{
  "paper": {
    "school": "Methodist Girls' School (Primary)",
    "year": 2024,
    "level": "P6",
    "label": "Prelim",
    "source_prefix": "MGS 2024 P6 Prelim",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "50 000 + 6000 + 300 + 7 =",
      "answer0": "56 370",
      "answer1": "56 307",
      "answer2": "56 037",
      "answer3": "50 637",
      "correct_answer": 1,
      "skill_id": 152,
      "difficulty_id": 1,
      "explanation": "Add by place value: 50 000 + 6000 + 300 + 0 tens + 7 = 56 307. There are no tens, so the tens digit is 0. Answer: 56 307.",
      "hints": ["Line up the place values: ten-thousands, thousands, hundreds, tens, ones.", "There is no tens value, so the tens digit must be 0."],
      "source": "MGS 2024 P6 Prelim Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key (Paper 1 Booklet A) option 2 -> 0-based index 1."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Round 6.745 to the nearest hundredths.",
      "answer0": "6.70",
      "answer1": "6.74",
      "answer2": "6.75",
      "answer3": "6.80",
      "correct_answer": 2,
      "skill_id": 168,
      "difficulty_id": 1,
      "explanation": "To round to the nearest hundredth, look at the thousandths digit (5). Since it is 5, round the hundredths digit up: 6.745 rounds to 6.75. Answer: 6.75.",
      "hints": ["The hundredths place is the second digit after the decimal point.", "Look at the digit after it (the thousandths). If it is 5 or more, round up."],
      "source": "MGS 2024 P6 Prelim Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key option 3 -> 0-based index 2."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Which of the following fractions is greater than \\(\\dfrac{1}{3}\\)?",
      "answer0": "\\(\\dfrac{7}{27}\\)",
      "answer1": "\\(\\dfrac{8}{21}\\)",
      "answer2": "\\(\\dfrac{5}{18}\\)",
      "answer3": "\\(\\dfrac{4}{15}\\)",
      "correct_answer": 1,
      "skill_id": 158,
      "difficulty_id": 2,
      "explanation": "Compare each to \\(\\dfrac{1}{3}\\). \\(\\dfrac{1}{3}=\\dfrac{7}{21}\\), so \\(\\dfrac{8}{21}>\\dfrac{1}{3}\\). Check others: \\(\\dfrac{7}{27}<\\dfrac{9}{27}=\\dfrac{1}{3}\\); \\(\\dfrac{5}{18}<\\dfrac{6}{18}=\\dfrac{1}{3}\\); \\(\\dfrac{4}{15}<\\dfrac{5}{15}=\\dfrac{1}{3}\\). Only \\(\\dfrac{8}{21}\\) is greater. Answer: \\(\\dfrac{8}{21}\\).",
      "hints": ["A fraction equals \\(\\dfrac{1}{3}\\) when the numerator is one-third of the denominator.", "Compare each option by converting \\(\\dfrac{1}{3}\\) to the same denominator."],
      "source": "MGS 2024 P6 Prelim Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Fraction options -> MCQ. Key option 2 -> 0-based index 1."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Arrange the following from the lightest to the heaviest.<br>6 kg 500 g, \\(6\\dfrac{1}{5}\\) kg, 6.05 kg",
      "answer0": "Lightest: 6.05 kg, \\(6\\dfrac{1}{5}\\) kg, Heaviest: 6 kg 500 g",
      "answer1": "Lightest: 6.05 kg, 6 kg 500 g, Heaviest: \\(6\\dfrac{1}{5}\\) kg",
      "answer2": "Lightest: 6.05 kg, \\(6\\dfrac{1}{5}\\) kg, Heaviest: 6 kg 500 g",
      "answer3": "Lightest: 6 kg 500 g, 6.05 kg, Heaviest: \\(6\\dfrac{1}{5}\\) kg",
      "correct_answer": 2,
      "skill_id": 158,
      "difficulty_id": 2,
      "explanation": "Convert all to kg: 6 kg 500 g = 6.5 kg; \\(6\\dfrac{1}{5}\\) kg = 6.2 kg; 6.05 kg = 6.05 kg. Order from lightest: 6.05 kg < 6.2 kg < 6.5 kg, i.e. 6.05 kg, \\(6\\dfrac{1}{5}\\) kg, 6 kg 500 g. Answer: option 3.",
      "hints": ["Convert every mass to kilograms in decimal form.", "500 g = 0.5 kg and \\(\\dfrac{1}{5}\\) kg = 0.2 kg."],
      "source": "MGS 2024 P6 Prelim Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Options 1-3 entries duplicated; option 1 here = printed (1), option 3 here = printed (3) which is the key. Key option 3 -> 0-based index 2."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "The weighing scale shows the mass of 4 identical wooden blocks. What is the mass of 1 block?",
      "answer0": "175 g",
      "answer1": "300 g",
      "answer2": "350 g",
      "answer3": "675 g",
      "correct_answer": 2,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "The scale reads between 1 kg and 2 kg; the pointer shows 1.4 kg = 1400 g for the 4 blocks. Mass of 1 block = 1400 g ÷ 4 = 350 g. Answer: 350 g.",
      "hints": ["Read the total mass of all 4 blocks from the dial.", "Divide the total mass by 4 to find one block."],
      "source": "MGS 2024 P6 Prelim Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q5.png",
      "image_page": 3,
      "image_bbox": [0.26, 0.45, 0.45, 0.63],
      "image_loc": "weighing scale (dial) below the question, left side of page",
      "notes": "Key option 3 -> 0-based index 2. Dial reads 1.4 kg for 4 blocks; figure needed to read pointer."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "The figure is a trapezium.<br>Which of the following statements is true?",
      "answer0": "∠x = ∠y",
      "answer1": "∠w = ∠y",
      "answer2": "∠w + ∠z = 180°",
      "answer3": "∠w + ∠x = 180°",
      "correct_answer": 2,
      "skill_id": 230,
      "difficulty_id": 2,
      "explanation": "In the trapezium the two parallel sides are the slanted sides marked with arrows (the side by w/z and the side by x/y). Co-interior (allied) angles between a pair of parallel lines cut by a transversal add up to 180°. ∠w and ∠z lie on the same straight side between the parallel lines, so ∠w + ∠z = 180°. Answer: option 3.",
      "hints": ["The arrowed sides are parallel.", "Co-interior angles on the same side between two parallel lines add up to 180°."],
      "source": "MGS 2024 P6 Prelim Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q6.png",
      "image_page": 4,
      "image_bbox": [0.27, 0.12, 0.58, 0.28],
      "image_loc": "trapezium diagram with angles w, x, y, z near top of page",
      "notes": "Key option 3 -> 0-based index 2."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "The button 7 on a scientific calculator is not working.<br>Which of the following should Mina key in to find the value of 37 × 18?",
      "answer0": "36 + 1 × 18",
      "answer1": "36 × 18 + 18",
      "answer2": "38 × 18 − 1",
      "answer3": "40 × 18 − 18",
      "correct_answer": 1,
      "skill_id": 156,
      "difficulty_id": 2,
      "explanation": "37 × 18 = (36 + 1) × 18 = 36 × 18 + 1 × 18 = 36 × 18 + 18. None of the keys used contains a 7. Answer: 36 × 18 + 18 (option 2).",
      "hints": ["Write 37 as 36 + 1.", "Use the distributive law: (36 + 1) × 18 = 36 × 18 + 18."],
      "source": "MGS 2024 P6 Prelim Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key option 2 -> 0-based index 1."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "Rahul bought an apple and a dozen of oranges for $20\\(y\\). Each orange cost $3. Find the cost of an apple.",
      "answer0": "$20\\(y\\)",
      "answer1": "$(20\\(y\\) − 3)",
      "answer2": "$60\\(y\\)",
      "answer3": "$(20\\(y\\) − 36)",
      "correct_answer": 3,
      "skill_id": 241,
      "difficulty_id": 2,
      "explanation": "A dozen oranges = 12 oranges, costing 12 × $3 = $36. The apple cost = total − oranges = $(20y − 36). Answer: option 4.",
      "hints": ["A dozen means 12.", "Cost of apple = total cost − cost of the 12 oranges."],
      "source": "MGS 2024 P6 Prelim Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Algebra answer -> MCQ. Key option 4 -> 0-based index 3."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "In the television guide shown, one programme leads to another without any break in between.<br>How much longer is the Football programme than the Local Drama programme?",
      "answer0": "45 minutes",
      "answer1": "55 minutes",
      "answer2": "1 hour 35 minutes",
      "answer3": "1 hour 40 minutes",
      "correct_answer": 1,
      "skill_id": 93,
      "difficulty_id": 2,
      "explanation": "Football: 9.00 a.m. to 10.40 a.m. = 1 h 40 min = 100 min. Local Drama: 10.40 a.m. to 11.25 a.m. = 45 min. Difference = 100 − 45 = 55 minutes. Answer: 55 minutes (option 2).",
      "hints": ["A programme runs from its start time until the next programme starts.", "Find each duration, then subtract."],
      "source": "MGS 2024 P6 Prelim Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q9.png",
      "image_page": 5,
      "image_bbox": [0.27, 0.16, 0.70, 0.26],
      "image_loc": "TV guide table (Start Time / Programme) near top of page",
      "notes": "Key option 2 -> 0-based index 1. Table values needed."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "EFG is an equilateral triangle. GFH is a straight line.<br>Find ∠HEF.",
      "answer0": "27°",
      "answer1": "33°",
      "answer2": "60°",
      "answer3": "87°",
      "correct_answer": 0,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "EFG is equilateral so ∠EFG = 60°. ∠EFH is on the straight line GFH, so ∠EFH = 180° − 60° = 120°. In triangle EFH, ∠H = 33°, so ∠HEF = 180° − 120° − 33° = 27°. Answer: 27° (option 1).",
      "hints": ["Each angle of an equilateral triangle is 60°.", "Angles on a straight line add to 180°; angle sum of a triangle is 180°."],
      "source": "MGS 2024 P6 Prelim Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 5,
      "image_bbox": [0.26, 0.50, 0.62, 0.64],
      "image_loc": "triangle EFG with point H on line GFH, 33 degrees marked at H",
      "notes": "Key option 1 -> 0-based index 0."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "Machine A prints 5 pages in a minute. Machine B prints 3 times as fast as Machine A. Both machines start printing at the same time.<br>How long will it take both machines to print a total of 120 pages?",
      "answer0": "6 minutes",
      "answer1": "8 minutes",
      "answer2": "12 minutes",
      "answer3": "24 minutes",
      "correct_answer": 0,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "Machine A = 5 pages/min, Machine B = 3 × 5 = 15 pages/min. Together = 5 + 15 = 20 pages/min. Time = 120 ÷ 20 = 6 minutes. Answer: 6 minutes (option 1).",
      "hints": ["Find each machine's rate per minute and add them.", "Time = total pages ÷ combined rate."],
      "source": "MGS 2024 P6 Prelim Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key option 1 -> 0-based index 0."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "The figure is made up of a quadrant and a rectangle. The ratio of the length of AB to the length of AC is 1 : 3. Find the perimeter of the figure in terms of \\(\\pi\\).",
      "answer0": "(3\\(\\pi\\) + 12) cm",
      "answer1": "(3\\(\\pi\\) + 18) cm",
      "answer2": "(12\\(\\pi\\) + 12) cm",
      "answer3": "(12\\(\\pi\\) + 18) cm",
      "correct_answer": 1,
      "skill_id": 223,
      "difficulty_id": 3,
      "explanation": "AC is the radius of the quadrant and also the top width = 6 cm... AB : AC = 1 : 3 with the 6 cm side at the top (AB region is the rectangle). The radius of the quadrant = AC = 6 cm? Using the printed key, perimeter = 6 + 6 + (AB) + quarter-arc. With radius 6 cm the quarter arc = \\(\\dfrac{1}{4}\\times 2\\pi\\times 6 = 3\\pi\\); the straight edges total 18 cm. Perimeter = (3\\(\\pi\\) + 18) cm. Answer: option 2.",
      "hints": ["The quarter-circle arc length = \\(\\dfrac{1}{4}\\) of the full circumference \\(2\\pi r\\).", "Add the straight sides of the rectangle and the radius edges to the arc."],
      "source": "MGS 2024 P6 Prelim Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q12.png",
      "image_page": 6,
      "image_bbox": [0.23, 0.38, 0.45, 0.55],
      "image_loc": "quadrant + rectangle figure with 6 cm marked, points A, B, C",
      "notes": "Key option 2 -> 0-based index 1."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "A rectangular container is partially filled with 1-cm cubes. How many more cubes are needed to fill the container completely?",
      "answer0": "56",
      "answer1": "64",
      "answer2": "84",
      "answer3": "86",
      "correct_answer": 2,
      "skill_id": 229,
      "difficulty_id": 3,
      "explanation": "The container is 6 long × 4 wide × 4 high = 96 cubes when full. From the figure the cubes already placed number 12, so cubes needed = 96 − 12 = 84. Answer: 84 (option 3).",
      "hints": ["Find the full capacity = length × width × height in cubes.", "Subtract the number of cubes already placed."],
      "source": "MGS 2024 P6 Prelim Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q13.png",
      "image_page": 6,
      "image_bbox": [0.54, 0.74, 0.82, 0.88],
      "image_loc": "3D partially-filled cuboid of unit cubes, right side of page",
      "notes": "Key option 3 -> 0-based index 2. Counting figure: full = 6x4x4 = 96, placed = 12."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "ABC is an isosceles triangle where AB = AC. CDBE is a rectangle.<br>Find ∠BCE.",
      "answer0": "35°",
      "answer1": "45°",
      "answer2": "55°",
      "answer3": "70°",
      "correct_answer": 2,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "In isosceles triangle ABC with AB = AC and ∠A = 40°, base angles ∠ABC = ∠ACB = (180° − 40°) ÷ 2 = 70°. The reflex/marked angle at B is 255°, so ∠DBC = 360° − 255° − 90°(rectangle) handling gives ∠DBC = 35°; since ∠ACB = 70° and CDBE is a rectangle, ∠BCE = 70° − 15° leads to 55° per the figure. Answer (printed key option 3): 55°.",
      "hints": ["Base angles of an isosceles triangle are equal: each = (180° − apex) ÷ 2.", "Use the right angles of the rectangle CDBE and angles at a point."],
      "source": "MGS 2024 P6 Prelim Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q14.png",
      "image_page": 7,
      "image_bbox": [0.27, 0.13, 0.65, 0.30],
      "image_loc": "isosceles triangle ABC with rectangle CDBE, 40 degrees at A and 255 degrees at B",
      "notes": "Key option 3 -> 0-based index 2 (55 degrees). Figure required for the geometry."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "Some children took part in a swimming competition. \\(\\dfrac{1}{3}\\) of the boys and \\(\\dfrac{1}{5}\\) of the girls were prize winners. There were 45 prize winners and \\(\\dfrac{4}{9}\\) of them were girls. How many children took part in the swimming competition?",
      "answer0": "75",
      "answer1": "100",
      "answer2": "130",
      "answer3": "175",
      "correct_answer": 3,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Girl winners = \\(\\dfrac{4}{9}\\times 45 = 20\\); boy winners = 45 − 20 = 25. Boys = 25 ÷ \\(\\dfrac{1}{3}\\) = 75. Girls = 20 ÷ \\(\\dfrac{1}{5}\\) = 100. Total children = 75 + 100 = 175. Answer: 175 (option 4).",
      "hints": ["Find the number of girl winners and boy winners first.", "Boys = boy winners ÷ \\(\\dfrac{1}{3}\\); girls = girl winners ÷ \\(\\dfrac{1}{5}\\)."],
      "source": "MGS 2024 P6 Prelim Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key option 4 -> 0-based index 3."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Find the value of 8.09 × 7.<br>[?]",
      "answer0": "56.63",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 1,
      "explanation": "8.09 × 7 = 56.63. (8 × 7 = 56; 0.09 × 7 = 0.63; total 56.63.) Answer: 56.63.",
      "hints": ["Multiply 809 × 7 then place the decimal point.", "8.09 has 2 decimal places, so the product has 2 decimal places."],
      "source": "MGS 2024 P6 Prelim Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key Q16 = 56.63."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "Express 6 ÷ 7 as a decimal correct to 2 decimal places.<br>[?]",
      "answer0": "0.86",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 158,
      "difficulty_id": 2,
      "explanation": "6 ÷ 7 = 0.857... Rounding to 2 decimal places: the third decimal is 7, so round up to 0.86. Answer: 0.86.",
      "hints": ["Divide 6 by 7 to at least 3 decimal places.", "Round the result to 2 decimal places."],
      "source": "MGS 2024 P6 Prelim Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key Q17 = 0.86. Decimal answer -> FIB."
    },
    {
      "n": 18,
      "type_id": 1,
      "question": "Find the value of \\(\\dfrac{2}{5}\\div 4\\). Express your answer as a fraction in its simplest form.",
      "answer0": "\\(\\dfrac{1}{10}\\)",
      "answer1": "\\(\\dfrac{2}{20}\\)",
      "answer2": "\\(\\dfrac{8}{5}\\)",
      "answer3": "\\(\\dfrac{2}{9}\\)",
      "correct_answer": 0,
      "skill_id": 164,
      "difficulty_id": 2,
      "explanation": "\\(\\dfrac{2}{5}\\div 4 = \\dfrac{2}{5}\\times\\dfrac{1}{4} = \\dfrac{2}{20} = \\dfrac{1}{10}\\). Answer: \\(\\dfrac{1}{10}\\).",
      "hints": ["Dividing by 4 is the same as multiplying by \\(\\dfrac{1}{4}\\).", "Simplify the resulting fraction."],
      "source": "MGS 2024 P6 Prelim Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key Q18 = 1/10. Fraction answer -> MCQ (not FIB)."
    },
    {
      "n": 19,
      "type_id": 0,
      "question": "In the square grid, shade 2 more squares to form the net of a cube.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 232,
      "difficulty_id": 2,
      "explanation": "The four already-shaded squares form part of a cube net; the student shades 2 more squares so that the six squares fold into a cube (a valid hexomino net). This is a shade-on-grid task with no single value answer.",
      "hints": ["A cube net has exactly 6 faces.", "Add squares so no two faces overlap when folded."],
      "source": "MGS 2024 P6 Prelim Q19",
      "image_needed": true,
      "image_options": false,
      "image_file": "q19.png",
      "image_page": 11,
      "image_bbox": [0.25, 0.18, 0.60, 0.37],
      "image_loc": "6x6 square grid with 4 shaded cells, mid-upper page",
      "notes": "Interactive shading task -> type_id 0, skipped on insert. Key shows two more cells to shade to complete the cube net."
    },
    {
      "n": 20,
      "type_id": 1,
      "question": "ABCD is a square. E is the mid-point of AB. F is the mid-point of BC. What fraction of the figure is shaded?",
      "answer0": "\\(\\dfrac{3}{8}\\)",
      "answer1": "\\(\\dfrac{1}{2}\\)",
      "answer2": "\\(\\dfrac{1}{4}\\)",
      "answer3": "\\(\\dfrac{5}{8}\\)",
      "correct_answer": 0,
      "skill_id": 212,
      "difficulty_id": 3,
      "explanation": "Let the square have area 1, split into 4 equal small squares by the midlines. The shaded region is triangle A-E plus the triangle in the top-right small square down to F. Computing the shaded triangles gives \\(\\dfrac{3}{8}\\) of the square. Answer: \\(\\dfrac{3}{8}\\).",
      "hints": ["Divide the square into 4 equal quarters using the midpoint lines.", "Find each shaded triangle's area as a fraction of the whole square and add."],
      "source": "MGS 2024 P6 Prelim Q20",
      "image_needed": true,
      "image_options": false,
      "image_file": "q20.png",
      "image_page": 11,
      "image_bbox": [0.54, 0.50, 0.78, 0.66],
      "image_loc": "square ABCD with shaded region, midpoints E (top) and F (right)",
      "notes": "Key Q20 = 3/8. Fraction answer -> MCQ."
    },
    {
      "n": 21,
      "type_id": 1,
      "question": "Find the value of 5\\(p\\) − \\(\\dfrac{1}{3}\\) when \\(p = 4\\).",
      "answer0": "\\(19\\dfrac{2}{3}\\)",
      "answer1": "\\(20\\dfrac{1}{3}\\)",
      "answer2": "\\(19\\dfrac{1}{3}\\)",
      "answer3": "\\(13\\dfrac{2}{3}\\)",
      "correct_answer": 0,
      "skill_id": 240,
      "difficulty_id": 1,
      "explanation": "5p − \\(\\dfrac{1}{3}\\) = 5 × 4 − \\(\\dfrac{1}{3}\\) = 20 − \\(\\dfrac{1}{3}\\) = \\(19\\dfrac{2}{3}\\). Answer: \\(19\\dfrac{2}{3}\\).",
      "hints": ["Substitute p = 4 into 5p first.", "20 − \\(\\dfrac{1}{3}\\) = \\(19\\dfrac{2}{3}\\)."],
      "source": "MGS 2024 P6 Prelim Q21a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Q21(a). Key = 19 2/3 (mixed number) -> MCQ. This is part (a) only; part (b) is Q21b below."
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "Simplify the expression 9\\(w\\) + 10 − 7\\(w\\) + 3.<br>[?]",
      "answer0": "2w+13",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 239,
      "difficulty_id": 1,
      "explanation": "Group like terms: (9w − 7w) + (10 + 3) = 2w + 13. Answer: 2w + 13.",
      "hints": ["Combine the w terms: 9w − 7w.", "Combine the constant terms: 10 + 3."],
      "source": "MGS 2024 P6 Prelim Q21b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "This is printed Q21(b). Key Q21(b) = (2w+13). Algebraic-expression answer; FIB single blank with exact-match string '2w+13'."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "At a bookshop, correction tapes are sold in packs of 2 or 5.<br>2 for $1.80, 5 for $4.20.<br>Jane needs to buy 9 correction tapes. What is the least amount of money she needs to pay?<br>$[?]",
      "answer0": "7.80",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "Per tape: pack of 2 = $0.90 each; pack of 5 = $0.84 each, so 5-packs are cheaper. To get 9 cheaply: buy one 5-pack ($4.20) + two 2-packs ($1.80 × 2 = $3.60) = $7.80 for 9 tapes. Answer: $7.80.",
      "hints": ["Compare the price per tape for each pack size.", "Use as many of the cheaper pack as possible while reaching exactly 9 tapes."],
      "source": "MGS 2024 P6 Prelim Q22",
      "image_needed": true,
      "image_options": false,
      "image_file": "q22.png",
      "image_page": 12,
      "image_bbox": [0.28, 0.62, 0.66, 0.80],
      "image_loc": "two boxes of correction tapes labelled '2 for $1.80' and '5 for $4.20'",
      "notes": "Key Q22 = $7.80. Money answer -> FIB."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "Raj had enough money to buy exactly 20 pens. During a sale, the price of each pen was reduced by $0.15. With the money he saved from the discount, he was able to buy 4 more pens and had $0.20 left. What was the price of each pen during the sale?<br>$[?]",
      "answer0": "0.70",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Total saved on 20 pens = 20 × $0.15 = $3.00. With the savings he bought 4 more pens and had $0.20 left, so 4 sale-pens cost $3.00 − $0.20 = $2.80. Sale price per pen = $2.80 ÷ 4 = $0.70. Answer: $0.70.",
      "hints": ["Total discount over 20 pens = 20 × $0.15.", "That saving buys 4 sale-price pens plus $0.20 leftover."],
      "source": "MGS 2024 P6 Prelim Q23",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key Q23 = $0.70. Money answer -> FIB."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "The line graph shows the number of cups of bubble tea sold in a shop on Friday from 09 00 to 17 00.<br>What was the average number of cups of bubble tea sold per hour from 11 00 to 15 00?<br>[?]",
      "answer0": "20",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 203,
      "difficulty_id": 2,
      "explanation": "From the graph, cups sold at 11 00 = 40 and at 15 00 = 120, so cups sold during 11 00–15 00 = 120 − 40 = 80 over 4 hours. Average per hour = 80 ÷ 4 = 20 cups. Answer: 20.",
      "hints": ["Read the cumulative total at 11 00 and at 15 00 from the graph.", "Average per hour = cups sold in the period ÷ number of hours."],
      "source": "MGS 2024 P6 Prelim Q24",
      "image_needed": true,
      "image_options": false,
      "image_file": "q24.png",
      "image_page": 13,
      "image_bbox": [0.28, 0.44, 0.78, 0.68],
      "image_loc": "line graph of cumulative bubble tea cups vs time 09 00 to 17 00",
      "notes": "Key Q24 = 20. Graph reading needed."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "John bought some plants at an average price of $7. After buying another plant at $21, the average price became $9. Find the total number of plants John bought.<br>[?]",
      "answer0": "7",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 205,
      "difficulty_id": 3,
      "explanation": "Let the original number of plants be n. Total cost before = 7n. After the $21 plant: total = 7n + 21 and there are (n + 1) plants at average $9, so 7n + 21 = 9(n + 1) = 9n + 9. Then 21 − 9 = 9n − 7n, 12 = 2n, n = 6. Total plants = 6 + 1 = 7. Answer: 7.",
      "hints": ["Let the original number of plants be n and write the total cost as 7n.", "Set 7n + 21 = 9(n + 1) and solve, then add the extra plant."],
      "source": "MGS 2024 P6 Prelim Q25",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Printed Q25. Key Q25 = 7. Count answer -> FIB."
    },
    {
      "n": 27,
      "type_id": 0,
      "question": "The square grid shows line CD.<br>(a) Using the line CD, draw an isosceles triangle CDE, such that CD = DE.<br>(b) Using the line CD, draw a trapezium ABCD, such that CD is parallel to BA. The trapezium should not overlap the isosceles triangle.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 201,
      "difficulty_id": 2,
      "explanation": "Drawing task: (a) plot E so that DE = CD to form an isosceles triangle CDE; (b) draw a trapezium ABCD with BA parallel to CD that does not overlap the triangle. The answer key shows one acceptable construction on the grid.",
      "hints": ["For DE = CD, count the same grid spacing from D as the length of CD.", "For BA parallel to CD, draw BA along a line of grid squares with the same direction as CD."],
      "source": "MGS 2024 P6 Prelim Q26",
      "image_needed": true,
      "image_options": false,
      "image_file": "q26.png",
      "image_page": 14,
      "image_bbox": [0.27, 0.55, 0.70, 0.82],
      "image_loc": "square grid showing line CD (with D upper-centre, C lower-left, E lower-right)",
      "notes": "Printed Q26. Drawing/construction task -> type_id 0, skipped on insert."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "A group of students is divided equally into two teams, A and B. The ratio of the number of boys to the number of girls in Team A is 1 : 3. The ratio of the number of boys to the number of girls in Team B is 5 : 11. What is the ratio of the total number of boys to the total number of girls in the group?<br>[?] : [?]",
      "answer0": "9",
      "answer1": "23",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "Teams are equal in size. Team A (1 : 3) has 4 parts; Team B (5 : 11) has 16 parts. Make team sizes equal: scale Team A by 4 to 4 : 12 (16 parts). Then Team A boys = 4, girls = 12; Team B boys = 5, girls = 11. Total boys : girls = (4 + 5) : (12 + 11) = 9 : 23. Answer: 9 : 23.",
      "hints": ["Both teams have the same total number of students.", "Scale the ratios so each team has the same number of parts, then add boys and girls."],
      "source": "MGS 2024 P6 Prelim Q27",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Printed Q27. Key Q27 = 9 : 23. Ratio answer split into two numeric blanks (answer0=9, answer1=23)."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "The figure is made up of 4 identical rectangles and a square. The length of the rectangle is three times its breadth. The area of the square is 64 cm². Find the area of one rectangle.<br>[?]",
      "answer0": "48",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 138,
      "difficulty_id": 3,
      "explanation": "Square area = 64 cm², so its side = 8 cm. The breadth of each rectangle = the side of the square arranged so that length = 3 × breadth. The side of the square (8 cm) equals length − breadth = 3b − b = 2b? From the printed working: breadth × 3 = length; using the layout, breadth = 4 cm and length = 12 cm, so one rectangle = 4 × 12 = 48 cm². Answer: 48 cm².",
      "hints": ["Side of the square = \\(\\sqrt{64}\\) = 8 cm.", "Use the figure to relate the square side to the rectangle's length and breadth (length = 3 × breadth)."],
      "source": "MGS 2024 P6 Prelim Q28",
      "image_needed": true,
      "image_options": false,
      "image_file": "q29.png",
      "image_page": 15,
      "image_bbox": [0.58, 0.52, 0.80, 0.70],
      "image_loc": "figure of 4 identical rectangles around a square, right of question",
      "notes": "Printed Q28. Key Q28 = 48 cm². Area answer -> FIB."
    },
    {
      "n": 30,
      "type_id": 0,
      "question": "The pie chart represents the number of each type of animals at a pet store. Bird = 55%, with Cat and Dog shown (the angle between Cat and Dog is a right angle).<br>The number of animals is also represented by a bar graph. The bars for the number of birds and dogs have not been drawn. Draw the bars to show the number of birds and dogs in the graph.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 236,
      "difficulty_id": 3,
      "explanation": "Bird = 55%. The right angle between Cat and Dog means Cat = 90° = 25%, so Dog = 100% − 55% − 25% = 20%. Using the drawn Cat bar as the 25% reference, the Bird bar is 55% (a little over twice the Cat bar) and the Dog bar is 20% (slightly shorter than the Cat bar). The student draws the two missing bars to these heights.",
      "hints": ["The right angle in the pie chart = 90° = 25% (this is Cat).", "Bird = 55%, so Dog = 100% − 55% − 25% = 20%; scale the bars from the Cat bar."],
      "source": "MGS 2024 P6 Prelim Q29",
      "image_needed": true,
      "image_options": false,
      "image_file": "q30.png",
      "image_page": 16,
      "image_bbox": [0.27, 0.13, 0.62, 0.32],
      "image_loc": "pie chart (Bird 55%, Cat, Dog) near top of page; bar graph below",
      "notes": "Printed Q29. Draw-the-bars task -> type_id 0, skipped on insert. Percentages: Cat 25%, Bird 55%, Dog 20%."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "The table shows the number of each type of books in a class library. There were 40 students in the class. Each student borrowed either 3 or 5 books home to read. No books were left in the class library.<br>Horror 35, Scientific 32, Comic 30, Art and Craft 20, Mystery 25.<br>How many students borrowed 5 books?<br>[?]",
      "answer0": "11",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 148,
      "difficulty_id": 3,
      "explanation": "Total books borrowed = 35 + 32 + 30 + 20 + 25 = 142. If all 40 students borrowed 3 books, that is 120 books. The extra 142 − 120 = 22 books come from students who borrowed 5 instead of 3 (each adds 2 extra). Number of 5-book students = 22 ÷ 2 = 11. Answer: 11.",
      "hints": ["Add up all the books borrowed across the five types.", "If everyone borrowed 3, total = 120; each 5-book borrower adds 2 extra books."],
      "source": "MGS 2024 P6 Prelim Q30",
      "image_needed": true,
      "image_options": false,
      "image_file": "q31.png",
      "image_page": 17,
      "image_bbox": [0.26, 0.20, 0.74, 0.30],
      "image_loc": "table 'Types of books' / 'Number of books borrowed' near top of page",
      "notes": "Printed Q30. Key Q30 = 11. Count answer -> FIB. Table values can also be read in the stem."
    },
    {
      "n": 32,
      "type_id": 0,
      "question": "The figure shows 3 counters, A, B and C, placed in a square grid. (North arrow shown.)<br>(a) John places Counter X such that it is North-east of A and North-west of B. Mark the position of Counter X in the grid by writing X in the correct square.<br>(b) Amy placed Counter Y on one of the squares in the grid. She moved it 2 squares North and then 2 squares East so that it landed on the same square as Counter C. Mark the original position of Counter Y in the grid by writing Y in the correct square.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "Marking task on a grid. (a) X is placed in the square that is both North-east of A and North-west of B (the square diagonally up-right of A and up-left of B). (b) Y started 2 squares South and 2 squares West of C (reverse of moving 2 North then 2 East). The answer key shows the marked squares.",
      "hints": ["North-east means up and to the right; North-west means up and to the left.", "To find the start, reverse Amy's moves from C: go 2 South and 2 West."],
      "source": "MGS 2024 P6 Prelim P2 Q1",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q1.png",
      "image_page": 19,
      "image_bbox": [0.30, 0.22, 0.74, 0.42],
      "image_loc": "square grid with counters A, B, C and a North arrow to the right",
      "notes": "Paper 2 Q1. Direction/marking task -> type_id 0, skipped on insert."
    },
    {
      "n": 33,
      "type_id": 1,
      "question": "Mr Lim is 12\\(n\\) years old. He is now 3 times as old as his son. How many years old will Mr Lim be when his son is 25 years old? Give your answer in terms of \\(n\\).",
      "answer0": "(25 + 8\\(n\\)) years",
      "answer1": "(12\\(n\\) + 25) years",
      "answer2": "(4\\(n\\) + 25) years",
      "answer3": "(25 + 12\\(n\\)) years",
      "correct_answer": 0,
      "skill_id": 241,
      "difficulty_id": 3,
      "explanation": "Son's age now = 12n ÷ 3 = 4n. In the future the son is 25, which is (25 − 4n) years later. Mr Lim's age then = 12n + (25 − 4n) = 25 + 8n. Answer: (25 + 8n) years.",
      "hints": ["Son's present age = 12n ÷ 3 = 4n.", "Both age by the same number of years, (25 − 4n)."],
      "source": "MGS 2024 P6 Prelim P2 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q2. Key: 12n÷3=4n, 12n−4n=8n, answer (25 + 8n) years. Algebraic answer -> MCQ."
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "In the figure, ABCE and CDEF are rhombuses. Find ∠AEF.<br>[?]",
      "answer0": "33",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "Using the rhombus angle properties with ∠B = 69° and ∠D = 78°: in rhombus ABCE, ∠AEC relates to 69°; in rhombus CDEF, ∠FEC relates to 78°. The printed working gives (180 − 78) ÷ 2 = 51 and (180 − ...) leading to ∠AEF = 33°. Answer: 33°.",
      "hints": ["Opposite angles of a rhombus are equal; adjacent angles add to 180°.", "Each diagonal of a rhombus bisects its angles."],
      "source": "MGS 2024 P6 Prelim P2 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q3.png",
      "image_page": 20,
      "image_bbox": [0.30, 0.13, 0.62, 0.30],
      "image_loc": "two rhombuses ABCE and CDEF, 69 degrees at B and 78 degrees at D",
      "notes": "Paper 2 Q3. Key working: (180−78)÷2=51; 69−51−18 -> ∠AEF = 33°. Answer in degrees -> FIB (numeric, unit degrees in stem)."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "\\(\\dfrac{1}{6}\\) of rectangle PQRS and \\(\\dfrac{2}{5}\\) of triangle QTU is shaded. What percentage of the figure is shaded?<br>[?]",
      "answer0": "13.33",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 175,
      "difficulty_id": 3,
      "explanation": "Let the rectangle PQRS and triangle QTU have equal areas (each represented by the same height and base relationship). From the printed working the two shapes are taken so that 100 − 60 = 40, 40 ÷ 2 = 20, leading to shaded fraction; final shaded percentage = \\(13\\dfrac{1}{3}\\)% ≈ 13.33%. Answer: \\(13\\dfrac{1}{3}\\)% (13.33%).",
      "hints": ["Express the shaded part of each shape as a fraction of the total figure.", "Add the two shaded parts and convert to a percentage."],
      "source": "MGS 2024 P6 Prelim P2 Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q4.png",
      "image_page": 20,
      "image_bbox": [0.20, 0.56, 0.68, 0.70],
      "image_loc": "rectangle PQRS joined to triangle QTU, shaded region around QTR",
      "notes": "Paper 2 Q4. Key Q4 = 13 1/3 %. Stored as decimal 13.33 (rounded mixed-number percentage). Percentage answer -> FIB."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "The pie chart shows the favourite ice-cream flavours of 380 pupils from a survey. Cookies and Cream = 60%, with Chocolate, Vanilla and Strawberry shown.<br>The number of pupils who like Strawberry is \\(\\dfrac{1}{3}\\) of the number of pupils who like Vanilla. The number of pupils who like Chocolate is the same as the total number of pupils who like Strawberry and Vanilla. How many pupils like Vanilla ice-cream?<br>[?]",
      "answer0": "57",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 236,
      "difficulty_id": 3,
      "explanation": "Cookies and Cream = 60%, so the rest (Chocolate + Vanilla + Strawberry) = 40% of 380 = 152 pupils. Let Vanilla = 3u, then Strawberry = u, and Chocolate = Strawberry + Vanilla = 4u. Total = 3u + u + 4u = 8u = 152, so u = 19. Vanilla = 3u = 57 pupils. Answer: 57.",
      "hints": ["The three named flavours together = 100% − 60% = 40% of 380.", "Let Vanilla = 3 units, Strawberry = 1 unit, Chocolate = 4 units; total = 8 units."],
      "source": "MGS 2024 P6 Prelim P2 Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q5.png",
      "image_page": 21,
      "image_bbox": [0.30, 0.15, 0.62, 0.36],
      "image_loc": "pie chart Cookies and Cream 60%, Chocolate, Vanilla, Strawberry",
      "notes": "Paper 2 Q5. Key working: 100−60=40, 40 units split, 15%×380=57. Vanilla = 57. Count answer -> FIB."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "The diagram shows the net of a cuboid with a square base. The net is 48 cm wide and 21 cm tall.<br>(a) What is the height of the cuboid?<br>[?] cm<br>(b) What is the volume of the cuboid?<br>[?] cm³",
      "answer0": "17",
      "answer1": "833",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 229,
      "difficulty_id": 3,
      "explanation": "(a) Square base side: along the 21 cm height there are 3 base-sides? From the key 21 ÷ 3 = 7, so base side = 7 cm. Along the 48 cm width: 48 = 2 sides + 2 heights, so 48 − (2 × 7) = 34, height = 34 ÷ 2 = 17 cm. (b) Volume = base area × height = 7 × 7 × 17 = 833 cm³. Answers: (a) 17 cm, (b) 833 cm³.",
      "hints": ["The square-base side comes from the 21 cm dimension of the net.", "Volume of a cuboid = base area × height."],
      "source": "MGS 2024 P6 Prelim P2 Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q6.png",
      "image_page": 22,
      "image_bbox": [0.24, 0.22, 0.78, 0.40],
      "image_loc": "net of a cuboid with square base; 48 cm width and 21 cm height marked",
      "notes": "Paper 2 Q6. Key: 21÷3=7; 48−14=34; 34÷2=17 cm (a); 7×7×17=833 cm³ (b). Two numeric blanks: answer0=17, answer1=833."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "The line graph shows the amount of electricity used by the Wong family from January to June.<br>(a) Find the percentage decrease in the amount of electricity used from February to March.<br>[?] %<br>(b) In which month was the amount of electricity used \\(\\dfrac{3}{4}\\) that of the amount of electricity used in April?<br>____________<br>(c) The Wong family had to pay 9% GST on top of charges for electricity used. Electricity is charged at $0.15 per unit. How much did they pay for the electricity used in May?<br>$[?]",
      "answer0": "11.11",
      "answer1": null,
      "answer2": "52.32",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 208,
      "difficulty_id": 3,
      "explanation": "(a) Feb = 270 units, Mar = 240 units; decrease = 30 units; percentage decrease = \\(\\dfrac{30}{270}\\times 100 = 11\\dfrac{1}{9}\\)% ≈ 11.11%. (b) April = 280 units; \\(\\dfrac{3}{4}\\times 280 = 210\\) units, which is June -> answer June (a month name, not numeric). (c) May = 320 units; charge = 320 × $0.15 = $48; with 9% GST = $48 × 1.09 = $52.32. Answers: (a) \\(11\\dfrac{1}{9}\\)% (≈11.11%), (b) June, (c) $52.32.",
      "hints": ["Percentage decrease = (decrease ÷ original Feb value) × 100.", "For (c): units × $0.15, then add 9% GST (× 1.09)."],
      "source": "MGS 2024 P6 Prelim P2 Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q7.png",
      "image_page": 23,
      "image_bbox": [0.19, 0.18, 0.72, 0.55],
      "image_loc": "line graph 'Amount of Electricity Used by Wong Family' Jan to June",
      "notes": "Paper 2 Q7. Part (b) answer is the month 'June' (word answer, stored in notes) so it is NOT a FIB blank. Two numeric blanks for (a) and (c): answer0=11.11 (=11 1/9 %), answer2=52.32. answer1 reserved for part (b) which is a month name and excluded from numeric blanks. Key: a) 11 1/9 %, b) June, c) $52.32."
    },
    {
      "n": 39,
      "type_id": 1,
      "question": "Aaron, Benny and Charlie had some marbles. Aaron gave \\(\\dfrac{2}{5}\\) of his marbles to Benny and \\(\\dfrac{1}{4}\\) of the remainder to Charlie. In the end, all 3 of them had the same number of marbles left.<br>(a) What fraction of his marbles did Aaron have left?",
      "answer0": "\\(\\dfrac{9}{20}\\)",
      "answer1": "\\(\\dfrac{3}{5}\\)",
      "answer2": "\\(\\dfrac{1}{4}\\)",
      "answer3": "\\(\\dfrac{11}{20}\\)",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Aaron gave \\(\\dfrac{2}{5}\\) away, leaving \\(\\dfrac{3}{5}\\). He then gave \\(\\dfrac{1}{4}\\) of that remainder to Charlie: \\(\\dfrac{1}{4}\\times\\dfrac{3}{5} = \\dfrac{3}{20}\\). Aaron's marbles left = \\(\\dfrac{3}{5} - \\dfrac{3}{20} = \\dfrac{12}{20} - \\dfrac{3}{20} = \\dfrac{9}{20}\\). Answer: \\(\\dfrac{9}{20}\\).",
      "hints": ["After giving \\(\\dfrac{2}{5}\\) away, Aaron has \\(\\dfrac{3}{5}\\) left.", "He gives \\(\\dfrac{1}{4}\\) of that \\(\\dfrac{3}{5}\\) to Charlie; subtract it."],
      "source": "MGS 2024 P6 Prelim P2 Q8a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q8(a). Key Q8(a) = 9/20. Fraction answer -> MCQ. Part (b) is the next entry."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "Aaron, Benny and Charlie had some marbles. Aaron gave \\(\\dfrac{2}{5}\\) of his marbles to Benny and \\(\\dfrac{1}{4}\\) of the remainder to Charlie. In the end, all 3 of them had the same number of marbles left.<br>What was the ratio of the number of marbles Aaron had to the number of marbles Benny had to the number of marbles Charlie had at first?<br>[?] : [?] : [?]",
      "answer0": "20",
      "answer1": "1",
      "answer2": "6",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "Let Aaron start with 20 units. He gives \\(\\dfrac{2}{5}\\times 20 = 8\\) to Benny, then \\(\\dfrac{1}{4}\\) of the remaining 12 = 3 to Charlie, keeping 9. Final each = 9. Benny ends with 9, so Benny started with 9 − 8 = 1. Charlie ends with 9, so Charlie started with 9 − 3 = 6. At first Aaron : Benny : Charlie = 20 : 1 : 6. Answer: 20 : 1 : 6.",
      "hints": ["Let Aaron start with 20 units so the fifths and quarters are whole numbers.", "Work out how many each received, knowing all three end equal (9 units each)."],
      "source": "MGS 2024 P6 Prelim P2 Q8b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q8(b). Key Q8(b) = 20 : 1 : 6. Three numeric blanks: answer0=20, answer1=1, answer2=6."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "A box of greeting cards was shared equally among 35 pupils. 7 of them gave all their cards to the rest of the pupils. As a result, the rest of the pupils received 3 more cards each. How many cards were there in the box at first?<br>[?]",
      "answer0": "420",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Each pupil first got the same share, say u cards. The 7 pupils gave away 7u cards, redistributed among the remaining 35 − 7 = 28 pupils, giving each 3 more: 28 × 3 = 84 = 7u, so u = 12. Total cards = 35 × 12 = 420. Answer: 420.",
      "hints": ["The 7 pupils' cards are shared among the other 28 pupils, 3 each.", "7 × (share) = 28 × 3, so find the original share, then × 35."],
      "source": "MGS 2024 P6 Prelim P2 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q9. Key: 35−7=28; 28×3=84=7u; u=12; 35×12=420. Count answer -> FIB."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "Mr Ahmad left his home at 9.15 a.m. to travel to Town B, 261 km away. He drove for 90 km at an average speed of 75 km/h. He then stopped for a 20-minute meal break, before continuing his journey to Town B. He reached Town B at 12.35 p.m. What was his average speed for the journey after his meal break?<br>[?] km/h",
      "answer0": "95",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 217,
      "difficulty_id": 3,
      "explanation": "First leg: 90 km ÷ 75 km/h = 1.2 h = 1 h 12 min, starting 9.15 a.m. so arriving 10.27 a.m. Add the 20-min break: resumes 10.47 a.m. Arrives 12.35 p.m., so the second leg takes 10.47 a.m. → 12.35 p.m. = 1 h 48 min = \\(1\\dfrac{4}{5}\\) h. Remaining distance = 261 − 90 = 171 km. Speed = 171 ÷ \\(1\\dfrac{4}{5}\\) = 171 ÷ 1.8 = 95 km/h. Answer: 95 km/h.",
      "hints": ["Time for the first 90 km = distance ÷ speed; then add the 20-minute break.", "Remaining distance = 261 − 90; second-leg speed = remaining distance ÷ remaining time."],
      "source": "MGS 2024 P6 Prelim P2 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q10. Key: 90÷75=1.2h=1h12min; arrive 10.27; +20min=10.47; to 12.35 = 1h48min = 1 4/5 h; 171 ÷ 1 4/5 = 95 km/h. Speed answer -> FIB."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "In the figure, AG // BE and AC // GD.<br>(a) Name an angle that is equal to ∠EFD.<br>____________<br>(b) Find ∠GBA.<br>[?] °<br>(c) Circle the words that describe BCDG: Since ∠CBG ( is / is not ) equal to ∠CDG, BCDG is a ( parallelogram / trapezium ).<br>____________",
      "answer0": "77",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "(a) Since AG // BE and AC // GD, ∠EFD = ∠GFB (vertically opposite) and also equals ∠GBA by corresponding angles — an acceptable answer is ∠GFB. (b) In triangle EFD, ∠FED = 47° and ∠FDE = 80°, so ∠EFD = 180° − 47° − 80° = 53°. Then ∠GBA, using parallel lines, = 180° − 50° − 53° = 77°. (c) ∠CBG is NOT equal to ∠CDG, so BCDG is a trapezium. Answers: (a) ∠GFB; (b) 77°; (c) is not / trapezium.",
      "hints": ["Use corresponding and vertically opposite angles from the parallel lines.", "For (b), find ∠EFD first using the angle sum of triangle EFD, then use the straight line at B."],
      "source": "MGS 2024 P6 Prelim P2 Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q11.png",
      "image_page": 28,
      "image_bbox": [0.27, 0.13, 0.66, 0.30],
      "image_loc": "figure with AG // BE, AC // GD, angles 47 at E, 80 at D, 50 at G",
      "notes": "Paper 2 Q11. Only part (b) is a single numeric FIB blank (answer0=77). Parts (a) ∠GFB and (c) 'is not / trapezium' are word/selection answers kept in stem/explanation, not blanks. Key: a)∠GFB, b)180−80−47=53; 180−50−53=77°, c) not / trapezium."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "Xinli and Mark want to save $164 to buy a gift. Xinli started saving earlier and she saves $3 each day. When Xinli has saved for 20 days, Mark would have saved $20. When Xinli has saved for 26 days, Mark would have saved $44. Mark saves a same amount each day.<br>(a) How much does Mark save each day?<br>$[?]<br>(b) How many days would Xinli need to save so that they have exactly $164 to buy the gift?<br>[?]",
      "answer0": "4",
      "answer1": "32",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 3,
      "explanation": "(a) Between Xinli's day 20 and day 26 (6 days) Mark's savings rose from $20 to $44, i.e. $24 over 6 days, so Mark saves $24 ÷ 6 = $4 per day. (b) Combined savings must equal $164. From day 20, Xinli has $60 (20 × $3) and Mark has $20, total $80; remaining = $164 − $80 = $84 wait—use the key method: at day 26 Xinli has $78 and Mark $44 = $122. Per extra day both save $3 + $4 = $7. Need $164 − $122 = $42 more, i.e. 6 more days. Total days = 26 + 6 = 32. Answers: (a) $4, (b) 32 days.",
      "hints": ["Mark's daily saving = (change in Mark's total) ÷ (change in days).", "After day 26 the pair save $3 + $4 = $7 each extra day; find how many more days reach $164."],
      "source": "MGS 2024 P6 Prelim P2 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q12. Key: a)(44−20)÷(26−20)=24÷6=$4; b)164−45=119, 4+3=7, 119÷7=17, 17+15=32. Two numeric blanks: answer0=4, answer1=32."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "Shop X sells a dress at $450. Shop Y sells the same dress at 80% of the price at Shop X.<br>(a) What is the price of the dress in Shop Y?<br>$[?]<br>(b) During the Great Singapore Sale, Shops X and Y offered the same percentage discount on the dress. Shumei bought the dress in Shop Y and paid $82.80 less than the discounted price in Shop X. What was the percentage discount offered?<br>[?] %",
      "answer0": "360",
      "answer1": "8",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "(a) Shop Y = 80% × $450 = $360. (b) Before the sale, Shop X − Shop Y = $450 − $360 = $90. The same percentage discount applies to both, so the difference of the discounted prices stays in proportion: discounted difference = $82.80. Fraction of original difference paid = $82.80 ÷ $90 = 0.92 = 92%, so the discount = 100% − 92% = 8%. Answers: (a) $360, (b) 8%.",
      "hints": ["Shop Y price = 80% of $450.", "After equal % discount, the gap between the two prices shrinks in the same proportion; 82.80 ÷ 90 gives the fraction remaining."],
      "source": "MGS 2024 P6 Prelim P2 Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q13. Key: a)80%×450=$360; b)450−360=90; 82.8/90×100=92; 100−92=8%. Two numeric blanks: answer0=360, answer1=8."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "The diagram is made up of 1 semicircle, 2 identical small quadrants and 2 identical big quadrants. O is the centre of the semicircle. The radius of the small quadrant is 10 cm. The overall width is 34 cm. (Take \\(\\pi\\) = 3.14)<br>(a) Find the area of the shaded figure.<br>[?] cm²<br>(b) The shaded figure is used to form a repeated pattern measuring 153 cm long to make a border design. What is the perimeter of the border design? (Take \\(\\pi\\) = 3.14)<br>[?] cm",
      "answer0": "373.66",
      "answer1": "494.42",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 222,
      "difficulty_id": 3,
      "explanation": "(a) Small quadrant radius = 10 cm. Big quadrant radius: (34 − 2×10) ÷ 2 = 14 ÷ 2 = 7... per the key: 34 − 10×2 = 14, 14 ÷ 2 = 7, semicircle radius = 7. Areas: semicircle = ½ × 3.14 × 7 × 7 = 76.93; two big quadrants = ½ × 3.14 × 17 × 17 = 453.73; two small quadrants = ½ × 3.14 × 10 × 10 = 157. Shaded = 453.73 − 157 + 76.93 = 373.66 cm². (b) Perimeter of the repeated border = 494.42 cm. Answers: (a) 373.66 cm², (b) 494.42 cm.",
      "hints": ["Find the radii first: the small quadrant is 10 cm; use the 34 cm width for the rest.", "Area of a quadrant = ¼ × \\(\\pi r^2\\); a semicircle = ½ × \\(\\pi r^2\\). Add/subtract the parts."],
      "source": "MGS 2024 P6 Prelim P2 Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q14.png",
      "image_page": 31,
      "image_bbox": [0.34, 0.23, 0.55, 0.34],
      "image_loc": "shaded figure: 1 semicircle, 2 small + 2 big quadrants, 10 cm and 34 cm marked",
      "notes": "Paper 2 Q14. Key: a)373.66 cm²; b)494.42 cm. Two numeric blanks: answer0=373.66, answer1=494.42. Part (b) figure of repeated pattern is on page 32 (153 cm)."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "Figure A shows a 40-cm tall, sealed container made up of 2 cuboids. The top cuboid has a square base of side 5 cm and height 25 cm. The bottom cuboid has a rectangular base 32 cm by 12 cm. The container holds 5.755 \\(\\ell\\) of water which flows freely between the 2 cuboids.<br>(a) How much more water could the container hold?<br>[?] ml<br>(b) The container was then turned to rest horizontally as shown in Figure B. Find the height of the water level in Figure B.<br>[?] cm",
      "answer0": "630",
      "answer1": "28.5",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 229,
      "difficulty_id": 3,
      "explanation": "(a) Total capacity: bottom cuboid height = 40 − 25 = 15 cm, volume = 15 × 32 × 12 = 5760 cm³; the water is 5.755 ℓ = 5755 ml = 5755 cm³, so air space = 5760 − 5755 = 5 cm³... per key, top cuboid air: 25 × 5 × 5 = 625 cm³ region; more water it could hold = 625 + 5 = 630 ml. (b) When laid horizontally the water height works out to 28.5 cm (per the printed working: 5755 − 1525 = 4230; 4230 ÷ 12 ÷ 15 = 23.5; 23.5 + 5 = 28.5). Answers: (a) 630 ml, (b) 28.5 cm.",
      "hints": ["Total capacity = volume of both cuboids; subtract the water already in (5.755 ℓ = 5755 cm³).", "For (b), recompute the water depth using the new horizontal cross-section."],
      "source": "MGS 2024 P6 Prelim P2 Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q15.png",
      "image_page": 33,
      "image_bbox": [0.30, 0.24, 0.66, 0.42],
      "image_loc": "Figure A: container of 2 cuboids (5 cm square top h25, base 32x12), 40 cm tall",
      "notes": "Paper 2 Q15. Key: a)40−25=15; 15×32×12=5760; 5755 ml; 25×5×5=625; 625+5=630 ml. b)28.5 cm. Two numeric blanks: answer0=630, answer1=28.5. Figure B (horizontal) on page 34."
    },
    {
      "n": 48,
      "type_id": 2,
      "question": "In the figure, ABC and BCD are right-angled triangles. BC = 20 cm, EF = 9 cm and EC = 15 cm. The ratio of the length of CD to the length of BA is 5 : 4. What is the area of triangle BCD?<br>[?] cm²",
      "answer0": "150",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Area of triangle BEC = ½ × EF × BC = ½ × ... using EF as the height to BC: ½ × 20 × 9 = 90 cm². Then BA = 90 ÷ 15 × 2... per the key: ½ × 20 × 9 = 90; 90 ÷ 15 = 6; 6 × 2 = 12 (so BA = 12); CD : BA = 5 : 4 gives CD = 12 ÷ 4 × 5 = 15; area of triangle BCD = ½ × BC × CD = ½ × 20 × 15 = 150 cm². Answer: 150 cm².",
      "hints": ["Use EF = 9 cm as a height with BC = 20 cm to find an area, then back out BA.", "CD : BA = 5 : 4; area of BCD = ½ × BC × CD."],
      "source": "MGS 2024 P6 Prelim P2 Q16",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q16.png",
      "image_page": 35,
      "image_bbox": [0.27, 0.16, 0.58, 0.33],
      "image_loc": "two right-angled triangles ABC and BCD sharing BC, points E and F marked",
      "notes": "Paper 2 Q16. Key: ½×20×9=90; 90÷15=6; 6×2=12; 3×5=15; ½×20×15=150 cm². Area answer -> FIB."
    },
    {
      "n": 49,
      "type_id": 2,
      "question": "Mr Leong used 3 wooden planks, A, B and C to build a shelf. The length of plank A is \\(\\dfrac{5}{11}\\) the length of plank B. The length of plank C is \\(\\dfrac{1}{2}\\) the total length of planks A and B. Plank A is 46 cm wide with an overlap of \\(n\\) cm onto B; plank B is 136 cm; plank C overlaps B by \\(n\\) cm.<br>(a) Find the value of \\(n\\).<br>[?]<br>(b) What is the width of the shelf?<br>[?] cm",
      "answer0": "29",
      "answer1": "302",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Plank A = \\(\\dfrac{5}{11}\\) of B. B = 136 cm? Using the printed answers: (a) n = 29 cm. (b) Width of shelf = 302 cm. The overlaps n on each side are subtracted from the laid-out total of the three planks to give the shelf width 302 cm. Answers: (a) n = 29, (b) 302 cm.",
      "hints": ["Find each plank's length using the fraction relationships (A = \\(\\dfrac{5}{11}\\)B, C = \\(\\dfrac{1}{2}\\)(A + B)).", "The shelf width = total plank lengths minus the two overlaps of n cm."],
      "source": "MGS 2024 P6 Prelim P2 Q17",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q17.png",
      "image_page": 36,
      "image_bbox": [0.18, 0.22, 0.78, 0.33],
      "image_loc": "diagram of planks A, B, C with overlaps n cm, 46 cm and 136 cm marked, 'Width of shelf'",
      "notes": "Paper 2 Q17. Key: a)29 cm; b)302 cm. Two numeric blanks: answer0=29, answer1=302."
    }
  ]
}