{
  "paper": {
    "school": "Raffles Girls' Primary School",
    "year": 2025,
    "level": "P6",
    "label": "Prelim",
    "source_prefix": "Raffles Girls 2025 P6 Prelim",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "What does the digit 9 in 190 284 stand for?",
      "answer0": "90",
      "answer1": "900",
      "answer2": "9000",
      "answer3": "90 000",
      "correct_answer": 3,
      "skill_id": 106,
      "difficulty_id": 1,
      "explanation": "The digit 9 is in the ten-thousands place, so it stands for 9 x 10 000 = 90 000.",
      "hints": ["Identify the place value of the 9.", "190 284 = 1 hundred-thousand, 9 ten-thousands, 0 thousands ..."],
      "source": "Raffles Girls 2025 P6 Prelim Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 4."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "The figure is made up of equilateral triangles. What fraction of the figure is shaded?",
      "answer0": "\\(\\dfrac{1}{3}\\)",
      "answer1": "\\(\\dfrac{1}{2}\\)",
      "answer2": "\\(\\dfrac{2}{3}\\)",
      "answer3": "\\(\\dfrac{5}{8}\\)",
      "correct_answer": 3,
      "skill_id": 120,
      "difficulty_id": 1,
      "explanation": "The large triangle is divided into 8 small equal triangles. 5 of them are shaded, so the shaded fraction is \\(\\dfrac{5}{8}\\).",
      "hints": ["Count the total number of small equal triangles.", "Count how many are shaded."],
      "source": "Raffles Girls 2025 P6 Prelim Q2",
      "image_needed": true,
      "image_page": 2,
      "image_bbox": [0.38, 0.36, 0.62, 0.49],
      "image_loc": "middle of page, below the question — a large triangle made of small triangles, some shaded",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 4 (5/8). Fraction options -> MCQ."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Which of the following is equal to \\(2\\dfrac{4}{5}\\)?",
      "answer0": "\\(\\dfrac{8}{5}\\)",
      "answer1": "\\(\\dfrac{11}{5}\\)",
      "answer2": "\\(\\dfrac{13}{5}\\)",
      "answer3": "\\(\\dfrac{14}{5}\\)",
      "correct_answer": 3,
      "skill_id": 119,
      "difficulty_id": 1,
      "explanation": "\\(2\\dfrac{4}{5} = \\dfrac{2 \\times 5 + 4}{5} = \\dfrac{14}{5}\\).",
      "hints": ["Multiply the whole number by the denominator, then add the numerator.", "Keep the same denominator."],
      "source": "Raffles Girls 2025 P6 Prelim Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 4. Fraction options -> MCQ."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "In the number line, what is the value represented by A?",
      "answer0": "3.02",
      "answer1": "3.04",
      "answer2": "3.2",
      "answer3": "3.4",
      "correct_answer": 3,
      "skill_id": 123,
      "difficulty_id": 2,
      "explanation": "The interval from 3 to 4 is divided into 5 equal parts, each 0.2. A is at the 2nd mark after 3, so A = 3 + 2 x 0.2 = 3.4.",
      "hints": ["Count the number of equal intervals between 3 and 4.", "Each interval = 1 / number of parts."],
      "source": "Raffles Girls 2025 P6 Prelim Q4",
      "image_needed": true,
      "image_page": 3,
      "image_bbox": [0.30, 0.11, 0.66, 0.18],
      "image_loc": "top of page, below the question — a number line marked 3 and 4 with arrow A",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 4 (3.4)."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "40% of a number is 80. What is the number?",
      "answer0": "32",
      "answer1": "50",
      "answer2": "120",
      "answer3": "200",
      "correct_answer": 3,
      "skill_id": 207,
      "difficulty_id": 2,
      "explanation": "40% of the number is 80, so 1% is 80 ÷ 40 = 2, and 100% is 2 x 100 = 200.",
      "hints": ["Find 1% first.", "Then multiply by 100."],
      "source": "Raffles Girls 2025 P6 Prelim Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 4 (200)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "Which of the following is the same as 8050 m?",
      "answer0": "8 km 5 m",
      "answer1": "8 km 50 m",
      "answer2": "80 km 5 m",
      "answer3": "80 km 50 m",
      "correct_answer": 1,
      "skill_id": 184,
      "difficulty_id": 1,
      "explanation": "1 km = 1000 m, so 8050 m = 8000 m + 50 m = 8 km 50 m.",
      "hints": ["1 km = 1000 m.", "Split 8050 into thousands and the remainder."],
      "source": "Raffles Girls 2025 P6 Prelim Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 2 (8 km 50 m)."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "PQRS is a parallelogram. Which of the following statement(s) is/are true?<br>A. ∠SPQ = ∠SRQ<br>B. ∠PSQ = ∠QSR<br>C. PQS is an isosceles triangle.",
      "answer0": "A only",
      "answer1": "A and B",
      "answer2": "A and C",
      "answer3": "All of the above",
      "correct_answer": 0,
      "skill_id": 199,
      "difficulty_id": 3,
      "explanation": "In a parallelogram opposite angles are equal, so ∠SPQ = ∠SRQ (A is true). The diagonal PR does not bisect ∠S, so ∠PSQ ≠ ∠QSR (B false), and PQS is not necessarily isosceles (C false). Only A is true.",
      "hints": ["Opposite angles of a parallelogram are equal.", "A diagonal does not always bisect an angle."],
      "source": "Raffles Girls 2025 P6 Prelim Q7",
      "image_needed": true,
      "image_page": 4,
      "image_bbox": [0.40, 0.07, 0.68, 0.18],
      "image_loc": "top right of page — parallelogram PQRS with diagonal SQ drawn",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 1 (A only)."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "Which of the following is a net of the cube?",
      "answer0": "Net 1",
      "answer1": "Net 2",
      "answer2": "Net 3",
      "answer3": "Net 4",
      "correct_answer": 1,
      "skill_id": 232,
      "difficulty_id": 2,
      "explanation": "Folding each net, only Net 2 forms a closed cube with no overlapping or missing faces.",
      "hints": ["A cube net has exactly 6 squares.", "Mentally fold each option."],
      "source": "Raffles Girls 2025 P6 Prelim Q8",
      "image_needed": true,
      "image_options": true,
      "image_page": 4,
      "image_bbox": [0.18, 0.69, 0.86, 0.86],
      "image_loc": "bottom of page — four net options (1)-(4) below the cube",
      "image_file": null,
      "notes": "Answer key: option 2. Options are pictures (nets); the cube figure is at the top of the question (page 4, around y 0.55-0.66). image_bbox here covers the four option nets."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "Which two lines are perpendicular to each other?",
      "answer0": "DC and GH",
      "answer1": "DC and EF",
      "answer2": "AB and DC",
      "answer3": "AB and AD",
      "correct_answer": 0,
      "skill_id": 100,
      "difficulty_id": 2,
      "explanation": "From the figure, line GH meets DC at a right angle, so DC and GH are perpendicular.",
      "hints": ["Perpendicular lines meet at 90°.", "Look for the right-angle in the figure."],
      "source": "Raffles Girls 2025 P6 Prelim Q9",
      "image_needed": true,
      "image_page": 5,
      "image_bbox": [0.32, 0.08, 0.74, 0.24],
      "image_loc": "top of page — quadrilateral ABCD with lines EF and GH crossing it",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 1 (DC and GH)."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "The pie chart shows the different ways a group of students goes to school.<br>What fraction of the students go to school by MRT?",
      "answer0": "\\(\\dfrac{1}{6}\\)",
      "answer1": "\\(\\dfrac{1}{4}\\)",
      "answer2": "\\(\\dfrac{1}{3}\\)",
      "answer3": "\\(\\dfrac{5}{12}\\)",
      "correct_answer": 0,
      "skill_id": 235,
      "difficulty_id": 2,
      "explanation": "Bus = 50% = \\(\\dfrac{6}{12}\\), Walk = \\(\\dfrac{1}{12}\\), and Car = \\(\\dfrac{3}{12}\\) (right angle). MRT = 1 − \\(\\dfrac{6}{12}\\) − \\(\\dfrac{1}{12}\\) − \\(\\dfrac{3}{12}\\) = \\(\\dfrac{2}{12}\\) = \\(\\dfrac{1}{6}\\).",
      "hints": ["Bus is 50% = half. Car is the right-angle slice = quarter.", "MRT is what remains after Bus, Walk and Car."],
      "source": "Raffles Girls 2025 P6 Prelim Q10",
      "image_needed": true,
      "image_page": 6,
      "image_bbox": [0.31, 0.13, 0.66, 0.40],
      "image_loc": "top of page — pie chart with MRT, Bus 50%, Car, Walk 1/12 slices",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 1 (1/6). Fraction options -> MCQ. The printed stem has 'Primary 6' struck through; transcribed as 'students'."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "The pie chart shows the different ways a group of students goes to school.<br>What is the ratio of the number of students who travel to school by bus to the number of students who walk to school?",
      "answer0": "1 : 5",
      "answer1": "1 : 6",
      "answer2": "5 : 1",
      "answer3": "6 : 1",
      "correct_answer": 3,
      "skill_id": 210,
      "difficulty_id": 2,
      "explanation": "Bus = 50% = \\(\\dfrac{6}{12}\\) and Walk = \\(\\dfrac{1}{12}\\). Ratio Bus : Walk = 6 : 1.",
      "hints": ["Express Bus and Walk as fractions with the same denominator.", "Compare the numerators."],
      "source": "Raffles Girls 2025 P6 Prelim Q11",
      "image_needed": true,
      "image_page": 6,
      "image_bbox": [0.31, 0.13, 0.66, 0.40],
      "image_loc": "top of page — same pie chart used for Q10",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 4 (6 : 1). Shares the pie chart figure with Q10."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "Arrange the mass from the heaviest to the lightest.",
      "answer0": "\\(7\\dfrac{3}{5}\\) kg, 7 kg 95 g, 7.45 kg",
      "answer1": "\\(7\\dfrac{3}{5}\\) kg, 7.45 kg, 7 kg 95 g",
      "answer2": "7.45 kg, \\(7\\dfrac{3}{5}\\) kg, 7 kg 95 g",
      "answer3": "7 kg 95 g, 7.45 kg, \\(7\\dfrac{3}{5}\\) kg",
      "correct_answer": 1,
      "skill_id": 124,
      "difficulty_id": 2,
      "explanation": "Convert all to kg: \\(7\\dfrac{3}{5}\\) kg = 7.6 kg, 7 kg 95 g = 7.095 kg, 7.45 kg. Heaviest to lightest: 7.6 kg, 7.45 kg, 7.095 kg, i.e. \\(7\\dfrac{3}{5}\\) kg, 7.45 kg, 7 kg 95 g.",
      "hints": ["Convert every mass to the same unit (kg).", "1000 g = 1 kg, so 95 g = 0.095 kg."],
      "source": "Raffles Girls 2025 P6 Prelim Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 2. Options contain fractions and ordering -> MCQ."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "The bar graphs show the sale of each type of stationery in a shop for two days. The scale of the graphs is not shown.<br>The total number of items sold on Day 1 was twice the total number sold on Day 2. What is the ratio of the number of pens sold on Day 1 to Day 2?",
      "answer0": "1 : 2",
      "answer1": "2 : 1",
      "answer2": "5 : 2",
      "answer3": "5 : 3",
      "correct_answer": 2,
      "skill_id": 104,
      "difficulty_id": 3,
      "explanation": "Reading the bars in units: Day 1 Files 1, Pens 5, Notebooks 2 -> total 8 units; Day 2 Files 3, Pens 5, Notebooks 2 -> total 10 units. Day 1 total = 2 x Day 2 total, so 8 large units = 2 x 10 small units, i.e. 1 large unit = 2.5 small units. Pens Day 1 = 5 x 2.5 = 12.5 small; Pens Day 2 = 5 small. Ratio = 12.5 : 5 = 5 : 2.",
      "hints": ["The two graphs use different scales.", "Use the 'twice the total' fact to relate the two scales."],
      "source": "Raffles Girls 2025 P6 Prelim Q13",
      "image_needed": true,
      "image_page": 7,
      "image_bbox": [0.18, 0.42, 0.86, 0.62],
      "image_loc": "middle of page — two bar graphs labelled Day 1 and Day 2 (Files, Pens, Notebooks)",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 3 (5 : 2)."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "The figure shows a semi-circle and a square. The diameter of the semi-circle is 21 cm. What is the perimeter of the figure? (Take \\(\\pi = \\dfrac{22}{7}\\))",
      "answer0": "54 cm",
      "answer1": "66 cm",
      "answer2": "68 cm",
      "answer3": "101 cm",
      "correct_answer": 2,
      "skill_id": 221,
      "difficulty_id": 3,
      "explanation": "Square side = 21 − 5 − 9 = 7 cm. Curved semicircle arc = \\(\\dfrac{1}{2} \\times \\dfrac{22}{7} \\times 21 = 33\\) cm. The perimeter is the semicircle arc plus the exposed straight edges (the two base segments 5 cm and 9 cm and the square's three outer sides), giving the key answer 68 cm.",
      "hints": ["Curved part = half the circumference = \\(\\dfrac{1}{2}\\pi d\\).", "Add the straight edges of the square and the exposed base of the diameter."],
      "source": "Raffles Girls 2025 P6 Prelim Q14",
      "image_needed": true,
      "image_page": 8,
      "image_bbox": [0.40, 0.14, 0.66, 0.31],
      "image_loc": "top of page — a square sitting on the diameter of a semi-circle, with 5 cm and 9 cm marked",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key (Booklet A table): Q14 = 3 (1-based) -> option index 2 (68 cm)."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "A piece of paper in the shape of a trapezium is folded along dotted line EF. Find ∠x.",
      "answer0": "20°",
      "answer1": "40°",
      "answer2": "60°",
      "answer3": "80°",
      "correct_answer": 0,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "The fold along EF reflects the corner at E (100°). Using the angle properties of the folded trapezium, ∠x works out to the value given by the key.",
      "hints": ["Folding creates equal (mirror) angles about line EF.", "Use angles on a straight line and the trapezium's angle sum."],
      "source": "Raffles Girls 2025 P6 Prelim Q15",
      "image_needed": true,
      "image_page": 8,
      "image_bbox": [0.18, 0.46, 0.92, 0.70],
      "image_loc": "lower half of page — 'Before folding' and 'After folding' trapezium diagrams with 100° at E and x marked",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key (Booklet A table): Q15 = 1 (1-based) -> option 0 (20°)."
    },
    {
      "n": 16,
      "type_id": 1,
      "question": "Find the value of \\(\\dfrac{8}{9} \\div 6\\). Give your answer in the simplest form.",
      "answer0": "\\(\\dfrac{4}{27}\\)",
      "answer1": "\\(\\dfrac{8}{54}\\)",
      "answer2": "\\(\\dfrac{48}{9}\\)",
      "answer3": "\\(\\dfrac{2}{27}\\)",
      "correct_answer": 0,
      "skill_id": 164,
      "difficulty_id": 1,
      "explanation": "\\(\\dfrac{8}{9} \\div 6 = \\dfrac{8}{9} \\times \\dfrac{1}{6} = \\dfrac{8}{54} = \\dfrac{4}{27}\\).",
      "hints": ["Dividing by 6 is the same as multiplying by 1/6.", "Simplify the resulting fraction."],
      "source": "Raffles Girls 2025 P6 Prelim Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 8/54 = 4/27. Fraction answer -> MCQ (cannot be FIB)."
    },
    {
      "n": 17,
      "type_id": 1,
      "question": "Jones started work at 9.30 a.m. and ended work at 5.50 p.m. How long did he work?",
      "answer0": "8 h 20 min",
      "answer1": "7 h 20 min",
      "answer2": "8 h 40 min",
      "answer3": "4 h 20 min",
      "correct_answer": 0,
      "skill_id": 135,
      "difficulty_id": 1,
      "explanation": "9.30 a.m. to 5.30 p.m. is 8 h, then to 5.50 p.m. is 20 min more. Total = 8 h 20 min.",
      "hints": ["Count the hours from 9.30 a.m. to 5.30 p.m.", "Add the extra minutes to 5.50 p.m."],
      "source": "Raffles Girls 2025 P6 Prelim Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 8 h 20 min. Answer is in h-min format (two-unit time) -> MCQ rather than FIB."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "The graph shows the number of cars sold each month from January to May. What was the increase in the number of cars sold from March to April? [?]",
      "answer0": "240",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 147,
      "difficulty_id": 2,
      "explanation": "From the line graph, March = 320 cars and April = 560 cars. Increase = 560 − 320 = 240.",
      "hints": ["Read the values for March and April off the graph.", "Subtract March from April."],
      "source": "Raffles Girls 2025 P6 Prelim Q18",
      "image_needed": true,
      "image_page": 11,
      "image_bbox": [0.18, 0.10, 0.82, 0.40],
      "image_loc": "top of page — line graph of number of cars sold Jan to May",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 560 − 320 = 240."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "A watch costs $200 before 9% GST. What is the cost of the watch including GST?<br>$ [?]",
      "answer0": "218",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 2,
      "explanation": "GST = 9% of $200 = $18. Cost including GST = 200 + 18 = $218.",
      "hints": ["Find 9% of $200.", "Add the GST to the original price."],
      "source": "Raffles Girls 2025 P6 Prelim Q19",
      "image_needed": true,
      "image_page": 12,
      "image_bbox": [0.20, 0.10, 0.52, 0.27],
      "image_loc": "top left — picture of a wrist watch (decorative)",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 200 + 18 = 218. Watch image is decorative; not essential to solving."
    },
    {
      "n": 20,
      "type_id": 0,
      "question": "Figures X, Y and Z are each made up of 9 squares. Name the figure(s) that has/have a line of symmetry.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 145,
      "difficulty_id": 2,
      "explanation": "Examining each 3x3 shaded grid for a line of symmetry: Figures X and Y each have a line of symmetry; Z does not. Answer: Figure X and Y.",
      "hints": ["Check vertical, horizontal and diagonal mirror lines.", "A line of symmetry maps shaded squares onto shaded squares."],
      "source": "Raffles Girls 2025 P6 Prelim Q20",
      "image_needed": true,
      "image_page": 12,
      "image_bbox": [0.18, 0.50, 0.72, 0.66],
      "image_loc": "middle of page — three 3x3 shaded grids labelled X, Y, Z",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 'Figure X and Y'. Word/letter answer naming figures -> type_id 0 (SKIPPED on insert). Answer: X and Y."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "Find the value of \\(8w - \\dfrac{2w}{3} + 5\\) when \\(w = 3\\). [?]",
      "answer0": "27",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 240,
      "difficulty_id": 2,
      "explanation": "Substitute w = 3: 8(3) − \\(\\dfrac{2 \\times 3}{3}\\) + 5 = 24 − 2 + 5 = 27.",
      "hints": ["Replace every w with 3.", "Work out 2w/3 = (2 x 3)/3 = 2."],
      "source": "Raffles Girls 2025 P6 Prelim Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: = 27."
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "JKM is a right-angled triangle and JLM is an isosceles triangle. Find ∠JKL.<br>[?]°",
      "answer0": "15",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "∠JML = 90° (right angle at M). JLM is isosceles with ∠MJL = 30°, so ∠MLJ = (180° − 90°)/2 ... key working: 180° − 90° = 90°, 90° ÷ 2 = 45°; then 180° − 45° − 30° − 90° gives ∠JKL = 15°.",
      "hints": ["Use the right angle at M and the 30° at J.", "Use the isosceles property and angle sum of a triangle."],
      "source": "Raffles Girls 2025 P6 Prelim Q22",
      "image_needed": true,
      "image_page": 13,
      "image_bbox": [0.18, 0.48, 0.56, 0.62],
      "image_loc": "middle of page — triangle JKM with M right angle, L on MK, 30° at J",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: ∠JKL = 15°."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "(a) Express \\(1\\dfrac{3}{25}\\) as a decimal. [?]<br>(b) Round 20.85 to the nearest tenth. [?]",
      "answer0": "1.12",
      "answer1": "20.9",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 128,
      "difficulty_id": 1,
      "explanation": "(a) \\(1\\dfrac{3}{25} = 1\\dfrac{12}{100} = 1.12\\). (b) 20.85 rounded to the nearest tenth is 20.9.",
      "hints": ["(a) Make the denominator 100.", "(b) Look at the hundredths digit to round to one decimal place."],
      "source": "Raffles Girls 2025 P6 Prelim Q23",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: (a) 1.12, (b) 20.9. Both decimal answers -> FIB with two blanks."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "The ratio of the length of rod M to the length of rod N is 8 : 5. Find the length of rod N.<br>[?] m",
      "answer0": "3.5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 182,
      "difficulty_id": 3,
      "explanation": "From the figure, the overlap relationship gives 8u − 5u = 3u and 3u = 3.7 − 1.6 = 2.1, so 1u = 0.7. Rod N = 5u = 5 x 0.7 = 3.5 m.",
      "hints": ["Use the diagram: M − N corresponds to (8 − 5) units.", "Find the value of one unit first."],
      "source": "Raffles Girls 2025 P6 Prelim Q24",
      "image_needed": true,
      "image_page": 14,
      "image_bbox": [0.28, 0.49, 0.74, 0.62],
      "image_loc": "middle of page — two horizontal rods M and N with 1.6 m and 3.7 m marked",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: rod N = 3.5 m."
    },
    {
      "n": 25,
      "type_id": 0,
      "question": "The solid shown is made up of 8 cubes.<br>(a) Draw the front view of the solid on the grid.<br>(b) Find the greatest number of cubes that can be added to the solid without changing the front view and the side view.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 231,
      "difficulty_id": 3,
      "explanation": "(a) The front view is drawn on the grid (a drawing task). (b) The greatest number of cubes that can be added without changing the front and side views is 2.",
      "hints": ["For (a), shade the silhouette seen from the front.", "For (b), fill hidden positions that do not change either view."],
      "source": "Raffles Girls 2025 P6 Prelim Q25",
      "image_needed": true,
      "image_page": 15,
      "image_bbox": [0.34, 0.10, 0.70, 0.30],
      "image_loc": "top of page — isometric solid of 8 cubes with Top/Front/Side view arrows",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: (a) front-view drawing on grid; (b) 2. Part (a) is a draw-on-grid task -> whole question set as type_id 0 (SKIPPED on insert). Answers: (a) drawing, (b) 2."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "AEGD and EBCG are two identical rectangles, each measuring 12 cm by 9 cm. The length of EF is twice the length of FG. Find the area of the shaded parts.<br>[?] cm²",
      "answer0": "36",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "EG = 9 cm, with EF = 2 x FG, so FG = 3 cm, EF = 6 cm. Each shaded triangle: left triangle base AE = 12, height FG = 3 -> \\(\\dfrac{1}{2} \\times 12 \\times 6 = 36\\) (per key working); combining the two shaded triangles gives 18 + 18 = 36 cm².",
      "hints": ["Split EG (= 9) into EF and FG with EF = 2 FG.", "Area of each shaded triangle = ½ x base x height."],
      "source": "Raffles Girls 2025 P6 Prelim Q26",
      "image_needed": true,
      "image_page": 16,
      "image_bbox": [0.18, 0.13, 0.66, 0.28],
      "image_loc": "top of page — two rectangles A-E-B over D-G-C with shaded triangles meeting at F/G, 12 cm and 9 cm marked",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 18 + 18 = 36 cm²."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "At a competition, Yuta swam \\(\\dfrac{4}{5}\\) of the distance in 5 min. She swam the remaining 80 m in 3 min. What was her average speed for the whole distance?<br>[?] m/min",
      "answer0": "50",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 219,
      "difficulty_id": 3,
      "explanation": "The remaining 80 m is \\(\\dfrac{1}{5}\\) of the distance, so total distance = 80 x 5 = 400 m. Total time = 5 + 3 = 8 min. Average speed = 400 ÷ 8 = 50 m/min.",
      "hints": ["The 80 m is 1/5 of the whole distance.", "Average speed = total distance ÷ total time."],
      "source": "Raffles Girls 2025 P6 Prelim Q27",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 400 ÷ 8 = 50 m/min."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "The average of three different 3-digit numbers is 120. The 1st number is 110. The 2nd and 3rd numbers have the smallest possible difference. What are the two numbers?<br>[?] , [?]",
      "answer0": "124",
      "answer1": "126",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 205,
      "difficulty_id": 3,
      "explanation": "Total of three numbers = 120 x 3 = 360. The 2nd and 3rd add to 360 − 110 = 250. For the smallest difference between two different numbers, take 124 and 126 (124 + 126 = 250).",
      "hints": ["Find the total of all three numbers.", "The two unknowns sum to 250; make them as close as possible while different."],
      "source": "Raffles Girls 2025 P6 Prelim Q28",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 124 , 126. Two values -> FIB with two blanks."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "The first 18 numbers of a number pattern are shown.<br>2 , 0 , 1 , 1 , 0 , 3 , 2 , 0 , 1 , 1 , 0 , 3 , 2 , 0 , 1 , 1 , 0 , 3 ...<br>The sum of all the numbers in the pattern is 32. What is the greatest possible number of digit \"0\" in the pattern? [?]",
      "answer0": "10",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 108,
      "difficulty_id": 3,
      "explanation": "One repeating block (2,0,1,1,0,3) sums to 7 and contains two 0s. 32 ÷ 7 = 4 remainder 4, so 4 complete blocks give 4 x 2 = 8 zeros. The leftover sum of 4 can be made with extra terms that add two more 0s, giving 8 + 2 = 10 zeros.",
      "hints": ["Find the sum and the number of 0s in one repeating block.", "Use the remainder to add as many 0-valued terms as possible."],
      "source": "Raffles Girls 2025 P6 Prelim Q29",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 8 + 2 = 10."
    },
    {
      "n": 30,
      "type_id": 0,
      "question": "A rhombus VWXY is drawn on a square grid. By joining dots on the grid with straight lines,<br>(a) draw a triangle WYZ such that its area is half of the rhombus VWXY.<br>(b) draw a rhombus YSTU such that it has a longer perimeter than rhombus VWXY. Rhombus YSTU must not overlap with triangle WYZ.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 201,
      "difficulty_id": 3,
      "explanation": "(a) Triangle WYZ is drawn with area half that of rhombus VWXY (e.g. half the diagonal split). (b) Rhombus YSTU is drawn adjacent to Y with longer sides so its perimeter exceeds VWXY and it does not overlap triangle WYZ. (See key diagram.)",
      "hints": ["A diagonal splits the rhombus into two equal triangles.", "Make the new rhombus's side length longer than the original's."],
      "source": "Raffles Girls 2025 P6 Prelim Q30",
      "image_needed": true,
      "image_page": 18,
      "image_bbox": [0.33, 0.10, 0.72, 0.36],
      "image_loc": "upper half of page — square dot grid with rhombus VWXY drawn",
      "image_options": false,
      "image_file": null,
      "notes": "Drawing-on-grid construction task -> type_id 0 (SKIPPED on insert). Answers are constructions shown in the key diagram."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "A baker baked a total of 300 pies to sell. The bar graph shows the number of each type of pie that was sold.<br>(a) How many banana and lime pies were sold altogether? [?]<br>(b) What was the total number of pies left unsold? [?]",
      "answer0": "76",
      "answer1": "56",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 104,
      "difficulty_id": 2,
      "explanation": "(a) Banana = 52, Lime = 24, so 52 + 24 = 76. (b) Sold: Apple 72, Banana 52, Cherry 36, Lime 24, Pineapple 60 -> 244. Unsold = 300 − 244 = 56 (key: 300 − 72 − 52 − 36 − 24 − 60 = 56).",
      "hints": ["(a) Read the banana and lime bars and add.", "(b) Add all pies sold, then subtract from 300."],
      "source": "Raffles Girls 2025 P6 Prelim P2 Q1",
      "image_needed": true,
      "image_page": 20,
      "image_bbox": [0.26, 0.20, 0.72, 0.45],
      "image_loc": "upper-middle of page — bar graph of pies sold (Apple, Banana, Cherry, Lime, Pineapple)",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q1. Answer key: (a) 76, (b) 56. Two values -> FIB with two blanks."
    },
    {
      "n": 32,
      "type_id": 2,
      "question": "Mr Johnson was paid for working as an assistant at the rate shown in the table. He was paid a total of $646 for working 58 hours last week. The rate for the first 50 hours was covered by an ink blot. How much was he paid each hour for the first 50 hours?<br>$ [?]",
      "answer0": "11",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 118,
      "difficulty_id": 3,
      "explanation": "Additional hours = 58 − 50 = 8 h at $12 = $96. First-50-hours pay = 646 − 96 = $550. Rate = 550 ÷ 50 = $11 per hour.",
      "hints": ["Work out the pay for the 8 additional hours.", "Subtract that from $646, then divide by 50."],
      "source": "Raffles Girls 2025 P6 Prelim P2 Q2",
      "image_needed": true,
      "image_page": 21,
      "image_bbox": [0.30, 0.16, 0.78, 0.30],
      "image_loc": "top of page — rate table (First 50 hours / Each additional hour) with an ink blot over the first rate",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q2. Answer key: $11. The ink-blot table is decorative context; values needed are in the stem."
    },
    {
      "n": 33,
      "type_id": 1,
      "question": "Mrs Lim has black, purple and red markers. The number of black markers is 3 times the number of purple markers. \\(\\dfrac{1}{10}\\) of the markers are red. What fraction of Mrs Lim's markers are black?",
      "answer0": "\\(\\dfrac{27}{40}\\)",
      "answer1": "\\(\\dfrac{3}{4}\\)",
      "answer2": "\\(\\dfrac{9}{40}\\)",
      "answer3": "\\(\\dfrac{9}{10}\\)",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Red = \\(\\dfrac{1}{10}\\), so black + purple = \\(\\dfrac{9}{10}\\). Black : purple = 3 : 1, so black = \\(\\dfrac{3}{4}\\) of \\(\\dfrac{9}{10}\\) = \\(\\dfrac{9}{10} \\times \\dfrac{3}{4} = \\dfrac{27}{40}\\).",
      "hints": ["Find the fraction that is black + purple after removing red.", "Black is 3/4 of that combined part."],
      "source": "Raffles Girls 2025 P6 Prelim P2 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q3. Answer key: 27/40. Fraction answer -> MCQ."
    },
    {
      "n": 34,
      "type_id": 0,
      "question": "The square grid shows the position of seven points.<br>(a) Raju stood at point X facing P. He turned 90°. Write down all the possible points that he could be facing.<br>(b) Soo Yan stood at one of the points facing X. She turned 45° clockwise and faced U. Which point was Soo Yan at?",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 452,
      "difficulty_id": 3,
      "explanation": "(a) From X facing P, a 90° turn (either direction) makes Raju face Point R and Point T. (b) Soo Yan was at Point P.",
      "hints": ["A 90° turn is a quarter turn from the facing direction.", "Trace the line of sight to U after a 45° clockwise turn."],
      "source": "Raffles Girls 2025 P6 Prelim P2 Q4",
      "image_needed": true,
      "image_page": 22,
      "image_bbox": [0.28, 0.08, 0.60, 0.27],
      "image_loc": "top of page — square grid with seven labelled points P, Q, R, S, T, U and a North arrow",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q4. Answer key: (a) Point R and T; (b) Point P. Word/letter answers naming grid points -> type_id 0 (SKIPPED on insert)."
    },
    {
      "n": 35,
      "type_id": 0,
      "question": "A rectangle is divided into 6 parts, A, B, C, D, E and F. D is a square and is \\(\\dfrac{1}{6}\\) of the figure. Triangles E and C are identical.<br>(a) Which two parts will add up to form \\(\\dfrac{1}{2}\\) of the rectangle?<br>(b) Which two parts will add up to form \\(\\dfrac{5}{12}\\) of the figure?",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 159,
      "difficulty_id": 3,
      "explanation": "(a) Parts B and F together make \\(\\dfrac{1}{2}\\) of the rectangle. (b) Parts A and B together make \\(\\dfrac{5}{12}\\) of the figure.",
      "hints": ["Work out each part's fraction of the whole figure.", "Combine parts whose fractions add to the target."],
      "source": "Raffles Girls 2025 P6 Prelim P2 Q5",
      "image_needed": true,
      "image_page": 23,
      "image_bbox": [0.31, 0.10, 0.70, 0.27],
      "image_loc": "top of page — rectangle divided into labelled regions A, B, C, D, E, F",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q5. Answer key: (a) B and F; (b) A and B. Letter/region-naming answers -> type_id 0 (SKIPPED on insert)."
    },
    {
      "n": 36,
      "type_id": 1,
      "question": "Jared is 5y years old now. His sister is twice as old as him. His brother is 8 years older than his sister.<br>(a) How old is his brother now? Give your answer in terms of y.",
      "answer0": "10y + 8",
      "answer1": "5y + 8",
      "answer2": "10y − 8",
      "answer3": "7y + 8",
      "correct_answer": 0,
      "skill_id": 238,
      "difficulty_id": 2,
      "explanation": "Jared = 5y. Sister = 2 x 5y = 10y. Brother = sister + 8 = 10y + 8.",
      "hints": ["Sister's age = twice Jared's age.", "Brother = sister + 8."],
      "source": "Raffles Girls 2025 P6 Prelim P2 Q6a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q6(a). Answer key: 10y + 8. Algebraic expression answer -> MCQ. (Part (b) handled as n=37.)"
    },
    {
      "n": 37,
      "type_id": 1,
      "question": "Jared is 5y years old now. His sister is twice as old as him. His brother is 8 years older than his sister.<br>What was the total age of the three siblings 2 years ago? Give your answer in terms of y.",
      "answer0": "25y + 2",
      "answer1": "25y + 8",
      "answer2": "25y − 6",
      "answer3": "25y + 14",
      "correct_answer": 0,
      "skill_id": 241,
      "difficulty_id": 3,
      "explanation": "Now: Jared 5y, sister 10y, brother 10y + 8; total = 25y + 8. Two years ago each was 2 less, so subtract 2 x 3 = 6: (25y + 8) − 6 = 25y + 2.",
      "hints": ["Add the three present ages.", "Subtract 2 for each of the three siblings (6 in total)."],
      "source": "Raffles Girls 2025 P6 Prelim P2 Q6b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q6(b). Answer key: 25y + 2. Algebraic expression answer -> MCQ."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "The figure shows three boxes, X, Y, Z and a 50-gram weight on a balance scale. The average mass of the 3 boxes is 140 g. The mass of Box X is 40 g heavier than Box Y. What is the mass of Box Y?<br>[?] g",
      "answer0": "97.5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 205,
      "difficulty_id": 3,
      "explanation": "Total of 3 boxes = 140 x 3 = 420 g. The balance gives X + Y = Z + 50; with total 420, working: 420 + 50 = 470, 470 ÷ 2 = 235 (= X + Y), then 235 − 40 = 195, 195 ÷ 2 = 97.5 g. So Box Y = 97.5 g.",
      "hints": ["Total mass = average x number of boxes.", "Use the balance equation X + Y = Z + 50 together with X = Y + 40."],
      "source": "Raffles Girls 2025 P6 Prelim P2 Q7",
      "image_needed": true,
      "image_page": 25,
      "image_bbox": [0.34, 0.12, 0.72, 0.32],
      "image_loc": "upper part of page — a balance scale with boxes X, Y on one side and Z plus a 50 g weight on the other",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q7. Answer key: 97.5 g."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "ABC is an isosceles triangle. AB = AC. DEF is an equilateral triangle. AB is parallel to DF. Find ∠w.<br>[?]°",
      "answer0": "118",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "In isosceles triangle ABC, ∠ABC = (180° − 56°) ÷ 2 = 62°. ∠w is the angle at G; using the parallel lines and the 62°, ∠w = 180° − 62° = 118°.",
      "hints": ["Find the base angles of the isosceles triangle first.", "Use the parallel lines AB ∥ DF to transfer the angle."],
      "source": "Raffles Girls 2025 P6 Prelim P2 Q8a",
      "image_needed": true,
      "image_page": 26,
      "image_bbox": [0.33, 0.09, 0.74, 0.40],
      "image_loc": "upper half of page — two overlapping triangles ABC and DEF with 56° at A and w marked at G",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q8(a). Answer key: ∠w = 118°. (Part (b) is a circle-the-words task; see n=40.)"
    },
    {
      "n": 40,
      "type_id": 0,
      "question": "Circle the words that describe DHBG correctly in the following statement.<br>DHBG ( is / is not ) a parallelogram because DH ( is / is not ) parallel to GB.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 199,
      "difficulty_id": 2,
      "explanation": "DHBG IS a parallelogram because DH IS NOT parallel to GB — per the answer key the correct circled words are 'is' and 'is not'.",
      "hints": ["Decide if DHBG has two pairs of parallel sides.", "Check whether DH and GB are parallel."],
      "source": "Raffles Girls 2025 P6 Prelim P2 Q8b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q8(b). Circle-the-words interactive task -> type_id 0 (SKIPPED on insert). Answer key: 'DHBG is a parallelogram because DH is not parallel to GB.'"
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "PQRS is a rectangle. The length of PS is twice the length of ST. The ratio of the lengths ST : TW : WR is 1 : 3 : 1. The perimeter of the unshaded part of the figure is 56 cm longer than the perimeter of the shaded area TUVW. Find the shaded area TUVW.<br>[?] cm²",
      "answer0": "147",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Let 1 unit = u. Working from the key: unshaded perimeter = 11u, shaded perimeter = 3u + 56, so 11u − 3u = 56, 8u = 56, u = 7. Then PS = 2 x ST and the shaded triangle area = \\(\\dfrac{1}{2} \\times 21 \\times 14 = 147\\) cm².",
      "hints": ["Set ST : TW : WR = 1 : 3 : 1 in units and PS = 2 units.", "Form the perimeter equation: unshaded = shaded + 56."],
      "source": "Raffles Girls 2025 P6 Prelim P2 Q9",
      "image_needed": true,
      "image_page": 27,
      "image_bbox": [0.30, 0.13, 0.74, 0.27],
      "image_loc": "top of page — rectangle PQRS with shaded triangle TUVW inside",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q9. Answer key: shaded area = 147 cm². (The printed sub-parts (a)/(b) are partly struck through; the final single answer is 147 cm².)"
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "Linda baked some blueberry and chocolate tarts. At first, the number of blueberry tarts was \\(\\dfrac{2}{3}\\) the number of chocolate tarts. \\(\\dfrac{1}{4}\\) of the blueberry tarts and \\(\\dfrac{4}{9}\\) of the chocolate tarts were given away. The number of chocolate tarts left was 12 more than the number of blueberry tarts left. How many tarts did Linda bake?<br>[?]",
      "answer0": "360",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "At first Blueberry : Chocolate = 12 : 18 (units). Left: blueberry = \\(\\dfrac{3}{4}\\) of 12 = 9, chocolate = \\(\\dfrac{5}{9}\\) of 18 = 10. 10u − 9u = 1u = 12, so total = 12u + 18u = 30u = 30 x 12 = 360 tarts.",
      "hints": ["Use units 12 and 18 for the 2 : 3 ratio so the fractions divide evenly.", "Set chocolate-left minus blueberry-left = 12."],
      "source": "Raffles Girls 2025 P6 Prelim P2 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q10. Answer key: 360 tarts."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "Mei and Ann each used the same amount of flour to bake some muffins and doughnuts. Mei made 108 doughnuts and had 640 g of flour left. Ann made 48 muffins and had 1.96 kg of flour left. The mass of flour used to make 3 muffins was the same as that for making 4 doughnuts.<br>(a) What was the mass of flour used to make 1 doughnut? [?] g<br>(b) Mei and Ann decided to combine both their remaining flour to make doughnuts. What was the most number of doughnuts they could make altogether? [?]",
      "answer0": "30",
      "answer1": "86",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "(a) 3 muffins = 4 doughnuts, so 48 muffins = 64 doughnuts. Flour difference = 1960 − 640 = 1320 g; doughnut difference = 108 − 64 = 44; per doughnut = 1320 ÷ 44 = 30 g. (b) Combined flour = 1960 + 640 = 2600 g; 2600 ÷ 30 = 86 R 20, so most = 86 doughnuts.",
      "hints": ["Convert 1.96 kg to grams and equate the muffins to doughnuts.", "For (b), divide total remaining flour by the mass per doughnut."],
      "source": "Raffles Girls 2025 P6 Prelim P2 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q11. Answer key: (a) 30 g, (b) 86. Two integer answers -> FIB with two blanks."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "JKM and NKM are triangles. NKLM is a trapezium with NM parallel to KL.<br>(a) Find ∠NML. [?]°<br>(b) Find ∠JMN. [?]°",
      "answer0": "125",
      "answer1": "13",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "(a) ∠KLM = 360° − 305° = 55°; since NM ∥ KL, ∠NML = 180° − 55° = 125°. (b) ∠LKM = 180° − 90° − 55° = 35°; ∠NKL = 180° − 100° = 80°; ∠NKM = 80° − 35° = 45°; ∠JMN = 180° − 19° − 45° − 35° − 68° = 13°.",
      "hints": ["Use angles at a point and the parallel sides for (a).", "Work out the component angles around K and M for (b)."],
      "source": "Raffles Girls 2025 P6 Prelim P2 Q12",
      "image_needed": true,
      "image_page": 30,
      "image_bbox": [0.20, 0.10, 0.82, 0.42],
      "image_loc": "upper half of page — triangles JKM and NKM with angles 19°, 68°, 100° and reflex 305° at L marked",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q12. Answer key: (a) 125°, (b) 13°. Two angle answers -> FIB with two blanks."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "The pie chart shows the favourite sport of all the members of a sports club. The information is also represented by a bar graph. The bars for tennis and softball are not shown.<br>(a) What is the total number of members in the sports club? [?]<br>(b) What percentage of the members chose basketball as their favourite sport? [?]%<br>(c) The number of members who chose tennis as their favourite sport was \\(\\dfrac{1}{3}\\) of the number of those who chose softball. How many members chose tennis as their favourite sport? [?]",
      "answer0": "240",
      "answer1": "15",
      "answer2": "21",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 236,
      "difficulty_id": 3,
      "explanation": "(a) Badminton corresponds to a quarter (90°) of the pie and equals 60 members, so total = 60 x 4 = 240. (b) Basketball = 36 members; \\(\\dfrac{36}{240} = \\dfrac{3}{20}\\), x 100 = 15%. (c) Remaining (tennis + softball) = 240 − 60 − 60 − 36 = 84; tennis : softball = 1 : 3, so tennis = 84 ÷ 4 = 21.",
      "hints": ["Use the quarter slice of the pie chart to find the total.", "For (c), split the remaining members in the 1 : 3 ratio."],
      "source": "Raffles Girls 2025 P6 Prelim P2 Q13",
      "image_needed": true,
      "image_page": 31,
      "image_bbox": [0.18, 0.15, 0.88, 0.37],
      "image_loc": "upper part of page — pie chart (Tennis, Badminton, Softball, Basketball, Swimming) and bar graph with Tennis and Softball bars missing",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q13. Answer key: (a) 240, (b) 15%, (c) 21. Three integer/percentage answers -> FIB with three blanks."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "The table shows the ticket prices for a theme park.<br>(a) Ramu bought 3 adult tickets and 5 children tickets. What was the least amount he could have paid? $ [?]<br>(b) Timothy purchased his tickets online and enjoyed a 10% discount. He bought tickets for 4 adults and 3 children. What was the least amount he could have paid? $ [?]<br>(c) Mr and Mrs Tan went to the theme park with their children. They spent $99 on tickets. How many children went to the theme park? [?]",
      "answer0": "134",
      "answer1": "110.70",
      "answer2": "4",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Prices: Child $15, Adult $24, Bundle A (1 adult + 1 child) $35, Bundle B (2 adults + 1 child) $54. (a) Cheapest for 3 adults + 5 children = Bundle B (2A+1C) + Bundle A (1A+1C) + 3 children = 54 + 35 + 3 x 15 = $134. (b) Cheapest for 4 adults + 3 children = 2 x Bundle B + 1 child = (54 x 2) + 15 = 123, then 10% off: 123 x 0.9 = $110.70. (c) 2 adults + children for $99: 99 − 54 = 45 (after one Bundle B uses 2 adults + 1 child), 45 ÷ 15 = 3 more children, total children = 3 + 1 = 4.",
      "hints": ["Use bundle deals to minimise the cost.", "For (c), one Bundle B already covers the 2 adults and 1 child."],
      "source": "Raffles Girls 2025 P6 Prelim P2 Q14",
      "image_needed": true,
      "image_page": 32,
      "image_bbox": [0.28, 0.09, 0.74, 0.22],
      "image_loc": "top of page — ticket-price table (Child, Adult, Bundle deal A, Bundle deal B)",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q14. Answer key: (a) $134, (b) $110.70, (c) 4. Three money/integer answers -> FIB with three blanks."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "Nisa bought an equal number of apples and oranges. She exchanged 48 apples for the same number of oranges and gave away 100 apples. After that, the ratio of the number of apples to the number of oranges Nisa had was 2 : 9.<br>(a) What was the total number of fruits Nisa had in the end? [?]<br>(b) She then packed the remaining fruits into as many bags as possible. The ratio of the number of apples to the number of oranges in each bag was 4 : 5. How many oranges were left unpacked? [?]",
      "answer0": "308",
      "answer1": "182",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "(a) Let original count of each = n. After exchanging 48 and giving away 100 apples: apples = n − 48 − 100, oranges = n + 48; ratio 2 : 9. Key working: 9u − 2u = 7u = 100 + 48 + 48 = 196, 1u = 28; total = 2u + 9u = 11u = 28 x 11 = 308. (b) In 4 : 5 bags, apples = 2u = 56 limit; using the key, 252 − 70 = 182 oranges left unpacked.",
      "hints": ["Track apples and oranges separately through the exchange and give-away.", "For (b), pack in 4 : 5 groups and find the leftover oranges."],
      "source": "Raffles Girls 2025 P6 Prelim P2 Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q15. Answer key: (a) 308, (b) 182. Two integer answers -> FIB with two blanks."
    },
    {
      "n": 48,
      "type_id": 2,
      "question": "There was a total of 28 040 cm³ of water in rectangular tanks X and Y at first. The height of the water level in tank X was 8 cm more than that of tank Y.<br>(a) Find the height of the water level in tank Y. [?] cm<br>(b) Kenneth poured some water from tank X into tank Y to fill it to the brim. What was the percentage decrease in the volume of water in tank X? Round your answer to 1 decimal place. [?]%",
      "answer0": "20",
      "answer1": "22.5",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 229,
      "difficulty_id": 3,
      "explanation": "Tank X base = 35 x 22 = 770 cm²; Tank Y base = 18 x 18 = 324 cm². (a) Let Y water height = h, X height = h + 8. 770(h + 8) + 324h = 28 040 -> 770 x 8 = 6160; 28 040 − 6160 = 21 880; 770 + 324 = 1094; 21 880 ÷ 1094 = 20 cm. (b) Y full height 35 cm; water moved = 15 x 18 x 18 = 4860 cm³; X original water = 35 x 22 x 28 = 21 560 cm³; percentage decrease = 4860 ÷ 21 560 x 100 = 22.5%.",
      "hints": ["Set up the combined-volume equation with Y's height as the unknown.", "For (b), find the volume poured out and divide by X's original water volume."],
      "source": "Raffles Girls 2025 P6 Prelim P2 Q16",
      "image_needed": true,
      "image_page": 34,
      "image_bbox": [0.16, 0.11, 0.88, 0.40],
      "image_loc": "upper half of page — two rectangular tanks X (35 cm x 22 cm) and Y (18 cm x 18 cm, 35 cm tall) with water levels shaded",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q16. Answer key: (a) 20 cm, (b) 22.5%. Two answers (integer, decimal-percent) -> FIB with two blanks."
    },
    {
      "n": 49,
      "type_id": 2,
      "question": "The figure shows three overlapping quarter circles and three overlapping squares of different sizes. AB = BC = CD = DE = EF = FG.<br>(a) The area of the unshaded part in Figure DGHL is 48 cm². Find the length of DE. [?] cm<br>(b) Find the area of the shaded part of the figure. (Take \\(\\pi = 3.14\\)) [?] cm²",
      "answer0": "4",
      "answer1": "171.36",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 222,
      "difficulty_id": 3,
      "explanation": "(a) The unshaded part in DGHL is 3 equal small squares = 48 cm², so each square = 16 cm², side DE = \\(\\sqrt{16}\\) = 4 cm. (b) Squares shaded = 16 x 6 = 96. Quarter circles: \\(\\dfrac{1}{4} \\times 3.14 \\times 12^2 = 113.04\\); \\(\\dfrac{1}{4} \\times 3.14 \\times 8^2 = 50.24\\); \\(\\dfrac{1}{4} \\times 3.14 \\times 4^2 = 12.56\\). 50.24 − 12.56 = 37.68; 113.04 − 37.68 = 75.36; shaded total = 75.36 + 96 = 171.36 cm².",
      "hints": ["DGHL unshaded is made of equal small squares.", "For (b), combine the shaded squares with the shaded ring of quarter circles."],
      "source": "Raffles Girls 2025 P6 Prelim P2 Q17",
      "image_needed": true,
      "image_page": 35,
      "image_bbox": [0.28, 0.10, 0.74, 0.40],
      "image_loc": "upper half of page — three overlapping quarter circles (A-G) and three overlapping squares (D, E, F, G, L, H)",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q17. Answer key: (a) DE = 4 cm, (b) 171.36 cm². Two answers (integer, decimal) -> FIB with two blanks."
    }
  ]
}