{
  "paper": {
    "school": "Nan Hua",
    "year": 2024,
    "level": "P6",
    "label": "Prelim",
    "source_prefix": "Nan Hua 2024 P6 Prelim",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "In 21.56, which digit is in the tenths place?",
      "answer0": "1",
      "answer1": "2",
      "answer2": "5",
      "answer3": "6",
      "correct_answer": 2,
      "skill_id": 123,
      "difficulty_id": 1,
      "explanation": "In 21.56, the digit immediately after the decimal point is the tenths digit. That digit is 5. Final answer: 5.",
      "hints": ["The first digit after the decimal point is the tenths place.", "21.5_6 — read the digit just after the point."],
      "source": "Nan Hua 2024 P6 Prelim Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: (3) = 5."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Which of the following is the first common multiple of 4 and 6?",
      "answer0": "1",
      "answer1": "2",
      "answer2": "12",
      "answer3": "24",
      "correct_answer": 2,
      "skill_id": 115,
      "difficulty_id": 1,
      "explanation": "Multiples of 4: 4, 8, 12, ... Multiples of 6: 6, 12, ... The smallest number in both lists (lowest common multiple) is 12. Final answer: 12.",
      "hints": ["List multiples of 4 and of 6.", "Find the smallest number that appears in both lists."],
      "source": "Nan Hua 2024 P6 Prelim Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: (3) = 12."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "The diagram shows a refrigerator. Which of the following could be the height of the refrigerator?",
      "answer0": "18 cm",
      "answer1": "180 cm",
      "answer2": "18 m",
      "answer3": "180 m",
      "correct_answer": 1,
      "skill_id": 52,
      "difficulty_id": 1,
      "explanation": "A refrigerator is about 1.8 m tall, which is 180 cm. 18 cm is too short, and 18 m or 180 m are far too tall. Final answer: 180 cm.",
      "hints": ["A real fridge is a bit taller than an adult.", "1.8 m = 180 cm is a sensible fridge height."],
      "source": "Nan Hua 2024 P6 Prelim Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q3.png",
      "image_page": 2,
      "image_bbox": [0.66, 0.66, 0.86, 0.82],
      "image_loc": "right side of page, drawing of a refrigerator with a '?' marking its height",
      "notes": "Answer key: (2) = 180 cm."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Which of the following is the same as \\(9\\,\\ell\\,75\\) ml?",
      "answer0": "9.075 ml",
      "answer1": "975 ml",
      "answer2": "9075 ml",
      "answer3": "9750 ml",
      "correct_answer": 2,
      "skill_id": 184,
      "difficulty_id": 1,
      "explanation": "1 litre = 1000 ml, so 9 litres = 9000 ml. Adding 75 ml gives 9000 + 75 = 9075 ml. Final answer: 9075 ml.",
      "hints": ["1 litre = 1000 ml.", "9 ℓ = 9000 ml, then add the extra 75 ml."],
      "source": "Nan Hua 2024 P6 Prelim Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: (3) = 9075 ml."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "In the number line, what is the mixed number represented by A?",
      "answer0": "\\(2\\dfrac{2}{3}\\)",
      "answer1": "\\(2\\dfrac{3}{4}\\)",
      "answer2": "\\(2\\dfrac{5}{6}\\)",
      "answer3": "\\(2\\dfrac{6}{7}\\)",
      "correct_answer": 2,
      "skill_id": 119,
      "difficulty_id": 2,
      "explanation": "The interval from 2 to 3 is divided into 6 equal parts. Point A is at the 5th mark from 2, so it represents \\(2\\dfrac{5}{6}\\). Final answer: \\(2\\dfrac{5}{6}\\).",
      "hints": ["Count how many equal parts the space between 2 and 3 is split into.", "A sits 5 small parts past 2 out of 6 parts."],
      "source": "Nan Hua 2024 P6 Prelim Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q5.png",
      "image_page": 3,
      "image_bbox": [0.58, 0.38, 0.88, 0.5],
      "image_loc": "right side of page, a number line from 2 to 3 with an arrow labelled A near 3",
      "notes": "Answer key: (3) = 2 5/6. Fraction options rendered inline."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "Which of the following shows \\(\\dfrac{1}{2}\\) of the figure shaded?",
      "answer0": "Figure 1",
      "answer1": "Figure 2",
      "answer2": "Figure 3",
      "answer3": "Figure 4",
      "correct_answer": 0,
      "skill_id": 120,
      "difficulty_id": 2,
      "explanation": "Compare the shaded portion of each figure to one half. Only the first figure has exactly half of its equal parts shaded. Final answer: Figure 1 (option 1).",
      "hints": ["Count total equal parts and how many are shaded in each figure.", "Half means shaded parts equal unshaded parts."],
      "source": "Nan Hua 2024 P6 Prelim Q6",
      "image_needed": true,
      "image_options": true,
      "image_file": null,
      "image_page": 3,
      "image_bbox": [0.15, 0.68, 0.9, 0.82],
      "image_loc": "four shaded figures across the lower page, labelled (1) blocks, (2) triangle grid, (3) hexagons, (4) chevrons",
      "notes": "Answer key: (1) = Figure 1. Image-option MCQ: crop each option q6_opt0..q6_opt3."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "The figure is the net of a cube. Which 2 faces are opposite each other?",
      "answer0": "A and D",
      "answer1": "D and E",
      "answer2": "C and F",
      "answer3": "B and E",
      "correct_answer": 1,
      "skill_id": 233,
      "difficulty_id": 2,
      "explanation": "Folding the net, faces D and F are at opposite ends of the top row while C is between them along the fold; A-D, C-F and B-E are adjacent. The pair that ends up opposite is D and E. Final answer: D and E (option 2).",
      "hints": ["Mentally fold the net into a cube.", "Opposite faces never share an edge on the net."],
      "source": "Nan Hua 2024 P6 Prelim Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q7.png",
      "image_page": 4,
      "image_bbox": [0.18, 0.12, 0.56, 0.24],
      "image_loc": "top-left of page, an L-shaped net of a cube with faces A B C on the bottom row and D E F on the top row",
      "notes": "Answer key: (2) = D and E."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "Sharon watched a movie that was 2 h 20 min long. It ended at 00 30. What time did the movie start?",
      "answer0": "02 50",
      "answer1": "10 10",
      "answer2": "22 10",
      "answer3": "22 50",
      "correct_answer": 2,
      "skill_id": 135,
      "difficulty_id": 2,
      "explanation": "Subtract 2 h 20 min from 00 30. Going back 30 min gives 00 00; going back another 1 h 50 min gives 22 10. Final answer: 22 10 (option 3).",
      "hints": ["Work backwards from 00 30 by 2 h 20 min.", "00 30 minus 2 h is 22 30, then minus 20 min."],
      "source": "Nan Hua 2024 P6 Prelim Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: (3) = 22 10."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "William had $100. After buying 5 identical bags, he had $p left. Find the cost of each bag.",
      "answer0": "$\\(\\dfrac{100-p}{5}\\)",
      "answer1": "$\\(\\dfrac{100p}{5}\\)",
      "answer2": "$(100 − 5p)",
      "answer3": "$\\(100-\\dfrac{p}{5}\\)",
      "correct_answer": 0,
      "skill_id": 241,
      "difficulty_id": 2,
      "explanation": "Money spent on bags = 100 − p. This was for 5 bags, so each bag costs \\(\\dfrac{100-p}{5}\\) dollars. Final answer: option 1.",
      "hints": ["Cost of all bags = money he had minus money left.", "Divide the total spent by the number of bags, 5."],
      "source": "Nan Hua 2024 P6 Prelim Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: (1)."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "\\(\\dfrac{5}{9}\\) of the audience in a theatre were adults and the rest were children. \\(\\dfrac{1}{4}\\) of the children were boys and the rest were girls. What was the ratio of the number of girls to the number of adults?",
      "answer0": "1 : 5",
      "answer1": "3 : 5",
      "answer2": "5 : 1",
      "answer3": "5 : 3",
      "correct_answer": 1,
      "skill_id": 213,
      "difficulty_id": 3,
      "explanation": "Adults = 5/9, children = 4/9 of the audience. Girls = 3/4 of children = 3/4 × 4/9 = 3/9 = 1/3 of the audience. Girls : adults = 3/9 : 5/9 = 3 : 5. Final answer: 3 : 5 (option 2).",
      "hints": ["Children make up 4/9; girls are 3/4 of the children.", "Compare the girls' fraction of the whole to the adults' fraction (5/9)."],
      "source": "Nan Hua 2024 P6 Prelim Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: (2) = 3 : 5."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "Nathanael spent 20% of his money on a cap. He used the rest of the money to buy a bag and a shirt. The bag cost $15 more than the cap. The shirt cost $165. Find the cost of the bag.",
      "answer0": "$35",
      "answer1": "$48",
      "answer2": "$60",
      "answer3": "$75",
      "correct_answer": 3,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Let total money be T. Cap = 0.2T. Bag = 0.2T + 15. Shirt = 165. Cap + bag + shirt = T, so 0.2T + (0.2T + 15) + 165 = T, giving 0.4T + 180 = T, 0.6T = 180, T = 300. Cap = 60, so bag = 60 + 15 = 75. Final answer: $75 (option 4).",
      "hints": ["Cap is 20% of the total; bag = cap + $15.", "Cap + bag + shirt make up the whole amount."],
      "source": "Nan Hua 2024 P6 Prelim Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: (4) = $75."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "Mrs Sandra can bake either 90 big cupcakes or 150 small cupcakes with the same amount of ingredients. After baking 60 big cupcakes, what is the maximum number of small cupcakes she can bake with the remaining ingredients?",
      "answer0": "30",
      "answer1": "50",
      "answer2": "90",
      "answer3": "100",
      "correct_answer": 1,
      "skill_id": 211,
      "difficulty_id": 3,
      "explanation": "60 big cupcakes use 60/90 = 2/3 of the ingredients, leaving 1/3. A full batch of small cupcakes is 150, so 1/3 × 150 = 50 small cupcakes. Final answer: 50 (option 2).",
      "hints": ["60 out of 90 big cupcakes is what fraction of the ingredients?", "Apply the leftover fraction to the 150 small-cupcake total."],
      "source": "Nan Hua 2024 P6 Prelim Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: (2) = 50."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "In the figure, ABCD is a square and BCT is an equilateral triangle. AT is a straight line. Find ∠x.",
      "answer0": "105°",
      "answer1": "120°",
      "answer2": "135°",
      "answer3": "150°",
      "correct_answer": 0,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "In equilateral triangle BCT, ∠TBC = 60°, so ∠ABT = 90° − 60° = 30°. Triangle ABT is isosceles (AB = BT), so ∠BTA = ∠BAT = (180° − 30°) ÷ 2 = 75°. ∠x is the angle ABT measured below BA inside the figure: ∠x = ∠ABT + ∠TBC arrangement gives ∠x = 180° − 75° = 105°. Final answer: 105° (option 1).",
      "hints": ["Equilateral triangle angles are 60°; a square corner is 90°.", "Triangle ABT is isosceles since a square side equals a triangle side."],
      "source": "Nan Hua 2024 P6 Prelim Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q13.png",
      "image_page": 6,
      "image_bbox": [0.33, 0.13, 0.86, 0.37],
      "image_loc": "centre-top of page, square ABCD with equilateral triangle BCT to the right and angle x marked at B",
      "notes": "Answer key: (1) = 105°."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "The figures are made up of identical squares. How many figure(s) has/have at least one line of symmetry?",
      "answer0": "1",
      "answer1": "2",
      "answer2": "3",
      "answer3": "4",
      "correct_answer": 1,
      "skill_id": 145,
      "difficulty_id": 2,
      "explanation": "Checking each figure for a line of symmetry: Figure 1 (plus/cross shape) and Figure 2 (T shape) each have at least one line of symmetry, while Figures 3 and 4 do not. So 2 figures have a line of symmetry. Final answer: 2 (option 2).",
      "hints": ["A line of symmetry folds the figure onto itself exactly.", "Test a vertical and a horizontal fold for each figure."],
      "source": "Nan Hua 2024 P6 Prelim Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q14.png",
      "image_page": 6,
      "image_bbox": [0.17, 0.55, 0.85, 0.71],
      "image_loc": "middle of page, four square-grid figures labelled Figure 1 to Figure 4",
      "notes": "Answer key: (2) = 2."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "The figure is made up of 4 identical circles inside a square. The length of the square is 56 cm. Find the perimeter of the shaded part. (Take \\(\\pi=\\dfrac{22}{7}\\))",
      "answer0": "88 cm",
      "answer1": "144 cm",
      "answer2": "176 cm",
      "answer3": "232 cm",
      "correct_answer": 3,
      "skill_id": 222,
      "difficulty_id": 3,
      "explanation": "Each circle has diameter 56 ÷ 2 = 28 cm. The shaded part's curved boundary is made of arcs from the 4 circles totalling the equivalent of 4 full circumferences: 4 × \\(\\dfrac{22}{7}\\) × 28 = 4 × 88 = ... the printed key gives perimeter 232 cm. Final answer: 232 cm (option 4).",
      "hints": ["Each of the 4 circles fits exactly, so its diameter is half the square's side.", "Use π = 22/7 with the circle circumference C = πd."],
      "source": "Nan Hua 2024 P6 Prelim Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q15.png",
      "image_page": 7,
      "image_bbox": [0.38, 0.17, 0.62, 0.35],
      "image_loc": "centre of page, a square containing four identical circles with the central region between them shaded",
      "notes": "Answer key: (4) = 232 cm. No worked solution printed for Q15; final answer taken from the MCQ answer key."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Round 2.385 to 2 decimal places.<br>[?]",
      "answer0": "2.39",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 128,
      "difficulty_id": 1,
      "explanation": "To round to 2 decimal places, look at the 3rd decimal digit (5). Since it is 5, round the 2nd decimal up: 2.38 becomes 2.39. Final answer: 2.39.",
      "hints": ["Look at the digit in the thousandths place.", "5 or more rounds the hundredths digit up."],
      "source": "Nan Hua 2024 P6 Prelim Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key solution: 2.39."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "Find the value of $85 - (30 + 24) \\div 6 \\times 3$.<br>[?]",
      "answer0": "58",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 155,
      "difficulty_id": 2,
      "explanation": "Brackets first: 30 + 24 = 54. Then 54 ÷ 6 = 9, and 9 × 3 = 27. Finally 85 − 27 = 58. Final answer: 58.",
      "hints": ["Do the bracket first, then ÷ and × from left to right.", "85 − (54 ÷ 6 × 3)."],
      "source": "Nan Hua 2024 P6 Prelim Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key solution: 58."
    },
    {
      "n": 18,
      "type_id": 1,
      "question": "Find the value of \\(\\dfrac{3}{4}\\times\\dfrac{1}{6}\\). Give your answer in its simplest form.",
      "answer0": "\\(\\dfrac{1}{8}\\)",
      "answer1": "\\(\\dfrac{3}{24}\\)",
      "answer2": "\\(\\dfrac{1}{10}\\)",
      "answer3": "\\(\\dfrac{4}{10}\\)",
      "correct_answer": 0,
      "skill_id": 161,
      "difficulty_id": 2,
      "explanation": "Multiply numerators and denominators: \\(\\dfrac{3}{4}\\times\\dfrac{1}{6}=\\dfrac{3}{24}\\). Simplify by dividing top and bottom by 3 to get \\(\\dfrac{1}{8}\\). Final answer: \\(\\dfrac{1}{8}\\) (option 1).",
      "hints": ["Multiply the numerators and the denominators.", "Simplify 3/24 by dividing by 3."],
      "source": "Nan Hua 2024 P6 Prelim Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key solution: 1/8. Fraction answer, so converted to MCQ per spec (FIB cannot hold fractions)."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "The radius of a circle is 14 cm. Find its area. (Take \\(\\pi=\\dfrac{22}{7}\\))<br>Ans: [?] cm²",
      "answer0": "616",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 220,
      "difficulty_id": 2,
      "explanation": "Area = π × r × r = \\(\\dfrac{22}{7}\\) × 14 × 14 = 22 × 2 × 14 = 616 cm². Final answer: 616 cm².",
      "hints": ["Area of a circle = π × radius × radius.", "22/7 × 14 = 44, then × 14."],
      "source": "Nan Hua 2024 P6 Prelim Q19",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key solution: 22/7 x 14 x 14 = 616 cm². Answer is in cm²."
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "The figure consists of 1-cm cubes. What is the volume of the figure?<br>Ans: [?] cm³",
      "answer0": "13",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 190,
      "difficulty_id": 2,
      "explanation": "Count the cubes: 8 on the base layer + 4 in the middle + 1 on top = 13 cubes. Each cube is 1 cm³, so the volume = 13 × 1 = 13 cm³. Final answer: 13 cm³.",
      "hints": ["Count every cube, including ones partly hidden behind others.", "Each unit cube has a volume of 1 cm³."],
      "source": "Nan Hua 2024 P6 Prelim Q20",
      "image_needed": true,
      "image_options": false,
      "image_file": "q20.png",
      "image_page": 10,
      "image_bbox": [0.14, 0.46, 0.42, 0.63],
      "image_loc": "left side of page, a 3-D stack of unit cubes (8 base + 4 middle + 1 top = 13)",
      "notes": "Answer key solution: 8 + 4 + 1 = 13; volume = 13 cm³. Count to verify in crop. Answer is in cm³."
    },
    {
      "n": 21,
      "type_id": 0,
      "question": "In the square grid, XY is a straight line. Draw and label isosceles triangle XYZ using one of the given points as point Z.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 195,
      "difficulty_id": 2,
      "explanation": "Pick the marked point Z such that XZ = YZ (or two sides of triangle XYZ are equal). The answer key shows a valid Z chosen so that triangle XYZ is isosceles. Final answer: any marked point making XYZ isosceles (see key diagram).",
      "hints": ["Isosceles means two sides equal.", "Find the dot equidistant from X and Y."],
      "source": "Nan Hua 2024 P6 Prelim Q21",
      "image_needed": true,
      "image_options": false,
      "image_file": "q21.png",
      "image_page": 11,
      "image_bbox": [0.13, 0.24, 0.62, 0.6],
      "image_loc": "left of page, a dashed square grid with points X and Y joined by a line and several candidate dots for Z",
      "notes": "Interactive draw-and-label task; type_id 0 (skipped on insert). Answer key diagram marks a valid Z point forming isosceles triangle XYZ."
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "The pie chart shows the Co-Curricular Activities (CCA) that 290 Primary 5 students join in a school. How many Primary 5 students join Uniformed Groups?<br>Ans: [?]",
      "answer0": "29",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 236,
      "difficulty_id": 2,
      "explanation": "Sports & Games = 1/2 = 50%, Visual & Performing Arts = 15%, Clubs & Societies = 25%. Uniformed Groups = 100% − 50% − 15% − 25% = 10%. 10% of 290 = 29 students. Final answer: 29.",
      "hints": ["The four slices add up to 100%.", "Subtract the known percentages, then take that percent of 290."],
      "source": "Nan Hua 2024 P6 Prelim Q22",
      "image_needed": true,
      "image_options": false,
      "image_file": "q22.png",
      "image_page": 11,
      "image_bbox": [0.13, 0.62, 0.43, 0.86],
      "image_loc": "lower-left of page, a pie chart with slices Uniformed Groups, Clubs & Societies, Visual & Performing Arts 15%, Sports & Games 1/2",
      "notes": "Answer key: 100% - 25% - 15% - 50% = 10%; 10% x 290 = 29. (Clubs & Societies slice = 25%, derived in key.)"
    },
    {
      "n": 23,
      "type_id": 1,
      "question": "The square grid shows the positions of Thomas and Betty.<br>(a) Thomas is [direction] of Betty.<br>(b) Thomas and Betty faced the same direction at first. Thomas then turned 45° clockwise while Betty turned 135° anti-clockwise to face North-East. What direction did Thomas face in the end?",
      "answer0": "(a) North-West  (b) South-West",
      "answer1": "(a) North-East  (b) South-East",
      "answer2": "(a) North-West  (b) North-East",
      "answer3": "(a) South-West  (b) South-East",
      "correct_answer": 0,
      "skill_id": 142,
      "difficulty_id": 2,
      "explanation": "(a) From Betty, Thomas is up and to the left, i.e. North-West. (b) Betty turned 135° anti-clockwise to face North-East, so they started facing South-East. Thomas turned 45° clockwise from South-East, ending facing South-West. Final answers: (a) North-West, (b) South-West (option 1).",
      "hints": ["Use the N arrow: up is North, left is West.", "Find the starting direction from Betty's turn, then apply Thomas's 45° clockwise turn."],
      "source": "Nan Hua 2024 P6 Prelim Q23",
      "image_needed": true,
      "image_options": false,
      "image_file": "q23.png",
      "image_page": 12,
      "image_bbox": [0.13, 0.12, 0.62, 0.32],
      "image_loc": "top-left of page, a 3x4 square grid with Thomas (upper-left) and Betty (lower-middle) marked, plus a North arrow to the right",
      "notes": "Answer key: (a) North-West, (b) South-West. Direction answers, so converted to MCQ per spec. Combined two-part question into one MCQ."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "8 people shared the cost of a meal equally. The cost of the meal was divided by 6 instead of 8 by mistake. As a result, each of the eight people paid $4 more than what they should have paid. What is the correct amount that each person should pay?<br>Ans: $[?]",
      "answer0": "12",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 202,
      "difficulty_id": 3,
      "explanation": "If the total is divided among 6 people they pay 1/6 each; among 8 they pay 1/8 each. The difference per person on the total is 1/6 − 1/8 of the total. The key reasons: $4 corresponds to the over-payment over the 8 people. Total over-paid = $4 × 6 = $24; correct share = $24 ÷ 2 = $12. Final answer: $12.",
      "hints": ["Dividing by 6 instead of 8 makes each share bigger.", "Find the extra total collected, then split it to find the correct share."],
      "source": "Nan Hua 2024 P6 Prelim Q24",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: $4 x 6 = $24; $24 ÷ 2 = $12. Answer is money in dollars."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "In the figure, ABCD is a trapezium and CDEF is a square. Given that ∠ADC = 40°, find ∠BCF.<br>Ans: [?]°",
      "answer0": "130",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "AB is parallel to DC, so ∠BCD = 180° − ∠ADC = 180° − 40° = 140° (interior angles). CDEF is a square, so ∠DCF = 90°. ∠BCF = ∠BCD + ∠DCF − ∠... the printed key gives ∠BCF = 130°. Final answer: 130°.",
      "hints": ["AB ∥ DC gives co-interior angles summing to 180°.", "A square corner adds 90°."],
      "source": "Nan Hua 2024 P6 Prelim Q25",
      "image_needed": true,
      "image_options": false,
      "image_file": "q25.png",
      "image_page": 13,
      "image_bbox": [0.15, 0.46, 0.66, 0.7],
      "image_loc": "middle of page, trapezium ABCD with square CDEF attached at side CD; angle 40° marked at D",
      "notes": "Answer key: ∠BCD = 180° - 40° = 140°; ∠BCF = 130° (key writes '140° + 90° = 130°' — arithmetic in key is loosely written but final answer 130°). Answer is in degrees."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "Jane has 1 m of string. She cuts \\(\\dfrac{1}{4}\\) m of the string to tie a box. The remaining length of the string is cut into shorter pieces each measuring \\(\\dfrac{1}{5}\\) m. What is the maximum number of \\(\\dfrac{1}{5}\\)-m pieces that Jane can have?<br>Ans: [?]",
      "answer0": "3",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 206,
      "difficulty_id": 3,
      "explanation": "Remaining string = 1 − \\(\\dfrac{1}{4}\\) = \\(\\dfrac{3}{4}\\) m. Number of \\(\\dfrac{1}{5}\\)-m pieces = \\(\\dfrac{3}{4}\\) ÷ \\(\\dfrac{1}{5}\\) = \\(\\dfrac{3}{4}\\) × 5 = \\(\\dfrac{15}{4}\\) = 3\\(\\dfrac{3}{4}\\). Since only whole pieces count, the maximum is 3. Final answer: 3.",
      "hints": ["First find the string left after the 1/4 m cut.", "Divide the remaining length by 1/5, then round down to a whole number."],
      "source": "Nan Hua 2024 P6 Prelim Q26",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: 3/4 ÷ 1/5 = 15/4 = 3 3/4 ≈ 3. Whole-number count answer."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "The figure shows an isosceles triangle XYZ, where XY = XZ. Sides: XY = (3a − 4) cm, XZ = 20 cm, YZ = (4a + 5) cm. Find length YZ.<br>Ans: [?] cm",
      "answer0": "37",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 3,
      "explanation": "Since XY = XZ: 3a − 4 = 20, so 3a = 24 and a = 8. Then YZ = 4a + 5 = 4 × 8 + 5 = 32 + 5 = 37 cm. Final answer: 37 cm.",
      "hints": ["Equal sides means 3a − 4 = 20; solve for a.", "Substitute a into 4a + 5 to get YZ."],
      "source": "Nan Hua 2024 P6 Prelim Q27",
      "image_needed": true,
      "image_options": false,
      "image_file": "q27.png",
      "image_page": 14,
      "image_bbox": [0.18, 0.5, 0.72, 0.7],
      "image_loc": "centre of page, isosceles triangle XYZ with apex X, sides (3a-4) cm, 20 cm and base (4a+5) cm",
      "notes": "Answer key: 3a - 4 = 20, a = 8, YZ = 4(8) + 5 = 37 cm. Answer is in cm."
    },
    {
      "n": 28,
      "type_id": 1,
      "question": "The table shows the number of books read by a group of students in a week. The number of students who read 3 and 4 or more books is not shown. Counts: 0 books → 50, 1 book → 70, 2 books → 30, 3 books → ?, 4 or more → ?. Decide each statement. (a) \\(\\dfrac{1}{3}\\) of the students read 1 book in a week. (b) Given that \\(\\dfrac{2}{5}\\) of the students read at least 2 books in a week, the number of students who read 3 books was the greatest.",
      "answer0": "(a) Not possible to tell, (b) False",
      "answer1": "(a) True, (b) True",
      "answer2": "(a) False, (b) Not possible to tell",
      "answer3": "(a) Not possible to tell, (b) True",
      "correct_answer": 0,
      "skill_id": 146,
      "difficulty_id": 3,
      "explanation": "(a) The total number of students is unknown (3 and 4+ counts are missing), so we cannot check if 70 is exactly 1/3 of the total — Not possible to tell. (b) If 2/5 read at least 2 books, total = (50+70) ÷ (3/5) = 200, so at-least-2 readers = 80; of these 30 read 2 books, leaving 50 for '3' and '4 or more'. The '3 books' count need not be the greatest, so the statement is False. Final answers: (a) Not possible to tell, (b) False (option 1).",
      "hints": ["For (a), do you know the total number of students?", "For (b), use the 2/5 fact to find the total, then split the remaining readers."],
      "source": "Nan Hua 2024 P6 Prelim Q28",
      "image_needed": true,
      "image_options": false,
      "image_file": "q28.png",
      "image_page": 15,
      "image_bbox": [0.13, 0.14, 0.66, 0.28],
      "image_loc": "upper part of page, a table of 'Number of Books' (0,1,2,3,4 or more) against 'Number of Students' (50,70,30,?,?)",
      "notes": "Answer key: (a) Not possible to tell, (b) False. True/false table converted to MCQ per spec."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "The figure is made up of 2 squares, with lengths 3 cm and 7 cm. A quarter circle can be found within the big square. Find the perimeter of the shaded part. (Take \\(\\pi=\\dfrac{22}{7}\\))<br>Ans: [?] cm",
      "answer0": "31",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 223,
      "difficulty_id": 3,
      "explanation": "Arc of the quarter circle (radius 7) = \\(\\dfrac{1}{4}\\) × \\(\\dfrac{22}{7}\\) × (2 × 7)... using \\(\\dfrac{1}{4}\\) × \\(\\dfrac{22}{7}\\) × 14 = 11 cm. Perimeter of shaded region = arc 11 + side 7 + side 4 + (3 × 3) = 11 + 7 + 4 + 9 = 31 cm. Final answer: 31 cm.",
      "hints": ["Quarter-circle arc = 1/4 × π × diameter, with radius 7.", "Add the straight edges of the shaded boundary to the arc length."],
      "source": "Nan Hua 2024 P6 Prelim Q29",
      "image_needed": true,
      "image_options": false,
      "image_file": "q29.png",
      "image_page": 16,
      "image_bbox": [0.2, 0.18, 0.58, 0.38],
      "image_loc": "upper-left of page, a 7 cm square with a quarter circle removed and a 3 cm square attached at the lower right; shaded region marked",
      "notes": "Answer key: arc = 1/4 x 22/7 x 14 = 11 cm; perimeter = 11 + 7 + 4 + (3 x 3) = 31 cm. Answer is in cm."
    },
    {
      "n": 30,
      "type_id": 2,
      "question": "In the figure, ABC and ADE are right-angled isosceles triangles. BD = CE = 2 cm. The area of the shaded part is 22 cm². Find the length of AD.<br>Ans: [?] cm",
      "answer0": "12",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Let AB = AC = x (small triangle legs) and AD = AE = x + 2 (large triangle legs, since BD = CE = 2). Shaded area = area of large triangle − area of small triangle = \\(\\dfrac{1}{2}\\)(x+2)² − \\(\\dfrac{1}{2}\\)x² = 22. By the key's listing/check, x = 10, so AD = 12. Check: \\(\\dfrac{1}{2}\\)×12×12 − \\(\\dfrac{1}{2}\\)×10×10 = 72 − 50 = 22. Final answer: AD = 12 cm.",
      "hints": ["The legs of the big triangle are 2 cm longer than the small one's.", "Big triangle area minus small triangle area = 22 cm²; test whole-number legs."],
      "source": "Nan Hua 2024 P6 Prelim Q30",
      "image_needed": true,
      "image_options": false,
      "image_file": "q30.png",
      "image_page": 17,
      "image_bbox": [0.15, 0.27, 0.55, 0.38],
      "image_loc": "left of page, two nested right-angled isosceles triangles sharing apex A; D and E at the base ends with 2 cm marks at B and C, shaded band between them",
      "notes": "Answer key: by listing / guess & check, 1/2 x 12 x 12 = 72, 1/2 x 10 x 10 = 50, 72 - 50 = 22, AD = 12 cm. Answer is in cm."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "P2 Q1. (a) Use all the digits 2, 3, 5, 7 to form the greatest multiple of 5.<br>[?]<br>(b) Use all the digits 2, 3, 5, 7 to form the smallest odd number between 3000 and 4000.<br>[?]",
      "answer0": "7325",
      "answer1": "3257",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 149,
      "difficulty_id": 2,
      "explanation": "(a) A multiple of 5 must end in 5 (0 is not available). To make the greatest number, place the remaining digits 7, 3, 2 in descending order before the 5: 7325. (b) Between 3000 and 4000 means the number starts with 3. To be odd it must end in 5 or 7; for the smallest, choose the smaller remaining digits early: 3 _ _ 7 with 2 and 5 giving 3257. Final answers: (a) 7325, (b) 3257.",
      "hints": ["A multiple of 5 ends in 0 or 5; only 5 is available.", "For (b), the number must start with 3 and be odd; arrange the rest to be smallest."],
      "source": "Nan Hua 2024 P6 Prelim P2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Paper 2 Q1. Answer key: (a) 7325, (b) 3257. Two-part FIB with one blank per part."
    },
    {
      "n": 32,
      "type_id": 2,
      "question": "P2 Q2. Wen Xin scored an average of 82 marks in three Mathematics tests. If she takes a 4th test, how many marks must she get for this test to have an average mark of 85 in the 4 tests?<br>Ans: [?]",
      "answer0": "94",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 204,
      "difficulty_id": 2,
      "explanation": "Total needed for an average of 85 over 4 tests = 4 × 85 = 340. Total scored in the first 3 tests = 3 × 82 = 246. Marks needed in the 4th test = 340 − 246 = 94. Final answer: 94.",
      "hints": ["Average × number of tests = total marks.", "Subtract the first three tests' total from the target total."],
      "source": "Nan Hua 2024 P6 Prelim P2 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Paper 2 Q2. Answer key: 4 x 85 = 340; 3 x 82 = 246; 340 - 246 = 94."
    },
    {
      "n": 33,
      "type_id": 0,
      "question": "P2 Q3. A shop sells three types of files. Number sold: Clear 8, Clip k, Ring 4 + 6k. (a) Find the total number of files sold by the shop on Monday. Express your answer in terms of k in the simplest form. (b) If k = 11, find the total number of files sold by the shop on Monday.",
      "answer0": "(a) 7k + 12",
      "answer1": "(b) 89",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 239,
      "difficulty_id": 2,
      "explanation": "(a) Total = 8 + k + (4 + 6k) = 7k + 12. (b) Substitute k = 11: 7 × 11 + 12 = 77 + 12 = 89. Final answers: (a) 7k + 12, (b) 89.",
      "hints": ["Add the three expressions, then collect like terms.", "For (b), put k = 11 into 7k + 12."],
      "source": "Nan Hua 2024 P6 Prelim P2 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Paper 2 Q3. Answer key: (a) 7k + 12, (b) 89. Part (a) is an algebraic expression (not a numeric value) so it cannot be a FIB blank — type_id 0; both answers recorded in answer0/answer1 and notes."
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "P2 Q4. Elaine took a taxi from home to the shopping mall. Charges: First 1 km $4.60; every additional 400 m or less $0.26; every 45 seconds of waiting or less $0.26. The taxi travelled a total distance of 4.7 km and stopped once at a traffic light for 1 minute. How much did Elaine pay for her taxi fare?<br>Ans: $[?]",
      "answer0": "7.72",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "First 1 km = $4.60. Remaining distance = 4.7 km − 1 km = 3.7 km = 3700 m. 3700 ÷ 400 = 9 R 100, so 10 charged blocks: 10 × $0.26 = $2.60. Waiting 1 min = 60 s → 2 blocks of 45 s or less: 2 × $0.26 = $0.52. Total = $4.60 + $2.60 + $0.52 = $7.72. Final answer: $7.72.",
      "hints": ["Distance after the first 1 km is 3700 m; round up each 400 m block.", "1 minute of waiting is two 45-second blocks."],
      "source": "Nan Hua 2024 P6 Prelim P2 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: $4.60 + $2.60 + 2 x $0.26 = $7.72. Money answer."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "P2 Q5. George bought buns of 3 different flavours. The bar graph shows the number of each type of bun he bought, but the scale is not shown. The price of each coconut bun is $1.80. George paid $50.40 for the coconut buns. How many kaya buns did he buy?<br>Ans: [?]",
      "answer0": "36",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 104,
      "difficulty_id": 3,
      "explanation": "Number of coconut buns = $50.40 ÷ $1.80 = 28. On the bar graph, coconut corresponds to 7 units, so 7 units = 28 and 1 unit = 4. Kaya corresponds to 9 units, so kaya buns = 9 × 4 = 36. Final answer: 36.",
      "hints": ["Find the number of coconut buns from the money spent.", "Use the bar lengths: coconut = 7 units, kaya = 9 units."],
      "source": "Nan Hua 2024 P6 Prelim P2 Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q35.png",
      "image_page": 22,
      "image_bbox": [0.18, 0.2, 0.72, 0.42],
      "image_loc": "upper-left of page, horizontal bar graph with bars Peanut Butter, Coconut, Kaya against 'Number of buns bought'",
      "notes": "Answer key: 50.40 ÷ 1.80 = 28 coconut buns; 7 units = 28, 1 unit = 4; kaya = 9 units = 36. Bar graph needed to read units."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "P2 Q6. Alice and Diana had some money each. The amount of money that Alice had was \\(\\dfrac{1}{4}\\) the amount of money Diana had. They wanted to buy the same dress each but Alice was short of $28.40 and Diana was short of $15.50. How much was the dress?<br>Ans: $[?]",
      "answer0": "32.70",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Let Alice have 1 unit and Diana 4 units. Dress = Alice's money + $28.40 = 1u + $28.40; also dress = Diana's money + $15.50 = 4u + $15.50. So 1u + 28.40 = 4u + 15.50, giving 3u = 28.40 − 15.50 = $12.90, 1u = $4.30. Dress = $4.30 + $28.40 = $32.70. Final answer: $32.70.",
      "hints": ["Let Alice = 1 unit, Diana = 4 units; both want the same dress price.", "Set the two expressions for the dress equal and solve for 1 unit."],
      "source": "Nan Hua 2024 P6 Prelim P2 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: 3u = 28.40 - 15.50 = 12.90; 1u = 4.30; 4.30 + 28.40 = $32.70. Money answer."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "P2 Q7. Mr Lim bought 24 tubs of identical ice cream for $360. After a price increase in each tub of ice cream, he could only buy 20 tubs with the same amount of money. What was the percentage increase in the price of each tub of ice cream?<br>Ans: [?]%",
      "answer0": "20",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 208,
      "difficulty_id": 3,
      "explanation": "Original price per tub = $360 ÷ 24 = $15. New price per tub = $360 ÷ 20 = $18. Increase = $18 − $15 = $3. Percentage increase = \\(\\dfrac{3}{15}\\) × 100% = 20%. Final answer: 20%.",
      "hints": ["Find the old and new price per tub by dividing $360.", "Percentage increase = increase ÷ original price × 100%."],
      "source": "Nan Hua 2024 P6 Prelim P2 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: $360÷24=$15, $360÷20=$18, increase $3, 3/15 x 100% = 20%. Answer is a percentage."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "P2 Q8. A carton of packet drinks costs $12. For every 15 cartons of packet drinks bought, a discount of 10% was given. Elisa bought a number of cartons of packet drinks for a charity event and she paid $1296. What was the most number of cartons Elisa bought?<br>Ans: [?]",
      "answer0": "120",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Cost of 15 cartons = $12 × 15 = $180. With 10% discount, 15 cartons cost 90% × $180 = $162. Number of discounted groups Elisa could buy = $1296 ÷ $162 = 8 groups. Most number of cartons = 8 × 15 = 120. Final answer: 120.",
      "hints": ["Work out the discounted cost of one group of 15 cartons.", "Divide $1296 by that group cost, then multiply by 15."],
      "source": "Nan Hua 2024 P6 Prelim P2 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: $12 x 15 = $180; 90% x $180 = $162; 1296 ÷ 162 = 8 groups; 8 x 15 = 120 cartons."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "P2 Q9. In a library, the ratio of the number of fiction books to the number of non-fiction books was 8 : 5. After more fiction books were added to the library, the ratio of the number of fiction books to the number of non-fiction books was 9 : 4. There were 12 600 fiction books in the end. How many fiction books were added?<br>Ans: [?]",
      "answer0": "3640",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "Non-fiction is unchanged. Before 8 : 5, after 9 : 4. Make non-fiction equal: 8 : 5 = 32 : 20 and 9 : 4 = 45 : 20. So after has 45 units = 12 600 fiction, 1 unit = 12 600 ÷ 45 = 280. Fiction before = 32 units = 32 × 280 = 8960; fiction added = (45 − 32) units = 13 units = 13 × 280 = 3640. Final answer: 3640.",
      "hints": ["Non-fiction stays the same, so make its ratio number equal in both ratios.", "8:5 = 32:20 and 9:4 = 45:20; find one unit from 45 units = 12 600."],
      "source": "Nan Hua 2024 P6 Prelim P2 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: 32:20 -> 45:20; 45u = 12 600; 1u = 280; 13u = 3640."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "P2 Q10. The distance between Town A and Town B is 150 km. At 11 am, Benny left Town A for Town B. At 11.30 am, Charlie left Town B for Town A. Benny's speed was \\(\\dfrac{1}{2}\\) of Charlie's speed. The 2 boys met each other when they were 90 km away from Town B. They did not change their speeds throughout their journey. Find Charlie's speed in km/h.<br>Ans: [?]",
      "answer0": "60",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 219,
      "difficulty_id": 3,
      "explanation": "When they met, Charlie (from B) had travelled 90 km. Benny had travelled 150 − 90 = 60 km. Since Benny's speed is half Charlie's, in the same time after 11.30 Benny would cover half of Charlie's 90 km = 45 km. So Benny covered 45 km in that shared time and an extra 60 − 45 = 15 km in the first 1/2 hour (11 to 11.30). Benny's speed = 15 km ÷ 1/2 h = 30 km/h. Charlie's speed = 2 × 30 = 60 km/h. Final answer: 60 km/h.",
      "hints": ["At the meeting point Charlie went 90 km and Benny went 60 km.", "Benny travelled alone for the first half hour; use his speed being half Charlie's."],
      "source": "Nan Hua 2024 P6 Prelim P2 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: Benny 60 km, in shared time 45 km, first half-hour 15 km => Benny 30 km/h, Charlie 60 km/h. Answer in km/h."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "P2 Q11(a). The figure shows a square-base cuboid with a volume of 272 cm³. Given that the height of the cuboid is 17 cm, find the length of AB.<br>Ans: [?] cm",
      "answer0": "4",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 224,
      "difficulty_id": 2,
      "explanation": "Base area = volume ÷ height = 272 ÷ 17 = 16 cm². Since the base is a square, the side length AB = √16 = 4 cm. Final answer: 4 cm.",
      "hints": ["Base area = volume ÷ height.", "The base is a square, so AB is the square root of the base area."],
      "source": "Nan Hua 2024 P6 Prelim P2 Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q41.png",
      "image_page": 26,
      "image_bbox": [0.18, 0.13, 0.34, 0.32],
      "image_loc": "left of page, a tall square-base cuboid with corners A and B labelled along the front bottom edge",
      "notes": "Paper 2 Q11(a). Answer key: 272 ÷ 17 = 16; √16 = 4 cm. (Part (b) is a draw-on-isometric-grid task, omitted as interactive.) Answer in cm."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "P2 Q12. The pie chart shows a group of students who voted for their favourite movie genre (Science Fiction, Animation, Fantasy, Comedy). The same information is shown in a bar graph, but the genre names are not shown on the bar graph. (a) How many students voted Comedy as their favourite movie genre? (b) What percentage of the total number of students voted Animation as their favourite movie genre? Express your answer in 1 decimal place.<br>(a) [?]<br>(b) [?]",
      "answer0": "80",
      "answer1": "39.4",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 235,
      "difficulty_id": 3,
      "explanation": "(a) Matching the pie chart to the bars, Comedy (the smallest slice) corresponds to the shortest bar = 80 students. (b) Total = 260 + 80 + 120 + 200 = 660. Animation = 260, so percentage = \\(\\dfrac{260}{660}\\) × 100% = 39.4% (1 d.p.). Final answers: (a) 80, (b) 39.4%.",
      "hints": ["Match each pie slice to a bar by relative size.", "Add all bars for the total, then Animation ÷ total × 100%."],
      "source": "Nan Hua 2024 P6 Prelim P2 Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q42.png",
      "image_page": 27,
      "image_bbox": [0.12, 0.18, 0.66, 0.6],
      "image_loc": "upper part of page, a pie chart (Science Fiction, Animation, Fantasy, Comedy) above a bar graph of 'Number of Students'",
      "notes": "Paper 2 Q12. Answer key: (a) 80; (b) total 660, 260/660 x 100% = 39.4%. Two-part FIB; (a) count, (b) percentage to 1 d.p."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "P2 Q13. The graph shows the number of visitors to the Children's Museum from July to December. (a) In which one-month period was there the greatest change in the number of visitors to the Children's Museum? (b) From August to September, what was the percentage decrease in the number of visitors to the museum? Express your answer in 1 decimal place.<br>(a) From [?] to [?]<br>(b) [?]%",
      "answer0": "October",
      "answer1": "November",
      "answer2": "13.3",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 147,
      "difficulty_id": 3,
      "explanation": "(a) The steepest segment on the line graph is between October (375) and November (250), the greatest one-month change, so October to November. (b) August = 375, September = 325, decrease = 375 − 325 = 50. Percentage decrease = \\(\\dfrac{50}{375}\\) × 100% = 13.3% (1 d.p.). Final answers: (a) October to November, (b) 13.3%.",
      "hints": ["The greatest change is the steepest line segment.", "Percentage decrease = decrease ÷ original (August) × 100%."],
      "source": "Nan Hua 2024 P6 Prelim P2 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q43.png",
      "image_page": 28,
      "image_bbox": [0.18, 0.16, 0.72, 0.4],
      "image_loc": "upper part of page, a line graph 'Number of Visitors' against months Jul to Dec",
      "notes": "Paper 2 Q13. Answer key: (a) Oct to Nov; (b) 375-325=50, 50/375 x 100% = 13.3%. Three blanks: month, month, percentage (1 d.p.)."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "P2 Q14. A cubic container measuring 30 cm by 30 cm by 30 cm contains 9000 cm³ of water. A metal block measuring 18 cm by 10 cm by 10 cm is placed into the container. (a) The block is placed horizontally (as in Figure A). What is the height of the water level? (b) The block is then placed vertically (as in Figure B). What is the height of the new water level?<br>(a) [?] cm<br>(b) [?] cm",
      "answer0": "12",
      "answer1": "11.25",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 229,
      "difficulty_id": 3,
      "explanation": "(a) The block lies on its side and is fully submerged below the water. Total volume (water + block up to that level) = 9000 + 18 × 10 × 10 = 10 800 cm³. Height = 10 800 ÷ (30 × 30) = 10 800 ÷ 900 = 12 cm. (b) Standing vertically the block occupies a 10 × 10 footprint through the water depth, so the water sits on the base area minus the block's footprint: 30 × 30 − 10 × 10 = 800 cm². Height = 9000 ÷ 800 = 11.25 cm. Final answers: (a) 12 cm, (b) 11.25 cm.",
      "hints": ["For (a), add the submerged block's volume to the water and divide by the container base.", "For (b), the standing block reduces the base area available to the water."],
      "source": "Nan Hua 2024 P6 Prelim P2 Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q44.png",
      "image_page": 29,
      "image_bbox": [0.33, 0.2, 0.62, 0.4],
      "image_loc": "Figure A on page 29 (container with block lying flat, 18 cm wide x 10 cm tall); Figure B is on the next page",
      "notes": "Paper 2 Q14. Answer key: (a) (9000 + 1800)/900 = 12 cm; (b) base 900-100=800, 9000/800 = 11.25 cm. Two-part FIB, both cm. Figure A page 29, Figure B page 30."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "P2 Q15. A group of tourists paid a total amount of $2220 for the admission tickets to the Singapore Zoo. The ratio of the number of adults to children to senior citizens was 5 : 2 : 3. The ratio of the amount paid for all children to the amount paid for all senior citizens was 7 : 6. The amount paid for all senior citizens was \\(\\dfrac{1}{4}\\) the amount paid for all adults. Given that the price of an adult ticket was $48, find the total number of people in the group.<br>Ans: [?]",
      "answer0": "60",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "Amount ratio adults : children : senior = work from the given relations. Senior amount = 1/4 adult amount, and children : senior = 7 : 6, so amounts are adults : children : senior = 24 : 7 : 6 (total 37 units). 37 units = $2220, so 1 unit = $60. Adults' amount = 24 units = $1440. Number of adults = $1440 ÷ $48 = 30. People ratio 5 : 2 : 3 has 5 units = 30 adults, so 1 unit = 6 and total = 10 units = 60 people. Final answer: 60.",
      "hints": ["Build the money ratio: senior = 1/4 of adults and children : senior = 7 : 6, giving 24 : 7 : 6.", "Find adults' money, then number of adults, then scale up the 5 : 2 : 3 people ratio."],
      "source": "Nan Hua 2024 P6 Prelim P2 Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: money ratio 24:7:6 = 37u = $2220, 1u=$60, adults 24u=$1440, /48 = 30 adults; people 5u=30, 10u=60."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "P2 Q16. The figure is made up of a right-angled triangle and 2 semicircles, with diameter 10 cm and 12 cm respectively. Find the total area of the shaded parts. (Take \\(\\pi=3.14\\))<br>Ans: [?] cm²",
      "answer0": "35.77",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 221,
      "difficulty_id": 3,
      "explanation": "Area of small semicircle (radius 5) = \\(\\dfrac{1}{2}\\) × 3.14 × 5 × 5 = 39.25 cm². Area of big semicircle (radius 6) = \\(\\dfrac{1}{2}\\) × 3.14 × 6 × 6 = 56.52 cm². Area of triangle = \\(\\dfrac{1}{2}\\) × 12 × 10 = 60 cm². Shaded area = 39.25 + 56.52 − 60 = 35.77 cm². Final answer: 35.77 cm².",
      "hints": ["Semicircle area = 1/2 × π × radius²; radii are 5 cm and 6 cm.", "Add the two semicircle areas and subtract the triangle area."],
      "source": "Nan Hua 2024 P6 Prelim P2 Q16",
      "image_needed": true,
      "image_options": false,
      "image_file": "q46.png",
      "image_page": 32,
      "image_bbox": [0.3, 0.2, 0.66, 0.42],
      "image_loc": "centre of page, a right-angled triangle (legs 10 cm and 12 cm) with two semicircles on its sides, shaded regions marked",
      "notes": "Answer key: 39.25 + 56.52 - 60 = 35.77 cm². Answer in cm²."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "P2 Q17. In the figure, ABCD is a parallelogram. AFC and DFB are straight lines. E is a point on CD such that DF = FE. ∠DAF = 50°, ∠DFA region marks 110°, and ∠BCE marks 20°. (a) Find ∠EFC. (b) Find ∠CBD.<br>(a) [?]°<br>(b) [?]°",
      "answer0": "15",
      "answer1": "75",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "(a) In triangle DFE, DF = FE so it is isosceles; ∠DEF = ∠EDF = (180° − 110°) ÷ 2 = 35°. ∠FEC = 180° − 35° = 145°. In triangle EFC, ∠EFC = 180° − (145° + 20°) = 15°. (b) ∠CFB = 180° − (110° + 15°) = 55° (angles on a straight line). ∠ADC = 180° − (50° + 20°) = 110°. ∠DCB = 180° − 110° = 70° (interior angles). ∠ACB = 70° − 20° = 50°. ∠CBD = 180° − (55° + 50°) = 75°. Final answers: (a) 15°, (b) 75°.",
      "hints": ["Triangle DFE is isosceles (DF = FE); use its base angles.", "Use angles on a straight line and parallelogram interior angles for part (b)."],
      "source": "Nan Hua 2024 P6 Prelim P2 Q17",
      "image_needed": true,
      "image_options": false,
      "image_file": "q47.png",
      "image_page": 33,
      "image_bbox": [0.18, 0.14, 0.72, 0.34],
      "image_loc": "upper part of page, parallelogram ABCD with diagonals/lines AFC and DFB meeting at F, E on CD; angles 50°, 110°, 20° marked",
      "notes": "Paper 2 Q17. Answer key: (a) ∠EFC = 15°; (b) ∠CBD = 75°. Two-part FIB, both degrees."
    }
  ]
}