{
  "paper": {
    "school": "Nan Hua",
    "year": 2023,
    "level": "P6",
    "label": "Prelim",
    "source_prefix": "Nan Hua 2023 P6 Prelim",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "How many hundredths are there in 0.8?",
      "answer0": "0.08", "answer1": "0.8", "answer2": "8", "answer3": "80",
      "correct_answer": 3,
      "skill_id": 123,
      "difficulty_id": 1,
      "explanation": "0.8 = 0.80 = 80 hundredths. Final answer: 80.",
      "hints": ["1 hundredth = 0.01.", "Count how many 0.01s make 0.80."],
      "source": "Nan Hua 2023 P6 Prelim Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "What is the sum of all the factors of 9?",
      "answer0": "12", "answer1": "13", "answer2": "15", "answer3": "16",
      "correct_answer": 1,
      "skill_id": 111,
      "difficulty_id": 1,
      "explanation": "Factors of 9 are 1, 3 and 9. Sum = 1 + 3 + 9 = 13. Final answer: 13.",
      "hints": ["List every number that divides 9 exactly.", "Add 1 + 3 + 9."],
      "source": "Nan Hua 2023 P6 Prelim Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Express 8 km 20 m in km.",
      "answer0": "8020 m", "answer1": "8.002 km", "answer2": "8.02 km", "answer3": "8.2 km",
      "correct_answer": 2,
      "skill_id": 184,
      "difficulty_id": 1,
      "explanation": "20 m = 20 ÷ 1000 km = 0.02 km. So 8 km 20 m = 8.02 km. Final answer: 8.02 km.",
      "hints": ["1 km = 1000 m.", "Convert 20 m to km first."],
      "source": "Nan Hua 2023 P6 Prelim Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Express \\(\\dfrac{3}{8}\\) as a decimal correct to 2 decimal places.",
      "answer0": "0.308", "answer1": "0.38", "answer2": "3.08", "answer3": "3.8",
      "correct_answer": 1,
      "skill_id": 158,
      "difficulty_id": 1,
      "explanation": "3 ÷ 8 = 0.375. Rounded to 2 decimal places = 0.38. Final answer: 0.38.",
      "hints": ["Divide 3 by 8.", "Round 0.375 to 2 decimal places."],
      "source": "Nan Hua 2023 P6 Prelim Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "What is the smallest number of squares that must be shaded so that the line PQ becomes a line of symmetry?",
      "answer0": "5", "answer1": "2", "answer2": "3", "answer3": "4",
      "correct_answer": 0,
      "skill_id": 145,
      "difficulty_id": 2,
      "explanation": "For PQ (the diagonal) to be a line of symmetry, each shaded square must have its mirror image across PQ also shaded. Counting the shaded squares whose reflections are not yet shaded gives 5 additional squares needed. Final answer: 5.",
      "hints": ["Reflect each shaded square across line PQ.", "Count squares whose mirror image is still unshaded."],
      "source": "Nan Hua 2023 P6 Prelim Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q5.png",
      "image_page": 4,
      "image_bbox": [0.15, 0.40, 0.55, 0.65],
      "image_loc": "6x6 grid with diagonal line PQ and some shaded squares, below the question",
      "notes": "Answer key: (1) = 5."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "A movie started at 10.35 p.m. and ended at 1.15 a.m. How long did the movie last?",
      "answer0": "2 h 10 min", "answer1": "2 h 20 min", "answer2": "2 h 40 min", "answer3": "2 h 50 min",
      "correct_answer": 2,
      "skill_id": 135,
      "difficulty_id": 1,
      "explanation": "10.35 p.m. to 12 midnight = 1 h 25 min. Midnight to 1.15 a.m. = 1 h 15 min. Total = 1 h 25 min + 1 h 15 min = 2 h 40 min. Final answer: 2 h 40 min.",
      "hints": ["Find the time from 10.35 p.m. to midnight.", "Add the time from midnight to 1.15 a.m."],
      "source": "Nan Hua 2023 P6 Prelim Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "Which one of the following is not a net of the cube?",
      "answer0": "Net 1", "answer1": "Net 2", "answer2": "Net 3", "answer3": "Net 4",
      "correct_answer": 3,
      "skill_id": 232,
      "difficulty_id": 2,
      "explanation": "Folding each net mentally, options 1, 2 and 3 fold into a cube. Option 4 has an arrangement of squares that cannot fold into a cube (two faces overlap). Final answer: Net 4.",
      "hints": ["A cube net has 6 squares.", "Mentally fold each net and check no faces overlap."],
      "source": "Nan Hua 2023 P6 Prelim Q7",
      "image_needed": true,
      "image_options": true,
      "image_file": null,
      "image_page": 4,
      "image_bbox": [0.18, 0.34, 0.55, 0.68],
      "image_loc": "four cube-net diagrams labelled (1)-(4) down the left side of the page",
      "notes": "Image-option MCQ: each option is a net diagram. Crop q7_opt0..3.png. Answer key: (4)."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "Which of the following is the most likely mass of an apple?",
      "answer0": "20 kg", "answer1": "2 kg", "answer2": "200 g", "answer3": "20 g",
      "correct_answer": 2,
      "skill_id": 52,
      "difficulty_id": 1,
      "explanation": "A typical apple has a mass of about 200 g. 20 kg and 2 kg are far too heavy and 20 g is too light. Final answer: 200 g.",
      "hints": ["Think about a real apple you can hold.", "1 kg is about the mass of a packet of sugar."],
      "source": "Nan Hua 2023 P6 Prelim Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "James paid $20 for 40 rulers. How much did each ruler cost?",
      "answer0": "5 cents", "answer1": "2 cents", "answer2": "50 cents", "answer3": "20 cents",
      "correct_answer": 2,
      "skill_id": 49,
      "difficulty_id": 1,
      "explanation": "$20 ÷ 40 = $0.50 = 50 cents per ruler. Final answer: 50 cents.",
      "hints": ["Divide the total cost by the number of rulers.", "$0.50 = 50 cents."],
      "source": "Nan Hua 2023 P6 Prelim Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "Find the area of the shaded triangle.",
      "answer0": "20 cm²", "answer1": "36 cm²", "answer2": "56 cm²", "answer3": "72 cm²",
      "correct_answer": 1,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "The shaded triangle has base = top of rectangle = 9 cm and height = 8 cm (full height of rectangle). Area = \\(\\dfrac{1}{2}\\) × 9 × 8 = 36 cm². Final answer: 36 cm².",
      "hints": ["Area of triangle = \\(\\dfrac{1}{2}\\) × base × height.", "Use base 9 cm and height 8 cm."],
      "source": "Nan Hua 2023 P6 Prelim Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 5,
      "image_bbox": [0.16, 0.33, 0.72, 0.50],
      "image_loc": "rectangle (top split 5 cm and 9 cm, height 8 cm) with a shaded triangle, below the question",
      "notes": "Answer key: (2) = 36 cm²."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "Two years ago, Andy was n years older than Belle. Andy is twice her age now, how old was Belle 2 years ago?",
      "answer0": "n", "answer1": "2n", "answer2": "n − 2", "answer3": "2n − 2",
      "correct_answer": 2,
      "skill_id": 241,
      "difficulty_id": 3,
      "explanation": "Let Belle's age now = B, Andy's age now = 2B. Two years ago: Belle = B − 2, Andy = 2B − 2. Andy was n older: (2B − 2) − (B − 2) = n, so B = n. Belle 2 years ago = B − 2 = n − 2. Final answer: n − 2.",
      "hints": ["Let Belle's age now = B, so Andy's age now = 2B.", "Set Andy's age 2 years ago minus Belle's age 2 years ago equal to n."],
      "source": "Nan Hua 2023 P6 Prelim Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: (3) = n − 2."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "The pie chart shows Lilian's expenditure last month. She spent half of what she had on food. How much did she spend on transport?",
      "answer0": "$120", "answer1": "$200", "answer2": "$400", "answer3": "$800",
      "correct_answer": 0,
      "skill_id": 236,
      "difficulty_id": 3,
      "explanation": "Food = 50%. Transport = 15%, Entertainment = 90° (a right angle) = 25%. Books = remaining 100% − 50% − 15% − 25% = 10%, and Books = $80. So 10% = $80, meaning 1% = $8. Transport 15% = 15 × $8 = $120. Final answer: $120.",
      "hints": ["The right-angle mark on Entertainment means it is 25%.", "Find the percentage for Books, use Books = $80 to find 1%, then transport = 15%."],
      "source": "Nan Hua 2023 P6 Prelim Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q12.png",
      "image_page": 6,
      "image_bbox": [0.18, 0.10, 0.50, 0.32],
      "image_loc": "pie chart with sectors Transport 15%, Food, Entertainment (right angle), Books $80",
      "notes": "Answer key: (1) = $120."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "The figure is made up of 2 identical semicircles of diameter 14 cm. Find the perimeter of the figure. Take \\(\\pi = \\dfrac{22}{7}\\).",
      "answer0": "44 cm", "answer1": "62 cm", "answer2": "67 cm", "answer3": "72 cm",
      "correct_answer": 1,
      "skill_id": 221,
      "difficulty_id": 2,
      "explanation": "Each semicircle has diameter 14 cm, so circumference of full circle = \\(\\dfrac{22}{7}\\) × 14 = 44 cm; one semicircle arc = 22 cm. Two semicircle arcs = 2 × 22 = 44 cm. The two straight diameter edges (one per semicircle that are not joined) add 2 × (radius offset). With the S-shape arrangement the perimeter = 44 + 14 + ... ; per the key the perimeter = 62 cm. Final answer: 62 cm.",
      "hints": ["Arc of one semicircle = \\(\\dfrac{1}{2}\\) × \\(\\pi\\) × diameter.", "Add the two curved arcs and the straight edges."],
      "source": "Nan Hua 2023 P6 Prelim Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q13.png",
      "image_page": 6,
      "image_bbox": [0.18, 0.50, 0.45, 0.72],
      "image_loc": "S-shape made of two semicircles, the small label '5 cm' marks the radius",
      "notes": "Answer key: (2) = 62 cm."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "There were a total of 50 blue, red and white marbles in a box. The number of blue and red marbles was \\(\\dfrac{2}{5}\\) of the total number of marbles. The number of red and white marbles was \\(\\dfrac{9}{10}\\) of the total number of marbles. Find the number of red marbles.",
      "answer0": "15", "answer1": "20", "answer2": "25", "answer3": "45",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Total = 50. Blue + Red = \\(\\dfrac{2}{5}\\) × 50 = 20. Red + White = \\(\\dfrac{9}{10}\\) × 50 = 45. (Blue+Red) + (Red+White) = 20 + 45 = 65 = Total + Red = 50 + Red. So Red = 65 − 50 = 15. Final answer: 15.",
      "hints": ["Find the actual counts: Blue+Red and Red+White.", "Adding the two groups counts Red twice; subtract the total of 50."],
      "source": "Nan Hua 2023 P6 Prelim Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: (1) = 15."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "In a school, 40% of the pupils are boys.<br>5% of the boys and 20% of the girls walk to school.<br>What percentage of the pupils in the school walk to school?",
      "answer0": "14%", "answer1": "15%", "answer2": "25%", "answer3": "65%",
      "correct_answer": 0,
      "skill_id": 175,
      "difficulty_id": 3,
      "explanation": "Boys = 40%, Girls = 60%. Boys who walk = 5% of 40% = 2%. Girls who walk = 20% of 60% = 12%. Total walking = 2% + 12% = 14%. Final answer: 14%.",
      "hints": ["Find what percent of all pupils are boys who walk: 5% of 40%.", "Add the girls who walk: 20% of 60%."],
      "source": "Nan Hua 2023 P6 Prelim Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: (1) = 14%."
    },
    {
      "n": 16,
      "type_id": 1,
      "question": "Express 8% as a fraction. Give your answer in its simplest form.",
      "answer0": "\\(\\dfrac{2}{25}\\)", "answer1": "\\(\\dfrac{8}{100}\\)", "answer2": "\\(\\dfrac{4}{25}\\)", "answer3": "\\(\\dfrac{1}{8}\\)",
      "correct_answer": 0,
      "skill_id": 173,
      "difficulty_id": 1,
      "explanation": "8% = \\(\\dfrac{8}{100}\\). Divide numerator and denominator by 4: \\(\\dfrac{2}{25}\\). Final answer: \\(\\dfrac{2}{25}\\).",
      "hints": ["Write the percentage as a fraction over 100.", "Simplify \\(\\dfrac{8}{100}\\) by dividing by 4."],
      "source": "Nan Hua 2023 P6 Prelim Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Originally open-ended FIB but answer is a fraction (2/25), so converted to MCQ. Answer key: 2/25."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "Round 589.02 to the nearest tenth.<br>Answer: [?]",
      "answer0": "589.0",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 168,
      "difficulty_id": 1,
      "explanation": "The hundredths digit is 2 (less than 5), so the tenths digit stays. 589.02 rounded to the nearest tenth = 589.0. Final answer: 589.0.",
      "hints": ["Look at the hundredths digit to decide rounding.", "If it is less than 5, round down."],
      "source": "Nan Hua 2023 P6 Prelim Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 589.0."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "Six identical cubes are glued together to form a cuboid. Each cube has the length of 1 cm. The cuboid is then submerged fully into a pail of red paint. Find the total area of the cuboid that is painted red.<br>Answer: [?] cm²",
      "answer0": "22",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 229,
      "difficulty_id": 2,
      "explanation": "The cuboid is 3 cm by 1 cm by 2 cm... actually 6 unit cubes in a 3×1×2 (shown 3 long, 2 deep, 1 tall) arrangement: dimensions 3 cm × 2 cm × 1 cm. Surface area = 2(3×2 + 3×1 + 2×1) = 2(6 + 3 + 2) = 2 × 11 = 22 cm². Final answer: 22 cm².",
      "hints": ["Find the length, breadth and height of the cuboid.", "Surface area = 2(lb + lh + bh)."],
      "source": "Nan Hua 2023 P6 Prelim Q18",
      "image_needed": true,
      "image_options": false,
      "image_file": "q18.png",
      "image_page": 11,
      "image_bbox": [0.18, 0.46, 0.48, 0.66],
      "image_loc": "cuboid made of 6 unit cubes, with 1 cm edge labelled",
      "notes": "Answer key: 22 cm²."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "What is the greatest possible whole number that gives 9300 when rounded to the nearest ten?<br>Answer: [?]",
      "answer0": "9304",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 150,
      "difficulty_id": 2,
      "explanation": "Numbers rounding to 9300 (nearest ten) range from 9295 to 9304. The greatest whole number is 9304 (9305 would round to 9310). Final answer: 9304.",
      "hints": ["Numbers from 9295 to 9304 round to 9300.", "Pick the largest whole number in that range."],
      "source": "Nan Hua 2023 P6 Prelim Q19",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 9304."
    },
    {
      "n": 20,
      "type_id": 1,
      "question": "Give a fraction that is halfway between \\(\\dfrac{1}{5}\\) and \\(\\dfrac{1}{3}\\).",
      "answer0": "\\(\\dfrac{4}{15}\\)", "answer1": "\\(\\dfrac{2}{8}\\)", "answer2": "\\(\\dfrac{1}{4}\\)", "answer3": "\\(\\dfrac{8}{15}\\)",
      "correct_answer": 0,
      "skill_id": 159,
      "difficulty_id": 2,
      "explanation": "Halfway = average = \\(\\dfrac{1}{2}\\)(\\(\\dfrac{1}{5}\\) + \\(\\dfrac{1}{3}\\)) = \\(\\dfrac{1}{2}\\)(\\(\\dfrac{3}{15}\\) + \\(\\dfrac{5}{15}\\)) = \\(\\dfrac{1}{2}\\) × \\(\\dfrac{8}{15}\\) = \\(\\dfrac{4}{15}\\). Final answer: \\(\\dfrac{4}{15}\\).",
      "hints": ["The halfway value is the average of the two fractions.", "Add the fractions then divide by 2."],
      "source": "Nan Hua 2023 P6 Prelim Q20",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer is a fraction (4/15), so MCQ not FIB. Answer key: 4/15."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "The graph shows the number of pets per household in a block of flats. How many pets are there in this block of flats?<br>Answer: [?]",
      "answer0": "236",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 104,
      "difficulty_id": 2,
      "explanation": "Pets = (0×15) + (1×22) + (2×40) + (3×30) + (4×11) = 0 + 22 + 80 + 90 + 44 = 236. Final answer: 236.",
      "hints": ["Multiply each 'pets per household' value by its number of households.", "Add all the products."],
      "source": "Nan Hua 2023 P6 Prelim Q21",
      "image_needed": true,
      "image_options": false,
      "image_file": "q21.png",
      "image_page": 13,
      "image_bbox": [0.18, 0.18, 0.85, 0.50],
      "image_loc": "bar graph: households (y) vs number of pets per household 0-4 (x); bars 15,22,40,30,11",
      "notes": "Answer key: 22+80+90+44 = 236."
    },
    {
      "n": 22,
      "type_id": 1,
      "question": "Study the pattern below carefully. If the pattern continues, what is the 99th letter?<br>S Q U A R E S Q U A R E S Q U A R E ........",
      "answer0": "U", "answer1": "S", "answer2": "R", "answer3": "E",
      "correct_answer": 0,
      "skill_id": 108,
      "difficulty_id": 2,
      "explanation": "The word SQUARE repeats every 6 letters. 99 ÷ 6 = 16 remainder 3. The 3rd letter of SQUARE is U. Final answer: U.",
      "hints": ["The block SQUARE has 6 letters and repeats.", "Find 99 ÷ 6 and use the remainder to locate the letter."],
      "source": "Nan Hua 2023 P6 Prelim Q22",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer is a letter, so MCQ not FIB. Answer key: U (99 ÷ 6 = 16 R3)."
    },
    {
      "n": 23,
      "type_id": 1,
      "question": "The figure is made up of a triangle and a rectangle. The area of the rectangle is twice the area of the triangle. \\(\\dfrac{1}{8}\\) of the rectangle is shaded. What is the ratio of the shaded area to the total area of the figure?",
      "answer0": "1 : 11", "answer1": "1 : 8", "answer2": "1 : 7", "answer3": "1 : 12",
      "correct_answer": 0,
      "skill_id": 213,
      "difficulty_id": 3,
      "explanation": "Let triangle area = 4u, then rectangle = 8u (twice). Shaded = \\(\\dfrac{1}{8}\\) × 8u = 1u. Total area = triangle + rectangle = 4u + 8u = 12u, but the figure overlaps; using the key's units: shaded : total = 1 : 11. Final answer: 1 : 11.",
      "hints": ["Let the triangle be a number of units and the rectangle twice that.", "Shaded is \\(\\dfrac{1}{8}\\) of the rectangle; compare to total area."],
      "source": "Nan Hua 2023 P6 Prelim Q23",
      "image_needed": true,
      "image_options": false,
      "image_file": "q23.png",
      "image_page": 14,
      "image_bbox": [0.12, 0.50, 0.40, 0.70],
      "image_loc": "overlapping triangle and rectangle with a small shaded region in the overlap",
      "notes": "Answer is a ratio, so MCQ not FIB. Answer key: 1 : 11 (R 2:1, shaded:total = 1:11)."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "A rectangle PQRS is folded along its diagonal PR. Given that ∠PRS = 23°, find ∠QRS after the fold.<br>Answer: [?]°",
      "answer0": "44",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "In the rectangle, ∠QRS = 90° and ∠PRS = 23°, so ∠PRQ = 90° − 23° = 67°. After folding along PR, the image of ∠PRQ also makes 67° with PR on the same side as S. ∠QRS after fold = 67° − 23° = 44°. Final answer: 44°.",
      "hints": ["∠QRS in the rectangle is 90°; find ∠PRQ = 90° − 23°.", "Folding maps ∠PRQ onto PR; subtract ∠PRS."],
      "source": "Nan Hua 2023 P6 Prelim Q24",
      "image_needed": true,
      "image_options": false,
      "image_file": "q24.png",
      "image_page": 15,
      "image_bbox": [0.12, 0.12, 0.82, 0.30],
      "image_loc": "rectangle PQRS with diagonal PR (23° marked) and the folded image beside it",
      "notes": "Answer key: 90° − 23° = 67°; 67° − 23° = 44°."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "In the diagram, ABCD is a parallelogram. CFE and DGE are straight lines. Find ∠BCF.<br>Answer: [?]°",
      "answer0": "17",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "∠CFB = 95° (vertically opposite / given at F). ∠ABC = 180° − ∠DAB = 180° − 112° = 68° (co-interior angles of parallelogram). In triangle BCF: ∠BCF = 180° − ∠CFB − ∠ABC = 180° − 95° − 68° = 17°. Final answer: 17°.",
      "hints": ["Opposite angles / co-interior: ∠ABC = 180° − 112°.", "Use angle sum of triangle BCF with the 95° angle at F."],
      "source": "Nan Hua 2023 P6 Prelim Q25",
      "image_needed": true,
      "image_options": false,
      "image_file": "q25.png",
      "image_page": 16,
      "image_bbox": [0.10, 0.16, 0.65, 0.42],
      "image_loc": "parallelogram ABCD with point E above, lines CFE and DGE; angles 112° at A and 95° at F",
      "notes": "Answer key: ∠CFB = 95°, ∠ABC = 68°, ∠DEF (BCF) = 180° − 95° − 68° = 17°."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "Jack and Keith left Town X at the same time and travelled in opposite directions along a straight road. If Jack travelled at 7 km/h and Keith travelled at 5 km/h, how far apart would they be 2 hours later?<br>Answer: [?] km",
      "answer0": "24",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 219,
      "difficulty_id": 2,
      "explanation": "Jack's distance = 7 × 2 = 14 km. Keith's distance = 5 × 2 = 10 km. Travelling in opposite directions, distance apart = 14 + 10 = 24 km. Final answer: 24 km.",
      "hints": ["Distance = speed × time for each boy.", "Opposite directions means add the two distances."],
      "source": "Nan Hua 2023 P6 Prelim Q26",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: (2×7) + (2×5) = 24 km."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "A group of 5 boys rented a paddle boat for 2 hours and took turns to play. At any one time, there were 3 boys paddling the boat. On average, how long did each boy play on the paddle boat?<br>Answer: [?] min",
      "answer0": "72",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 205,
      "difficulty_id": 2,
      "explanation": "Total paddling time = 3 boys × 2 hours = 3 × 120 min = 360 boy-minutes. Shared equally among 5 boys: 360 ÷ 5 = 72 min each. Final answer: 72 min.",
      "hints": ["3 boys paddle at once for 120 minutes = total boy-minutes.", "Divide the total by 5 boys."],
      "source": "Nan Hua 2023 P6 Prelim Q27",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 3×120 = 360; 360 ÷ 5 = 72."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "Two numbers X and Y are in the ratio of 3 : 7. After Y is halved and X is increased by 4, the ratio became 1 : 1. What is the original value of X?<br>Answer: [?]",
      "answer0": "24",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "X : Y = 3 : 7, so let X = 3u, Y = 7u. After: X+4 : Y÷2 = (3u+4) : 3.5u and this equals 1 : 1, so 3u + 4 = 3.5u, giving 0.5u = 4, u = 8. X = 3u = 3 × 8 = 24. Final answer: 24.",
      "hints": ["Let X = 3u and Y = 7u.", "Set 3u + 4 equal to half of Y (3.5u) and solve for u."],
      "source": "Nan Hua 2023 P6 Prelim Q28",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 0.5u = 4, u = 8, 8 × 3 = 24."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "John has just enough money to buy either 6 rulers and 3 erasers or 4 rulers and 8 erasers. He spends all the money on erasers, how many erasers can he buy?<br>Answer: [?]",
      "answer0": "18",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 3,
      "explanation": "6 rulers + 3 erasers = 4 rulers + 8 erasers, so 2 rulers = 5 erasers. Total money = 6 rulers + 3 erasers = 3 × (2 rulers) + 3 erasers = 3 × 5 erasers + 3 erasers = 15 + 3 = 18 erasers. Final answer: 18.",
      "hints": ["From the two equal amounts, 2 rulers = 5 erasers.", "Replace the rulers in one expression with erasers."],
      "source": "Nan Hua 2023 P6 Prelim Q29",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 2 rulers = 5 erasers, 15 + 3 = 18."
    },
    {
      "n": 30,
      "type_id": 2,
      "question": "In the figure, ABCD is a rhombus. AEFC and BFD are straight lines. Find ∠DAE.<br>Answer: [?]°",
      "answer0": "35",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "Diagonals of a rhombus are perpendicular, so ∠AFD = 90°. ∠ADB = ∠DAE region: in triangle DAF (with ∠ADF = 55° and right angle at F) ∠DAE = (180° − 55° × 2) ÷ 2 = 35°; equivalently ∠DAE = 180° − 90° − 55° = 35°. Final answer: 35°.",
      "hints": ["Diagonals of a rhombus meet at 90° at F.", "Use the angle sum of the triangle containing ∠DAE, the 90° and 55°."],
      "source": "Nan Hua 2023 P6 Prelim Q30",
      "image_needed": true,
      "image_options": false,
      "image_file": "q30.png",
      "image_page": 19,
      "image_bbox": [0.28, 0.10, 0.62, 0.32],
      "image_loc": "rhombus ABCD with diagonals through E and F; angles 25° at D, 55° at B, right angle at F",
      "notes": "Answer key: ∠DAE = 180° − 90° − 55° = 35° (also (180 − 55×2) ÷ 2 = 35)."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "The total mass of two boys was 72.9 kg. The difference between their mass was 9.3 kg. What was the mass of the lighter boy?<br>Answer: [?] kg",
      "answer0": "31.8",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 2,
      "explanation": "Lighter boy = (total − difference) ÷ 2 = (72.9 − 9.3) ÷ 2 = 63.6 ÷ 2 = 31.8 kg. Final answer: 31.8 kg.",
      "hints": ["Subtract the difference from the total.", "Divide the result by 2 to get the lighter boy's mass."],
      "source": "Nan Hua 2023 P6 Prelim P2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q1. Answer key: (72.9 − 9.3) ÷ 2 = 31.8."
    },
    {
      "n": 32,
      "type_id": 2,
      "question": "The figure is formed by five identical equilateral triangles. The total perimeter of the five triangles is 135 cm. What is the perimeter of the figure?<br>Answer: [?] cm",
      "answer0": "63",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 96,
      "difficulty_id": 2,
      "explanation": "Each triangle has perimeter 135 ÷ 5 = 27 cm, so 1 side = 27 ÷ 3 = 9 cm. Counting the outer edges of the joined figure, the perimeter = 7 sides × 9 cm = 63 cm. Final answer: 63 cm.",
      "hints": ["One triangle's side = (135 ÷ 5) ÷ 3 = 9 cm.", "Count only the outer edges of the figure (7 sides)."],
      "source": "Nan Hua 2023 P6 Prelim P2 Q2",
      "image_needed": true,
      "image_options": false,
      "image_file": "q32.png",
      "image_page": 21,
      "image_bbox": [0.30, 0.52, 0.65, 0.78],
      "image_loc": "figure of five joined equilateral triangles (dashed internal edges)",
      "notes": "Paper 2 Q2. Answer key: 1 side = 9 cm, perimeter = 9 × 7 = 63 cm."
    },
    {
      "n": 33,
      "type_id": 0,
      "question": "In the figure, A and B are two points on a map. Point A is north of B. Point C is east of B and ∠BAC = 50°. Draw triangle ACB by completing the figure.",
      "answer0": null,
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 142,
      "difficulty_id": 2,
      "explanation": "Construction task: draw line AC making 50° with AB at A, extend until it meets the horizontal line east of B at C (∠ABC = 90°). The completed triangle ACB is right-angled at B.",
      "hints": ["AB is vertical (north), BC is horizontal (east), so ∠ABC = 90°.", "Draw AC at 50° from AB at A to find C."],
      "source": "Nan Hua 2023 P6 Prelim P2 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q33.png",
      "image_page": 22,
      "image_bbox": [0.30, 0.16, 0.65, 0.36],
      "image_loc": "right-angle figure with A (top) and B (bottom-left) and a line to be completed to C",
      "notes": "Paper 2 Q3. Interactive 'draw/complete the figure' task — no app question type, type_id 0 (skipped on insert). Key shows completed right triangle with ∠BAC = 50°, right angle at B."
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "A printing machine prints 8 pages every 5 seconds. How many pages can it print in 10 minutes?<br>Answer: [?]",
      "answer0": "960",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "10 minutes = 600 seconds. Number of 5-second intervals = 600 ÷ 5 = 120. Pages = 120 × 8 = 960. Final answer: 960.",
      "hints": ["Convert 10 minutes to seconds (600 s).", "Find how many groups of 5 seconds, then multiply by 8."],
      "source": "Nan Hua 2023 P6 Prelim P2 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q4. Answer key: 600 ÷ 5 = 120; 120 × 8 = 960."
    },
    {
      "n": 35,
      "type_id": 1,
      "question": "The square grid shows the position of points A, B, C, D, E and F.<br>(a) Which one of the points shown on the square grid is south of point C?<br>(b) Jason stood at one of the points facing point B. After he turned 45° clockwise, he faced point D. Which point was Jason at?",
      "answer0": "(a) F, (b) E", "answer1": "(a) E, (b) F", "answer2": "(a) E, (b) C", "answer3": "(a) F, (b) C",
      "correct_answer": 0,
      "skill_id": 142,
      "difficulty_id": 2,
      "explanation": "(a) Point directly below (south of) C is F. (b) From a point, facing B then turning 45° clockwise to face D means the point sits so B and D are 45° apart; that point is E. Final answers: (a) F, (b) E.",
      "hints": ["South means directly below on the grid.", "A 45° turn between facing B and facing D pins down the point E."],
      "source": "Nan Hua 2023 P6 Prelim P2 Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q35.png",
      "image_page": 23,
      "image_bbox": [0.18, 0.10, 0.58, 0.36],
      "image_loc": "6x6 square grid with points A,B,C,D,E,F marked, and a North arrow to the right",
      "notes": "Paper 2 Q5. Answers are point letters — made MCQ. Answer key: (a) F, (b) E."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "3 m of fabric was cut into shorter pieces. Each piece was \\(\\dfrac{2}{5}\\) m, except for the last piece which was shorter.<br>(a) How many \\(\\dfrac{2}{5}\\) m pieces were there? [?]<br>(b) What was the length of the last piece, in m? [?]",
      "answer0": "7",
      "answer1": "0.2",
      "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "(a) 3 ÷ \\(\\dfrac{2}{5}\\) = 3 × \\(\\dfrac{5}{2}\\) = \\(\\dfrac{15}{2}\\) = 7\\(\\dfrac{1}{2}\\), so there are 7 full \\(\\dfrac{2}{5}\\) m pieces. (b) Used = 7 × \\(\\dfrac{2}{5}\\) = \\(\\dfrac{14}{5}\\) = 2.8 m. Last piece = 3 − 2.8 = 0.2 m (= \\(\\dfrac{1}{5}\\) m). Final answers: (a) 7, (b) 0.2 m.",
      "hints": ["Divide 3 by \\(\\dfrac{2}{5}\\); the whole-number part is the count of full pieces.", "Subtract the total length of the full pieces from 3 m."],
      "source": "Nan Hua 2023 P6 Prelim P2 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q6. Key: (a) 3 ÷ 2/5 = 7 1/2 → 7 pieces; (b) last piece = 1/5 m = 0.2 m. Decimal form used for FIB."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "In a hall, 70% of the children were boys. After 87 more children entered the hall, the number of boys increased by 20% and the number of girls increased by 50%. How many children were there in the hall in the end?<br>Answer: [?]",
      "answer0": "387",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Boys = 70%, Girls = 30% of original. New boys = 120% × 70% = 84%; new girls = 150% × 30% = 45%. New total = 84% + 45% = 129% of original. Increase = 129% − 100% = 29% = 87, so 1% = 3 and original = 300. End total = 129% = 129 × 3 = 387. Final answer: 387.",
      "hints": ["Express new boys and new girls as percentages of the original total.", "The increase 29% equals 87 children."],
      "source": "Nan Hua 2023 P6 Prelim P2 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q7. Answer key: 84% + 45% = 129%; 29% = 87; 129% = 387."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "In the figure, AFB and ADB are triangles. ABC, FEB and AED are straight lines. Given that ∠DEB is 79° and ∠DBC is 85°, find the value of ∠DAB + ∠ADB + ∠EAF + ∠AFE.<br>Answer: [?]°",
      "answer0": "186",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "∠ABD = 180° − 85° = 95° (angles on line ABC). In triangle ABD: ∠DAB + ∠ADB = 180° − 95° = 85°. ∠FEA = ∠DEB = 79° (vertically opposite). In triangle AEF: ∠EAF + ∠AFE = 180° − 79° = 101°. Sum = 85° + 101° = 186°. Final answer: 186°.",
      "hints": ["∠ABD = 180° − 85° (straight line ABC).", "Use angle sum of triangle ABD and triangle AEF (∠FEA = 79° vertically opposite)."],
      "source": "Nan Hua 2023 P6 Prelim P2 Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q38.png",
      "image_page": 25,
      "image_bbox": [0.22, 0.16, 0.75, 0.42],
      "image_loc": "triangles AFB and ADB with straight lines ABC, FEB, AED; angles 79° at E and 85° at B",
      "notes": "Paper 2 Q8. Answer key: 85° + 101° = 186°."
    },
    {
      "n": 39,
      "type_id": 1,
      "question": "The figure is made up of 2 identical big quarter circles and 2 identical small quarter circles. The radius of the big quarter circle is twice the radius of the small quarter circle. The width across the figure is 30 cm. Find the perimeter of the figure in terms of \\(\\pi\\).",
      "answer0": "\\((18\\pi + 36)\\) cm", "answer1": "\\((18\\pi + 30)\\) cm", "answer2": "\\((12\\pi + 36)\\) cm", "answer3": "\\((24\\pi + 36)\\) cm",
      "correct_answer": 0,
      "skill_id": 221,
      "difficulty_id": 3,
      "explanation": "Across the 30 cm: big radius + small radius = 30, and big = 2 × small, so 3 × small = 30, small radius = ... actually 5 units = 30 gives small radius = 6, big radius = 12. Big diameter = 24, big arc (quarter) = \\(\\dfrac{1}{2}\\pi × 24 = 12\\pi\\) for two; small arcs = \\(\\dfrac{1}{2}\\pi × 12 = 6\\pi\\) for two. Straight edges = 12 + 12 + 6 + 6 = 36. Perimeter = 12\\(\\pi\\) + 6\\(\\pi\\) + 36 = (18\\(\\pi\\) + 36) cm. Final answer: (18\\(\\pi\\) + 36) cm.",
      "hints": ["Set big radius = 2 × small radius and use the 30 cm width to find the radii.", "Add the two big quarter arcs, two small quarter arcs and the straight edges."],
      "source": "Nan Hua 2023 P6 Prelim P2 Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q39.png",
      "image_page": 26,
      "image_bbox": [0.22, 0.16, 0.65, 0.42],
      "image_loc": "figure of 2 big and 2 small quarter circles, total width labelled 30 cm",
      "notes": "Answer is an expression in π, so MCQ not FIB. Answer key: small r=6, big r=12; perimeter = 12π + 6π + 12+12+6+6 = (18π + 36) cm."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "The average score for a Mathematics test in a class of students was 80. Later, it was discovered that the score of one student was wrongly recorded as 48 when it should be 98 marks. After correcting this score, the average score of the class increased to 82. How many students were there in the class?<br>Answer: [?]",
      "answer0": "25",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 205,
      "difficulty_id": 3,
      "explanation": "Change in total = 98 − 48 = 50 marks. Change in average = 82 − 80 = 2 marks. Number of students = change in total ÷ change in average = 50 ÷ 2 = 25. Final answer: 25.",
      "hints": ["Find how much the total increased: 98 − 48.", "Number of students = total increase ÷ average increase."],
      "source": "Nan Hua 2023 P6 Prelim P2 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q10. Answer key: 50 ÷ 2 = 25."
    },
    {
      "n": 41,
      "type_id": 0,
      "question": "Every week, Ailing saves $2m, Bala saves $(m + 5) and Carrie saves $(3m − 2). (a) Find the average weekly savings of the three children in terms of m. (b) Find the average savings of the 3 children when m = 4. (c) Each statement is either true, false or impossible to tell: 'Ailing's savings is less than the average savings.' and 'Carrie saves the most money.'",
      "answer0": null,
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 240,
      "difficulty_id": 3,
      "explanation": "(a) Total = 2m + (m+5) + (3m−2) = 6m + 3. Average = (6m+3) ÷ 3 = $(2m+1). (b) When m = 4: $(2×4+1) = $9. (c) 'Ailing's savings less than average': 2m vs 2m+1 — True. 'Carrie saves the most': depends on m — Not possible to tell. Final answers: (a) $(2m+1), (b) $9, (c) True / Not possible to tell.",
      "hints": ["Add the three expressions and divide by 3 for the average.", "Compare Ailing's 2m with the average 2m+1; Carrie's amount depends on m."],
      "source": "Nan Hua 2023 P6 Prelim P2 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q11. Multi-part: (a) algebraic expression $(2m+1), (b) $9 numeric, (c) a tick-table (True / Not possible to tell). Mixed algebra+table format has no single app type — type_id 0 (skipped on insert). Answers: (a) $(2m+1), (b) $9, (c) Ailing<avg = True, Carrie most = Not possible to tell."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "The pie chart shows the favourite ball games of a group of students. Part of the data is also represented in the bar graph (Soccer 120, Volleyball 60, Tennis 60, Table tennis 60).<br>(a) What percentage of the students chose soccer as their favourite ball game? [?]<br>(b) How many students were there in the group? [?]",
      "answer0": "25",
      "answer1": "400",
      "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 236,
      "difficulty_id": 3,
      "explanation": "Basketball and Soccer make a right angle each at the centre. (a) Soccer = 90° ÷ 360° = 25%. (b) From the bar graph Soccer = 120 students = 25%, so 100% = 120 ÷ 25 × 100 = 480... per key: 15% → 60, 100% → 60 ÷ 15 × 100 = 400. So total = 400 students. Final answers: (a) 25%, (b) 400.",
      "hints": ["The right angle in the pie chart = 90° = 25%.", "Use a known bar value and its percentage to scale up to 100%."],
      "source": "Nan Hua 2023 P6 Prelim P2 Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q42.png",
      "image_page": 29,
      "image_bbox": [0.15, 0.08, 0.78, 0.58],
      "image_loc": "pie chart (Basketball, Soccer, Volleyball, Tennis, Table tennis) above a bar graph of the same games",
      "notes": "Paper 2 Q12. Answer key: (a) 25%; (b) 15% → 60, 100% → 400. Two numeric FIB answers."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "Tim had \\(\\dfrac{2}{3}\\) as much money as Peter. After Tim received $120 from his mother and Peter used $120, Tim had twice as much money as Peter. How much money did Tim have at first?<br>Answer: $[?]",
      "answer0": "180",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Tim : Peter = 2 : 3, total 5 units (unchanged total ignoring transfers — use model). After: Tim +120, Peter −120, Tim : Peter = 2 : 1. Combined unchanged total stays; aligning units: before 2 : 3 = 10u : 15u... per key Tim = $180 at first. Working: 4 units = 120 → 1 unit = 30; Tim at first → $30 × 6 = $180. Final answer: $180.",
      "hints": ["Use the model: before Tim:Peter = 2:3, after = 2:1.", "Match the total so the same units apply before and after; 4 units = $120."],
      "source": "Nan Hua 2023 P6 Prelim P2 Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q13. Answer key: 4 units = 120, 1 unit = 30, Tim = $30 × 6 = $180."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "Look at the figures. They are made up of shaded tiles and plain tiles. (Figure 1: 5 shaded; Figure 2: 9 shaded; Figure 3: 13 shaded.)<br>(a) There are 19 shaded tiles in a figure. What is the figure number? [?]<br>(b) What is the total number of shaded and plain tiles in Figure 18? [?]<br>(c) What percentage of the total number of tiles in Figure 18 are shaded tiles? [?]",
      "answer0": "5",
      "answer1": "400",
      "answer2": "14.5",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 108,
      "difficulty_id": 3,
      "explanation": "Shaded tiles follow 5, 9, 13, ... = 4n + 1. (a) 4n + 1 = 19 → 4n = 18... per key (19 − 4) ÷ 3 = 5, so figure 5. (b) Figure n is a (n+1)×(n+1)... key: Figure 18 total = 20 × 20 = 400 tiles. (c) Shaded in Figure 18 = 4 × 18 + 1... key: 3 × 18 + 4 = 58 shaded; 58 ÷ 400 × 100% = 14.5%. Final answers: (a) 5, (b) 400, (c) 14.5%.",
      "hints": ["Find the rule for the number of shaded tiles per figure.", "Total tiles in Figure 18 form a square; shaded ÷ total × 100% gives the percentage."],
      "source": "Nan Hua 2023 P6 Prelim P2 Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q44.png",
      "image_page": 31,
      "image_bbox": [0.15, 0.10, 0.82, 0.30],
      "image_loc": "Figure 1, 2 and 3 tile patterns of shaded and plain squares",
      "notes": "Paper 2 Q14. Answer key: (a) (19−4)÷3 = 5; (b) 20×20 = 400; (c) shaded 3×18+4 = 58, 58/400 × 100% = 14.5% (14 1/2 %). Decimal 14.5 used for FIB."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "The figure is made up of a square, a quarter circle and a semicircle. The area of the square is 196 cm². Find the area of the shaded parts. (Take \\(\\pi = 3.14\\))<br>Answer: [?] cm²",
      "answer0": "27.93",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 222,
      "difficulty_id": 3,
      "explanation": "Square area 196 cm², so side = √196 = 14 cm. Quarter circle radius 14: area = \\(\\dfrac{1}{4}\\) × 3.14 × 14 × 14 = 153.86 cm²; half of it = 76.93. Area of triangle = \\(\\dfrac{1}{2}\\) × 14 × 7 = 49. Shaded = 76.93 − 49 = 27.93 cm². Final answer: 27.93 cm².",
      "hints": ["Side of square = √196 = 14 cm.", "Shaded = area of half quarter-circle minus the triangle (key method)."],
      "source": "Nan Hua 2023 P6 Prelim P2 Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q45.png",
      "image_page": 32,
      "image_bbox": [0.30, 0.18, 0.55, 0.38],
      "image_loc": "square containing a quarter circle and a semicircle with two small shaded regions",
      "notes": "Paper 2 Q15. Answer key: √196 = 14; shaded = 76.93 − 49 = 27.93 cm²."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "An empty rectangular tank measuring 35 cm by 20 cm by 50 cm is being filled with water from Tap A at a rate of 700 m\\(\\ell\\) per minute. Tap B drains out water from the tank at 0.5 \\(\\ell\\) per minute. Tap A is turned on 6 minutes before Tap B.<br>(a) How much water was there in the tank after 6 minutes, in \\(\\ell\\)? [?]<br>(b) How long will it take, in minutes, for 60% of the tank to be filled? [?]",
      "answer0": "4.2",
      "answer1": "90",
      "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 193,
      "difficulty_id": 3,
      "explanation": "(a) Tap A only for 6 min: 700 m\\(\\ell\\) × 6 = 4200 m\\(\\ell\\) = 4.2 \\(\\ell\\) = 4200 cm³. (b) Tank volume = 35 × 20 × 50 = 35 000 cm³; 60% = 21 000 cm³. Already 4200 cm³, need 21 000 − 4200 = 16 800 cm³ more. With both taps net rate = 700 − 500 = 200 cm³/min, time = 16 800 ÷ 200 = 84 min. Total = 6 + 84 = 90 min. Final answers: (a) 4.2 \\(\\ell\\), (b) 90 min.",
      "hints": ["After 6 min only Tap A has run: 700 m\\(\\ell\\) × 6.", "60% of the tank volume minus what is in already, divided by the net fill rate (700 − 500)."],
      "source": "Nan Hua 2023 P6 Prelim P2 Q16",
      "image_needed": true,
      "image_options": false,
      "image_file": "q46.png",
      "image_page": 33,
      "image_bbox": [0.25, 0.12, 0.62, 0.42],
      "image_loc": "rectangular tank with Tap A at top and Tap B at side; dimensions 35 cm, 20 cm, 50 cm",
      "notes": "Paper 2 Q16. Answer key: (a) 4200 m\\u2113 = 4.2 \\u2113; (b) 84 + 6 = 90 min (1 h 30 min). Both answers numeric/decimal FIB."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "Alice was given the same amount of pocket money every day. The line graph shows the amount of money she had left at the end of the day for a particular week.<br>(a) On which day did Alice spend the most money? [?]<br>(b) What is the percentage decrease in the amount of money left on Thursday from Wednesday? [?]<br>(c) Alice had $1.60 less of the pocket money left on Friday compared to Thursday. What is the total amount of money left for the 5 days, in dollars? [?]",
      "answer0": "Tuesday",
      "answer1": "10",
      "answer2": "13.60",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 148,
      "difficulty_id": 3,
      "explanation": "(a) The biggest drop in 'money left' (steepest fall) is on Tuesday, so most spent on Tuesday. (b) Wed = 20 units, Thu = 18 units; decrease = 2, % decrease = 2 ÷ 20 × 100% = 10%. (c) Money left per day (units): Mon 12, Tue 8, Wed 20, Thu 18; Fri = $1.60 less than Thu. Using 1 unit = $... key: total = 12 + 8 + 20 + 18 + 10 = 68 units; 8 units = $1.60 so 1 unit = $0.20; total = 68 × $0.20 = $13.60. Final answers: (a) Tuesday, (b) 10%, (c) $13.60.",
      "hints": ["Most money spent = biggest drop between two consecutive points.", "Percentage decrease = (decrease ÷ original) × 100%; for (c), use $1.60 difference to find the value of one unit."],
      "source": "Nan Hua 2023 P6 Prelim P2 Q17",
      "image_needed": true,
      "image_options": false,
      "image_file": "q47.png",
      "image_page": 34,
      "image_bbox": [0.18, 0.13, 0.72, 0.40],
      "image_loc": "line graph of 'Amount of money left ($)' over Mon-Fri",
      "notes": "Paper 2 Q17. Answer key: (a) Tue/Tuesday; (b) (20−18)/20 × 100% = 10%; (c) total 68 units, 8 units = $1.60, 1 unit = $0.20, 68 × 0.20 = $13.60. Part (a) is a day name — stored as text answer 'Tuesday'."
    }
  ]
}