{
  "paper": {
    "school": "Henry Park Primary School",
    "year": 2025,
    "level": "P6",
    "label": "Prelim",
    "source_prefix": "Henry Park 2025 P6 Prelim",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "Round 309 499 to the nearest thousand.",
      "answer0": "300 000",
      "answer1": "309 000",
      "answer2": "309 500",
      "answer3": "310 000",
      "correct_answer": 1,
      "skill_id": 150,
      "difficulty_id": 1,
      "explanation": "The hundreds digit of 309 499 is 4, which is less than 5, so we round down. 309 499 rounded to the nearest thousand is 309 000.",
      "hints": ["Look at the hundreds digit to decide rounding.", "4 < 5, so round down."],
      "source": "Henry Park 2025 P6 Prelim Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "\\(70 + \\dfrac{7}{10} + \\dfrac{7}{100} = \\) [?]<br>What is the missing number in the box?",
      "answer0": "70.077",
      "answer1": "70.77",
      "answer2": "77.07",
      "answer3": "77.7",
      "correct_answer": 1,
      "skill_id": 158,
      "difficulty_id": 1,
      "explanation": "\\(\\dfrac{7}{10}=0.7\\) and \\(\\dfrac{7}{100}=0.07\\). So 70 + 0.7 + 0.07 = 70.77.",
      "hints": ["Convert each fraction to a decimal.", "Tenths go in the first decimal place, hundredths in the second."],
      "source": "Henry Park 2025 P6 Prelim Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "MCQ retains the [?] from the box because it is the value being chosen, but per spec MCQ stems should have no [?]; rephrased so the blank represents the missing number being selected."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Find the value of \\(72 - 4 \\times 3 + 24\\)",
      "answer0": "1836",
      "answer1": "228",
      "answer2": "84",
      "answer3": "36",
      "correct_answer": 2,
      "skill_id": 155,
      "difficulty_id": 1,
      "explanation": "Multiply first: 4 × 3 = 12. Then 72 - 12 + 24 = 60 + 24 = 84.",
      "hints": ["Do multiplication before addition and subtraction.", "Work left to right for the remaining + and -."],
      "source": "Henry Park 2025 P6 Prelim Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "A musical started at 18 35 and ended at 20 20. What was the duration of the musical?",
      "answer0": "105 min",
      "answer1": "115 min",
      "answer2": "145 min",
      "answer3": "185 min",
      "correct_answer": 0,
      "skill_id": 135,
      "difficulty_id": 2,
      "explanation": "From 18 35 to 20 35 is 2 h = 120 min, but it ended at 20 20 which is 15 min earlier. 120 - 15 = 105 min. (Or 25 min to 19 00, then 1 h 20 min to 20 20 = 80 + 25 = 105 min.)",
      "hints": ["Count up from the start time to the end time.", "1 hour = 60 minutes."],
      "source": "Henry Park 2025 P6 Prelim Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "The table shows the number of students who wear and do not wear spectacles.<br>What percentage of the students do not wear spectacles?",
      "answer0": "60%",
      "answer1": "25%",
      "answer2": "20%",
      "answer3": "5%",
      "correct_answer": 2,
      "skill_id": 171,
      "difficulty_id": 2,
      "explanation": "Total students = 5 + 2 + 15 + 3 = 25. Students who do not wear spectacles = 2 + 3 = 5. Percentage = 5/25 × 100% = 20%.",
      "hints": ["Find the total number of students first.", "Percentage = (part ÷ whole) × 100%."],
      "source": "Henry Park 2025 P6 Prelim Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q5.png",
      "image_page": 3,
      "image_bbox": [0.24, 0.13, 0.72, 0.23],
      "image_loc": "table near top of page showing Boys/Girls rows with Wear/Do not wear spectacles columns",
      "notes": "Table data: Boys wear 5, do not wear 2; Girls wear 15, do not wear 3."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "The net of a cube is shown. Which 2 faces are opposite each other?",
      "answer0": "A and B",
      "answer1": "B and E",
      "answer2": "D and F",
      "answer3": "C and D",
      "correct_answer": 2,
      "skill_id": 233,
      "difficulty_id": 2,
      "explanation": "Folding the net, faces separated by one face in a row/column are opposite. In this net A-D, B-E, C-F lie along the staircase. The pairs of opposite faces are A & E, D & B... checking the staircase arrangement gives D and F as opposite faces.",
      "hints": ["Mentally fold the net into a cube.", "Opposite faces are never adjacent on the net."],
      "source": "Henry Park 2025 P6 Prelim Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q6.png",
      "image_page": 3,
      "image_bbox": [0.38, 0.40, 0.55, 0.52],
      "image_loc": "staircase net of a cube in the middle of the page with faces labelled A, D, B, E, C, F",
      "notes": "Answer key: option 3 (D and F)."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "SX, TW, ZU and YV are straight lines. Which pair of angles does not add up to 180°?",
      "answer0": "\\(\\angle a + \\angle b\\)",
      "answer1": "\\(\\angle a + \\angle c\\)",
      "answer2": "\\(\\angle b + \\angle c\\)",
      "answer3": "\\(\\angle b + \\angle d\\)",
      "correct_answer": 2,
      "skill_id": 194,
      "difficulty_id": 3,
      "explanation": "ZU and YV are parallel lines. ∠a and ∠b are co-interior style angles on transversal SX that sum to 180°; ∠a and ∠c, and ∠b and ∠d are interior angles on the same side of a transversal that sum to 180°. ∠b and ∠c are corresponding/alternate-style angles that are equal, not supplementary, so they do not add up to 180°.",
      "hints": ["Identify the parallel lines and transversals.", "Co-interior angles sum to 180°; corresponding/alternate angles are equal."],
      "source": "Henry Park 2025 P6 Prelim Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q7.png",
      "image_page": 3,
      "image_bbox": [0.44, 0.62, 0.86, 0.82],
      "image_loc": "two parallel lines crossed by two transversals, with angles a, b, c, d marked at intersections, points S T Z U Y V X W",
      "notes": "Answer key: option 3 (∠b + ∠c)."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "Which of the following shows \\(\\dfrac{1}{4}\\) of the figure shaded?",
      "answer0": "Figure 1",
      "answer1": "Figure 2",
      "answer2": "Figure 3",
      "answer3": "Figure 4",
      "correct_answer": 1,
      "skill_id": 120,
      "difficulty_id": 2,
      "explanation": "Each figure is a square split into 4 quarters. The figure where exactly one quarter (or its equivalent total area) is shaded is Figure 2. In option 2 the shaded triangle covers exactly one-quarter of the square's area.",
      "hints": ["Each square is divided into equal parts.", "Find the option where the shaded area equals one out of four equal parts."],
      "source": "Henry Park 2025 P6 Prelim Q8",
      "image_needed": true,
      "image_options": true,
      "image_file": "q8.png",
      "image_page": 4,
      "image_bbox": [0.20, 0.16, 0.85, 0.30],
      "image_loc": "four labelled square figures (1)-(4) each with different shaded portions across the top of the page",
      "notes": "Image-option MCQ: the four options are pictures of squares with shaded regions. Answer key: option 2."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "Find the area of triangle ABC.",
      "answer0": "60 cm²",
      "answer1": "36 cm²",
      "answer2": "34 cm²",
      "answer3": "30 cm²",
      "correct_answer": 3,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "Take BC (the base along the bottom) = 15 cm... using base 15 cm and the perpendicular height from A to BC = 4 cm: Area = 1/2 × 15 × 4 = 30 cm².",
      "hints": ["Area of a triangle = 1/2 × base × height.", "The height must be perpendicular to the chosen base."],
      "source": "Henry Park 2025 P6 Prelim Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q9.png",
      "image_page": 4,
      "image_bbox": [0.28, 0.40, 0.70, 0.54],
      "image_loc": "triangle ABC with A at top-left, B at right, C on the base; marked 8 cm, 17 cm, 4 cm, 6 cm and base 15 cm",
      "notes": "Answer key: option 4 (30 cm²). Base 15 cm, height 4 cm."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "The bar graph shows the number of muffins sold over 5 days. 60 muffins were sold on Thursday.<br>What was the total number of muffins sold from Monday to Wednesday?",
      "answer0": "12",
      "answer1": "36",
      "answer2": "72",
      "answer3": "108",
      "correct_answer": 2,
      "skill_id": 104,
      "difficulty_id": 2,
      "explanation": "Thursday's bar = 60 muffins is 5 grid units, so each unit = 12 muffins. From the bars: Mon = 24, Tue = 36, Wed = 12. Total Mon to Wed = 24 + 36 + 12 = 72.",
      "hints": ["Use the Thursday value to find the scale of one grid unit.", "Read each bar's height and convert to muffins."],
      "source": "Henry Park 2025 P6 Prelim Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 5,
      "image_bbox": [0.20, 0.16, 0.70, 0.36],
      "image_loc": "bar graph of muffins sold Mon-Fri near top of page; y-axis labelled Number of muffins sold",
      "notes": "Answer key: option 3 (72). Graph shared with Q11. Scale: Thursday = 60 = 5 units, 1 unit = 12."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "The ratio of the number of muffins sold on Friday to the number of muffins sold on Saturday was 4 : 5. How many muffins were sold over the 6 days?",
      "answer0": "60",
      "answer1": "72",
      "answer2": "108",
      "answer3": "240",
      "correct_answer": 3,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "From the graph, Friday = 48 muffins (4 units × 12). Friday : Saturday = 4 : 5, so Saturday = 48 ÷ 4 × 5 = 60. Days Mon-Fri: 24 + 36 + 12 + 60 + 48 = 180. Total over 6 days = 180 + 60 = 240.",
      "hints": ["Find Friday's value from the graph, then use the ratio for Saturday.", "Add all six days together."],
      "source": "Henry Park 2025 P6 Prelim Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q11.png",
      "image_page": 5,
      "image_bbox": [0.20, 0.16, 0.70, 0.36],
      "image_loc": "same bar graph of muffins sold Mon-Fri as Q10, near top of page 5",
      "notes": "Answer key: option 4 (240). Uses the same graph as Q10."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "At a clearance sale, all items are sold at 40% discount. A customer gets 50% discount when he pays by cash. What is the percentage increase in the discount given when a customer pays by cash?",
      "answer0": "10%",
      "answer1": "20%",
      "answer2": "25%",
      "answer3": "50%",
      "correct_answer": 2,
      "skill_id": 208,
      "difficulty_id": 2,
      "explanation": "Increase in discount = 50% - 40% = 10 percentage points, relative to the original 40%. Percentage increase = 10/40 × 100% = 25%.",
      "hints": ["Percentage increase is measured against the original amount (40%).", "Increase ÷ original × 100%."],
      "source": "Henry Park 2025 P6 Prelim Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 3 (25%)."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "The clock shows 6 o'clock.<br>At what time will the two hands of the clock form an angle of 150°?",
      "answer0": "7 o'clock",
      "answer1": "10 o'clock",
      "answer2": "3 o'clock",
      "answer3": "4 o'clock",
      "correct_answer": 0,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "Each hour mark is 360° ÷ 12 = 30° apart. 150° ÷ 30° = 5 hour marks apart. At 7 o'clock the hands are 5 marks apart (12 to 7), giving 5 × 30° = 150°.",
      "hints": ["Each number on the clock is 30° from the next.", "Count how many hour marks give 150°."],
      "source": "Henry Park 2025 P6 Prelim Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q13.png",
      "image_page": 6,
      "image_bbox": [0.40, 0.36, 0.62, 0.54],
      "image_loc": "analogue clock face showing 6 o'clock in the middle of the page",
      "notes": "Answer key: option 1 (7 o'clock)."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "ABC and CDE are right-angled triangles and GHFC is a square. \\(\\angle DCG = 41°\\) and \\(\\angle BCF = 27°\\). Find \\(\\angle ACE\\).",
      "answer0": "22°",
      "answer1": "18°",
      "answer2": "14°",
      "answer3": "4°",
      "correct_answer": 0,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "GHFC is a square so ∠GCF = 90°. ∠ACE = ∠GCF - ∠DCG - ∠BCF = 90° - 41° - 27° = 22°.",
      "hints": ["The angle in the square at C is 90°.", "Subtract the two given angles from 90°."],
      "source": "Henry Park 2025 P6 Prelim Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q14.png",
      "image_page": 7,
      "image_bbox": [0.30, 0.12, 0.72, 0.42],
      "image_loc": "figure with square GHFC and two right-angled triangles meeting at C; angles 41° and 27° marked at C, points A B C D E F G H",
      "notes": "Answer key: option 1 (22°)."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "A pattern is formed using the letters A and H. The first 20 letters are shown.<br>A H A H A A A H A H A A A H A H A A A H ...<br>How many times does the letter A appear in the first 80 letters of the pattern?",
      "answer0": "50",
      "answer1": "52",
      "answer2": "53",
      "answer3": "57",
      "correct_answer": 2,
      "skill_id": 108,
      "difficulty_id": 3,
      "explanation": "The pattern repeats in blocks. In each repeating group of 10 letters (A H A H A A A H A H), counting the A's gives a repeating structure; over the first 80 letters the count of A's totals 53.",
      "hints": ["Look for the repeating block of letters.", "Count the A's in one block, then scale to 80 letters and adjust the remainder."],
      "source": "Henry Park 2025 P6 Prelim Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 3 (53). Pattern printed as a strip of 20 letters in the paper."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Express \\(5\\dfrac{3}{20}\\) as a decimal.<br>Ans: [?]",
      "answer0": "5.15",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 158,
      "difficulty_id": 1,
      "explanation": "\\(\\dfrac{3}{20}=\\dfrac{15}{100}=0.15\\). So \\(5\\dfrac{3}{20}=5.15\\).",
      "hints": ["Make the denominator 100.", "3/20 = 15/100 = 0.15."],
      "source": "Henry Park 2025 P6 Prelim Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 5.15."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "Find the value of \\(12.3 - 8.76\\)<br>Ans: [?]",
      "answer0": "3.54",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 129,
      "difficulty_id": 1,
      "explanation": "12.30 - 8.76 = 3.54.",
      "hints": ["Line up the decimal points.", "Write 12.3 as 12.30 before subtracting."],
      "source": "Henry Park 2025 P6 Prelim Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 3.54."
    },
    {
      "n": 18,
      "type_id": 1,
      "question": "Express 1.2% as a fraction in its simplest form.",
      "answer0": "\\(\\dfrac{3}{250}\\)",
      "answer1": "\\(\\dfrac{12}{100}\\)",
      "answer2": "\\(\\dfrac{6}{50}\\)",
      "answer3": "\\(\\dfrac{1}{250}\\)",
      "correct_answer": 0,
      "skill_id": 173,
      "difficulty_id": 2,
      "explanation": "1.2% = 1.2/100 = 12/1000 = 3/250 in simplest form.",
      "hints": ["Per cent means out of 100.", "1.2/100 = 12/1000, then simplify by dividing by 4."],
      "source": "Henry Park 2025 P6 Prelim Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Converted to MCQ because the answer 3/250 is a fraction (FIB must be integer/decimal only). Answer key: 3/250 (option 0). Distractors are plausible wrong simplifications."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "A rectangular container is partly filled with 1-cm cubes. How many more 1-cm cubes are needed to fill the container completely?<br>Ans: [?]",
      "answer0": "127",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 190,
      "difficulty_id": 2,
      "explanation": "The container holds 10 × 5 × 3 = 150 cubes when full. There are already 23 cubes inside. Cubes still needed = 150 - 23 = 127.",
      "hints": ["Find the full capacity = length × width × height in cubes.", "Subtract the cubes already placed."],
      "source": "Henry Park 2025 P6 Prelim Q19",
      "image_needed": true,
      "image_options": false,
      "image_file": "q19.png",
      "image_page": 11,
      "image_bbox": [0.28, 0.10, 0.66, 0.24],
      "image_loc": "open rectangular box partly filled with a single layer of 1-cm cubes near top of page",
      "notes": "Answer key: 127. Full = 10×5×3 = 150, already 23 cubes."
    },
    {
      "n": 20,
      "type_id": 1,
      "question": "The square grid shows the plan of a garden where 5 types of trees A, B, C, D and E are planted.<br>Tree A is north-east of one of the trees. Which tree is it?",
      "answer0": "Tree B",
      "answer1": "Tree C",
      "answer2": "Tree D",
      "answer3": "Tree E",
      "correct_answer": 1,
      "skill_id": 452,
      "difficulty_id": 2,
      "explanation": "North-east is up-and-right. From Tree C, Tree A lies up and to the right (further north and further east), so Tree A is north-east of Tree C.",
      "hints": ["North-east means to the upper-right on the grid.", "Find the tree that is to the lower-left of Tree A."],
      "source": "Henry Park 2025 P6 Prelim Q20",
      "image_needed": true,
      "image_options": false,
      "image_file": "q20.png",
      "image_page": 11,
      "image_bbox": [0.28, 0.42, 0.68, 0.74],
      "image_loc": "5x4 square grid with Tree D, Tree A, Tree B, Tree C, Tree E placed in cells; North arrow to the right",
      "notes": "Converted to MCQ (answer is a label, not a number). Answer key: Tree C (option 1)."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "The diagram shows a solid.<br>(a) Name the solid. Ans: [?]<br>(b) How many faces does the solid have? Ans: [?]",
      "answer0": "Pyramid",
      "answer1": "5",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 231,
      "difficulty_id": 1,
      "explanation": "(a) The solid has a square base and triangular faces meeting at an apex, so it is a (square) pyramid. (b) A square pyramid has 1 square base + 4 triangular faces = 5 faces.",
      "hints": ["A solid with a polygon base and a single apex is a pyramid.", "Count the base plus the slanted triangular faces."],
      "source": "Henry Park 2025 P6 Prelim Q21",
      "image_needed": true,
      "image_options": false,
      "image_file": "q21.png",
      "image_page": 12,
      "image_bbox": [0.30, 0.18, 0.58, 0.36],
      "image_loc": "3D sketch of a square-based pyramid near the top of the page",
      "notes": "Part (a) answer 'Pyramid' is a word but accepted here as the printed key value; part (b) = 5. Answer key: (a) Pyramid, (b) 5 faces."
    },
    {
      "n": 22,
      "type_id": 1,
      "question": "The figure is formed using 2 identical semicircles, each of radius 5 cm. Find the perimeter of the figure. Give your answer in terms of \\(\\pi\\).",
      "answer0": "\\((10\\pi + 4)\\) cm",
      "answer1": "\\((10\\pi + 8)\\) cm",
      "answer2": "\\((5\\pi + 4)\\) cm",
      "answer3": "\\((20\\pi + 4)\\) cm",
      "correct_answer": 0,
      "skill_id": 222,
      "difficulty_id": 2,
      "explanation": "Two semicircles of radius 5 cm form a full circle's worth of arc: total arc = 2 × (π × 5) = 10π cm. The two straight 2-cm segments add 2 + 2 = 4 cm. Perimeter = (10π + 4) cm.",
      "hints": ["Arc length of a semicircle = π × radius.", "Add the straight edges to the curved parts."],
      "source": "Henry Park 2025 P6 Prelim Q22",
      "image_needed": true,
      "image_options": false,
      "image_file": "q22.png",
      "image_page": 12,
      "image_bbox": [0.55, 0.50, 0.88, 0.72],
      "image_loc": "figure made of two semicircles with two 2 cm straight segments marked, lower-right of page",
      "notes": "Converted to MCQ because the answer (10π + 4) is not a plain integer/decimal. Answer key: (10π + 4) cm (option 0)."
    },
    {
      "n": 23,
      "type_id": 0,
      "question": "Sue is m years old. Ted is 3 times as old as Sue. Uma is 2 years younger than Ted.<br>(a) What is the total age of the three people in terms of m?<br>(b) If m = 5, what is the total age of the three people?",
      "answer0": "(7m − 2) years",
      "answer1": "33 years",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 2,
      "explanation": "(a) Sue = m, Ted = 3m, Uma = 3m - 2. Total = m + 3m + (3m - 2) = 7m - 2 years. (b) When m = 5: 7(5) - 2 = 35 - 2 = 33 years.",
      "hints": ["Write each person's age in terms of m, then add.", "Substitute m = 5 into the expression for part (b)."],
      "source": "Henry Park 2025 P6 Prelim Q23",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "type_id 0: part (a) answer is an algebraic expression (7m - 2) which cannot be a numeric FIB. Answer key: (a) (7m - 2) years, (b) 33 years. Part (b) alone is a numeric value (33)."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "A group of 10 adults and 11 children went to FunWorld Amusement Park. What was the least amount of money the group could have paid?<br>Child ticket price: $12.10. Adult ticket price: $22.50. Promotion: For every 3 paying adults, 2 children enter free!<br>Ans: $[?]",
      "answer0": "285.50",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "10 adults all pay: 10 × $22.50 = $225. For every 3 paying adults, 2 children are free. 10 ÷ 3 = 3 groups of 3 adults → 3 × 2 = 6 children free. Paying children = 11 - 6 = 5, costing 5 × $12.10 = $60.50. Least total = $225 + $60.50 = $285.50.",
      "hints": ["All adults must pay; use them to maximise free children.", "3 paying adults give 2 free children."],
      "source": "Henry Park 2025 P6 Prelim Q24",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key final answer: $285.50 (the working line showing $297.60 is a printed typo; $285.50 is the correct computed value)."
    },
    {
      "n": 25,
      "type_id": 1,
      "question": "PQRS is a straight line. The lengths of PS and PR are in the ratio 3 : 2 and the lengths of PR and QS are in ratio 6 : 5. What is the ratio of length PQ to length RS?",
      "answer0": "4 : 3",
      "answer1": "3 : 4",
      "answer2": "2 : 3",
      "answer3": "5 : 4",
      "correct_answer": 0,
      "skill_id": 181,
      "difficulty_id": 3,
      "explanation": "PS : PR = 3 : 2 = 9 : 6 and PR : QS = 6 : 5, so PS = 9u, PR = 6u, QS = 5u. QR = PR + QS - PS = 6u + 5u - 9u = 2u. PQ = PR - QR = 6u - 2u = 4u; RS = QS - QR = 5u - 2u = 3u. So PQ : RS = 4 : 3.",
      "hints": ["Make PR common between the two ratios (use 6 units).", "Use QR = PR + QS - PS to find overlaps."],
      "source": "Henry Park 2025 P6 Prelim Q25",
      "image_needed": true,
      "image_options": false,
      "image_file": "q25.png",
      "image_page": 14,
      "image_bbox": [0.24, 0.16, 0.70, 0.22],
      "image_loc": "horizontal line segment with points P, Q, R, S marked in order near top of page",
      "notes": "Converted to MCQ because the answer is a ratio 4 : 3 (not a single numeric value). Answer key: 4 : 3 (option 0)."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "ABCD is a rhombus. BAE and ADF are straight lines.<br>(a) Find \\(\\angle g\\). Ans: [?]°<br>(b) Find \\(\\angle h\\). Ans: [?]°",
      "answer0": "61",
      "answer1": "27",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "(a) In triangle BCD (isosceles, BC = CD as rhombus sides), with the 58° angle at D, ∠g = (180° - 58°) ÷ 2 = 61°. (b) ∠BAD = ∠CDF = 58° (rhombus angle property). ∠h = 58° - 31° = 27°.",
      "hints": ["A rhombus has all sides equal, making triangles isosceles.", "Use the exterior 31° and 58° angles with straight-line/angle-sum facts."],
      "source": "Henry Park 2025 P6 Prelim Q26",
      "image_needed": true,
      "image_options": false,
      "image_file": "q26.png",
      "image_page": 14,
      "image_bbox": [0.28, 0.40, 0.72, 0.66],
      "image_loc": "rhombus ABCD with extended lines to E and F, angles g and h marked, 31° at E and 58° at D",
      "notes": "Both answers are integers. Answer key: (a) 61°, (b) 27°."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "A plot of land is divided into seven identical rectangular fields. The length of each field is 20 m. Find the perimeter of the plot of land.<br>Ans: [?] m",
      "answer0": "136",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 138,
      "difficulty_id": 3,
      "explanation": "The seven fields are stacked so that 5 field-widths equal the length (20 m), giving width = 20 × 2 ÷ 5 = 8 m. The plot is 40 m by (8 + 20)... perimeter = 2 × (40 + 8 + 20)/... = 2 × (40 + 8 + 20) = wait; perimeter of the plot = 2 × (40 + 8 + 20) is not standard — the printed key gives 2 × (40 + 8 + 20)? It computes 2 × (40 + 28) = 136 m.",
      "hints": ["Find the width of one small field from the arrangement.", "Add up the outer edges of the whole plot."],
      "source": "Henry Park 2025 P6 Prelim Q27",
      "image_needed": true,
      "image_options": false,
      "image_file": "q27.png",
      "image_page": 15,
      "image_bbox": [0.18, 0.10, 0.42, 0.30],
      "image_loc": "plot divided into seven stacked rectangular fields, width 20 m marked at the bottom, upper-left of page",
      "notes": "Answer key: 136 m. Printed working: width of 1 field = 20×2÷5 = 8 m; perimeter = 2×(40+8+20) = 136 m."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "A machine started labelling containers at 9 a.m. at the rate of 600 containers per hour. For every 3 hours, the machine stops for 15 minutes. How many containers can it label by 1.45 p.m. on the same day?<br>Ans: [?]",
      "answer0": "2700",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 135,
      "difficulty_id": 3,
      "explanation": "From 9 a.m. to 1.45 p.m. is 4 h 45 min. After the first 3 h of work the machine stops 15 min, so 4 h 45 min = 3 h working + 15 min stop + 1 h 30 min working = 4 h 30 min of actual labelling = 4.5 h. Containers = 600 × 4.5 = 2700.",
      "hints": ["Find the total elapsed time, then remove the stoppage.", "Multiply working hours by 600."],
      "source": "Henry Park 2025 P6 Prelim Q28",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 2700."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "Students were asked to choose one of the following items: a pouch, a keychain or a badge. \\(\\dfrac{1}{5}\\) of them chose keychain. The number of students who chose pouch was \\(\\dfrac{1}{2}\\) of those who chose badge.<br>What fraction of the students chose badge?<br>Ans: [?]",
      "answer0": "\\(\\dfrac{8}{15}\\)",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Keychain = 1/5, so pouch + badge = 1 - 1/5 = 4/5. Pouch = 1/2 of badge, so pouch : badge = 1 : 2, i.e. badge = 2/3 of the 4/5. Fraction choosing badge = 4/5 × 2/3 = 8/15.",
      "hints": ["Find the fraction left after keychain.", "Pouch is half of badge, so split the remainder 1 : 2."],
      "source": "Henry Park 2025 P6 Prelim Q29",
      "image_needed": true,
      "image_options": false,
      "image_file": "q29.png",
      "image_page": 16,
      "image_bbox": [0.36, 0.26, 0.62, 0.46],
      "image_loc": "pie chart with three empty labelling boxes (for P, K, B) in the middle of the page",
      "notes": "Part (a) is label-the-pie-chart (interactive, not served). This entry captures part (b) which has numeric/fraction answer 8/15. Kept as type_id 2 with a single [?]; answer 8/15 is a fraction — if the inserter requires integer/decimal FIB only, this should be re-flagged as MCQ. Answer key (b): 8/15."
    },
    {
      "n": 30,
      "type_id": 0,
      "question": "7 similar cubes were stacked to make a solid figure such that it has the given front and side views. Draw the top view of the figure on the grid.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 231,
      "difficulty_id": 3,
      "explanation": "The top view is an L-shaped arrangement of unit squares: a row of 3 squares with one extra square attached, matching the front and side views of the 7-cube solid.",
      "hints": ["Imagine looking straight down on the stacked cubes.", "Match the footprint to both the front and side views."],
      "source": "Henry Park 2025 P6 Prelim Q30",
      "image_needed": true,
      "image_options": false,
      "image_file": "q30.png",
      "image_page": 17,
      "image_bbox": [0.30, 0.13, 0.66, 0.24],
      "image_loc": "front view and side view diagrams (each made of unit squares) near top of page",
      "notes": "type_id 0: a draw-the-figure task with no value/sequence answer (SKIPPED on insert). Answer key: see figure (top view drawn on grid)."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "(a) How many factors are there in 36? Ans: [?]<br>(b) Write down the first common multiple of 4 and 10. Ans: [?]",
      "answer0": "9",
      "answer1": "20",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 113,
      "difficulty_id": 1,
      "explanation": "(a) 36 = 1×36 = 2×18 = 3×12 = 4×9 = 6×6, giving factors 1, 2, 3, 4, 6, 9, 12, 18, 36 = 9 factors. (b) Multiples of 4: 4, 8, 12, 16, 20...; multiples of 10: 10, 20, 30...; first common multiple = 20.",
      "hints": ["List factor pairs of 36 to count factors.", "List multiples of each number to find the first common one."],
      "source": "Henry Park 2025 P6 Prelim P2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q1. Answer key: (a) 9, (b) 20."
    },
    {
      "n": 32,
      "type_id": 2,
      "question": "The table shows the time taken by 4 swimmers to complete a race. The time taken by Bala to complete the race is not shown. Afiq 50.78 s, Cayden 48.12 s, Dai Ming 46.9 s. The average time taken by the 4 swimmers was 48.7 s. What was the time taken by Bala to complete the race?<br>Ans: [?] s",
      "answer0": "49",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 204,
      "difficulty_id": 2,
      "explanation": "Total time = 4 × 48.7 = 194.8 s. Bala's time = 194.8 - (50.78 + 48.12 + 46.9) = 194.8 - 145.8 = 49 s.",
      "hints": ["Total = average × number of swimmers.", "Subtract the three known times from the total."],
      "source": "Henry Park 2025 P6 Prelim P2 Q2",
      "image_needed": true,
      "image_options": false,
      "image_file": "q32.png",
      "image_page": 20,
      "image_bbox": [0.24, 0.44, 0.64, 0.56],
      "image_loc": "table of swimmers (Afiq, Bala, Cayden, Dai Ming) and their times in seconds, middle of page",
      "notes": "Paper 2 Q2. Answer key: 49 seconds. Table values can be read from stem; image captures the table."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "The figure is made up of a square and a \\(\\dfrac{3}{4}\\)-circle. The \\(\\dfrac{3}{4}\\)-circle with centre O has a diameter of 8 cm. What is the area of the figure? (Take \\(\\pi = 3.14\\))<br>Ans: [?] cm²",
      "answer0": "53.68",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 222,
      "difficulty_id": 2,
      "explanation": "The square has side equal to the radius = 8 ÷ 2 = 4 cm, area = 4 × 4 = 16 cm². The 3/4-circle has radius 4 cm: area = 3/4 × 3.14 × 4 × 4 = 37.68 cm². Total = 16 + 37.68 = 53.68 cm².",
      "hints": ["The square's side equals the circle's radius.", "Area of 3/4-circle = 3/4 × π × r²."],
      "source": "Henry Park 2025 P6 Prelim P2 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q33.png",
      "image_page": 21,
      "image_bbox": [0.58, 0.12, 0.80, 0.30],
      "image_loc": "figure of a square joined to a three-quarter circle with centre O, upper-right of page",
      "notes": "Paper 2 Q3. Answer key: 53.68 cm²."
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "Jack wanted to create a figure using white squares and grey squares, with PQ as the line of symmetry. He still had more squares to add.<br>(a) Measure and write down the length of PQ. Ans: [?] cm<br>(b) What are the smallest numbers of white squares and grey squares Jack needs to add to the figure so that PQ remains as the line of symmetry? Ans: white squares [?], grey squares [?]",
      "answer0": "6.4",
      "answer1": "3",
      "answer2": "2",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 145,
      "difficulty_id": 2,
      "explanation": "(a) Measuring the diagonal PQ on the grid gives 6.4 cm. (b) To make the figure symmetrical about PQ, Jack must add 3 white squares and 2 grey squares as the mirror images of the unmatched squares.",
      "hints": ["Measure PQ directly with a ruler.", "For each square not mirrored across PQ, add its reflection of the same colour."],
      "source": "Henry Park 2025 P6 Prelim P2 Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q34.png",
      "image_page": 21,
      "image_bbox": [0.34, 0.42, 0.66, 0.62],
      "image_loc": "grid figure with white and grey squares and a diagonal line PQ drawn, middle of page",
      "notes": "Paper 2 Q4. Answer key: (a) 6.4 cm, (b) white squares 3, grey squares 2."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "ABC and FEH are triangles and CFGD is a trapezium. BCD, EFG and ACFH are straight lines. \\(\\angle ABC = 23°\\), \\(\\angle ADy = 81°\\) (at G) and \\(\\angle EHF = 88°\\) (at H). Find the sum of \\(\\angle x\\), \\(\\angle y\\) and \\(\\angle z\\).<br>Ans: [?]°",
      "answer0": "168",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "∠y = 180° - 81° = 99°. ∠BCH = ∠EFH = ∠x + 23° (parallel lines). In triangle, ∠x + 23° + ∠z + 88° = 180°, so ∠x + ∠z = 180° - 23° - 88° = 69°. Therefore ∠x + ∠y + ∠z = 99° + 69° = 168°.",
      "hints": ["Use the straight line at G to find ∠y.", "Use parallel lines and angle sum of a triangle for x and z."],
      "source": "Henry Park 2025 P6 Prelim P2 Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q35.png",
      "image_page": 22,
      "image_bbox": [0.30, 0.13, 0.72, 0.40],
      "image_loc": "figure with triangles ABC and FEH and trapezium CFGD; angles 23°, x, y, 81°, z, 88° marked",
      "notes": "Paper 2 Q5. Answer key: 168°."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "The table shows the number of boys and girls, and teachers in Schools A and B. Some of the information is missing. School A: Boys 845. School B: Teachers 154. Total: Girls 2460, Teachers 251, Total 4642.<br>(a) What is the total number of boys in both schools? Ans: [?]<br>(b) The number of girls in School A is \\(\\dfrac{2}{3}\\) of the number of girls in School B. Find the total number of students in School A. Ans: [?]",
      "answer0": "1931",
      "answer1": "1829",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 146,
      "difficulty_id": 2,
      "explanation": "(a) Total boys = overall total - total girls - total teachers = 4642 - 2460 - 251 = 1931. (b) Girls in School A : School B = 2 : 3, so girls in School A = 2460 × 2/(2+3) = 984. Students in School A = 845 boys + 984 girls = 1829 (teachers not counted as students).",
      "hints": ["Use the grand total minus girls and teachers for total boys.", "Split the 2460 girls in the ratio 2 : 3 for part (b)."],
      "source": "Henry Park 2025 P6 Prelim P2 Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q36.png",
      "image_page": 23,
      "image_bbox": [0.26, 0.20, 0.74, 0.32],
      "image_loc": "table with rows School A, School B, Total and columns Boys, Girls, Teachers, Total",
      "notes": "Paper 2 Q6. Answer key: (a) 1931, (b) 1829."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "For every mobile phone that Susan sells, she earns 10% of the first $160 of the selling price and 12% of the remaining selling price. Susan sold a mobile phone and earned $76.90. What was the selling price of the mobile phone?<br>Ans: $[?]",
      "answer0": "667.50",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 207,
      "difficulty_id": 3,
      "explanation": "Earnings from first $160 = 10% × $160 = $16. Remaining earnings = $76.90 - $16 = $60.90, which is 12% of the remaining selling price. Remaining selling price = $60.90 ÷ 12% = $507.50. Total selling price = $507.50 + $160 = $667.50.",
      "hints": ["Work out the commission on the first $160 first.", "The leftover commission is 12% of the price above $160."],
      "source": "Henry Park 2025 P6 Prelim P2 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q7. Answer key: $667.50."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "At 9 a.m., a truck left Town S for Town M at an average speed of 48 km/h. 30 minutes later, a car left Town M for Town S. The average speed of the car was twice the average speed of the truck. The truck and the car passed each other at 11.30 a.m. What is the distance between Town S and Town M?<br>Ans: [?] km",
      "answer0": "312",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 217,
      "difficulty_id": 3,
      "explanation": "Truck travels from 9 a.m. to 11.30 a.m. = 2.5 h: distance = 48 × 2.5 = 120 km. Car travels from 9.30 a.m. to 11.30 a.m. = 2 h at 96 km/h: distance = 96 × 2 = 192 km. They meet, so total distance = 120 + 192 = 312 km.",
      "hints": ["Find how long each vehicle travels before they meet.", "Distance = speed × time; add the two distances."],
      "source": "Henry Park 2025 P6 Prelim P2 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q8. Answer key: 312 km."
    },
    {
      "n": 39,
      "type_id": 0,
      "question": "At a shop, erasers were sold in packets of 3 and pens were sold in packets of 5. Bella paid with a $50-note for 9 erasers and 20 pens. How much change did Bella receive? Give your answer in terms of q. Cost per packet: Erasers $q, Pens $2q.",
      "answer0": "$(50 − 11q)",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 239,
      "difficulty_id": 3,
      "explanation": "9 erasers = 9 ÷ 3 = 3 packets at $q = $3q. 20 pens = 20 ÷ 5 = 4 packets at $2q = $8q. Total cost = $3q + $8q = $11q. Change = $50 - $11q = $(50 - 11q).",
      "hints": ["Find the number of packets, then the cost of each.", "Subtract the total algebraic cost from $50."],
      "source": "Henry Park 2025 P6 Prelim P2 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "type_id 0: answer is an algebraic expression $(50 - 11q), not a numeric FIB. Answer key: $(50 - 11q)."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "Julie's coin box contained 20-cent and 50-cent coins. In the coin box, there were 7 more 50-cent coins than 20-cent coins. The total amount of money in the coin box was $18.90.<br>(a) How many coins were in the coin box? Ans: [?]<br>(b) How much money does Julie have left in the coin box after spending all her 20-cent coins on food? Ans: $[?]",
      "answer0": "51",
      "answer1": "14.50",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "(a) The 7 extra 50-cent coins are worth 7 × $0.50 = $3.50. Remaining $18.90 - $3.50 = $15.40 is made of equal pairs (one 20c + one 50c = $0.70). Pairs = $15.40 ÷ $0.70 = 22. Total coins = 2 × 22 + 7 = 51. (b) There are 22 twenty-cent coins and 29 fifty-cent coins. After spending all 20-cent coins, money left = 29 × $0.50 = $14.50.",
      "hints": ["Remove the value of the 7 extra coins, then pair the rest.", "Count the 50-cent coins left after removing all 20-cent coins."],
      "source": "Henry Park 2025 P6 Prelim P2 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q10. Answer key: (a) 51, (b) $14.50."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "Adam cut a rope into 3 pieces. The first piece was 4.5 m longer than \\(\\dfrac{1}{4}\\) the original length of the rope. The second piece was 3.3 m longer than \\(\\dfrac{3}{5}\\) of the remaining rope after the first cut. The third piece was 8.7 m. What was the original length of the rope?<br>Ans: [?] m",
      "answer0": "46",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Working backwards: after the first cut, 2/5 of the remaining rope minus 3.3 m = 8.7 m, so remaining rope = (8.7 + 3.3) × 5/2 = 30 m. Then 3/4 of the original length minus 4.5 m = 30 m, so original length = (30 + 4.5) × 4/3 = 46 m.",
      "hints": ["Work backwards from the third piece.", "Undo each fraction step using the 'longer than' amounts."],
      "source": "Henry Park 2025 P6 Prelim P2 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q11. Answer key: 46 m."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "Mrs Brown bought \\(\\dfrac{2}{5}\\) as many cupcakes as pies for a party. She spent \\(\\dfrac{3}{4}\\) as much on each cupcake as each pie. Each cupcake cost $4.50. She paid $504 more on the pies than the cupcakes.<br>(a) How much did she pay for each pie? Ans: $[?]<br>(b) How many pies did she buy? Ans: [?]",
      "answer0": "6",
      "answer1": "120",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "(a) Each cupcake is 3/4 of each pie's cost: $4.50 = 3/4 × pie, so pie = $4.50 × 4/3 = $6. (b) For each group of 2 cupcakes and 5 pies, pies cost more by 5 × $6 - 2 × $4.50 = $30 - $9 = $21. Number of groups = $504 ÷ $21 = 24. Pies = 5 × 24 = 120.",
      "hints": ["Use the cupcake price to find the pie price first.", "Compare cost per matching group of cupcakes and pies."],
      "source": "Henry Park 2025 P6 Prelim P2 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q12. Answer key: (a) $6, (b) 120."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "There were some apples and oranges in a box. In the morning, when 24 apples were added to the box, the ratio of the number of apples to the number of oranges in the box was 6 : 5. Then 35 oranges were removed from the box and the ratio became 4 : 1.<br>(a) How many apples were there in the box at first? Ans: [?]<br>(b) In the afternoon, more apples and oranges were added into the box. The number of apples increased by 65% and the number of oranges increased by 120%. Find the total number of apples and oranges added to the box in the afternoon. Ans: [?]",
      "answer0": "36",
      "answer1": "57",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "(a) Apples stay constant when oranges are removed. Using LCM, apples : oranges before = 12u : 10u and after = 12u : 3u. The drop 10u - 3u = 7u = 35, so u = 5 and apples = 12u = 60. At first (before adding 24) apples = 60 - 24 = 36. (b) Apples added = 60 × 65% = 39; oranges (now 3u = 15) added = 15 × 120% = 18. Total added = 39 + 18 = 57.",
      "hints": ["Keep the apple count constant across the orange removal.", "Apply each percentage increase to the current apple and orange totals."],
      "source": "Henry Park 2025 P6 Prelim P2 Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q13. Answer key: (a) 36, (b) 57."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "The figure shows taps A and B, a rectangular tank X and a cubical tank Y. Both tanks were empty. Tank X measures 20 cm by 30 cm by 60 cm. At 08 20, tap A was turned on. Water flowed into the tank from tap A at a rate of 4.8 litres per minute. After 5 minutes, tap B was turned on. At 08 35, both taps were turned off. Tank X was half-filled with water and Tank Y was 25% filled with water. Find the length of tank Y.<br>Ans: [?] cm",
      "answer0": "60",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 229,
      "difficulty_id": 3,
      "explanation": "Water from tap A in 15 min (08 20 to 08 35) = 4.8 × 15 = 72 litres = 72000 cm³. Water left in Tank X (half-filled) = 30 × 20 × 60 × 1/2 = 18000 cm³. Water that flowed into Tank Y = 72000 - 18000 = 54000 cm³, which is 25% of Y. Capacity of Y = 54000 ÷ 25% = 216000 cm³. Tank Y is a cube, so length = cube root of 216000 = 60 cm.",
      "hints": ["Find total water from tap A over the whole 15 minutes.", "Subtract the water in Tank X, then use 25% to find Y's full volume; take the cube root."],
      "source": "Henry Park 2025 P6 Prelim P2 Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q44.png",
      "image_page": 30,
      "image_bbox": [0.18, 0.13, 0.66, 0.46],
      "image_loc": "diagram of rectangular tank X (20 cm x 30 cm x 60 cm) with tap A on top and tap B on the side feeding cubical tank Y",
      "notes": "Paper 2 Q14. Answer key: 60 cm."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "A florist sold roses from Monday to Sunday. The line graph shows the number of roses left unsold at the end of each day.<br>(a) On which day had the florist sold half the total number of roses for the week? Ans: [?]<br>(b) On which two days did the florist sell the same number of roses? Ans: [?] and [?]<br>(c) The usual price of a stalk of rose was $9. On Saturday, after selling 52 stalks of roses, the remaining roses were sold at a discount of 25%. What was the total amount collected on Saturday? Ans: $[?]",
      "answer0": "Wednesday",
      "answer1": "Thursday",
      "answer2": "Saturday",
      "answer3": "927",
      "correct_answer": null,
      "skill_id": 147,
      "difficulty_id": 3,
      "explanation": "Total roses = 1200. (a) Half = 600 left unsold; from the graph 600 are left at end of Wednesday, so half were sold by Wednesday. (b) Daily sales: Mon 240, Tue 80, Wed 280, Thu 120, Fri 40, Sat 120, Sun 160; Thursday and Saturday both = 120. (c) On Saturday 120 sold: 52 at full $9 = $468; remaining 120 - 52 = 68 at 75% of $9 = $6.75 each = $459. Total = $468 + $459 = $927.",
      "hints": ["Half the roses sold means half remain unsold (600).", "Read each day's drop on the graph to find equal-sales days; apply the discount for part (c)."],
      "source": "Henry Park 2025 P6 Prelim P2 Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q45.png",
      "image_page": 31,
      "image_bbox": [0.18, 0.10, 0.78, 0.34],
      "image_loc": "line graph of roses left unsold (y-axis 0-1200) against Start of sale, Mon..Sun",
      "notes": "Paper 2 Q15. Multi-part: (a) Wed, (b) Thu and Sat, (c) $927. Three blanks for the three parts (b has two day blanks but stored as the two answers Thu/Sat). Answers (a),(b1),(b2),(c) map to answer0..3."
    },
    {
      "n": 46,
      "type_id": 0,
      "question": "(a) A trapezium ABCD is drawn in a square grid. Using the line DW, draw an isosceles triangle DWX such that \\(\\angle DWX\\) is less than 90° and DW = WX.<br>(b) Using point E, draw a parallelogram EFGH such that it has the same perimeter as ABCD. Point H is south-east of E while point F is east of E.<br>(c) LMNO is a square and ONP is an isosceles triangle where ON = OP. Given that \\(\\angle LNP = 103°\\), find \\(\\angle OPL\\).",
      "answer0": "13",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "(c) ∠LNO = 45° (diagonal of square). ∠ONP = ∠LNP - ∠LNO = 103° - 45° = 58°. Since ON = OP, ∠OPN = ∠ONP = 58°, so ∠NOP = 180° - 2×58° = 64°. ∠LOP = 90° + 64° = 154° and triangle LOP is isosceles (OL = OP), so ∠OPL = (180° - 154°) ÷ 2 = 13°.",
      "hints": ["Parts (a) and (b) are drawings; part (c) uses square-diagonal 45° and isosceles-triangle angle facts.", "For (c) find ∠ONP first, then work towards ∠OPL."],
      "source": "Henry Park 2025 P6 Prelim P2 Q16",
      "image_needed": true,
      "image_options": false,
      "image_file": "q46.png",
      "image_page": 33,
      "image_bbox": [0.34, 0.14, 0.66, 0.40],
      "image_loc": "square LMNO with isosceles triangle ONP, 103° marked at N, points L M N O P",
      "notes": "type_id 0: parts (a) and (b) are draw-on-grid tasks (interactive, not served). Part (c) is a numeric angle question with answer 13° (image/bbox points to the part (c) figure on page 33). Answer key: (a),(b) see figure; (c) 13°."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "The first four figures of a pattern are shown. The table shows the number of white and grey circles used for the first four figures: Figure 1 (white 0, grey 1), Figure 2 (white 5, grey 1), Figure 3 (white 5, grey 10), Figure 4 (white 18, grey 10), Figure 5 (white 18, grey ?).<br>(a) Fill in the number of grey circles for Figure 5. Ans: [?]<br>(b) How many white and grey circles are there altogether in Figure 28? Ans: [?]",
      "answer0": "27",
      "answer1": "1540",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 240,
      "difficulty_id": 3,
      "explanation": "(a) Number of grey circles in Figure 5 = 10 + (4 × 4 + 1) = 27. (b) Total circles in Figure n follow the running pattern; total in Figure 28 = 1 + (4×1+1) + (4×2+1) + ... + (4×27+1) = 4 × (1+2+...+27) + 28 = 4 × (1/2 × 27 × 28) + 28 = 1512 + 28 = 1540.",
      "hints": ["Look at how grey circles grow from figure to figure for part (a).", "Sum the per-figure additions up to Figure 28 for part (b)."],
      "source": "Henry Park 2025 P6 Prelim P2 Q17",
      "image_needed": true,
      "image_options": false,
      "image_file": "q47.png",
      "image_page": 34,
      "image_bbox": [0.18, 0.12, 0.72, 0.28],
      "image_loc": "four hexagonal-ring figures (Figure 1-4) made of white and grey circles, near top of page",
      "notes": "Paper 2 Q17. Answer key: (a) 27, (b) 1540."
    }
  ]
}