{
  "paper": {
    "school": "Catholic High School",
    "year": 2025,
    "level": "P6",
    "label": "Prelim",
    "source_prefix": "Catholic High 2025 P6 Prelim",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "Which of the following decimals is the smallest?",
      "answer0": "0.15",
      "answer1": "0.51",
      "answer2": "0.105",
      "answer3": "0.501",
      "correct_answer": 2,
      "skill_id": 113,
      "difficulty_id": 1,
      "explanation": "Compare place values: 0.105 < 0.15 < 0.501 < 0.51. The smallest is 0.105.",
      "hints": ["Line up the decimal points and compare digit by digit.", "0.105 has the smallest tenths/hundredths value."],
      "source": "Catholic High 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 -> index 2."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Which of the following is the same as 2040 cm?",
      "answer0": "0.24 m",
      "answer1": "2.04 m",
      "answer2": "2 m 40 cm",
      "answer3": "20 m 40 cm",
      "correct_answer": 3,
      "skill_id": 113,
      "difficulty_id": 1,
      "explanation": "2040 cm = 20 m 40 cm (since 100 cm = 1 m, 2000 cm = 20 m).",
      "hints": ["Divide 2040 cm by 100 to get metres.", "2040 cm = 20 m and 40 cm."],
      "source": "Catholic High 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 4 -> index 3."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Which of the following shows \\(\\dfrac{1}{5}\\) of the figure shaded?",
      "answer0": "Figure 1",
      "answer1": "Figure 2",
      "answer2": "Figure 3",
      "answer3": "Figure 4",
      "correct_answer": 0,
      "skill_id": 106,
      "difficulty_id": 2,
      "explanation": "Figure 1 (the 5x5 grid with 5 squares shaded) has 5 of 25 = 1/5 shaded. The other figures are not exactly 1/5.",
      "hints": ["Count shaded parts out of total equal parts in each figure.", "Look for a figure where shaded : total = 1 : 5."],
      "source": "Catholic High 2025 P6 Prelim Q3",
      "image_needed": true,
      "image_options": true,
      "image_file": null,
      "image_page": 2,
      "image_bbox": [0.3, 0.5, 0.46, 0.85],
      "image_loc": "four candidate shaded figures labelled (1)-(4): grid, circle, bar, pentagon",
      "notes": "Key: option 1 -> index 0. Options are pictures (image_options=true); crop each as q3_opt0..3."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Which of the following is likely to be the length of a road bicycle?",
      "answer0": "17 cm",
      "answer1": "170 cm",
      "answer2": "17 m",
      "answer3": "170 m",
      "correct_answer": 1,
      "skill_id": 114,
      "difficulty_id": 1,
      "explanation": "A road bicycle is about 1.7 m long, i.e. 170 cm. The other values are too small or far too large.",
      "hints": ["Estimate a realistic bicycle length.", "170 cm = 1.7 m is reasonable."],
      "source": "Catholic High 2025 P6 Prelim Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q4.png",
      "image_page": 3,
      "image_bbox": [0.4, 0.13, 0.64, 0.24],
      "image_loc": "drawing of a road bicycle with its length marked '?'",
      "notes": "Key: option 2 -> index 1."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "In the number line, what is the mixed number represented by A?",
      "answer0": "\\(1\\dfrac{2}{3}\\)",
      "answer1": "\\(1\\dfrac{3}{4}\\)",
      "answer2": "\\(1\\dfrac{5}{6}\\)",
      "answer3": "\\(1\\dfrac{6}{7}\\)",
      "correct_answer": 1,
      "skill_id": 108,
      "difficulty_id": 2,
      "explanation": "The interval from 1 to 2 is divided into 4 equal parts. A is at the 3rd mark, so A = 1 3/4.",
      "hints": ["Count the equal divisions between 1 and 2.", "A sits at the 3rd of 4 parts."],
      "source": "Catholic High 2025 P6 Prelim Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q5.png",
      "image_page": 3,
      "image_bbox": [0.28, 0.42, 0.64, 0.5],
      "image_loc": "horizontal number line from 1 to 2 with arrow A near the 3/4 mark",
      "notes": "Key: option 2 -> index 1. MCQ because the answer is a mixed number."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "Rachel watched a movie at the cinema. The movie lasted for 2 h 15 min. After the movie ended, she walked 25 minutes to reach her home. She reached home at 6.55 p.m. What time did the movie start?",
      "answer0": "4.15 p.m.",
      "answer1": "4.40 p.m.",
      "answer2": "7.20 p.m.",
      "answer3": "9.35 p.m.",
      "correct_answer": 0,
      "skill_id": 116,
      "difficulty_id": 2,
      "explanation": "Work backwards from 6.55 p.m.: subtract 25 min walk -> 6.30 p.m. (movie ended). Subtract 2 h 15 min -> 4.15 p.m. start.",
      "hints": ["Subtract the 25-minute walk first.", "Then subtract the 2 h 15 min movie length."],
      "source": "Catholic High 2025 P6 Prelim Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: option 1 -> index 0."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "Which of the following is a net of a cuboid?",
      "answer0": "Net 1",
      "answer1": "Net 2",
      "answer2": "Net 3",
      "answer3": "Net 4",
      "correct_answer": 3,
      "skill_id": 126,
      "difficulty_id": 2,
      "explanation": "Folding each candidate, only net 4 folds into a closed cuboid (six faces, no overlap).",
      "hints": ["Mentally fold each net.", "A cuboid net has six rectangular faces that close up."],
      "source": "Catholic High 2025 P6 Prelim Q7",
      "image_needed": true,
      "image_options": true,
      "image_file": null,
      "image_page": 4,
      "image_bbox": [0.3, 0.33, 0.56, 0.92],
      "image_loc": "four candidate nets labelled (1)-(4)",
      "notes": "Key: option 4 -> index 3. Options are net pictures (image_options=true); crop each as q7_opt0..3."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "Which line in the square grid is perpendicular to BC?",
      "answer0": "AC",
      "answer1": "BA",
      "answer2": "CD",
      "answer3": "DA",
      "correct_answer": 1,
      "skill_id": 119,
      "difficulty_id": 2,
      "explanation": "On the grid, BA has a gradient that is the negative reciprocal of BC's gradient, so BA is perpendicular to BC.",
      "hints": ["Perpendicular lines have gradients that multiply to -1.", "Compare each line's rise/run with BC's on the grid."],
      "source": "Catholic High 2025 P6 Prelim Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 5,
      "image_bbox": [0.3, 0.1, 0.64, 0.3],
      "image_loc": "square grid with points A, B, C, D joined by lines",
      "notes": "Key: option 2 -> index 1."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "The square grid shows the position of 5 landmarks A, B, C, D and E.<br>Julian is standing at a location north-west of landmark D and east of landmark A. In what direction is landmark C from Julian?",
      "answer0": "North-east",
      "answer1": "North-west",
      "answer2": "South-east",
      "answer3": "South-west",
      "correct_answer": 0,
      "skill_id": 118,
      "difficulty_id": 3,
      "explanation": "Julian's position is fixed by being NW of D and due east of A. From that point, landmark C lies to the upper-right, i.e. north-east.",
      "hints": ["First locate Julian: NW of D and level (east) with A.", "Then read the direction of C relative to that grid point."],
      "source": "Catholic High 2025 P6 Prelim Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q9.png",
      "image_page": 5,
      "image_bbox": [0.3, 0.42, 0.7, 0.66],
      "image_loc": "square grid with landmarks A, B, C, D, E and a North arrow to the right",
      "notes": "Key: option 1 -> index 0."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "The pie chart shows the number of pupils taking part in various activities at a sports carnival. The same information is shown in a bar graph, but the names of the activities are not shown on the bar graph.<br>How many pupils took part in Soccer and Hockey altogether?",
      "answer0": "120",
      "answer1": "130",
      "answer2": "150",
      "answer3": "170",
      "correct_answer": 2,
      "skill_id": 130,
      "difficulty_id": 3,
      "explanation": "Match each sector of the pie chart to its bar. Soccer + Hockey read off the corresponding bars total 150 pupils.",
      "hints": ["Match the pie sectors to the bars by size order.", "Add the Soccer and Hockey bar values."],
      "source": "Catholic High 2025 P6 Prelim Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 6,
      "image_bbox": [0.26, 0.16, 0.86, 0.37],
      "image_loc": "pie chart (Badminton, Soccer, Hockey, Golf) and a bar graph 'Activities at sports carnival'",
      "notes": "Key: option 3 -> index 2 (150)."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "In the figure, FCEB and DGE are straight lines. ABC is an equilateral triangle. DGE = FCE and ∠CFD = 70°. Find ∠CGE.",
      "answer0": "40°",
      "answer1": "80°",
      "answer2": "100°",
      "answer3": "140°",
      "correct_answer": 2,
      "skill_id": 120,
      "difficulty_id": 3,
      "explanation": "ABC equilateral so ∠ACB = 60°, giving ∠FCD relationships; with ∠CFD = 70° and the parallel/equal-angle conditions, ∠CGE works out to 100° (the printed key gives option 3).",
      "hints": ["Use the 60° angles of the equilateral triangle.", "Track exterior angles along the straight lines FCEB and DGE."],
      "source": "Catholic High 2025 P6 Prelim Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q11.png",
      "image_page": 6,
      "image_bbox": [0.3, 0.56, 0.66, 0.74],
      "image_loc": "triangle ABC with points D, F, C, G, E and 70° marked at F",
      "notes": "Key: option 3 -> index 2 (100°)."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "Alex and Ben had $190 altogether at first. After Alex gave Ben $30, Alex had $40 more than Ben. How much did Ben have at first?",
      "answer0": "$45",
      "answer1": "$75",
      "answer2": "$120",
      "answer3": "$160",
      "correct_answer": 0,
      "skill_id": 137,
      "difficulty_id": 2,
      "explanation": "After the transfer the total is still $190. Alex = (190 + 40)/2 = $115, Ben = $75 after. Before, Ben had $75 - $30 = $45.",
      "hints": ["Total stays $190 after the transfer.", "Find each after-amount, then undo the $30 transfer."],
      "source": "Catholic High 2025 P6 Prelim Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: option 1 -> index 0 ($45)."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "Arrange these volumes from the smallest to the largest.<br>2.25 ℓ, \\(2\\dfrac{2}{5}\\) ℓ, 2 ℓ 225 ml",
      "answer0": "\\(2\\dfrac{2}{5}\\) ℓ, 2.25 ℓ, 2 ℓ 225 ml",
      "answer1": "\\(2\\dfrac{2}{5}\\) ℓ, 2 ℓ 225 ml, 2.25 ℓ",
      "answer2": "2 ℓ 225 ml, 2.25 ℓ, \\(2\\dfrac{2}{5}\\) ℓ",
      "answer3": "2.25 ℓ, 2 ℓ 225 ml, \\(2\\dfrac{2}{5}\\) ℓ",
      "correct_answer": 2,
      "skill_id": 113,
      "difficulty_id": 2,
      "explanation": "Convert to litres: 2 2/5 ℓ = 2.4 ℓ, 2.25 ℓ = 2.25 ℓ, 2 ℓ 225 ml = 2.225 ℓ. Smallest to largest: 2 ℓ 225 ml, 2.25 ℓ, 2 2/5 ℓ.",
      "hints": ["Express every volume in litres.", "2 ℓ 225 ml = 2.225 ℓ; 2 2/5 ℓ = 2.4 ℓ."],
      "source": "Catholic High 2025 P6 Prelim Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: option 3 -> index 2. MCQ because options contain a fraction (2 2/5 ℓ)."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "The figure is made up of one big semicircle and a small semicircle. The large semicircle with centre O has a radius of 6 cm. Find the perimeter of the figure. Leave your answer in terms of π.",
      "answer0": "6π cm",
      "answer1": "9π cm",
      "answer2": "(6π + 6) cm",
      "answer3": "(9π + 6) cm",
      "correct_answer": 1,
      "skill_id": 125,
      "difficulty_id": 3,
      "explanation": "Big semicircle radius 6 cm: arc = π x 6 = 6π. The small semicircle has radius 3 cm (diameter = 6 cm): arc = π x 3 = 3π. Perimeter = 6π + 3π = 9π cm (the straight diameter is replaced by the small arc).",
      "hints": ["Big semicircle arc = π x radius.", "The small semicircle sits on the diameter; add its arc."],
      "source": "Catholic High 2025 P6 Prelim Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q14.png",
      "image_page": 7,
      "image_bbox": [0.46, 0.62, 0.72, 0.76],
      "image_loc": "shaded figure of a large semicircle (centre O, radius 6 cm) with a small semicircle",
      "notes": "Key: option 2 -> index 1 (9π cm)."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "Joe baked some chocolate muffins and vanilla muffins. He sold an equal number of chocolate muffins and vanilla muffins. He had \\(\\dfrac{3}{4}\\) of the vanilla muffins and \\(\\dfrac{3}{7}\\) of the chocolate muffins left. What fraction of the muffins were sold?",
      "answer0": "\\(\\dfrac{5}{28}\\)",
      "answer1": "\\(\\dfrac{8}{23}\\)",
      "answer2": "\\(\\dfrac{23}{28}\\)",
      "answer3": "\\(\\dfrac{15}{23}\\)",
      "correct_answer": 1,
      "skill_id": 109,
      "difficulty_id": 3,
      "explanation": "Sold vanilla = 1/4 of vanilla; sold chocolate = 4/7 of chocolate; these are equal. Let vanilla = 4u (sold u), chocolate = 7v (sold 4v). u = 4v so vanilla units = 16v, chocolate = 7v. Total = 23v, sold = u + 4v = 4v + 4v = 8v. Fraction sold = 8/23.",
      "hints": ["Set the sold amounts equal (1/4 of V = 4/7 of C).", "Express V and C in the same unit, then sold/total."],
      "source": "Catholic High 2025 P6 Prelim Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: option 2 -> index 1 (8/23). MCQ because options are fractions."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Write three million, six thousand and forty in numerals.<br>Ans: [?]",
      "answer0": "3006040",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 100,
      "difficulty_id": 1,
      "explanation": "Three million = 3 000 000; six thousand = 6 000; forty = 40. Total = 3 006 040.",
      "hints": ["Build it place by place.", "3 000 000 + 6 000 + 40 = 3 006 040."],
      "source": "Catholic High 2025 P6 Prelim Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: 3 006 040."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "Round 39 470 to the nearest thousand.<br>Ans: [?]",
      "answer0": "39000",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 100,
      "difficulty_id": 1,
      "explanation": "The hundreds digit is 4 (less than 5), so round down: 39 470 -> 39 000.",
      "hints": ["Look at the hundreds digit (4).", "Less than 5 rounds the thousands down."],
      "source": "Catholic High 2025 P6 Prelim Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: 39 000."
    },
    {
      "n": 18,
      "type_id": 1,
      "question": "Find the value of \\(\\dfrac{3}{8} \\div 18\\). Give your answer as a fraction in the simplest form.",
      "answer0": "\\(\\dfrac{1}{48}\\)",
      "answer1": "\\(\\dfrac{3}{144}\\)",
      "answer2": "\\(\\dfrac{1}{6}\\)",
      "answer3": "\\(\\dfrac{3}{26}\\)",
      "correct_answer": 0,
      "skill_id": 107,
      "difficulty_id": 2,
      "explanation": "3/8 ÷ 18 = 3/8 x 1/18 = 3/144 = 1/48.",
      "hints": ["Dividing by 18 is multiplying by 1/18.", "3/144 simplifies to 1/48."],
      "source": "Catholic High 2025 P6 Prelim Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: 1/48. Converted to MCQ because the answer is a fraction (FIB must be integer/decimal only)."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "Find the value of \\(3w - 9 + \\dfrac{w}{4}\\) when \\(w = 8\\).<br>Ans: [?]",
      "answer0": "17",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 137,
      "difficulty_id": 2,
      "explanation": "3(8) - 9 + 8/4 = 24 - 9 + 2 = 17.",
      "hints": ["Substitute w = 8 into each term.", "24 - 9 + 2 = 17."],
      "source": "Catholic High 2025 P6 Prelim Q19",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: 17."
    },
    {
      "n": 20,
      "type_id": 1,
      "question": "Write down all the common factors of 12 and 20.",
      "answer0": "1, 2, 4",
      "answer1": "1, 2, 3, 4",
      "answer2": "1, 2, 4, 6",
      "answer3": "2, 4",
      "correct_answer": 0,
      "skill_id": 101,
      "difficulty_id": 2,
      "explanation": "Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 20: 1, 2, 4, 5, 10, 20. Common: 1, 2, 4.",
      "hints": ["List the factors of each number.", "Pick the values that appear in both lists."],
      "source": "Catholic High 2025 P6 Prelim Q20",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: 1, 2, 4. Made MCQ because the answer is a multi-value set (not a single number a FIB can grade)."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "At a fruit stall, there were 320 fruits altogether. \\(\\dfrac{1}{4}\\) of them were apples, \\(\\dfrac{5}{8}\\) of them were oranges and the rest were mangoes. The fruit stall sold \\(\\dfrac{3}{4}\\) of the mangoes. How many mangoes did the fruit stall sell?<br>Ans: [?]",
      "answer0": "30",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 109,
      "difficulty_id": 2,
      "explanation": "Fraction that are mangoes = 1 - 1/4 - 5/8 = (8 - 2 - 5)/8 = 1/8. Mangoes = 320 x 1/8 = 40. Sold = 3/4 x 40 = 30.",
      "hints": ["Find the mango fraction first (1 - 1/4 - 5/8).", "Then take 3/4 of the number of mangoes."],
      "source": "Catholic High 2025 P6 Prelim Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: 30 mangoes."
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "The table shows the charges to post a parcel.<br>First 500 g: $2; Every additional 1 kg: $1.50.<br>Mr Yap posted a parcel that weighed 4.8 kg. How much did Mr Yap pay to post the parcel?<br>Ans: $[?]",
      "answer0": "9.50",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 115,
      "difficulty_id": 3,
      "explanation": "First 500 g = $2. Remaining 4.3 kg needs 5 lots of 'additional 1 kg' (round up): the key takes 4.8 kg = 0.5 kg + 4 kg + 0.3 kg, charging $2 + 4 x $1.50 + $1.50 = $9.50.",
      "hints": ["Charge the first 500 g, then each additional 1 kg (round up).", "$2 + (number of 1 kg steps) x $1.50."],
      "source": "Catholic High 2025 P6 Prelim Q22",
      "image_needed": true,
      "image_options": false,
      "image_file": "q22.png",
      "image_page": 12,
      "image_bbox": [0.18, 0.5, 0.56, 0.6],
      "image_loc": "table 'Postage Rates': Mass Step / Rate, First 500 g $2, Every additional 1 kg $1.50",
      "notes": "Key: $9.50."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "ABCD is a rectangle with AB = 12 cm and BC = 5 cm. Point E lies on DC. DE = 4 cm. Find the area of the shaded triangle.<br>Ans: [?] cm²",
      "answer0": "20",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 124,
      "difficulty_id": 2,
      "explanation": "EC = DC - DE = 12 - 4 = 8 cm. The shaded triangle has base EC = 8 cm and height BC = 5 cm: area = 1/2 x 8 x 5 = 20 cm².",
      "hints": ["Find EC = 12 - 4.", "Area = 1/2 x base x height with the rectangle's height."],
      "source": "Catholic High 2025 P6 Prelim Q23",
      "image_needed": true,
      "image_options": false,
      "image_file": "q23.png",
      "image_page": 13,
      "image_bbox": [0.28, 0.1, 0.66, 0.24],
      "image_loc": "rectangle ABCD (AB 12 cm, BC 5 cm) with E on DC (DE 4 cm), shaded triangle",
      "notes": "Key: EC = 8; area = 0.5 x 8 x 5 = 20 cm²."
    },
    {
      "n": 24,
      "type_id": 0,
      "question": "The average mass of some children is 48 kg. There is an equal number of boys and girls. The average mass of the boys is 50 kg.<br>Each statement below is either true, false or not possible to tell from the information given. For each statement, put a tick in the correct column.<br>(a) The total mass of the boys is heavier than the total mass of the girls.<br>(b) The mass of each girl is 46 kg.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 128,
      "difficulty_id": 3,
      "explanation": "Let boys = girls = n. Total children mass = 48 x 2n = 96n; boys = 50n; girls = 46n. (a) True (50n > 46n). (b) Average girl mass is 46 kg, but individual masses are not possible to tell.",
      "hints": ["Use equal numbers of boys and girls.", "Distinguish average mass from each individual mass."],
      "source": "Catholic High 2025 P6 Prelim Q24",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "type_id 0: tick-True/False/Not-possible table. Key: (a) True; (b) Not possible to tell."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "Jack wanted to buy 16 chicken wings but found that he needed another $5. He bought 7 chicken wings and had $5.80 left. What was the cost of a chicken wing?<br>Ans: $[?]",
      "answer0": "1.20",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 117,
      "difficulty_id": 3,
      "explanation": "Jack bought 7 instead of 16, i.e. 9 fewer wings, leaving him $5.00 (the shortfall he no longer needed) + $5.80 = $10.80. So 9 wings cost $10.80, and one wing = $10.80 ÷ 9 = $1.20.",
      "hints": ["He has 16 - 7 = 9 wings' worth of money spare.", "That spare = $5.00 + $5.80 = $10.80 for 9 wings."],
      "source": "Catholic High 2025 P6 Prelim Q25",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: 16 - 7 = 9 wings -> $10.80; $10.80 ÷ 9 = $1.20."
    },
    {
      "n": 26,
      "type_id": 0,
      "question": "There are 11 shaded squares in the figure. Shade 2 more squares to form a symmetric figure with AB as the line of symmetry.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 121,
      "difficulty_id": 2,
      "explanation": "Reflect across the diagonal line AB; the 2 squares whose mirror images are not yet shaded must be shaded to make the figure symmetric.",
      "hints": ["Reflect each shaded square across diagonal AB.", "Shade the 2 missing mirror-image squares."],
      "source": "Catholic High 2025 P6 Prelim Q26",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 14,
      "image_bbox": [0.3, 0.45, 0.56, 0.7],
      "image_loc": "square grid with diagonal line of symmetry AB and 11 squares shaded",
      "notes": "type_id 0: shade-to-complete-symmetry task (no single value answer)."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "7 unit cubes are glued together to form the solid shown (Top, Front and Side views indicated).<br>(a) Draw the side view of the solid on the grid.<br>(b) What is the least number of unit cubes to be added to the above solid to form a cube?<br>Ans: [?]",
      "answer0": "57",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 126,
      "difficulty_id": 3,
      "explanation": "The smallest cube enclosing the solid is 4 x 4 x 4 = 64 unit cubes. The solid already has 7, so 64 - 7 = 57 cubes must be added.",
      "hints": ["Find the smallest cube that encloses the solid (4x4x4).", "Subtract the 7 existing cubes."],
      "source": "Catholic High 2025 P6 Prelim Q27",
      "image_needed": true,
      "image_options": false,
      "image_file": "q27.png",
      "image_page": 15,
      "image_bbox": [0.28, 0.13, 0.62, 0.32],
      "image_loc": "isometric drawing of 7 unit cubes with Top/Front/Side views labelled",
      "notes": "Part (a) is a draw-the-side-view task (omitted from answers); answer covers (b) = 57. Key: 4x4x4 = 64; 64 - 7 = 57."
    },
    {
      "n": 28,
      "type_id": 1,
      "question": "The figure is made up of a square and a rectangle overlapping each other. The ratio of the shaded area to the area of the square is 1 : 5. The ratio of shaded area to the area of rectangle is 2 : 9. What is the ratio of the area of square to the area of the rectangle?",
      "answer0": "10 : 9",
      "answer1": "9 : 10",
      "answer2": "5 : 9",
      "answer3": "2 : 9",
      "correct_answer": 0,
      "skill_id": 135,
      "difficulty_id": 3,
      "explanation": "Shaded : square = 1 : 5 = 2 : 10 (scale by 2). Shaded : rectangle = 2 : 9. With shaded common at 2: square : rectangle = 10 : 9.",
      "hints": ["Make the shaded part the same number in both ratios.", "Scale 1 : 5 to 2 : 10, then compare with 2 : 9."],
      "source": "Catholic High 2025 P6 Prelim Q28",
      "image_needed": true,
      "image_options": false,
      "image_file": "q28.png",
      "image_page": 16,
      "image_bbox": [0.3, 0.16, 0.52, 0.3],
      "image_loc": "a square and rectangle overlapping, with the overlap shaded",
      "notes": "Key: 10 : 9. MCQ because the answer is a ratio."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "At a party, 87 blue balloons and green balloons line one side of the wall. There are at least 3 blue balloons between any 2 green balloons. What is the greatest possible number of green balloons along the wall?<br>Ans: [?]",
      "answer0": "22",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 103,
      "difficulty_id": 3,
      "explanation": "Each green balloon (after the first) needs at least 3 blue balloons before it: pattern unit = 1 green + 3 blue = 4 balloons. 87 ÷ 4 = 21 remainder 3, so 21 full units plus 1 more green = 22 green balloons.",
      "hints": ["Group as 1 green + 3 blue = 4 balloons.", "87 ÷ 4 = 21 r 3; the remainder allows one more green."],
      "source": "Catholic High 2025 P6 Prelim Q29",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: 22 green balloons."
    },
    {
      "n": 30,
      "type_id": 0,
      "question": "In the square grid, AB and AD are straight lines. Both lines are part of a trapezium ABCD.<br>(a) AB is parallel to CD. CD is half the length of AB. Draw trapezium ABCD on the grid.<br>(b) AD is one side of a rhombus ADEF. Draw ADEF on the grid such that it does not overlap with trapezium ABCD.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 119,
      "difficulty_id": 2,
      "explanation": "Construct on the dot grid: (a) trapezium ABCD with CD parallel to AB and half its length; (b) rhombus ADEF on side AD, not overlapping ABCD. The marked answer shows valid constructions.",
      "hints": ["For (a) make CD parallel and half of AB.", "For (b) all four sides of the rhombus must be equal to AD."],
      "source": "Catholic High 2025 P6 Prelim Q30",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 17,
      "image_bbox": [0.18, 0.26, 0.66, 0.66],
      "image_loc": "square grid with straight lines AB and AD drawn, points A, B, D labelled",
      "notes": "type_id 0: draw-on-the-grid construction task (no single value answer)."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "Richard took 90 minutes to run 5.4 km. What was his average speed in km/h?<br>Ans: [?] km/h",
      "answer0": "3.6",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 133,
      "difficulty_id": 2,
      "explanation": "90 min = 1.5 h. Average speed = 5.4 km ÷ 1.5 h = 3.6 km/h.",
      "hints": ["Convert 90 minutes to hours.", "Speed = distance ÷ time."],
      "source": "Catholic High 2025 P6 Prelim P2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: 3.6 km/h."
    },
    {
      "n": 32,
      "type_id": 2,
      "question": "During a sale, a laptop was sold for $1072 after a 20% discount. How much was the usual price of the laptop?<br>Ans: $[?]",
      "answer0": "1340",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 111,
      "difficulty_id": 2,
      "explanation": "$1072 is 80% of the usual price. Usual price = $1072 ÷ 0.80 = $1340.",
      "hints": ["After a 20% discount, $1072 = 80% of usual price.", "Divide by 0.8."],
      "source": "Catholic High 2025 P6 Prelim P2 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: $1340."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "A fruit seller packed 860 apples into bags of 4 for sale. The price of each bag of apples was $7.80. How much money did the fruit seller collect after selling all the bags of apples?<br>Ans: $[?]",
      "answer0": "1677",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 117,
      "difficulty_id": 2,
      "explanation": "Number of bags = 860 ÷ 4 = 215. Money collected = 215 x $7.80 = $1677.",
      "hints": ["Find the number of bags first.", "Multiply by $7.80 per bag."],
      "source": "Catholic High 2025 P6 Prelim P2 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: $1677."
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "Figure 1 is a triangle with a perimeter of 39 cm. Each side of the triangle has a different design. Figure 2 is made up of 5 such triangles. The perimeter of Figure 2 is 87 cm. What is the length of ST in Figure 1?<br>Ans: [?] cm",
      "answer0": "15",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 123,
      "difficulty_id": 3,
      "explanation": "Let the sides be a, b, c with a + b + c = 39 and Figure 2 perimeter 3a + 3b + c = 87. Then 3(a+b+c) - (3a+3b+c) = 3x39 - 87 gives 2c = 30, c = ST = 15 cm.",
      "hints": ["Write the perimeter of one triangle and of Figure 2 in terms of the three sides.", "Eliminate to isolate ST."],
      "source": "Catholic High 2025 P6 Prelim P2 Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q34.png",
      "image_page": 21,
      "image_bbox": [0.18, 0.5, 0.78, 0.78],
      "image_loc": "Figure 1 single triangle STT with patterned sides; Figure 2 made of 5 such triangles",
      "notes": "Key: ST = 15 cm."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "A shop sells only three types of toys. The table shows the number of each type of toy sold: Robot = p, Car = 2p + 8, Doll = 45.<br>(a) Find the total number of toys sold by the shop in terms of p. Ans: (a) [?]<br>(b) The shop sold a total of 140 toys. How many toy robots did the shop sell? Ans: (b) [?]",
      "answer0": "3p + 53",
      "answer1": "29",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 137,
      "difficulty_id": 2,
      "explanation": "(a) Total = p + (2p + 8) + 45 = 3p + 53. (b) 3p + 53 = 140 -> 3p = 87 -> p = 29 robots.",
      "hints": ["(a) Add the three expressions.", "(b) Set 3p + 53 = 140 and solve for p."],
      "source": "Catholic High 2025 P6 Prelim P2 Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q35.png",
      "image_page": 22,
      "image_bbox": [0.2, 0.14, 0.6, 0.22],
      "image_loc": "table: Type of Toy / Number of toys sold — Robot p, Car 2p + 8, Doll 45",
      "notes": "Key: (a) 3p + 53; (b) 29. Part (a) answer is an algebraic expression stored as text in answer0."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "The table shows the number of visitors to a zoo from Thursday to Saturday (Sunday not shown): Thursday 3100, Friday 2690, Saturday 3580, Sunday ?<br>(a) The number of visitors to the zoo on Sunday increased by 15% when compared to Saturday. What was the number of visitors to the zoo on Sunday? Ans: (a) [?]<br>(b) What was the percentage decrease in the number of visitors to the zoo on Friday compared to Thursday? Round your answer to 1 decimal place. Ans: (b) [?]%",
      "answer0": "4117",
      "answer1": "13.2",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 111,
      "difficulty_id": 3,
      "explanation": "(a) Sunday = 3580 x 115% = 4117. (b) Decrease = (3100 - 2690)/3100 x 100% = 410/3100 x 100% = 13.2% (1 d.p.).",
      "hints": ["(a) Multiply Saturday's count by 1.15.", "(b) Percentage decrease = (drop ÷ original) x 100%."],
      "source": "Catholic High 2025 P6 Prelim P2 Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q36.png",
      "image_page": 23,
      "image_bbox": [0.3, 0.2, 0.66, 0.34],
      "image_loc": "table: Day / Number of visitors — Thursday 3100, Friday 2690, Saturday 3580, Sunday ?",
      "notes": "Key: (a) 4117; (b) 13.2%."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "In the figure, ABC is an isosceles triangle. AB = BC. BDEC is a parallelogram. AFE is a straight line. ∠CBD = 142°. Find ∠FED.<br>Ans: [?]°",
      "answer0": "119",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 120,
      "difficulty_id": 3,
      "explanation": "∠ACB = (180 - 48)/2 = 66° (isosceles ABC). ∠BCE = 180 - 142 = 38° (int. angles, BC parallel DE). ∠AEC = 180 - 53 - 66 - 38 = 23° (angle sum of triangle ACE). ∠FED = 142 - 23 = 119° (opposite angles of parallelogram relationship).",
      "hints": ["Use the isosceles triangle and parallelogram angle properties.", "Track angles along the straight line AFE."],
      "source": "Catholic High 2025 P6 Prelim P2 Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q37.png",
      "image_page": 24,
      "image_bbox": [0.18, 0.12, 0.72, 0.28],
      "image_loc": "isosceles triangle ABC with parallelogram BDEC; 53°, 48°, 142° marked",
      "notes": "Key: ∠FED = 119°."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "A baker sold some boxes of tarts and cookies. Each box of tarts cost $3.10 and each box of cookies cost $5.50. The baker sold twice as many boxes of tarts as boxes of cookies. He earned a total of $1439.10. How many boxes of tarts did he sell?<br>Ans: [?]",
      "answer0": "246",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 137,
      "difficulty_id": 3,
      "explanation": "For each box of cookies there are 2 boxes of tarts: 2 x $3.10 + 1 x $5.50 = $11.70 per group. Boxes of cookies = $1439.10 ÷ $11.70 = 123. Boxes of tarts = 2 x 123 = 246.",
      "hints": ["Group 2 tart boxes + 1 cookie box = $11.70.", "Divide the total by the group cost, then double for tarts."],
      "source": "Catholic High 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: 246 boxes of tarts."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "The first four figures of a pattern are shown. The table shows the number of dots and lines: Figure 1 = 4 dots/4 lines, Figure 2 = 7/8, Figure 3 = 10/12, Figure 4 = 13/16.<br>(a) A figure in the pattern has 232 lines. What is the Figure number? Ans: (a) [?]<br>(b) Find the total number of dots in Figure 70. Ans: (b) [?]",
      "answer0": "58",
      "answer1": "211",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 103,
      "difficulty_id": 3,
      "explanation": "(a) Lines = 4 x figure number, so 232 ÷ 4 = Figure 58. (b) Dots = 4 + (n - 1) x 3, so Figure 70 = 4 + 69 x 3 = 211 dots.",
      "hints": ["Lines increase by 4 each figure (lines = 4n).", "Dots increase by 3 each figure: 4 + (n-1)x3."],
      "source": "Catholic High 2025 P6 Prelim P2 Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q39.png",
      "image_page": 26,
      "image_bbox": [0.18, 0.13, 0.78, 0.42],
      "image_loc": "Figures 1-4 of dot/line pattern and the dots-and-lines table",
      "notes": "Key: (a) Figure 58; (b) 211 dots."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "Walter and Cedric started cycling from the same place in opposite directions along a straight path. Walter's speed was 40 m/min faster than Cedric's speed. Both of them did not change their speeds throughout. They were 23.38 km apart after they finished cycling. Walter cycled 2.8 km more than Cedric. What was Cedric's speed in m/min?<br>Ans: [?] m/min",
      "answer0": "147",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 133,
      "difficulty_id": 3,
      "explanation": "Time = extra distance ÷ extra speed = 2800 m ÷ 40 m/min = 70 min. Combined speed = 23380 m ÷ 70 min = 334 m/min. Cedric's speed = (334 - 40) ÷ 2 = 147 m/min.",
      "hints": ["Walter's 2.8 km lead at 40 m/min faster gives the time.", "Combined distance ÷ time = combined speed; then split."],
      "source": "Catholic High 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: 147 m/min."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "The figure shows two stacks of identical paper cups. There are 4 paper cups in the shorter stack and 6 paper cups in the taller stack. The height of the shorter stack is 21 cm and the height of the taller stack is 25 cm.<br>(a) Find the height of a paper cup. Ans: (a) [?] cm<br>(b) Mrs Ong wants to pack the paper cups as a single stack into a box of length 50 cm. What is the most number of paper cups she can pack into the box? Ans: (b) [?]",
      "answer0": "15",
      "answer1": "18",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 137,
      "difficulty_id": 3,
      "explanation": "(a) Each extra cup adds (25 - 21) ÷ (6 - 4) = 4 ÷ 2 = 2 cm. Height of one cup = 21 - 3 x 2 = 15 cm (a 4-cup stack = 15 + 3x2). (b) After the first cup (15 cm), each extra cup adds 2 cm. 50 - 15 = 35, 35 ÷ 2 = 17 r 1, so 17 + 1 = 18 cups.",
      "hints": ["(a) The rim added per extra cup = (25-21)/(6-4).", "(b) First cup full height, then 2 cm per extra cup, fit within 50 cm."],
      "source": "Catholic High 2025 P6 Prelim P2 Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q41.png",
      "image_page": 28,
      "image_bbox": [0.2, 0.15, 0.7, 0.36],
      "image_loc": "two stacks of paper cups (4-cup stack 21 cm, 6-cup stack 25 cm) and a 50 cm box",
      "notes": "Key: (a) 15 cm; (b) 18 cups."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "At first, \\(\\dfrac{1}{11}\\) of a tank was filled with water. A tap was turned on at 10 00 for more water to flow into the tank. It was turned off at 10 20. The graph shows the volume of water in the tank over the 20 minutes.<br>(a) How many litres of water flowed from the tap in 1 minute? Ans: (a) [?] ℓ<br>(b) At 10 30, the tap was turned on again to fill the tank to the brim at the same rate as before. At what time will the tank be filled to the brim with water? Ans: (b) [?]",
      "answer0": "7.5",
      "answer1": "1150",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 130,
      "difficulty_id": 3,
      "explanation": "(a) From the graph, water rose from 75 ℓ to 225 ℓ in 20 min: (225 - 75) ÷ 20 = 7.5 ℓ/min. (b) Tank capacity = 75 ÷ 1/11 = 825 ℓ. Remaining = 825 - 225 = 600 ℓ; time = 600 ÷ 7.5 = 80 min. 80 min after 10 30 = 11 50.",
      "hints": ["(a) Rate = rise in volume ÷ 20 minutes.", "(b) Find full capacity (75 = 1/11), then time to fill the rest from 10 30."],
      "source": "Catholic High 2025 P6 Prelim P2 Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q42.png",
      "image_page": 29,
      "image_bbox": [0.2, 0.16, 0.74, 0.46],
      "image_loc": "line graph: Volume of water (litres) vs Time 10 00 to 10 20, rising from 75 to 225",
      "notes": "Key: (a) 7.5 ℓ/min; (b) 11 50."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "Susan designed a logo. The logo is made up of 3 identical small quarter circles, 3 identical big quarter circles and 2 different squares. O is the centre of the small and big quarter circles. The radius of the small quarter circle is 10 cm. (Take π = 3.14)<br>(a) What is the radius of a big quarter circle? Ans: (a) [?] cm<br>(b) What is the total area of the logo that is shaded? Ans: (b) [?] cm²",
      "answer0": "16",
      "answer1": "523.38",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 125,
      "difficulty_id": 3,
      "explanation": "(a) Big quarter-circle radius = 32 ÷ 2 = 16 cm. (b) Shaded area = 0.75 x 3.14 x (16² - 10²) + (16² - 10²) = 367.38 + 156 = 523.38 cm².",
      "hints": ["(a) The 32 cm spans two big radii.", "(b) Combine the quarter-circle ring area with the square region."],
      "source": "Catholic High 2025 P6 Prelim P2 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q43.png",
      "image_page": 30,
      "image_bbox": [0.3, 0.16, 0.6, 0.36],
      "image_loc": "logo of nested quarter circles with centre O; 10 cm radius and 32 cm width marked",
      "notes": "Key: (a) 16 cm; (b) 523.38 cm²."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "A and B are two rectangular containers. The base area of container A is twice the base area of container B. Container A was filled with water to a height of 10 cm and container B was empty. Container A has base 36 cm by 12 cm; container B has height 32 cm.<br>(a) What was the volume of the water in container A? Ans: (a) [?] ml<br>(b) All the water from container A was poured into container B without spilling. How much more water was needed to fill container B to the brim? Ans: (b) [?] ml",
      "answer0": "4320",
      "answer1": "2592",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 127,
      "difficulty_id": 3,
      "explanation": "(a) Volume in A = 36 x 12 x 10 = 4320 cm³ = 4320 ml. (b) Base area of B = half of A = 0.5 x 36 x 12 = 216 cm². Capacity of B = 216 x 32 = 6912 cm³. Water needed = 6912 - 4320 = 2592 cm³ = 2592 ml.",
      "hints": ["(a) Volume = base area x height of water.", "(b) B's base area is half A's; find B's capacity then subtract the water poured in."],
      "source": "Catholic High 2025 P6 Prelim P2 Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q44.png",
      "image_page": 31,
      "image_bbox": [0.2, 0.16, 0.74, 0.4],
      "image_loc": "container A (36 cm x 12 cm, water 10 cm) and taller container B (height 32 cm)",
      "notes": "Key: (a) 4320 ml; (b) 2592 ml."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "Mr Lee and Mrs Sim bought muffins at the price shown: chocolate muffins 3 for $5, vanilla muffins 4 for $6.<br>(a) Mr Lee bought an equal number of chocolate muffins and vanilla muffins. He spent $24 more on the chocolate muffins. How many muffins did he buy altogether? Ans: (a) [?]<br>(b) Mrs Sim spent an equal amount of money on the chocolate muffins and vanilla muffins. What fraction of the muffins she bought were chocolate? Leave your answer in the simplest form. Ans: (b) [?]",
      "answer0": "288",
      "answer1": "9/19",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 109,
      "difficulty_id": 3,
      "explanation": "(a) For 12 muffins of each: chocolate cost 4 x $5 = $20, vanilla 3 x $6 = $18, difference $2 per 12-and-12 set. $24 ÷ $2 = 12 sets; total = 12 x (12 + 12) = 288. (b) For equal money $30n: chocolate bought = $30n ÷ $5 x 3 = 18n; vanilla = $30n ÷ $6 x 4 = 20n. Fraction chocolate = 18n/(18n+20n) = 18/38 = 9/19.",
      "hints": ["(a) Compare cost of equal numbers using a common quantity (12 each).", "(b) Spend equal money, compute muffin counts, simplify the fraction."],
      "source": "Catholic High 2025 P6 Prelim P2 Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q45.png",
      "image_page": 32,
      "image_bbox": [0.18, 0.13, 0.78, 0.27],
      "image_loc": "table of chocolate muffins (3 for $5) and vanilla muffins (4 for $6) with pictures",
      "notes": "Key: (a) 288 muffins; (b) 9/19. Part (b) answer is a fraction stored as text in answer1."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "Chloe spent \\(\\dfrac{5}{8}\\) of her money on 3 identical books and 7 identical files. The cost of each book was 3 times the cost of each file. She bought some more files with \\(\\dfrac{5}{6}\\) of her remaining money and had $4 left. How much did Chloe spend on the files altogether?<br>Ans: $[?]",
      "answer0": "37.50",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 109,
      "difficulty_id": 3,
      "explanation": "1 book = 3 files, so 3 books + 7 files = 9 + 7 = 16 files = 5/8 of money. Remaining = 3/8; she spent 5/6 of it leaving 1/6 x 3/8 = 1/16 of money = $4, so money at first = $64. 16 files cost 5/8 x $64 = $40, so 1 file = $40 ÷ 16 = $2.50. Files bought with 5/6 of remaining = (5/6 x 3/8 x $64) ÷ $2.50 = $20 ÷ $2.50 = 8 files. Total files = 7 + 8 = 15; spend on files = 15 x $2.50 = $37.50.",
      "hints": ["Convert books to files (1 book = 3 files).", "Find total money from the $4 left, then the cost per file."],
      "source": "Catholic High 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: $37.50 spent on files (15 files at $2.50)."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "Three boys Lionel, Michael and Nate had the same number of coins. Lionel and Michael each had a mix of fifty-cent and ten-cent coins. Lionel had 10 ten-cent coins, while Michael had 15 ten-cent coins. Nate had only fifty-cent coins.<br>(a) How much more money did Lionel have than Michael? Ans: (a) $[?]<br>(b) Michael used all his fifty-cent coins to buy some food. He then had $8 less in coins than Nate. How many fifty-cent coins did Nate have? Ans: (b) [?]",
      "answer0": "2",
      "answer1": "19",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 117,
      "difficulty_id": 3,
      "explanation": "(a) Same total coins: Lionel has 5 fewer ten-cent coins than Michael, so 5 more fifty-cent coins. Difference = 5 x (50c - 10c) = 5 x 40c = 200c = $2. (b) Michael left with 15 x 10c = 150c. Nate's money = $8 + 150c = 800c + 150c = 950c. Nate's fifty-cent coins = 950c ÷ 50c = 19.",
      "hints": ["(a) Equal totals means swapping 5 ten-cent for 5 fifty-cent coins.", "(b) Michael's leftover ten-cent value plus $8 gives Nate's all-fifty-cent total."],
      "source": "Catholic High 2025 P6 Prelim P2 Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: (a) $2; (b) 19 fifty-cent coins."
    }
  ]
}