following cuboid on the isometric grid provided.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 187,
      "difficulty_id": 1,
      "explanation": "Draw a 3 cm by 2 cm by 2 cm cuboid on the isometric dot grid following the given dimensions.",
      "hints": [],
      "source": "Ai Tong 2024 P5 Term 2 Review Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "fig-q4.png",
      "image_page": 3,
      "image_bbox": [0.13, 0.12, 0.45, 0.36],
      "image_loc": "wireframe cuboid labelled 2 cm, 2 cm, 3 cm next to an isometric dot grid",
      "notes": "Drawing task — no value/sequence answer (type_id 0, skipped on insert). Key answer is a drawn cuboid."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "The figure shows triangle ABC with E on AB (right angle at E for the line from C) and the height from A meeting the line through C at D. Which height is related to the base BC?",
      "answer0": "AD",
      "answer1": "EC",
      "answer2": "AE",
      "answer3": "CD",
      "correct_answer": 0,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "The height to base BC is the perpendicular from the opposite vertex A to the line containing BC. That perpendicular is AD.",
      "hints": ["The height to a base is perpendicular to that base, from the opposite vertex.", "From vertex A, the perpendicular to BC is AD."],
      "source": "Ai Tong 2024 P5 Term 2 Review Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "fig-q5.png",
      "image_page": 3,
      "image_bbox": [0.13, 0.46, 0.5, 0.66],
      "image_loc": "triangle ABC, A top-right, B bottom-left, C on base, E on AB with right-angle mark, dashed AD to D right of C",
      "notes": "Key: 5a) AD. Letter answer rendered as MCQ per spec. Part (b) is served as Q5b below."
    },
    {
      "n": 5.2,
      "type_id": 1,
      "question": "The figure shows triangle ABC with E on AB (right angle at E for the line from C). Which base is related to the height EC?",
      "answer0": "AB",
      "answer1": "BA",
      "answer2": "BC",
      "answer3": "AC",
      "correct_answer": 1,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "EC is perpendicular to AB at E, so EC is the height to the base AB (named BA in the key). The matching base is BA.",
      "hints": ["The base for a height is the side the height is perpendicular to.", "EC meets AB at a right angle, so the base is AB / BA."],
      "source": "Ai Tong 2024 P5 Term 2 Review Q5b",
      "image_needed": true,
      "image_options": false,
      "image_file": "fig-q5.png",
      "image_page": 3,
      "image_bbox": [0.13, 0.46, 0.5, 0.66],
      "image_loc": "triangle ABC, A top-right, B bottom-left, C on base, E on AB with right-angle mark, dashed EC",
      "notes": "Key: 5b) BA. Letter answer rendered as MCQ. Option 2 (BA) is the printed key; AB is the same side but key writes BA."
    },
    {
      "n": 6,
      "type_id": 2,
      "question": "The figure is made up of 4 identical squares. \\(PQ = 18\\) cm. Find the unshaded area, in cm². [?]",
      "answer0": "202.5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "PQ = 18 cm spans 2 squares, so each square has side 9 cm. The shaded arrow-shape is made of triangles; the unshaded region = two large triangles of \\(\\dfrac{18 \\times 9}{2} = 81\\) cm² each plus a corner triangle of 40.5 cm²: 81 + 81 + 40.5 = 202.5 cm².",
      "hints": ["Each small square has side 18 \\div 2 = 9 cm.", "Add the unshaded triangle areas: 81 + 81 + 40.5."],
      "source": "Ai Tong 2024 P5 Term 2 Review Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "fig-q6.png",
      "image_page": 4,
      "image_bbox": [0.37, 0.27, 0.72, 0.5],
      "image_loc": "square PQRS (2x2 grid of squares) with a shaded arrow/dart shape pointing left from Q-R edge, 18 cm marked along PQ",
      "notes": "Key: 202.5 cm². Decimal answer, FIB is fine."
    },
    {
      "n": 7,
      "type_id": 2,
      "question": "Alicia had 96 stickers. She used \\(\\dfrac{5}{8}\\) of them and gave away \\(\\dfrac{1}{6}\\) of the remaining stickers to her sister. How many stickers did she have left? [?]",
      "answer0": "30",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "Used \\(\\dfrac{5}{8}\\) of 96, so remaining = \\(\\dfrac{3}{8} \\times 96 = 36\\). Gave away \\(\\dfrac{1}{6}\\) of 36 = 6, leaving 36 - 6 = 30. (Key: 16 units = 96, 1 unit = 6, left = 5 units = 30.)",
      "hints": ["After using \\(\\dfrac{5}{8}\\), \\(\\dfrac{3}{8}\\) remains.", "She keeps \\(\\dfrac{5}{6}\\) of that remainder."],
      "source": "Ai Tong 2024 P5 Term 2 Review Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 30 stickers. Final answer is a whole number, FIB is fine."
    },
    {
      "n": 8,
      "type_id": 2,
      "question": "The ratio of Henry's age to Jessie's age is \\(3 : 2\\) this year. In 5 years' time, their total age will be 100 years. Find Henry's age this year. [?]",
      "answer0": "54",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "In 5 years their total is 100, so this year their total is 100 - 5 - 5 = 90. The ratio 3 : 2 means 5 units = 90, so 1 unit = 18. Henry = 3 units = 54 years.",
      "hints": ["Subtract the two lots of 5 years to get this year's total (90).", "5 units = 90, so Henry's 3 units = 54."],
      "source": "Ai Tong 2024 P5 Term 2 Review Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 54 years. Integer answer, FIB is fine."
    },
    {
      "n": 9,
      "type_id": 2,
      "question": "Two triangles WXV and WZV are overlapped in Rectangle TUVW. WV = 30 cm, the rectangle height is 12 cm, and the height from XZ down to Y is 5 cm. Find the area, in cm², of the figure WXYZV. [?]",
      "answer0": "255",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Triangle WXV and triangle WZV each have base WV = 30 and height 12, area \\(\\dfrac{30 \\times 12}{2} = 180\\). Their overlap is triangle WYV with base 30 and height (12 - 5) = ... the key computes: 180 - 105 = 75 for each ear, plus the overlap 105: 75 + 75 + 105 = 255 cm².",
      "hints": ["Each big triangle on base WV (30 cm) has area \\(\\dfrac{30 \\times 12}{2} = 180\\).", "Subtract and re-add the overlapping triangle as the key does: 75 + 75 + 105 = 255."],
      "source": "Ai Tong 2024 P5 Term 2 Review Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "fig-q9.png",
      "image_page": 6,
      "image_bbox": [0.27, 0.14, 0.68, 0.28],
      "image_loc": "rectangle TUVW with X and Z on top edge, diagonals WZ and XV crossing at Y, 5 cm and 12 cm and 30 cm marked",
      "notes": "Key: 255 cm². Integer answer, FIB is fine."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "The rectangular tank contains 7200 cm³ of water. The tank is 80 cm long, 18 cm wide and 60 cm high. What fraction of the tank is filled with water? Leave your answer in its simplest form.",
      "answer0": "\\(\\dfrac{1}{12}\\)",
      "answer1": "\\(\\dfrac{1}{10}\\)",
      "answer2": "\\(\\dfrac{1}{8}\\)",
      "answer3": "\\(\\dfrac{1}{6}\\)",
      "correct_answer": 0,
      "skill_id": 190,
      "difficulty_id": 2,
      "explanation": "Tank volume = 80 \\times 18 \\times 60 = 86 400 cm³. Fraction filled = \\(\\dfrac{7200}{86400} = \\dfrac{1}{12}\\).",
      "hints": ["Find the full tank volume: 80 \\times 18 \\times 60.", "Write \\(\\dfrac{7200}{86400}\\) and simplify."],
      "source": "Ai Tong 2024 P5 Term 2 Review Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "fig-q10.png",
      "image_page": 7,
      "image_bbox": [0.28, 0.11, 0.68, 0.32],
      "image_loc": "open rectangular tank with a shallow layer of water at the bottom, 80 cm, 18 cm, 60 cm marked",
      "notes": "Key: 10a) 1/12. Fraction answer rendered as MCQ per spec. Part (b) served as Q10b below."
    },
    {
      "n": 10.2,
      "type_id": 2,
      "question": "The rectangular tank (80 cm by 18 cm by 60 cm) contains 7200 cm³ of water. How much more water, in litres, is needed to fill up the tank completely? [?]",
      "answer0": "79.2",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 192,
      "difficulty_id": 2,
      "explanation": "Full tank = 86 400 cm³. Water to add = 86 400 - 7200 = 79 200 cm³ = 79.2 L (since 1 L = 1000 cm³).",
      "hints": ["Empty space = full volume minus water already in (86 400 - 7200).", "Convert cm³ to litres by dividing by 1000."],
      "source": "Ai Tong 2024 P5 Term 2 Review Q10b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 10b) 79.2 L. Decimal answer in litres, FIB is fine."
    },
    {
      "n": 11,
      "type_id": 2,
      "question": "In the figure, rectangle ABCD is made up of 6 identical smaller rectangles. DC = 32 cm and E is the midpoint of DC.<br>(a) Find the length, in cm, of BC. [?]<br>(b) Find the area, in cm², of triangle BDE. [?]",
      "answer0": "24",
      "answer1": "192",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "(a) The 6 small rectangles form a 3-by-2 arrangement. DC = 32 is 2 small-rectangle widths, so 1 width = 16 cm; the short side is 16 \\div 2 = 8 cm and BC (height = 3 short sides) = ... the key gives: 32 \\div 2 = 16, 16 \\div 2 = 8, BC = 16 + 8 = 24 cm. (b) Triangle BDE has base DE = 16 cm and height BC = 24 cm: \\(\\dfrac{16 \\times 24}{2} = 192\\) cm².",
      "hints": ["(a) Use DC = 32 split across the small rectangles to find the side lengths; BC = 24 cm.", "(b) Triangle BDE: base DE = 16 cm, height 24 cm."],
      "source": "Ai Tong 2024 P5 Term 2 Review Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "fig-q11.png",
      "image_page": 8,
      "image_bbox": [0.34, 0.13, 0.68, 0.32],
      "image_loc": "rectangle ABCD split into 6 small rectangles, shaded triangle BDE from B to D to E, 32 cm marked along DC",
      "notes": "Key: 11a) BC = 24 cm, 11b) area of triangle BDE = 192. Printed key labels (b) as cm³ but it is an area, so the correct unit is cm² (flagged). Both answers integers, FIB fine."
    },
    {
      "n": 12,
      "type_id": 2,
      "question": "Daryl has a rectangular block of wood with only the top face painted. The block is 120 cm by 36 cm by 20 cm.<br>(a) What is the volume, in cm³, of the block of wood? [?]<br>(b) Daryl cuts the largest possible cube from one corner of the block. What is the volume, in cm³, of the cube? [?]<br>(c) What is the area, in cm², of the painted face of the remaining block of wood? [?]",
      "answer0": "86400",
      "answer1": "8000",
      "answer2": "3920",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 190,
      "difficulty_id": 3,
      "explanation": "(a) Volume = 120 \\times 36 \\times 20 = 86 400 cm³. (b) The largest cube has edge equal to the smallest dimension, 20 cm: 20 \\times 20 \\times 20 = 8000 cm³. (c) The painted top face was 120 \\times 36 = 4320 cm². Cutting the 20 cm cube removes a 20 \\times 20 = 400 cm² square from that face: 4320 - 400 = 3920 cm².",
      "hints": ["(a) Multiply all three dimensions.", "(b) Largest cube edge = the smallest side (20 cm). (c) Subtract the 20 \\times 20 square removed from the painted top."],
      "source": "Ai Tong 2024 P5 Term 2 Review Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "fig-q12.png",
      "image_page": 9,
      "image_bbox": [0.28, 0.11, 0.7, 0.26],
      "image_loc": "rectangular block of wood drawn in 3D with top face shaded, 120 cm, 36 cm, 20 cm marked",
      "notes": "Key: 12a) 86400 cm³, 12b) 8000 cm³, 12c) 3920 cm². All integers, FIB fine."
    }
  ]
}