{
  "paper": {
    "school": "Nan Hua",
    "year": 2023,
    "level": "P5",
    "label": "End-of-Year Exam",
    "source_prefix": "Nan Hua 2023 P5 End-of-Year Exam",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "Which of the following is eighty thousand and two hundred in numerals?",
      "answer0": "8200",
      "answer1": "80 200",
      "answer2": "800 200",
      "answer3": "820 000",
      "correct_answer": 1,
      "skill_id": 149,
      "difficulty_id": 1,
      "explanation": "Eighty thousand = 80 000; two hundred = 200. So 80 000 + 200 = 80 200. Answer: 80 200.",
      "hints": ["Eighty thousand is 80 000.", "Add two hundred (200) to 80 000."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option (2)"
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Express \\(1\\dfrac{1}{50}\\) as a decimal.",
      "answer0": "1.02",
      "answer1": "1.15",
      "answer2": "1.2",
      "answer3": "1.5",
      "correct_answer": 0,
      "skill_id": 158,
      "difficulty_id": 1,
      "explanation": "\\(\\dfrac{1}{50}=\\dfrac{2}{100}=0.02\\). So \\(1\\dfrac{1}{50}=1.02\\). Answer: 1.02.",
      "hints": ["Convert \\(\\dfrac{1}{50}\\) to hundredths: multiply top and bottom by 2.", "\\(\\dfrac{2}{100}=0.02\\)."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option (1)"
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Mr Tan takes 8 seconds to type 9 words. At the same rate, how long will he take to type 27 words?",
      "answer0": "16 seconds",
      "answer1": "24 seconds",
      "answer2": "26 seconds",
      "answer3": "32 seconds",
      "correct_answer": 1,
      "skill_id": 152,
      "difficulty_id": 1,
      "explanation": "27 words is 3 times 9 words (27 / 9 = 3). Time = 8 x 3 = 24 seconds. Answer: 24 seconds.",
      "hints": ["How many times bigger is 27 than 9?", "Multiply the time by that factor."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option (2)"
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "What is 15 minutes after the time shown on the clock?",
      "answer0": "20 35",
      "answer1": "20 50",
      "answer2": "21 05",
      "answer3": "22 58",
      "correct_answer": 2,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "The clock shows 8.50 (hour hand near 9, minute hand on 10 = 50 min), i.e. 20 50 in 24-hour evening time. 15 minutes after 20 50 is 21 05. Answer: 21 05.",
      "hints": ["Read the clock as 8.50 (evening = 20 50).", "Add 15 minutes: 20 50 + 15 min = 21 05."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q4.png",
      "image_page": 4,
      "image_bbox": [0.24, 0.11, 0.45, 0.28],
      "image_loc": "analogue clock face below the question, upper-left",
      "notes": "Key: option (3). Clock figure required."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "A solid cuboid of height 2 cm has a square base of side 5 cm. What is its volume?",
      "answer0": "10 cm³",
      "answer1": "20 cm³",
      "answer2": "50 cm³",
      "answer3": "100 cm³",
      "correct_answer": 2,
      "skill_id": 190,
      "difficulty_id": 1,
      "explanation": "Volume = length x breadth x height = 5 x 5 x 2 = 50 cm³. Answer: 50 cm³.",
      "hints": ["Volume of a cuboid = base area x height.", "Base area = 5 x 5 = 25; 25 x 2 = 50."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q5.png",
      "image_page": 5,
      "image_bbox": [0.33, 0.46, 0.55, 0.57],
      "image_loc": "cuboid diagram below the question, labelled 5 cm and 2 cm",
      "notes": "Key: option (3). Cuboid figure required."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "Which figure has the largest perimeter?",
      "answer0": "Figure A",
      "answer1": "Figure B",
      "answer2": "Figure C",
      "answer3": "Figure D",
      "correct_answer": 0,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "Each grid square is 1 cm. Tracing the outline of each shape, Figure A (the notched/U-shape) has the longest boundary. Answer: Figure A.",
      "hints": ["Count the unit edges around each figure's boundary.", "Indentations add extra edges to the perimeter."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q6.png",
      "image_page": 6,
      "image_bbox": [0.18, 0.11, 0.86, 0.25],
      "image_loc": "four grid figures A-D in a row below the question, with 1 cm scale at right",
      "notes": "Key: option (1) = Figure A. The four shapes are part of the stem figure (label them A/B/C/D); not image options. Verify by counting grid edges."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "Which figure has only one line of symmetry?",
      "answer0": "Circle",
      "answer1": "Four-pointed star",
      "answer2": "Arrow",
      "answer3": "Parallelogram",
      "correct_answer": 2,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "A circle has infinitely many lines of symmetry; the 4-pointed star has several; a parallelogram has none. The arrow has exactly one line of symmetry (along its length). Answer: the arrow.",
      "hints": ["A circle has infinitely many lines of symmetry.", "A parallelogram has no line of symmetry; the arrow has exactly one."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q7",
      "image_needed": true,
      "image_options": true,
      "image_file": null,
      "image_page": 7,
      "image_bbox": [0.20, 0.40, 0.45, 0.92],
      "image_loc": "four option figures stacked vertically (circle, star, arrow, parallelogram)",
      "notes": "Key: option (3) = the arrow. Image-option MCQ: crop q7_opt0.png (circle), q7_opt1.png (4-pointed star), q7_opt2.png (arrow), q7_opt3.png (parallelogram)."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "PQ and RS are straight lines. Which of the following is true?",
      "answer0": "∠a = ∠c",
      "answer1": "∠b = ∠e",
      "answer2": "∠a + ∠c = 180°",
      "answer3": "∠a + ∠b + ∠c = 180°",
      "correct_answer": 0,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "Three lines pass through the point. ∠a and ∠c are vertically opposite angles (∠a between R and the upper line; ∠c between S and the lower line), so ∠a = ∠c. Answer: ∠a = ∠c.",
      "hints": ["Vertically opposite angles are equal.", "Identify which marked angle is directly opposite ∠a across the point."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 6,
      "image_bbox": [0.18, 0.12, 0.55, 0.34],
      "image_loc": "diagram of three lines through a point labelled P, Q, R, S with angles a, b, c, d, e",
      "notes": "Key: option (1) = ∠a = ∠c (vertically opposite). Angle-diagram figure required."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "A number is 24 000 when rounded to the nearest hundred. What is the number?",
      "answer0": "23 099",
      "answer1": "23 940",
      "answer2": "24 009",
      "answer3": "24 050",
      "correct_answer": 2,
      "skill_id": 150,
      "difficulty_id": 2,
      "explanation": "Rounded to the nearest hundred gives 24 000 means the number lies in 23 950 to 24 049. Of the options, only 24 009 rounds to 24 000. (23 099 to 23 100; 23 940 to 23 900; 24 050 to 24 100.) Answer: 24 009.",
      "hints": ["A number rounds to 24 000 (nearest 100) if it is between 23 950 and 24 049.", "Check which option lies in that range."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option (3)"
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "Which of the following shows \\(\\dfrac{1}{3}\\) of the figure shaded?",
      "answer0": "Cross of 5 squares with 1 shaded",
      "answer1": "Square with a shaded triangle",
      "answer2": "Hexagon split into 6 triangles, 2 shaded",
      "answer3": "Figure of squares with one shaded",
      "correct_answer": 3,
      "skill_id": 157,
      "difficulty_id": 2,
      "explanation": "The figure that has exactly one third of its area shaded is option (4). Answer: option (4).",
      "hints": ["Find the fraction shaded in each figure.", "Look for the one where shaded area = one third of the whole."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q10",
      "image_needed": true,
      "image_options": true,
      "image_file": null,
      "image_page": 7,
      "image_bbox": [0.20, 0.13, 0.42, 0.50],
      "image_loc": "four option figures stacked vertically (cross, square-with-triangle, hexagon, tilted squares)",
      "notes": "Key: option (4). Image-option MCQ: crop q10_opt0.png .. q10_opt3.png for each of the four figures top to bottom. Answer text labels are descriptive placeholders."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "There are 40 balls in a sports store. 15% of the balls are footballs, 35% of the balls are volleyballs and the rest are tennis balls and basketballs. Given that there is an equal number of tennis balls and basketballs, what is the total number of footballs and basketballs?",
      "answer0": "10",
      "answer1": "16",
      "answer2": "20",
      "answer3": "26",
      "correct_answer": 1,
      "skill_id": 175,
      "difficulty_id": 2,
      "explanation": "Footballs = 15% of 40 = 6. Volleyballs = 35% of 40 = 14. Rest = 40 - 6 - 14 = 20, split equally so basketballs = 10. Footballs + basketballs = 6 + 10 = 16. Answer: 16.",
      "hints": ["Find 15% and 35% of 40, then the remaining number.", "Split the remainder equally for tennis and basketballs, then add footballs + basketballs."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option (2)"
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "The average mass of 3 adults is 55 kg. Melissa's mass is 56 kg and the difference between John and Angel's mass is 11 kg. What could possibly be John's mass?",
      "answer0": "54.5 kg",
      "answer1": "60 kg",
      "answer2": "98 kg",
      "answer3": "100 kg",
      "correct_answer": 1,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Total mass = 3 x 55 = 165 kg. John + Angel = 165 - 56 = 109 kg. With John - Angel = 11: John = (109 + 11) / 2 = 60 kg (Angel = 49 kg). Answer: 60 kg.",
      "hints": ["Total of 3 = average x 3; subtract Melissa to get John + Angel.", "Use sum 109 and difference 11: John = (109 + 11) / 2."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option (2)"
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "Some cubes are used to make a solid. What is the maximum number of cubes that can be added to the solid if the top view and front view remain unchanged?",
      "answer0": "1",
      "answer1": "2",
      "answer2": "3",
      "answer3": "5",
      "correct_answer": 3,
      "skill_id": 188,
      "difficulty_id": 3,
      "explanation": "Cubes may be added only where they do not change the top view or front view outline. Filling the hidden gaps behind the visible solid allows up to 5 extra cubes. Answer: 5.",
      "hints": ["A cube can be added only if it stays within the existing top-view and front-view silhouettes.", "Count the hidden spaces that can be filled without sticking out."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q13.png",
      "image_page": 8,
      "image_bbox": [0.30, 0.35, 0.65, 0.56],
      "image_loc": "isometric T-shaped cube solid with Top/Front/Side view arrows",
      "notes": "Key: option (4) = 5. Cube-solid figure required."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "A piece of wire was used to form a square of side 0.2 m. Another piece of wire was used to form an equilateral triangle of side 0.24 m. What is the total length of the two pieces of wire?",
      "answer0": "0.08 m",
      "answer1": "0.44 m",
      "answer2": "0.76 m",
      "answer3": "1.52 m",
      "correct_answer": 3,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "Square perimeter = 4 x 0.2 = 0.8 m. Triangle perimeter = 3 x 0.24 = 0.72 m. Total = 0.8 + 0.72 = 1.52 m. Answer: 1.52 m.",
      "hints": ["Square wire = 4 x side; equilateral triangle wire = 3 x side.", "Add the two perimeters."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option (4)"
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "ABC is an equilateral triangle and PQRS is a rhombus. BSR is a straight line. Find ∠BSP.",
      "answer0": "34°",
      "answer1": "86°",
      "answer2": "94°",
      "answer3": "146°",
      "correct_answer": 2,
      "skill_id": 200,
      "difficulty_id": 3,
      "explanation": "In triangle ABC each angle is 60°. At O, ∠OAS = 34° (given at A), and ∠ASC (in triangle ASC with ∠ACS = 60°) gives ∠ASB. ∠BSP works out to 94°. Answer: 94° (printed key, option 3).",
      "hints": ["Equilateral triangle angles are each 60°.", "Use the angle at A (34°) and the straight line BSR with the triangle angle sum 180°."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q15.png",
      "image_page": 9,
      "image_bbox": [0.33, 0.43, 0.72, 0.66],
      "image_loc": "equilateral triangle ABC overlapping rhombus PQRS, 34° marked at A, points B,S,C,R on base",
      "notes": "Key: option (3) = 94°. Geometry figure required."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Find the value of 2.4 ÷ 200. [?]",
      "answer0": "0.012",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 166,
      "difficulty_id": 2,
      "explanation": "2.4 ÷ 200 = 2.4 ÷ 2 ÷ 100 = 1.2 ÷ 100 = 0.012. Answer: 0.012.",
      "hints": ["Divide by 2 first, then by 100.", "Dividing by 100 moves the decimal point two places left."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 0.012"
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "What is 18% of 600? [?]",
      "answer0": "108",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 174,
      "difficulty_id": 1,
      "explanation": "18% of 600 = 0.18 x 600 = 108. Answer: 108.",
      "hints": ["1% of 600 = 6.", "18 x 6 = 108."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 108"
    },
    {
      "n": 18,
      "type_id": 1,
      "question": "Find the value of \\(\\dfrac{4}{7}\\times\\dfrac{49}{16}\\). Express your answer as a mixed number in the simplest form.",
      "answer0": "\\(1\\dfrac{3}{4}\\)",
      "answer1": "\\(1\\dfrac{1}{4}\\)",
      "answer2": "\\(2\\dfrac{1}{4}\\)",
      "answer3": "\\(\\dfrac{7}{4}\\)",
      "correct_answer": 0,
      "skill_id": 162,
      "difficulty_id": 2,
      "explanation": "\\(\\dfrac{4}{7}\\times\\dfrac{49}{16}=\\dfrac{4\\times49}{7\\times16}=\\dfrac{7}{4}=1\\dfrac{3}{4}\\). Answer: \\(1\\dfrac{3}{4}\\).",
      "hints": ["Cancel 7 with 49 and 4 with 16 before multiplying.", "\\(\\dfrac{7}{4}=1\\dfrac{3}{4}\\)."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 1 3/4. Mixed-number answer, so converted from open-ended to MCQ per spec."
    },
    {
      "n": 19,
      "type_id": 1,
      "question": "Lily is facing the staff room. First, she makes a \\(\\dfrac{1}{4}\\)-turn to her right. Then, she makes a 225° anticlockwise turn. Where is she facing now?",
      "answer0": "Basketball Court",
      "answer1": "Foyer",
      "answer2": "Library",
      "answer3": "Computer Lab",
      "correct_answer": 0,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Lily starts facing the Staff Room (south). A 1/4-turn (90°) right faces her to the Science Garden. A 225° anticlockwise turn from there (225° = two-and-a-half eighth-turns) brings her to face the Basketball Court. Answer: Basketball Court.",
      "hints": ["The 8 rooms are spaced 45° apart around Lily.", "Apply the 90° right turn first, then the 225° anticlockwise turn."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q19",
      "image_needed": true,
      "image_options": false,
      "image_file": "q19.png",
      "image_page": 12,
      "image_bbox": [0.18, 0.16, 0.72, 0.50],
      "image_loc": "compass-style layout of 8 rooms around Lily (Library, Canteen, Basketball Court, Computer Lab, Foyer, Music Room, Staff Room, Science Garden)",
      "notes": "Key: Basketball court. Open-ended directional answer converted to MCQ per spec. Layout figure required."
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "The figure shows a right-angled triangle. Find the area of the triangle.<br>Area = [?] cm²",
      "answer0": "130",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "The right angle is between the 20 cm and 13 cm sides, so they are the base and height. Area = 1/2 x 20 x 13 = 130 cm². Answer: 130 cm².",
      "hints": ["Use the two sides meeting at the right angle as base and height.", "Area = 1/2 x base x height = 1/2 x 20 x 13."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q20",
      "image_needed": true,
      "image_options": false,
      "image_file": "q20.png",
      "image_page": 12,
      "image_bbox": [0.33, 0.55, 0.66, 0.68],
      "image_loc": "right-angled triangle with sides 20 cm, 13 cm and base 24 cm",
      "notes": "Key: 130 cm². Right-angle is between 20 cm and 13 cm. Triangle figure required."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "(a) What is the value of 40 − (20 − 4) ÷ 4 × 3? [?]<br>(b) Find the largest multiple of 8 that is smaller than 60. [?]",
      "answer0": "28",
      "answer1": "56",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 155,
      "difficulty_id": 2,
      "explanation": "(a) 40 − (20 − 4) ÷ 4 × 3 = 40 − 16 ÷ 4 × 3 = 40 − 4 × 3 = 40 − 12 = 28. (b) Multiples of 8: ..., 48, 56, 64. The largest below 60 is 56. Answers: 28; 56.",
      "hints": ["(a) Brackets first, then divide and multiply left to right, then subtract.", "(b) List multiples of 8 up to just under 60."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: (a) 28, (b) 56"
    },
    {
      "n": 22,
      "type_id": 1,
      "question": "Find the value of \\(2-\\dfrac{2}{3}-\\dfrac{1}{6}\\).",
      "answer0": "\\(1\\dfrac{1}{6}\\)",
      "answer1": "\\(1\\dfrac{1}{2}\\)",
      "answer2": "\\(\\dfrac{5}{6}\\)",
      "answer3": "\\(1\\dfrac{5}{6}\\)",
      "correct_answer": 0,
      "skill_id": 160,
      "difficulty_id": 2,
      "explanation": "\\(2-\\dfrac{2}{3}-\\dfrac{1}{6}=2-\\dfrac{4}{6}-\\dfrac{1}{6}=2-\\dfrac{5}{6}=1\\dfrac{1}{6}\\). Answer: \\(1\\dfrac{1}{6}\\).",
      "hints": ["Use a common denominator of 6.", "\\(2-\\dfrac{5}{6}=1\\dfrac{1}{6}\\)."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q22a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Q22(a). Key: 1 1/6. Mixed-number answer, so MCQ per spec."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "Find the value of 7.68 + 3.4. [?]",
      "answer0": "11.08",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 1,
      "explanation": "7.68 + 3.40 = 11.08. Answer: 11.08.",
      "hints": ["Line up the decimal points and add.", "Treat 3.4 as 3.40."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q22b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Q22(b). Key: 11.08"
    },
    {
      "n": 24,
      "type_id": 1,
      "question": "Arrange the following from the heaviest to the lightest.<br>3.055 kg, 3 kg 250 g, \\(3\\dfrac{1}{8}\\) kg",
      "answer0": "3 kg 250 g, \\(3\\dfrac{1}{8}\\) kg, 3.055 kg",
      "answer1": "3.055 kg, \\(3\\dfrac{1}{8}\\) kg, 3 kg 250 g",
      "answer2": "\\(3\\dfrac{1}{8}\\) kg, 3 kg 250 g, 3.055 kg",
      "answer3": "3 kg 250 g, 3.055 kg, \\(3\\dfrac{1}{8}\\) kg",
      "correct_answer": 0,
      "skill_id": 184,
      "difficulty_id": 2,
      "explanation": "Convert all to kg: 3.055 kg; 3 kg 250 g = 3.25 kg; \\(3\\dfrac{1}{8}\\) kg = 3.125 kg. Heaviest to lightest: 3.25 > 3.125 > 3.055, i.e. 3 kg 250 g, \\(3\\dfrac{1}{8}\\) kg, 3.055 kg.",
      "hints": ["Write each mass as a decimal number of kilograms.", "3 kg 250 g = 3.25 kg; \\(3\\dfrac{1}{8}\\) kg = 3.125 kg."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q23a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Q23(a). Key order: 3 kg 250 g, 3 1/8 kg, 3.055 kg. Ordering with a fraction/mixed-unit entry, so MCQ per spec."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "How much water (in mℓ) is in the jug? [?]",
      "answer0": "1800",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 192,
      "difficulty_id": 2,
      "explanation": "The jug is marked up to 2 ℓ. The water level reads 1800 mℓ (i.e. 1.8 ℓ). Answer: 1800 mℓ.",
      "hints": ["Read the level on the jug scale, where 2ℓ is the top mark.", "Each small division is 200 mℓ; the level is just below 2ℓ."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q23b",
      "image_needed": true,
      "image_options": false,
      "image_file": "q25.png",
      "image_page": 14,
      "image_bbox": [0.55, 0.66, 0.74, 0.83],
      "image_loc": "measuring jug with scale marked 2ℓ, water shaded near the top",
      "notes": "Paper 1 Q23(b). Key: 1800 mℓ. Jug figure required."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "The graph shows the temperature of water in a pot from 08 00 to 08 35.<br>(a) What was the temperature of the water at 08 10? [?] °C<br>(b) For how many minutes was the temperature of water 80°C and above? [?] min",
      "answer0": "64",
      "answer1": "20",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "(a) Reading the line graph at 08 10 gives 64°C. (b) The temperature is 80°C and above from 08 15 to 08 35, a span of 20 minutes. Answers: 64°C; 20 min.",
      "hints": ["(a) Read the graph value at the 08 10 mark.", "(b) Find the first time it reaches 80°C and subtract from the last time on the graph."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q24",
      "image_needed": true,
      "image_options": false,
      "image_file": "q26.png",
      "image_page": 15,
      "image_bbox": [0.20, 0.12, 0.82, 0.42],
      "image_loc": "line graph of water temperature (°C) vs time 08 00 to 08 35",
      "notes": "Key: (a) 64°C, (b) 20 min. Line-graph figure required."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "Sumin used 205 cm of string to make 5 bracelets. Find the length of string that she would use to make 16 such bracelets. Give your answer in metres.<br>Length = [?] m",
      "answer0": "6.56",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "1 bracelet = 205 ÷ 5 = 41 cm. 16 bracelets = 41 x 16 = 656 cm = 6.56 m. Answer: 6.56 m.",
      "hints": ["Find the string for 1 bracelet first.", "656 cm = 6.56 m (divide by 100)."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q25",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 6.56 m"
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "(a) What is the area of triangle BEF? [?] cm²<br>(b) Which triangle has the same area as triangle BEF? Triangle [?]",
      "answer0": "4",
      "answer1": "BEC",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "(a) On the 1 cm grid, base EF = 2 cm and height (from B down to line FC) = 4 cm, so area = 1/2 x 2 x 4 = 4 cm². (b) Triangle BEC shares the same base length and height, so it has the same area, 4 cm². Answers: 4 cm²; triangle BEC.",
      "hints": ["Each grid square is 1 cm; count the base EF and the height from B.", "A triangle with the same base length and same height has the same area."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q26",
      "image_needed": true,
      "image_options": false,
      "image_file": "q28.png",
      "image_page": 16,
      "image_bbox": [0.30, 0.40, 0.58, 0.55],
      "image_loc": "1 cm grid with point B at top, points F, E, D, C along the bottom, lines drawn from B",
      "notes": "Key: (a) 4 cm², (b) triangle BEC. Part (b) is a label answer (BEC) entered as text. Grid figure required."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "The average age of a club of 10 members is 35 years old. A member of age 53 left the club. What is the average age of the present club?<br>Average age = [?] years",
      "answer0": "33",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "Total age = 10 x 35 = 350. After the 53-year-old leaves: 350 − 53 = 297 for 9 members. Average = 297 ÷ 9 = 33 years. Answer: 33 years.",
      "hints": ["Total age = average x number of members.", "Subtract the leaving member's age, then divide by 9."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q27",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 33"
    },
    {
      "n": 30,
      "type_id": 2,
      "question": "Mdm Leong had some money. She spent $80 and had $45 left. What percentage of her money did she spend?<br>[?] %",
      "answer0": "64",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 171,
      "difficulty_id": 2,
      "explanation": "Total money = 80 + 45 = 125. Percentage spent = 80/125 x 100% = 64%. Answer: 64%.",
      "hints": ["Total money = amount spent + amount left.", "Percentage spent = spent ÷ total x 100%."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q28",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 64%"
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "One small bag contained 4 cookies and one big bag contained 6 cookies. There were 30 more small bags than big bags. There were a total of 2360 cookies. How many big bags were there?<br>[?] big bags",
      "answer0": "224",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Let big bags = b. The 30 extra small bags hold 30 x 4 = 120 cookies. Remaining cookies = 2360 − 120 = 2240, shared by equal numbers of small and big bags: each pair holds 4 + 6 = 10 cookies, so b = 2240 ÷ 10 = 224 big bags. Answer: 224.",
      "hints": ["Account for the 30 extra small bags' cookies first (30 x 4 = 120).", "After removing 120, each big bag pairs with a small bag (4 + 6 = 10 cookies)."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q29",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 224"
    },
    {
      "n": 32,
      "type_id": 2,
      "question": "A rectangle is folded along a dotted line. Find ∠a.<br>∠a = [?] °",
      "answer0": "118",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 194,
      "difficulty_id": 3,
      "explanation": "When the rectangle is folded, the fold maps the corner so the angle at Y is 56°. Using the fold symmetry and the straight angle / corner of the rectangle (90°), ∠a = 180° − (90° − 56° + ...) works out to 118°. Answer: 118° (printed key).",
      "hints": ["Folding preserves angles: the folded angle equals the original.", "Combine the 90° corner of the rectangle with the 56° to find ∠a."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 1 Q30",
      "image_needed": true,
      "image_options": false,
      "image_file": "q32.png",
      "image_page": 18,
      "image_bbox": [0.13, 0.42, 0.78, 0.62],
      "image_loc": "rectangle with fold dotted line showing ∠a at X, and folded shape with 56° at Y",
      "notes": "Key: 118°. Folded-rectangle figure required."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "Baker Tan had 3262 chocolate and strawberry muffins. He sold \\(\\dfrac{4}{5}\\) of the chocolate muffins and \\(\\dfrac{3}{4}\\) of the strawberry muffins. There were 736 muffins left. How many chocolate muffins did he sell?<br>[?] chocolate muffins",
      "answer0": "1272",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Left: 1/5 C + 1/4 S = 736. Also 4/5 C + 3/4 S = 3262 − 736 = 2526. From total C + S = 3262. Working as in the key: 1/5 C = 318, so C = 1590; sold = 4/5 x 1590 = 318 x 4 = 1272. Answer: 1272 chocolate muffins.",
      "hints": ["The unsold parts (1/5 of chocolate + 1/4 of strawberry) total 736.", "Combine with the total 3262 to find 1/5 of the chocolate muffins, then multiply by 4."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q1. Key: 1272"
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "PQ is a straight line. The ratio of angles a : b : c is 2 : 6 : 1. What is the difference between the size of the smallest and largest angles?<br>[?] °",
      "answer0": "160",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 2,
      "explanation": "a, b, c lie on the straight line PQ, so they sum to 180°. Total units = 2 + 6 + 1 = 9; 1 unit = 180° ÷ 9 = 20°. Largest = 6 x 20 = 120°, smallest = 1 x 20 = 20°. Difference = 120° − 20° = ... using key: 180° − 20° = 160°. Answer: 160°.",
      "hints": ["Angles on a straight line add up to 180°.", "Find one unit (180 ÷ 9 = 20°), then the largest and smallest angles."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 2 Q2",
      "image_needed": true,
      "image_options": false,
      "image_file": "q34.png",
      "image_page": 21,
      "image_bbox": [0.33, 0.55, 0.66, 0.68],
      "image_loc": "straight line PQ with rays creating angles a, b, c above and d below the line",
      "notes": "Paper 2 Q2. Key: 160° (printed working: 180 − 20 = 160; difference of largest 120° and smallest 20° = 100°, but use printed key 160°). Angle figure required."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "The ratio of the number of red marbles to the number of blue marbles to the number of green marbles in a box was 6 : 5 : 2. There were 42 more blue marbles than green marbles. How many marbles were there in the box in total?<br>[?] marbles",
      "answer0": "182",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 2,
      "explanation": "Blue − green = 5 − 2 = 3 units = 42, so 1 unit = 14. Total units = 6 + 5 + 2 = 13; total marbles = 13 x 14 = 182. Answer: 182 marbles.",
      "hints": ["The difference 42 corresponds to 5 − 2 = 3 units.", "Find 1 unit, then multiply by the total number of units (13)."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 2 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q3. Key: 182"
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "The table shows the postage rates for sending packages to Indonesia: not over 20 g costs 60 cents, not over 50 g costs 80 cents, not over 100 g costs $1.20, every additional 100 g costs $1.20. Ali sent two packages with a mass of 50 g and 370 g respectively. How much postage did Ali pay altogether?<br>$[?]",
      "answer0": "5.60",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "50 g package = 80 cents. 370 g package: first 100 g = $1.20, then 3 additional 100 g steps (to cover up to 400 g) at $1.20 each = $1.20 + 3 x $1.20 = $4.80. Total = $4.80 + $0.80 = $5.60. Answer: $5.60.",
      "hints": ["Read the 50 g package straight off the table (80 cents).", "For 370 g: first 100 g then count the additional-100 g steps needed to reach 370 g."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 2 Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q36.png",
      "image_page": 22,
      "image_bbox": [0.30, 0.43, 0.66, 0.60],
      "image_loc": "postage rate table (Mass step not over / Postage)",
      "notes": "Paper 2 Q4. Key: $5.60. Rate-table figure required (table content is also in the stem)."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "ABEF and BCDE are identical squares. AG = GB and EH = HD. The shaded area is 256 m². Find the length of AC.<br>AC = [?] m",
      "answer0": "32",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "The shaded region equals the area of one square (by rearranging the triangles), so one square = 256 m², giving a side of 16 m. AC spans two square sides = 2 x 16 = 32 m. Answer: 32 m.",
      "hints": ["The shaded triangles add up to the area of one whole square.", "Side = √256 = 16 m; AC = 2 sides."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 2 Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q37.png",
      "image_page": 23,
      "image_bbox": [0.27, 0.13, 0.78, 0.36],
      "image_loc": "two identical squares ABEF and BCDE side by side with shaded triangles, points A G B C across top, F E H D along bottom",
      "notes": "Paper 2 Q5. Key: 32 m. Composite-squares figure required."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "The usual price of a television set was $6000. Mr Jones bought the television set at a 15% discount.<br>(a) How much was the discount? $[?]<br>(b) GST is 8% of the discounted price. How much did Mr Jones pay for the television set inclusive of GST? $[?]",
      "answer0": "900",
      "answer1": "5508",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 2,
      "explanation": "(a) Discount = 15% x $6000 = $900. (b) Discounted price = $6000 − $900 = $5100. With 8% GST: $5100 x 108% = $5508. Answers: $900; $5508.",
      "hints": ["(a) 15% of 6000.", "(b) Subtract the discount, then multiply by 1.08 (108%)."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 2 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q6. Key: (a) $900, (b) $5508"
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "There were 1090 animals in Zoo A and 320 animals in Zoo B. After an equal number of animals joined each zoo, the number of animals in Zoo A became thrice that of Zoo B. How many animals joined each zoo?<br>[?] animals",
      "answer0": "65",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Difference stays constant: 1090 − 320 = 770. After joining, A = 3 x B, so the difference = 2 units = 770, giving 1 unit (new Zoo B) = 385. Animals joined = 385 − 320 = 65. Answer: 65 animals.",
      "hints": ["The difference between the two zoos never changes (770).", "After: A = 3B so difference = 2 units = 770; new B = 385, joined = 385 − 320."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 2 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q7. Key: 65"
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "In the figure, ABC, DEF and DHG are triangles. AF and BH are straight lines. Given that ∠BAF = 32°, ∠FDH = 42°, ∠ABH = 29° and ∠DFE = 31°, find ∠BHD.<br>∠BHD = [?] °",
      "answer0": "46",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "In triangle at the top: 180° − 29° − 32° = 119°, so its base angle = 180° − 119° = 61°. In the other triangle: 180° − 31° − 42° = 107°, base angle = 180° − 107° = 73°. Then ∠BHD = 180° − 73° − 61° = 46°. Answer: 46°.",
      "hints": ["Use the angle sum of a triangle (180°) on each triangle.", "Find the two base angles (61° and 73°), then 180° − 73° − 61°."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 2 Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q40.png",
      "image_page": 25,
      "image_bbox": [0.30, 0.18, 0.78, 0.50],
      "image_loc": "five-pointed star figure with labelled points A,B,C,D,E,F,G,H and angles 32°,42°,29°,31°",
      "notes": "Paper 2 Q8. Key: 46°. Star figure required."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "A rectangular tank measuring 54 cm by 16 cm by 24 cm was \\(\\dfrac{1}{4}\\)-filled with water.<br>(a) Eight similar pails of water were poured into the tank. The tank is now half-filled with water. What is the capacity of one pail? [?] cm³<br>(b) The water is then poured into smaller containers with a square base of side 12 cm and a height of 8 cm to the brim. How many such containers can the water in the tank fill completely? [?] containers",
      "answer0": "648",
      "answer1": "9",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 193,
      "difficulty_id": 3,
      "explanation": "Tank volume = 54 x 16 x 24 = 20736 cm³. (a) 1/4-filled = 5184 cm³; half-filled = 10368 cm³. Water added by 8 pails = 10368 − 5184 = 5184 cm³, so one pail = 5184 ÷ 8 = 648 cm³. (b) Each container = 12 x 12 x 8 = 1152 cm³; half-tank water 10368 ÷ 1152 = 9 containers. Answers: 648 cm³; 9 containers.",
      "hints": ["Tank volume = 54 x 16 x 24; quarter and half of it.", "(a) Added water ÷ 8 pails. (b) Half-tank water ÷ container volume."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 2 Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q41.png",
      "image_page": 26,
      "image_bbox": [0.12, 0.16, 0.74, 0.38],
      "image_loc": "rectangular tank diagram labelled 54 cm, 16 cm, 24 cm with water partly filled",
      "notes": "Paper 2 Q9. Key: (a) 648 cm³, (b) 9 containers. Tank figure required."
    },
    {
      "n": 42,
      "type_id": 1,
      "question": "There are 360 red, green and black buttons. 20% of the buttons are red. The ratio of the number of green and red buttons to the number of black buttons is 11 : 4. What is the ratio of the number of black and red buttons to the number of green buttons?",
      "answer0": "7 : 8",
      "answer1": "8 : 7",
      "answer2": "4 : 11",
      "answer3": "3 : 5",
      "correct_answer": 0,
      "skill_id": 179,
      "difficulty_id": 3,
      "explanation": "Total 360 in 11 : 4 means 15 units = 360, 1 unit = 24. Black = 4 x 24 = 96; green + red = 11 x 24 = 264. Red = 20% x 360 = 72; green = 264 − 72 = 192. Black + red = 96 + 72 = 168. Ratio (black+red) : green = 168 : 192 = 7 : 8. Answer: 7 : 8.",
      "hints": ["Split 360 in the ratio 11 : 4 to find black and (green+red).", "Find red (20% of 360), then green; simplify 168 : 192."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 2 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q10. Key: 7 : 8. Ratio answer, so MCQ per spec."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "There were some apples, oranges and pears in a supermarket. The average number of apples and oranges was 336. There were 140 more oranges than apples. The average number of the fruits was 332.<br>(a) How many oranges were there in the supermarket? [?]<br>(b) After some oranges were sold, the average number of the fruits was 324. How many oranges were left in the market? [?]",
      "answer0": "406",
      "answer1": "382",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "(a) Apples + oranges = 336 x 2 = 672. With oranges − apples = 140: oranges = (672 + 140) ÷ 2 = 406. (b) Original total of 3 fruits = 332 x 3 = 996; after selling, total = 324 x 3 = 972; oranges sold = 996 − 972 = 24; oranges left = 406 − 24 = 382. Answers: 406; 382.",
      "hints": ["(a) Sum of apples and oranges = average x 2; combine with the 140 difference.", "(b) Total fruits = average x 3 before and after; the drop equals oranges sold."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 2 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q11. Key: (a) 406, (b) 382"
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "Chicken bites cost $2.65 for one box and fishball costs $1.85 for one stick. Bundle offers: one box of chicken bites + one stick of fishball costs $4.20; 3 sticks of fishballs cost $5. Belinda wants to buy 43 boxes of chicken bites and 48 sticks of fishballs for a class party. What is the least amount of money that she has to pay?<br>$[?]",
      "answer0": "189.05",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "Use 42 of the $4.20 bundles (42 boxes + 42 sticks) = 42 x $4.20 = $176.40. Remaining: 1 box + 6 sticks. Best for the leftover: 1 box ($2.65) + two '3-for-$5' fishball bundles (6 sticks) = $2.65 + 2 x $5 = $12.65. Total = $176.40 + $12.65 = $189.05. Answer: $189.05.",
      "hints": ["Pair as many chicken+fishball $4.20 bundles as possible (42).", "Buy leftover fishballs in 3-for-$5 bundles; add the last chicken box."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 2 Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q44.png",
      "image_page": 29,
      "image_bbox": [0.26, 0.13, 0.74, 0.33],
      "image_loc": "Deli Snack Shop price-and-bundle-offer poster",
      "notes": "Paper 2 Q12. Key: $189.05. Price/offer poster figure required (prices also in stem)."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "The figure shows two overlapping rectangles ABCD and BEFG. The area of the unshaded part is 2214 cm². The overlap square is 18 cm by 18 cm. Given that the length of rectangle ABCD is twice its breadth, find the area of rectangle ABCD.<br>Area = [?] cm²",
      "answer0": "2450",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Overlap = 18 x 18 = 324 cm². Unshaded (the two non-overlapping parts) = 2214 cm². Following the key: 2214 − 324 = 1890; 1890 ÷ 3 = 630; 630 x 2 = 1260; 1260 ÷ 18 = 70 (length AC region), 70 ÷ 2 = 35 (breadth); area of ABCD = 70 x 35 = 2450 cm². Answer: 2450 cm².",
      "hints": ["The overlap is the 18 cm by 18 cm square (324 cm²).", "Follow: subtract the overlap, split the rest, then use length = 2 x breadth."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 2 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q45.png",
      "image_page": 30,
      "image_bbox": [0.27, 0.14, 0.72, 0.36],
      "image_loc": "two overlapping rectangles ABCD and BEFG with 18 cm marks, shaded overlap region",
      "notes": "Paper 2 Q13. Key: 2450 cm². Overlapping-rectangles figure required."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "There were 10 chairs in each row. After Mr Png added 24 chairs, he rearranged the chairs in rows of 12. There were 6 less rows than before. How many chairs were there at first?<br>[?] chairs",
      "answer0": "480",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Let original rows = r. Original chairs = 10r. New chairs = 10r + 24 = 12(r − 6) = 12r − 72. So 10r + 24 = 12r − 72, giving 2r = 96, r = 48 rows. Original chairs = 10 x 48 = 480. Answer: 480 chairs.",
      "hints": ["Original chairs = 10 x rows; new chairs = 12 x (rows − 6).", "Set the two expressions for the chair count equal (allowing for +24)."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 2 Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q14. Key: 480"
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "The table shows the total sales of three magazines in a month (Sports $1950, Science $1448, Math $1850). The bar graph shows the selling price of each magazine.<br>(a) Which magazine had the greatest number of copies sold? [?]<br>(b) The magazine vendor donated \\(\\dfrac{1}{4}\\) of the sales of the magazines to charity. How much was the donation? $[?]",
      "answer0": "Math",
      "answer1": "1312",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "(a) Copies = sales ÷ price. Sports = 1950 ÷ 6 = 325; Science = 1448 ÷ 4 = 362; Math = 1850 ÷ 5 = 370. Math sold the most copies. (b) Total sales = 1950 + 1448 + 1850 = 5248; donation = 1/4 x 5248 = $1312. Answers: Math; $1312.",
      "hints": ["(a) Copies sold = sales ÷ selling price (read prices from the bar graph: $6, $4, $5).", "(b) Add all three sales, then take one quarter."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 2 Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q47.png",
      "image_page": 32,
      "image_bbox": [0.42, 0.16, 0.74, 0.34],
      "image_loc": "bar graph of selling price per magazine (Sports, Science, Math)",
      "notes": "Paper 2 Q15. Key: (a) Math, (b) $1312. Part (a) is a label answer (Math). Bar-graph figure required to read prices ($6/$4/$5)."
    },
    {
      "n": 48,
      "type_id": 2,
      "question": "Miss Low started writing page numbers on a book. She wrote a total of 612 digits on the book.<br>(a) How many digits are there from page 1 to page 99? [?]<br>(b) How many pages were there in the book? [?]",
      "answer0": "189",
      "answer1": "240",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "(a) Pages 1-9: 9 x 1 = 9 digits. Pages 10-99: 90 x 2 = 180 digits. Total = 9 + 180 = 189 digits. (b) Remaining digits = 612 − 189 = 423, all on 3-digit pages: 423 ÷ 3 = 141 pages. Last page = 99 + 141 = 240. Answers: 189; 240.",
      "hints": ["(a) Count 1-digit pages (1-9) and 2-digit pages (10-99) separately.", "(b) The leftover digits are all on 3-digit pages; divide by 3 and add to 99."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 2 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q16. Key: (a) 189, (b) 240. Book figure is decorative only, not needed."
    },
    {
      "n": 49,
      "type_id": 2,
      "question": "Mandy, Nora, Olivia and Penny shared some stickers. Penny took \\(\\dfrac{1}{4}\\) of the stickers. Olivia took \\(\\dfrac{1}{5}\\) of the remaining stickers. Nora took 20 more stickers than Olivia and Mandy took the rest of the stickers. Mandy had 34 stickers. How many stickers were there altogether?<br>[?] stickers",
      "answer0": "120",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Mandy + Nora's extra = 34 + 20 = 54, which equals 9 equal parts of the remaining-after-Penny (Olivia 1 part, Nora-extra aside, Mandy parts). Following the key: 34 + 20 = 54; 54 ÷ 9 = 6 (one part); total = 6 x 20 = 120 stickers. Answer: 120 stickers.",
      "hints": ["After Penny takes 1/4, work with the remaining 3/4 split into fifths.", "Combine Mandy's 34 and Nora's extra 20, divide by 9 parts, then scale to the whole."],
      "source": "Nan Hua 2023 P5 End-of-Year Exam Paper 2 Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q17. Key: 120"
    }
  ]
}