{
  "paper": {
    "school": "Red Swastika School",
    "year": 2025,
    "level": "P6",
    "label": "Prelim",
    "source_prefix": "Red Swastika 2025 P6 Prelim",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "What is the value of the digit 3 in 30 245?",
      "answer0": "30",
      "answer1": "300",
      "answer2": "3000",
      "answer3": "30 000",
      "correct_answer": 3,
      "skill_id": 106,
      "difficulty_id": 1,
      "explanation": "The digit 3 is in the ten-thousands place, so its value is 3 x 10 000 = 30 000.",
      "hints": ["Identify the place value of the 3.", "30 245 = 3 ten-thousands ..."],
      "source": "Red Swastika 2025 P6 Prelim Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 4 (30 000)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Find the value of 24 − 18 ÷ (12 − 9) x 2",
      "answer0": "1",
      "answer1": "12",
      "answer2": "21",
      "answer3": "4",
      "correct_answer": 1,
      "skill_id": 156,
      "difficulty_id": 2,
      "explanation": "Brackets first: 12 − 9 = 3. Then 18 ÷ 3 = 6, 6 x 2 = 12. Finally 24 − 12 = 12.",
      "hints": ["Work out the brackets first.", "Do division and multiplication before subtraction."],
      "source": "Red Swastika 2025 P6 Prelim Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 2 (12)."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Which fraction is greater than \\(\\dfrac{1}{3}\\)?",
      "answer0": "\\(\\dfrac{2}{5}\\)",
      "answer1": "\\(\\dfrac{2}{6}\\)",
      "answer2": "\\(\\dfrac{3}{10}\\)",
      "answer3": "\\(\\dfrac{3}{11}\\)",
      "correct_answer": 0,
      "skill_id": 159,
      "difficulty_id": 2,
      "explanation": "\\(\\dfrac{1}{3} \\approx 0.333\\). \\(\\dfrac{2}{5} = 0.4 > 0.333\\); the others are all less than or equal to \\(\\dfrac{1}{3}\\). So \\(\\dfrac{2}{5}\\) is greater.",
      "hints": ["Convert each option to a decimal or common denominator.", "Compare with 1/3 ≈ 0.333."],
      "source": "Red Swastika 2025 P6 Prelim Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 1 (2/5). Fraction options -> MCQ."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "What fraction of the circles are shaded?",
      "answer0": "\\(\\dfrac{1}{2}\\)",
      "answer1": "\\(\\dfrac{4}{5}\\)",
      "answer2": "\\(\\dfrac{4}{9}\\)",
      "answer3": "\\(\\dfrac{5}{9}\\)",
      "correct_answer": 3,
      "skill_id": 120,
      "difficulty_id": 1,
      "explanation": "There are 9 circles in total and 5 of them are shaded, so the shaded fraction is \\(\\dfrac{5}{9}\\).",
      "hints": ["Count the total number of circles.", "Count the shaded ones."],
      "source": "Red Swastika 2025 P6 Prelim Q4",
      "image_needed": true,
      "image_page": 4,
      "image_bbox": [0.30, 0.30, 0.70, 0.45],
      "image_loc": "below the question — a group of circles, some shaded",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 4 (5/9). 9 circles total, 5 shaded. Fraction options -> MCQ."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "550 + \\(\\dfrac{5}{10}\\) + \\(\\dfrac{5}{100}\\) =",
      "answer0": "555.5",
      "answer1": "550.55",
      "answer2": "550.055",
      "answer3": "550.505",
      "correct_answer": 1,
      "skill_id": 123,
      "difficulty_id": 2,
      "explanation": "\\(\\dfrac{5}{10} = 0.5\\) (tenths) and \\(\\dfrac{5}{100} = 0.05\\) (hundredths). 550 + 0.5 + 0.05 = 550.55.",
      "hints": ["5/10 is 0.5; 5/100 is 0.05.", "Add the decimals to 550."],
      "source": "Red Swastika 2025 P6 Prelim Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 2 (550.55)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "The ratio of the number of apples to the number of oranges is 3 : 5. There are 15 apples. How many oranges are there?",
      "answer0": "40",
      "answer1": "25",
      "answer2": "24",
      "answer3": "9",
      "correct_answer": 1,
      "skill_id": 181,
      "difficulty_id": 2,
      "explanation": "3 units = 15 apples, so 1 unit = 5. Oranges = 5 units = 5 x 5 = 25.",
      "hints": ["Find the value of one unit from the apples.", "Multiply by the oranges' number of units."],
      "source": "Red Swastika 2025 P6 Prelim Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 2 (25)."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "Simplify 5y + 10 − 4y − 6",
      "answer0": "y + 4",
      "answer1": "y + 16",
      "answer2": "9y + 4",
      "answer3": "9y + 16",
      "correct_answer": 0,
      "skill_id": 239,
      "difficulty_id": 1,
      "explanation": "Group like terms: 5y − 4y = y, 10 − 6 = 4. So the expression simplifies to y + 4.",
      "hints": ["Collect the y terms.", "Collect the number terms."],
      "source": "Red Swastika 2025 P6 Prelim Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 1 (y + 4)."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "What is the length of the pencil?",
      "answer0": "4.1 cm",
      "answer1": "4.2 cm",
      "answer2": "5.1 cm",
      "answer3": "5.2 cm",
      "correct_answer": 1,
      "skill_id": 124,
      "difficulty_id": 1,
      "explanation": "Reading the ruler, the pencil ends at the 4.2 cm mark.",
      "hints": ["Read where the pencil ends against the ruler.", "Note the start point of the pencil."],
      "source": "Red Swastika 2025 P6 Prelim Q8",
      "image_needed": true,
      "image_page": 5,
      "image_bbox": [0.18, 0.10, 0.82, 0.22],
      "image_loc": "below the question — a pencil aligned along a ruler",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 2 (4.2 cm)."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "The figure shows a cuboid. Two of its faces have areas 30 cm² and 24 cm². What is the volume of the cuboid?",
      "answer0": "720 cm³",
      "answer1": "180 cm³",
      "answer2": "144 cm³",
      "answer3": "120 cm³",
      "correct_answer": 3,
      "skill_id": 227,
      "difficulty_id": 3,
      "explanation": "From the two given face areas and the shared edge, the cuboid dimensions give a volume of 120 cm³ (per the answer key).",
      "hints": ["Adjacent faces share a common edge.", "Use the face areas to find each dimension."],
      "source": "Red Swastika 2025 P6 Prelim Q9",
      "image_needed": true,
      "image_page": 5,
      "image_bbox": [0.30, 0.40, 0.70, 0.58],
      "image_loc": "below the question — a cuboid with two faces labelled 30 cm² and 24 cm²",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 4 (120 cm³)."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "ABCD is a rhombus and ECD is a straight line. Which of the following statements is false?",
      "answer0": "∠BAC = ∠DAC",
      "answer1": "∠ABC = ∠BCE",
      "answer2": "∠ADC + ∠BCE = 180°",
      "answer3": "∠DCA + ∠BAC + ∠BCE = 180°",
      "correct_answer": 2,
      "skill_id": 200,
      "difficulty_id": 3,
      "explanation": "Using the properties of a rhombus and the straight line ECD, statements (1), (2) and (4) are true. Statement (3) ∠ADC + ∠BCE = 180° is false.",
      "hints": ["Diagonals of a rhombus bisect the angles.", "Use the straight-line angle at C."],
      "source": "Red Swastika 2025 P6 Prelim Q10",
      "image_needed": true,
      "image_page": 6,
      "image_bbox": [0.30, 0.08, 0.70, 0.26],
      "image_loc": "below the question — rhombus ABCD with line ECD extended",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 3 (the false statement)."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "Some shapes are drawn on a grid. Which two shapes have the same area?",
      "answer0": "A and B",
      "answer1": "B and C",
      "answer2": "B and D",
      "answer3": "C and D",
      "correct_answer": 1,
      "skill_id": 138,
      "difficulty_id": 2,
      "explanation": "Counting the grid squares (and half-squares) of each shape, shapes B and C have equal areas.",
      "hints": ["Count whole and half grid squares for each shape.", "Compare the totals."],
      "source": "Red Swastika 2025 P6 Prelim Q11",
      "image_needed": true,
      "image_page": 6,
      "image_bbox": [0.30, 0.40, 0.70, 0.62],
      "image_loc": "below the question — shapes A, B, C, D drawn on a square grid",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 2 (B and C)."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "Points A to F are marked on a square grid. Cathy is at the centre facing F. She turns 45° anti-clockwise. Which point is she now facing?",
      "answer0": "A",
      "answer1": "B",
      "answer2": "D",
      "answer3": "E",
      "correct_answer": 0,
      "skill_id": 452,
      "difficulty_id": 2,
      "explanation": "Turning 45° anti-clockwise from facing F moves Cathy's line of sight to point A.",
      "hints": ["45° is half of a right-angle turn.", "Trace the new direction on the grid."],
      "source": "Red Swastika 2025 P6 Prelim Q12",
      "image_needed": true,
      "image_page": 7,
      "image_bbox": [0.30, 0.08, 0.70, 0.30],
      "image_loc": "below the question — a square grid with points A-F marked around a centre",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 1 (A)."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "A pie chart and a bar graph show the modes of transport of a group of students. What is the total number of students who travel by green and blue?",
      "answer0": "33",
      "answer1": "27",
      "answer2": "24",
      "answer3": "21",
      "correct_answer": 2,
      "skill_id": 236,
      "difficulty_id": 3,
      "explanation": "Reading the pie chart and bar graph together, the number of students for green and blue add up to 24.",
      "hints": ["Use the pie chart and bar graph together.", "Add the green and blue values."],
      "source": "Red Swastika 2025 P6 Prelim Q13",
      "image_needed": true,
      "image_page": 7,
      "image_bbox": [0.18, 0.40, 0.86, 0.62],
      "image_loc": "below the question — a pie chart alongside a bar graph",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 3 (24)."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "ABC is an equilateral triangle and ADE is an isosceles triangle. Find ∠EAC.",
      "answer0": "35°",
      "answer1": "40°",
      "answer2": "45°",
      "answer3": "75°",
      "correct_answer": 0,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "ABC equilateral gives ∠BAC = 60°. Using the given 15° and 50° and the isosceles triangle ADE, ∠EAC = 35°.",
      "hints": ["Each angle of an equilateral triangle is 60°.", "Use the base angles of the isosceles triangle."],
      "source": "Red Swastika 2025 P6 Prelim Q14",
      "image_needed": true,
      "image_page": 8,
      "image_bbox": [0.30, 0.08, 0.70, 0.30],
      "image_loc": "below the question — overlapping triangles ABC and ADE with 15° and 50° marked",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 1 (35°)."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "With her money, Jane can buy exactly 5 large balloons, or 25 medium balloons, or 125 small balloons. She bought 2 large balloons, some medium balloons and 15 small balloons. What is the greatest number of medium balloons she could have bought?",
      "answer0": "12",
      "answer1": "23",
      "answer2": "110",
      "answer3": "138",
      "correct_answer": 0,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Express all balloons in the same money units (5 large = 25 medium = 125 small). After buying 2 large and 15 small, the money left buys at most 12 medium balloons.",
      "hints": ["Convert large and small balloons into the equivalent medium-balloon cost.", "Subtract from the total medium-balloon budget of 25."],
      "source": "Red Swastika 2025 P6 Prelim Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 1 (12)."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Find the value of 1944 ÷ 6 [?]",
      "answer0": "324",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 117,
      "difficulty_id": 1,
      "explanation": "1944 ÷ 6 = 324.",
      "hints": ["Use long division.", "6 x 300 = 1800; 144 ÷ 6 = 24."],
      "source": "Red Swastika 2025 P6 Prelim Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 324."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "How much water is in the container?<br>[?] ml",
      "answer0": "1600",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 191,
      "difficulty_id": 1,
      "explanation": "Reading the beaker's measuring scale, the water level is at 1600 ml.",
      "hints": ["Read the scale on the container.", "Note the unit (ml)."],
      "source": "Red Swastika 2025 P6 Prelim Q17",
      "image_needed": true,
      "image_page": 11,
      "image_bbox": [0.32, 0.10, 0.66, 0.40],
      "image_loc": "below the question — a measuring beaker with water",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 1600 ml."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "What is 8% of 400? [?]",
      "answer0": "32",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 174,
      "difficulty_id": 1,
      "explanation": "8% of 400 = \\(\\dfrac{8}{100} \\times 400\\) = 32.",
      "hints": ["1% of 400 is 4.", "Multiply by 8."],
      "source": "Red Swastika 2025 P6 Prelim Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 32."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "What is the volume of the cube?<br>[?] cm³",
      "answer0": "343",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 190,
      "difficulty_id": 1,
      "explanation": "Volume of a cube = side³ = 7 x 7 x 7 = 343 cm³.",
      "hints": ["Volume of a cube = side x side x side.", "The side is 7 cm."],
      "source": "Red Swastika 2025 P6 Prelim Q19",
      "image_needed": true,
      "image_page": 12,
      "image_bbox": [0.34, 0.10, 0.66, 0.28],
      "image_loc": "below the question — a cube with side 7 cm marked",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 343 cm³."
    },
    {
      "n": 20,
      "type_id": 0,
      "question": "Four letters are drawn on a square grid. Which letter(s) is/are symmetrical?",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 144,
      "difficulty_id": 2,
      "explanation": "Examining each letter for a line of symmetry, 3 of the four letters have a line of symmetry (per the answer key).",
      "hints": ["Check each letter for a mirror line.", "A symmetrical letter folds onto itself."],
      "source": "Red Swastika 2025 P6 Prelim Q20",
      "image_needed": true,
      "image_page": 12,
      "image_bbox": [0.18, 0.40, 0.82, 0.58],
      "image_loc": "below the question — four letters drawn on a square grid",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key prints '3'. The question asks 'which letter(s)' (a naming/identification task), so set type_id 0 (SKIPPED on insert). Ambiguity: key may mean a count of 3 symmetrical letters, or the specific letters. Answer recorded as: 3 of the letters are symmetrical."
    },
    {
      "n": 21,
      "type_id": 1,
      "question": "Find the value of \\(\\dfrac{3}{4} + \\dfrac{1}{6}\\)",
      "answer0": "\\(\\dfrac{11}{12}\\)",
      "answer1": "\\(\\dfrac{4}{10}\\)",
      "answer2": "\\(\\dfrac{9}{12}\\)",
      "answer3": "\\(\\dfrac{5}{6}\\)",
      "correct_answer": 0,
      "skill_id": 159,
      "difficulty_id": 2,
      "explanation": "Common denominator 12: \\(\\dfrac{3}{4} = \\dfrac{9}{12}\\), \\(\\dfrac{1}{6} = \\dfrac{2}{12}\\). Sum = \\(\\dfrac{11}{12}\\).",
      "hints": ["Find a common denominator.", "Add the numerators."],
      "source": "Red Swastika 2025 P6 Prelim Q21a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Q21(a). Answer key: 11/12. Fraction answer -> MCQ."
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "Find the value of \\(12 \\div \\dfrac{2}{5}\\) [?]",
      "answer0": "30",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 206,
      "difficulty_id": 2,
      "explanation": "\\(12 \\div \\dfrac{2}{5} = 12 \\times \\dfrac{5}{2} = \\dfrac{60}{2} = 30\\).",
      "hints": ["Dividing by a fraction = multiplying by its reciprocal.", "12 x 5/2 = 30."],
      "source": "Red Swastika 2025 P6 Prelim Q21b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Q21(b). Answer key: 30. Whole-number answer -> FIB."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "Find the value of 12.3 − 7.72 [?]",
      "answer0": "4.58",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 129,
      "difficulty_id": 1,
      "explanation": "12.30 − 7.72 = 4.58.",
      "hints": ["Line up the decimal points.", "Borrow where needed."],
      "source": "Red Swastika 2025 P6 Prelim Q22a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Q22(a). Answer key: 4.58. Decimal answer -> FIB."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "Find the value of 5 ÷ 8. Express your answer in decimal. [?]",
      "answer0": "0.625",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 125,
      "difficulty_id": 1,
      "explanation": "5 ÷ 8 = 0.625.",
      "hints": ["Add a decimal point and zeros to 5.", "Divide step by step."],
      "source": "Red Swastika 2025 P6 Prelim Q22b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Q22(b). Answer key: 0.625. Decimal answer -> FIB."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "Write down all the common factors of 24 and 64.<br>[?] , [?] , [?] , [?]",
      "answer0": "1",
      "answer1": "2",
      "answer2": "4",
      "answer3": "8",
      "correct_answer": null,
      "skill_id": 113,
      "difficulty_id": 2,
      "explanation": "Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Factors of 64: 1, 2, 4, 8, 16, 32, 64. Common factors: 1, 2, 4, 8.",
      "hints": ["List the factors of each number.", "Pick the factors that appear in both lists."],
      "source": "Red Swastika 2025 P6 Prelim Q23a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Q23(a). Answer key: 1, 2, 4, 8. Sequence of values -> FIB with four blanks."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "Write down all the common multiples of 6 and 8 smaller than 50.<br>[?] , [?]",
      "answer0": "24",
      "answer1": "48",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 115,
      "difficulty_id": 2,
      "explanation": "The LCM of 6 and 8 is 24. Common multiples smaller than 50: 24 and 48.",
      "hints": ["Find the lowest common multiple of 6 and 8.", "List its multiples below 50."],
      "source": "Red Swastika 2025 P6 Prelim Q23b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Q23(b). Answer key: 24, 48. Sequence of values -> FIB with two blanks."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "Cindy had 2.04 kg of sugar. She used 150 g of it. How many kilograms of sugar did she have left?<br>[?] kg",
      "answer0": "1.89",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 184,
      "difficulty_id": 2,
      "explanation": "150 g = 0.15 kg. 2.04 − 0.15 = 1.89 kg.",
      "hints": ["Convert 150 g to kilograms.", "Subtract from 2.04 kg."],
      "source": "Red Swastika 2025 P6 Prelim Q24",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 1.89 kg. Decimal answer -> FIB."
    },
    {
      "n": 28,
      "type_id": 1,
      "question": "Susan has 8p stickers. John has half as many stickers as Susan. John has 5 more stickers than Ahmad. How many stickers does Ahmad have, in terms of p?",
      "answer0": "4p − 5",
      "answer1": "4p + 5",
      "answer2": "8p − 5",
      "answer3": "16p − 5",
      "correct_answer": 0,
      "skill_id": 238,
      "difficulty_id": 2,
      "explanation": "John = half of 8p = 4p. Ahmad = John − 5 = 4p − 5.",
      "hints": ["John has half of Susan's 8p.", "Ahmad has 5 fewer than John."],
      "source": "Red Swastika 2025 P6 Prelim Q25a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Q25(a). Answer key: 4p − 5. Algebraic expression answer -> MCQ."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "Susan has 8p stickers. John has half as many stickers as Susan. John has 5 more stickers than Ahmad. How many stickers do they have altogether when p = 4? [?]",
      "answer0": "59",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 240,
      "difficulty_id": 2,
      "explanation": "Susan = 8p = 32, John = 4p = 16, Ahmad = 4p − 5 = 11. Total = 32 + 16 + 11 = 59.",
      "hints": ["Substitute p = 4 into each expression.", "Add the three amounts."],
      "source": "Red Swastika 2025 P6 Prelim Q25b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Q25(b). Answer key: 59. Whole-number answer -> FIB."
    },
    {
      "n": 30,
      "type_id": 2,
      "question": "20 students each borrow 2 or 3 books. The table shows the number of each type of book borrowed: Horror 12, Science 8, Adventure 20, Mystery 15. How many students borrowed only 2 books? [?]",
      "answer0": "5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 148,
      "difficulty_id": 3,
      "explanation": "Total books borrowed = 12 + 8 + 20 + 15 = 55. If all 20 students borrowed 2 books that would be 40; the extra 15 books means 15 students borrowed 3 books, so 20 − 15 = 5 students borrowed only 2 books.",
      "hints": ["Add the total number of books borrowed.", "Compare with 20 students x 2 books."],
      "source": "Red Swastika 2025 P6 Prelim Q26",
      "image_needed": true,
      "image_page": 15,
      "image_bbox": [0.30, 0.10, 0.70, 0.28],
      "image_loc": "below the question — a table of book types and counts",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 5."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "ABC is a right-angled triangle and BDEF is a trapezium. Find ∠BFE.<br>[?]°",
      "answer0": "110",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "Using the given angles 38°, 135° and 103° together with the right angle and the trapezium's angle properties, ∠BFE = 110°.",
      "hints": ["Use the right angle in triangle ABC.", "Use the angle properties of the trapezium BDEF."],
      "source": "Red Swastika 2025 P6 Prelim Q27",
      "image_needed": true,
      "image_page": 16,
      "image_bbox": [0.30, 0.08, 0.70, 0.30],
      "image_loc": "below the question — right-angled triangle ABC with trapezium BDEF, angles 38°, 135°, 103° marked",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: ∠BFE = 110°."
    },
    {
      "n": 32,
      "type_id": 2,
      "question": "Mr Tan stacked 7 cubes and painted the whole solid, including its base. How many cubes had exactly four faces painted? [?]",
      "answer0": "3",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 231,
      "difficulty_id": 3,
      "explanation": "Examining the stacked solid, 3 of the cubes have exactly four of their faces exposed and painted.",
      "hints": ["Count exposed faces of each cube.", "Look for cubes with exactly 4 sides showing."],
      "source": "Red Swastika 2025 P6 Prelim Q28a",
      "image_needed": true,
      "image_page": 16,
      "image_bbox": [0.30, 0.40, 0.70, 0.60],
      "image_loc": "below the question — a solid of 7 stacked cubes",
      "image_options": false,
      "image_file": null,
      "notes": "Q28(a). Answer key: 3."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "What is the greatest number of cubes Mr Tan could add so that the front view is the same as the side view? [?]",
      "answer0": "6",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 231,
      "difficulty_id": 3,
      "explanation": "Adding cubes to make the front and side views match, at most 6 cubes can be added (per the answer key).",
      "hints": ["The front and side views must end up identical.", "Add cubes only where both views allow."],
      "source": "Red Swastika 2025 P6 Prelim Q28b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Q28(b). Answer key: 6."
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "The average price of a set of books is $12. When one more book costing $42 is added, the average becomes $18. How many books were there at first? [?]",
      "answer0": "4",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 205,
      "difficulty_id": 3,
      "explanation": "Let there be n books at first. Total = 12n; after adding the $42 book: (12n + 42) ÷ (n + 1) = 18, so 12n + 42 = 18n + 18, 24 = 6n, n = 4.",
      "hints": ["Write the total before and after adding the book.", "Set the new average equal to 18 and solve."],
      "source": "Red Swastika 2025 P6 Prelim Q29",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 4."
    },
    {
      "n": 35,
      "type_id": 1,
      "question": "Miss Wong has red and blue stars. \\(\\dfrac{3}{4}\\) of the total stars are red. She used \\(\\dfrac{3}{5}\\) of the red stars and some blue stars, using \\(\\dfrac{1}{2}\\) of the total stars in all. What fraction of the blue stars did she use?",
      "answer0": "\\(\\dfrac{1}{5}\\)",
      "answer1": "\\(\\dfrac{2}{5}\\)",
      "answer2": "\\(\\dfrac{1}{4}\\)",
      "answer3": "\\(\\dfrac{3}{10}\\)",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Red = \\(\\dfrac{3}{4}\\), blue = \\(\\dfrac{1}{4}\\) of total. Red used = \\(\\dfrac{3}{5} \\times \\dfrac{3}{4} = \\dfrac{9}{20}\\). Total used = \\(\\dfrac{1}{2} = \\dfrac{10}{20}\\), so blue used = \\(\\dfrac{10}{20} - \\dfrac{9}{20} = \\dfrac{1}{20}\\) of total = \\(\\dfrac{1}{20} \\div \\dfrac{1}{4} = \\dfrac{1}{5}\\) of the blue stars.",
      "hints": ["Work in fractions of the total first.", "Divide the blue used by the total blue to get the fraction of blue."],
      "source": "Red Swastika 2025 P6 Prelim Q30",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 1/5. Fraction answer -> MCQ."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "Mrs Chia bought an iron and a kettle for $279.30. The kettle cost $39.70 less than the iron. How much did the iron cost?<br>$ [?]",
      "answer0": "159.50",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 2,
      "explanation": "Iron + kettle = 279.30 and iron − kettle = 39.70. Adding: 2 x iron = 319.00, so iron = $159.50.",
      "hints": ["Iron + kettle = total; iron − kettle = difference.", "Add the two equations to find twice the iron."],
      "source": "Red Swastika 2025 P6 Prelim P2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q1. Answer key: $159.50. Money/decimal answer -> FIB."
    },
    {
      "n": 37,
      "type_id": 1,
      "question": "A clock shows 13 20 but it is 15 minutes slow. What is the actual time?",
      "answer0": "13 35",
      "answer1": "13 05",
      "answer2": "13 15",
      "answer3": "13 45",
      "correct_answer": 0,
      "skill_id": 134,
      "difficulty_id": 1,
      "explanation": "The clock is slow by 15 min, so the actual time is 15 min ahead: 13 20 + 15 min = 13 35.",
      "hints": ["A slow clock shows an earlier time than actual.", "Add 15 minutes."],
      "source": "Red Swastika 2025 P6 Prelim P2 Q2a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q2(a). Answer key: 13 35. 24-hour time format answer -> MCQ."
    },
    {
      "n": 38,
      "type_id": 1,
      "question": "An activity lasted 2 h 45 min and finished at the actual time of 13 35. At what time did it start? Give your answer in 12-hour notation.",
      "answer0": "10.50 am",
      "answer1": "11.50 am",
      "answer2": "10.20 am",
      "answer3": "11.20 am",
      "correct_answer": 0,
      "skill_id": 135,
      "difficulty_id": 2,
      "explanation": "13 35 minus 2 h 45 min = 10 50, i.e. 10.50 am.",
      "hints": ["Subtract 2 h 45 min from 13 35.", "Convert to 12-hour notation."],
      "source": "Red Swastika 2025 P6 Prelim P2 Q2b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q2(b). Answer key: 10.50 am. 12-hour time format answer -> MCQ."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "Tanvi took 10 min to walk 450 m and then 10 min to walk 600 m. What was her average speed for the whole journey, in km/h?<br>[?] km/h",
      "answer0": "3.15",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 219,
      "difficulty_id": 3,
      "explanation": "Total distance = 450 + 600 = 1050 m = 1.05 km. Total time = 20 min = \\(\\dfrac{1}{3}\\) h. Average speed = 1.05 ÷ \\(\\dfrac{1}{3}\\) = 3.15 km/h.",
      "hints": ["Add the distances and convert to km.", "Add the times and convert to hours, then divide."],
      "source": "Red Swastika 2025 P6 Prelim P2 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q3. Answer key: 3.15 km/h. Decimal answer -> FIB."
    },
    {
      "n": 40,
      "type_id": 0,
      "question": "A triangle has sides 3x, 5x − 2 and 4x + 2. For each statement, decide whether it is True, False or Not possible to tell.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 240,
      "difficulty_id": 3,
      "explanation": "Per the answer key: (a) Not possible to tell, (b) False, (c) False.",
      "hints": ["Compare the side expressions algebraically.", "Consider the triangle's side relationships."],
      "source": "Red Swastika 2025 P6 Prelim P2 Q4",
      "image_needed": true,
      "image_page": 22,
      "image_bbox": [0.18, 0.10, 0.82, 0.40],
      "image_loc": "below the question — a triangle with sides 3x, 5x − 2, 4x + 2 and a True/False/Not-possible tick table",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q4. Tick-table (True/False/Not possible) interactive task -> type_id 0 (SKIPPED on insert). Answer key: (a) Not possible to tell, (b) False, (c) False."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "24 lamps are placed at equal distances along the sides AB, BC and CD of a rectangle. The length AB is 195 m. Find the breadth.<br>[?] m",
      "answer0": "75",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 137,
      "difficulty_id": 3,
      "explanation": "The equal spacing along the sides gives the distance between lamps; using the 195 m length and the lamp count, the breadth works out to 75 m (per the answer key).",
      "hints": ["Find the gap between consecutive lamps from AB.", "Use that gap along the breadth."],
      "source": "Red Swastika 2025 P6 Prelim P2 Q5",
      "image_needed": true,
      "image_page": 23,
      "image_bbox": [0.28, 0.10, 0.74, 0.30],
      "image_loc": "below the question — a rectangle with lamps along sides AB, BC, CD",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q5. Answer key: 75 m."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "John folded a shape along AB and AC, with DB = DA.<br>(a) Find ∠x. [?]°<br>(b) Find ∠y. [?]°",
      "answer0": "109",
      "answer1": "63",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "Using the folds along AB and AC, the equal sides DB = DA, and the given angles 45°, 54° and 26°, the angles work out to ∠x = 109° and ∠y = 63°.",
      "hints": ["Folding creates equal mirror angles.", "Use the isosceles property DB = DA and angle sums."],
      "source": "Red Swastika 2025 P6 Prelim P2 Q6",
      "image_needed": true,
      "image_page": 24,
      "image_bbox": [0.28, 0.08, 0.74, 0.36],
      "image_loc": "below the question — a folded figure with angles 45°, 54°, 26° and x, y marked",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q6. Answer key: (a) 109°, (b) 63°. Two angle answers -> FIB with two blanks."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "A pattern is made with black and white squares. The table shows the numbers for each figure.<br>(a) What is the difference between the number of black and white squares in Figure 4? [?]<br>(b) In a figure with 20 more black squares than white squares, what is the total number of squares? [?]",
      "answer0": "4",
      "answer1": "104",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 108,
      "difficulty_id": 3,
      "explanation": "(a) Following the pattern of the table, the difference at Figure 4 is 4. (b) When black exceeds white by 20, the total number of squares is 104.",
      "hints": ["Extend the table's pattern to Figure 4 for (a).", "Use the rule relating black, white and figure number for (b)."],
      "source": "Red Swastika 2025 P6 Prelim P2 Q7",
      "image_needed": true,
      "image_page": 25,
      "image_bbox": [0.28, 0.10, 0.74, 0.30],
      "image_loc": "below the question — a black/white squares pattern with a table",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q7. Answer key: (a) 4, (b) 104. Two integer answers -> FIB with two blanks."
    },
    {
      "n": 44,
      "type_id": 1,
      "question": "Tap A takes 50 min and Tap B takes 80 min to fill a tank. The faster tap fills 30 ml more per minute than the slower tap. Which tap is faster?",
      "answer0": "Tap A",
      "answer1": "Tap B",
      "answer2": "Both equal",
      "answer3": "Cannot be determined",
      "correct_answer": 0,
      "skill_id": 167,
      "difficulty_id": 2,
      "explanation": "Tap A fills the tank in less time (50 min vs 80 min), so it flows faster. Tap A is the faster tap.",
      "hints": ["The tap that fills in less time is faster.", "Compare 50 min and 80 min."],
      "source": "Red Swastika 2025 P6 Prelim P2 Q8a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q8(a). Answer key: A. Letter/choice answer -> MCQ."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "What is the capacity of each bucket, in litres?<br>[?] ℓ",
      "answer0": "4",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 192,
      "difficulty_id": 3,
      "explanation": "Using the difference of 30 ml/min between the two taps and the fill times of 50 min and 80 min, the bucket capacity works out to 4 litres.",
      "hints": ["Let the slower rate be r ml/min; the faster is r + 30.", "Both fill the same volume in their respective times."],
      "source": "Red Swastika 2025 P6 Prelim P2 Q8b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q8(b). Answer key: 4 litres. Whole-number answer -> FIB."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "In January, Jeremy spent $30. In February he spent 30% less and saved $27.<br>(a) How much did Jeremy spend in February? $ [?]<br>(b) What was the percentage increase in the amount he saved in February? [?]%",
      "answer0": "21",
      "answer1": "50",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 208,
      "difficulty_id": 3,
      "explanation": "(a) February spending = 30 − 30% of 30 = 30 − 9 = $21. (b) Using the savings figures, the percentage increase in the amount saved in February is 50%.",
      "hints": ["Reduce $30 by 30% for (a).", "Compare February savings with the previous month for (b)."],
      "source": "Red Swastika 2025 P6 Prelim P2 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q9. Answer key: (a) $21, (b) 50%. Two money/integer answers -> FIB with two blanks."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "A bar graph shows the number of TV sets owned by families, but the bar for 2 TV sets is missing. \\(\\dfrac{1}{3}\\) of the families have 2 TV sets.<br>(a) How many families have only 2 TV sets? [?]<br>(b) What is the average number of TV sets per family? [?]",
      "answer0": "40",
      "answer1": "1.7",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 205,
      "difficulty_id": 3,
      "explanation": "(a) Since families with 2 TVs are \\(\\dfrac{1}{3}\\) of the total, working from the bar graph gives 40 families with only 2 TVs. (b) The average number of TV sets per family is 1.7.",
      "hints": ["Use the 1/3 fraction with the known bars to find the total.", "Average = total TV sets ÷ total families."],
      "source": "Red Swastika 2025 P6 Prelim P2 Q10",
      "image_needed": true,
      "image_page": 28,
      "image_bbox": [0.20, 0.10, 0.82, 0.36],
      "image_loc": "below the question — a bar graph of number of TV sets per family with the 2-TV bar missing",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q10. Answer key: (a) 40, (b) 1.7. Two answers (integer, decimal) -> FIB with two blanks."
    },
    {
      "n": 48,
      "type_id": 2,
      "question": "The figure is made up of two quarter circles and a rectangle of length 14 cm. (Take \\(\\pi = 3.14\\))<br>(a) Find the value of k. [?] cm<br>(b) Find the area of the shaded figure. [?] cm²",
      "answer0": "10",
      "answer1": "92.36",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 222,
      "difficulty_id": 3,
      "explanation": "(a) From the rectangle length of 14 cm and the quarter-circle radii, k = 10 cm. (b) Combining the rectangle area with the quarter-circle areas (π = 3.14) gives a shaded area of 92.36 cm².",
      "hints": ["Use the 14 cm length to find k.", "Add or subtract the quarter-circle areas from the rectangle for (b)."],
      "source": "Red Swastika 2025 P6 Prelim P2 Q11",
      "image_needed": true,
      "image_page": 29,
      "image_bbox": [0.28, 0.08, 0.74, 0.34],
      "image_loc": "below the question — two quarter circles and a rectangle, length 14 cm marked",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q11. Answer key: (a) k = 10 cm, (b) 92.36 cm². Two answers (integer, decimal) -> FIB with two blanks."
    },
    {
      "n": 49,
      "type_id": 2,
      "question": "Joanna placed 4 large cubes and some small cubes in a container. The first layer is shown.<br>(a) How many small cubes are there? [?]<br>(b) Each small cube has a length of 4 cm. Find the volume of the rectangular container. [?] cm³",
      "answer0": "27",
      "answer1": "2592",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 229,
      "difficulty_id": 3,
      "explanation": "(a) From the first-layer arrangement, the number of small cubes is 27. (b) Using a small-cube edge of 4 cm and the cube counts, the container volume is 2592 cm³.",
      "hints": ["Use the shown first layer to deduce the small-cube count.", "Find the container's dimensions in cm, then multiply."],
      "source": "Red Swastika 2025 P6 Prelim P2 Q12",
      "image_needed": true,
      "image_page": 30,
      "image_bbox": [0.28, 0.08, 0.74, 0.34],
      "image_loc": "below the question — a container with 4 large cubes and a first layer of small cubes",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q12. Answer key: (a) 27, (b) 2592 cm³. Two integer answers -> FIB with two blanks."
    },
    {
      "n": 50,
      "type_id": 2,
      "question": "A right-angled triangle ABC is drawn on a grid.<br>Measure ∠ACB. [?]°",
      "answer0": "34",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 140,
      "difficulty_id": 2,
      "explanation": "Using a protractor on the triangle, ∠ACB measures 34°.",
      "hints": ["Place the protractor at vertex C.", "Read the angle ACB."],
      "source": "Red Swastika 2025 P6 Prelim P2 Q13a",
      "image_needed": true,
      "image_page": 31,
      "image_bbox": [0.28, 0.10, 0.74, 0.34],
      "image_loc": "below the question — right-angled triangle ABC drawn on a grid",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q13(a). Answer key: 34°. (Part (b) is a drawing task; see n=51.)"
    },
    {
      "n": 51,
      "type_id": 0,
      "question": "Draw a parallelogram WXYZ that has the same perimeter as Triangle ABC.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 201,
      "difficulty_id": 3,
      "explanation": "A parallelogram WXYZ is drawn on the grid with a perimeter equal to that of triangle ABC (a construction task).",
      "hints": ["Find the perimeter of triangle ABC first.", "Choose parallelogram sides that add to the same perimeter."],
      "source": "Red Swastika 2025 P6 Prelim P2 Q13b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q13(b). Draw-on-grid construction task -> type_id 0 (SKIPPED on insert)."
    },
    {
      "n": 52,
      "type_id": 2,
      "question": "ABCD is a square, BCF is an equilateral triangle, ADEF is a trapezium and AGF is a straight line. ∠DEF = 102°.<br>(a) Find ∠AGC. [?]°<br>(b) Find ∠CFE. [?]°",
      "answer0": "105",
      "answer1": "33",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "Using the square ABCD, equilateral triangle BCF, trapezium ADEF, straight line AGF and ∠DEF = 102°, the angles work out to ∠AGC = 105° and ∠CFE = 33°.",
      "hints": ["Each angle of the square is 90° and of the equilateral triangle is 60°.", "Use the trapezium's parallel sides and the straight line AGF."],
      "source": "Red Swastika 2025 P6 Prelim P2 Q14",
      "image_needed": true,
      "image_page": 32,
      "image_bbox": [0.28, 0.08, 0.74, 0.36],
      "image_loc": "below the question — square ABCD, equilateral triangle BCF, trapezium ADEF with ∠DEF = 102° marked",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q14. Answer key: (a) 105°, (b) 33°. Two angle answers -> FIB with two blanks."
    },
    {
      "n": 53,
      "type_id": 2,
      "question": "There were 1425 apples and pears altogether. 40% of the apples and 225 pears were sold, leaving apples and pears in the ratio 3 : 1.<br>(a) How many pears were left? [?]<br>(b) In the afternoon more apples were sold so that the ratio of apples to pears left became 3 : 2. How many apples were sold in the afternoon? [?]",
      "answer0": "200",
      "answer1": "300",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "(a) After selling 40% of the apples and 225 pears, the leftover apples : pears = 3 : 1, giving 200 pears left. (b) Selling more apples so the ratio becomes 3 : 2 means 300 apples were sold in the afternoon.",
      "hints": ["Set up the totals and use the 3 : 1 ratio for (a).", "Apply the new 3 : 2 ratio to find the apples sold in (b)."],
      "source": "Red Swastika 2025 P6 Prelim P2 Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q15. Answer key: (a) 200, (b) 300. Two integer answers -> FIB with two blanks."
    },
    {
      "n": 54,
      "type_id": 2,
      "question": "Wei Li used \\(\\dfrac{1}{4}\\) of her pocket money to buy 3 pens and 7 erasers. Each pen costs 3 times as much as an eraser. She bought more erasers with \\(\\dfrac{5}{6}\\) of her remaining money, spending $36.10 more on erasers.<br>(a) How many erasers can be bought with the money for 3 pens? [?]<br>(b) What is the cost of one eraser? $ [?]",
      "answer0": "9",
      "answer1": "0.95",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "(a) Each pen = 3 erasers, so 3 pens cost the same as 9 erasers. (b) Working through the fractions of pocket money and the $36.10 difference, each eraser costs $0.95.",
      "hints": ["A pen costs 3 erasers, so 3 pens = 9 erasers in cost.", "Use the $36.10 difference to find the eraser price."],
      "source": "Red Swastika 2025 P6 Prelim P2 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q16. Answer key: (a) 9, (b) $0.95. Two answers (integer, money) -> FIB with two blanks."
    },
    {
      "n": 55,
      "type_id": 1,
      "question": "There were 100 handphones on sale at a 25% discount over 7 days. A line graph shows the daily sales. On which day were the most handphones sold?",
      "answer0": "Day 1",
      "answer1": "Day 2",
      "answer2": "Day 4",
      "answer3": "Day 7",
      "correct_answer": 0,
      "skill_id": 147,
      "difficulty_id": 2,
      "explanation": "The highest point on the line graph is on Day 1, so the most handphones were sold on Day 1.",
      "hints": ["Find the highest point on the line graph.", "Read off the day."],
      "source": "Red Swastika 2025 P6 Prelim P2 Q17a",
      "image_needed": true,
      "image_page": 35,
      "image_bbox": [0.20, 0.10, 0.82, 0.34],
      "image_loc": "below the question — a line graph of daily handphone sales over 7 days",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q17(a). Answer key: Day 1. Day-label answer -> MCQ."
    },
    {
      "n": 56,
      "type_id": 1,
      "question": "What fraction of the total handphones were sold in the first 4 days?",
      "answer0": "\\(\\dfrac{3}{4}\\)",
      "answer1": "\\(\\dfrac{2}{3}\\)",
      "answer2": "\\(\\dfrac{1}{2}\\)",
      "answer3": "\\(\\dfrac{4}{7}\\)",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "From the line graph, 75 of the 100 handphones were sold in the first 4 days, i.e. \\(\\dfrac{75}{100} = \\dfrac{3}{4}\\).",
      "hints": ["Add the sales for Days 1 to 4.", "Express as a fraction of 100 and simplify."],
      "source": "Red Swastika 2025 P6 Prelim P2 Q17b",
      "image_needed": true,
      "image_page": 35,
      "image_bbox": [0.20, 0.10, 0.82, 0.34],
      "image_loc": "below the question — same daily-sales line graph used in part (a)",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q17(b). Answer key: 75/100 = 3/4. Fraction answer -> MCQ."
    },
    {
      "n": 57,
      "type_id": 2,
      "question": "The remaining handphones were sold at no discount. Altogether $32 330 was collected for all 100 handphones. What was the price of one handphone before the discount?<br>$ [?]",
      "answer0": "424",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Let the pre-discount price be $p. Discounted price (25% off) = 0.75p. Using the split of discounted and full-price sales totalling $32 330 for 100 handphones, p = $424.",
      "hints": ["Discounted price is 75% of the original.", "Set up: (discounted units x 0.75p) + (full-price units x p) = 32 330."],
      "source": "Red Swastika 2025 P6 Prelim P2 Q17c",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q17(c). Answer key: $424. Money answer -> FIB."
    }
  ]
}