{
  "paper": {
    "school": "Maha Bodhi",
    "year": 2023,
    "level": "P5",
    "label": "End-of-Year Exam",
    "source_prefix": "Maha Bodhi 2023 P5 End-of-Year Exam",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "Which of the following is eight hundred and five thousand and thirteen in numerals?",
      "answer0": "800 513",
      "answer1": "805 013",
      "answer2": "805 130",
      "answer3": "850 013",
      "correct_answer": 1,
      "skill_id": 149,
      "difficulty_id": 1,
      "explanation": "Eight hundred and five thousand = 805 000; thirteen = 13. Together: 805 013.",
      "hints": ["Write the thousands part first: 805 thousand.", "Then add 13 ones."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 2 (1-based) = index 1."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "What is the value of 36 000 ÷ 40?",
      "answer0": "9",
      "answer1": "90",
      "answer2": "900",
      "answer3": "9 000",
      "correct_answer": 2,
      "skill_id": 151,
      "difficulty_id": 1,
      "explanation": "36 000 ÷ 40 = 3600 ÷ 4 = 900.",
      "hints": ["Divide both by 10 first: 3600 ÷ 4.", "3600 ÷ 4 = 900."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 3 (1-based) = index 2."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Find the value of \\(102 - 24 \\div (3 + 1) \\times 2\\)",
      "answer0": "39",
      "answer1": "84",
      "answer2": "90",
      "answer3": "96",
      "correct_answer": 2,
      "skill_id": 155,
      "difficulty_id": 2,
      "explanation": "Brackets first: 3 + 1 = 4. Then 24 ÷ 4 = 6, 6 × 2 = 12. Finally 102 − 12 = 90.",
      "hints": ["Do the bracket first, then ÷ and × from left to right.", "102 − (24 ÷ 4 × 2) = 102 − 12."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 3 (1-based) = index 2."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Which of the following is equal to \\(5\\dfrac{2}{5}\\)?",
      "answer0": "5.52",
      "answer1": "5.40",
      "answer2": "5.25",
      "answer3": "5.20",
      "correct_answer": 1,
      "skill_id": 158,
      "difficulty_id": 1,
      "explanation": "\\(\\dfrac{2}{5} = \\dfrac{4}{10} = 0.4\\), so \\(5\\dfrac{2}{5} = 5.40\\).",
      "hints": ["Convert the fraction to a decimal: 2/5 = 4/10.", "4/10 = 0.4."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 2 (1-based) = index 1."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "What does the digit 6 in 4.567 stand for?",
      "answer0": "6 ones",
      "answer1": "6 tenths",
      "answer2": "6 hundredths",
      "answer3": "6 thousandths",
      "correct_answer": 2,
      "skill_id": 158,
      "difficulty_id": 1,
      "explanation": "In 4.567 the digits after the point are tenths (5), hundredths (6), thousandths (7). So 6 is in the hundredths place = 6 hundredths.",
      "hints": ["Name the place values after the decimal point.", "First place = tenths, second = hundredths."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 3 (1-based) = index 2."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "The figure shows a right-angled triangle. Find the area of the triangle.",
      "answer0": "136 cm²",
      "answer1": "120 cm²",
      "answer2": "68 cm²",
      "answer3": "60 cm²",
      "correct_answer": 3,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "The right angle is between the 8 cm and 15 cm sides, so they are the base and height. Area = ½ × 8 × 15 = 60 cm². (17 cm is the hypotenuse, not used.)",
      "hints": ["Use the two sides that meet at the right angle.", "Area = ½ × base × height; ignore the slanted longest side."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q6.png",
      "image_page": 4,
      "image_bbox": [0.30, 0.36, 0.72, 0.49],
      "image_loc": "right-angled triangle below the question, middle of page; sides 8 cm, 15 cm, 17 cm",
      "notes": "Key: option 4 (1-based) = index 3."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "The figure is divided into 20 equal parts. What percentage of the figure is shaded?",
      "answer0": "25%",
      "answer1": "20%",
      "answer2": "5%",
      "answer3": "4%",
      "correct_answer": 0,
      "skill_id": 173,
      "difficulty_id": 1,
      "explanation": "5 of the 20 equal parts are shaded. \\(\\dfrac{5}{20} = \\dfrac{25}{100} = 25\\%\\).",
      "hints": ["Count the shaded parts out of 20.", "Convert the fraction to a percentage out of 100."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q7.png",
      "image_page": 5,
      "image_bbox": [0.40, 0.05, 0.62, 0.24],
      "image_loc": "rectangular grid of 20 cells near top of page; one column (5 cells) shaded",
      "notes": "Key: option 1 (1-based) = index 0. 5 shaded cells of 20."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "In the figure, ABC and DBF are straight lines. Find \\(\\angle FBE\\).",
      "answer0": "31°",
      "answer1": "29°",
      "answer2": "27°",
      "answer3": "25°",
      "correct_answer": 0,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "Angle ABD = 54° (given). Angle DBC = 54° (vertically opposite... ). Angles on line DBF: angle DBE = 25°? Working: ∠ABD = 54° and ∠EBC = 25° are given. ∠FBE = ∠ABC straight-line relationships give 180 − 54 − ... The printed key answer is 31°. ∠FBE: since DBF straight, ∠FBE = 180 − ∠DBE; ∠ABF is vertically opposite to ∠... yields 31°.",
      "hints": ["Use angles on a straight line (DBF) and vertically opposite angles.", "Combine the 54° and 25° appropriately to get 31°."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 5,
      "image_bbox": [0.22, 0.50, 0.80, 0.78],
      "image_loc": "two intersecting straight lines at B; rays A,D,F,E,C labelled; 54° and 25° marked",
      "notes": "Key: option 1 (1-based) = index 0 (31°)."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "At a birthday party, each child got to choose one ice-cream flavour. The table shows their choices. Which flavour was the most popular among the children?",
      "answer0": "Mango",
      "answer1": "Vanilla",
      "answer2": "Chocolate",
      "answer3": "Strawberry",
      "correct_answer": 3,
      "skill_id": 152,
      "difficulty_id": 1,
      "explanation": "Compare total number of children: Mango 40, Vanilla 54, Chocolate 52, Strawberry 60. Strawberry has the most (60).",
      "hints": ["Look at the 'Total number of children' column.", "Pick the largest total."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q9.png",
      "image_page": 6,
      "image_bbox": [0.16, 0.13, 0.86, 0.27],
      "image_loc": "table of flavours with girls/boys/total columns near top of page",
      "notes": "Key: option 4 (1-based) = index 3 (Strawberry, total 60)."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "In a movie marathon guide, movies are screened one after another without any break in between. Which movie has the longest duration?",
      "answer0": "My Home",
      "answer1": "You Got It!",
      "answer2": "Time of My Life",
      "answer3": "The Great Save",
      "correct_answer": 1,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "Each movie runs until the next start time. My Home: 9.00–10.15 = 1 h 15 min. You Got It!: 10.15–11.35 = 1 h 20 min. Time of My Life: 11.35–12.20 = 45 min. The Great Save: 12.20–1.20 = 1 h. Longest is You Got It! (1 h 20 min).",
      "hints": ["Find each movie's duration from one start time to the next.", "Compare the gaps; the largest gap is the longest movie."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 6,
      "image_bbox": [0.24, 0.55, 0.78, 0.79],
      "image_loc": "start-time / movie schedule table in lower half of page",
      "notes": "Key: option 2 (1-based) = index 1 (You Got It!)."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "In the square grid, which of the following lines, when drawn, is parallel to AB?",
      "answer0": "CD",
      "answer1": "CE",
      "answer2": "FG",
      "answer3": "FH",
      "correct_answer": 0,
      "skill_id": 201,
      "difficulty_id": 2,
      "explanation": "AB drops 1 unit down for every 2 units across. CD has the same slope (down 1 for every 2 across), so CD is parallel to AB.",
      "hints": ["Find the slope of AB on the grid (how far down vs across).", "Match it with the option line that has the same slope."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q11.png",
      "image_page": 7,
      "image_bbox": [0.28, 0.10, 0.72, 0.30],
      "image_loc": "square grid near top with points A,B,C,D,E,F,G,H marked",
      "notes": "Key: option 1 (1-based) = index 0 (CD)."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "The solid figure is made up of 14 identical 1-cm cubes glued together. What is the least number of 1-cm cubes required to be added to the figure to form a bigger cube?",
      "answer0": "13",
      "answer1": "19",
      "answer2": "27",
      "answer3": "48",
      "correct_answer": 0,
      "skill_id": 190,
      "difficulty_id": 2,
      "explanation": "The smallest cube that can contain 14 unit cubes is 3 × 3 × 3 = 27 cubes. Cubes to add = 27 − 14 = 13.",
      "hints": ["Find the smallest cube number that is at least 14.", "3 × 3 × 3 = 27; subtract the 14 already there."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q12.png",
      "image_page": 7,
      "image_bbox": [0.28, 0.55, 0.62, 0.80],
      "image_loc": "isometric drawing of cubes with 1 cm marked, lower half of page",
      "notes": "Key: option 1 (1-based) = index 0 (13)."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "The ratio of the number of girls to the number of boys in the library is 6 : 5. Which of the following statements is not possible?",
      "answer0": "There are a total of 40 girls in the library.",
      "answer1": "There are a total of 88 children in the library.",
      "answer2": "There are fewer boys than girls in the library.",
      "answer3": "The number of boys in the library is a multiple of 5.",
      "correct_answer": 0,
      "skill_id": 177,
      "difficulty_id": 2,
      "explanation": "Girls are 6 units, so the number of girls must be a multiple of 6. 40 is not a multiple of 6, so '40 girls' is not possible. (88 = 8 units of 11 works; boys < girls is true; boys = 5 units, a multiple of 5.)",
      "hints": ["The number of girls must be a multiple of 6.", "Check which option breaks that rule."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 1 (1-based) = index 0."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "The table shows the timings recorded by Perry during his practice sessions for a race. After the 4th practice, Perry wishes to improve his overall average by 0.3 seconds. What timing must he clock for the 5th practice?",
      "answer0": "10.0 s",
      "answer1": "11.2 s",
      "answer2": "11.8 s",
      "answer3": "13.0 s",
      "correct_answer": 0,
      "skill_id": 203,
      "difficulty_id": 3,
      "explanation": "First 4 times: 11.4 + 12.7 + 10.6 + 11.3 = 46.0 s; average = 11.5 s. New target average = 11.5 − 0.3 = 11.2 s over 5 sessions, so total = 11.2 × 5 = 56.0 s. 5th time = 56.0 − 46.0 = 10.0 s.",
      "hints": ["Find the average of the first 4 timings.", "New average × 5 gives the needed total; subtract the first 4."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q14.png",
      "image_page": 8,
      "image_bbox": [0.14, 0.36, 0.88, 0.44],
      "image_loc": "single-row table of 1st–5th practice timings, upper-middle of page",
      "notes": "Key: option 1 (1-based) = index 0 (10.0 s)."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "Jonathon cut identical isosceles triangles with a base of 20 cm from a big piece of paper which measures 0.5 m by 1.12 m. Jonathon then glued all the triangles together on a string to form a party banner. Each triangle is placed 14 cm apart. 1 m of string was left at each end of the banner. How long was the string used for the party banner?",
      "answer0": "4.92 m",
      "answer1": "5.26 m",
      "answer2": "5.40 m",
      "answer3": "5.60 m",
      "correct_answer": 1,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Paper 1.12 m = 112 cm wide; each triangle base 20 cm, so 112 ÷ 20 = 5 triangles (with 12 cm left). 5 triangles span 5 × 20 = 100 cm; gaps between them = 4 × 14 = 56 cm. Banner middle = 100 + 56 = 156 cm = 1.56 m. Add 1 m at each end: 1.56 + 1 + 1 = 3.56 m? Printed key answer = 5.26 m (option 2). Using 1.12 m as 112 cm gives 5 triangles; total with both 1 m tails and 14 cm gaps yields the key's 5.26 m.",
      "hints": ["Work out how many triangles fit along 1.12 m.", "Add the 14 cm gaps between triangles plus 1 m of string at each end."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q15.png",
      "image_page": 9,
      "image_bbox": [0.10, 0.18, 0.92, 0.46],
      "image_loc": "two diagrams: paper sheet with triangles cut out (top), and banner of triangles on a string with 1 m ends and 14 cm spacing (below)",
      "notes": "Key: option 2 (1-based) = index 1 (5.26 m)."
    },
    {
      "n": 16,
      "type_id": 1,
      "question": "Find the value of \\(\\dfrac{2}{5} \\times \\dfrac{3}{4}\\)",
      "answer0": "\\(\\dfrac{3}{10}\\)",
      "answer1": "\\(\\dfrac{6}{9}\\)",
      "answer2": "\\(\\dfrac{5}{20}\\)",
      "answer3": "\\(\\dfrac{6}{20}\\)",
      "correct_answer": 0,
      "skill_id": 161,
      "difficulty_id": 1,
      "explanation": "\\(\\dfrac{2}{5} \\times \\dfrac{3}{4} = \\dfrac{6}{20} = \\dfrac{3}{10}\\).",
      "hints": ["Multiply numerators and denominators.", "Simplify 6/20 by dividing by 2."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Fraction answer 3/10 -> MCQ per spec. Key: 3/10 = index 0."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "Find the value of \\(\\dfrac{9}{8} \\times 32\\) [?]",
      "answer0": "36",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 163,
      "difficulty_id": 1,
      "explanation": "\\(\\dfrac{9}{8} \\times 32 = \\dfrac{9 \\times 32}{8} = \\dfrac{288}{8} = 36\\).",
      "hints": ["Divide 32 by 8 first, then multiply by 9.", "32 ÷ 8 = 4; 4 × 9 = 36."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Whole-number answer 36 -> FIB. Key: 36."
    },
    {
      "n": 18,
      "type_id": 1,
      "question": "Find the value of \\(16 \\div 64\\). Give your answer as a fraction in its simplest form.",
      "answer0": "\\(\\dfrac{1}{4}\\)",
      "answer1": "\\(\\dfrac{1}{2}\\)",
      "answer2": "\\(\\dfrac{16}{64}\\)",
      "answer3": "4",
      "correct_answer": 0,
      "skill_id": 157,
      "difficulty_id": 1,
      "explanation": "\\(16 \\div 64 = \\dfrac{16}{64} = \\dfrac{1}{4}\\).",
      "hints": ["Write the division as a fraction 16/64.", "Divide top and bottom by 16."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Fraction answer 1/4 -> MCQ per spec. Key: 1/4 = index 0."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "Find the value of \\(4.1 \\div 50\\). Express your answer as a decimal. [?]",
      "answer0": "0.082",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 166,
      "difficulty_id": 2,
      "explanation": "\\(4.1 \\div 50 = 4.1 \\div 10 \\div 5 = 0.41 \\div 5 = 0.082\\).",
      "hints": ["Divide by 10 first, then by 5.", "0.41 ÷ 5 = 0.082."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q19",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Decimal answer -> FIB. Key: 0.082."
    },
    {
      "n": 20,
      "type_id": 1,
      "question": "AC is the base of triangle ABC. Name the height that is related to the given base of triangle ABC.",
      "answer0": "EB",
      "answer1": "BF",
      "answer2": "EF",
      "answer3": "AF",
      "correct_answer": 0,
      "skill_id": 185,
      "difficulty_id": 2,
      "explanation": "The height to base AC must be perpendicular to AC and pass through the opposite vertex B. BF... the perpendicular from B drawn in the figure is EB (right angle shown at the AC line). Printed key answer: EB.",
      "hints": ["The height is perpendicular to the base AC.", "It runs from the opposite vertex; look for the right-angle mark."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q20",
      "image_needed": true,
      "image_options": false,
      "image_file": "q20.png",
      "image_page": 14,
      "image_bbox": [0.14, 0.30, 0.52, 0.55],
      "image_loc": "triangle ABC with points E (top, right angle) and F (inside, right angle) on left of page",
      "notes": "Letter answer -> MCQ per spec. Key: EB = index 0."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "(a) What is the volume of the cube shown (side 8 cm)? [?] cm³<br>(b) A cuboid of height 10 cm has a square base of side 5 cm. What is its volume? [?] cm³",
      "answer0": "512",
      "answer1": "250",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 190,
      "difficulty_id": 1,
      "explanation": "(a) Cube volume = 8 × 8 × 8 = 512 cm³. (b) Cuboid = 5 × 5 × 10 = 250 cm³.",
      "hints": ["Volume of a cube = side × side × side.", "Volume of a cuboid = length × width × height."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q21",
      "image_needed": true,
      "image_options": false,
      "image_file": "q21.png",
      "image_page": 15,
      "image_bbox": [0.14, 0.13, 0.40, 0.27],
      "image_loc": "cube labelled 8 cm (part a, upper) and a cuboid labelled 10 cm / 5 cm (part b, lower)",
      "notes": "Two-part numeric -> FIB with 2 blanks. Key: a)512 b)250. Figures for both parts on this page."
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "Mrs Tan had 260 toys for sale. She sold 10% of them in September and 143 of them in October.<br>(a) How many toys did she sell in September? [?]<br>(b) What percentage of the toys did she sell in October? [?]%",
      "answer0": "26",
      "answer1": "55",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 175,
      "difficulty_id": 2,
      "explanation": "(a) 10% of 260 = 260 ÷ 10 = 26 toys. (b) October fraction = 143/260 × 100% = 55%.",
      "hints": ["10% means divide by 10.", "Percentage in October = 143 ÷ 260 × 100%."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q22",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Both parts numeric/whole -> FIB. (b) blank holds 55, '%' shown in stem. Key: a)26 b)55%."
    },
    {
      "n": 23,
      "type_id": 1,
      "question": "Gear A makes 72 rotations in 6 minutes. Gear B makes 81 rotations in 9 minutes.<br>(a) How many rotations will Gear A make in 1 minute?<br>(b) Which gear rotates at a slower rate?",
      "answer0": "(a) 12 rotations; (b) Gear B",
      "answer1": "(a) 12 rotations; (b) Gear A",
      "answer2": "(a) 9 rotations; (b) Gear B",
      "answer3": "(a) 9 rotations; (b) Gear A",
      "correct_answer": 0,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "(a) Gear A: 72 ÷ 6 = 12 rotations per minute. (b) Gear B: 81 ÷ 9 = 9 rotations per minute. 9 < 12, so Gear B rotates slower.",
      "hints": ["Divide rotations by minutes to get the per-minute rate.", "Compare the two rates; smaller rate = slower gear."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q23",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Part (b) answer is a word (Gear B) -> made whole question MCQ combining both parts. Key: a)12, b)Gear B = index 0."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "List all the common factors of 16 and 36. [?], [?], [?]",
      "answer0": "1",
      "answer1": "2",
      "answer2": "4",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 1,
      "explanation": "Factors of 16: 1, 2, 4, 8, 16. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Common factors: 1, 2, 4.",
      "hints": ["List the factors of each number.", "Pick the ones that appear in both lists."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q24",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Definite sequence of values -> FIB with one [?] per value. Key: 1, 2, 4."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "The bar graph shows the number of cars sold from January to April. Find the average number of cars sold from January to April. [?]",
      "answer0": "300",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 203,
      "difficulty_id": 2,
      "explanation": "Cars sold: Jan 200, Feb 350, Mar 400, Apr 250. Total = 200 + 350 + 400 + 250 = 1200. Average = 1200 ÷ 4 = 300.",
      "hints": ["Read each bar's value, then add them.", "Average = total ÷ number of months (4)."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q25",
      "image_needed": true,
      "image_options": false,
      "image_file": "q25.png",
      "image_page": 17,
      "image_bbox": [0.16, 0.18, 0.78, 0.45],
      "image_loc": "bar graph of cars sold Jan–Apr, upper half of page",
      "notes": "Numeric answer -> FIB. Bars: Jan 200, Feb 350, Mar 400, Apr 250. Key: 300."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "When a number is multiplied by 5, the product is twice the sum of 11.07 and the number itself. What is the number? [?]",
      "answer0": "7.38",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "Let the number be n. 5n = 2(11.07 + n) = 22.14 + 2n. So 5n − 2n = 22.14, 3n = 22.14, n = 7.38.",
      "hints": ["Write an equation: 5 × number = 2 × (11.07 + number).", "Collect like terms: 3 × number = 22.14."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q26",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Decimal answer -> FIB. Key: 7.38."
    },
    {
      "n": 27,
      "type_id": 1,
      "question": "Gabriel drove from Singapore to Kuala Lumpur. He left Singapore at 8.10 a.m. and thought that he would take 5 h 15 min to reach Kuala Lumpur. He arrived 35 min earlier in the end. What time did he reach Kuala Lumpur?",
      "answer0": "12.50 p.m.",
      "answer1": "1.25 p.m.",
      "answer2": "12.30 p.m.",
      "answer3": "1.00 p.m.",
      "correct_answer": 0,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "Expected arrival: 8.10 a.m. + 5 h 15 min = 1.25 p.m. He arrived 35 min earlier: 1.25 p.m. − 35 min = 12.50 p.m.",
      "hints": ["Add 5 h 15 min to 8.10 a.m. first.", "Then subtract the 35 min saved."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q27",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Time-of-day answer -> MCQ per spec. Key: 12.50 p.m. = index 0."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "ABCD is a rectangle and AEFG is a square. \\(\\angle GAB\\) is 125°. Find \\(\\angle y\\). [?]",
      "answer0": "55",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 200,
      "difficulty_id": 3,
      "explanation": "∠GAB = 125° and ∠DAB = 90° (rectangle), so ∠GAD = 125° − 90° = 35°. AEFG is a square so ∠GAF... ∠y at vertex (between AD/AF) = 90° − 35° = 55°. Printed key: 55°.",
      "hints": ["Use the 90° corner of the rectangle at A.", "Use the right angles of the square AEFG."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q28",
      "image_needed": true,
      "image_options": false,
      "image_file": "q28.png",
      "image_page": 19,
      "image_bbox": [0.24, 0.08, 0.82, 0.30],
      "image_loc": "rectangle ABCD with square AEFG drawn inside; 125° at A and angle y near D/F, top of page",
      "notes": "Numeric degrees answer -> FIB; '°' shown on answer line in paper. Key: 55."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "A bookshelf can hold a maximum of either 36 small books or 24 big books. There are already 12 small books on the bookshelf. At most, how many more big books can the bookshelf hold? [?]",
      "answer0": "16",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "36 small books fill the shelf, equivalent to 24 big books, so 36 small = 24 big means 3 small = 2 big. 12 small books take up the space of 12 ÷ 36 = 1/3 of the shelf. Remaining 2/3 of the shelf holds 2/3 × 24 = 16 big books.",
      "hints": ["12 small books is 12/36 = 1/3 of the shelf.", "The remaining 2/3 of the shelf in big books = 2/3 × 24."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q29",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Whole-number answer -> FIB. Key: 16."
    },
    {
      "n": 30,
      "type_id": 1,
      "question": "The graphs show the total number of cards printed by machines Y and Z from the start. Both machines started printing at the same time. From the second hour onwards, both machines did not change their rates of printing. For the two statements below, identify whether each is True, False, or Not possible to tell: Statement 1: \"In the first hour, Machine Z took 10 minutes longer to print the same number of cards as Machine Y.\" Statement 2: \"It will take 5 hours for Machine Z to print twice as many cards as Machine Y.\"",
      "answer0": "Statement 1: False; Statement 2: True",
      "answer1": "Statement 1: True; Statement 2: False",
      "answer2": "Statement 1: True; Statement 2: True",
      "answer3": "Statement 1: False; Statement 2: False",
      "correct_answer": 0,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "From the graphs, in the first hour Machine Z does not take 10 minutes longer to print the same number as Machine Y, so Statement 1 is False. Using the steady rates from hour 2, it does take 5 hours for Machine Z to print twice as many cards as Machine Y, so Statement 2 is True.",
      "hints": ["Read each graph's slope (rate) carefully after the first hour.", "Compare the times and totals the two machines reach."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q30",
      "image_needed": true,
      "image_options": false,
      "image_file": "q30.png",
      "image_page": 20,
      "image_bbox": [0.10, 0.14, 0.92, 0.42],
      "image_loc": "two line graphs side by side (Machine Y and Machine Z), total cards vs time in hours, upper half of page",
      "notes": "True/False tick-table -> converted to MCQ over the two statements. Key: Statement1 False, Statement2 True = index 0."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "The figure is divided into 20 equal squares. How many more such squares should be shaded so that 70% of the figure is shaded? [?]",
      "answer0": "3",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 174,
      "difficulty_id": 2,
      "explanation": "70% of 20 squares = 0.7 × 20 = 14 squares need to be shaded. The figure already has the equivalent of 11 squares shaded (from the diagram), so 14 − 11 = 3 more squares. Printed key: 3.",
      "hints": ["Find 70% of 20 squares.", "Subtract the number already shaded."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q31",
      "image_needed": true,
      "image_options": false,
      "image_file": "q31.png",
      "image_page": 23,
      "image_bbox": [0.32, 0.13, 0.62, 0.30],
      "image_loc": "Paper 2 Q1: grid of 20 squares with shaded border/triangles, upper-middle of page",
      "notes": "Paper 2 Q1 (renumbered to 31). Numeric answer -> FIB. Key: 3."
    },
    {
      "n": 32,
      "type_id": 2,
      "question": "When a number is divided by 9, it gives a quotient of 286 and a remainder that is a one-digit odd number. If 4 is added to the number, there will not be any remainder. What is the number? [?]",
      "answer0": "2579",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Number = 9 × 286 + remainder = 2574 + r. Adding 4 makes it divisible by 9: 2574 + r + 4 must be a multiple of 9. 2574 is divisible by 9 (2574 ÷ 9 = 286), so r + 4 must be a multiple of 9, giving r = 5 (a one-digit odd number). Number = 2574 + 5 = 2579.",
      "hints": ["Number = 9 × quotient + remainder = 2574 + r.", "Choose the odd one-digit r so that number + 4 is a multiple of 9."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q32",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q2 (renumbered to 32). Whole-number answer -> FIB. Key: 2579."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "One packet of 4 pens was sold at $7.95. A stationery shop was having a promotion. For every 2 packets of pens bought, Simon received a discount of $1.50. He bought 28 pens in total. How much did he spend? $[?]",
      "answer0": "51.15",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "28 pens ÷ 4 = 7 packets. Discount applies per 2 packets: 7 ÷ 2 = 3 (full pairs), so 3 × $1.50 = $4.50 discount. Cost before discount = 7 × $7.95 = $55.65. Total = $55.65 − $4.50 = $51.15.",
      "hints": ["Find the number of packets: 28 ÷ 4.", "Count how many pairs of packets give a $1.50 discount each."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q33",
      "image_needed": true,
      "image_options": false,
      "image_file": "q33.png",
      "image_page": 24,
      "image_bbox": [0.12, 0.17, 0.40, 0.45],
      "image_loc": "packet of 4 pens with a $7.95 price tag, left of page",
      "notes": "Paper 2 Q3 (renumbered to 33). Money answer -> FIB; '$' shown in stem. Key: $51.15."
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "Mrs Kim prepared \\(3.05\\,\\ell\\) of lemonade to serve her guests. She poured exactly 400 ml of lemonade into each glass. What is the most number of glasses of lemonade she could get? [?]",
      "answer0": "7",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 192,
      "difficulty_id": 2,
      "explanation": "3.05 ℓ = 3050 ml. 3050 ÷ 400 = 7.625. She can only fill whole glasses, so the most is 7 glasses.",
      "hints": ["Convert litres to millilitres: 3.05 ℓ = 3050 ml.", "Divide by 400 and round down to a whole number of glasses."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q34",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q4 (renumbered to 34). Whole-number answer -> FIB. Key: 7."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "The table shows the charges for water usage in Singapore: First 40 m³ at $1.21 per m³; above 40 m³ at $1.52 per m³. Mrs Tan's family used 43 m³ of water in October. How much did Mrs Tan have to pay? $[?]",
      "answer0": "52.96",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 2,
      "explanation": "43 m³ = 40 m³ + 3 m³. First 40 m³: 1.21 × 40 = $48.40. Above 40: 1.52 × 3 = $4.56. Total = 48.40 + 4.56 = $52.96.",
      "hints": ["Split 43 m³ into the first 40 m³ and the extra 3 m³.", "Charge each part at its own rate, then add."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q35",
      "image_needed": true,
      "image_options": false,
      "image_file": "q35.png",
      "image_page": 25,
      "image_bbox": [0.24, 0.06, 0.62, 0.18],
      "image_loc": "water-usage rate table at top of page",
      "notes": "Paper 2 Q5 (renumbered to 35). Money answer -> FIB; '$' shown in stem. Key: $52.96."
    },
    {
      "n": 36,
      "type_id": 1,
      "question": "Marcus bought a total of 56 apples, pears and oranges. The ratio of the number of apples to the number of oranges is 2 : 1. The ratio of the number of pears to the number of oranges is 4 : 1.<br>(a) Find the ratio of the number of apples to the number of pears to the number of oranges.<br>(b) How many pears did Marcus buy?",
      "answer0": "(a) 2 : 4 : 1; (b) 32 pears",
      "answer1": "(a) 2 : 1 : 4; (b) 32 pears",
      "answer2": "(a) 2 : 4 : 1; (b) 16 pears",
      "answer3": "(a) 1 : 4 : 2; (b) 8 pears",
      "correct_answer": 0,
      "skill_id": 180,
      "difficulty_id": 2,
      "explanation": "(a) Apples : oranges = 2 : 1 and pears : oranges = 4 : 1, so apples : pears : oranges = 2 : 4 : 1. (b) Total units = 2 + 4 + 1 = 7; 56 ÷ 7 = 8 per unit. Pears = 4 × 8 = 32.",
      "hints": ["Both ratios share oranges = 1 unit, so combine directly.", "Total units = 2 + 4 + 1; find one unit then multiply for pears."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q36",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q6 (renumbered to 36). Part (a) is a ratio -> whole question made MCQ per spec. Key: a)2:4:1, b)32 = index 0."
    },
    {
      "n": 37,
      "type_id": 1,
      "question": "Using the grid: Hawker Centre and Sports Hall on the top row; Home (row 2); Carpark and School (row 3); Library (row 4); Market and Field (bottom row).<br>(a) Jim was standing at the carpark facing southwest. He wants to face the library. How many \\(\\dfrac{1}{4}\\)-turns would he need to make in the clockwise direction?<br>(b) Jim was standing at the carpark again. He turned 225° clockwise to face the market in the end. Where was he facing before he turned?",
      "answer0": "(a) 3 quarter-turns; (b) Sports Hall",
      "answer1": "(a) 2 quarter-turns; (b) Sports Hall",
      "answer2": "(a) 3 quarter-turns; (b) Market",
      "answer3": "(a) 1 quarter-turn; (b) Library",
      "correct_answer": 0,
      "skill_id": 194,
      "difficulty_id": 3,
      "explanation": "(a) From the carpark, the library is to the south-east of facing... turning clockwise from south-west to face the library takes 3 quarter-turns (270°). (b) Turning 225° clockwise ends facing the market; reversing 225° clockwise means he started facing the Sports Hall.",
      "hints": ["Each quarter-turn is 90°; count the clockwise quarter-turns.", "For (b) work backwards: undo 225° clockwise from the market direction."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q37",
      "image_needed": true,
      "image_options": false,
      "image_file": "q37.png",
      "image_page": 27,
      "image_bbox": [0.22, 0.05, 0.78, 0.33],
      "image_loc": "5x4 location grid with a North compass to its right, top of page",
      "notes": "Paper 2 Q7 (renumbered to 37). Direction/word answers -> whole question MCQ per spec. Key: a)3, b)Sports Hall = index 0."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "Mr Chan had a sum of money at first. He gave \\(\\dfrac{2}{5}\\) of it to his wife. He gave \\(\\dfrac{3}{4}\\) of the remainder to his two children. Each child received the same amount of money. Mr Chan saved the rest of his money. He saved $378. How much did Mr Chan give to each of his children? $[?]",
      "answer0": "567",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "After the wife: remainder = 3/5 of the money. He gave 3/4 of that to the children and saved the remaining 1/4 of the remainder. That saved 1/4 = $378, so the remainder = 4 × $378 = $1512. The children together got 3/4 × $1512 = $1134; shared between 2 children = $1134 ÷ 2 = $567 each.",
      "hints": ["The amount saved is 1/4 of the remainder after the wife's share.", "Find the remainder, then 3/4 of it, then split between 2 children."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q38",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q8 (renumbered to 38). Money answer -> FIB; '$' shown in stem. Printed key = $567 (each child). answer0 corrected to 567."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "A sofa cost $1850. Bala bought the sofa during a sale and a discount of 25% was given.<br>(a) What was the discounted price? $[?]<br>(b) Bala was charged 8% GST on the discounted price. How much did he pay for the sofa including GST? $[?]",
      "answer0": "1387.50",
      "answer1": "1498.50",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 2,
      "explanation": "(a) 25% discount means pay 75%: 1850 ÷ 4 = 462.50; 462.50 × 3 = $1387.50. (b) 8% GST on 1387.50 = 1387.50 ÷ 100 × 8 = $111; total = 1387.50 + 111 = $1498.50.",
      "hints": ["Discounted price = 75% of the original.", "GST adds 8% of the discounted price to the bill."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q39",
      "image_needed": true,
      "image_options": false,
      "image_file": "q39.png",
      "image_page": 29,
      "image_bbox": [0.10, 0.10, 0.80, 0.30],
      "image_loc": "drawing of a sofa with a SALE starburst (Original price $1850, 25% Discount), upper part of page",
      "notes": "Paper 2 Q9 (renumbered to 39). Both parts money -> FIB with 2 blanks. Key: a)$1387.50 b)$1498.50."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "At a carnival, a child ticket is $10 and an adult ticket is $25. The number of children was thrice the number of women. The number of women was twice the number of men. There were 210 children at the carnival. How much more was collected from the sale of adult tickets compared to child tickets? $[?]",
      "answer0": "525",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Children = 3 × women = 210, so women = 70. Women = 2 × men, so men = 35. Adults = women + men = 70 + 35 = 105. Adult collection = 105 × $25 = $2625. Child collection = 210 × $10 = $2100. Difference = 2625 − 2100 = $525.",
      "hints": ["Work out women from children, then men from women.", "Adults = women + men; compare adult and child ticket totals."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q40",
      "image_needed": true,
      "image_options": false,
      "image_file": "q40.png",
      "image_page": 30,
      "image_bbox": [0.30, 0.10, 0.66, 0.20],
      "image_loc": "small ticket-price table (Child $10, Adult $25) near top of page",
      "notes": "Paper 2 Q10 (renumbered to 40). Money answer -> FIB; '$' in stem. Key: $525."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "A container, when completely packed, can hold 20 identical bags. When the container is packed with 6 such bags, the mass of the container of bags is 4.71 kg. When the container is packed with 14 such bags, the mass of the container of bags is 8.31 kg.<br>(a) Find the mass of the empty container. [?] kg<br>(b) Find the mass of the container when it is completely packed. [?] kg",
      "answer0": "2.01",
      "answer1": "11.01",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "Difference of 14 − 6 = 8 bags weighs 8.31 − 4.71 = 3.60 kg, so 1 bag = 0.45 kg. (a) Empty container = 4.71 − 6 × 0.45 = 4.71 − 2.70 = 2.01 kg. (b) Full (20 bags) = 2.01 + 20 × 0.45 = 2.01 + 9.00 = 11.01 kg.",
      "hints": ["The mass difference comes from the extra bags (14 − 6 = 8 bags).", "Find one bag's mass, then back out the empty container."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q41",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q11 (renumbered to 41). Both parts numeric (kg) -> FIB with 2 blanks; 'kg' shown in stem. Key: a)2.01 b)11.01."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "In the figure, ACDE is a parallelogram and ABDE is a trapezium. \\(\\angle ABD = 114°\\), \\(\\angle BCD = 66°\\) and \\(\\angle AFE = 99°\\).<br>(a) Find \\(\\angle AED\\). [?]<br>(b) Find \\(\\angle FDB\\). [?]",
      "answer0": "66",
      "answer1": "51",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 200,
      "difficulty_id": 3,
      "explanation": "(a) In parallelogram ACDE, ∠AED = ∠ACD = 66° (opposite angles equal). (b) ∠FDE = 180° − 66° − 99° = 15° (angle sum of triangle FDE... ). ∠FDB = 180° − 114° − 15° = 51°.",
      "hints": ["Use the property that opposite angles of a parallelogram are equal.", "Use the angle sum of a triangle (180°) to find the remaining angles."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q42",
      "image_needed": true,
      "image_options": false,
      "image_file": "q42.png",
      "image_page": 32,
      "image_bbox": [0.26, 0.08, 0.74, 0.24],
      "image_loc": "parallelogram/trapezium figure with vertices A,B,C,D,E,F; angles 114°, 66°, 99° marked, top of page",
      "notes": "Paper 2 Q12 (renumbered to 42). Both parts numeric degrees -> FIB with 2 blanks; '°' on answer lines. Key: a)66° b)51°."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "XYZ is a piece of triangular paper with XY = YZ = XZ (equilateral). The triangular piece of paper is folded as shown. After folding, an angle of 77° is formed at the fold, and angles a and b are marked. Find \\(\\angle a\\). [?]",
      "answer0": "94",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "Each angle of the equilateral triangle is 60°. From the fold, ∠b = 180° − 77° − 60° = 43°. Then ∠a = 180° − 43° − 43° = 94°. Printed key: 94°.",
      "hints": ["An equilateral triangle has all angles 60°.", "Use angle sums of 180° in the triangles formed by the fold."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q43",
      "image_needed": true,
      "image_options": false,
      "image_file": "q43.png",
      "image_page": 33,
      "image_bbox": [0.10, 0.13, 0.92, 0.36],
      "image_loc": "two triangle diagrams (before folding XYZ, after folding with 77°, a, b marked), upper half of page",
      "notes": "Paper 2 Q13 (renumbered to 43). Numeric degrees answer -> FIB; '°' on answer line. Key: 94°."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "A container measures 15 cm by 15 cm by 8 cm. It contains water to a depth of 2 cm at first. The container was then placed below a leaking tap. The graph shows the volume of water that leaked into the container over 3 hours (about 450 cm³ at 6 a.m., 600 cm³ at 7 a.m., 750 cm³ at 8 a.m., 900 cm³ at 9 a.m.).<br>(a) What was the volume of water in the water tank at first? [?] cm³<br>(b) Water continued to leak into the container at the same rate. The container was removed from the tap when it was completely filled. At what time will the container be completely filled?",
      "answer0": "450",
      "answer1": "3 p.m.",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 191,
      "difficulty_id": 3,
      "explanation": "(a) Initial water = 2 × 15 × 15 = 450 cm³. (b) Leak rate: from 600 cm³ (7 a.m.) the reading rose 150 cm³ per hour, so 1 hour = 150 cm³. Full container = 8 × 15 × 15 = 1800 cm³; extra water needed = 1800 − 450 = 1350 cm³; time = 1350 ÷ 150 = 9 hours from 6 a.m. = 3 p.m.",
      "hints": ["Initial volume = depth × base area (2 × 15 × 15).", "Find the leak rate per hour, then how long to reach the full 1800 cm³."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q44",
      "image_needed": true,
      "image_options": false,
      "image_file": "q44.png",
      "image_page": 34,
      "image_bbox": [0.10, 0.36, 0.92, 0.66],
      "image_loc": "line graph of volume of water leaked vs time (6 a.m.–9 a.m.), middle of page (container diagram is above it)",
      "notes": "Paper 2 Q14 (renumbered to 44). (a) numeric cm³, (b) time-of-day. FIB with 2 blanks: blank0 = 450, blank1 = 3 p.m. (text time accepted). 'cm³' shown for part a in stem. Key: a)450 b)3 p.m."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "A pattern is made up of squares and circles. Figure 1 is made up of 1 square and 8 circles; Figure 2 is made up of 4 identical squares and 16 circles, and so on. Each figure has the same number of circles on one side.<br>(a) In which figure will there be 12 circles on each side of the figure? Figure [?]<br>(b) How many squares will there be in Figure 15? [?]<br>(c) Which figure contains 712 circles? Figure [?]",
      "answer0": "6",
      "answer1": "225",
      "answer2": "89",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "(a) The number of circles on one side is twice the figure number, so 12 circles per side -> 12 ÷ 2 = Figure 6. (b) The number of squares in Figure n is n × n, so Figure 15 = 15 × 15 = 225 squares. (c) Total circles in Figure n = 4 × (2n) = 8n... 712 ÷ 4 = 178, then 178 ÷ 2 = 89, so Figure 89 contains 712 circles.",
      "hints": ["(b) The number of squares is n × n for Figure n.", "(c) Total circles grow by a fixed multiple each figure; divide 712 down to the figure number."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q45",
      "image_needed": true,
      "image_options": false,
      "image_file": "q45.png",
      "image_page": 36,
      "image_bbox": [0.18, 0.08, 0.72, 0.92],
      "image_loc": "four pattern diagrams (Figure 1 to Figure 4) of squares bordered by circles, full page",
      "notes": "Paper 2 Q15 (renumbered to 45). Three numeric parts -> FIB with 3 blanks. Key: a)Figure 6 (12÷2=6), b)225 (15×15), c)Figure 89 (712÷4=178, 178÷2=89)."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "WXYZ is a square piece of paper of side 28 cm. Two identical squares and two identical isosceles triangles have been drawn and shaded on WXYZ. Find the unshaded area. [?] cm²",
      "answer0": "343",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Side 28 cm; the shaded shapes are two squares of side 14 cm and two isosceles triangles. One small square = 14 × 14 = 196 cm²; two squares = 392 cm². Each triangle = ½ × 7 × 7 = 24.5 cm²; two triangles = 49 cm². Total shaded = 392 + 49 = 441 cm². Whole square = 28 × 28 = 784 cm². Unshaded = 784 − 441 = 343 cm².",
      "hints": ["Find the area of the whole 28 cm square first.", "Subtract the two shaded squares and two shaded triangles."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q46",
      "image_needed": true,
      "image_options": false,
      "image_file": "q46.png",
      "image_page": 38,
      "image_bbox": [0.12, 0.12, 0.56, 0.36],
      "image_loc": "square WXYZ (28 cm) with two shaded squares and two shaded triangles, upper-left of page",
      "notes": "Paper 2 Q16 (renumbered to 46). Numeric area answer -> FIB; 'cm²' shown in stem. Key: 343 cm²."
    },
    {
      "n": 47,
      "type_id": 1,
      "question": "Anna, Brenda and Christine had some beads. Brenda had 176 more beads than Anna at first. Anna gave away \\(\\dfrac{2}{9}\\) of her beads, Brenda gave away \\(\\dfrac{4}{7}\\) of her beads and Christine received 29 more beads. In the end, all three girls had the same number of beads. Express the number of beads Anna had at first as a fraction of the total number of beads Brenda and Christine had at first. Leave your answer in the simplest form.",
      "answer0": "\\(\\dfrac{24}{59}\\)",
      "answer1": "\\(\\dfrac{216}{531}\\)",
      "answer2": "\\(\\dfrac{168}{531}\\)",
      "answer3": "\\(\\dfrac{59}{24}\\)",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Anna keeps 7/9 of her beads; Brenda keeps 3/7 of hers. Setting them equal: 7/9 × Anna = 3/7 × Brenda, so 21/27... gives 49 units (Anna) = 27 units (Brenda) after scaling. With Brenda = Anna + 176, solving gives Anna = 216 and Brenda = 392. Christine's first amount works out to 168 − ... The printed key: Anna at first = 216; Brenda + Christine at first = 531; 216/531 = 24/59 in simplest form.",
      "hints": ["After giving away, Anna has 7/9 and Brenda has 3/7 of their beads; set these equal.", "Use Brenda = Anna + 176 to find the actual numbers, then form the fraction and simplify."],
      "source": "Maha Bodhi 2023 P5 End-of-Year Exam Q47",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q17 (renumbered to 47). Fraction answer -> MCQ per spec. Printed key working gives 216/531 = 24/59 (simplest form). correct_answer = index 0 (24/59)."
    }
  ]
}