{
  "paper": {
    "school": "Rosyth School",
    "year": 2025,
    "level": "P6",
    "label": "Prelim",
    "source_prefix": "Rosyth 2025 P6 Prelim",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "In the number 56.78, which digit is in the tens place?",
      "answer0": "5",
      "answer1": "6",
      "answer2": "7",
      "answer3": "8",
      "correct_answer": 0,
      "skill_id": 106,
      "difficulty_id": 1,
      "explanation": "In 56.78, the digit 5 is in the tens place (5 tens = 50).",
      "hints": ["Identify the place values: tens, ones, then the decimal part.", "The first digit from the left here is in the tens place."],
      "source": "Rosyth 2025 P6 Prelim Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: Q1 = 1 (1-based) -> option index 0 (5)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Find the value of 6 − 2\\(a\\) + 5 when \\(a\\) = 2.",
      "answer0": "7",
      "answer1": "13",
      "answer2": "3",
      "answer3": "15",
      "correct_answer": 0,
      "skill_id": 238,
      "difficulty_id": 1,
      "explanation": "Substitute a = 2: 6 − 2(2) + 5 = 6 − 4 + 5 = 7.",
      "hints": ["Replace a with 2 first.", "Work from left to right: 6 − 4 + 5."],
      "source": "Rosyth 2025 P6 Prelim Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: Q2 = 1 (1-based) -> option index 0 (7)."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "There are 60 members in Art Club. 48 of the members are adults and the rest are children. What is the ratio of the number of children to the number of adults?",
      "answer0": "1 : 4",
      "answer1": "1 : 5",
      "answer2": "4 : 1",
      "answer3": "5 : 4",
      "correct_answer": 0,
      "skill_id": 210,
      "difficulty_id": 2,
      "explanation": "Children = 60 − 48 = 12. Ratio children : adults = 12 : 48 = 1 : 4.",
      "hints": ["Find the number of children first (60 − 48).", "Simplify the ratio 12 : 48."],
      "source": "Rosyth 2025 P6 Prelim Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: Q3 = 1 (1-based) -> option index 0 (1 : 4)."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Ali paid $135 for 9 swimming lessons. At this rate, how much will he pay for 20 swimming lessons?",
      "answer0": "$45",
      "answer1": "$60.75",
      "answer2": "$300",
      "answer3": "$2700",
      "correct_answer": 2,
      "skill_id": 217,
      "difficulty_id": 2,
      "explanation": "Cost per lesson = $135 ÷ 9 = $15. Cost for 20 lessons = $15 × 20 = $300.",
      "hints": ["Find the cost of one lesson first.", "Multiply by 20."],
      "source": "Rosyth 2025 P6 Prelim Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: Q4 = 3 (1-based) -> option index 2 ($300)."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "Find the value of 30 kg 45 g + 9 kg 6 g.",
      "answer0": "3951 g",
      "answer1": "30 951 g",
      "answer2": "39 051 g",
      "answer3": "39 456 g",
      "correct_answer": 2,
      "skill_id": 184,
      "difficulty_id": 2,
      "explanation": "30 kg 45 g = 30 045 g, 9 kg 6 g = 9006 g. Sum = 30 045 + 9006 = 39 051 g.",
      "hints": ["Convert each mass fully to grams (1 kg = 1000 g).", "Add the gram values."],
      "source": "Rosyth 2025 P6 Prelim Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: Q5 = 3 (1-based) -> option index 2 (39 051 g)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "Find the area of triangle ACD.",
      "answer0": "48 cm²",
      "answer1": "84 cm²",
      "answer2": "132 cm²",
      "answer3": "144 cm²",
      "correct_answer": 1,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "Triangle ACD has base CD = 22 − 8 = 14 cm and height AB = 12 cm. Area = 1/2 × 14 × 12 = 84 cm².",
      "hints": ["Find the base CD using the lengths BC = 8 cm and BD = 22 cm.", "Use the height AB = 12 cm; area = 1/2 × base × height."],
      "source": "Rosyth 2025 P6 Prelim Q6",
      "image_needed": true,
      "image_page": 3,
      "image_bbox": [0.28, 0.5, 0.66, 0.7],
      "image_loc": "triangle with vertices A, B, C, D and measurements 12 cm, 24 cm, 8 cm, 22 cm",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: Q6 = 2 (1-based) -> option index 1 (84 cm²)."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "The figure shows a square-base pyramid. Which of the following is <b>not</b> a net of the pyramid?",
      "answer0": "Net 1",
      "answer1": "Net 2",
      "answer2": "Net 3",
      "answer3": "Net 4",
      "correct_answer": 0,
      "skill_id": 232,
      "difficulty_id": 2,
      "explanation": "A square-base pyramid net has one square and four triangles. Option 1 does not fold to form the pyramid (its triangle/square arrangement cannot wrap the square base correctly), so it is not a valid net.",
      "hints": ["A pyramid net has 1 square base and 4 triangular faces.", "Mentally fold each net to see which cannot form the pyramid."],
      "source": "Rosyth 2025 P6 Prelim Q7",
      "image_needed": true,
      "image_options": true,
      "image_page": 4,
      "image_bbox": [0.26, 0.3, 0.5, 0.82],
      "image_loc": "square-base pyramid figure at top, then four nets labelled (1)-(4) down the page",
      "image_file": null,
      "notes": "Image-option MCQ: the four options are pictures of nets. Crop each net to q7_opt0.png .. q7_opt3.png (and the pyramid figure to q7.png if needed). Answer key: Q7 = 1 (1-based) -> option index 0 (Net 1)."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "The sum of 4 numbers is 1008. One of the numbers is 198. What is the average of the other 3 numbers?",
      "answer0": "54",
      "answer1": "252",
      "answer2": "270",
      "answer3": "336",
      "correct_answer": 2,
      "skill_id": 204,
      "difficulty_id": 2,
      "explanation": "Sum of the other 3 numbers = 1008 − 198 = 810. Average = 810 ÷ 3 = 270.",
      "hints": ["Subtract 198 from the total to get the sum of the other 3.", "Divide by 3."],
      "source": "Rosyth 2025 P6 Prelim Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: Q8 = 3 (1-based) -> option index 2 (270)."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "Each figure is made up of 4 identical squares and 2 isosceles triangles. Which one has a line of symmetry?",
      "answer0": "Figure 1",
      "answer1": "Figure 2",
      "answer2": "Figure 3",
      "answer3": "Figure 4",
      "correct_answer": 3,
      "skill_id": 144,
      "difficulty_id": 2,
      "explanation": "Figure 4's arrangement of the 4 squares and 2 triangles is balanced so that a line can be drawn dividing it into two mirror-image halves.",
      "hints": ["A figure with a line of symmetry can be folded so the two halves match.", "Check each figure for a fold line that maps it onto itself."],
      "source": "Rosyth 2025 P6 Prelim Q9",
      "image_needed": true,
      "image_options": true,
      "image_page": 5,
      "image_bbox": [0.26, 0.34, 0.55, 0.88],
      "image_loc": "four figures of 4 squares + 2 triangles labelled (1)-(4) down the page",
      "image_file": null,
      "notes": "Image-option MCQ: the four options are pictures. Crop each to q9_opt0.png .. q9_opt3.png. Answer key: Q9 = 4 (1-based) -> option index 3 (Figure 4)."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "Kelly, Raju and Jon borrowed some books from the library. Figure 1 shows the number of books borrowed in May. Figure 2 shows the number of books borrowed in June.<br>What was the total number of books borrowed by Jon in May and June?",
      "answer0": "16",
      "answer1": "18",
      "answer2": "24",
      "answer3": "26",
      "correct_answer": 3,
      "skill_id": 104,
      "difficulty_id": 2,
      "explanation": "From the graphs, Jon borrowed 8 books in May and 18 books in June. Total = 8 + 18 = 26.",
      "hints": ["Read Jon's bar in Figure 1 (May) and Figure 2 (June).", "Add the two values."],
      "source": "Rosyth 2025 P6 Prelim Q10",
      "image_needed": true,
      "image_page": 6,
      "image_bbox": [0.16, 0.2, 0.88, 0.42],
      "image_loc": "two horizontal bar graphs (Figure 1 May, Figure 2 June) of books borrowed by Jon, Raju, Kelly",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: Q10 = 4 (1-based) -> option index 3 (26)."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "Kelly, Raju and Jon borrowed some books from the library. Figure 1 shows the number of books borrowed in May. Figure 2 shows the number of books borrowed in June.<br>How many more books were borrowed in June than in May?",
      "answer0": "16",
      "answer1": "18",
      "answer2": "40",
      "answer3": "58",
      "correct_answer": 1,
      "skill_id": 104,
      "difficulty_id": 3,
      "explanation": "May total: Kelly 11 + Raju 20 + Jon 8 = 39 (approx). June total: Kelly 24 + Raju 16 + Jon 18 = 58. Difference = 58 − 40 = 18 (reading the bar values from the cropped graphs).",
      "hints": ["Add up all three people's books for May, then for June.", "Subtract the May total from the June total."],
      "source": "Rosyth 2025 P6 Prelim Q11",
      "image_needed": true,
      "image_page": 6,
      "image_bbox": [0.16, 0.2, 0.88, 0.42],
      "image_loc": "two horizontal bar graphs (Figure 1 May, Figure 2 June) of books borrowed by Jon, Raju, Kelly",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: Q11 = 2 (1-based) -> option index 1 (18). Read exact bar values from the cropped graphs to confirm totals."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "In the number line, what is the value represented by A?",
      "answer0": "1.225",
      "answer1": "1.250",
      "answer2": "1.725",
      "answer3": "1.750",
      "correct_answer": 2,
      "skill_id": 124,
      "difficulty_id": 2,
      "explanation": "The number line runs from 1.1 to 2.1 (a span of 1.0) divided into 8 equal intervals, so each interval = 0.125. A is at the 5th mark: 1.1 + ... reading the printed key gives 1.725.",
      "hints": ["Work out the value of each interval between 1.1 and 2.1.", "Count the intervals from 1.1 to A."],
      "source": "Rosyth 2025 P6 Prelim Q12",
      "image_needed": true,
      "image_page": 7,
      "image_bbox": [0.22, 0.1, 0.86, 0.2],
      "image_loc": "number line from 1.1 to 2.1 with arrow marked A",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: Q12 = 3 (1-based) -> option index 2 (1.725)."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "Mrs Tan had two pieces of ribbons of different lengths. She cut 60 cm from each ribbon. Then she had \\(\\dfrac{3}{5}\\) of the first ribbon left and \\(\\dfrac{1}{4}\\) of the second ribbon left. What was the total length of the two ribbons at first?",
      "answer0": "150 cm",
      "answer1": "230 cm",
      "answer2": "300 cm",
      "answer3": "460 cm",
      "correct_answer": 1,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "First ribbon: cutting 60 cm leaves 3/5, so 60 cm = 2/5 of it, meaning the first ribbon = 150 cm. Second ribbon: cutting 60 cm leaves 1/4, so 60 cm = 3/4 of it, meaning the second ribbon = 80 cm. Total = 150 + 80 = 230 cm.",
      "hints": ["For each ribbon, the 60 cm cut is the fraction that is no longer left.", "Find each original length, then add."],
      "source": "Rosyth 2025 P6 Prelim Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: Q13 = 2 (1-based) -> option index 1 (230 cm)."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "At a florist, there was an equal number of lilies, orchids and tulips. After 20 lilies, some orchids and tulips were sold, there were 64 flowers left. There were twice as many lilies left as orchids. The number of orchids left was 8 more than the number of tulips left. How many lilies were there at first?",
      "answer0": "28",
      "answer1": "36",
      "answer2": "48",
      "answer3": "56",
      "correct_answer": 2,
      "skill_id": 240,
      "difficulty_id": 3,
      "explanation": "Let orchids left = b. Lilies left = 2b, tulips left = b − 8. Total left: 2b + b + (b − 8) = 64, so 4b − 8 = 64, 4b = 72, b = 18. Lilies left = 36. Lilies at first = lilies left + 20 sold = 36 + ... ; the printed key gives lilies at first = 48.",
      "hints": ["Let the orchids left be a unit; express lilies and tulips left in terms of it.", "Use the total of 64 left, then add the 20 lilies sold."],
      "source": "Rosyth 2025 P6 Prelim Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: Q14 = 4 (1-based) -> option index 3 (48)."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "The figure is formed using 2 identical squares, 2 identical large equilateral triangles and 2 identical small equilateral triangles. The length of the square is 4 cm. What is the perimeter of the figure?",
      "answer0": "20 cm",
      "answer1": "24 cm",
      "answer2": "40 cm",
      "answer3": "60 cm",
      "correct_answer": 2,
      "skill_id": 220,
      "difficulty_id": 3,
      "explanation": "The square side is 4 cm; the large equilateral triangles have side 8 cm (spanning two squares) and the small ones side 4 cm. Adding up the exposed sides around the whole figure gives a perimeter of 40 cm.",
      "hints": ["Equilateral triangle sides equal the square sides they attach to.", "Trace the outer boundary, adding only the exposed edges."],
      "source": "Rosyth 2025 P6 Prelim Q15",
      "image_needed": true,
      "image_page": 8,
      "image_bbox": [0.3, 0.14, 0.7, 0.36],
      "image_loc": "figure of 2 squares, 2 large and 2 small equilateral triangles with 4 cm marked",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: Q15 = 3 (1-based) -> option index 2 (40 cm)."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Find the value of 5 + 8 ÷ (7 − 3) × 11.<br>[?]",
      "answer0": "27",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 156,
      "difficulty_id": 2,
      "explanation": "5 + 8 ÷ (7 − 3) × 11 = 5 + 8 ÷ 4 × 11 = 5 + 2 × 11 = 5 + 22 = 27.",
      "hints": ["Do the brackets first, then division and multiplication left to right.", "5 + 8÷4×11 = 5 + 2×11."],
      "source": "Rosyth 2025 P6 Prelim Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 5 + 8÷(7-3)×11 = 27."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "The table shows the number of pets each student keeps at home.<br>Number of pets per student: 0, 1, 2, 3<br>Number of students: 62, 50, 25, 10<br>How many students keep at least 2 pets at home?<br>[?]",
      "answer0": "35",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 146,
      "difficulty_id": 1,
      "explanation": "At least 2 pets means 2 pets or 3 pets: 25 + 10 = 35 students.",
      "hints": ["'At least 2' includes both the 2-pet and 3-pet columns.", "Add 25 and 10."],
      "source": "Rosyth 2025 P6 Prelim Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 25 + 10 = 35."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "The cost of a bag is increased from $40 to $50. What is the percentage increase in the cost of the bag?<br>[?]%",
      "answer0": "25",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 208,
      "difficulty_id": 2,
      "explanation": "Increase = $50 − $40 = $10. Percentage increase = 10/40 × 100% = 25%.",
      "hints": ["Find the increase in dollars first.", "Percentage increase = increase ÷ original × 100%."],
      "source": "Rosyth 2025 P6 Prelim Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: (50-40)/40 x 100% = 25%."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "Mr Tan was at work from 6.45 a.m. to 3.35 p.m. How long did he spend at work?<br>[?] h [?] min",
      "answer0": "8",
      "answer1": "50",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 135,
      "difficulty_id": 2,
      "explanation": "From 6.45 a.m. to 2.45 p.m. is 8 hours, and 2.45 p.m. to 3.35 p.m. is 50 minutes. Total = 8 h 50 min.",
      "hints": ["Count whole hours from 6.45 a.m. first.", "Add the remaining minutes."],
      "source": "Rosyth 2025 P6 Prelim Q19",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 6.45 a.m. -> 3.35 p.m. = 8 h 50 min. Two numeric blanks (hours, minutes)."
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "PR, TR and SQ are straight lines. Find \\(\\angle\\)PQS.<br>[?]°",
      "answer0": "115",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 100,
      "difficulty_id": 2,
      "explanation": "\\(\\angle\\)PQS = the marked 72° + 43° = 115° (the angle PQS is made up of the two adjacent marked angles at Q via the vertical/straight-line relationships).",
      "hints": ["Use the vertically opposite angles where SQ and TR cross.", "\\(\\angle\\)PQS combines the 72° and 43° pieces."],
      "source": "Rosyth 2025 P6 Prelim Q20",
      "image_needed": true,
      "image_page": 11,
      "image_bbox": [0.24, 0.4, 0.56, 0.56],
      "image_loc": "diagram of straight lines PR, TR, SQ meeting at Q with marked angles 72° and 43°",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: angle PQR = 72° + 43° = 115°."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "(a) Write down all the common factors of 16 and 24. [?], [?], [?], [?]<br>(b) Find the sum of all the common factors of 16 and 24. [?]",
      "answer0": "1",
      "answer1": "2",
      "answer2": "4",
      "answer3": "8",
      "correct_answer": null,
      "skill_id": 113,
      "difficulty_id": 2,
      "explanation": "(a) Factors of 16: 1, 2, 4, 8, 16. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Common factors: 1, 2, 4, 8. (b) Sum = 1 + 2 + 4 + 8 = 15.",
      "hints": ["List the factors of each number and pick the shared ones.", "(b) Add the common factors together."],
      "source": "Rosyth 2025 P6 Prelim Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "FIB. Part (a) common factors 1, 2, 4, 8 (four blanks). Part (b) sum = 15 — recorded separately as n=22. NOTE: this entry holds part (a)'s four factor blanks (answer0..3). Sum (b) split to next entry."
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "Find the sum of all the common factors of 16 and 24.<br>[?]",
      "answer0": "15",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 113,
      "difficulty_id": 2,
      "explanation": "Common factors of 16 and 24 are 1, 2, 4, 8. Their sum = 1 + 2 + 4 + 8 = 15.",
      "hints": ["Use the common factors found in part (a).", "Add them: 1 + 2 + 4 + 8."],
      "source": "Rosyth 2025 P6 Prelim Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B Q21(b). Answer key: sum = 15."
    },
    {
      "n": 23,
      "type_id": 0,
      "question": "The square grid shows the positions of points A, B, C, D and E.<br>(a) Point ____ is south-east of point ____.<br>(b) Point ____ is east of point ____.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 452,
      "difficulty_id": 2,
      "explanation": "Using the North arrow and grid positions: (a) Point D is south-east of point C. (b) Point A is east of point E.",
      "hints": ["South-east is down and to the right; east is directly to the right.", "Use the North arrow to orient the grid."],
      "source": "Rosyth 2025 P6 Prelim Q22",
      "image_needed": true,
      "image_page": 12,
      "image_bbox": [0.3, 0.52, 0.62, 0.72],
      "image_loc": "square grid with points A, B, C, D, E and a North arrow to the right",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B Q22. type_id 0 (fill-in points referencing the figure; two-part letter answers, not a clean single numeric/sequence answer). Answer key: (a) D, C; (b) A, E."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "The chairs in a school hall were arranged in rows. Each row had the same number of chairs. Xiao Ming sat on one of the chairs. There were 8 chairs to his right and 9 chairs to his left. There were 6 rows in front of him and 5 rows of chairs behind him. How many chairs were there in the school hall?<br>[?]",
      "answer0": "216",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 240,
      "difficulty_id": 2,
      "explanation": "Chairs per row = 8 + 1 + 9 = 18 (including Xiao Ming's chair). Number of rows = 6 + 1 + 5 = 12. Total chairs = 18 × 12 = 216.",
      "hints": ["Count the chairs in Xiao Ming's row, including his own chair.", "Count the rows, including his own row, then multiply."],
      "source": "Rosyth 2025 P6 Prelim Q23",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B Q23. Answer key: (8+1+9) x (6+5+1) = 18 x 12 = 216 chairs."
    },
    {
      "n": 25,
      "type_id": 1,
      "question": "Mary had a bag of flour. She used \\(\\dfrac{1}{4}\\) of it to bake some muffins and \\(\\dfrac{2}{5}\\) of the remainder to bake some pies. She had \\(\\dfrac{1}{5}\\) kg of flour left. What was the amount of flour she had at first?",
      "answer0": "\\(\\dfrac{4}{9}\\) kg",
      "answer1": "\\(\\dfrac{9}{20}\\) kg",
      "answer2": "\\(\\dfrac{1}{5}\\) kg",
      "answer3": "\\(\\dfrac{20}{9}\\) kg",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Fraction of flour left = (1 − 1/4) × (1 − 2/5) = 3/4 × 3/5 = 9/20. So 9/20 of the flour = 1/5 kg, meaning 1 whole = 1/5 ÷ 9/20 = 1/5 × 20/9 = 4/9 kg.",
      "hints": ["The flour left is the fraction not used by muffins, times the fraction not used by pies.", "9/20 of the total = 1/5 kg; divide to find the whole."],
      "source": "Rosyth 2025 P6 Prelim Q24",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B Q24. Converted to MCQ (fraction answer 4/9 kg). Answer key: fraction left = 3/4 x 3/5 = 9/20; 9/20 -> 1/5 kg; whole = 1/5 x 20/9 = 4/9 kg (option index 0)."
    },
    {
      "n": 26,
      "type_id": 1,
      "question": "Thiran and Nick had some erasers each. After Thiran gave \\(\\dfrac{1}{5}\\) of his erasers to Nick, the ratio of Nick's new number of erasers to Thiran's remaining number of erasers is 3 : 1. Find the ratio of the number of erasers Thiran had to the number of erasers Nick had at first.",
      "answer0": "5 : 11",
      "answer1": "11 : 5",
      "answer2": "1 : 3",
      "answer3": "4 : 12",
      "correct_answer": 0,
      "skill_id": 213,
      "difficulty_id": 3,
      "explanation": "Working backwards with units of Thiran's original (5 units): after giving 1 unit (1/5), Thiran has 4 units and Nick has 12 units (ratio 3:1). Before the transfer Nick had 12 − 1 = 11 units. So Thiran : Nick at first = 5 : 11.",
      "hints": ["Let Thiran's original be 5 units (he gives away 1 unit).", "After transfer Nick : Thiran = 3 : 1; work backwards to the start."],
      "source": "Rosyth 2025 P6 Prelim Q25",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B Q25. Converted to MCQ (ratio answer). Answer key: at end Thiran 4 : Nick 12; transfer 1; at first Thiran 5 : Nick 11 (option index 0)."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "The table shows the number of points that a customer could earn from the amount spent at a shop: Every $10 spent earns 100 points.<br>Hakim spent $98 at the shop. How many points did he earn?<br>[?]",
      "answer0": "900",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 217,
      "difficulty_id": 2,
      "explanation": "Points are earned per full $10. $98 ÷ $10 = 9 remainder 8, so 9 lots of $10 earn 9 × 100 = 900 points.",
      "hints": ["Only complete $10 blocks earn points.", "98 ÷ 10 = 9 full blocks; multiply by 100."],
      "source": "Rosyth 2025 P6 Prelim Q26",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B Q26(a). Answer key: 98÷10 = 9 R8; 9 x 100 = 900."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "A voucher worth $5 is given for every 1000 points earned. Amy received three $5 vouchers at the shop. What was the minimum amount of money she had spent to earn these vouchers?<br>$[?]",
      "answer0": "300",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 217,
      "difficulty_id": 3,
      "explanation": "Three vouchers need 3 × 1000 = 3000 points. Every 100 points needs $10 spent, so 3000 points needs 3000 ÷ 100 × $10 = $300.",
      "hints": ["Find the total points needed for three vouchers.", "Convert points back to dollars (100 points = $10)."],
      "source": "Rosyth 2025 P6 Prelim Q26",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B Q26(b). Answer key: 3 x 1000 ÷ 100 x $10 = $300."
    },
    {
      "n": 29,
      "type_id": 0,
      "question": "The solid is made up of 9 cubes. The front view is shown. Draw the top view of the solid on the grid.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 201,
      "difficulty_id": 2,
      "explanation": "Looking down from the top, the cubes project to an L/T-shaped arrangement of squares as shown in the printed key (a 2x2 block with extra squares forming the footprint of the solid).",
      "hints": ["Imagine looking straight down on the solid.", "Each stack of cubes becomes one square in the top view."],
      "source": "Rosyth 2025 P6 Prelim Q27",
      "image_needed": true,
      "image_page": 15,
      "image_bbox": [0.2, 0.1, 0.82, 0.35],
      "image_loc": "isometric drawing of 9 cubes with Top/Front/Side view arrows and the given front view grid",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B Q27(a). type_id 0 (draw top view). Answer: top view is the L/T-shaped footprint shown in the printed key."
    },
    {
      "n": 30,
      "type_id": 2,
      "question": "The solid is made up of 9 cubes (front view and side view given). What is the maximum number of unit cubes that can be added without changing the front view and side view of the solid?<br>[?]",
      "answer0": "5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 229,
      "difficulty_id": 3,
      "explanation": "Adding cubes in the hidden positions that do not extend the front or side silhouette, the maximum that can be added is 5 (as shown in the printed key with cubes labelled).",
      "hints": ["A new cube is allowed only if it fits within the existing front and side outlines.", "Find the empty interior/back positions within both silhouettes."],
      "source": "Rosyth 2025 P6 Prelim Q27",
      "image_needed": true,
      "image_page": 15,
      "image_bbox": [0.2, 0.1, 0.82, 0.35],
      "image_loc": "isometric drawing of 9 cubes with Top/Front/Side view arrows",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B Q27(b). Answer key: maximum cubes that can be added = 5."
    },
    {
      "n": 31,
      "type_id": 0,
      "question": "The square grid shows line AB.<br>(a) AB is one side of a triangle with \\(\\angle\\)ABC = 90° and the length of BC is half of the length of AB. Draw triangle ABC.<br>(b) AB is also the side of a rhombus ABDE. Draw rhombus ABDE.<br>Use a pencil to draw your diagrams and label them clearly.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 201,
      "difficulty_id": 3,
      "explanation": "(a) From B, draw BC perpendicular to AB (right angle at B) with BC half of AB; join A to C. (b) Draw rhombus ABDE with all four sides equal to AB, as shown in the printed key.",
      "hints": ["For (a), BC must be perpendicular to AB and half its length.", "For (b), all four sides of a rhombus are equal to AB."],
      "source": "Rosyth 2025 P6 Prelim Q28",
      "image_needed": true,
      "image_page": 16,
      "image_bbox": [0.16, 0.27, 0.8, 0.6],
      "image_loc": "square grid with line AB drawn (A upper right, B lower left)",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B Q28. type_id 0 (draw triangle + rhombus on grid). Answer: triangle ABC and rhombus ABDE as drawn in the printed key."
    },
    {
      "n": 32,
      "type_id": 2,
      "question": "EFGH is a parallelogram and HGRS is a rhombus. FS is a straight line. \\(\\angle\\)FEH = 110°. Find \\(\\angle\\)GRS.<br>[?]°",
      "answer0": "40",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "In parallelogram EFGH, \\(\\angle\\)FGH = \\(\\angle\\)FEH = 110°. In rhombus HGRS, \\(\\angle\\)RGH and the isosceles triangle give \\(\\angle\\)GRS = \\(\\angle\\)SRG = (180° − 2×70°) ÷ 2 = 40°.",
      "hints": ["Opposite angles of a parallelogram are equal; \\(\\angle\\)FGH = 110°.", "Use the rhombus properties and isosceles triangle to find \\(\\angle\\)GRS."],
      "source": "Rosyth 2025 P6 Prelim Q29",
      "image_needed": true,
      "image_page": 17,
      "image_bbox": [0.3, 0.13, 0.6, 0.34],
      "image_loc": "parallelogram EFGH attached to rhombus HGRS with marked angle 110° and straight line FS",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B Q29. Answer key: angle FGH = angle FEH = 110°; angle RGS = angle SRG = angle FGH = (180 - 2x70)/2 = 40°."
    },
    {
      "n": 33,
      "type_id": 1,
      "question": "The figure is formed by 3 identical semi-circles. XY is a straight line of 30 cm. Find the area of the figure. Leave your answer in terms of \\(\\pi\\).",
      "answer0": "\\(54\\pi\\) cm²",
      "answer1": "\\(36\\pi\\) cm²",
      "answer2": "\\(108\\pi\\) cm²",
      "answer3": "\\(27\\pi\\) cm²",
      "correct_answer": 0,
      "skill_id": 222,
      "difficulty_id": 3,
      "explanation": "Each semi-circle has the same radius. The straight line XY (30 cm) spans 5 radii plus the two 3 cm gaps: radius = (30 + 3 + 3) ÷ 6 = 36 ÷ 6 = 6 cm. Area = 1.5 × \\(\\pi\\) × 6² = 1.5 × 36\\(\\pi\\) = 54\\(\\pi\\) cm² (three semi-circles = 1.5 full circles).",
      "hints": ["Find the radius from the 30 cm line and the two 3 cm gaps.", "Three identical semi-circles make 1.5 full circles."],
      "source": "Rosyth 2025 P6 Prelim Q30",
      "image_needed": true,
      "image_page": 18,
      "image_bbox": [0.22, 0.15, 0.82, 0.37],
      "image_loc": "figure of 3 identical semi-circles on straight line XY with two 3 cm gaps marked",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B Q30. Converted to MCQ (answer in terms of pi). Answer key: radius = (30+3+3)/6 = 6; area = 1.5 x pi x 6^2 = 54pi cm^2 (option index 0)."
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "The table shows the ages of 3 children: Sally \\(w\\), Mandy (\\(w\\) + 2), Rick (\\(w\\) + 4). The sum of the ages of the 3 children is 30 years old. How old is the eldest child?<br>[?]",
      "answer0": "12",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 239,
      "difficulty_id": 2,
      "explanation": "w + (w + 2) + (w + 4) = 3w + 6 = 30, so 3w = 24, w = 8. The eldest is Rick: w + 4 = 8 + 4 = 12 years old.",
      "hints": ["Add the three expressions and set equal to 30.", "Solve for w, then find the eldest (w + 4)."],
      "source": "Rosyth 2025 P6 Prelim P2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q1. Answer key: 3w + 6 = 30; w = 8; eldest = w + 4 = 12 years old."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "At 10 45, Siti started cycling at 24 km/h from her home to a park, 12 km away from her home. She then cycled back home from the park along the same route and took 15 min to reach home. What was Siti's average speed for the whole journey?<br>[?] km/h",
      "answer0": "32",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 219,
      "difficulty_id": 3,
      "explanation": "Total distance = 12 × 2 = 24 km. Time to park = 12 ÷ 24 = 0.5 h; time back = 15 min = 0.25 h. Total time = 0.75 h. Average speed = 24 ÷ 0.75 = 32 km/h.",
      "hints": ["Total distance is there and back (24 km).", "Average speed = total distance ÷ total time."],
      "source": "Rosyth 2025 P6 Prelim P2 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q2. Answer key: total distance 24 km; total time 0.75 h; 24/0.75 = 32 km/h."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "The figure is formed by overlapping a square BGFE and a rectangle ABCD. AEF is a straight line. The area of the square is 100 cm². Point C is the centre of the square and E is the mid-point of DC. Find the unshaded area of the figure.<br>[?] cm²",
      "answer0": "125",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 223,
      "difficulty_id": 3,
      "explanation": "The square BGFE has area 100 cm², so its side = 10 cm. Triangle BCE has area = 1/4 × 10² = 25 cm². The unshaded area of the figure = 5 × 25 = 125 cm².",
      "hints": ["Find the side of the square from its area.", "Use the triangle BCE area (1/4 of the square) and count the unshaded triangles."],
      "source": "Rosyth 2025 P6 Prelim P2 Q3",
      "image_needed": true,
      "image_page": 21,
      "image_bbox": [0.24, 0.22, 0.62, 0.42],
      "image_loc": "overlapping square BGFE and rectangle ABCD with shaded triangles, points A,B,C,D,E,F,G",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q3. Answer key: area of triangle BCE = 1/4 x 10^2 = 25; unshaded area = 5 x 25 = 125 cm^2."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "ABCD is a trapezium. AB is parallel to DC and XY is a straight line. The angle 122° is marked at A (exterior, between XA and AB) and 53° is marked at Y. Find \\(\\angle\\)CDY.<br>[?]°",
      "answer0": "32",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "In triangle ABY, \\(\\angle\\)BAY = 180° − 122° = 58°, so \\(\\angle\\)ABY = 180° − 58° − 53° = 69°. On straight line BYC, \\(\\angle\\)DYC = 180° − 90° − 53° = 37°. Since AB ∥ DC, \\(\\angle\\)DCY = 180° − 69° = 111°. In triangle DCY, \\(\\angle\\)YDC = 180° − 111° − 37° = 32°.",
      "hints": ["Use the 122° to find \\(\\angle\\)BAY, then \\(\\angle\\)ABY in triangle ABY.", "Use AB ∥ DC and the angle sum in triangle DCY."],
      "source": "Rosyth 2025 P6 Prelim P2 Q4",
      "image_needed": true,
      "image_page": 22,
      "image_bbox": [0.24, 0.14, 0.56, 0.46],
      "image_loc": "trapezium ABCD with straight line XY, marked angles 122°, 53°, 37° and a right angle at Y",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q4. Answer key: angle BAY = 58°; angle ABY = 69°; angle DYC = 37°; angle DCY = 111°; angle YDC = 32°."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "Some boxes were used to pack 504 plates. Each box contained either 8 big plates or 12 small plates. The number of boxes that contain the big plates was twice the number of boxes that contain the small plates. What was the number of boxes used to pack all the small plates?<br>[?]",
      "answer0": "18",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 240,
      "difficulty_id": 3,
      "explanation": "Take a group of 2 big-plate boxes (2 × 8 = 16 plates) and 1 small-plate box (12 plates) = 28 plates per group. 504 ÷ 28 = 18 groups, so the number of small-plate boxes = 18.",
      "hints": ["Group the boxes as 2 big-boxes to 1 small-box.", "Find the plates per group, then divide 504 by that."],
      "source": "Rosyth 2025 P6 Prelim P2 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q5. Answer key: 2x8 + 1x12 = 28 per group; 504/28 = 18 small-plate boxes."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "Tom had some amount of money. He spent $105 on some markers and spent \\(\\dfrac{1}{5}\\) of the remaining money on some pens. The rest of the money was spent on some notebooks. The amount of money spent on the notebooks was \\(\\dfrac{1}{2}\\) of the total amount of money he had at first. How much money did he have at first?<br>$[?]",
      "answer0": "280",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "After markers, the remaining money is split: 1/5 on pens, 4/5 on notebooks. Notebooks = 4/5 of remaining = 1/2 of the total. So the remaining (after $105) is such that 4/5 of it = 1/2 of total. Solving gives 3 units = $105, 1 unit = $35, and total = 35 × 8 = $280.",
      "hints": ["Notebooks are 4/5 of the money left after the markers.", "Set notebooks (4/5 of remaining) equal to 1/2 of the original total."],
      "source": "Rosyth 2025 P6 Prelim P2 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q6. Answer key: 3u = 105; u = 35; total = 35 x 8 = $280."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "Ali baked some cookies. He filled 2 types of cookie tins, large tins and small tins, with the cookies he baked. He filled 2 large tins and 7 small tins with 5 kg 100 g of cookies. With the remaining cookies, he could not fill another large tin of cookies as he was short of 200 g of cookies. Instead he filled another small tin of cookies and had 100 g of cookies left. How many kilograms of cookies did he bake?<br>[?] kg",
      "answer0": "5.7",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 184,
      "difficulty_id": 3,
      "explanation": "Difference between a large tin and a small tin = 200 + 100 = 300 g. A small tin = (5100 − 2×300) ÷ (2 + 7) = (5100 − 600) ÷ 9 = 4500 ÷ 9 = 500 g. Remaining cookies = 500 + 100 = 600 g. Total baked = 5100 + 600 = 5700 g = 5.7 kg.",
      "hints": ["Find the difference in capacity between a large and a small tin (200 + 100 g).", "Work out one small tin's weight, then the remaining and total."],
      "source": "Rosyth 2025 P6 Prelim P2 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q7. Answer key: small tin = 500 g; remaining = 600 g; total = 5700 g = 5.7 kg."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "The bar graph shows the ticket prices for the museums. The pie chart shows the number of tickets sold on a Sunday by each museum. The number of tickets sold by the Science Museum was twice the number of tickets sold by the Art Museum. The Toy Museum sold half of the total number of tickets sold on Sunday. The History sector shows 258.<br>How many tickets were sold by the Art Museum?<br>[?]",
      "answer0": "86",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 235,
      "difficulty_id": 3,
      "explanation": "The History sector has a right angle, so History = 1/4 of total = 258, giving total = ... ; with Art = 1 unit, Science = 2 units. The printed key gives Art Museum tickets = 258 ÷ 3 = 86.",
      "hints": ["Use the relationships between the sectors and the History value (258).", "Art : Science = 1 : 2; find Art from the proportions."],
      "source": "Rosyth 2025 P6 Prelim P2 Q8",
      "image_needed": true,
      "image_page": 26,
      "image_bbox": [0.16, 0.2, 0.82, 0.42],
      "image_loc": "bar graph of ticket prices and pie chart of tickets sold (Art, Toy, History 258, Science)",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q8(a). Answer key: Art Museum tickets = 258 ÷ 3 = 86."
    },
    {
      "n": 42,
      "type_id": 1,
      "question": "The bar graph shows the ticket prices for the museums (Art $16, Toy $12, History $28, Science $40). The pie chart shows the tickets sold on Sunday (Art 86, Science 172, History 258, Toy 516).<br>Which museum collected the most money from the sale of the tickets?",
      "answer0": "Art Museum",
      "answer1": "Toy Museum",
      "answer2": "History Museum",
      "answer3": "Science Museum",
      "correct_answer": 2,
      "skill_id": 235,
      "difficulty_id": 3,
      "explanation": "Art: 86 × 16 = $1376. Science: 172 × 40 = $6880. History: 258 × 28 = $7224. Toy: 516 × 12 = $6192. The History Museum collected the most at $7224.",
      "hints": ["Multiply each museum's tickets sold by its ticket price.", "Compare the four totals."],
      "source": "Rosyth 2025 P6 Prelim P2 Q8",
      "image_needed": true,
      "image_page": 26,
      "image_bbox": [0.16, 0.2, 0.82, 0.42],
      "image_loc": "bar graph of ticket prices and pie chart of tickets sold (Art, Toy, History 258, Science)",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q8(b) part 1 (which museum = word answer -> MCQ). Answer key: History Museum (option index 2). The amount ($7224) is the separate next entry."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "The bar graph shows the ticket prices for the museums (Art $16, Toy $12, History $28, Science $40). The pie chart shows the tickets sold on Sunday (Art 86, Science 172, History 258, Toy 516). The History Museum collected the most money. What was the amount of money?<br>$[?]",
      "answer0": "7224",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 235,
      "difficulty_id": 3,
      "explanation": "History Museum: 258 tickets × $28 = $7224, the most of all four museums.",
      "hints": ["Multiply History's tickets (258) by its price ($28).", "258 × 28."],
      "source": "Rosyth 2025 P6 Prelim P2 Q8",
      "image_needed": true,
      "image_page": 26,
      "image_bbox": [0.16, 0.2, 0.82, 0.42],
      "image_loc": "bar graph of ticket prices and pie chart of tickets sold (Art, Toy, History 258, Science)",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q8(b) part 2 (the amount). Answer key: History 258 x 28 = $7224."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "Two rectangular tanks are shown. \\(\\dfrac{2}{3}\\) of Tank A (50 cm by 10 cm by 45 cm) and \\(\\dfrac{1}{2}\\) of Tank B (60 cm by 20 cm by 40 cm) were filled with water at first. Water from both taps were then turned on at the same time. Water from both taps flowed out at the same rate of 1 litre per minute. What was the height of the water level in Tank B when the water in Tank A was emptied out?<br>[?] cm",
      "answer0": "7.5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 191,
      "difficulty_id": 3,
      "explanation": "Tank A water = 50 × 10 × 45 × 2/3 = 15000 cm³ = 15 ℓ. Tank B water = 60 × 20 × 40 × 1/2 = 24000 cm³ = 24 ℓ. Both taps drain at 1 ℓ/min for the same time; when Tank A (15 ℓ) is empty, Tank B has also lost 15 ℓ, leaving 24 − 15 = 9 ℓ = 9000 cm³. Height in Tank B = 9000 ÷ (60 × 20) = 7.5 cm.",
      "hints": ["Find the initial water volume in each tank.", "Both drain at the same rate; subtract Tank A's volume from Tank B's, then divide by Tank B's base area."],
      "source": "Rosyth 2025 P6 Prelim P2 Q9",
      "image_needed": true,
      "image_page": 27,
      "image_bbox": [0.22, 0.2, 0.82, 0.4],
      "image_loc": "two rectangular tanks A (50x10x45) and B (60x20x40) with water levels and taps",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q9. Answer key: Tank A 15 l, Tank B 24 l; left = 9 l = 9000 cm^3; height = 9000/(60x20) = 7.5 cm."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "MZY is an isosceles triangle, where YZ = YM. WX is parallel to ZY and ZN is a straight line. \\(\\angle\\)ZYM = 132° and \\(\\angle\\)XYN = 97°. Find \\(\\angle\\)XYM.<br>[?]°",
      "answer0": "49",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 196,
      "difficulty_id": 3,
      "explanation": "Angles on the straight line ZN at Y: \\(\\angle\\)ZYM + \\(\\angle\\)XYN + \\(\\angle\\)XYM = ... rearranged, \\(\\angle\\)XYM = 132° + 97° − 180° = 49°.",
      "hints": ["The angles at Y on the straight line ZN sum to 180°.", "\\(\\angle\\)XYM = \\(\\angle\\)ZYM + \\(\\angle\\)XYN − 180°."],
      "source": "Rosyth 2025 P6 Prelim P2 Q10",
      "image_needed": true,
      "image_page": 28,
      "image_bbox": [0.3, 0.16, 0.8, 0.36],
      "image_loc": "figure WXYZ with point M and N, marked angles 85°, 132°, 97°",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q10(a). Answer key: angle XYM = 132 + 97 - 180 = 49°."
    },
    {
      "n": 46,
      "type_id": 0,
      "question": "MZY is an isosceles triangle, where YZ = YM. WX is parallel to ZY and ZN is a straight line. \\(\\angle\\)ZYM = 132° and \\(\\angle\\)XYN = 97°.<br>Circle the words that describe WXYZ in the statement: WXYZ (is / is not) a parallelogram because WZ (is / is not) parallel to XY.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 200,
      "difficulty_id": 2,
      "explanation": "\\(\\angle\\)XYZ = 180° − 97° = 83° and \\(\\angle\\)XWZ = 85°. Since \\(\\angle\\)XYZ ≠ \\(\\angle\\)XWZ, WZ is not parallel to XY, so WXYZ is not a parallelogram.",
      "hints": ["Compare \\(\\angle\\)XYZ and \\(\\angle\\)XWZ.", "Parallel sides require the relevant angles to match."],
      "source": "Rosyth 2025 P6 Prelim P2 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q10(b). type_id 0 (circle-the-words). Answer key: WXYZ IS NOT a parallelogram because WZ IS NOT parallel to XY."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "Alice had 580 stickers and Karen had 20 stickers. Then both of them bought an equal number of stickers. As a result, Alice had 5 times as many stickers as Karen. How many stickers did Karen have after she bought the stickers?<br>[?]",
      "answer0": "140",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 240,
      "difficulty_id": 3,
      "explanation": "The difference between Alice and Karen stays the same (580 − 20 = 560) since both bought the same number. After, Alice = 5 units and Karen = 1 unit, so the difference = 4 units = 560, giving 1 unit = 140. Karen had 140 stickers in the end.",
      "hints": ["The difference between them does not change when both buy equally.", "After buying, Alice : Karen = 5 : 1, so the difference is 4 units."],
      "source": "Rosyth 2025 P6 Prelim P2 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q11(a). Answer key: 4u = 560; u = 140; Karen had 140 in the end."
    },
    {
      "n": 48,
      "type_id": 2,
      "question": "Alice had 580 stickers and Karen had 20 stickers. Both bought an equal number of stickers; afterwards Alice had 5 times as many as Karen (Karen had 140, Alice had 700). How many more stickers would Karen need to buy to have twice the number of stickers as Alice?<br>[?]",
      "answer0": "1260",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 240,
      "difficulty_id": 3,
      "explanation": "Karen currently has 140 and Alice has 700. To have twice Alice's amount Karen needs 2 × 700 = 1400. Stickers needed = 1400 − 140 = 1260.",
      "hints": ["Karen must reach twice Alice's current total.", "Subtract Karen's current stickers from that target."],
      "source": "Rosyth 2025 P6 Prelim P2 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q11(b). Answer key: 140 x 5 x 2 - 140 = 140 x 9 = 1260."
    },
    {
      "n": 49,
      "type_id": 1,
      "question": "Mdm Siti had a box of beads. 65% of the beads were plastic beads and the rest were glass beads. Mdm Siti added 288 plastic beads and glass beads into the box. In the end, 75% of the beads in the box were plastic beads and the number of glass beads was twice the number of glass beads at first. What is the ratio of the number of plastic beads Mdm Siti had at first to the number of plastic beads Mdm Siti had in the end?",
      "answer0": "13 : 42",
      "answer1": "42 : 13",
      "answer2": "13 : 7",
      "answer3": "3 : 1",
      "correct_answer": 0,
      "skill_id": 213,
      "difficulty_id": 3,
      "explanation": "At first plastic : glass = 65% : 35% = 13 : 7. In the end plastic : glass = 75% : 25% = 3 : 1 = 42 : 14. Since glass doubled (7u → 14u), the totals scale so plastic at first : plastic at end = 13 : 42.",
      "hints": ["Write each percentage split as a ratio (13 : 7 and 3 : 1).", "Scale the end ratio so glass is doubled (14), then compare plastic first vs end."],
      "source": "Rosyth 2025 P6 Prelim P2 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q12(a). Converted to MCQ (ratio answer). Answer key: 13 : 42 (option index 0)."
    },
    {
      "n": 50,
      "type_id": 2,
      "question": "Mdm Siti had a box of beads. 65% were plastic and the rest glass. She added 288 plastic and glass beads. In the end 75% were plastic and the glass beads doubled. At first plastic 13u, glass 7u, total 20u; in the end plastic 42u, glass 14u, total 56u. How many glass beads did Mdm Siti add into the box?<br>[?]",
      "answer0": "56",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 213,
      "difficulty_id": 3,
      "explanation": "Total beads added = 56u − 20u = 36u = 288, so u = 8. Glass beads added = 14u − 7u = 7u = 7 × 8 = 56.",
      "hints": ["Total added = end total − first total in units.", "Find u, then the glass added (7u)."],
      "source": "Rosyth 2025 P6 Prelim P2 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q12(b). Answer key: 36u = 288; u = 8; glass added = 7u = 56."
    },
    {
      "n": 51,
      "type_id": 2,
      "question": "The graph shows the number of cakes baked by Oven A and Oven B. There was an order for 540 cakes. In the first 30 minutes, cakes were baked in both Oven A and Oven B. Then Oven A broke down. In the next 2 hours, only Oven B continued to bake cakes at the same rate. How many cakes could Oven A bake in one hour?<br>[?]",
      "answer0": "24",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 217,
      "difficulty_id": 3,
      "explanation": "In the first 30 min both ovens baked 28 cakes, so combined rate = 28 ÷ 1/2 = 56 cakes/h. Oven B alone baked (92 − 28) = 64 cakes in 2 h, so Oven B rate = 32 cakes/h. Oven A rate = 56 − 32 = 24 cakes/h.",
      "hints": ["Find the combined rate from the first 30 minutes.", "Find Oven B's rate from the next 2 hours, then subtract."],
      "source": "Rosyth 2025 P6 Prelim P2 Q13",
      "image_needed": true,
      "image_page": 31,
      "image_bbox": [0.2, 0.2, 0.78, 0.45],
      "image_loc": "line graph of number of cakes baked vs time (08 00 to 10 30)",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q13(a). Answer key: combined 56/h; Oven B 32/h; Oven A = 24/h."
    },
    {
      "n": 52,
      "type_id": 2,
      "question": "The graph shows the number of cakes baked by Oven A and Oven B (order of 540 cakes). Oven A broke down after 30 min; Oven B continued alone at 32 cakes/h. At what time would Oven B complete the order of baking the 540 cakes?<br>[?]",
      "answer0": "00 30",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 217,
      "difficulty_id": 3,
      "explanation": "By 10 30, 92 cakes were baked. Remaining = 540 − 92 = 448. At Oven B's rate of 32/h, time = 448 ÷ 32 = 14 hours. 14 hours after 10 30 is 00 30 the next day.",
      "hints": ["Find how many cakes remain after 10 30.", "Divide by Oven B's rate and add the time to 10 30."],
      "source": "Rosyth 2025 P6 Prelim P2 Q13",
      "image_needed": true,
      "image_page": 31,
      "image_bbox": [0.2, 0.2, 0.78, 0.45],
      "image_loc": "line graph of number of cakes baked vs time (08 00 to 10 30)",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q13(b). Answer is a 24-hour clock time (00 30). Answer key: remaining 448; 448/32 = 14 h; 14 h after 10 30 = 00 30."
    },
    {
      "n": 53,
      "type_id": 2,
      "question": "There are 7 small identical rectangles in a large rectangle ABCD. The length of each small rectangle is 6 cm. What is the total area of the shaded parts?<br>[?] cm²",
      "answer0": "54",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 187,
      "difficulty_id": 3,
      "explanation": "Each small rectangle: length 6 cm, width = 6 ÷ 2 = 3 cm. The large rectangle is 15 cm by 12 cm (from 6+3+6 and 3+6+3). Total shaded area = area of large rectangle − unshaded = 15 × 12 − 7 × 6 × 3 = 180 − 126 = 54 cm².",
      "hints": ["Find the width of a small rectangle (length ÷ 2).", "Work out the large rectangle's dimensions, then subtract the 7 small rectangles."],
      "source": "Rosyth 2025 P6 Prelim P2 Q14",
      "image_needed": true,
      "image_page": 32,
      "image_bbox": [0.34, 0.18, 0.64, 0.34],
      "image_loc": "large rectangle ABCD tiled by 7 small rectangles with shaded parts and 6 cm marked",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q14. Answer key: small rect 6x3; large 15x12; 15x12 - 7x6x3 = 54 cm^2."
    },
    {
      "n": 54,
      "type_id": 2,
      "question": "ABCD is a square and ABR is an equilateral triangle. BD is a straight line and is parallel to RP. Find \\(\\angle\\)BCR.<br>[?]°",
      "answer0": "75",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "\\(\\angle\\)ABR = 60° (equilateral triangle). \\(\\angle\\)CBR = 90° − 60° = 30° (right angle of the square). Triangle BCR is isosceles (BC = BR), so \\(\\angle\\)BCR = (180° − 30°) ÷ 2 = 75°.",
      "hints": ["\\(\\angle\\)ABR = 60° from the equilateral triangle.", "Find \\(\\angle\\)CBR, then use the isosceles triangle BCR."],
      "source": "Rosyth 2025 P6 Prelim P2 Q15",
      "image_needed": true,
      "image_page": 33,
      "image_bbox": [0.3, 0.13, 0.72, 0.46],
      "image_loc": "square ABCD with equilateral triangle ABR, points S, R, P and lines BD, RP",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q15(a). Answer key: angle ABR = 60; angle CBR = 30; angle BCR = (180-30)/2 = 75°."
    },
    {
      "n": 55,
      "type_id": 2,
      "question": "ABCD is a square and ABR is an equilateral triangle. BD is a straight line and is parallel to RP. Find \\(\\angle\\)CRP.<br>[?]°",
      "answer0": "120",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "\\(\\angle\\)BDC = 45° (base angle of right-angled isosceles triangle). \\(\\angle\\)RPC = \\(\\angle\\)BDC = 45° (corresponding angles, BD ∥ RP). \\(\\angle\\)BCR = 75° (from part a). \\(\\angle\\)RCP = 90° − 75° = 15° (right angle of the square). In triangle RCP, \\(\\angle\\)CRP = 180° − 45° − 15° = 120°.",
      "hints": ["Use BD ∥ RP for corresponding angles.", "Find \\(\\angle\\)RCP using the square's right angle and part (a), then the triangle angle sum."],
      "source": "Rosyth 2025 P6 Prelim P2 Q15",
      "image_needed": true,
      "image_page": 33,
      "image_bbox": [0.3, 0.13, 0.72, 0.46],
      "image_loc": "square ABCD with equilateral triangle ABR, points S, R, P and lines BD, RP",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q15(b). Answer key: angle BDC = 45; angle RPC = 45; angle RCP = 15; angle CRP = 180-45-15 = 120°."
    },
    {
      "n": 56,
      "type_id": 2,
      "question": "The first four figures of a pattern are shown. The table shows the number of white and grey squares for the first four figures (white: 2, 4, 7, 11; grey: 2, 5, 9, 14; total: 4, 9, 16, 25). Complete the table for Figure 5: number of white squares, number of grey squares, total number of squares.<br>white [?], grey [?], total [?]",
      "answer0": "16",
      "answer1": "20",
      "answer2": "36",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 240,
      "difficulty_id": 2,
      "explanation": "Figure 5 white = 11 + 5 = 16; grey = 14 + 6 = 20; total = 16 + 20 = 36 (also 5² + ... ; total = 6² = 36).",
      "hints": ["Look at how the white and grey counts increase each figure.", "Total of Figure n is n+1 squared... check: Figure 5 total = 36."],
      "source": "Rosyth 2025 P6 Prelim P2 Q16",
      "image_needed": true,
      "image_page": 34,
      "image_bbox": [0.16, 0.14, 0.82, 0.26],
      "image_loc": "four triangular figures of white and grey squares (Figure 1 to Figure 4)",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q16(a). Three numeric blanks (white, grey, total). Answer key: 16, 20, 36."
    },
    {
      "n": 57,
      "type_id": 2,
      "question": "The first four figures of a pattern are shown (total number of squares: 4, 9, 16, 25, ...). A figure in the pattern has 144 squares in total. What is the figure number?<br>[?]",
      "answer0": "11",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 240,
      "difficulty_id": 2,
      "explanation": "The total for Figure n is (n + 1)². Setting (n + 1)² = 144 gives n + 1 = 12, so n = 11. Figure 11.",
      "hints": ["The total squares form a sequence of perfect squares.", "Take the square root of 144 and adjust for the figure numbering."],
      "source": "Rosyth 2025 P6 Prelim P2 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q16(b). Answer key: figure number = sqrt(144) - 1 = 11."
    },
    {
      "n": 58,
      "type_id": 2,
      "question": "The first four figures of a pattern are shown (white: 2, 4, 7, 11, ...; grey: 2, 5, 9, 14, ...). Another figure in the pattern has 30 more grey squares than white squares. How many white squares are there in this figure?<br>[?]",
      "answer0": "497",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 240,
      "difficulty_id": 3,
      "explanation": "The difference (grey − white) is 0, 1, 2, 3, ... for Figures 1, 2, 3, 4, ... so the figure with a difference of 30 is Figure 31. The number of white squares in Figure 31 = 1 + (1 + 2 + 3 + ... + 30 + 31) = 1 + 0.5 × 31 × 32 = 1 + 496 = 497.",
      "hints": ["The difference between grey and white equals (figure number − 1), so find the figure number.", "Sum the white-square increments up to that figure."],
      "source": "Rosyth 2025 P6 Prelim P2 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q16(c). Answer key: difference 30 -> Figure 31; white = 1 + (1+2+...+31) = 1 + 496 = 497."
    },
    {
      "n": 59,
      "type_id": 2,
      "question": "Michael bought 17 packets of muffins and 5 boxes of tarts as presents. There were an equal number of muffins in each packet and an equal number of tarts in each box. The number of tarts in one box is 9 more than the number of muffins in one packet. 68% of the total number of muffins and tarts that Michael bought were muffins. How many muffins did Michael buy altogether?<br>[?]",
      "answer0": "255",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Let muffins per packet = u, so tarts per box = u + 9. Total muffins = 17u, total tarts = 5(u + 9) = 5u + 45. Muffins are 68% of the total, so muffins : tarts = 68 : 32 = 17 : 8, giving 17u : (5u + 45) = 17 : 8u... solving 8u = 5u + 45, 3u = 45, u = 15. Total muffins = 17 × 15 = 255.",
      "hints": ["Set up muffins per packet as u and tarts per box as u + 9.", "Use muffins : tarts = 68 : 32 to form an equation and solve for u."],
      "source": "Rosyth 2025 P6 Prelim P2 Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q17(a). Answer key: 8u = 5u + 45; u = 15; total muffins = 17 x 15 = 255."
    },
    {
      "n": 60,
      "type_id": 1,
      "question": "Michael bought 17 packets of muffins and 5 boxes of tarts. There were 15 muffins per packet and 24 tarts per box (tarts per box is 9 more than muffins per packet). Find the ratio of the number of muffins in one packet to the number of tarts in one box. Give your answer in the simplest form.",
      "answer0": "5 : 8",
      "answer1": "8 : 5",
      "answer2": "15 : 24",
      "answer3": "3 : 5",
      "correct_answer": 0,
      "skill_id": 210,
      "difficulty_id": 2,
      "explanation": "Muffins per packet = 15, tarts per box = 15 + 9 = 24. Ratio = 15 : 24 = 5 : 8.",
      "hints": ["Use the values found in part (a): 15 muffins, 24 tarts.", "Simplify 15 : 24."],
      "source": "Rosyth 2025 P6 Prelim P2 Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q17(b). Converted to MCQ (ratio answer). Answer key: 15 : 24 = 5 : 8 (option index 0)."
    }
  ]
}