{
  "paper": {
    "school": "Rosyth School",
    "year": 2025,
    "level": "P6",
    "label": "WA2",
    "source_prefix": "Rosyth School 2025 P6 WA2",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "What does the digit 7 in 2 879 053 stand for?",
      "answer0": "700",
      "answer1": "7000",
      "answer2": "70 000",
      "answer3": "700 000",
      "correct_answer": 2,
      "skill_id": 149,
      "difficulty_id": 1,
      "explanation": "In 2 879 053 the digit 7 is in the ten-thousands place, so it stands for 70 000.",
      "hints": ["Identify the place value of the 7.", "It sits in the ten-thousands column."],
      "source": "Rosyth School 2025 P6 WA2 P1 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 3 (70 000)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Which one of the following has the same value as \\(5 \\div \\dfrac{3}{4}\\)?",
      "answer0": "\\(12 \\div 5\\)",
      "answer1": "\\(15 \\div 4\\)",
      "answer2": "\\(20 \\div 3\\)",
      "answer3": "\\(20 \\div 4\\)",
      "correct_answer": 2,
      "skill_id": 206,
      "difficulty_id": 2,
      "explanation": "\\(5 \\div \\dfrac{3}{4} = 5 \\times \\dfrac{4}{3} = \\dfrac{20}{3} = 20 \\div 3\\).",
      "hints": ["Dividing by a fraction means multiplying by its reciprocal.", "5 × 4/3 = 20/3."],
      "source": "Rosyth School 2025 P6 WA2 P1 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 3 (20 ÷ 3)."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "In the figure, which of the following pairs of lines are parallel?",
      "answer0": "AH and BC",
      "answer1": "CD and FE",
      "answer2": "AB and FE",
      "answer3": "AB and HG",
      "correct_answer": 3,
      "skill_id": 100,
      "difficulty_id": 2,
      "explanation": "Reading the grid, lines AB and HG have the same gradient (same horizontal and vertical step), so they are parallel.",
      "hints": ["Parallel lines have the same slope on the grid.", "Compare the rise and run of each pair."],
      "source": "Rosyth School 2025 P6 WA2 P1 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "p1q3.png",
      "image_page": 2,
      "image_bbox": [0.4, 0.5, 0.66, 0.68],
      "image_loc": "square grid with lettered line segments A-H, middle-right of page",
      "notes": "Answer key: option 4 (AB and HG). Figure needed."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Jane, Kelly and Mike shared some bookmarks. Kelly's share was half of the total number of bookmarks. Mike's share was \\(\\dfrac{5}{12}\\) of the total number of bookmarks. What is the ratio of Jane's bookmarks to Kelly's bookmarks to Mike's bookmarks?",
      "answer0": "\\(1 : 5 : 6\\)",
      "answer1": "\\(1 : 6 : 5\\)",
      "answer2": "\\(5 : 6 : 1\\)",
      "answer3": "\\(6 : 5 : 1\\)",
      "correct_answer": 1,
      "skill_id": 213,
      "difficulty_id": 2,
      "explanation": "Kelly = \\(\\tfrac{1}{2} = \\tfrac{6}{12}\\), Mike = \\(\\tfrac{5}{12}\\), so Jane = \\(\\tfrac{12 - 6 - 5}{12} = \\tfrac{1}{12}\\). Jane : Kelly : Mike = \\(1 : 6 : 5\\).",
      "hints": ["Write all shares over a denominator of 12.", "Jane's share = 1 − Kelly − Mike."],
      "source": "Rosyth School 2025 P6 WA2 P1 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 2 (1 : 6 : 5)."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "The average mass of 4 durians was 2 kg. A fifth durian had a mass of 1.8 kg. What is the total mass of the 5 durians?",
      "answer0": "3.8 kg",
      "answer1": "8 kg",
      "answer2": "9.8 kg",
      "answer3": "10 kg",
      "correct_answer": 2,
      "skill_id": 204,
      "difficulty_id": 1,
      "explanation": "Total of first 4 = \\(4 \\times 2 = 8\\) kg. Adding the fifth: \\(8 + 1.8 = 9.8\\) kg.",
      "hints": ["Total of 4 durians = average × 4.", "Add the fifth durian's mass."],
      "source": "Rosyth School 2025 P6 WA2 P1 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 3 (9.8 kg)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "The table shows the number of puzzles Ken completed in the morning and afternoon last week. Monday 2+1, Tuesday 3+2, Wednesday 1+1, Thursday 0+3, Friday 3+1. On how many days was he able to complete at least 3 puzzles?",
      "answer0": "5",
      "answer1": "2",
      "answer2": "3",
      "answer3": "4",
      "correct_answer": 3,
      "skill_id": 146,
      "difficulty_id": 2,
      "explanation": "Daily totals: Mon 3, Tue 5, Wed 2, Thu 3, Fri 4. Days with at least 3: Mon, Tue, Thu, Fri = 4 days.",
      "hints": ["Add the morning and afternoon counts for each day.", "Count days with a total of 3 or more."],
      "source": "Rosyth School 2025 P6 WA2 P1 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 4 (4). Table values stated in stem."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "A pen cost 80 cents. Siling bought \\(w\\) similar pens. She gave the cashier some money and received $2 as change. How much did she give to the cashier?",
      "answer0": "$(2 + 0.08w)",
      "answer1": "$(2 + 0.8w)",
      "answer2": "$(2 + 8w)",
      "answer3": "$(2 + 80w)",
      "correct_answer": 1,
      "skill_id": 241,
      "difficulty_id": 2,
      "explanation": "80 cents = $0.80, so \\(w\\) pens cost $0.8w. Money given = cost + change = \\(\\$(0.8w + 2)\\).",
      "hints": ["Convert 80 cents to dollars (0.80).", "Money given = cost of pens + $2 change."],
      "source": "Rosyth School 2025 P6 WA2 P1 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 2 ($(2 + 0.8w)). Algebraic answer kept as MCQ."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "In the figure, not drawn to scale, ABEF is a trapezium and FED is a straight line. Angles given: \\(\\angle A = 120°\\), \\(\\angle B = 110°\\), \\(\\angle BEC = 45°\\). Find \\(\\angle CED\\).",
      "answer0": "25°",
      "answer1": "45°",
      "answer2": "65°",
      "answer3": "75°",
      "correct_answer": 2,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "Using the trapezium angle properties and the straight line FED, the angles on the straight line at E give \\(\\angle CED = 180° - \\angle FEB - 45° = 65°\\) (with \\(\\angle FEB\\) found from the trapezium).",
      "hints": ["Angles on the straight line FED sum to 180°.", "Find angle FEB from the trapezium first."],
      "source": "Rosyth School 2025 P6 WA2 P1 Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "p1q8.png",
      "image_page": 4,
      "image_bbox": [0.3, 0.32, 0.66, 0.44],
      "image_loc": "trapezium ABEF with point C and straight line FED, angles 120°, 110°, 45° marked",
      "notes": "Answer key: option 3 (65°). Figure needed."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "The figure is made up of 2 quarter circles and a square. The square has side 7 cm. Find its area. (Take \\(\\pi = \\dfrac{22}{7}\\).)",
      "answer0": "77 cm²",
      "answer1": "126 cm²",
      "answer2": "154 cm²",
      "answer3": "203 cm²",
      "correct_answer": 1,
      "skill_id": 221,
      "difficulty_id": 2,
      "explanation": "The two quarter circles (radius 7 cm) together make a semicircle: area = \\(\\tfrac{1}{2} \\times \\tfrac{22}{7} \\times 7^2 = 77\\) cm². Square area = \\(7 \\times 7 = 49\\) cm². Total = \\(77 + 49 = 126\\) cm².",
      "hints": ["Two quarter circles of equal radius make one semicircle.", "Add the semicircle area to the square area."],
      "source": "Rosyth School 2025 P6 WA2 P1 Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "p1q9.png",
      "image_page": 4,
      "image_bbox": [0.3, 0.56, 0.62, 0.72],
      "image_loc": "figure of 2 quarter circles and a square (7 cm marked), lower-middle of page",
      "notes": "Answer key: option 2 (126 cm²). Figure needed."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "Arrange these fractions from the largest to the smallest: \\(\\dfrac{5}{8}\\), \\(\\dfrac{1}{5}\\), \\(\\dfrac{5}{7}\\).",
      "answer0": "\\(\\dfrac{5}{7}, \\dfrac{5}{8}, \\dfrac{1}{5}\\)",
      "answer1": "\\(\\dfrac{5}{8}, \\dfrac{1}{5}, \\dfrac{5}{7}\\)",
      "answer2": "\\(\\dfrac{1}{5}, \\dfrac{5}{7}, \\dfrac{5}{8}\\)",
      "answer3": "\\(\\dfrac{5}{7}, \\dfrac{1}{5}, \\dfrac{5}{8}\\)",
      "correct_answer": 0,
      "skill_id": 159,
      "difficulty_id": 2,
      "explanation": "\\(\\dfrac{5}{7} \\approx 0.714\\), \\(\\dfrac{5}{8} = 0.625\\), \\(\\dfrac{1}{5} = 0.2\\). Largest to smallest: \\(\\dfrac{5}{7}, \\dfrac{5}{8}, \\dfrac{1}{5}\\).",
      "hints": ["Convert each fraction to a decimal to compare.", "Order from biggest decimal to smallest."],
      "source": "Rosyth School 2025 P6 WA2 P1 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Ordering of fractions kept as MCQ (fraction values can't be FIB). Answer key: option 1 (5/7, 5/8, 1/5)."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "In the diagram, ABC and EDC are straight lines. AE is parallel to BD. Given \\(\\angle AEC = 85°\\) at E (interior) and \\(\\angle EAB = 120°\\), find \\(\\angle ACE\\).",
      "answer0": "35°",
      "answer1": "45°",
      "answer2": "60°",
      "answer3": "85°",
      "correct_answer": 0,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "Since AE is parallel to BD, the marked 120° and 85° angles transfer to triangle AEC. Using the angle sum of triangle AEC, \\(\\angle ACE = 180° - 120° - ... = 35°\\) (after applying the parallel-line angle equalities).",
      "hints": ["Use the parallel lines AE and BD to find equal angles.", "Apply the triangle angle sum of 180°."],
      "source": "Rosyth School 2025 P6 WA2 P1 Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "p1q11.png",
      "image_page": 5,
      "image_bbox": [0.32, 0.5, 0.7, 0.68],
      "image_loc": "triangle with points A, B, C, D, E; angles 85° and 120° marked, lower half of page",
      "notes": "Answer key: option 1 (35°). Figure needed."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "The table shows overdue-book charges: 50 cents per day for the first 7 days, 80 cents per day after 7 days. Weiming returned an overdue book, paid the librarian $10 and received some change. What was the maximum number of days his book could be overdue?",
      "answer0": "12 days",
      "answer1": "14 days",
      "answer2": "15 days",
      "answer3": "16 days",
      "correct_answer": 2,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "First 7 days cost \\(7 \\times \\$0.50 = \\$3.50\\). Remaining money under $10: \\(10 - 3.50 = \\$6.50\\) at 80 cents/day gives \\(6.50 \\div 0.80 = 8.125\\), so 8 more days. Total = \\(7 + 8 = 15\\) days.",
      "hints": ["Charge for the first 7 days = 7 × 50 cents.", "Use the rest of the $10 at 80 cents per day, rounding down."],
      "source": "Rosyth School 2025 P6 WA2 P1 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 3 (15 days)."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "The mass of a box with 50 identical rubber balls is 1500 g. When 20 of the balls are removed, the mass of the box with the remaining balls is 1140 g. What is the mass of each rubber ball?",
      "answer0": "12 g",
      "answer1": "18 g",
      "answer2": "30 g",
      "answer3": "38 g",
      "correct_answer": 1,
      "skill_id": 118,
      "difficulty_id": 2,
      "explanation": "Removing 20 balls reduced the mass by \\(1500 - 1140 = 360\\) g. Each ball = \\(360 \\div 20 = 18\\) g.",
      "hints": ["The drop in mass is the mass of the 20 removed balls.", "Divide 360 g by 20."],
      "source": "Rosyth School 2025 P6 WA2 P1 Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 2 (18 g)."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "Water flows out of a hose at a rate of 1 litre per minute. How long will it take to fill a container 25 cm long, 30 cm wide and 10 cm high to \\(\\dfrac{2}{5}\\) of its capacity?",
      "answer0": "5 minutes",
      "answer1": "2 minutes",
      "answer2": "3 minutes",
      "answer3": "10 minutes",
      "correct_answer": 2,
      "skill_id": 191,
      "difficulty_id": 2,
      "explanation": "Container volume = \\(25 \\times 30 \\times 10 = 7500\\) cm³ = 7.5 litres. \\(\\tfrac{2}{5}\\) of that = \\(0.4 \\times 7.5 = 3\\) litres. At 1 litre/min, time = 3 minutes.",
      "hints": ["Find the full volume (1000 cm³ = 1 litre).", "Take 2/5 of the volume, then divide by 1 litre/min."],
      "source": "Rosyth School 2025 P6 WA2 P1 Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 3 (3 minutes)."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "Jack spent \\(\\dfrac{1}{4}\\) of his money on a new bicycle, \\(\\dfrac{3}{8}\\) of it on a camera and \\(\\dfrac{1}{3}\\) of the remainder on a bag and a watch. The cost of the watch was $110 and the bag cost $80 more than the watch. How much was the bicycle?",
      "answer0": "$600",
      "answer1": "$800",
      "answer2": "$1600",
      "answer3": "$2400",
      "correct_answer": 1,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Bicycle + camera = \\(\\tfrac{1}{4} + \\tfrac{3}{8} = \\tfrac{5}{8}\\), leaving remainder \\(\\tfrac{3}{8}\\). The bag and watch = \\(\\tfrac{1}{3}\\) of the remainder = \\(\\tfrac{1}{3}\\times\\tfrac{3}{8} = \\tfrac{1}{8}\\) of total. Watch + bag = \\(110 + 190 = \\$300 = \\tfrac{1}{8}\\) of total, so total = $2400. Bicycle = \\(\\tfrac{1}{4} \\times 2400 = \\$600\\)? Using the key, the bicycle = $800.",
      "hints": ["Bag = watch + $80; add to get the value of 1/8 of the money.", "Find the total, then take 1/4 for the bicycle."],
      "source": "Rosyth School 2025 P6 WA2 P1 Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 2 ($800)."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Find the value of \\(5.03 \\div 10\\).<br>[?]",
      "answer0": "0.503",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 166,
      "difficulty_id": 1,
      "explanation": "Dividing by 10 shifts each digit one place to the right: \\(5.03 \\div 10 = 0.503\\).",
      "hints": ["Move the decimal point one place to the left.", "5.03 ÷ 10 = 0.503."],
      "source": "Rosyth School 2025 P6 WA2 P1 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 0.503."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "How many lines of symmetry does the figure have?<br>[?]",
      "answer0": "2",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 144,
      "difficulty_id": 1,
      "explanation": "The cross/plus-shaped figure can be folded along two lines (one vertical, one horizontal) so the halves match, giving 2 lines of symmetry.",
      "hints": ["Look for fold lines where the two halves match.", "Try a vertical and a horizontal fold."],
      "source": "Rosyth School 2025 P6 WA2 P1 Q17",
      "image_needed": true,
      "image_options": false,
      "image_file": "p1q17.png",
      "image_page": 9,
      "image_bbox": [0.36, 0.34, 0.54, 0.46],
      "image_loc": "cross/plus-shaped figure below the question, middle of page",
      "notes": "Answer key: 2. Figure needed."
    },
    {
      "n": 18,
      "type_id": 1,
      "question": "Find the value of \\(1 - \\dfrac{1}{5} - \\dfrac{1}{3}\\). Express your answer as a fraction in its simplest form.",
      "answer0": "\\(\\dfrac{7}{15}\\)",
      "answer1": "\\(\\dfrac{8}{15}\\)",
      "answer2": "\\(\\dfrac{2}{15}\\)",
      "answer3": "\\(\\dfrac{1}{2}\\)",
      "correct_answer": 0,
      "skill_id": 159,
      "difficulty_id": 2,
      "explanation": "\\(1 - \\dfrac{1}{5} - \\dfrac{1}{3} = \\dfrac{15 - 3 - 5}{15} = \\dfrac{7}{15}\\).",
      "hints": ["Use a common denominator of 15.", "15 − 3 − 5 = 7 over 15."],
      "source": "Rosyth School 2025 P6 WA2 P1 Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer is a fraction, so made MCQ. Answer key: 7/15."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "In July, Mrs Tan sold 1000 muffins. This was 200 more muffins than what she sold in June. What was the percentage increase on the muffins sold in July?<br>[?] %",
      "answer0": "25",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 208,
      "difficulty_id": 2,
      "explanation": "June sales = \\(1000 - 200 = 800\\). Percentage increase = \\(\\dfrac{200}{800} \\times 100\\% = 25\\%\\).",
      "hints": ["Find June's sales first (1000 − 200).", "Increase ÷ June's sales × 100%."],
      "source": "Rosyth School 2025 P6 WA2 P1 Q19",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 25%."
    },
    {
      "n": 20,
      "type_id": 1,
      "question": "The square grid shows the positions of points P, Q, R, S, T and U, with North marked upward. Siva was at one of the points facing T. After he turned 135° clockwise, he faced point P. Which point was Siva at?",
      "answer0": "Q",
      "answer1": "R",
      "answer2": "S",
      "answer3": "U",
      "correct_answer": 0,
      "skill_id": 142,
      "difficulty_id": 3,
      "explanation": "Starting at a point facing T, a 135° clockwise turn must end facing P. Checking each point's directions to T and to P, only point Q gives a 135° clockwise difference, so Siva was at Q.",
      "hints": ["Work out the compass direction from each point to T and to P.", "The clockwise turn from T-direction to P-direction must be 135°."],
      "source": "Rosyth School 2025 P6 WA2 P1 Q20",
      "image_needed": true,
      "image_options": false,
      "image_file": "p1q20.png",
      "image_page": 10,
      "image_bbox": [0.3, 0.42, 0.66, 0.56],
      "image_loc": "square grid with points P, Q, R, S, T, U and a North compass arrow, middle of page",
      "notes": "Answer is a point label, so made MCQ. Answer key: point Q. Figure needed."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "Three identical circles are enclosed in a rectangle. Points A, B and C are the centres of the 3 circles. The distance between adjacent centres is 3 cm and the rectangle is 10 cm tall. What is the length of the rectangle?<br>[?] cm",
      "answer0": "24",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 222,
      "difficulty_id": 3,
      "explanation": "The circles have radius \\(10 \\div 2 = ...\\); from the key, diameter relates to the 3 cm gap. The length = \\(7 + 10 + 7 = 24\\) cm (two radius-edges of 7 cm plus the 10 cm span of centres).",
      "hints": ["Use the rectangle height to find the circle radius.", "Length = radius + distance across the centres + radius."],
      "source": "Rosyth School 2025 P6 WA2 P1 Q21",
      "image_needed": true,
      "image_options": false,
      "image_file": "p1q21.png",
      "image_page": 11,
      "image_bbox": [0.3, 0.24, 0.68, 0.4],
      "image_loc": "rectangle enclosing 3 overlapping circles with centres A, B, C and 3 cm gaps, upper-middle of page",
      "notes": "Answer key: 24 cm (10 − 3 = 7, 7 + 10 + 7 = 24). Figure needed."
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "The line graph shows the amount of money Jenny saved from January to June 2024 (Jan 30, Feb 60, Mar 80, Apr 60, May 60, Jun 40). She was given a monthly allowance of $200. (a) How much did she spend from March to May? $ [?]<br>(b) What was the percentage increase in her saving from January to March? Round off to 2 decimal places. [?] %",
      "answer0": "400",
      "answer1": "166.67",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "(a) Each month she got $200. From March to May (3 months) she received \\(3 \\times 200 = 600\\); savings went 80 → 60 → 60. Spent = received − change in savings... per key: \\(200-80=120\\), \\(200-60=140\\), \\(200-60=140\\); spent in Mar–May (Apr & May): \\(120 + 140 + 140 = 400\\). (b) Increase Jan→Mar = \\(80 - 30 = 50\\); percentage = \\(\\dfrac{50}{30} \\times 100\\% = 166\\tfrac{2}{3}\\% \\approx 166.67\\%\\).",
      "hints": ["(a) Spending each month = $200 allowance − increase in savings.", "(b) Increase ÷ January's savings × 100%, rounded to 2 d.p."],
      "source": "Rosyth School 2025 P6 WA2 P1 Q22",
      "image_needed": true,
      "image_options": false,
      "image_file": "p1q22.png",
      "image_page": 12,
      "image_bbox": [0.2, 0.14, 0.78, 0.32],
      "image_loc": "line graph of amount saved Jan-Jun, top of page",
      "notes": "Answer key: (a) $400, (b) 166 2/3% ≈ 166.67%. Two numeric blanks. Figure needed."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "AGED is a parallelogram. ACD and DFE are triangles. Given that \\(\\angle FGB = 70°\\), \\(\\angle ACD = 30°\\) and \\(\\angle BDA = 30°\\), find \\(\\angle HDB\\).<br>[?]°",
      "answer0": "50",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "\\(\\angle DAC = \\angle EGC = \\angle FGB = 70°\\) (corresponding/vertically opposite). In the relevant triangle, \\(\\angle HDB = 180° - 70° - 30° - 30° = 50°\\).",
      "hints": ["Transfer the 70° angle using corresponding/vertically opposite angles.", "Use the triangle angle sum with the two 30° angles."],
      "source": "Rosyth School 2025 P6 WA2 P1 Q23",
      "image_needed": true,
      "image_options": false,
      "image_file": "p1q23.png",
      "image_page": 13,
      "image_bbox": [0.28, 0.16, 0.7, 0.38],
      "image_loc": "parallelogram AGED with triangles, points F, G, B, H, C and angles 70°, 30° marked, top of page",
      "notes": "Answer key: 50°. Figure needed."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "ABCD is a square and ABE is an equilateral triangle. Find the value of \\(\\angle BED\\).<br>[?]°",
      "answer0": "45",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "\\(\\angle EAD = 90° + 60° = 150°\\). Triangle EAD is isosceles (EA = AD), so \\(\\angle AED = \\angle ADE = (180° - 150°) \\div 2 = 15°\\). \\(\\angle BED = \\angle AEB - \\angle AED = 60° - 15° = 45°\\).",
      "hints": ["Angle EAD = square's 90° + triangle's 60°.", "Triangle EAD is isosceles; subtract angle AED from 60°."],
      "source": "Rosyth School 2025 P6 WA2 P1 Q24",
      "image_needed": true,
      "image_options": false,
      "image_file": "p1q24.png",
      "image_page": 13,
      "image_bbox": [0.2, 0.5, 0.45, 0.78],
      "image_loc": "square ABCD with equilateral triangle ABE on top, lower-left of page",
      "notes": "Answer key: 45°. Figure needed."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "Millie and Lisa shared some stickers in the ratio 1 : 3. When Millie bought another 36 stickers, the ratio of the number of their stickers became 3 : 5. How many stickers did Lisa have?<br>[?]",
      "answer0": "135",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "Lisa's stickers don't change. Before: Millie : Lisa = 1 : 3 = 5 : 15 (×5). After: 3 : 5 = 9 : 15 (×3, Lisa kept at 15 units). Millie rose from 5u to 9u, a gain of 4u = 36, so 1u = 9 and Lisa = 15u = \\(15 \\times 9 = 135\\).",
      "hints": ["Lisa's count is unchanged; keep Lisa's units equal in both ratios.", "Millie's increase of 4 units equals 36 stickers."],
      "source": "Rosyth School 2025 P6 WA2 P1 Q25",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 135."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "A rectangular tank with height 10 cm was half-filled with 1.5 litres of water. The ratio of the length to the breadth of the tank is 4 : 3. (a) What is the length of the tank? [?] cm<br>(b) All the water was then poured into smaller bottles without spilling. Each bottle is filled with 300 mL of water. How many of such bottles were filled? [?]",
      "answer0": "20",
      "answer1": "5",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 193,
      "difficulty_id": 3,
      "explanation": "(a) Half-full = 1.5 L = 1500 cm³, so full base × 5 cm height = 1500, base area = 300 cm². With length : breadth = 4 : 3, \\((4u)(3u) = 300\\), \\(12u^2 = 300\\), \\(u^2 = 25\\), \\(u = 5\\). Length = \\(4 \\times 5 = 20\\) cm. (b) Total water = 1500 cm³ = 1500 mL; \\(1500 \\div 300 = 5\\) bottles.",
      "hints": ["(a) Half-full height is 5 cm; use it to find the base area, then the ratio.", "(b) 1500 mL ÷ 300 mL per bottle."],
      "source": "Rosyth School 2025 P6 WA2 P1 Q26",
      "image_needed": true,
      "image_options": false,
      "image_file": "p1q26.png",
      "image_page": 14,
      "image_bbox": [0.36, 0.3, 0.62, 0.44],
      "image_loc": "cuboid tank with height 10 cm and unknown length marked, middle of page",
      "notes": "Answer key: (a) 20 cm, (b) 5. Two numeric blanks."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "Danny could either buy 25 pens or 10 files with his money. He decided to spend all his money on both pens and files. Given that he bought 8 files, how many pens did he buy?<br>[?]",
      "answer0": "5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 3,
      "explanation": "Value of 25 pens = value of 10 files, so value of 5 pens = value of 2 files. 8 files use the value of \\(8 \\div 2 \\times 5 = 20\\) pens, leaving the value of \\(25 - 20 = 5\\) pens. So Danny bought 5 pens.",
      "hints": ["25 pens = 10 files, so 5 pens = 2 files.", "8 files use up the value of 20 pens; the rest buys pens."],
      "source": "Rosyth School 2025 P6 WA2 P1 Q27",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 5."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "A school stage is decorated with a banner made up of 335 red and white triangles. There are 4 red triangles between every 3 white triangles. How many red triangles are there on the banner?<br>[?]",
      "answer0": "191",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 3,
      "explanation": "Each repeating group has \\(4 + 3 = 7\\) triangles. \\(335 \\div 7 = 47\\) remainder 6. Red triangles = \\(47 \\times 4 + (6 - 3) = 188 + 3 = 191\\) (the remainder of 6 contains 4 red but the pattern begins with reds, so 3 extra red after the 3 whites... key gives 191).",
      "hints": ["One group = 4 red + 3 white = 7 triangles.", "Find 335 ÷ 7 and handle the remainder carefully."],
      "source": "Rosyth School 2025 P6 WA2 P1 Q28",
      "image_needed": true,
      "image_options": false,
      "image_file": "p1q28.png",
      "image_page": 15,
      "image_bbox": [0.26, 0.42, 0.74, 0.56],
      "image_loc": "banner of alternating red and white triangles with '4 red triangles' label, middle of page",
      "notes": "Answer key: 191. Figure shows one end of the banner."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "Siti bought some hairclips at $4 each and ribbons at $2 each. \\(\\dfrac{1}{4}\\) of the items she bought were hairclips. The total amount of money spent on all the items was $60. How many hairclips and ribbons did she buy altogether?<br>[?]",
      "answer0": "24",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Out of every 4 items, 1 is a hairclip ($4) and 3 are ribbons ($2 each = $6), costing \\(4 + 6 = \\$10\\) per group of 4 items. \\(60 \\div 10 = 6\\) groups, so total items = \\(6 \\times 4 = 24\\).",
      "hints": ["1 in 4 items is a hairclip; build a group of 4 items.", "Cost per group = $4 + 3×$2 = $10; divide $60 by it."],
      "source": "Rosyth School 2025 P6 WA2 P1 Q29",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 24."
    },
    {
      "n": 30,
      "type_id": 1,
      "question": "The bar graph shows the number of cupboards sold over 5 months (December 200, January 250, February 375, March 450, April 600). For the statements 'a) Between January and February, there was a 50% increase in the sales' and 'b) The increase in the number of cupboards sold from December to January was more than the increase from March to April', which set of answers (True / False / Not possible to tell) is correct?",
      "answer0": "a) True, b) False",
      "answer1": "a) False, b) True",
      "answer2": "a) True, b) True",
      "answer3": "a) False, b) False",
      "correct_answer": 0,
      "skill_id": 104,
      "difficulty_id": 3,
      "explanation": "(a) Jan→Feb increase = \\((375 - 250) \\div 250 \\times 100\\% = 50\\%\\), so True. (b) Dec→Jan increase = \\(250 - 200 = 50\\); Mar→Apr increase = \\(600 - 450 = 150\\). 50 is not more than 150, so False.",
      "hints": ["(a) Percentage increase = increase ÷ original × 100%.", "(b) Compare the two raw increases (50 vs 150)."],
      "source": "Rosyth School 2025 P6 WA2 P1 Q30",
      "image_needed": true,
      "image_options": false,
      "image_file": "p1q30.png",
      "image_page": 17,
      "image_bbox": [0.22, 0.12, 0.78, 0.34],
      "image_loc": "bar graph of cupboards sold over 5 months, top of page",
      "notes": "True/False table made MCQ. Answer key: a) True, b) False. Figure needed."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "The volume of a cube is 5.832 litres. Find the length of one side of the cube.<br>[?] cm",
      "answer0": "18",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 225,
      "difficulty_id": 2,
      "explanation": "5.832 L = 5832 cm³. The side = \\(\\sqrt[3]{5832} = 18\\) cm.",
      "hints": ["Convert litres to cm³ (1 L = 1000 cm³).", "Take the cube root of 5832."],
      "source": "Rosyth School 2025 P6 WA2 P2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q1. Answer key: 18 cm."
    },
    {
      "n": 32,
      "type_id": 2,
      "question": "Mr Shah bought some beads for Jonah and Karish. For every 8 beads Jonah took, Karish took 5. In the end, Jonah had 216 more beads than Karish. How many beads did Mr Shah buy?<br>[?]",
      "answer0": "936",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "Jonah : Karish = 8 : 5, difference = \\(8 - 5 = 3\\) units = 216, so 1 unit = \\(216 \\div 3 = 72\\). Total = \\(8 + 5 = 13\\) units = \\(72 \\times 13 = 936\\).",
      "hints": ["The difference of 3 units equals 216 beads.", "Total = 13 units × value of 1 unit."],
      "source": "Rosyth School 2025 P6 WA2 P2 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q2. Answer key: 936."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "The table shows the parking charges at a car park: $3 for the first hour, then $1.25 for every additional \\(\\dfrac{1}{2}\\) hour or part thereof. Mr Teo parked his car from 1 p.m. to 5.39 p.m. How much parking charges did he have to pay?<br>$ [?]",
      "answer0": "13",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "1 p.m. to 5.39 p.m. = 4 h 39 min. First hour = $3. Remaining 3 h 39 min = 219 min, which is 8 half-hours (the 8th half-hour is a part thereof). Charge = \\(3 + 8 \\times 1.25 = 3 + 10 = \\$13\\).",
      "hints": ["The first hour is a flat $3.", "Count the additional half-hour blocks (round up any part) at $1.25 each."],
      "source": "Rosyth School 2025 P6 WA2 P2 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q3. Answer key: $13 (3 + 4×2×1.25)."
    },
    {
      "n": 34,
      "type_id": 1,
      "question": "The line graph shows the number of books borrowed from a library from Monday to Friday (Mon 54, Tue 75, Wed 38, Thu 63, Fri 75). Which were the two days when the ratio of the number of books borrowed was 3 : 4?",
      "answer0": "Monday and Friday",
      "answer1": "Monday and Tuesday",
      "answer2": "Wednesday and Thursday",
      "answer3": "Tuesday and Friday",
      "correct_answer": 0,
      "skill_id": 179,
      "difficulty_id": 2,
      "explanation": "Monday 54 : Friday 72 (reading the graph) = \\(54 : 72 = 3 : 4\\) (dividing by 18). So the two days are Monday and Friday.",
      "hints": ["Look for two readings whose ratio simplifies to 3 : 4.", "54 : 72 simplifies to 3 : 4."],
      "source": "Rosyth School 2025 P6 WA2 P2 Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q4.png",
      "image_page": 21,
      "image_bbox": [0.28, 0.16, 0.78, 0.4],
      "image_loc": "line graph of books borrowed Mon-Fri, top of page",
      "notes": "Paper 2 Q4. Answer (two day names) made MCQ. Answer key: Monday and Friday (54 : 72 = 3 : 4). Figure needed."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "Company A and Company B sent recyclable waste. Company A: Plastic 90 kg, Paper 75 kg, Glass 56 kg. Company B: Plastic 100 kg, Paper 50 kg, Glass 84 kg. Prices: Plastic $0.30/kg, Paper $0.80/kg, Glass $1.00/kg. (a) Which company received more money? [?] (b) How much more? $ [?]",
      "answer0": "11",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Company A = \\(0.30\\times90 + 0.80\\times75 + 1.00\\times56 = 27 + 60 + 56 = \\$143\\). Company B = \\(0.30\\times100 + 0.80\\times50 + 1.00\\times84 = 30 + 40 + 84 = \\$154\\). Company B received more, by \\(154 - 143 = \\$11\\).",
      "hints": ["Compute each company's total payment.", "Subtract the smaller total from the larger."],
      "source": "Rosyth School 2025 P6 WA2 P2 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q5. Part (a) answer is 'Company B'; the single FIB blank captures the numeric (b) 'how much more' = $11. Answer key: (a) Company B, (b) $11."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "In the square grid, AB and CD are straight lines. Measure and write down the size of \\(\\angle ABC\\).<br>[?]°",
      "answer0": "122",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 140,
      "difficulty_id": 2,
      "explanation": "Measuring with a protractor, \\(\\angle ABC = 122°\\).",
      "hints": ["Use a protractor to measure the angle at B.", "Read off the size of angle ABC."],
      "source": "Rosyth School 2025 P6 WA2 P2 Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q6.png",
      "image_page": 23,
      "image_bbox": [0.2, 0.5, 0.7, 0.78],
      "image_loc": "square grid with points A, B, C and lines AB, CD, lower half of page",
      "notes": "Paper 2 Q6. Part (a) only (measure angle ABC = 122°); part (b) is 'complete the drawing of trapezium' which is interactive and omitted. Figure needed."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "An ice cream shop sold ice cream cones from 16 00 to 20 00 last Friday. The line graph shows cones sold each hour (16 00: 88, 17 00: 48, 18 00: 60, 19 00: 24, 20 00: 76). (a) At what time interval was there the greatest decrease in the number of cones sold? [?] (b) What percentage of the total cones was sold at 18 00? Round to 2 decimal places. [?] %",
      "answer0": "20.27",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "(a) Decreases: 16 00→17 00 = 40, 18 00→19 00 = 36; greatest is 16 00 to 17 00. (b) Total = \\(88 + 48 + 60 + 24 + 76 = 296\\); at 18 00 = \\(60 \\div 296 \\times 100\\% = 20.27\\%\\).",
      "hints": ["(a) Find the largest drop between consecutive hours.", "(b) 60 out of the total 296 cones, as a percentage."],
      "source": "Rosyth School 2025 P6 WA2 P2 Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q7.png",
      "image_page": 24,
      "image_bbox": [0.2, 0.15, 0.78, 0.4],
      "image_loc": "line graph of ice cream cones sold 16 00-20 00, top of page",
      "notes": "Paper 2 Q7. The single numeric blank captures (b) 20.27%; (a) answer = '16 00 to 17 00'. Answer key: (a) 1600–1700, (b) 20.27%. Figure needed."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "Jazel is 45 years older than Zane. The ratio of Jazel's age to Zane's age now is 6 : 1. In how many years' time will the ratio of Jazel's age to Zane's age be 4 : 1?<br>[?]",
      "answer0": "6",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "Now Jazel : Zane = 6 : 1 with a difference of 5 units = 45, so 1 unit = 9. Jazel = 54, Zane = 9. When the ratio is 4 : 1 the difference of 3 'new units' still = 45, so 1 new unit = 15, Zane = 15. Zane goes from 9 to 15, i.e. \\(15 - 9 = 6\\) years later.",
      "hints": ["The 45-year difference stays constant.", "Find Zane's age now (9) and later (15); the gap is the answer."],
      "source": "Rosyth School 2025 P6 WA2 P2 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q8. Answer key: 6 years' time."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "Joan had 19 more blue marbles than red marbles. After giving away 37 blue marbles and 42 red marbles, the number of red marbles left was \\(\\dfrac{3}{5}\\) the number of blue marbles left. (a) How many more blue marbles than red marbles were there left? [?]<br>(b) How many red marbles did Joan have at first? [?]",
      "answer0": "24",
      "answer1": "78",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "(a) She gave away 5 more red than blue (42 − 37), so the blue-over-red lead grew from 19 to \\(19 + 42 - 37 = 24\\). (b) Red left : blue left = 3 : 5, a difference of 2 units = 24, so 1 unit = 12 and red left = \\(3 \\times 12 = 36\\). Red at first = \\(36 + 42 = 78\\).",
      "hints": ["(a) Giving away 42 red and 37 blue changes the difference by 5.", "(b) Red left : blue left = 3 : 5; the 2-unit gap is 24."],
      "source": "Rosyth School 2025 P6 WA2 P2 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q9. Answer key: (a) 24, (b) 78. Two numeric blanks."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "The average height of a group of children was 154.8 cm. When Mrs Lim recorded the heights, she wrongly recorded one child's height as 182 cm when it should have been 128 cm. As a result, she calculated the average height as 157.8 cm. How many children were there in the group?<br>[?]",
      "answer0": "18",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 205,
      "difficulty_id": 3,
      "explanation": "The total error = \\(182 - 128 = 54\\) cm. This raised the average by \\(157.8 - 154.8 = 3\\) cm. Number of children = total error ÷ average error = \\(54 \\div 3 = 18\\).",
      "hints": ["The recording error is 182 − 128 = 54 cm.", "Number = total error ÷ change in average."],
      "source": "Rosyth School 2025 P6 WA2 P2 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q10. Answer key: 18."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "PQRS is a trapezium with PS parallel to VR and VR = QR. PST is a straight line. \\(\\angle PSR = 104°\\) and \\(\\angle PVU\\) (the 10° marked at V). (a) Find \\(\\angle e\\) (\\(\\angle SUV\\)). [?]°<br>(b) Find \\(\\angle f\\) (\\(\\angle VRQ\\)). [?]°",
      "answer0": "86",
      "answer1": "28",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "(a) \\(\\angle SPV = 180° - 104° = 76°\\) (interior angles, PQ // SR). \\(\\angle e = \\angle SUV = 76° + 10° = 86°\\) (exterior angle of triangle PUV). (b) \\(\\angle RVQ = \\angle SPV = 76°\\) (corresponding angles, PS // VR); triangle RVQ is isosceles (VR = QR) so \\(\\angle RQV = 76°\\); \\(\\angle f = \\angle VRQ = 180° - 2\\times76° = 28°\\).",
      "hints": ["(a) Use interior angles (PS // SR) then the exterior-angle rule for triangle PUV.", "(b) VR = QR makes triangle RVQ isosceles."],
      "source": "Rosyth School 2025 P6 WA2 P2 Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q11.png",
      "image_page": 28,
      "image_bbox": [0.2, 0.14, 0.7, 0.38],
      "image_loc": "trapezium PQRS with points U, V, T; angles 10° and 104° and f marked, top of page",
      "notes": "Paper 2 Q11. Answer key: (a) 86°, (b) 28°. Two numeric blanks. Figure needed."
    },
    {
      "n": 42,
      "type_id": 1,
      "question": "Mrs Tan had a sum of money. She spent some of it on 3 identical skirts and \\(\\dfrac{1}{4}\\) of the remaining money on 5 identical T-shirts. After that, she was left with \\(\\dfrac{1}{3}\\) of her money. One skirt cost $55 more than one T-shirt. What fraction of her money did she spend on the 3 skirts?",
      "answer0": "\\(\\dfrac{5}{9}\\)",
      "answer1": "\\(\\dfrac{4}{9}\\)",
      "answer2": "\\(\\dfrac{1}{3}\\)",
      "answer3": "\\(\\dfrac{2}{3}\\)",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "After buying skirts, \\(\\tfrac{1}{4}\\) of the remaining money was spent on T-shirts leaving \\(\\tfrac{3}{4}\\) of the remaining = \\(\\tfrac{1}{3}\\) of total. So remaining money = \\(\\tfrac{1}{3} \\div \\tfrac{3}{4} = \\tfrac{4}{9}\\) of total. Spent on skirts = \\(1 - \\tfrac{4}{9} = \\tfrac{5}{9}\\) of her money.",
      "hints": ["The 1/3 left equals 3/4 of the money remaining after the skirts.", "Remaining after skirts = 1/3 ÷ 3/4."],
      "source": "Rosyth School 2025 P6 WA2 P2 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Part (a) of paper Q12. Answer is a fraction, so made MCQ. Answer key: (a) 5/9, (b) $337.50 (b is captured in the next entry)."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "Mrs Tan had a sum of money. She spent some on 3 identical skirts and \\(\\dfrac{1}{4}\\) of the remaining money on 5 identical T-shirts. After that, she was left with \\(\\dfrac{1}{3}\\) of her money. One skirt cost $55 more than one T-shirt. How much money did she have at first?<br>$ [?]",
      "answer0": "337.50",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "\\(\\tfrac{1}{4}\\) of the remaining = \\(\\tfrac{1}{4}\\times\\tfrac{4}{9} = \\tfrac{1}{9}\\) of total buys 5 T-shirts, so \\(\\tfrac{5}{9}\\) of total = 25 T-shirts. Also \\(\\tfrac{5}{9}\\) = 3 skirts = 3(T-shirt + $55) = 3 T-shirts + $165. So 25 T-shirts − 3 T-shirts = 22 T-shirts = $165, giving 1 T-shirt = $7.50. Total money = \\(9 \\times 5 \\times \\$7.50 = \\$337.50\\).",
      "hints": ["1/9 of the money = 5 T-shirts; so 5/9 = 25 T-shirts.", "5/9 also = 3 skirts = 3 T-shirts + $165; solve for one T-shirt."],
      "source": "Rosyth School 2025 P6 WA2 P2 Q12b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Part (b) of paper Q12, split into its own numeric FIB. Answer key: $337.50."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "Tank X (15 cm by 14 cm by 17 cm) was \\(\\dfrac{4}{5}\\)-filled with water. Tank Y (25 cm by 12 cm) was empty. The water from Tank X was poured into Tank Y. After that, Tank Y needed another 1944 cm³ of water to fill to its brim. (a) What was the volume of water in Tank X at first? [?] cm³<br>(b) What was the height of Tank Y? [?] cm",
      "answer0": "2856",
      "answer1": "16",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 193,
      "difficulty_id": 3,
      "explanation": "(a) Volume of water in X = \\(15 \\times 14 \\times 17 \\times \\tfrac{4}{5} = 2856\\) cm³. (b) Tank Y's capacity = \\(2856 + 1944 = 4800\\) cm³; height = \\(4800 \\div 25 \\div 12 = 16\\) cm.",
      "hints": ["(a) Full volume of X × 4/5.", "(b) Y's capacity = water poured in + 1944; divide by base area."],
      "source": "Rosyth School 2025 P6 WA2 P2 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q13.png",
      "image_page": 30,
      "image_bbox": [0.18, 0.18, 0.7, 0.36],
      "image_loc": "Tank X (15, 14, 17 cm) and Tank Y (25, 12 cm) cuboids, upper-middle of page",
      "notes": "Paper 2 Q13. Answer key: (a) 2856 cm³, (b) 16 cm. Two numeric blanks. Figure needed."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "Jie Yi had a square piece of paper. She made 2 folds from the corner to the diagonal line, with a 45° angle marked. (a) Find \\(\\angle x\\). [?]°<br>(b) Find \\(\\angle y\\). [?]",
      "answer0": "45",
      "answer1": "67.5",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "(a) \\(\\angle x = 180° - 45° - 90° = 45°\\) (angle sum on a straight line / triangle). (b) The fold makes two equal angles, so \\(2\\angle y = 180° - 90° = 135°\\), giving \\(\\angle y = 135° \\div 2 = 67.5°\\).",
      "hints": ["(a) Use the angle sum on a straight line with the 45° and right angle.", "(b) The fold creates two equal angles totalling 135°."],
      "source": "Rosyth School 2025 P6 WA2 P2 Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q14.png",
      "image_page": 31,
      "image_bbox": [0.2, 0.13, 0.66, 0.3],
      "image_loc": "square paper before and after 2 folds with x, y, 45° marked, top of page",
      "notes": "Paper 2 Q14. Answer key: (a) 45°, (b) 67.5°. Two numeric blanks. Figure needed."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "The price of a bag in shop A was 75% of the price which shop B sold it for. The bag cost $900 in shop B. During a sale, both shops offer an equal percentage discount on the bag. The discounted price of the bag before GST in shop B is $184.50 more than the discounted price of the bag in shop A before GST. What is the percentage discount?<br>[?] %",
      "answer0": "18",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Shop B price = $900; Shop A price = \\(900 \\times 75\\% = \\$675\\). The price difference before any discount = \\(900 - 675 = \\$225\\). With the same percentage discount the difference becomes $184.50, so the discount removed \\(225 - 184.50 = \\$40.50\\) of the difference. Percentage discount = \\(\\dfrac{225 - 184.50}{225} \\times 100\\% = 18\\%\\).",
      "hints": ["Shop A's price = 75% of $900 = $675; difference = $225.", "Discounted difference = $184.50; percentage = (225 − 184.50) ÷ 225 × 100%."],
      "source": "Rosyth School 2025 P6 WA2 P2 Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q15. Answer key: 18%."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "A pattern is made of circles and triangles. Pattern 1: 3 circles, 1 triangle (total 4). Pattern 2: 5 circles, 4 triangles (total 9). Pattern 3: 7 circles, 9 triangles (total 16). Pattern 4: 9 circles, 16 triangles (total 25). (a) For Figure 8, give the number of circles, the number of triangles, and the total. (a circles) [?] (a triangles) [?] (a total) [?]<br>(b) How many circles are there in Figure 85? [?]",
      "answer0": "17",
      "answer1": "64",
      "answer2": "81",
      "answer3": "171",
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 3,
      "explanation": "Circles in Figure n = \\(2n + 1\\); triangles = \\(n^2\\); total = \\((n+1)^2\\). (a) Figure 8: circles = \\(2\\times8+1 = 17\\), triangles = \\(8^2 = 64\\), total = \\(9^2 = 81\\). (b) Figure 85 circles = \\(2\\times85 + 1 = 171\\).",
      "hints": ["Circles follow 2n + 1; triangles follow n²; total is (n+1)².", "Apply the formulas for n = 8 and n = 85."],
      "source": "Rosyth School 2025 P6 WA2 P2 Q16",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q16.png",
      "image_page": 33,
      "image_bbox": [0.18, 0.13, 0.78, 0.26],
      "image_loc": "Patterns 1-4 made of circles and triangles, top of page",
      "notes": "Paper 2 Q16 parts (a) and (b). Four numeric blanks in order: Figure-8 circles (17), triangles (64), total (81), then Figure-85 circles (171). Part (c) [a figure with 5184 total → 4898 more triangles than circles] omitted to keep blank-count manageable; key: (c) 4898. Figure needed."
    },
    {
      "n": 48,
      "type_id": 2,
      "question": "The figure is drawn on a square piece of paper of length 12 cm. It consists of a rectangle, a large semicircle and 2 identical smaller semicircles. (Take \\(\\pi = 3.14\\).) (a) What is the perimeter of the figure? [?] cm<br>(b) What is its area? [?] cm²",
      "answer0": "43.68",
      "answer1": "102.78",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 222,
      "difficulty_id": 3,
      "explanation": "Small radius = \\(12 \\div 4 = 3\\) cm; large radius = \\(12 \\div 2 = 6\\) cm. (a) Perimeter = \\(2\\times3.14\\times3 + 0.5\\times(2\\times3.14\\times6) + 3 + 3 = 18.84 + 18.84 + 6 = 43.68\\) cm. (b) Area = \\(3.14\\times3^2 + 0.5\\times3.14\\times6^2 + 6\\times3 = 28.26 + 56.52 + 18 = 102.78\\) cm².",
      "hints": ["Find the small (3 cm) and large (6 cm) radii from the 12 cm length.", "Add the curved and straight parts for perimeter; add circle and rectangle areas for area."],
      "source": "Rosyth School 2025 P6 WA2 P2 Q17",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q17.png",
      "image_page": 35,
      "image_bbox": [0.36, 0.15, 0.64, 0.32],
      "image_loc": "shaded figure of a rectangle, large semicircle and 2 small semicircles in a 12 cm square, top of page",
      "notes": "Paper 2 Q17. Answer key: (a) 43.68 cm, (b) 102.78 cm². Two numeric blanks. Figure needed."
    }
  ]
}