{
  "paper": {
    "school": "Nanyang",
    "year": 2024,
    "level": "P5",
    "label": "End-of-Year Exam",
    "source_prefix": "Nanyang 2024 P5 End-of-Year Exam",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "In the number 87.65, the digit ____________ is in the tenths place.",
      "answer0": "8",
      "answer1": "7",
      "answer2": "6",
      "answer3": "5",
      "correct_answer": 2,
      "skill_id": 123,
      "difficulty_id": 1,
      "explanation": "In 87.65, the digits after the decimal point are tenths then hundredths. The tenths place holds 6 and the hundredths place holds 5. So the digit 6 is in the tenths place. Answer: 6.",
      "hints": ["The first digit after the decimal point is the tenths place.", "87.65 = 8 tens, 7 ones, 6 tenths, 5 hundredths."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: (3) = 6"
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Express 7045 grams in kilograms.",
      "answer0": "7.045 kg",
      "answer1": "7.45 kg",
      "answer2": "70.45 kg",
      "answer3": "704.5 kg",
      "correct_answer": 0,
      "skill_id": 184,
      "difficulty_id": 1,
      "explanation": "1 kg = 1000 g, so divide grams by 1000. 7045 g ÷ 1000 = 7.045 kg. Answer: 7.045 kg.",
      "hints": ["1 kg = 1000 g.", "Dividing by 1000 moves the decimal point 3 places left."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: (1) = 7.045 kg"
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "In the square grid, which line is perpendicular to FD?",
      "answer0": "AF",
      "answer1": "BC",
      "answer2": "BE",
      "answer3": "ED",
      "correct_answer": 0,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "FD runs from F to D on the grid. The line that meets FD at a right angle (perpendicular) is AF. Answer: AF.",
      "hints": ["Perpendicular lines meet at 90°.", "Compare the grid slopes of each line against FD."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q3.png",
      "image_page": 4,
      "image_bbox": [0.33, 0.13, 0.73, 0.36],
      "image_loc": "square grid with points A,B,C,D,E,F near top of page",
      "notes": "Key: (1) = AF"
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "A printer can print 12 pages in 60 seconds. How long will this printer take to print 30 pages?",
      "answer0": "24 seconds",
      "answer1": "120 seconds",
      "answer2": "126 seconds",
      "answer3": "150 seconds",
      "correct_answer": 3,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "12 pages take 60 s, so 1 page takes 60 ÷ 12 = 5 s. 30 pages take 30 × 5 = 150 s. Answer: 150 seconds.",
      "hints": ["Find the time for 1 page first.", "60 ÷ 12 = 5 seconds per page."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: (4) = 150 seconds"
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "Susan baked 80 cupcakes. 56 of them were strawberry cupcakes and the rest were chocolate cupcakes. What percentage of the cupcakes baked were strawberry cupcakes?",
      "answer0": "24%",
      "answer1": "30%",
      "answer2": "56%",
      "answer3": "70%",
      "correct_answer": 3,
      "skill_id": 171,
      "difficulty_id": 2,
      "explanation": "Strawberry fraction = \\(\\dfrac{56}{80}\\). As a percentage: \\(\\dfrac{56}{80} \\times 100\\% = 70\\%\\). Answer: 70%.",
      "hints": ["Percentage = (part ÷ whole) × 100%.", "56 ÷ 80 × 100% = 70%."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: (4) = 70%"
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "Muthu had $220. He spent 20% of his money. How much money did he spend?",
      "answer0": "$11",
      "answer1": "$44",
      "answer2": "$176",
      "answer3": "$200",
      "correct_answer": 1,
      "skill_id": 174,
      "difficulty_id": 1,
      "explanation": "20% of $220 = \\(\\dfrac{20}{100} \\times 220 = 44\\). Answer: $44.",
      "hints": ["20% means 20 out of 100.", "$220 × 20 ÷ 100 = $44."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: (2) = $44"
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "In the figure, AEC is a straight line and BC is perpendicular to AC. AE = 8 cm, BE = 10 cm and BC = 7 cm. What is the area of triangle ABE?",
      "answer0": "28 cm²",
      "answer1": "40 cm²",
      "answer2": "56 cm²",
      "answer3": "80 cm²",
      "correct_answer": 0,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "Triangle ABE has base AE = 8 cm and the perpendicular height equals BC = 7 cm (since BC ⊥ AC and AEC is a straight line). Area = \\(\\dfrac{1}{2} \\times 8 \\times 7 = 28\\) cm². Answer: 28 cm².",
      "hints": ["Use base AE and the height BC.", "Area of triangle = ½ × base × height."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q7.png",
      "image_page": 6,
      "image_bbox": [0.27, 0.16, 0.62, 0.28],
      "image_loc": "triangle ABE figure with vertices A,E,C on baseline and B at top",
      "notes": "Key: (1) = 28 cm²"
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "In the square grids, which of the following is true for the triangles?",
      "answer0": "B is an obtuse-angled triangle.",
      "answer1": "C is an equilateral triangle.",
      "answer2": "A and D are isosceles triangles.",
      "answer3": "B and D are right-angled triangles.",
      "correct_answer": 2,
      "skill_id": 195,
      "difficulty_id": 2,
      "explanation": "Triangles A and D both have two equal sides, so they are isosceles. B is a right-angled triangle (not obtuse), C is not equilateral (its sides are not all equal), and D is not right-angled. Answer: A and D are isosceles triangles.",
      "hints": ["An isosceles triangle has two equal sides.", "Check each triangle's sides against the grid squares."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 6,
      "image_bbox": [0.2, 0.51, 0.82, 0.68],
      "image_loc": "four triangles A, B, C, D drawn on square grids in a row",
      "notes": "Key: (3) = A and D are isosceles triangles"
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "In a class of 45 children, 27 are girls and the rest are boys. What is the ratio of the number of boys to the number of girls?",
      "answer0": "2 : 3",
      "answer1": "3 : 2",
      "answer2": "3 : 5",
      "answer3": "5 : 3",
      "correct_answer": 0,
      "skill_id": 180,
      "difficulty_id": 2,
      "explanation": "Boys = 45 − 27 = 18. Ratio boys : girls = 18 : 27. Dividing both by 9 gives 2 : 3. Answer: 2 : 3.",
      "hints": ["Find the number of boys first: 45 − 27.", "Simplify 18 : 27 by dividing by 9."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: (1) = 2 : 3"
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "The figure shows a solid formed using 1-cm cubes. What is the volume of the solid?",
      "answer0": "9 cm³",
      "answer1": "10 cm³",
      "answer2": "12 cm³",
      "answer3": "13 cm³",
      "correct_answer": 3,
      "skill_id": 188,
      "difficulty_id": 2,
      "explanation": "Count the cubes: the bottom layer has 10 cubes and the top layer has 3 cubes, giving 10 + 3 = 13 cubes. Each cube is 1 cm³, so the volume is 13 cm³. Answer: 13 cm³.",
      "hints": ["Count layer by layer, including hidden cubes.", "Bottom layer = 10 cubes, top layer = 3 cubes."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 7,
      "image_bbox": [0.4, 0.41, 0.68, 0.56],
      "image_loc": "isometric drawing of a solid built from unit cubes, middle of page",
      "notes": "Count to verify = 13 cubes. Key: (4) = 13 cm³"
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "\\(\\dfrac{1}{3}\\) of a number is 15. What is the number?",
      "answer0": "5",
      "answer1": "12",
      "answer2": "18",
      "answer3": "45",
      "correct_answer": 3,
      "skill_id": 165,
      "difficulty_id": 1,
      "explanation": "If \\(\\dfrac{1}{3}\\) of the number is 15, the whole number is 15 × 3 = 45. Answer: 45.",
      "hints": ["The whole is 3 thirds.", "15 × 3 = 45."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: (4) = 45"
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "Arrange the following fractions from the smallest to the greatest.<br>\\(\\dfrac{1}{10}\\), \\(\\dfrac{2}{7}\\), \\(\\dfrac{1}{3}\\), \\(\\dfrac{2}{21}\\)",
      "answer0": "\\(\\dfrac{1}{3}\\), \\(\\dfrac{1}{10}\\), \\(\\dfrac{2}{7}\\), \\(\\dfrac{2}{21}\\)",
      "answer1": "\\(\\dfrac{2}{21}\\), \\(\\dfrac{2}{7}\\), \\(\\dfrac{1}{10}\\), \\(\\dfrac{1}{3}\\)",
      "answer2": "\\(\\dfrac{2}{21}\\), \\(\\dfrac{1}{10}\\), \\(\\dfrac{2}{7}\\), \\(\\dfrac{1}{3}\\)",
      "answer3": "\\(\\dfrac{1}{10}\\), \\(\\dfrac{1}{3}\\), \\(\\dfrac{2}{21}\\), \\(\\dfrac{2}{7}\\)",
      "correct_answer": 2,
      "skill_id": 159,
      "difficulty_id": 3,
      "explanation": "Rewrite with common comparisons: \\(\\dfrac{1}{10}=\\dfrac{2}{20}\\) and \\(\\dfrac{1}{3}=\\dfrac{2}{6}\\). Now all have numerator 2: \\(\\dfrac{2}{21}, \\dfrac{2}{20}, \\dfrac{2}{7}, \\dfrac{2}{6}\\). With the same numerator, a bigger denominator is a smaller fraction. So smallest to greatest: \\(\\dfrac{2}{21}, \\dfrac{1}{10}, \\dfrac{2}{7}, \\dfrac{1}{3}\\). Answer: option (3).",
      "hints": ["Make the numerators the same to compare.", "Same numerator: bigger denominator = smaller fraction."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: (3). Order: 2/21, 1/10, 2/7, 1/3"
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "Find the average of the following 5 numbers.<br>0, 24, 36, 36, 44",
      "answer0": "28",
      "answer1": "35",
      "answer2": "36",
      "answer3": "140",
      "correct_answer": 0,
      "skill_id": 203,
      "difficulty_id": 1,
      "explanation": "Total = 0 + 24 + 36 + 36 + 44 = 140. Average = 140 ÷ 5 = 28. Answer: 28.",
      "hints": ["Average = total ÷ number of items.", "Add all 5 numbers, then divide by 5."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Numbers shown in boxes: 0, 24, 36, 36, 44. Key: (1) = 28"
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "Peter made a total of 12 800 keychains in 40 weeks. The number of keychains he made each day from Monday to Wednesday was twice as many as the number of keychains he made each day from Thursday to Friday. He did not make any keychains on Saturdays and Sundays. How many keychains did he make every Friday?",
      "answer0": "32",
      "answer1": "40",
      "answer2": "46",
      "answer3": "64",
      "correct_answer": 1,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Per week = 12 800 ÷ 40 = 320 keychains. Let each Thu/Fri day = 1 unit, so each Mon–Wed day = 2 units. Weekly units = 3 days × 2u + 2 days × 1u = 6u + 2u = 8u = 320. So 1u = 320 ÷ 8 = 40. He made 40 keychains every Friday. Answer: 40.",
      "hints": ["First find the keychains made in 1 week.", "Mon–Wed = 2 units each, Thu–Fri = 1 unit each; total 8 units per week."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: (2) = 40"
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "A tank contained 5.4 ℓ of water. All the water was poured into three empty bottles. The first bottle contained twice as much water as the second bottle. The second bottle contained 3 times as much water as the third bottle. How much water was there in the second bottle?",
      "answer0": "2.70 ℓ",
      "answer1": "1.62 ℓ",
      "answer2": "0.90 ℓ",
      "answer3": "0.54 ℓ",
      "correct_answer": 1,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "Let the third bottle = 1 unit. Second = 3 units, first = 2 × second = 6 units. Total = 6 + 3 + 1 = 10 units = 5.4 ℓ, so 1 unit = 0.54 ℓ. The second bottle = 3 units = 3 × 0.54 = 1.62 ℓ. Answer: 1.62 ℓ.",
      "hints": ["Let the third bottle be 1 unit; second = 3 units; first = 6 units.", "Total 10 units = 5.4 ℓ, so 1 unit = 0.54 ℓ; second bottle = 3 units."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "PRINTED KEY ERROR: key circles (4) 0.54 l, which is the THIRD bottle (1 unit). The question asks for the SECOND bottle = 3 units = 1.62 l = option (2). Used the mathematically correct value: correct_answer = 1 (1.62 l)."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Find the value of (87 − 3 × 7) ÷ 6 − (2 + 2).<br>[?]",
      "answer0": "7",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 155,
      "difficulty_id": 2,
      "explanation": "Work brackets and order of operations: (87 − 21) ÷ 6 − 4 = 66 ÷ 6 − 4 = 11 − 4 = 7. Answer: 7.",
      "hints": ["Do brackets and multiplication first.", "87 − 3×7 = 66; 66 ÷ 6 = 11; 11 − 4 = 7."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 7"
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "Find the value of 3 ÷ 8. Express your answer as a decimal.<br>[?]",
      "answer0": "0.375",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 158,
      "difficulty_id": 1,
      "explanation": "3 ÷ 8 = \\(\\dfrac{3 \\times 125}{8 \\times 125} = \\dfrac{375}{1000} = 0.375\\). Answer: 0.375.",
      "hints": ["Convert the fraction to thousandths.", "\\(\\dfrac{3}{8} = \\dfrac{375}{1000} = 0.375\\)."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 0.375"
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "In the figure, AOC and BOE are straight lines. \\(\\angle\\)AOE = 31° and \\(\\angle\\)DOE = 90°. Find \\(\\angle\\)COD.<br>[?]",
      "answer0": "59",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "\\(\\angle\\)AOE and \\(\\angle\\)COD are angles on the straight line AOC together with \\(\\angle\\)DOE. \\(\\angle\\)COD = 180° − \\(\\angle\\)DOE − \\(\\angle\\)AOE = 180° − 90° − 31° = 59°. Answer: 59°.",
      "hints": ["Angles on a straight line add up to 180°.", "180° − 90° − 31° = 59°."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q18",
      "image_needed": true,
      "image_options": false,
      "image_file": "q18.png",
      "image_page": 13,
      "image_bbox": [0.24, 0.17, 0.82, 0.32],
      "image_loc": "two crossing straight lines through point O with rays to A,B,C,D,E",
      "notes": "Answer in degrees. Key: 59"
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "XYZ is a triangle. \\(\\angle\\)XYZ = 84° and \\(\\angle\\)YZX = 43°. Find \\(\\angle\\)ZXY.<br>[?]",
      "answer0": "53",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 1,
      "explanation": "Angles in a triangle add to 180°. \\(\\angle\\)ZXY = 180° − 84° − 43° = 180° − 127° = 53°. Answer: 53°.",
      "hints": ["The three angles of a triangle sum to 180°.", "180° − 84° − 43° = 53°."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q19",
      "image_needed": true,
      "image_options": false,
      "image_file": "q19.png",
      "image_page": 13,
      "image_bbox": [0.24, 0.5, 0.82, 0.74],
      "image_loc": "triangle XYZ with 84° at Y and 43° at Z",
      "notes": "Answer in degrees. Key: 53"
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "What is the missing number in the box?<br>[?] : 9 = 54 : 81",
      "answer0": "6",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 181,
      "difficulty_id": 2,
      "explanation": "54 : 81 simplifies (÷9) to 6 : 9. So the missing number is 6. (Check: 54 ÷ 9 = 6, 81 ÷ 9 = 9.) Answer: 6.",
      "hints": ["Simplify 54 : 81 by dividing both by 9.", "The second term 81 becomes 9, so the first term 54 becomes 6."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q20",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 6"
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "A cuboid of height 15 cm has a square base of 6 cm. What is the volume of the cuboid?<br>[?] cm³",
      "answer0": "540",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 190,
      "difficulty_id": 2,
      "explanation": "Volume = length × width × height = 6 × 6 × 15 = 540 cm³. Answer: 540 cm³.",
      "hints": ["Square base means length = width = 6 cm.", "6 × 6 × 15 = 540."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q21",
      "image_needed": true,
      "image_options": false,
      "image_file": "q21.png",
      "image_page": 14,
      "image_bbox": [0.2, 0.4, 0.42, 0.57],
      "image_loc": "tall cuboid labelled 15 cm height and 6 cm base, left side of page",
      "notes": "Answer in cm³. Key: 540"
    },
    {
      "n": 22,
      "type_id": 1,
      "question": "What is the product of \\(\\dfrac{2}{7}\\) and \\(\\dfrac{5}{12}\\)? Express your answer as a fraction in the simplest form.",
      "answer0": "\\(\\dfrac{5}{42}\\)",
      "answer1": "\\(\\dfrac{7}{42}\\)",
      "answer2": "\\(\\dfrac{10}{84}\\)",
      "answer3": "\\(\\dfrac{5}{84}\\)",
      "correct_answer": 0,
      "skill_id": 161,
      "difficulty_id": 2,
      "explanation": "\\(\\dfrac{2}{7} \\times \\dfrac{5}{12} = \\dfrac{2 \\times 5}{7 \\times 12} = \\dfrac{10}{84}\\). Simplify by dividing by 2: \\(\\dfrac{5}{42}\\). Answer: \\(\\dfrac{5}{42}\\).",
      "hints": ["Multiply numerators together and denominators together.", "Cancel the 2 with 12 before multiplying: \\(\\dfrac{2}{12}=\\dfrac{1}{6}\\)."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q22",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Fraction answer -> MCQ. Key: 5/42"
    },
    {
      "n": 23,
      "type_id": 1,
      "question": "Ahmad bought 4 bottles of oil. Each bottle contained \\(\\dfrac{3}{4}\\) litres of oil. He then used \\(\\dfrac{3}{10}\\) litres of oil. How many litres of oil had Ahmad left?",
      "answer0": "\\(2\\dfrac{7}{10}\\)",
      "answer1": "\\(3\\dfrac{3}{10}\\)",
      "answer2": "\\(2\\dfrac{3}{10}\\)",
      "answer3": "\\(3\\dfrac{7}{10}\\)",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "Total bought = 4 × \\(\\dfrac{3}{4}\\) = 3 litres. After using \\(\\dfrac{3}{10}\\): 3 − \\(\\dfrac{3}{10}\\) = \\(2\\dfrac{10}{10} - \\dfrac{3}{10} = 2\\dfrac{7}{10}\\) litres. Answer: \\(2\\dfrac{7}{10}\\) litres.",
      "hints": ["First find the total oil bought: 4 × ¾ = 3 litres.", "Subtract \\(\\dfrac{3}{10}\\) from 3."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q23",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Mixed-number answer -> MCQ. Key: 2 7/10"
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "In the figure, ABCD is a parallelogram. \\(\\angle\\)ABC = 62°. Find \\(\\angle\\)DAB.<br>[?]",
      "answer0": "118",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 200,
      "difficulty_id": 2,
      "explanation": "In a parallelogram, co-interior angles between parallel sides add up to 180°. \\(\\angle\\)DAB = 180° − \\(\\angle\\)ABC = 180° − 62° = 118°. Answer: 118°.",
      "hints": ["Angles ABC and DAB are co-interior (interior) angles.", "180° − 62° = 118°."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q24",
      "image_needed": true,
      "image_options": false,
      "image_file": "q24.png",
      "image_page": 15,
      "image_bbox": [0.32, 0.45, 0.78, 0.62],
      "image_loc": "parallelogram ABCD with 62° marked at B",
      "notes": "Answer in degrees. Key: 118"
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "A tin of paint costs $24.50. Steve needs to buy 7 tins of paint, but he is short of $5. How much money does Steve have?<br>$[?]",
      "answer0": "166.50",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 2,
      "explanation": "Cost of 7 tins = $24.50 × 7 = $171.50. Steve is short of $5, so he has $171.50 − $5 = $166.50. Answer: $166.50.",
      "hints": ["Find the cost of 7 tins first.", "He has $5 less than the total cost."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q25",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Money answer in dollars. Key: $166.50"
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "A factory produced some toys. All the toys were placed into boxes of 65 with no left over. There were 396 such boxes. Round the number of toys produced by the factory to the nearest thousand.<br>[?]",
      "answer0": "26000",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 150,
      "difficulty_id": 2,
      "explanation": "Total toys = 65 × 396 = 25 740. Rounded to the nearest thousand: 25 740 ≈ 26 000 (since the hundreds digit 7 ≥ 5, round up). Answer: 26 000.",
      "hints": ["First find the total: 65 × 396.", "25 740 rounds up to 26 000."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q26",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 26000"
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "What is the price of the backpack after a discount of 8%? Usual price: $50<br>$[?]",
      "answer0": "46",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 2,
      "explanation": "Discount = 8% of $50 = \\(\\dfrac{8}{100} \\times 50 = 4\\). Price after discount = $50 − $4 = $46. Answer: $46.",
      "hints": ["Find 8% of $50 first.", "Subtract the discount from the usual price."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q27",
      "image_needed": true,
      "image_options": false,
      "image_file": "q27.png",
      "image_page": 16,
      "image_bbox": [0.43, 0.57, 0.57, 0.67],
      "image_loc": "small backpack icon with 'Usual price: $50' below it, centre of page",
      "notes": "Money answer in dollars. Key: $46"
    },
    {
      "n": 28,
      "type_id": 0,
      "question": "Louis built a solid using 8 unit cubes. Draw the front view and the side view of the solid on the grids.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 188,
      "difficulty_id": 2,
      "explanation": "From the printed key, the front view is an L-shape: a bottom row of 2 squares with 1 square stacked on the left (an upright two-step shape), and the side view is a staircase of squares (2 squares on the bottom with 1 on top forming steps). This is a draw-on-grid task with no single value answer.",
      "hints": ["The front view shows what you see looking from the front arrow.", "The side view shows what you see looking from the side arrow."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q28",
      "image_needed": true,
      "image_options": false,
      "image_file": "q28.png",
      "image_page": 17,
      "image_bbox": [0.4, 0.16, 0.66, 0.39],
      "image_loc": "isometric solid of 8 unit cubes with Top/Front/Side view arrows",
      "notes": "DRAW task (front/side view on grids) -> type_id 0, skipped on insert. Key shows front view = two-step L; side view = staircase shape."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "A rectangle is made up of 4 triangles E, F, G and H. The area of triangle F is 3 times the area of triangle H. The area of triangle H is 12 cm². What is the area of the rectangle?<br>[?] cm²",
      "answer0": "96",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Let triangle H = 1 unit = 12 cm², so triangle F = 3 units = 36 cm². Triangles F and H together lie along the base and make up half the rectangle, while E and G make up the other half. F + H = 4 units, and this equals half the rectangle, so the whole rectangle = 4 units × 2 = 8 units. 1 unit = 12 cm², so the rectangle = 8 × 12 = 96 cm². Answer: 96 cm².",
      "hints": ["Let H be 1 unit (12 cm²); then F is 3 units.", "F + H is half the rectangle, so the rectangle is 8 units."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q29",
      "image_needed": true,
      "image_options": false,
      "image_file": "q29.png",
      "image_page": 18,
      "image_bbox": [0.33, 0.15, 0.72, 0.3],
      "image_loc": "rectangle divided into 4 triangles labelled E, F, G, H",
      "notes": "Answer in cm². Key: 96"
    },
    {
      "n": 30,
      "type_id": 2,
      "question": "At first, the average number of coins owned by a group of boys was 7. A new boy who owned 63 coins joined the group and the new average number of coins owned by the boys became 11. How many boys were there at first?<br>[?]",
      "answer0": "13",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 205,
      "difficulty_id": 3,
      "explanation": "The new boy raised the average from 7 to 11 (a rise of 4 per boy). His 63 coins are 63 − 11 = 52 coins above the new average of 11. These 52 'extra' coins were spread to raise everyone (including himself implicitly) — distributing 52 over the rise of 4 gives 52 ÷ 4 = 13 boys at first. Answer: 13.",
      "hints": ["The new average is 11; the new boy has 63 − 11 = 52 above it.", "Each existing boy's average rose by 11 − 7 = 4; 52 ÷ 4 = 13."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q30",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 13"
    },
    {
      "n": 31,
      "type_id": 1,
      "question": "Mr Tan used \\(2\\dfrac{1}{8}\\) ℓ of water on Monday. He used \\(3\\dfrac{2}{5}\\) ℓ of water on Tuesday. How much water did Mr Tan use on both days? Give your answer as a mixed number in the simplest form.",
      "answer0": "\\(5\\dfrac{21}{40}\\)",
      "answer1": "\\(5\\dfrac{3}{13}\\)",
      "answer2": "\\(5\\dfrac{17}{40}\\)",
      "answer3": "\\(6\\dfrac{1}{40}\\)",
      "correct_answer": 0,
      "skill_id": 160,
      "difficulty_id": 2,
      "explanation": "\\(2\\dfrac{1}{8} + 3\\dfrac{2}{5}\\). Whole numbers: 2 + 3 = 5. Fractions: \\(\\dfrac{1}{8} + \\dfrac{2}{5} = \\dfrac{5}{40} + \\dfrac{16}{40} = \\dfrac{21}{40}\\). Total = \\(5\\dfrac{21}{40}\\) ℓ. Answer: \\(5\\dfrac{21}{40}\\) ℓ.",
      "hints": ["Add the whole numbers and fractions separately.", "Common denominator of 8 and 5 is 40."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q31",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q1. Mixed-number answer -> MCQ. Key: 5 21/40"
    },
    {
      "n": 32,
      "type_id": 1,
      "question": "Sandy jogged \\(4\\dfrac{4}{5}\\) km each day last week. What was the total distance she jogged from Wednesday to Saturday last week? Give your answer as a mixed number in the simplest form.",
      "answer0": "\\(19\\dfrac{1}{5}\\)",
      "answer1": "\\(14\\dfrac{2}{5}\\)",
      "answer2": "\\(24\\)",
      "answer3": "\\(19\\dfrac{4}{5}\\)",
      "correct_answer": 0,
      "skill_id": 163,
      "difficulty_id": 2,
      "explanation": "Wednesday to Saturday is 4 days. Total = \\(4\\dfrac{4}{5} \\times 4 = \\dfrac{24}{5} \\times 4 = \\dfrac{96}{5} = 19\\dfrac{1}{5}\\) km. Answer: \\(19\\dfrac{1}{5}\\) km.",
      "hints": ["Wed, Thu, Fri, Sat = 4 days.", "\\(4\\dfrac{4}{5} = \\dfrac{24}{5}\\); multiply by 4."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q32",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q2. Mixed-number answer -> MCQ. Key: 19 1/5"
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "The average mass of 6 girls and 1 boy is 47 kg. The average mass of the girls is 45 kg. What is the mass of the boy?<br>[?] kg",
      "answer0": "59",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 204,
      "difficulty_id": 2,
      "explanation": "Total mass of all 7 = 47 × 7 = 329 kg... using the printed key: 47 × 7 = 329; total mass of 6 girls = 45 × 6 = 270 kg; boy = 329 − 270 = 59 kg. Answer: 59 kg.",
      "hints": ["Total of all 7 = average × 7.", "Total of girls = 45 × 6; subtract from the grand total."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q33",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q3. Answer in kg. Printed key writes 47x7=325 (arithmetic slip; 47x7=329) but 329-270=59 matches the boxed answer 59. Key: 59"
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "ACD is a right-angled triangle. \\(\\angle\\)ADC = 90°. BD = CD. Find \\(\\angle\\)ADB.<br>[?]",
      "answer0": "28",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "\\(\\angle\\)DBC = 121° is the exterior angle at B; the interior \\(\\angle\\)DBC of triangle BDC = 180° − 121° = 59°. Since BD = CD, triangle BDC is isosceles with \\(\\angle\\)DBC = \\(\\angle\\)BCD = 59°. So \\(\\angle\\)BDC = 180° − 59° − 59° = 62°. Then \\(\\angle\\)ADB = \\(\\angle\\)ADC − \\(\\angle\\)BDC = 90° − 62° = 28°. Answer: 28°.",
      "hints": ["121° at B is the exterior angle; the angle inside triangle BDC is 180° − 121° = 59°.", "BD = CD makes triangle BDC isosceles; then ∠ADB = 90° − ∠BDC."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q34",
      "image_needed": true,
      "image_options": false,
      "image_file": "q34.png",
      "image_page": 21,
      "image_bbox": [0.2, 0.15, 0.72, 0.6],
      "image_loc": "large right-angled triangle ACD with B on AC, 121° marked at B, right angle at D",
      "notes": "Paper 2 Q4. Answer in degrees. Key: 28"
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "Meili has a roll of ribbon to give to a group of friends. If she gives 0.7 m of ribbon to each of her friends, she will have 0.4 m of ribbon left. If she gives 0.8 m of ribbon to each of her friends, she will be short of 0.3 m of ribbon. What is the length of the roll of ribbon Meili has?<br>[?] m",
      "answer0": "5.3",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "The difference per friend between the two scenarios is 0.8 − 0.7 = 0.1 m. The total difference in ribbon needed is 0.4 + 0.3 = 0.7 m (0.4 left over versus 0.3 short). Number of friends = 0.7 ÷ 0.1 = 7. Length of roll = 7 × 0.7 + 0.4 = 4.9 + 0.4 = 5.3 m. Answer: 5.3 m.",
      "hints": ["Compare the two scenarios: extra needed per friend is 0.1 m.", "Total extra = 0.4 + 0.3 = 0.7 m; friends = 0.7 ÷ 0.1 = 7."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q35",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q5. Answer in m. Key: 5.3"
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "The line graph shows the amount of money Liling saved each week over a period of 4 weeks.<br>(a) In which week did Liling save twice the amount of money she saved in Week 3? Week [?]<br>(b) How much did Liling save in Week 4? $[?]<br>(c) How much less money did Liling save in Week 1 than in Week 2? $[?]",
      "answer0": "2",
      "answer1": "60",
      "answer2": "24",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 147,
      "difficulty_id": 2,
      "explanation": "From the graph: Week 1 = $16, Week 2 = $40, Week 3 = $20, Week 4 = $60. (a) Twice Week 3 = 2 × $20 = $40, which is Week 2. (b) Week 4 = $60. (c) Week 2 − Week 1 = $40 − $16 = $24. Answers: (a) Week 2, (b) $60, (c) $24.",
      "hints": ["Read each week's value off the line graph.", "Week 3 = $20, so twice is $40."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q36",
      "image_needed": true,
      "image_options": false,
      "image_file": "q36.png",
      "image_page": 23,
      "image_bbox": [0.14, 0.26, 0.85, 0.46],
      "image_loc": "line graph of 'Amount Liling saved ($)' vs Week 1-4",
      "notes": "Paper 2 Q6. 3 blanks. Key: (a) Week 2, (b) $60, (c) $24"
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "Two apples cost $0.30 more than a pear. The pear costs $0.45 more than each apple. How much will 2 such pears and 1 such apple cost altogether?<br>$[?]",
      "answer0": "3.15",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "2 apples = 1 pear + $0.30, and 1 pear = 1 apple + $0.45. Substituting: 2 apples = (apple + 0.45) + 0.30, so apple + 0.45 + 0.30 = 2 apples, giving 1 apple = $0.75. Then 1 pear = 0.75 + 0.45 = $1.20. Cost of 2 pears + 1 apple = 1.20 × 2 + 0.75 = 2.40 + 0.75 = $3.15. Answer: $3.15.",
      "hints": ["Let 1 apple = a. Two apples cost a pear plus $0.30.", "1 pear = 1 apple + $0.45; solve for the apple first."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q37",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q7. Money answer in dollars. Key: $3.15"
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "At first, Mary had 60 erasers and 85 pencils. After she gave away some erasers and 20% of the pencils, she had a total of 118 erasers and pencils left. How many erasers did Mary give away?<br>[?]",
      "answer0": "10",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 175,
      "difficulty_id": 3,
      "explanation": "20% of 85 pencils = 17 pencils given away, so pencils left = 85 − 17 = 68. Total left = 118, so erasers left = 118 − 68 = 50. Erasers given away = 60 − 50 = 10. Answer: 10.",
      "hints": ["Find 20% of 85 pencils first.", "Pencils left = 68; erasers left = 118 − 68 = 50."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q38",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q8. Key: 10"
    },
    {
      "n": 39,
      "type_id": 0,
      "question": "Lines PQ and QR are drawn on a square grid inside a box. By joining dots on the grid with straight lines, (a) draw a trapezium PQRS such that PQ is parallel to SR and SR is twice the length of PQ. (b) draw a rhombus QRYZ such that it does not overlap with trapezium PQRS.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 201,
      "difficulty_id": 3,
      "explanation": "This is a construction/drawing task on a dot grid. (a) Add point S so that SR is parallel to PQ and twice its length, forming trapezium PQRS. (b) Add points Y and Z so QRYZ is a rhombus (all four sides equal) positioned not to overlap PQRS. The printed key notes more than one correct answer is possible.",
      "hints": ["A trapezium has one pair of parallel sides.", "A rhombus has 4 equal sides."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q39",
      "image_needed": true,
      "image_options": false,
      "image_file": "q39.png",
      "image_page": 25,
      "image_bbox": [0.22, 0.13, 0.85, 0.48],
      "image_loc": "large dot grid with points P, Q, R marked and lines PQ, QR drawn",
      "notes": "Paper 2 Q9. DRAW-on-grid task -> type_id 0, skipped on insert. Key: more than 1 possible answer."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "A bag contained some green balls and some yellow balls in the ratio 4 : 11. The number of green balls in the bag is 180. How many yellow balls are there in the bag?<br>[?]",
      "answer0": "495",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 182,
      "difficulty_id": 2,
      "explanation": "Green : Yellow = 4 : 11. 4 units = 180 green balls, so 1 unit = 180 ÷ 4 = 45. Yellow = 11 units = 11 × 45 = 495. Answer: 495.",
      "hints": ["4 units represent the 180 green balls.", "1 unit = 45; yellow = 11 units."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q40",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q10(a) only. Part (b) is a true/false/not-possible-to-tell tick table (interactive) -> not an answerable value, omitted. (b) answers per key: S1 False, S2 not possible to tell, S3 True. Key (a): 495"
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "Sam read 35 pages more than \\(\\dfrac{2}{7}\\) of his storybook. There were 175 pages left to be read.<br>(a) What was the total number of pages in his storybook? [?]<br>(b) How many pages did Sam read? [?]",
      "answer0": "294",
      "answer1": "119",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Sam read \\(\\dfrac{2}{7}\\) of the book + 35 pages. Pages left = 175. The remaining 175 pages plus the extra 35 pages make up the other \\(\\dfrac{5}{7}\\) of the book: 175 + 35 = 210 = \\(\\dfrac{5}{7}\\) of the book. So 1 unit (\\(\\dfrac{1}{7}\\)) = 210 ÷ 5 = 42, and the total = 7 units = 7 × 42 = 294 pages. (b) Pages read = total − pages left = 294 − 175 = 119 (or \\(\\dfrac{2}{7}\\) of 294 + 35 = 84 + 35 = 119). Answers: (a) 294, (b) 119.",
      "hints": ["The 35 extra pages plus the 175 left make up 5/7 of the book.", "175 + 35 = 210 = 5 units, so 1 unit = 42."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q41",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q11. 2 blanks. Key: (a) 294, (b) 119"
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "Kevin had a pail containing 6500 ml of water. He poured water from the pail into an empty rectangular container measuring 15 cm by 10 cm by 8 cm until the rectangular container was \\(\\dfrac{5}{6}\\) filled with water.<br>(a) Find the volume of water Kevin poured into the rectangular container. [?] cm³<br>(b) The remaining amount of water left in the pail was then poured into empty identical bottles. Each bottle was filled to the brim. The capacity of each bottle was 575 ml. How many such bottles were completely filled with water? [?]",
      "answer0": "1000",
      "answer1": "9",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 191,
      "difficulty_id": 3,
      "explanation": "(a) Full container volume = 15 × 10 × 8 = 1200 cm³. Water poured = \\(\\dfrac{5}{6}\\) × 1200 = 1000 cm³ (= 1000 ml). (b) Remaining water = 6500 − 1000 = 5500 ml. Bottles completely filled = 5500 ÷ 575 = 9.56…, so 9 bottles were completely filled. Answers: (a) 1000 cm³, (b) 9.",
      "hints": ["Container full volume = 15 × 10 × 8; take 5/6 of it.", "Remaining = 6500 − 1000; divide by 575 and take the whole number."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q42",
      "image_needed": true,
      "image_options": false,
      "image_file": "q42.png",
      "image_page": 28,
      "image_bbox": [0.33, 0.17, 0.68, 0.34],
      "image_loc": "rectangular container partly filled with water, labelled 15 cm, 10 cm, 8 cm",
      "notes": "Paper 2 Q12. 2 blanks. Key: (a) 1000 cm³, (b) 9"
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "A factory worker packed 880 marbles into four boxes, A, B, C and D. Box A had the greatest number of marbles and Box D had the least number of marbles. The difference in the number of marbles between Box A and the number of marbles in the other three boxes were 14, 114 and 312.<br>(a) Find the difference in the number of marbles between Box B and Box C. [?]<br>(b) How many marbles were there in Box D? [?]",
      "answer0": "100",
      "answer1": "18",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Box A is the greatest. A − B = 14, A − C = 114, A − D = 312 (B is next largest, then C, then D smallest). (a) Difference between B and C = 114 − 14 = 100. (b) Total: A + B + C + D = 880. B = A − 14, C = A − 114, D = A − 312. So 4A − (14 + 114 + 312) = 880, i.e. 4A − 440 = 880, 4A = 1320, A = 330. Box D = 330 − 312 = 18. Answers: (a) 100, (b) 18.",
      "hints": ["B = A − 14, C = A − 114, D = A − 312.", "Sum all four: 4A − 440 = 880, so A = 330."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q43",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q13. 2 blanks. Key: (a) 100, (b) 18"
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "The outline of figure ABDEHG is formed by a square, a rectangle and 2 triangles. BCD, GJE and GFC are straight lines. EG = 13 cm, FG = 12 cm, HJ = 3 cm and BC = CD = 5 cm.<br>(a) Find the area of triangle GHE. [?] cm²<br>(b) Find the area of figure ABDEHG. [?] cm²",
      "answer0": "19.5",
      "answer1": "120.5",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "(a) Triangle GHE has base GE = 13 cm and height HJ = 3 cm. Area = \\(\\dfrac{1}{2}\\) × 13 × 3 = 19.5 cm². (b) Triangle GFE (base GE = 13, height FG = 12): area = \\(\\dfrac{1}{2}\\) × 13 × 12 = ... using the key's working: area of triangle GFE = \\(\\dfrac{1}{2}\\) × 12 × 5 = 30 cm²; square FCDE = 5 × 5 = 25 cm²; rectangle ABCG = (12 + 5) × 5 = 85 cm². Area of the notch (GFE − GHE) = 30 − 19.5 = 10.5. Total figure = 10.5 + 25 + 85 = 120.5 cm². Answers: (a) 19.5 cm², (b) 120.5 cm².",
      "hints": ["Triangle GHE: base GE = 13 cm, height HJ = 3 cm.", "Add the square, rectangle, and the triangular region per the figure."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q44",
      "image_needed": true,
      "image_options": false,
      "image_file": "q44.png",
      "image_page": 30,
      "image_bbox": [0.2, 0.14, 0.68, 0.32],
      "image_loc": "composite figure ABDEHG with points A,B,C,D,E,F,G,H,J and measurements 12cm, 13cm, 3cm, 5cm",
      "notes": "Paper 2 Q14. 2 blanks. Key: (a) 19.5 cm², (b) 120.5 cm²"
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "In the figure, ABCD is a rhombus. AE = CD and \\(\\angle\\)ADC = 68°.<br>(a) Find \\(\\angle\\)DAC. [?]<br>(b) Find \\(\\angle\\)CAE. [?]",
      "answer0": "56",
      "answer1": "12",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 200,
      "difficulty_id": 3,
      "explanation": "(a) In rhombus ABCD, AD = CD, so triangle ADC is isosceles with \\(\\angle\\)ADC = 68°. \\(\\angle\\)DAC = \\(\\angle\\)DCA = (180° − 68°) ÷ 2 = 56°. (b) \\(\\angle\\)BAC = \\(\\angle\\)DCA = 56° (alternate angles). \\(\\angle\\)ABC = \\(\\angle\\)ADC = 68° (opposite angles of rhombus). Since AE = CD = AB, triangle ABE is isosceles with \\(\\angle\\)ABE = \\(\\angle\\)AEB = 68°, so \\(\\angle\\)EAB = 180° − 68° − 68° = 44°. Then \\(\\angle\\)CAE = \\(\\angle\\)BAC − \\(\\angle\\)EAB = 56° − 44° = 12°. Answers: (a) 56°, (b) 12°.",
      "hints": ["Triangle ADC is isosceles (AD = CD); use ∠ADC = 68°.", "AE = CD = AB makes triangle ABE isosceles; find ∠EAB then subtract."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q45",
      "image_needed": true,
      "image_options": false,
      "image_file": "q45.png",
      "image_page": 31,
      "image_bbox": [0.24, 0.12, 0.74, 0.32],
      "image_loc": "rhombus ABCD with point E near C, 68° marked at D",
      "notes": "Paper 2 Q15. 2 blanks. Key: (a) 56°, (b) 12°"
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "A tap was turned on to fill an empty 68-litre tank. It took 8 minutes to fill the tank completely.<br>(a) What was the rate of flow of water from the tap in litres per minute? [?]<br>(b) The same tap was used to fill an empty 700-litre tank and was turned off after 75 minutes. How much more water was needed to completely fill the 700-litre tank? [?]",
      "answer0": "8.5",
      "answer1": "62.5",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 193,
      "difficulty_id": 3,
      "explanation": "(a) Rate = 68 ℓ ÷ 8 min = 8.5 ℓ/min. (b) In 75 minutes the tap delivers 8.5 × 75 = 637.5 ℓ. Water still needed = 700 − 637.5 = 62.5 ℓ. Answers: (a) 8.5 ℓ/min, (b) 62.5 ℓ.",
      "hints": ["Rate = volume ÷ time = 68 ÷ 8.", "Water in 75 min = rate × 75; subtract from 700."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q46",
      "image_needed": true,
      "image_options": false,
      "image_file": "q46.png",
      "image_page": 32,
      "image_bbox": [0.2, 0.13, 0.82, 0.31],
      "image_loc": "tap with small 68-litre cube tank and large 700-litre cuboid tank",
      "notes": "Paper 2 Q16. 2 blanks. (a) in litres per minute, (b) in litres. Key: (a) 8.5, (b) 62.5"
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "Eric uses grey squares and white squares to form figures that follow a pattern. The table shows the number of grey squares, white squares and total squares for Figures 1 to 5.<br>(a) Complete the table for Figure 6: total number of squares. [?]<br>(b) Find the number of white squares in Figure 10. [?]<br>(c) Find the total number of squares in Figure 77. [?]",
      "answer0": "21",
      "answer1": "25",
      "answer2": "3003",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Total squares follow triangular numbers: 1, 3, 6, 10, 15, ... (a) Figure 6 total = 15 + 6 = 21. (b) White squares: for an even figure number n, white = (n ÷ 2)². For Figure 10: (10 ÷ 2)² = 5² = 25. (c) Total in Figure n = 1 + 2 + ... + n. For Figure 77: 1 + 2 + ... + 77 = (77 + 1) × 38 + 77 = (78 × 38) + 77 = 2964 + ... using the key's grouping: pairs sum to 78, with 38 pairs plus the middle term 77, giving 3003. Answers: (a) 21, (b) 25, (c) 3003.",
      "hints": ["Total squares are triangular numbers: each figure adds the next counting number.", "Sum 1+2+...+77 = (77×78)/2 = 3003."],
      "source": "Nanyang 2024 P5 End-of-Year Exam Q47",
      "image_needed": true,
      "image_options": false,
      "image_file": "q47.png",
      "image_page": 33,
      "image_bbox": [0.22, 0.13, 0.85, 0.25],
      "image_loc": "row of 5 grey-and-white square pattern figures (Figure 1 to Figure 5)",
      "notes": "Paper 2 Q17. 3 blanks. Key: (a) 21, (b) 25, (c) 3003"
    }
  ]
}