{
  "paper": {
    "school": "Anglo-Chinese School (Junior)",
    "year": 2025,
    "level": "P6",
    "label": "Prelim",
    "source_prefix": "Anglo-Chinese School (Junior) 2025 P6 Prelim",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "Which of the following is fifty thousand and fifty-six in numerals?",
      "answer0": "5056",
      "answer1": "50 056",
      "answer2": "500 056",
      "answer3": "5 000 056",
      "correct_answer": 1,
      "skill_id": 149,
      "difficulty_id": 1,
      "explanation": "Fifty thousand = 50 000; fifty-six = 56. Together = 50 056. Answer: 50 056.",
      "hints": ["Fifty thousand is written 50 000.", "Add 56 to 50 000."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Booklet A Q1: option 2 (50 056)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Which decimal is greater than 0.07 but smaller than 0.19?",
      "answer0": "0.1",
      "answer1": "0.2",
      "answer2": "0.01",
      "answer3": "0.06",
      "correct_answer": 0,
      "skill_id": 124,
      "difficulty_id": 2,
      "explanation": "Check each: 0.1 is between 0.07 and 0.19. 0.2 is too big, 0.01 and 0.06 are too small. Answer: 0.1.",
      "hints": ["Compare each option with 0.07 and 0.19.", "0.1 lies between 0.07 and 0.19."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Booklet A Q2: option 1 (0.1)."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "In the number line, what is the mixed number represented by A?",
      "answer0": "\\(2\\dfrac{2}{3}\\)",
      "answer1": "\\(2\\dfrac{5}{6}\\)",
      "answer2": "\\(2\\dfrac{6}{7}\\)",
      "answer3": "\\(2\\dfrac{7}{8}\\)",
      "correct_answer": 1,
      "skill_id": 119,
      "difficulty_id": 2,
      "explanation": "The interval from 2 to 3 is divided into 6 equal parts. A is at the 5th mark, so it is \\(2\\dfrac{5}{6}\\). Answer: \\(2\\dfrac{5}{6}\\).",
      "hints": ["Count how many equal parts the gap from 2 to 3 is split into.", "A sits at the 5th of 6 parts, so it is \\(2\\dfrac{5}{6}\\)."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q3",
      "image_needed": true,
      "image_options": false,
      "image_page": 2,
      "image_bbox": [0.37, 0.66, 0.68, 0.78],
      "image_loc": "number line from 2 to 3 with arrow A, middle of page 2",
      "image_file": "q3.png",
      "notes": "Answer key Booklet A Q3: option 2 (2 5/6). Fraction options so MCQ."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "What is the value of \\(18 + (30 - 6) \\div 3 \\times 2\\)?",
      "answer0": "7",
      "answer1": "22",
      "answer2": "34",
      "answer3": "52",
      "correct_answer": 2,
      "skill_id": 155,
      "difficulty_id": 2,
      "explanation": "Order of operations: brackets first, then \\(\\div\\) and \\(\\times\\) from left to right, then \\(+\\). \\(30 - 6 = 24\\); \\(24 \\div 3 = 8\\); \\(8 \\times 2 = 16\\); \\(18 + 16 = 34\\). Answer: 34.",
      "hints": ["Do the bracket first, then divide and multiply from left to right.", "Add 18 last."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Booklet A Q4: option 3 (34)."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "The figure shows part of a weighing scale. Which of the following is the closest to the reading indicated by the arrow?",
      "answer0": "73",
      "answer1": "75",
      "answer2": "77",
      "answer3": "78",
      "correct_answer": 2,
      "skill_id": 147,
      "difficulty_id": 2,
      "explanation": "The scale is marked in tens (50, 60, 70, 80, 90, 100) with smaller divisions in between. The arrow points just before 80, closest to 77. Answer: 77.",
      "hints": ["Work out the value of each small division between the labelled numbers.", "The arrow is just before 80, closest to 77."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q5",
      "image_needed": true,
      "image_options": false,
      "image_page": 3,
      "image_bbox": [0.25, 0.34, 0.78, 0.52],
      "image_loc": "curved weighing-scale dial with arrow, middle of page 3",
      "image_file": "q5.png",
      "notes": "Answer key Booklet A Q5: option 3 (77)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "Which of the following is the same as 6020 m\\(\\ell\\)?",
      "answer0": "60 \\(\\ell\\) 2 m\\(\\ell\\)",
      "answer1": "60 \\(\\ell\\) 20 m\\(\\ell\\)",
      "answer2": "6 \\(\\ell\\) 2 m\\(\\ell\\)",
      "answer3": "6 \\(\\ell\\) 20 m\\(\\ell\\)",
      "correct_answer": 3,
      "skill_id": 184,
      "difficulty_id": 1,
      "explanation": "1 \\(\\ell\\) = 1000 m\\(\\ell\\). 6020 m\\(\\ell\\) = 6000 m\\(\\ell\\) + 20 m\\(\\ell\\) = 6 \\(\\ell\\) 20 m\\(\\ell\\). Answer: 6 \\(\\ell\\) 20 m\\(\\ell\\).",
      "hints": ["1 litre = 1000 millilitres.", "6020 = 6000 + 20, so 6 \\(\\ell\\) and 20 m\\(\\ell\\)."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Booklet A Q6: option 4 (6 l 20 ml)."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "A prism has two right-angled triangular faces and three rectangular faces. Which of the following will complete the net of the prism?",
      "answer0": "rectangle 3 cm by 6 cm",
      "answer1": "rectangle 4 cm by 6 cm",
      "answer2": "rectangle 5 cm by 6 cm",
      "answer3": "rectangle 6 cm by 6 cm",
      "correct_answer": 2,
      "skill_id": 233,
      "difficulty_id": 3,
      "explanation": "The triangular face has sides 3 cm, 4 cm and 5 cm (right-angled). The net already shows the 3 cm by 6 cm and 4 cm by 6 cm rectangular faces. The missing rectangular face uses the third triangle side (5 cm) and the prism length (6 cm), giving a 5 cm by 6 cm rectangle. Answer: option with 5 cm by 6 cm.",
      "hints": ["A triangular prism has 3 rectangular faces, one for each side of the triangle.", "The two sides 3 cm and 4 cm are already in the net; the missing rectangle uses the 5 cm side and the 6 cm length."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q7",
      "image_needed": true,
      "image_options": true,
      "image_page": 4,
      "image_bbox": [0.16, 0.07, 0.92, 0.85],
      "image_loc": "prism and incomplete net at top of page 4, with four rectangle options (1)-(4) below",
      "image_file": "q7.png",
      "notes": "Answer key Booklet A Q7: option 3 (5 cm by 6 cm rectangle). image_options true: the 4 options are rectangle figures with dimensions; option labels in answer0..3 describe them. Crop the whole prism+net+options region."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "Five letters are drawn on the square grid. How many of the letters have both perpendicular and parallel lines?",
      "answer0": "5",
      "answer1": "2",
      "answer2": "3",
      "answer3": "4",
      "correct_answer": 1,
      "skill_id": 100,
      "difficulty_id": 3,
      "explanation": "The five letters are F, X, M, Y, N. A letter needs at least one pair of perpendicular lines AND one pair of parallel lines. F has perpendicular lines but its two horizontal strokes are parallel (yes both). N has parallel verticals but no perpendicular pair to them... Checking each against the key: 2 of the letters have both perpendicular and parallel lines. Answer: 2.",
      "hints": ["A letter qualifies only if it has BOTH a perpendicular pair and a parallel pair of lines.", "Check each letter F, X, M, Y, N carefully."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q8",
      "image_needed": true,
      "image_options": false,
      "image_page": 5,
      "image_bbox": [0.2, 0.1, 0.75, 0.21],
      "image_loc": "five letters (F, X, M, Y, N) drawn on a square grid near top of page 5",
      "image_file": "q8.png",
      "notes": "Answer key Booklet A Q8: option 2 (2)."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "The table shows the departure times of buses A, B, C and D at the Bus Terminal. Keith arrived at the Bus Terminal at 1 p.m. Which is the earliest bus he can take?",
      "answer0": "A",
      "answer1": "B",
      "answer2": "C",
      "answer3": "D",
      "correct_answer": 1,
      "skill_id": 135,
      "difficulty_id": 2,
      "explanation": "1 p.m. is 1300 in 24-hour time. Bus A leaves at 1245 (already gone). The next bus is B at 1330, which is after 1300. Answer: B.",
      "hints": ["1 p.m. is 1300 in 24-hour clock.", "Pick the earliest bus that leaves at or after 1300."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q9",
      "image_needed": true,
      "image_options": false,
      "image_page": 5,
      "image_bbox": [0.2, 0.5, 0.85, 0.65],
      "image_loc": "bus departure-times table in the middle of page 5",
      "image_file": "q9.png",
      "notes": "Answer key Booklet A Q9: option 2 (B). Table: A 1245, B 1330, C 1415, D 1500."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "The number of pies sold at a bakery decreased by 150 from Wednesday to Thursday and increased by 60 from Thursday to Friday. Which graph shows the number of pies sold at the bakery from Wednesday to Friday?",
      "answer0": "Graph 1",
      "answer1": "Graph 2",
      "answer2": "Graph 3",
      "answer3": "Graph 4",
      "correct_answer": 3,
      "skill_id": 147,
      "difficulty_id": 2,
      "explanation": "From Wed to Thu the line must fall (decrease by 150), and from Thu to Fri it must rise (increase by 60), but the rise is smaller than the fall, so Friday is lower than Wednesday. The graph showing a large drop then a small rise (Friday below Wednesday) is graph 4. Answer: Graph 4.",
      "hints": ["The line goes down from Wed to Thu, then up from Thu to Fri.", "The rise (60) is smaller than the fall (150), so Friday ends lower than Wednesday."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q10",
      "image_needed": true,
      "image_options": true,
      "image_page": 6,
      "image_bbox": [0.18, 0.21, 0.86, 0.5],
      "image_loc": "four line-graph options (1)-(4) in the upper half of page 6",
      "image_file": "q10.png",
      "notes": "Answer key Booklet A Q10: option 4. image_options true: the 4 options are graphs; answer labels are placeholders."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "A plank of wood was first cut into two pieces in the ratio 2 : 3. The longer piece was then cut into 2 pieces in the ratio 1 : 3. The shortest piece of wood among the three pieces was 18 cm long. What was the length of the original plank of wood?",
      "answer0": "72 cm",
      "answer1": "90 cm",
      "answer2": "108 cm",
      "answer3": "120 cm",
      "correct_answer": 3,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "First cut 2 : 3. The longer piece (3 parts) is cut 1 : 3, giving sub-pieces of 1 and 3 of those parts. Make the longer piece 4 small-units, so original 2 : 3 becomes 2 small-units... scaling: take the longer piece as 4u (1u and 3u). The first-cut shorter piece equals 2/3 of the longer = (2/3)(4u). The three pieces are: first short = 8/3 u, then 1u and 3u. The shortest is 1u = 18 cm. Then longer = 4u = 72 cm; first short = (2/3)(72) = 48 cm; total = 48 + 72 = 120 cm. Answer: 120 cm.",
      "hints": ["Make the longer piece 4 units so the 1 : 3 cut gives whole units (1u and 3u).", "The shortest piece is 1u = 18 cm; work back to the longer piece and then the original plank."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Booklet A Q11: option 4 (120 cm)."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "The shaded figure is made up of a large semicircle and a square with a small semicircle cut-out from the square. The diameter of the small semicircle is 10 cm, and the diameter of the large semicircle is twice the length of the diameter of the small semicircle. What is the perimeter of the shaded figure? (Take \\(\\pi = 3.14\\))",
      "answer0": "77.1 cm",
      "answer1": "71.4 cm",
      "answer2": "67.1 cm",
      "answer3": "61.4 cm",
      "correct_answer": 0,
      "skill_id": 222,
      "difficulty_id": 3,
      "explanation": "Small semicircle diameter = 10 cm; large semicircle diameter = 20 cm. Large semicircle arc = \\(\\dfrac{1}{2} \\times 3.14 \\times 20 = 31.4\\) cm. Small semicircle arc = \\(\\dfrac{1}{2} \\times 3.14 \\times 10 = 15.7\\) cm. The square has side 10 cm (matching the small semicircle diameter); the perimeter is made up of the large arc, two square sides exposed and the small arc cut-out, giving 31.4 + 15.7 + (square edges) = 77.1 cm. Answer: 77.1 cm.",
      "hints": ["Large semicircle diameter is 20 cm; find each arc length with \\(\\pi = 3.14\\).", "Add the large arc, the exposed straight sides of the square, and the small cut-out arc."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q12",
      "image_needed": true,
      "image_options": false,
      "image_page": 7,
      "image_bbox": [0.42, 0.16, 0.64, 0.3],
      "image_loc": "mushroom-shaped shaded figure (semicircle on a square with a semicircle cut-out), middle of page 7",
      "image_file": "q12.png",
      "notes": "Answer key Booklet A Q12: option 1 (77.1 cm)."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "The table shows the rates for renting a bicycle at a shop.<br>Daniel rented a bicycle at 8.20 a.m. What is the latest time Daniel must return his bicycle if he only has $20 to spend on rental fees?",
      "answer0": "10.20 a.m.",
      "answer1": "10.50 a.m.",
      "answer2": "11.20 a.m.",
      "answer3": "11.50 a.m.",
      "correct_answer": 1,
      "skill_id": 135,
      "difficulty_id": 3,
      "explanation": "First hour = $6, leaving $20 - $6 = $14 for the additional 30-minute blocks at $4 each. $14 \\(\\div\\) $4 = 3 blocks (3 \\(\\times\\) $4 = $12, leaving $2 which is not enough for another block). So 1 hour + 3 half-hours = 2 h 30 min. From 8.20 a.m. + 2 h 30 min = 10.50 a.m. Answer: 10.50 a.m.",
      "hints": ["Pay the first hour ($6) first, then see how many $4 half-hour blocks the rest buys.", "Add the total time to 8.20 a.m."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q13",
      "image_needed": true,
      "image_options": false,
      "image_page": 7,
      "image_bbox": [0.2, 0.5, 0.62, 0.57],
      "image_loc": "bicycle rental rates table in the middle of page 7",
      "image_file": "q13.png",
      "notes": "Answer key Booklet A Q13: option 2 (10.50 a.m.). Table: first hour $6; every additional 30 min or part thereof $4."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "Two figures PQRS and WXYZ are shown on the square grid. Which of the following statement(s) is/are true?<br>A. SR // WX<br>B. \\(\\angle SPQ = \\angle XYZ\\)<br>C. Figure PQRS and Figure WXYZ has the same perimeter.",
      "answer0": "A only",
      "answer1": "A and B only",
      "answer2": "A and C only",
      "answer3": "All the above",
      "correct_answer": 2,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "Reading the grid: SR is parallel to WX (A true). The two figures are made of the same edge lengths, so they have the same perimeter (C true). Angle SPQ is not equal to angle XYZ (B false). So A and C only. Answer: A and C only.",
      "hints": ["Use the grid to check whether SR and WX run in the same direction.", "Compare edge lengths to check the perimeters, and the marked angles for statement B."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q14",
      "image_needed": true,
      "image_options": false,
      "image_page": 8,
      "image_bbox": [0.18, 0.1, 0.86, 0.32],
      "image_loc": "two quadrilaterals PQRS and WXYZ on a square grid near top of page 8",
      "image_file": "q14.png",
      "notes": "Answer key Booklet A Q14: option 3 (A and C only)."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "Mollie had a container full of flour. Nellie and Ollie each had \\(\\dfrac{2}{7}\\) of what Mollie had. Mollie gave away some flour to Nellie and Ollie so that all 3 of them have the same amount of flour in the end. What fraction of flour did Mollie give away?",
      "answer0": "\\(\\dfrac{5}{7}\\)",
      "answer1": "\\(\\dfrac{5}{14}\\)",
      "answer2": "\\(\\dfrac{5}{21}\\)",
      "answer3": "\\(\\dfrac{10}{21}\\)",
      "correct_answer": 3,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Let Mollie have 1 (i.e. \\(\\dfrac{21}{21}\\)). Nellie = Ollie = \\(\\dfrac{2}{7} = \\dfrac{6}{21}\\) each. Total flour = \\(\\dfrac{21 + 6 + 6}{21} = \\dfrac{33}{21}\\). Shared equally, each gets \\(\\dfrac{33}{21} \\div 3 = \\dfrac{11}{21}\\). Mollie gave away \\(\\dfrac{21}{21} - \\dfrac{11}{21} = \\dfrac{10}{21}\\). Answer: \\(\\dfrac{10}{21}\\).",
      "hints": ["Let Mollie's amount be 1 (use 21 as a common denominator).", "Find the total flour, share it equally three ways, then see how much Mollie loses."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Booklet A Q15: option 4 (10/21). Fraction options so MCQ."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Find the value of \\(4.5 \\div 300\\). Ans: [?]",
      "answer0": "0.015",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 166,
      "difficulty_id": 2,
      "explanation": "Method: \\(4.5 \\div 3 = 1.5\\), then \\(1.5 \\div 100 = 0.015\\). Answer: 0.015.",
      "hints": ["Split 300 into 3 \\(\\times\\) 100.", "Divide by 3 first, then by 100."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Booklet B Q16: 4.5 / 300 = 0.015."
    },
    {
      "n": 17,
      "type_id": 1,
      "question": "Find the value of \\(\\dfrac{3}{8} \\times 12\\). Give your answer in its simplest form.",
      "answer0": "\\(4\\dfrac{1}{2}\\)",
      "answer1": "\\(4\\dfrac{1}{8}\\)",
      "answer2": "\\(3\\dfrac{1}{2}\\)",
      "answer3": "\\(\\dfrac{9}{8}\\)",
      "correct_answer": 0,
      "skill_id": 163,
      "difficulty_id": 2,
      "explanation": "Method: \\(\\dfrac{3}{8} \\times 12 = \\dfrac{3 \\times 12}{8} = \\dfrac{36}{8} = \\dfrac{9}{2} = 4\\dfrac{1}{2}\\). Answer: \\(4\\dfrac{1}{2}\\).",
      "hints": ["Multiply the numerator 3 by 12, keep the denominator 8.", "Simplify \\(\\dfrac{36}{8}\\) to a mixed number."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Booklet B Q17: 9/2 or 4 1/2. Mixed-number answer so converted to MCQ; correct option 1."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "A hairclip is placed next to a ruler. Find the length of the hairclip. Ans: [?] cm",
      "answer0": "6.8",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 85,
      "difficulty_id": 2,
      "explanation": "Method: read the two ends of the hairclip on the ruler. Each cm is divided into 5 parts, so each small mark = 0.4 cm. The hairclip runs from about 2 cm to 8.8 cm. Length = 8.8 - 2 = 6.8 cm. Answer: 6.8 cm.",
      "hints": ["Each centimetre is split into 5 equal parts (0.2 cm each on the marked working, read the end carefully).", "Subtract the start reading from the end reading."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q18",
      "image_needed": true,
      "image_options": false,
      "image_page": 10,
      "image_bbox": [0.16, 0.56, 0.72, 0.72],
      "image_loc": "hairclip drawn above a ruler (0 to 12 cm), lower-middle of page 10",
      "image_file": "q18.png",
      "notes": "Answer key Booklet B Q18: (8 + 2 x 0.4) - 2 = 8.8 - 2 = 6.8 cm."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "Benson took 210 min to complete a race. He was 25 min slower than Carson. How long did Carson take to complete the race? Give your answer in min. Ans: [?] min",
      "answer0": "185",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 76,
      "difficulty_id": 1,
      "explanation": "Method: Benson was slower, so Carson took less time. Carson = 210 - 25 = 185 min. Answer: 185 min.",
      "hints": ["Slower means more time, so Carson took less time than Benson.", "Subtract 25 min from 210 min."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q19",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Booklet B Q19: 210 - 25 = 185 min."
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "The figure shows a cuboid with a square base of area 25 cm². The area of the shaded face is 60 cm². What is the height of the cuboid? Ans: [?] cm",
      "answer0": "12",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 226,
      "difficulty_id": 2,
      "explanation": "Method: the square base has area 25 cm², so each base side = \\(\\sqrt{25}\\) = 5 cm. The shaded face is a rectangle = base side \\(\\times\\) height = 5 \\(\\times\\) height = 60, so height = 60 \\(\\div\\) 5 = 12 cm. Answer: 12 cm.",
      "hints": ["The square base side = \\(\\sqrt{25}\\) = 5 cm.", "The shaded side face area = 5 \\(\\times\\) height; divide 60 by 5."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q20",
      "image_needed": true,
      "image_options": false,
      "image_page": 11,
      "image_bbox": [0.55, 0.4, 0.74, 0.55],
      "image_loc": "cuboid with shaded face labelled 60 cm², middle-right of page 11",
      "image_file": "q20.png",
      "notes": "Answer key Booklet B Q20: side = sqrt(25) = 5; height = 60 / 5 = 12 cm."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "Find the value of \\(6 \\div 7\\). Round your answer to 2 decimal places. Ans: [?]",
      "answer0": "0.86",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 168,
      "difficulty_id": 2,
      "explanation": "Method: \\(6 \\div 7 = 0.857...\\); rounded to 2 decimal places = 0.86 (the third decimal 7 rounds the 5 up to 6). Answer: 0.86.",
      "hints": ["Divide 6 by 7 to get 0.857...", "Round to 2 decimal places: look at the third decimal digit."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Booklet B Q21: 6 / 7 = 0.857... = 0.86."
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "Jason used a calculator to divide a 4-digit number by a 1-digit number. For the 1-digit number, he made a mistake by pressing 6 instead of 7. He obtained an incorrect answer of 210. What should be the correct answer? Ans: [?]",
      "answer0": "180",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 76,
      "difficulty_id": 2,
      "explanation": "Method: recover the 4-digit number from the wrong division, then divide correctly. The 4-digit number = 210 \\(\\times\\) 6 = 1260. The correct answer = 1260 \\(\\div\\) 7 = 180. Answer: 180.",
      "hints": ["Find the original 4-digit number by multiplying the wrong answer by 6.", "Divide that number by 7 to get the correct answer."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q22",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Booklet B Q22 final ANS: 180 (1260 / 7 = 180). The key's working line '1260 / 7 = 188' is a typo; 7 x 180 = 1260, so 180 is correct."
    },
    {
      "n": 23,
      "type_id": 1,
      "question": "The table shows the number of visitors to Bird Paradise.<br>Monday to Friday: 3p each day; Saturday: 6p + 70; Sunday: 9p - 25.<br>(a) What was the total number of visitors to Bird Paradise in the week? Express your answer in terms of p in the simplest form.",
      "answer0": "30p + 45",
      "answer1": "18p + 45",
      "answer2": "30p + 95",
      "answer3": "15p + 45",
      "correct_answer": 0,
      "skill_id": 239,
      "difficulty_id": 2,
      "explanation": "Method: Monday to Friday total = 5 \\(\\times\\) 3p = 15p. Add Saturday and Sunday: 15p + (6p + 70) + (9p - 25) = 15p + 6p + 9p + 70 - 25 = 30p + 45. Answer: 30p + 45.",
      "hints": ["Monday to Friday is 5 days of 3p each = 15p.", "Add the Saturday and Sunday expressions and combine like terms."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q23a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Booklet B Q23a: 15p + (6p+70) + (9p-25) = 30p + 45. Algebraic expression answer so converted to MCQ; correct option 1."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "The table shows the number of visitors to Bird Paradise.<br>Monday to Friday: 3p each day; Saturday: 6p + 70; Sunday: 9p - 25.<br>The total number of visitors to Bird Paradise in the week was 7395. Find the value of p. Ans: [?]",
      "answer0": "245",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 2,
      "explanation": "Method: use the total expression 30p + 45 = 7395. So 30p = 7395 - 45 = 7350; p = 7350 \\(\\div\\) 30 = 245. Answer: 245.",
      "hints": ["Set the total expression 30p + 45 equal to 7395.", "Subtract 45, then divide by 30."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q23b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Booklet B Q23b: 30p + 45 = 7395; 30p = 7350; p = 245."
    },
    {
      "n": 25,
      "type_id": 1,
      "question": "The pie chart represents the type of sports the Primary 6 students liked. The number of students who liked bowling is the same as those who liked cycling. Basketball is 32% and Rugby is 28%.<br>What is the percentage of students who liked bowling?",
      "answer0": "20%",
      "answer1": "18%",
      "answer2": "22%",
      "answer3": "40%",
      "correct_answer": 0,
      "skill_id": 235,
      "difficulty_id": 2,
      "explanation": "Method: bowling + cycling = 100% - basketball - rugby = 100% - 32% - 28% = 40%. Since bowling = cycling, each = 40% \\(\\div\\) 2 = 20%. Answer: 20%.",
      "hints": ["Bowling and cycling together make up the rest of the 100% after basketball and rugby.", "Bowling = cycling, so split that remainder in half."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q24a",
      "image_needed": true,
      "image_options": false,
      "image_page": 14,
      "image_bbox": [0.35, 0.13, 0.66, 0.37],
      "image_loc": "pie chart (Cycling, Basketball 32%, Rugby 28%, Bowling) middle-top of page 14",
      "image_file": "q25.png",
      "notes": "Answer key Booklet B Q24a: (100-28-32)/2 = 20%. Made MCQ to split the multi-part item; correct option 1."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "The pie chart represents the type of sports the Primary 6 students liked. The number of students who liked bowling is the same as those who liked cycling. Basketball is 32% and Rugby is 28%.<br>There were 10 more students who liked basketball than rugby. What was the total number of Primary 6 students? Ans: [?]",
      "answer0": "250",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Method: the difference 32% - 28% = 4% corresponds to 10 students. So 1% = 10 \\(\\div\\) 4 = 2.5 students; 100% = 2.5 \\(\\times\\) 100 = 250. Answer: 250.",
      "hints": ["The 4% difference equals 10 students.", "Find 1% then multiply by 100 for the total."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q24b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Booklet B Q24b: 32%-28%=4% -> 10; 100% -> 10/4 x 100 = 250."
    },
    {
      "n": 27,
      "type_id": 0,
      "question": "The figure is made up of squares. Shade two more squares so that the figure has a line of symmetry.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 145,
      "difficulty_id": 2,
      "explanation": "Shade the two squares that mirror the existing shaded squares across the horizontal line of symmetry so the pattern is symmetric top-to-bottom. (See the answer-key figure.)",
      "hints": ["Find the line of symmetry that the shading should follow.", "Each shaded square needs a matching shaded square on the other side of the line."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q25",
      "image_needed": true,
      "image_options": false,
      "image_page": 15,
      "image_bbox": [0.34, 0.1, 0.66, 0.32],
      "image_loc": "grid of shaded/unshaded squares, top of page 15",
      "image_file": "q27.png",
      "notes": "Interactive shade-the-squares task; type_id 0 (skipped on insert). Answer key: shade to make a horizontal line of symmetry (see figure)."
    },
    {
      "n": 28,
      "type_id": 1,
      "question": "The square grid shows the plan of a playground. The rocking horse is north of the see-saw.<br>In which direction is the rocking horse from the swing?",
      "answer0": "North",
      "answer1": "South",
      "answer2": "East",
      "answer3": "West",
      "correct_answer": 2,
      "skill_id": 142,
      "difficulty_id": 1,
      "explanation": "Method: on the plan, the swing is in the top-left corner and the rocking horse is in the top-right corner, on the same row. Moving from the swing to the rocking horse is moving to the right, which is East. Answer: East.",
      "hints": ["Locate the swing and the rocking horse on the grid.", "They are on the same row; moving right is East."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q26a",
      "image_needed": true,
      "image_options": false,
      "image_page": 15,
      "image_bbox": [0.28, 0.42, 0.62, 0.74],
      "image_loc": "4x4 playground plan grid (Swing, Slide, Rocking horse, See-saw, Roundabout), middle of page 15",
      "image_file": "q28.png",
      "notes": "Answer key Booklet B Q26a: East. Made MCQ; correct option 3. Part (b) 'put a cross in the square' is an interactive task and is omitted."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "The bar graph shows the amount of rainfall each month from Jul to Dec in 2024.<br>(a) What is the difference between the highest amount of rainfall in a month and the lowest amount of rainfall in a month? Ans: [?] mm",
      "answer0": "150",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 104,
      "difficulty_id": 2,
      "explanation": "Method: read the tallest and shortest bars. The highest is December at 290 mm; the lowest is September at 140 mm. Difference = 290 - 140 = 150 mm. Answer: 150 mm.",
      "hints": ["Find the tallest bar (highest rainfall) and the shortest bar (lowest rainfall).", "Subtract the lowest from the highest."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q27a",
      "image_needed": true,
      "image_options": false,
      "image_page": 16,
      "image_bbox": [0.2, 0.1, 0.82, 0.37],
      "image_loc": "bar graph of monthly rainfall Jul-Dec, upper half of page 16",
      "image_file": "q29.png",
      "notes": "Answer key Booklet B Q27a: 290 - 140 = 150 mm."
    },
    {
      "n": 30,
      "type_id": 2,
      "question": "The bar graph shows the amount of rainfall each month from Jul to Dec in 2024. Aug rainfall is 160 mm and Sep rainfall is 140 mm.<br>(b) What is the percentage decrease in rainfall in Sep as compared to Aug? Ans: [?]%",
      "answer0": "12.5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 208,
      "difficulty_id": 2,
      "explanation": "Method: percentage decrease = (decrease \\(\\div\\) original) \\(\\times\\) 100%. Decrease = 160 - 140 = 20 mm. \\(\\dfrac{20}{160} \\times 100\\% = 12.5\\%\\). Answer: 12.5%.",
      "hints": ["The decrease is from Aug (160) to Sep (140).", "Percentage decrease = decrease \\(\\div\\) the Aug value \\(\\times\\) 100%."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q27b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Booklet B Q27b: (160-140)/160 x 100% = 12.5%."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "During a sale, a store gave a storewide discount of 20%. Darryl signed up as a member and received an additional 10% discount on the discounted price. He paid $720 for the coffee machine. What was the total amount of his discount? Ans: $[?]",
      "answer0": "280",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 207,
      "difficulty_id": 3,
      "explanation": "Method: work backwards through each discount. After the member's 10% off, $720 is 90% of the discounted price, so discounted price = $720 \\(\\div\\) 0.9 = $800. The $800 is 80% of the marked price (20% storewide off), so marked price = $800 \\(\\div\\) 0.8 = $1000. Total discount = $1000 - $720 = $280. Answer: $280.",
      "hints": ["$720 is 90% of the price after the storewide discount; find that price first.", "That price is 80% of the original; find the original, then subtract $720."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q28",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Booklet B Q28: $720/90% = $800; $800/80% = $1000; $1000 - $720 = $280."
    },
    {
      "n": 32,
      "type_id": 2,
      "question": "Nancy had a rectangular piece of paper. She folded along the line AB as shown. \\(\\angle x = 124^\\circ\\). Find \\(\\angle y\\). Ans: [?]°",
      "answer0": "68",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "Method: the angle on the other side of the straight line at B is 180° - 124° = 56°. The fold makes two equal angles, so \\(\\angle y = 180^\\circ - 2 \\times 56^\\circ = 180^\\circ - 112^\\circ = 68^\\circ\\). Answer: 68°.",
      "hints": ["Find the angle next to \\(\\angle x\\) on the straight line (180° - 124°).", "The fold creates two equal angles; use the angle sum to find \\(\\angle y\\)."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q29",
      "image_needed": true,
      "image_options": false,
      "image_page": 17,
      "image_bbox": [0.18, 0.46, 0.82, 0.66],
      "image_loc": "before-and-after folding diagrams of the rectangular paper, middle of page 17",
      "image_file": "q32.png",
      "notes": "Answer key Booklet B Q29: 180-124=56; y = 180 - 2x56 = 68."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "Lisha used 16 identical right-angled triangle tiles to form a rectangle. The perimeter of the rectangle is 80 cm. Find the area of one triangle. Ans: [?] cm²",
      "answer0": "24",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Method: let the two perpendicular sides of each triangle be u and 3u. The rectangle's perimeter is 2 \\(\\times\\) (6u + 4u) = 80, so 20u = 80, u = 4. The triangle sides are 4 cm and 12 cm. Area of one triangle = \\(\\dfrac{1}{2} \\times 4 \\times 12 = 24\\) cm². Answer: 24 cm².",
      "hints": ["Use the arrangement to write the rectangle's sides in terms of one unit u.", "Solve the perimeter equation for u, then use \\(\\dfrac{1}{2} \\times\\) base \\(\\times\\) height for one triangle."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 1 Q30",
      "image_needed": true,
      "image_options": false,
      "image_page": 18,
      "image_bbox": [0.21, 0.13, 0.46, 0.27],
      "image_loc": "rectangle made of 16 right-angled triangle tiles, top-left of page 18",
      "image_file": "q33.png",
      "notes": "Answer key Booklet B Q30: 20u = 80, u = 4; area = 0.5 x 4 x 12 = 24 cm²."
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "Samad saves $2.50 every day. For every $15 saved, his father will give him an additional $3. How much money will Samad save in 50 days? Ans: $[?]",
      "answer0": "149",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Method: find how many full $15 savings periods occur. Saving $15 takes $15 \\(\\div\\) $2.50 = 6 days, and each such period earns an extra $3, giving $18 per 6 days. In 50 days: 50 \\(\\div\\) 6 = 8 full periods with 2 days left over. Total = 8 \\(\\times\\) $18 + 2 \\(\\times\\) $2.50 = $144 + $5 = $149. Answer: $149.",
      "hints": ["Saving $15 takes 6 days and earns an extra $3 (so $18 per 6 days).", "Find how many full 6-day periods fit in 50 days, then add the leftover days at $2.50."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Paper 2 Q1: 50/6 = 8 R 2; 8 x $18 + 2 x $2.50 = $149."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "Eric gives \\(\\dfrac{1}{4}\\) of his income to his parents. When his income increased by 20%, his parents received $240 more. What is his income before the increase? Ans: $[?]",
      "answer0": "4800",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Method: the parents get \\(\\dfrac{1}{4}\\) of income, so a 20% rise in income raises their share by 20% too. The $240 extra is 20% of the original amount Eric gave his parents, so that amount = $240 \\(\\div\\) 0.2 = $1200. Since this is \\(\\dfrac{1}{4}\\) of his income, his income = $1200 \\(\\times\\) 4 = $4800. Answer: $4800.",
      "hints": ["The $240 extra is 20% of what Eric originally gave his parents.", "Find that original amount, then multiply by 4 (it is a quarter of his income)."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 2 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Paper 2 Q2: 20% -> $240; 100% -> $1200; income = $1200 x 4 = $4800."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "In the figure, PQRS is a rectangle. RTUV is a rhombus. \\(\\angle RTU = 122^\\circ\\) and \\(\\angle VRS = 256^\\circ\\). Find \\(\\angle QRT\\). Ans: [?]°",
      "answer0": "44",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "Method: \\(\\angle VRQ = 360^\\circ - 256^\\circ - 90^\\circ = 14^\\circ\\) (using the reflex 256° and the right angle of the rectangle at R). In the rhombus, \\(\\angle VRT\\) relates to \\(\\angle RTU = 122^\\circ\\), so \\(\\angle QRT = 180^\\circ - 122^\\circ - 14^\\circ = 44^\\circ\\). Answer: 44°.",
      "hints": ["Use angles at a point (360°) and the rectangle's right angle to find \\(\\angle VRQ\\).", "Use the rhombus angle and the angle sum to reach \\(\\angle QRT\\)."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 2 Q3",
      "image_needed": true,
      "image_options": false,
      "image_page": 21,
      "image_bbox": [0.22, 0.12, 0.74, 0.34],
      "image_loc": "rectangle PQRS with rhombus RTUV figure, upper part of page 21",
      "image_file": "q36.png",
      "notes": "Answer key Paper 2 Q3: angle VRQ = 360-256-90 = 14; angle QRT = 180-122-14 = 44."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "The average of four different 2-digit numbers is 92. Of the four numbers, find the smallest possible number. Ans: [?]",
      "answer0": "74",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 204,
      "difficulty_id": 3,
      "explanation": "Method: total of the four numbers = 92 \\(\\times\\) 4 = 368. To make one number as small as possible, make the other three as large as possible: the three largest different 2-digit numbers are 99, 98, 97. Smallest = 368 - (99 + 98 + 97) = 368 - 294 = 74. Answer: 74.",
      "hints": ["Total = average \\(\\times\\) 4 = 368.", "Make the other three numbers the largest possible 2-digit numbers (99, 98, 97)."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 2 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Paper 2 Q4: total 368; 368 - (99+98+97) = 74."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "The solid is made up of 8 cubes.<br>What is the maximum number of cubes that can be added to the solid without changing the front view and side view? Ans: [?]",
      "answer0": "8",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 188,
      "difficulty_id": 3,
      "explanation": "Method: cubes may be added only where they do not stick out beyond the existing front view or side view outline. Filling all the hidden positions that keep both silhouettes unchanged allows 8 more cubes. Answer: 8.",
      "hints": ["Added cubes must not change the front or side silhouette.", "Fill every hidden position behind or beside the existing cubes that stays within both views."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 2 Q5b",
      "image_needed": true,
      "image_options": false,
      "image_page": 22,
      "image_bbox": [0.3, 0.1, 0.66, 0.3],
      "image_loc": "isometric drawing of 8-cube solid with Top/Front/Side view arrows, top of page 22",
      "image_file": "q38.png",
      "notes": "Answer key Paper 2 Q5b: 8 cubes. Part (a) 'draw the front view on the grid' is an interactive drawing task and is omitted."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "The pie chart shows how Isabelle spent her money. Transport is 24%.<br>The amount of money Isabelle spent on transport is \\(\\dfrac{2}{5}\\) of the amount she spent on food.<br>(a) What is the percentage of Isabelle's money spent on food? Ans: [?]%",
      "answer0": "60",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 174,
      "difficulty_id": 2,
      "explanation": "Method: transport is \\(\\dfrac{2}{5}\\) of food, so food = transport \\(\\div \\dfrac{2}{5}\\) = transport \\(\\times \\dfrac{5}{2}\\). Food = 24% \\(\\times \\dfrac{5}{2}\\) = 12% \\(\\times\\) 5 = 60%. Answer: 60%.",
      "hints": ["If transport is \\(\\dfrac{2}{5}\\) of food, then food = transport \\(\\times \\dfrac{5}{2}\\).", "Multiply 24% by \\(\\dfrac{5}{2}\\)."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 2 Q6a",
      "image_needed": true,
      "image_options": false,
      "image_page": 23,
      "image_bbox": [0.34, 0.16, 0.66, 0.4],
      "image_loc": "pie chart (Clothes, Transport 24%, Savings, Food), upper part of page 23",
      "image_file": "q39.png",
      "notes": "Answer key Paper 2 Q6a: 24% / (2/5) = 60%."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "The pie chart shows how Isabelle spent her money. Transport is 24% and Food is 60%.<br>The amount of money Isabelle saved is 25% of the amount she spent on transport.<br>(b) Isabelle saved $90. How much money did she spend in total? Ans: $[?]",
      "answer0": "1410",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 207,
      "difficulty_id": 3,
      "explanation": "Method: savings = 25% of transport (24%) = \\(\\dfrac{25}{100} \\times 24\\% = 6\\%\\) of her total money. Savings = 6% = $90, so 1% = $90 \\(\\div\\) 6 = $15. The money she spent (not saved) = 100% - 6% = 94% = $15 \\(\\times\\) 94 = $1410. Answer: $1410.",
      "hints": ["Savings is 25% of the 24% transport share, which is 6% of the total.", "6% = $90, so find 1%, then take the 94% she spent."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 2 Q6b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Paper 2 Q6b: savings 6% = $90; spent = 94% = $1410. (Question asks money spent in total = total minus savings.)"
    },
    {
      "n": 41,
      "type_id": 1,
      "question": "A rectangular tank measuring 80 cm by 60 cm by 50 cm was \\(\\dfrac{2}{3}\\) full of water. Tap A can fill the empty tank in 8 minutes. How long did it take to fill the tank completely?",
      "answer0": "\\(2\\dfrac{2}{3}\\) min",
      "answer1": "\\(5\\dfrac{1}{3}\\) min",
      "answer2": "\\(2\\dfrac{1}{3}\\) min",
      "answer3": "3 min",
      "correct_answer": 0,
      "skill_id": 193,
      "difficulty_id": 2,
      "explanation": "Method: the tank is \\(\\dfrac{2}{3}\\) full, so \\(\\dfrac{1}{3}\\) is still empty. Filling the whole tank takes 8 min, so filling \\(\\dfrac{1}{3}\\) takes 8 \\(\\times \\dfrac{1}{3} = \\dfrac{8}{3} = 2\\dfrac{2}{3}\\) min (2 minutes 40 seconds). Answer: \\(2\\dfrac{2}{3}\\) min.",
      "hints": ["Only \\(\\dfrac{1}{3}\\) of the tank still needs filling.", "Multiply the full-fill time (8 min) by \\(\\dfrac{1}{3}\\)."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 2 Q7",
      "image_needed": true,
      "image_options": false,
      "image_page": 24,
      "image_bbox": [0.4, 0.13, 0.78, 0.32],
      "image_loc": "rectangular tank with Tap A above it, upper part of page 24",
      "image_file": "q41.png",
      "notes": "Answer key Paper 2 Q7: 8 x 1/3 = 8/3 = 2 2/3 min = 2 min 40 s. Mixed-number answer so converted to MCQ; correct option 1."
    },
    {
      "n": 42,
      "type_id": 1,
      "question": "Frank's mass is \\(y\\) kg. His mass is \\(\\dfrac{1}{3}\\) of Gideon's mass. Henry is 4 kg lighter than Gideon.<br>(a) What is the total mass of the 3 boys in terms of \\(y\\)?",
      "answer0": "\\((7y - 4)\\) kg",
      "answer1": "\\((5y - 4)\\) kg",
      "answer2": "\\((7y + 4)\\) kg",
      "answer3": "\\((3y - 4)\\) kg",
      "correct_answer": 0,
      "skill_id": 239,
      "difficulty_id": 2,
      "explanation": "Method: Frank = y; Gideon = 3y (since Frank is \\(\\dfrac{1}{3}\\) of Gideon); Henry = Gideon - 4 = 3y - 4. Total = y + 3y + (3y - 4) = 7y - 4. Answer: \\((7y - 4)\\) kg.",
      "hints": ["Gideon = 3 \\(\\times\\) Frank = 3y; Henry = Gideon - 4.", "Add all three masses and combine like terms."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 2 Q8a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Paper 2 Q8a: y + 3y + (3y-4) = 7y - 4. Algebraic answer so converted to MCQ; correct option 1."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "Frank's mass is \\(y\\) kg. His mass is \\(\\dfrac{1}{3}\\) of Gideon's mass. Henry is 4 kg lighter than Gideon.<br>(b) If Frank's mass is 28 kg, what is the difference between Frank's mass and Henry's mass? Ans: [?] kg",
      "answer0": "52",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 2,
      "explanation": "Method: Henry = 3y - 4 and Frank = y, so the difference = (3y - 4) - y = 2y - 4. With y = 28: 2(28) - 4 = 56 - 4 = 52 kg. Answer: 52 kg.",
      "hints": ["Difference = Henry - Frank = (3y - 4) - y = 2y - 4.", "Substitute y = 28."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 2 Q8b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Paper 2 Q8b: 2y - 4 = 2(28) - 4 = 52 kg."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "In the square grid, ABC is a triangle. Measure \\(\\angle ACB\\). Ans: [?]°",
      "answer0": "36",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 140,
      "difficulty_id": 2,
      "explanation": "Method: measure the angle at vertex C between CA and CB using a protractor. \\(\\angle ACB = 36^\\circ\\). Answer: 36°.",
      "hints": ["Place the protractor centre at C with the baseline along CB.", "Read the angle up to CA."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 2 Q9a",
      "image_needed": true,
      "image_options": false,
      "image_page": 25,
      "image_bbox": [0.18, 0.55, 0.62, 0.86],
      "image_loc": "triangle ABC on a square grid, lower part of page 25",
      "image_file": "q44.png",
      "notes": "Answer key Paper 2 Q9a: angle ACB = 36°. Part (b) 'complete the trapezium' is an interactive drawing task and is omitted."
    },
    {
      "n": 45,
      "type_id": 1,
      "question": "A shop offered 120 T-shirts at a 20% discount during a 7-day sale. The line graph shows the number of T-shirts left unsold at the end of each day.<br>(a) On which day was the most number of T-shirts sold?",
      "answer0": "Day 1",
      "answer1": "Day 2",
      "answer2": "Day 3",
      "answer3": "Day 4",
      "correct_answer": 3,
      "skill_id": 147,
      "difficulty_id": 2,
      "explanation": "Method: the most T-shirts were sold on the day the line drops the steepest. The biggest fall in 'unsold' happens on Day 4. Answer: Day 4.",
      "hints": ["Look for the steepest downward step in the graph.", "The largest drop in unsold T-shirts is the day with the most sold (Day 4)."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 2 Q10a",
      "image_needed": true,
      "image_options": false,
      "image_page": 26,
      "image_bbox": [0.16, 0.13, 0.84, 0.4],
      "image_loc": "line graph of unsold T-shirts over Start of Sale to Day 7, upper part of page 26",
      "image_file": "q45.png",
      "notes": "Answer key Paper 2 Q10a: Day 4. Made MCQ; correct option 4."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "A shop offered 120 T-shirts at a 20% discount during a 7-day sale. The line graph shows the number of T-shirts left unsold at the end of each day.<br>(b) What percentage of 120 T-shirts were sold in the first 5 days of the sale? Correct your answer to the nearest percent. Ans: [?]%",
      "answer0": "83",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 174,
      "difficulty_id": 2,
      "explanation": "Method: at the end of Day 5, 20 T-shirts were left unsold, so 120 - 20 = 100 were sold. Percentage = \\(\\dfrac{100}{120} \\times 100\\% = 83.3...\\% \\approx 83\\%\\) (nearest percent). Answer: 83%.",
      "hints": ["Read the unsold value at Day 5 (20) and subtract from 120 to get sold.", "Percentage sold = sold \\(\\div\\) 120 \\(\\times\\) 100%, rounded to the nearest percent."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 2 Q10b",
      "image_needed": true,
      "image_options": false,
      "image_page": 26,
      "image_bbox": [0.16, 0.13, 0.84, 0.4],
      "image_loc": "same line graph of unsold T-shirts, upper part of page 26",
      "image_file": "q46.png",
      "notes": "Answer key Paper 2 Q10b: (120-20)/120 x 100% = 83% (nearest percent). Shares the same graph figure as Q45."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "A shop offered 120 T-shirts at a 20% discount during a 7-day sale. The line graph shows the number of T-shirts left unsold at the end of each day.<br>(c) The shop collected $192 on Day 3 of the sale. What was the price of each T-shirt before the discount? Ans: $[?]",
      "answer0": "15",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 3,
      "explanation": "Method: from the graph, T-shirts sold on Day 3 = 76 - 60 = 16. Discounted price each = $192 \\(\\div\\) 16 = $12. This is after a 20% discount, so $12 is 80% of the original; original = $12 \\(\\div\\) 0.8 = $15. Answer: $15.",
      "hints": ["Find the T-shirts sold on Day 3 from the graph (drop from 76 to 60).", "Get the discounted price each, then divide by 80% for the original price."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 2 Q10c",
      "image_needed": true,
      "image_options": false,
      "image_page": 26,
      "image_bbox": [0.16, 0.13, 0.84, 0.4],
      "image_loc": "same line graph of unsold T-shirts, upper part of page 26",
      "image_file": "q47.png",
      "notes": "Answer key Paper 2 Q10c: Day 3 sold = 76-60 = 16; $192/16 = $12; $12/80% = $15. Shares the graph figure with Q45/Q46."
    },
    {
      "n": 48,
      "type_id": 2,
      "question": "Ray and Wayne ran in a race around a 400-m track. Ray ran at a speed of 195 m/min and Wayne at a speed that was 25 m/min slower than Ray throughout the race.<br>(a) How long would it take Ray to run a distance of 350 m more than Wayne? Ans: [?] min",
      "answer0": "14",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 217,
      "difficulty_id": 3,
      "explanation": "Method: every minute, Ray gains (195 - (195 - 25)) = 25 m on Wayne. To gain 350 m, time = 350 \\(\\div\\) 25 = 14 min. Answer: 14 min.",
      "hints": ["Each minute Ray gains 25 m on Wayne (the speed difference).", "Divide 350 m by 25 m/min."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 2 Q11a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Paper 2 Q11a: 350 / 25 = 14 min."
    },
    {
      "n": 49,
      "type_id": 2,
      "question": "Ray and Wayne ran in a race around a 400-m track. Ray ran at a speed of 195 m/min and Wayne at a speed that was 25 m/min slower than Ray throughout the race.<br>(b) How many complete rounds would Ray have finished when the above happened? Ans: [?]",
      "answer0": "6",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 219,
      "difficulty_id": 3,
      "explanation": "Method: in 14 min, Ray runs 195 \\(\\times\\) 14 = 2730 m. Number of rounds = 2730 \\(\\div\\) 400 = 6.825, so Ray finished 6 complete rounds. Answer: 6.",
      "hints": ["Distance Ray runs = speed \\(\\times\\) time = 195 \\(\\times\\) 14.", "Divide by 400 m and take only the whole-number (complete) rounds."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 2 Q11b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Paper 2 Q11b: 195 x 14 = 2730 m; 2730/400 = 6.825 -> 6 complete rounds."
    },
    {
      "n": 50,
      "type_id": 2,
      "question": "In the figure, five squares are drawn within a rectangular piece of paper. The left-over part of the paper is shaded. The side of square X measures 4 cm.<br>(a) What is the length of the side of square Y? Ans: [?] cm",
      "answer0": "2",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 138,
      "difficulty_id": 2,
      "explanation": "Method: from the figure, square Y's side is half of square X's side. Side of Y = 4 \\(\\div\\) 2 = 2 cm. Answer: 2 cm.",
      "hints": ["Compare square Y's side with square X's side in the figure.", "Y's side is half of X's side."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 2 Q12a",
      "image_needed": true,
      "image_options": false,
      "image_page": 28,
      "image_bbox": [0.24, 0.08, 0.66, 0.22],
      "image_loc": "rectangle with five squares (X and Y labelled), top of page 28",
      "image_file": "q50.png",
      "notes": "Answer key Paper 2 Q12a: side of Y = 4 / 2 = 2 cm."
    },
    {
      "n": 51,
      "type_id": 2,
      "question": "In the figure, five squares are drawn within a rectangular piece of paper. The left-over part of the paper is shaded. The side of square X measures 4 cm.<br>(b) The breadth of the left-over paper is 1.5 cm. What is the length of the rectangular piece of paper? Ans: [?] cm",
      "answer0": "17.5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 138,
      "difficulty_id": 3,
      "explanation": "Method: work along the length using the square sizes. From Y (2 cm) and X (4 cm): 2 + 4 = 6, 6 + 4 = 10. The length = the largest square row (10) + 4 + 2 + the 1.5 cm leftover strip = 10 + 4 + 2 + 1.5 = 17.5 cm. Answer: 17.5 cm.",
      "hints": ["Use the side lengths of the squares (2 cm, 4 cm, ...) to build up the length.", "Add the 1.5 cm left-over strip at the end."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 2 Q12b",
      "image_needed": true,
      "image_options": false,
      "image_page": 28,
      "image_bbox": [0.24, 0.08, 0.66, 0.22],
      "image_loc": "same five-squares rectangle figure, top of page 28",
      "image_file": "q51.png",
      "notes": "Answer key Paper 2 Q12b: 2+4=6, 6+4=10; 10+4+2+1.5 = 17.5 cm. Shares figure with Q50."
    },
    {
      "n": 52,
      "type_id": 2,
      "question": "In the figure, five squares are drawn within a rectangular piece of paper. The side of square X measures 4 cm.<br>(c) Paul cut out each of the five squares on the rectangular paper into 2-cm squares. He then used the 2-cm squares to form cubes. What is the greatest number of cubes Paul can make? Ans: [?]",
      "answer0": "6",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 234,
      "difficulty_id": 3,
      "explanation": "Method: count 2-cm squares from each big square. A 2 cm square gives 1; a 4 cm square gives 4; a 6 cm square gives 9; a 10 cm square gives 25. The five squares give: 25 + 9 + 4 + (the two smaller) = 40 small squares in total. Each cube needs 6 faces, so 40 \\(\\div\\) 6 = 6 remainder 4 → 6 complete cubes. Answer: 6.",
      "hints": ["Each big square of side n cm gives \\((n \\div 2)^2\\) small 2-cm squares.", "Total the 2-cm squares, then divide by 6 (a cube has 6 faces)."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 2 Q12c",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Paper 2 Q12c: 2-cm squares total 25+9+4+2 = 40; 40/6 = 6 R 4 -> 6 cubes."
    },
    {
      "n": 53,
      "type_id": 2,
      "question": "In the figure, ABCD is a rhombus and ADEF is a trapezium. AF is parallel to DE. \\(\\angle\\) at F is 21° and \\(\\angle\\) at C is 108° and the angle 33° is marked at A.<br>(a) Find \\(\\angle x\\). Ans: [?]°",
      "answer0": "18",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "Method: in the rhombus, \\(\\angle ABD = \\angle CBD = \\angle CDB = (180^\\circ - 108^\\circ) \\div 2 = 36^\\circ\\). Then \\(\\angle x = \\angle BHA = 36^\\circ \\div 2 = 18^\\circ\\). Answer: 18°.",
      "hints": ["Use the rhombus property: the 108° angle gives base angles of (180 - 108) \\(\\div\\) 2 = 36°.", "\\(\\angle x\\) is half of 36°."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 2 Q13a",
      "image_needed": true,
      "image_options": false,
      "image_page": 29,
      "image_bbox": [0.2, 0.1, 0.7, 0.36],
      "image_loc": "rhombus ABCD and trapezium ADEF figure with labelled angles, upper part of page 29",
      "image_file": "q53.png",
      "notes": "Answer key Paper 2 Q13a: angle ABD=CBD=CDB=(180-108)/2=36; x = 36/2 = 18."
    },
    {
      "n": 54,
      "type_id": 2,
      "question": "In the figure, ABCD is a rhombus and ADEF is a trapezium. AF is parallel to DE. The angle at F is 21°, the angle at C is 108° and the angle 33° is marked at A.<br>(b) Find \\(\\angle y\\). Ans: [?]°",
      "answer0": "126",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "Method: \\(\\angle AFD = \\angle FAB = 33^\\circ\\). \\(\\angle AFE = \\angle AFD + \\angle DFE = 33^\\circ + 21^\\circ = 54^\\circ\\). Since AF is parallel to DE, \\(\\angle y = \\angle DEF = 180^\\circ - 54^\\circ = 126^\\circ\\) (co-interior angles). Answer: 126°.",
      "hints": ["Find \\(\\angle AFE\\) by adding 33° and 21°.", "AF // DE means \\(\\angle y\\) and \\(\\angle AFE\\) are co-interior angles summing to 180°."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 2 Q13b",
      "image_needed": true,
      "image_options": false,
      "image_page": 29,
      "image_bbox": [0.2, 0.1, 0.7, 0.36],
      "image_loc": "same rhombus-and-trapezium figure, upper part of page 29",
      "image_file": "q54.png",
      "notes": "Answer key Paper 2 Q13b: angle AFE = 33+21 = 54; y = 180 - 54 = 126. Shares figure with Q53."
    },
    {
      "n": 55,
      "type_id": 1,
      "question": "There were almond and chocolate cookies in a container. Mrs Tan took out 35 almond cookies and 60% of the chocolate cookies. After that, the ratio of the number of almond cookies to the number of chocolate cookies in the container was 2 : 5.<br>(a) What fraction of chocolate cookies did Mrs Tan take out from the container? Give your answer in the simplest form.",
      "answer0": "\\(\\dfrac{3}{5}\\)",
      "answer1": "\\(\\dfrac{2}{5}\\)",
      "answer2": "\\(\\dfrac{3}{10}\\)",
      "answer3": "\\(\\dfrac{6}{10}\\)",
      "correct_answer": 0,
      "skill_id": 212,
      "difficulty_id": 1,
      "explanation": "Method: 60% taken out = \\(\\dfrac{60}{100} = \\dfrac{3}{5}\\) in simplest form. Answer: \\(\\dfrac{3}{5}\\).",
      "hints": ["60% as a fraction is \\(\\dfrac{60}{100}\\).", "Simplify \\(\\dfrac{60}{100}\\) by dividing top and bottom by 20."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 2 Q14a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Paper 2 Q14a: 60% = 60/100 = 3/5. Fraction answer so converted to MCQ; correct option 1."
    },
    {
      "n": 56,
      "type_id": 2,
      "question": "There were almond and chocolate cookies in a container. Mrs Tan took out 35 almond cookies and 60% of the chocolate cookies. After that, the ratio of the number of almond cookies to the number of chocolate cookies in the container was 2 : 5.<br>(b) Mrs Tan had 154 more chocolate cookies than almond cookies at first. How many almond and chocolate cookies were left in the container in the end? Ans: [?]",
      "answer0": "126",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "Method: at the end almond : chocolate = 2 : 5, so let almond left = 4u, chocolate left = 10u (using 2u and 5u doubled to match the 60% removal: chocolate at first = 10u \\(\\div\\) 40% = 25u, since 40% remains). Then almond at first = 4u + 35. The difference at first: 25u - (4u + 35) = 154, so 21u = 189, u = 9. Cookies left = almond left + chocolate left = 4u + 10u = 14u = 14 \\(\\times\\) 9 = 126. Answer: 126.",
      "hints": ["Chocolate left is 40% of the original chocolate; set the end ratio with units that account for that.", "Use the 154 difference at first to solve for the unit, then total the cookies left (14u)."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 2 Q14b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Paper 2 Q14b: end almond 4u, chocolate 10u; first chocolate 25u, almond 4u+35; 25u-(4u+35)=154; 21u=189; u=9; left = 14u = 126."
    },
    {
      "n": 57,
      "type_id": 2,
      "question": "Figure OABCD is formed by overlapping 2 similar quarter circles OAC and OBD. OA = OB = OC = OD = 10 cm. The area of the shaded part OBC is 30 cm² and the perimeter of the shaded part OBC is 26 cm.<br>(a) Find the area of figure OABCD. Take \\(\\pi = 3.14\\). Ans: [?] cm²",
      "answer0": "127",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 221,
      "difficulty_id": 3,
      "explanation": "Method: figure OABCD = (two quarter circles) - (the overlap counted twice). Area = 2 \\(\\times \\dfrac{1}{4} \\times 3.14 \\times 10^2 - 30 = 2 \\times 78.5 - 30 = 157 - 30 = 127\\) cm². Answer: 127 cm².",
      "hints": ["Each quarter circle has area \\(\\dfrac{1}{4} \\times \\pi \\times 10^2\\).", "Two quarter circles overlap once, so subtract the overlap (shaded OBC, 30 cm²)."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 2 Q15a",
      "image_needed": true,
      "image_options": false,
      "image_page": 31,
      "image_bbox": [0.3, 0.1, 0.68, 0.27],
      "image_loc": "overlapping quarter circles figure OABCD, upper part of page 31",
      "image_file": "q57.png",
      "notes": "Answer key Paper 2 Q15a: 2 x (1/4 x 3.14 x 100) - 30 = 157 - 30 = 127 cm²."
    },
    {
      "n": 58,
      "type_id": 2,
      "question": "Figure OABCD is formed by overlapping 2 similar quarter circles OAC and OBD. OA = OB = OC = OD = 10 cm. The area of the shaded part OBC is 30 cm² and the perimeter of the shaded part OBC is 26 cm.<br>(b) Find the perimeter of figure OABCD. Take \\(\\pi = 3.14\\). Ans: [?] cm",
      "answer0": "45.4",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 221,
      "difficulty_id": 3,
      "explanation": "Method: arc BC = perimeter of OBC - the two radii = 26 - 10 - 10 = 6 cm. The outer arc AD of a quarter circle = \\(\\dfrac{1}{4} \\times 2 \\times 3.14 \\times 10 = 15.7\\)... using the key: arc AD = 3.14 \\(\\times\\) 10 - 6 = 25.4 cm. Perimeter of OABCD = arc AD + OA + OD = 25.4 + 10 + 10 = 45.4 cm. Answer: 45.4 cm.",
      "hints": ["Arc BC = perimeter of OBC minus the two 10 cm radii.", "Find the outer arc AD, then add the two straight radii OA and OD."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 2 Q15b",
      "image_needed": true,
      "image_options": false,
      "image_page": 31,
      "image_bbox": [0.3, 0.1, 0.68, 0.27],
      "image_loc": "same overlapping quarter circles figure OABCD, upper part of page 31",
      "image_file": "q58.png",
      "notes": "Answer key Paper 2 Q15b: arc BC = 26-20 = 6; arc AD = 3.14 x 10 - 6 = 25.4; perimeter = 25.4 + 10 + 10 = 45.4 cm. Shares figure with Q57."
    },
    {
      "n": 59,
      "type_id": 2,
      "question": "At a bookshop, erasers are sold only in packs of 8 (8 for $2) and pencils are sold only in packs of 5 (5 for $3). Mr Tan bought erasers and pencils for his company. He spent \\(\\dfrac{1}{3}\\) of his money on erasers and the rest of his money on pencils. He bought 36 more erasers than pencils. How much did Mr Tan spend altogether? Ans: $[?]",
      "answer0": "162",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "Method: money spent on erasers : pencils = 1 : 2. Using prices, $2 buys 8 erasers and $4 buys ... scaling money to $6 : $12 means 3 eraser packs and 4 pencil packs per unit, i.e. erasers = 3 \\(\\times\\) 8 = 24 and pencils = 4 \\(\\times\\) 5 = 20 per money-unit. Difference per unit = 24 - 20 = 4 items. For 36 more erasers, 36 \\(\\div\\) 4 = 9 units. Total spent = 9 \\(\\times\\) ($6 + $12) = 9 \\(\\times\\) $18 = $162. Answer: $162.",
      "hints": ["Eraser money : pencil money = 1 : 2; convert to a common money-unit ($6 : $12).", "Find erasers and pencils per unit, use the 36-item difference to find the number of units, then total the money."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 2 Q16",
      "image_needed": true,
      "image_options": false,
      "image_page": 32,
      "image_bbox": [0.16, 0.1, 0.86, 0.27],
      "image_loc": "erasers (8 for $2) and pencils (5 for $3) price box near top of page 32",
      "image_file": "q59.png",
      "notes": "Answer key Paper 2 Q16: ratio $6:$12 -> 24 erasers : 20 pencils per unit; 24-20=4; 36/4=9; total = 9 x $18 = $162. Price details also in stem so figure is optional context."
    },
    {
      "n": 60,
      "type_id": 1,
      "question": "Ann filled some orange juice into large and small bottles. She filled \\(\\dfrac{3}{5}\\) of the orange juice into 4 large bottles and \\(\\dfrac{3}{4}\\) of the remaining orange juice into 9 small bottles.<br>(a) What fraction of the orange juice was filled into the 9 small bottles?",
      "answer0": "\\(\\dfrac{3}{10}\\)",
      "answer1": "\\(\\dfrac{2}{5}\\)",
      "answer2": "\\(\\dfrac{3}{20}\\)",
      "answer3": "\\(\\dfrac{9}{20}\\)",
      "correct_answer": 0,
      "skill_id": 161,
      "difficulty_id": 2,
      "explanation": "Method: remaining after the large bottles = 1 - \\(\\dfrac{3}{5} = \\dfrac{2}{5}\\). The small bottles got \\(\\dfrac{3}{4}\\) of this remaining: \\(\\dfrac{3}{4} \\times \\dfrac{2}{5} = \\dfrac{6}{20} = \\dfrac{3}{10}\\). Answer: \\(\\dfrac{3}{10}\\).",
      "hints": ["Find the fraction remaining after the 4 large bottles (1 - \\(\\dfrac{3}{5}\\)).", "Multiply \\(\\dfrac{3}{4}\\) by that remaining fraction."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 2 Q17a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Paper 2 Q17a: 1 - 3/5 = 2/5; 3/4 x 2/5 = 3/10. Fraction answer so converted to MCQ; correct option 1."
    },
    {
      "n": 61,
      "type_id": 1,
      "question": "Ann filled some orange juice into large and small bottles. She filled \\(\\dfrac{3}{5}\\) of the orange juice into 4 large bottles and \\(\\dfrac{3}{4}\\) of the remaining orange juice into 9 small bottles.<br>(b) After that, she wanted to fill 1 large bottle with the left-over orange juice but was short of \\(0.6\\,\\ell\\). Instead, she filled another 1 small bottle and had \\(0.8\\,\\ell\\) of orange juice left in the end. How many litres of orange juice did Ann have at first?",
      "answer0": "\\(12\\,\\ell\\)",
      "answer1": "\\(10\\,\\ell\\)",
      "answer2": "\\(14\\,\\ell\\)",
      "answer3": "\\(7.2\\,\\ell\\)",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Method: a large bottle holds 0.6 + 0.8 = 1.4 \\(\\ell\\) more than a small bottle. \\(\\dfrac{3}{5}\\) of the juice fills 4 large bottles; \\(\\dfrac{3}{5}\\) also equals 18 small bottles (since \\(\\dfrac{3}{10}\\) = 9 small bottles, so \\(\\dfrac{3}{5}\\) = 18 small bottles). So 4 large = 18 small in juice-volume terms: 4 large = 4 small + 5.6 \\(\\ell\\) (4 \\(\\times\\) 1.4). Then 18 small = 4 small + 5.6 \\(\\ell\\), giving 14 small = 5.6 \\(\\ell\\), so 1 small bottle = 0.4 \\(\\ell\\). \\(\\dfrac{3}{5}\\) of juice = 18 \\(\\times\\) 0.4 = 7.2 \\(\\ell\\); total = 7.2 \\(\\div \\dfrac{3}{5}\\) = 12 \\(\\ell\\). Answer: \\(12\\,\\ell\\).",
      "hints": ["A large bottle holds 1.4 \\(\\ell\\) more than a small bottle (0.6 + 0.8).", "Express \\(\\dfrac{3}{5}\\) of the juice as both 4 large bottles and 18 small bottles, then solve for one small bottle and scale up."],
      "source": "Anglo-Chinese School (Junior) 2025 P6 Prelim Paper 2 Q17b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Paper 2 Q17b: 1 small = 0.4 l; 3/5 of juice = 7.2 l; total = 7.2 / (3/5) = 12 l. Answer 12 l is a whole number but options kept as MCQ to present the volume choices; correct option 1."
    }
  ]
}