{
  "paper": {
    "school": "Paya Lebar Methodist Girls' School (Primary)",
    "year": 2025,
    "level": "P6",
    "label": "Prelim",
    "source_prefix": "PLMGS 2025 P6 Prelim",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "3 710 562 = 3 000 000 + 700 000 + ____________ + 500 + 60 + 2",
      "answer0": "100",
      "answer1": "1000",
      "answer2": "10 000",
      "answer3": "100 000",
      "correct_answer": 2,
      "skill_id": 1,
      "difficulty_id": 1,
      "explanation": "The missing place value is the ten-thousands. 3 710 562 has 1 ten-thousand, so the term is 10 000.",
      "hints": ["Compare the expanded form to the number digit by digit.", "The gap sits in the ten-thousands place."],
      "source": "PLMGS 2025 P6 Prelim Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: option 3 (10 000)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Which of the following is the same as 40 km 70 m?",
      "answer0": "40 700 m",
      "answer1": "40 070 m",
      "answer2": "4700 m",
      "answer3": "4070 m",
      "correct_answer": 1,
      "skill_id": 67,
      "difficulty_id": 1,
      "explanation": "40 km = 40 000 m. 40 km 70 m = 40 000 + 70 = 40 070 m.",
      "hints": ["1 km = 1000 m.", "Add the metres to 40 000."],
      "source": "PLMGS 2025 P6 Prelim Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: option 2 (40 070 m)."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "The total mass of 3 students is 162 kg. Another student, Megan, joins the group. She has a mass of 42 kg. What is the average mass of the 4 students?",
      "answer0": "55 kg",
      "answer1": "51 kg",
      "answer2": "32 kg",
      "answer3": "24 kg",
      "correct_answer": 1,
      "skill_id": 79,
      "difficulty_id": 1,
      "explanation": "New total mass = 162 + 42 = 204 kg. Average of 4 students = 204 ÷ 4 = 51 kg.",
      "hints": ["Add Megan's mass to the total first.", "Average = total ÷ number of students."],
      "source": "PLMGS 2025 P6 Prelim Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: option 2 (51 kg)."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "The figure is a parallelogram with angles a, b, c, d.<br>Which of the following is true?",
      "answer0": "∠a + ∠c = 180°",
      "answer1": "∠b + ∠d = 180°",
      "answer2": "∠a = ∠c",
      "answer3": "∠b = ∠c",
      "correct_answer": 2,
      "skill_id": 70,
      "difficulty_id": 2,
      "explanation": "In a parallelogram, opposite angles are equal. ∠a and ∠c are opposite angles, so ∠a = ∠c.",
      "hints": ["Recall the angle properties of a parallelogram.", "Opposite angles are equal; co-interior angles sum to 180°."],
      "source": "PLMGS 2025 P6 Prelim Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 3,
      "image_bbox": [0.38, 0.12, 0.70, 0.24],
      "image_loc": "parallelogram with angles labelled a (top-left), b (top-right), c (bottom-right), d (bottom-left)",
      "notes": "Key: option 3 (∠a = ∠c)."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "Simplify 8b + 15 − 3b − 9.",
      "answer0": "5b + 6",
      "answer1": "5b + 24",
      "answer2": "11b + 6",
      "answer3": "11b + 24",
      "correct_answer": 0,
      "skill_id": 62,
      "difficulty_id": 1,
      "explanation": "Combine like terms: 8b − 3b = 5b and 15 − 9 = 6. So the expression simplifies to 5b + 6.",
      "hints": ["Group the b terms and the number terms separately.", "8b − 3b = 5b; 15 − 9 = 6."],
      "source": "PLMGS 2025 P6 Prelim Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: option 1 (5b + 6)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "In the number line, what is the mixed number represented by X?",
      "answer0": "\\(3\\dfrac{4}{9}\\)",
      "answer1": "\\(3\\dfrac{3}{8}\\)",
      "answer2": "\\(3\\dfrac{3}{7}\\)",
      "answer3": "\\(3\\dfrac{3}{4}\\)",
      "correct_answer": 1,
      "skill_id": 41,
      "difficulty_id": 2,
      "explanation": "The interval between 3 and 4 is divided into 8 equal parts. X is at the 3rd mark past 3, so it represents \\(3\\dfrac{3}{8}\\).",
      "hints": ["Count the number of equal divisions between 3 and 4.", "X sits at the 3rd of 8 small intervals."],
      "source": "PLMGS 2025 P6 Prelim Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 3,
      "image_bbox": [0.26, 0.66, 0.66, 0.74],
      "image_loc": "number line from 3 to 4 with arrow X marking a point",
      "notes": "Key: option 2 (3 3/8). MCQ because the answer is a mixed number."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "Shay took a ferry from 8.25 a.m. to 1.00 p.m. How long was the ferry ride?",
      "answer0": "4 h 25 min",
      "answer1": "4 h 35 min",
      "answer2": "5 h 25 min",
      "answer3": "5 h 35 min",
      "correct_answer": 1,
      "skill_id": 65,
      "difficulty_id": 1,
      "explanation": "From 8.25 a.m. to 12.25 p.m. is 4 hours; from 12.25 p.m. to 1.00 p.m. is another 35 minutes. Total = 4 h 35 min.",
      "hints": ["Count whole hours first, then the remaining minutes.", "8.25 a.m. to 12.25 p.m. is 4 hours."],
      "source": "PLMGS 2025 P6 Prelim Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: option 2 (4 h 35 min)."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "The table shows the number of vouchers some participants won in a contest. Number of vouchers: 0, 1, 2, 3, 4 with number of participants 4, 15, 11, 8, 5 respectively.<br>How many participants won at least 2 vouchers?",
      "answer0": "11",
      "answer1": "19",
      "answer2": "24",
      "answer3": "26",
      "correct_answer": 2,
      "skill_id": 79,
      "difficulty_id": 2,
      "explanation": "At least 2 vouchers means 2, 3 or 4 vouchers: 11 + 8 + 5 = 24 participants.",
      "hints": ["'At least 2' includes 2, 3 and 4 vouchers.", "Add the participant counts for those columns."],
      "source": "PLMGS 2025 P6 Prelim Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 4,
      "image_bbox": [0.14, 0.27, 0.78, 0.36],
      "image_loc": "table of number of vouchers vs number of participants",
      "notes": "Key: option 3 (24). Table values can be read in the stem."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "The shaded figure is a quarter circle of radius 21 cm. Find the perimeter of the shaded figure. (Take \\(\\pi=\\dfrac{22}{7}\\))",
      "answer0": "33 cm",
      "answer1": "54 cm",
      "answer2": "66 cm",
      "answer3": "75 cm",
      "correct_answer": 3,
      "skill_id": 74,
      "difficulty_id": 2,
      "explanation": "Perimeter = two radii + quarter of the circumference = 21 + 21 + \\(\\dfrac{1}{4}\\times2\\times\\dfrac{22}{7}\\times21\\) = 42 + 33 = 75 cm.",
      "hints": ["A quarter-circle perimeter includes two straight radii and the curved arc.", "Arc length = \\(\\dfrac{1}{4}\\) of the full circumference."],
      "source": "PLMGS 2025 P6 Prelim Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 4,
      "image_bbox": [0.20, 0.58, 0.55, 0.78],
      "image_loc": "shaded quarter circle with radius 21 cm marked",
      "notes": "Key: option 4 (75 cm)."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "Which of the following is not the net of a pyramid?",
      "answer0": "Net 1",
      "answer1": "Net 2",
      "answer2": "Net 3",
      "answer3": "Net 4",
      "correct_answer": 0,
      "skill_id": 77,
      "difficulty_id": 2,
      "explanation": "A pyramid net has one base with triangular faces attached to each edge folding up to a single apex. Net 1 has an extra rectangular/square arrangement that does not fold into a single-apex pyramid, so it is not the net of a pyramid.",
      "hints": ["A pyramid has one base and triangular faces meeting at an apex.", "Check which net cannot fold to a single apex."],
      "source": "PLMGS 2025 P6 Prelim Q10",
      "image_needed": true,
      "image_options": true,
      "image_file": null,
      "image_page": 5,
      "image_bbox": [0.18, 0.08, 0.75, 0.92],
      "image_loc": "four candidate nets (1)-(4) stacked vertically",
      "notes": "Key: option 1. image_options true: the four options are diagrams of nets. Each option should be cropped to q10_opt0..3."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "Ariana had $28. After buying 7 identical cups, she had $y left. Express the cost of 1 cup in terms of y.",
      "answer0": "$(28 − 7y)",
      "answer1": "\\($\\left(28-\\dfrac{y}{7}\\right)\\)",
      "answer2": "\\($\\left(\\dfrac{28y}{7}\\right)\\)",
      "answer3": "\\($\\left(\\dfrac{28-y}{7}\\right)\\)",
      "correct_answer": 3,
      "skill_id": 62,
      "difficulty_id": 2,
      "explanation": "Money spent on cups = $(28 − y). This buys 7 cups, so the cost of 1 cup = \\($\\dfrac{28-y}{7}\\).",
      "hints": ["First find the total amount spent on the cups.", "Divide the amount spent by 7 cups."],
      "source": "PLMGS 2025 P6 Prelim Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: option 4. MCQ because the answer is an algebraic fraction."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "Ryan uses 4 different shapes to form a pattern. The first 17 shapes are: triangle, heart, triangle, arrow, circle, triangle, triangle, heart, triangle, arrow, circle, triangle, triangle, heart, triangle, arrow, circle (repeating in groups).<br>What fraction of the first 27 shapes are triangles?",
      "answer0": "\\(\\dfrac{4}{9}\\)",
      "answer1": "\\(\\dfrac{5}{9}\\)",
      "answer2": "\\(\\dfrac{8}{27}\\)",
      "answer3": "\\(\\dfrac{14}{27}\\)",
      "correct_answer": 1,
      "skill_id": 48,
      "difficulty_id": 3,
      "explanation": "The pattern repeats every 6 shapes (triangle, heart, triangle, arrow, circle, triangle) containing 3 triangles. In 27 shapes there are 27 ÷ 6 = 4 full groups (24 shapes, 12 triangles) plus 3 more shapes (triangle, heart, triangle = 2 triangles +1). Triangles in 27 = 12 + 3 = 15, giving \\(\\dfrac{15}{27}=\\dfrac{5}{9}\\).",
      "hints": ["Find the repeating block and how many triangles it contains.", "27 ÷ 6 gives the number of full blocks plus a remainder."],
      "source": "PLMGS 2025 P6 Prelim Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 6,
      "image_bbox": [0.14, 0.40, 0.86, 0.50],
      "image_loc": "row of 17 small shapes (triangles, hearts, arrows, circles) labelled 1st to 17th",
      "notes": "Key: option 2 (5/9). MCQ because the answer is a fraction. The shape sequence is in the figure."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "A group of children was asked to name their favorite sports. 45% of the children chose floorball and table tennis. The pie chart shows Floorball = 60, Table Tennis = 75, Badminton = 45%, Volleyball = 10%.<br>How many more children chose badminton than volleyball as their favourite sport?",
      "answer0": "35",
      "answer1": "45",
      "answer2": "105",
      "answer3": "135",
      "correct_answer": 2,
      "skill_id": 78,
      "difficulty_id": 3,
      "explanation": "Floorball + Table Tennis = 60 + 75 = 135 children = 45% of the total, so total = 135 ÷ 45 × 100 = 300. Badminton = 45% of 300 = 135; Volleyball = 10% of 300 = 30. Difference = 135 − 30 = 105.",
      "hints": ["Use the 45% to find the total number of children.", "Find badminton and volleyball counts, then subtract."],
      "source": "PLMGS 2025 P6 Prelim Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 7,
      "image_bbox": [0.30, 0.13, 0.70, 0.38],
      "image_loc": "pie chart with Floorball 60, Table Tennis 75, Badminton 45%, Volleyball 10% sectors",
      "notes": "Key: option 3 (105)."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "Alyssa baked some muffins for sale. She sold a total of 480 muffins in the morning. In the afternoon, she sold \\(\\dfrac{1}{8}\\) of the remaining muffins. In the end, she had 35% of the muffins left. How many muffins did she bake?",
      "answer0": "520",
      "answer1": "648",
      "answer2": "792",
      "answer3": "800",
      "correct_answer": 3,
      "skill_id": 56,
      "difficulty_id": 3,
      "explanation": "After the morning, the remaining muffins are split: she sells \\(\\dfrac{1}{8}\\) and keeps \\(\\dfrac{7}{8}\\). The \\(\\dfrac{7}{8}\\) left equals 35% of the total bake. So the remaining (after morning) = 35% ÷ \\(\\dfrac{7}{8}\\) = 40% of total. Thus the morning sale of 480 = 60% of the total, giving total = 480 ÷ 0.60 = 800.",
      "hints": ["The final 35% equals 7/8 of what was left after the morning.", "Work out what fraction of the total the morning 480 represents."],
      "source": "PLMGS 2025 P6 Prelim Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: option 4 (800)."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "In a park, there were two identical circular running tracks with centres at R and T. QRST is a square with a perimeter of 56 m. Benny started running from Q. He ran round each circular track once. Find the distance Benny ran. (Take \\(\\pi=\\dfrac{22}{7}\\))",
      "answer0": "28 m",
      "answer1": "88 m",
      "answer2": "176 m",
      "answer3": "616 m",
      "correct_answer": 2,
      "skill_id": 74,
      "difficulty_id": 3,
      "explanation": "QRST is a square of perimeter 56 m, so each side = 14 m, which is the radius of each circle. Circumference of one circle = \\(2\\times\\dfrac{22}{7}\\times14 = 88\\) m. Two circles = 2 × 88 = 176 m.",
      "hints": ["The square's side equals each circle's radius.", "Find one circumference, then double it for two tracks."],
      "source": "PLMGS 2025 P6 Prelim Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 8,
      "image_bbox": [0.24, 0.14, 0.78, 0.34],
      "image_loc": "two overlapping circles with centres T and R and points Q, S forming square QRST",
      "notes": "Key: option 3 (176 m)."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Express \\(\\dfrac{3}{8}\\) as a decimal. [?]",
      "answer0": "0.375",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 51,
      "difficulty_id": 1,
      "explanation": "\\(\\dfrac{3}{8}=3\\div8 = 0.375\\).",
      "hints": ["Divide 3 by 8.", "8 goes into 3.000 to give 0.375."],
      "source": "PLMGS 2025 P6 Prelim P2 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: 0.375."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "The volume of the cube is 125 m³. Find the length of one side of the cube. [?] m",
      "answer0": "5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 76,
      "difficulty_id": 1,
      "explanation": "Side = cube root of the volume = \\(\\sqrt[3]{125}=5\\) m (since 5 × 5 × 5 = 125).",
      "hints": ["Side of a cube = cube root of its volume.", "What number cubed gives 125?"],
      "source": "PLMGS 2025 P6 Prelim P2 Q17",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 10,
      "image_bbox": [0.35, 0.55, 0.52, 0.66],
      "image_loc": "small cube with side marked '?'",
      "notes": "Key: 5 m. Cube image is illustrative."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "XYZ, VY and YW are straight lines. Find ∠a. [?]°",
      "answer0": "83",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 70,
      "difficulty_id": 1,
      "explanation": "Angles on the straight line XYZ at Y add up to 180°: 62° + ∠a + 35° = 180°, so ∠a = 180° − 62° − 35° = 83°.",
      "hints": ["Angles on a straight line sum to 180°.", "Subtract the two known angles from 180°."],
      "source": "PLMGS 2025 P6 Prelim P2 Q18",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 11,
      "image_bbox": [0.28, 0.12, 0.62, 0.27],
      "image_loc": "straight line XYZ with rays YV and YW; angles 62°, a, 35° at Y",
      "notes": "Key: 83°."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "Find the missing number in the box. 6 : 8 = [?] : 36",
      "answer0": "27",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 60,
      "difficulty_id": 2,
      "explanation": "8 × ? gives 36 means the multiplier from 8 to 36 is 36 ÷ 8 = 4.5. So missing number = 6 × 4.5 = 27. (Equivalently 36 ÷ 8 × 6 = 27.)",
      "hints": ["Find the multiplier that turns 8 into 36.", "Apply the same multiplier to 6."],
      "source": "PLMGS 2025 P6 Prelim P2 Q19",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: 27."
    },
    {
      "n": 20,
      "type_id": 1,
      "question": "Find the value of \\(\\dfrac{3}{4}-\\dfrac{2}{5}\\).",
      "answer0": "\\(\\dfrac{7}{20}\\)",
      "answer1": "\\(\\dfrac{1}{20}\\)",
      "answer2": "\\(\\dfrac{1}{2}\\)",
      "answer3": "\\(\\dfrac{11}{20}\\)",
      "correct_answer": 0,
      "skill_id": 52,
      "difficulty_id": 1,
      "explanation": "Common denominator 20: \\(\\dfrac{3}{4}=\\dfrac{15}{20}\\), \\(\\dfrac{2}{5}=\\dfrac{8}{20}\\). \\(\\dfrac{15}{20}-\\dfrac{8}{20}=\\dfrac{7}{20}\\).",
      "hints": ["Use a common denominator of 20.", "Subtract the numerators."],
      "source": "PLMGS 2025 P6 Prelim P2 Q20",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: 7/20. MCQ because the answer is a fraction."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "(a) Find the value of \\(18\\div\\dfrac{3}{5}\\). [?]<br>(b) Find the value of (60 − 24) ÷ 9 + 3. [?]",
      "answer0": "30",
      "answer1": "7",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 53,
      "difficulty_id": 1,
      "explanation": "(a) \\(18\\div\\dfrac{3}{5}=18\\times\\dfrac{5}{3}=30\\). (b) (60 − 24) ÷ 9 + 3 = 36 ÷ 9 + 3 = 4 + 3 = 7.",
      "hints": ["Dividing by a fraction means multiplying by its reciprocal.", "For (b), do the bracket first, then ÷, then +."],
      "source": "PLMGS 2025 P6 Prelim P2 Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: (a) 30, (b) 7. Two answer blanks (both whole numbers)."
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "Find the area of the shaded triangle. The base is 10 cm and the perpendicular height is 13 cm (the slanted side is 11 cm). [?] cm²",
      "answer0": "65",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 73,
      "difficulty_id": 2,
      "explanation": "Area of a triangle = \\(\\dfrac{1}{2}\\times\\text{base}\\times\\text{height}\\) = \\(\\dfrac{1}{2}\\times10\\times13 = 65\\) cm². (The 11 cm is a slant side, not used.)",
      "hints": ["Use base 10 cm and the perpendicular height 13 cm.", "Ignore the slant length of 11 cm."],
      "source": "PLMGS 2025 P6 Prelim P2 Q22",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 12,
      "image_bbox": [0.30, 0.55, 0.60, 0.78],
      "image_loc": "shaded triangle with 10 cm (top), 11 cm and 13 cm sides marked",
      "notes": "Key: 65 cm². Base 10 cm, height 13 cm; 11 cm is a slant side."
    },
    {
      "n": 23,
      "type_id": 0,
      "question": "Shade 2 more unit squares so that AB is the line of symmetry for the figure.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 80,
      "difficulty_id": 2,
      "explanation": "Shading task: reflect the existing shaded squares across the diagonal line AB and shade the 2 squares needed to complete the symmetry. The answer key shows the squares to shade.",
      "hints": ["AB is a diagonal line of symmetry.", "Mirror each shaded square across AB."],
      "source": "PLMGS 2025 P6 Prelim P2 Q23",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 13,
      "image_bbox": [0.24, 0.13, 0.62, 0.36],
      "image_loc": "grid of unit squares with diagonal AB and some shaded",
      "notes": "type_id 0: interactive shading task, no value answer. Answer key (PDF page 39) shows the 2 squares to shade."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "A tank with a square base has a capacity of 1280 ml. The height of the tank is 80 cm. Find one side of the square base. [?] cm",
      "answer0": "4",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 76,
      "difficulty_id": 2,
      "explanation": "1280 ml = 1280 cm³. Base area = volume ÷ height = 1280 ÷ 80 = 16 cm². The base is square, so one side = \\(\\sqrt{16}=4\\) cm.",
      "hints": ["1 ml = 1 cm³.", "Base area = volume ÷ height; side = square root of base area."],
      "source": "PLMGS 2025 P6 Prelim P2 Q24",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 13,
      "image_bbox": [0.34, 0.50, 0.55, 0.72],
      "image_loc": "tall cuboid tank with height 80 cm and base side '?'",
      "notes": "Key: 4 cm."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "Aiden's scores for 5 games are: 1st 7, 2nd 16, 3rd 8, 4th 0, 5th 24.<br>(a) Find his average score. [?]<br>(b) After Aiden played his 6th game, his average score becomes 12. What was his score for his 6th game? [?]",
      "answer0": "11",
      "answer1": "17",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 79,
      "difficulty_id": 2,
      "explanation": "(a) Average = (7 + 16 + 8 + 0 + 24) ÷ 5 = 55 ÷ 5 = 11. (b) New total for 6 games = 12 × 6 = 72. 6th game score = 72 − 55 = 17.",
      "hints": ["Average = total ÷ number of games.", "Use the new average to find the new total, then subtract the old total."],
      "source": "PLMGS 2025 P6 Prelim P2 Q25",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 14,
      "image_bbox": [0.14, 0.13, 0.72, 0.20],
      "image_loc": "table of game (1st-5th) vs score",
      "notes": "Key: (a) 11, (b) 17. Two answer blanks. Scores can be read in the stem."
    },
    {
      "n": 26,
      "type_id": 0,
      "question": "Kate builds a solid using 8 identical unit cubes (with given Top View, Front View and Side View). (a) Draw the top view of the solid in the square grid. (b) Find the greatest number of cubes that Kate can add to the above solid without changing the front view and side view.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 77,
      "difficulty_id": 3,
      "explanation": "(a) Drawing task: the top view is the footprint of the solid on the grid (see answer key). (b) The greatest number of cubes that can be added without changing the front and side views is 5 (filling the hidden interior positions). Note part (b) has a definite numeric answer of 5, but part (a) is a drawing task, so the whole question is non-standard.",
      "hints": ["For (a), draw the outline seen looking straight down.", "For (b), fill all hidden positions that don't alter the front/side silhouettes."],
      "source": "PLMGS 2025 P6 Prelim P2 Q26",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 15,
      "image_bbox": [0.24, 0.16, 0.66, 0.40],
      "image_loc": "isometric drawing of an 8-unit-cube solid with Top/Front/Side view labels",
      "notes": "type_id 0: part (a) is a draw-on-grid task. Key: (a) see figure, (b) 5 cubes."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "At 12 00, Helen and Thomas travelled in opposite directions from a shopping mall. Helen cycled at a constant speed of 24 km/h and Thomas drove at a constant speed of 57 km/h. How far apart were they at 14 00? [?] km",
      "answer0": "162",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 65,
      "difficulty_id": 2,
      "explanation": "From 12 00 to 14 00 is 2 hours. Since they move in opposite directions, their combined speed = 24 + 57 = 81 km/h. Distance apart = 81 × 2 = 162 km.",
      "hints": ["Opposite directions means you add their speeds.", "Multiply the combined speed by the 2 hours travelled."],
      "source": "PLMGS 2025 P6 Prelim P2 Q27",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: 162 km."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "A rectangular container with a base area of 4800 cm² is \\(\\dfrac{1}{5}\\) filled with water. Water flows into the container from a tap at a rate of 8 litres per minute. It takes 6 minutes to fill the container to its brim. Find the height of the container. [?] cm",
      "answer0": "12.5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 76,
      "difficulty_id": 3,
      "explanation": "Water added = 8 litres/min × 6 min = 48 litres = 48 000 cm³. This raises the level by 48 000 ÷ 4800 = 10 cm, which represents the empty \\(\\dfrac{4}{5}\\) of the container. So full height = 10 ÷ \\(\\dfrac{4}{5}\\) = 10 × \\(\\dfrac{5}{4}\\) = 12.5 cm.",
      "hints": ["Total inflow fills the empty 4/5 of the tank.", "Find the height of that 4/5, then scale up to the full height."],
      "source": "PLMGS 2025 P6 Prelim P2 Q28",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 16,
      "image_bbox": [0.42, 0.40, 0.70, 0.58],
      "image_loc": "rectangular container partly filled with water and a tap above",
      "notes": "Key: 12.5 cm."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "The pie chart represents the number of bottled drinks sold at a stall. Half of the bottled drinks sold were Chocolate Milk. Grape Juice = \\(\\dfrac{3}{10}\\), with Soft Drink and Yogurt drink making up the rest. The number of bottled drinks sold is also represented by a bar graph (Yogurt = 15, Soft Drink = 45, with Grape Juice and Chocolate Milk bars partly stained).<br>How many bottles of Chocolate Milk were sold? [?]",
      "answer0": "150",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 78,
      "difficulty_id": 3,
      "explanation": "Fraction for Yogurt + Soft Drink = 1 − \\(\\dfrac{1}{2}\\) − \\(\\dfrac{3}{10}\\) = \\(\\dfrac{2}{10}=\\dfrac{1}{5}\\). From the bar graph, Yogurt + Soft Drink = 15 + 45 = 60, which is \\(\\dfrac{1}{5}\\) of the total. Total = 60 × 5 = 300. Chocolate Milk = \\(\\dfrac{1}{2}\\) × 300 = 150.",
      "hints": ["Find the fraction made up by Yogurt and Soft Drink.", "Use the bar values (15 + 45) to find the total, then take half."],
      "source": "PLMGS 2025 P6 Prelim P2 Q29",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 17,
      "image_bbox": [0.14, 0.10, 0.78, 0.62],
      "image_loc": "pie chart (top) and bar graph (below) of bottled drinks sold",
      "notes": "Key: 150. Bar values Yogurt 15, Soft Drink 45 read from graph."
    },
    {
      "n": 30,
      "type_id": 0,
      "question": "The figure is not drawn to scale. AGDJ, FCG and CDH are straight lines. BCFE is a trapezium. BC is parallel to EF. Given the marked angles (∠HDJ region 102°, ∠GCD region 10°, ∠ABE 132°, ∠CBE 125°, ∠CFE 67°), decide whether each statement is true, false or not possible to tell: (i) ∠BCD = 67°, (ii) ∠ABC = 103°, (iii) ABCD is a rhombus.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 70,
      "difficulty_id": 3,
      "explanation": "∠BCD = ∠GCD + ∠GCB = 10° + ∠GFE = 10° + 67° = 77°, so (i) ∠BCD = 67° is FALSE. ∠ABC = 360° − ∠ABE − ∠CBE = 360° − 132° − 125° = 103°, so (ii) is TRUE. ∠BCD + ∠ADC = 77° + 102° = 179° ≠ 180°, so AD is not parallel to BC, ABCD is not a parallelogram and cannot be a rhombus, so (iii) ABCD is a rhombus is FALSE.",
      "hints": ["Compute ∠BCD and ∠ABC from the given angles.", "Check whether AD is parallel to BC to test the rhombus claim."],
      "source": "PLMGS 2025 P6 Prelim P2 Q30",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 18,
      "image_bbox": [0.18, 0.13, 0.66, 0.44],
      "image_loc": "geometric figure with points A,B,C,D,E,F,G,H,J and angles 102°,10°,132°,125°,67°",
      "notes": "type_id 0: true/false/not-possible-to-tell tick-table format, no numeric/sequence answer. Key: (i) False, (ii) True, (iii) False (∠BCD=77°, ∠ABC=103°)."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "The area of the shaded face is 49 cm². What is the volume of the solid? The solid is a cuboid with length 9 cm and a square shaded face of 49 cm². [?] cm³",
      "answer0": "441",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 76,
      "difficulty_id": 1,
      "explanation": "Volume = area of the shaded (cross-section) face × length = 49 × 9 = 441 cm³.",
      "hints": ["Volume of a prism = cross-section area × length.", "Multiply 49 cm² by the 9 cm length."],
      "source": "PLMGS 2025 P6 Prelim P2 Q1",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 20,
      "image_bbox": [0.14, 0.20, 0.48, 0.36],
      "image_loc": "cuboid with shaded end face and length 9 cm marked",
      "notes": "Key: 441 cm³."
    },
    {
      "n": 32,
      "type_id": 2,
      "question": "Measure and write down (a) the length of PR. [?] cm<br>(b) the size of ∠PQR. [?]°",
      "answer0": "9",
      "answer1": "125",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 70,
      "difficulty_id": 1,
      "explanation": "(a) Measuring with a ruler, PR = 9 cm. (b) Measuring with a protractor, ∠PQR = 125°.",
      "hints": ["Use a ruler for the length and a protractor for the angle.", "Read the printed answer key values: 9 cm and 125°."],
      "source": "PLMGS 2025 P6 Prelim P2 Q2",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 20,
      "image_bbox": [0.22, 0.42, 0.78, 0.60],
      "image_loc": "triangle PQR drawn to scale for measuring",
      "notes": "Key: (a) 9 cm, (b) 125°. Two answer blanks. This is a measuring (ruler/protractor) question; answers depend on the printed scale."
    },
    {
      "n": 33,
      "type_id": 1,
      "question": "A triangle is formed by bending a piece of wire. The three sides are (2x + 10) cm, (3x) cm and (5x − 3) cm. What is the length of the piece of wire? Express your answer in terms of x in its simplest form.",
      "answer0": "(10x + 7) cm",
      "answer1": "(10x − 7) cm",
      "answer2": "(10x + 13) cm",
      "answer3": "(9x + 7) cm",
      "correct_answer": 0,
      "skill_id": 62,
      "difficulty_id": 2,
      "explanation": "Total length = sum of the three sides = (2x + 10) + (3x) + (5x − 3) = (2x + 3x + 5x) + (10 − 3) = 10x + 7 cm.",
      "hints": ["Add the three side expressions.", "Combine the x terms and the number terms separately."],
      "source": "PLMGS 2025 P6 Prelim P2 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 21,
      "image_bbox": [0.22, 0.14, 0.66, 0.30],
      "image_loc": "triangle with sides (2x+10) cm, (3x) cm, (5x-3) cm",
      "notes": "Key: (10x + 7) cm. MCQ because the answer is an algebraic expression."
    },
    {
      "n": 34,
      "type_id": 1,
      "question": "A fruit seller stored oranges in crates A and B. Crate A contained twice as many oranges as crate B. In crate A, \\(\\dfrac{1}{2}\\) of the oranges were ripe. In crate B, \\(\\dfrac{5}{6}\\) of the oranges were ripe. What fraction of all the oranges were ripe?",
      "answer0": "\\(\\dfrac{11}{18}\\)",
      "answer1": "\\(\\dfrac{2}{3}\\)",
      "answer2": "\\(\\dfrac{5}{9}\\)",
      "answer3": "\\(\\dfrac{13}{18}\\)",
      "correct_answer": 0,
      "skill_id": 53,
      "difficulty_id": 3,
      "explanation": "Crate A is \\(\\dfrac{2}{3}\\) of all oranges and crate B is \\(\\dfrac{1}{3}\\). Ripe fraction = \\(\\dfrac{2}{3}\\times\\dfrac{1}{2} + \\dfrac{1}{3}\\times\\dfrac{5}{6} = \\dfrac{1}{3} + \\dfrac{5}{18} = \\dfrac{6}{18}+\\dfrac{5}{18} = \\dfrac{11}{18}\\).",
      "hints": ["Crate A : Crate B = 2 : 1, so the fractions of the total are 2/3 and 1/3.", "Multiply each crate's share by its ripe fraction, then add."],
      "source": "PLMGS 2025 P6 Prelim P2 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: 11/18. MCQ because the answer is a fraction."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "Mei had 18 more stickers than Aisha at first. After Mei gave some stickers to Aisha, she had 24 fewer stickers than Aisha. How many stickers did Mei give to Aisha? [?]",
      "answer0": "21",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 60,
      "difficulty_id": 2,
      "explanation": "The total swing in the gap between Mei and Aisha = 18 + 24 = 42 (Mei goes from 18 ahead to 24 behind). Each sticker Mei gives changes the gap by 2 (Mei −1, Aisha +1), so stickers given = 42 ÷ 2 = 21.",
      "hints": ["The difference changes by 2 for each sticker transferred.", "Total change in difference = 18 + 24 = 42."],
      "source": "PLMGS 2025 P6 Prelim P2 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: 21."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "Mr Tan drove 57 km from Point A to Point B at an average speed of 76 km/h. From Point B, he drove another 60 km for \\(1\\dfrac{1}{2}\\) hours to reach Point C. What was his average speed for the entire journey? Express your answer in km/h. [?]",
      "answer0": "52",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 65,
      "difficulty_id": 3,
      "explanation": "Total distance = 57 + 60 = 117 km. Time A to B = 57 ÷ 76 = 0.75 h. Total time = 0.75 + 1.5 = 2.25 h. Average speed = 117 ÷ 2.25 = 52 km/h.",
      "hints": ["Average speed = total distance ÷ total time.", "Find the time for the first leg using distance ÷ speed."],
      "source": "PLMGS 2025 P6 Prelim P2 Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 23,
      "image_bbox": [0.22, 0.24, 0.70, 0.32],
      "image_loc": "line A-B-C with 57 km and 60 km marked",
      "notes": "Key: 52 km/h. Distance diagram is illustrative."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "Figure X shows a square tile ABCD made up of a triangle BCD, a quarter circle AFE and a shaded part BDEF. AF = FB.<br>(a) The area of triangle BCD is 32 cm². What is the radius of the quarter circle AFE? [?] cm<br>(b) Figure Y is made up of four such square tiles. Find the total shaded area in Figure Y. (Take \\(\\pi=3.14\\)) [?] cm²",
      "answer0": "4",
      "answer1": "77.76",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 74,
      "difficulty_id": 3,
      "explanation": "(a) Triangle BCD is half the square ABCD, so the square area = 32 × 2 = 64 cm², giving side AB = 8 cm. The quarter circle's radius = 8 ÷ 2 = 4 cm. (b) Total shaded area in Figure Y = (square area total) − (circle area) = 32 × 4 − 3.14 × 4 × 4 = 128 − 50.24 = 77.76 cm².",
      "hints": ["Triangle BCD is half the square tile.", "For (b), four shaded tiles minus the full circle they enclose."],
      "source": "PLMGS 2025 P6 Prelim P2 Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 24,
      "image_bbox": [0.30, 0.10, 0.66, 0.34],
      "image_loc": "Figure X square tile ABCD; Figure Y (lower) four tiles with circle",
      "notes": "Key: (a) 4 cm, (b) 77.76 cm². Two answer blanks. Figure Y is lower on the same page (bbox approx [0.40,0.50,0.75,0.78])."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "Callys always spends 70% of her salary. Her salary for December was 40% more than that for November. As a result, she spent $560 more in December than in November. How much was her salary in December? [?]",
      "answer0": "2800",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 56,
      "difficulty_id": 3,
      "explanation": "Her December expenditure is also 40% more than November's. So the extra 40% of her November expenditure = $560, meaning 140% (December expenditure) = $560 ÷ 40 × 140 = $1960. Since she spends 70% of her salary, her December salary = $1960 ÷ 70% = $2800.",
      "hints": ["The $560 extra spent equals 40% of her November expenditure.", "December expenditure is 70% of the December salary."],
      "source": "PLMGS 2025 P6 Prelim P2 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: $2800. Answer entered as number 2800."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "The line graph shows the number of visitors who took the tram in the zoo from Monday to Friday in a particular week (Mon 210, Tue 0, Wed 350, Thu 180, Fri 420).<br>(a) On which day was the tram service in the zoo closed for maintenance? [?]<br>(b) Find the percentage increase in the number of visitors who took the tram from Thursday to Friday. [?]%",
      "answer0": "Tuesday",
      "answer1": "\\(133\\dfrac{1}{3}\\)",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 78,
      "difficulty_id": 3,
      "explanation": "(a) The graph shows 0 visitors on Tuesday, so the tram service was closed for maintenance on Tuesday. (b) Increase = 420 − 180 = 240; percentage = \\(\\dfrac{240}{180}\\times100\\% = \\dfrac{400}{3}\\% = 133\\dfrac{1}{3}\\%\\).",
      "hints": ["The maintenance day has zero visitors on the graph.", "Percentage increase = increase ÷ original (Thursday) × 100%."],
      "source": "PLMGS 2025 P6 Prelim P2 Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 26,
      "image_bbox": [0.10, 0.13, 0.78, 0.42],
      "image_loc": "line graph of number of visitors Mon-Fri",
      "notes": "Key: (a) Tuesday, (b) 133 1/3 %. Two answer blanks. Part (b) answer is a mixed-number percentage (entered as text)."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "Winnie and Sophie were paid a total of $3620 for a job. Winnie was paid $1960 more than Sophie.<br>(a) How much was Winnie paid for the job? $[?]<br>(b) Winnie and Sophie were paid based on the number of days they worked. Winnie worked 3 times as many days as Sophie. Winnie was paid $5 more than Sophie per day. How many days did Sophie work? [?]",
      "answer0": "2790",
      "answer1": "20",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 61,
      "difficulty_id": 3,
      "explanation": "(a) Winnie's pay = (3620 + 1960) ÷ 2 = $2790. (b) Sophie's pay = 2790 − 1960 = $830. If Winnie were paid Sophie's daily rate for the same days, she'd get 2790 ÷ 3 = $930 for Sophie's number of days. The $5/day extra over those days accounts for 930 − 830 = $100, so Sophie's days = 100 ÷ 5 = 20.",
      "hints": ["For (a), use the sum and difference of the two amounts.", "For (b), compare Winnie's per-day premium of $5 over the days Sophie worked."],
      "source": "PLMGS 2025 P6 Prelim P2 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: (a) $2790, (b) 20 days. Two answer blanks."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "At first, \\(\\dfrac{1}{5}\\) of a rectangular container was filled with water. More water was collected into the container from a leaking tap for 30 minutes. The line graph shows the volume of water in the tank (75 cm³ at 0 min rising to 225 cm³ at 30 min).<br>(a) How much water flowed into the container in one minute? [?] cm³<br>(b) At the end of 30 minutes, what fraction of the container was filled with water? [?]",
      "answer0": "5",
      "answer1": "\\(\\dfrac{3}{5}\\)",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 76,
      "difficulty_id": 3,
      "explanation": "(a) Water added over 30 min = 225 − 75 = 150 cm³, so rate = 150 ÷ 30 = 5 cm³ per minute. (b) At first \\(\\dfrac{1}{5}\\) = 75 cm³, so the container's capacity = 75 × 5 = 375 cm³. Fraction filled at the end = \\(\\dfrac{225}{375}=\\dfrac{3}{5}\\).",
      "hints": ["Rate = (final volume − start volume) ÷ time.", "Use the starting 1/5 = 75 cm³ to find the full capacity."],
      "source": "PLMGS 2025 P6 Prelim P2 Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 28,
      "image_bbox": [0.16, 0.16, 0.70, 0.40],
      "image_loc": "line graph of volume of water (cm³) over time (min)",
      "notes": "Key: (a) 5 cm³, (b) 3/5. Two answer blanks. Part (c) of this question continues as n=42."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "At the end of 30 minutes, the container was filled with water to a height of 3 cm (Figure Z), holding 225 cm³ of water. Find the possible pair of length and breadth of the container, given that both dimensions are whole numbers greater than 1 cm. [?] cm, [?] cm",
      "answer0": "15",
      "answer1": "5",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 76,
      "difficulty_id": 3,
      "explanation": "Base area = volume of water ÷ height = 225 ÷ 3 = 75 cm². Find two whole numbers greater than 1 whose product is 75: 15 × 5 = 75. So length = 15 cm and breadth = 5 cm.",
      "hints": ["Base area = water volume ÷ water height.", "Factorise 75 into two whole-number factors each greater than 1."],
      "source": "PLMGS 2025 P6 Prelim P2 Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 29,
      "image_bbox": [0.24, 0.13, 0.62, 0.34],
      "image_loc": "Figure Z: container with water at height 3 cm",
      "notes": "Key: 15 cm, 5 cm (base area 75 cm²). This is part (c) of Paper 2 Q11; two answer blanks. Other valid factor pairs of 75 (e.g. 25×3) exist but the key gives 15 and 5."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "In the figure, ABFG is a parallelogram and BCDE is a rhombus. ABC is a straight line. ∠AGF = 67°, ∠BFE = 11° and ∠CED = 38°.<br>(a) Find ∠FBE. [?]°<br>(b) Find ∠DEF. [?]°",
      "answer0": "9",
      "answer1": "124",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 70,
      "difficulty_id": 3,
      "explanation": "(a) ∠ABF = ∠AGF = 67° (opposite angles of the parallelogram). In the rhombus, ∠BEC = ∠CED = 38°, so ∠CBE = 180° − 38° − 38° = 104°. Since ABC is a straight line, ∠FBE = 180° − ∠ABF − ∠CBE = 180° − 67° − 104° = 9°. (b) ∠BEF = 180° − 11° − 9° = 160°. ∠DEF = 360° − 160° − 38° − 38° = 124°.",
      "hints": ["Use the parallelogram's opposite-angle property for ∠ABF.", "The rhombus gives an isosceles triangle for ∠CBE."],
      "source": "PLMGS 2025 P6 Prelim P2 Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 30,
      "image_bbox": [0.14, 0.12, 0.72, 0.42],
      "image_loc": "parallelogram ABFG with rhombus BCDE attached; angles 67°, 11°, 38° marked",
      "notes": "Key: (a) 9°, (b) 124°. Two answer blanks."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "The table shows the prices of entry tickets for a theme park: Adult below 65 years old $24, Adult 65 years and above $17, Child below 12 years $10. The number of adult tickets sold was 6 times the number of child tickets sold. \\(\\dfrac{4}{5}\\) of the adult tickets sold were for adults aged below 65 years old. A total of $9464 was collected from the sale of tickets.<br>(a) What fraction of the tickets sold were for adults aged 65 years and above? Give your answer in the simplest form.<br>(b) What was the total number of tickets sold? [?]",
      "answer0": "\\(\\dfrac{6}{35}\\)",
      "answer1": "455",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 60,
      "difficulty_id": 3,
      "explanation": "Adults are 6 units and children 1 unit (adults = 6 × children). Of the 6 adult units, \\(\\dfrac{4}{5}\\) are below 65 and \\(\\dfrac{1}{5}\\) are 65+. Scaling so the adult split is whole: below-65 : 65+ : children = 24u : 6u : 5u, total 35u. (a) Fraction 65+ = \\(\\dfrac{6u}{35u}=\\dfrac{6}{35}\\). (b) Revenue: 24u × $24 + 6u × $17 + 5u × $10 = 728u = $9464, so u = 13. Total tickets = 35u = 35 × 13 = 455. Note: part (a) answer is a fraction; recorded as text in notes since FIB must be integer — see notes.",
      "hints": ["Set the adult/child counts as units, splitting adults 4:1 (below 65 : 65+).", "Use the total revenue $9464 to find the unit value."],
      "source": "PLMGS 2025 P6 Prelim P2 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 31,
      "image_bbox": [0.14, 0.12, 0.78, 0.24],
      "image_loc": "table of ticket type/age vs price per ticket",
      "notes": "Key: (a) 6/35 (a fraction), (b) 455. Part (a)'s answer is a fraction so it cannot be a numeric FIB blank; answer0 holds the fraction text for reference and the [?] in the stem corresponds to part (b) (455). Inserter should treat part (a) as MCQ/explanation. Single [?] kept for the numeric part (b)."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "Ben baked three types of muffins for sale. The number of each type is shown by a bar graph; the chocolate and vanilla bars are not drawn (strawberry is shown). (a) The ratio of chocolate : strawberry : vanilla muffins is 7 : 5 : 9. Draw the bars for chocolate and vanilla. (b) Ben sold all his strawberry muffins at $3.20 each. He collected a total of $192 from the sale of the strawberry muffins. How many muffins did he bake altogether? [?]",
      "answer0": "252",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 60,
      "difficulty_id": 3,
      "explanation": "(a) is a drawing task (bars in ratio 7 : 5 : 9 with strawberry = 5 units shown). (b) Strawberry muffins sold = $192 ÷ $3.20 = 60, which is the 5-unit part, so 1 unit = 12. Total muffins = (7 + 5 + 9) units = 21 units = \\(\\dfrac{60}{5}\\times21 = 252\\).",
      "hints": ["Strawberry count = total takings ÷ price each.", "Strawberry = 5 units; scale to the full 7+5+9 = 21 units."],
      "source": "PLMGS 2025 P6 Prelim P2 Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 32,
      "image_bbox": [0.12, 0.13, 0.66, 0.55],
      "image_loc": "bar graph with only the strawberry bar drawn (chocolate and vanilla blank)",
      "notes": "Key: (a) draw bars (see figure), (b) 252. The single [?] corresponds to numeric part (b). Part (a) is a graph-drawing task."
    },
    {
      "n": 46,
      "type_id": 0,
      "question": "In the 1-cm square grid, line CB forms one side of an isosceles triangle CBE in which CB = BE. (a) Complete the drawing of triangle CBE on the grid such that Point E is east of Point C. (b) Draw a right-angled triangle CEF on the grid such that EF is twice the length of BC, with triangle CEF not overlapping triangle CBE. (c) Find the area of figure CBEF. [?] cm²",
      "answer0": "18",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 73,
      "difficulty_id": 3,
      "explanation": "Parts (a) and (b) are drawing tasks on a grid. (c) Using the constructed figure, area of CBEF = \\(\\dfrac{1}{2}\\times4\\times3 + \\dfrac{1}{2}\\times4\\times6 = 6 + 12 = 18\\) cm².",
      "hints": ["For (a), place E so CE is horizontal with CB = BE.", "For (c), split CBEF into the two triangles and add their areas."],
      "source": "PLMGS 2025 P6 Prelim P2 Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 34,
      "image_bbox": [0.20, 0.18, 0.66, 0.50],
      "image_loc": "1-cm square grid with points C and B and line CB drawn",
      "notes": "type_id 0: parts (a) and (b) are draw-on-grid tasks, so the question is non-standard. Key: (c) area = 18 cm² (a definite value), but (a)/(b) cannot be a value answer. Stored as type_id 0 with the numeric (c) answer noted."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "There were some books on Shelf A and Shelf B. Emily took out \\(\\dfrac{1}{7}\\) of the books from Shelf A and placed them onto Shelf B. As a result, the ratio of the number of books on Shelf A to the number of books on Shelf B became 3 : 5. There were then 156 more books on Shelf B than on Shelf A.<br>(a) What was the ratio of the number of books on Shelf A to the number of books on Shelf B at first? Give your answer in the simplest form.<br>(b) How many books were there on Shelf B at first? [?]",
      "answer0": "7 : 9",
      "answer1": "351",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 60,
      "difficulty_id": 3,
      "explanation": "After the move the ratio is 3 : 5 = 6u : 10u. Taking out \\(\\dfrac{1}{7}\\) of Shelf A means 1 unit moved (6u + u = 7u was Shelf A's original; 10u − u = 9u was Shelf B's original). (a) Original ratio = 7u : 9u = 7 : 9. (b) After the move the difference 10u − 6u = 4u = 156, so u = 39. Shelf B at first = 9u = 9 × 39 = 351.",
      "hints": ["Work backwards: 1/7 of Shelf A moved equals 1 unit of the 3:5 split.", "Use the difference of 156 (= 4u) to find one unit."],
      "source": "PLMGS 2025 P6 Prelim P2 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: (a) 7 : 9 (a ratio), (b) 351. Part (a)'s answer is a ratio (not numeric), so the single [?] corresponds to numeric part (b) = 351; answer0 holds the ratio text for part (a)."
    },
    {
      "n": 48,
      "type_id": 2,
      "question": "Stall A and Stall B sold the same total number of burgers and sandwiches at a school carnival. A burger costs $4.50 and a sandwich costs $2.00. Stall A sold some burgers and 64 sandwiches. Stall B sold some burgers and 96 sandwiches.<br>(a) Which stall collected more money? Stall: [?]. How much more? $[?]<br>(b) The total mass of burgers and sandwiches sold at Stall A was 8.32 kg. Each burger is 60 g heavier than each sandwich. What is the total mass of burgers and sandwiches sold by Stall B in kg? [?] kg",
      "answer0": "80",
      "answer1": "6.40",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 61,
      "difficulty_id": 3,
      "explanation": "(a) Both stalls sold the same total number of items, but Stall A sold fewer sandwiches (64 vs 96), so it sold 32 more burgers than Stall B. Since a burger costs $2.50 more than a sandwich, Stall A collected 32 × $2.50 = $80 more. So Stall A collected more money, by $80. (b) Stall A had 32 more burgers than Stall B, and each burger is 60 g heavier than a sandwich. Replacing 32 burgers with 32 sandwiches (to match Stall B's mix) reduces mass by 32 × 60 g = 1920 g = 1.92 kg. So Stall B's total mass = 8.32 − 1.92 = 6.40 kg.",
      "hints": ["Equal totals but different sandwich counts means the burger counts differ by 32.", "A burger is worth $2.50 more and weighs 60 g more than a sandwich."],
      "source": "PLMGS 2025 P6 Prelim P2 Q17",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 36,
      "image_bbox": [0.24, 0.13, 0.66, 0.27],
      "image_loc": "Prices poster: Burger $4.50, Sandwich $2.00",
      "notes": "Key: (a) Stall A, $80 more; (b) 6.40 kg. Part (a) asks which stall (a label) plus a numeric amount; answer0 holds the $80 numeric amount. The 'which stall' = Stall A is recorded here in notes. Two answer values overall (amount $80, mass 6.40)."
    }
  ]
}