{
  "paper": {
    "school": "Red Swastika",
    "year": 2023,
    "level": "P6",
    "label": "Prelim",
    "source_prefix": "Red Swastika 2023 P6 Prelim",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "70 000 + 2000 + 300 + 8 =",
      "answer0": "72 380",
      "answer1": "72 308",
      "answer2": "72 038",
      "answer3": "70 238",
      "correct_answer": 1,
      "skill_id": 105,
      "difficulty_id": 1,
      "explanation": "Add the place values: 70 000 + 2000 + 300 + 8 = 72 308.",
      "hints": ["Line up by place value: ten-thousands, thousands, hundreds, ones.", "There are no tens, so the tens digit is 0."],
      "source": "Red Swastika 2023 P6 Prelim Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 2 (72 308)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Round 769 481 to the nearest thousand.",
      "answer0": "769 000",
      "answer1": "769 480",
      "answer2": "769 500",
      "answer3": "770 000",
      "correct_answer": 0,
      "skill_id": 150,
      "difficulty_id": 1,
      "explanation": "The hundreds digit is 4 (< 5), so round down: 769 481 rounds to 769 000.",
      "hints": ["Look at the hundreds digit to decide.", "4 is less than 5, so round down."],
      "source": "Red Swastika 2023 P6 Prelim Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 1 (769 000)."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Express \\(9\\dfrac{1}{5}\\) as a decimal.",
      "answer0": "9.1",
      "answer1": "9.2",
      "answer2": "9.02",
      "answer3": "9.15",
      "correct_answer": 1,
      "skill_id": 158,
      "difficulty_id": 1,
      "explanation": "\\(\\dfrac{1}{5}=\\dfrac{2}{10}=0.2\\), so \\(9\\dfrac{1}{5}=9.2\\).",
      "hints": ["Convert the fraction part to a decimal first.", "1/5 = 2/10 = 0.2."],
      "source": "Red Swastika 2023 P6 Prelim Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 2 (9.2)."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "The diagram shows a cup of milo sold in a school canteen.<br>Which of the following could be the volume of the milo sold in the cup?",
      "answer0": "20 ml",
      "answer1": "20 l",
      "answer2": "200 ml",
      "answer3": "200 l",
      "correct_answer": 2,
      "skill_id": 192,
      "difficulty_id": 1,
      "explanation": "A typical cup holds about 200 ml. 20 ml is too little, while 20 l and 200 l are far too much.",
      "hints": ["A drinking cup holds a few hundred millilitres.", "1 litre = 1000 ml, so litres are far too large."],
      "source": "Red Swastika 2023 P6 Prelim Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q4.png",
      "image_page": 3,
      "image_bbox": [0.36, 0.62, 0.62, 0.79],
      "image_loc": "middle of page, drawing of a mug below the question",
      "notes": "Key: option 3 (200 ml)."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "Mrs Tan bought 16 apples, 10 oranges and 2 watermelons. What was the ratio of the total number of apples and watermelons to the number of oranges?",
      "answer0": "5 : 9",
      "answer1": "5 : 14",
      "answer2": "9 : 5",
      "answer3": "14 : 5",
      "correct_answer": 2,
      "skill_id": 180,
      "difficulty_id": 1,
      "explanation": "Apples + watermelons = 16 + 2 = 18. Ratio 18 : 10 = 9 : 5.",
      "hints": ["Add apples and watermelons first.", "Simplify 18 : 10 by dividing both by 2."],
      "source": "Red Swastika 2023 P6 Prelim Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 3 (9 : 5)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "The figure is made up of two triangles, PQR and STU.<br>Which two lines in the figure are perpendicular to each other?",
      "answer0": "PQ and TS",
      "answer1": "PR and RQ",
      "answer2": "US and SR",
      "answer3": "UT and TS",
      "correct_answer": 3,
      "skill_id": 100,
      "difficulty_id": 2,
      "explanation": "From the figure, UT meets TS at a right angle, so UT and TS are perpendicular.",
      "hints": ["Perpendicular lines meet at 90 degrees.", "Look for the right-angle corner in the figure."],
      "source": "Red Swastika 2023 P6 Prelim Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q6.png",
      "image_page": 4,
      "image_bbox": [0.30, 0.27, 0.72, 0.41],
      "image_loc": "below the question, two joined triangles labelled P, Q, R, S, T, U",
      "notes": "Key: option 4 (UT and TS)."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "What is the value of \\(\\dfrac{2}{3} \\div \\dfrac{4}{5}\\)?",
      "answer0": "\\(\\dfrac{8}{15}\\)",
      "answer1": "\\(\\dfrac{5}{6}\\)",
      "answer2": "\\(1\\dfrac{1}{5}\\)",
      "answer3": "\\(1\\dfrac{7}{8}\\)",
      "correct_answer": 1,
      "skill_id": 206,
      "difficulty_id": 2,
      "explanation": "\\(\\dfrac{2}{3} \\div \\dfrac{4}{5} = \\dfrac{2}{3} \\times \\dfrac{5}{4} = \\dfrac{10}{12} = \\dfrac{5}{6}\\).",
      "hints": ["Dividing by a fraction means multiplying by its reciprocal.", "Simplify 10/12."],
      "source": "Red Swastika 2023 P6 Prelim Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 2 (5/6)."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "Which decimal is greater than 0.07 but smaller than 0.15?",
      "answer0": "0.1",
      "answer1": "0.9",
      "answer2": "0.01",
      "answer3": "0.19",
      "correct_answer": 0,
      "skill_id": 124,
      "difficulty_id": 1,
      "explanation": "0.1 lies between 0.07 and 0.15. The others are outside the range.",
      "hints": ["Compare each option with 0.07 and 0.15.", "0.07 < answer < 0.15."],
      "source": "Red Swastika 2023 P6 Prelim Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 1 (0.1)."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "Find the value of \\(\\dfrac{80 - 2p}{2}\\) when \\(p = 6\\).",
      "answer0": "27",
      "answer1": "34",
      "answer2": "54",
      "answer3": "68",
      "correct_answer": 1,
      "skill_id": 240,
      "difficulty_id": 1,
      "explanation": "Substitute p = 6: (80 - 12) / 2 = 68 / 2 = 34.",
      "hints": ["Work out 2p first.", "Then subtract from 80 and divide by 2."],
      "source": "Red Swastika 2023 P6 Prelim Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 2 (34)."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "The table shows the number of points scored by different groups of students in a quiz.<br>How many groups scored at least two points?",
      "answer0": "5",
      "answer1": "7",
      "answer2": "9",
      "answer3": "11",
      "correct_answer": 3,
      "skill_id": 147,
      "difficulty_id": 1,
      "explanation": "At least 2 points means 2, 3 or 4 points: 4 + 5 + 2 = 11 groups.",
      "hints": ["'At least two' means 2 or more.", "Add the group counts for 2, 3 and 4 points."],
      "source": "Red Swastika 2023 P6 Prelim Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 5,
      "image_bbox": [0.22, 0.42, 0.83, 0.50],
      "image_loc": "table of points scored (0-4) vs number of groups",
      "notes": "Key: option 4 (11). Table: points 0,1,2,3,4 -> groups 2,3,4,5,2."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "The table shows the height of different plants, W, X, Y and Z grown in a room over a month.<br>Which plant has the greatest increase in height?",
      "answer0": "W",
      "answer1": "X",
      "answer2": "Y",
      "answer3": "Z",
      "correct_answer": 0,
      "skill_id": 147,
      "difficulty_id": 2,
      "explanation": "Increases: W 127-110=17, X 131-116=15, Y 132-119=13, Z 129-118=11. W has the greatest increase (17 cm).",
      "hints": ["Find end height minus start height for each plant.", "Compare the differences."],
      "source": "Red Swastika 2023 P6 Prelim Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q11.png",
      "image_page": 5,
      "image_bbox": [0.21, 0.62, 0.85, 0.78],
      "image_loc": "table of plant W/X/Y/Z start and end heights",
      "notes": "Key: option 1 (W). Carries 2 marks."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "Kamie is standing at K facing north. Kamie turns through an angle of 135° in an anti-clockwise direction, followed by \\(\\dfrac{1}{4}\\)-turn in the clockwise direction. Which point will Kamie be facing?",
      "answer0": "A",
      "answer1": "B",
      "answer2": "C",
      "answer3": "D",
      "correct_answer": 2,
      "skill_id": 452,
      "difficulty_id": 3,
      "explanation": "Net turn = 135° anti-clockwise then 90° clockwise = 45° anti-clockwise from north, i.e. north-west. From K the north-west direction points to C.",
      "hints": ["A quarter turn is 90 degrees.", "135 deg anti-clockwise then 90 deg clockwise leaves 45 deg anti-clockwise (north-west)."],
      "source": "Red Swastika 2023 P6 Prelim Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q12.png",
      "image_page": 6,
      "image_bbox": [0.30, 0.14, 0.78, 0.41],
      "image_loc": "square grid with points A, B, C, D, K and a north arrow on the right",
      "notes": "Key: option 3 (C). Carries 2 marks."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "The usual price of a study table was $300. During a sale, Mrs Kumar bought 2 such study tables at a discount of 60%. How much was the total discount?",
      "answer0": "$120",
      "answer1": "$180",
      "answer2": "$240",
      "answer3": "$360",
      "correct_answer": 3,
      "skill_id": 176,
      "difficulty_id": 2,
      "explanation": "Discount on one table = 60% of $300 = $180. For 2 tables = 2 x $180 = $360.",
      "hints": ["Find the discount on one table first.", "Then multiply by 2 tables."],
      "source": "Red Swastika 2023 P6 Prelim Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 4 ($360). Carries 2 marks."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "Figure 1 is formed using four identical squares. The perimeter of Figure 1 is 80 cm. Another three identical squares were added to Figure 1 to form Figure 2.<br>Find the perimeter of Figure 2.",
      "answer0": "120 cm",
      "answer1": "128 cm",
      "answer2": "136 cm",
      "answer3": "140 cm",
      "correct_answer": 1,
      "skill_id": 96,
      "difficulty_id": 3,
      "explanation": "Figure 1 perimeter is 80 cm made of 10 square-side lengths, so 1 side = 8 cm. Counting the outer edges of Figure 2 gives 16 sides: 16 x 8 = 128 cm.",
      "hints": ["First find one square's side from Figure 1's perimeter.", "Count the exposed unit edges around Figure 2."],
      "source": "Red Swastika 2023 P6 Prelim Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q14.png",
      "image_page": 7,
      "image_bbox": [0.22, 0.13, 0.82, 0.29],
      "image_loc": "two figures (Figure 1 and Figure 2) made of overlapping squares, side by side",
      "notes": "Key: option 2 (128 cm). Carries 2 marks."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "Xavier planned to save $21 using his pocket money. The table shows his saving plan for his weekly pocket money from Monday to Friday. Xavier started to save on a Friday. On which day of the week did Xavier manage to save exactly $21?",
      "answer0": "Monday",
      "answer1": "Tuesday",
      "answer2": "Wednesday",
      "answer3": "Thursday",
      "correct_answer": 3,
      "skill_id": 49,
      "difficulty_id": 3,
      "explanation": "Weekly total = 50+50+60+60+80 = 300c = $3. Starting on Friday, after 7 full weeks he has $21 reached on the Thursday of the 7th cycle (per key). Answer: Thursday.",
      "hints": ["Find the total saved in one full week first.", "Track the running total, remembering he starts on Friday."],
      "source": "Red Swastika 2023 P6 Prelim Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q15.png",
      "image_page": 7,
      "image_bbox": [0.27, 0.50, 0.74, 0.66],
      "image_loc": "table of Day (Mon-Fri) vs Amount saved in cents",
      "notes": "Key: option 4 (Thursday). Carries 2 marks."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Write two hundred and five thousand and three in numerals. [?]",
      "answer0": "205003",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 149,
      "difficulty_id": 1,
      "explanation": "Two hundred and five thousand and three = 205 003.",
      "hints": ["Two hundred and five thousand is 205 000.", "Add 3 for the ones."],
      "source": "Red Swastika 2023 P6 Prelim Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 205003."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "Find the value of \\(60 - 20 \\div 2 + 4\\). [?]",
      "answer0": "54",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 155,
      "difficulty_id": 1,
      "explanation": "Divide first: 20 ÷ 2 = 10. Then 60 - 10 + 4 = 50 + 4 = 54.",
      "hints": ["Do division before addition and subtraction.", "60 - 10 + 4."],
      "source": "Red Swastika 2023 P6 Prelim Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 54."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "Find the value of \\(\\dfrac{2}{3} \\times 18\\). [?]",
      "answer0": "12",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 163,
      "difficulty_id": 1,
      "explanation": "\\(\\dfrac{2}{3} \\times 18 = \\dfrac{2 \\times 18}{3} = \\dfrac{36}{3} = 12\\).",
      "hints": ["18 ÷ 3 = 6.", "6 × 2 = 12."],
      "source": "Red Swastika 2023 P6 Prelim Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 12. Answer is a whole number, so FIB is fine."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "Find the value of \\(5 \\div 8\\). Express your answer as a decimal. [?]",
      "answer0": "0.625",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 125,
      "difficulty_id": 1,
      "explanation": "5 ÷ 8 = 0.625.",
      "hints": ["Divide 5 by 8 using long division.", "5.000 ÷ 8 = 0.625."],
      "source": "Red Swastika 2023 P6 Prelim Q19",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 0.625."
    },
    {
      "n": 20,
      "type_id": 1,
      "question": "Simplify \\(20r + 5r + 7 - r\\).",
      "answer0": "\\(24r + 7\\)",
      "answer1": "\\(26r + 7\\)",
      "answer2": "\\(24r - 7\\)",
      "answer3": "\\(31r\\)",
      "correct_answer": 0,
      "skill_id": 239,
      "difficulty_id": 1,
      "explanation": "Combine the r terms: 20r + 5r - r = 24r. So the expression is 24r + 7.",
      "hints": ["Group the terms with r together.", "20 + 5 - 1 = 24."],
      "source": "Red Swastika 2023 P6 Prelim Q20",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 24r + 7. Algebraic answer, so MCQ per spec (distractors plausible)."
    },
    {
      "n": 21,
      "type_id": 1,
      "question": "Write an algebraic expression for each.<br>(a) Subtract 15 from \\(k\\).<br>(b) Jane typed 45 words in \\(n\\) minutes. Express the number of words she can type in 1 minute in terms of \\(n\\).",
      "answer0": "(a) \\(k - 15\\), (b) \\(\\dfrac{45}{n}\\)",
      "answer1": "(a) \\(15 - k\\), (b) \\(\\dfrac{45}{n}\\)",
      "answer2": "(a) \\(k - 15\\), (b) \\(45n\\)",
      "answer3": "(a) \\(15 - k\\), (b) \\(\\dfrac{n}{45}\\)",
      "correct_answer": 0,
      "skill_id": 238,
      "difficulty_id": 2,
      "explanation": "(a) Subtract 15 from k gives k - 15. (b) 45 words in n minutes means 45/n words in 1 minute.",
      "hints": ["'Subtract 15 from k' starts from k.", "Words per minute = total words ÷ number of minutes."],
      "source": "Red Swastika 2023 P6 Prelim Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: a) k-15, b) 45/n. Algebraic answers, so MCQ per spec; both parts combined into one item."
    },
    {
      "n": 22,
      "type_id": 1,
      "question": "Five letters, T, E, A, M and S are drawn on a square grid.<br>(a) How many of the letters have a line of symmetry? (b) Which letter(s) have both parallel and perpendicular lines?",
      "answer0": "(a) 4, (b) E and M",
      "answer1": "(a) 3, (b) T and E",
      "answer2": "(a) 4, (b) E only",
      "answer3": "(a) 5, (b) E, M and T",
      "correct_answer": 0,
      "skill_id": 144,
      "difficulty_id": 2,
      "explanation": "(a) T, E, A and M each have a line of symmetry; S does not, so 4 letters. (b) E and M each contain both parallel and perpendicular lines.",
      "hints": ["A line of symmetry folds the letter onto itself.", "Look for letters with both parallel and right-angle segments."],
      "source": "Red Swastika 2023 P6 Prelim Q22",
      "image_needed": true,
      "image_options": false,
      "image_file": "q22.png",
      "image_page": 12,
      "image_bbox": [0.16, 0.50, 0.84, 0.63],
      "image_loc": "the word TEAMS drawn on a square grid",
      "notes": "Key: a) 4, b) E and M. Letters-as-answers, so MCQ per spec."
    },
    {
      "n": 23,
      "type_id": 1,
      "question": "The net drawn for the solid shown is incorrect.<br>Name the solid.",
      "answer0": "Pyramid",
      "answer1": "Prism",
      "answer2": "Cone",
      "answer3": "Cuboid",
      "correct_answer": 0,
      "skill_id": 233,
      "difficulty_id": 2,
      "explanation": "The solid has a base and triangular faces meeting at an apex, so it is a pyramid.",
      "hints": ["The faces are triangles meeting at one point.", "A solid with one base and triangular sides to an apex is a pyramid."],
      "source": "Red Swastika 2023 P6 Prelim Q23",
      "image_needed": true,
      "image_options": false,
      "image_file": "q23.png",
      "image_page": 13,
      "image_bbox": [0.22, 0.12, 0.66, 0.30],
      "image_loc": "a pyramid solid on the left and its (incorrect) net on the right",
      "notes": "Original part (b) asks to shade a triangular face on the net (interactive, not served). Item served as the name-the-solid MCQ. Key: a) pyramid."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "The table shows the timing of the movie XYZ shown in a cinema: 11.15 a.m., 2.30 p.m., 4.30 p.m., 7.15 p.m., 10.30 p.m.<br>(a) The duration of the movie is 2 h 10 min. What time will the last screening of movie XYZ end? Express your answer using the 24-hour clock. [?]<br>(b) Wendy arrived at the cinema at 11.45 a.m. How long must she wait for the next screening? Give your answer in h and min. [?] h [?] min",
      "answer0": "0040",
      "answer1": "2",
      "answer2": "45",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 135,
      "difficulty_id": 2,
      "explanation": "(a) Last screening 10.30 p.m. = 2230. Add 2 h 10 min = 0040 (the next day). (b) From 11.45 a.m. the next screening is 2.30 p.m.; the wait is 2 h 45 min.",
      "hints": ["Convert 10.30 p.m. to 24-hour time before adding.", "From 11.45 a.m. to 2.30 p.m. is 2 h 45 min."],
      "source": "Red Swastika 2023 P6 Prelim Q24",
      "image_needed": true,
      "image_options": false,
      "image_file": "q24.png",
      "image_page": 13,
      "image_bbox": [0.34, 0.40, 0.62, 0.53],
      "image_loc": "boxed list 'Timing for movie XYZ' with five times",
      "notes": "Key: a) 0040, b) 2 h 45 min. (a) is a 24-hour clock time treated as integer 0040; (b) splits into h and min blanks. Three blanks, three answers."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "The pie chart shows the different ways a group of students go to school. The number of students who travel by car and MRT are shown in the bar graph. How many students walk to school? [?]",
      "answer0": "550",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 236,
      "difficulty_id": 2,
      "explanation": "From the bar graph, Car = 220 students = 1/5 of the total, so total = 220 x 5 = 1100. Walk is 50% of the total = 1100 ÷ 2 = 550.",
      "hints": ["Car is 1/5 of the whole, and the bar graph shows 220 for Car.", "Walk is 50% of the total students."],
      "source": "Red Swastika 2023 P6 Prelim Q25",
      "image_needed": true,
      "image_options": false,
      "image_file": "q25.png",
      "image_page": 14,
      "image_bbox": [0.16, 0.16, 0.85, 0.43],
      "image_loc": "pie chart (Bus, MRT, Car=1/5, Walk=50%) on left and bar graph of Car vs MRT on right",
      "notes": "Key: 550. Shares figure with Q26. Carries 2 marks."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "The pie chart shows the different ways a group of students go to school. The number of students who travel by car and MRT are shown in the bar graph. How many students travel to school by bus? [?]",
      "answer0": "230",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 236,
      "difficulty_id": 3,
      "explanation": "Total = 1100. Walk = 550, Car = 220, MRT = 100 (from bar graph). Bus = 1100 - 550 - 220 - 100 = 230.",
      "hints": ["Find the total students and each known group first.", "Bus = total - walk - car - MRT."],
      "source": "Red Swastika 2023 P6 Prelim Q26",
      "image_needed": true,
      "image_options": false,
      "image_file": "q26.png",
      "image_page": 14,
      "image_bbox": [0.16, 0.16, 0.85, 0.43],
      "image_loc": "same pie chart and bar graph as Q25",
      "notes": "Key: 230 (1100 - 220 - 550 - 100). Carries 2 marks. MRT read as 100 from bar graph."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "Machine A prints 10 pages more than Machine B every minute. Machine C prints half as fast as Machine A. The three machines print a total of 270 pages in 3 minutes. At this rate, how many pages does Machine C print in 1 minute? [?]",
      "answer0": "20",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 3,
      "explanation": "In 1 minute the three print 270 ÷ 3 = 90 pages. Subtract the fixed 10 (A is 10 more than B) and 15 (C is half of A's 10-more part): 270 - (10x3) - (5x3) = 225 over 3 min works out to A:B:C = 2:2:1 parts; 5 parts → 1 part = (90-15)/... The key gives C = 20 pages/min.",
      "hints": ["Pages per minute total = 270 ÷ 3 = 90.", "Let B = u, then A = u + 10, C = (u + 10)/2; solve for u."],
      "source": "Red Swastika 2023 P6 Prelim Q27",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key working: 270-(10x3)-(5x3)=225; 2+2+1=5; 5x3=15; 15+5=20. Machine C = 20 pages/min. Carries 2 marks."
    },
    {
      "n": 28,
      "type_id": 1,
      "question": "The figure ABCD is formed by two different squares and two identical rectangles. The area of the small square is \\(\\dfrac{1}{4}\\) the area of the big square.<br>(a) What fraction of EBCF is shaded? (b) What fraction of ABCD is shaded?",
      "answer0": "(a) \\(\\dfrac{1}{3}\\), (b) \\(\\dfrac{4}{9}\\)",
      "answer1": "(a) \\(\\dfrac{1}{2}\\), (b) \\(\\dfrac{1}{3}\\)",
      "answer2": "(a) \\(\\dfrac{1}{3}\\), (b) \\(\\dfrac{1}{3}\\)",
      "answer3": "(a) \\(\\dfrac{2}{3}\\), (b) \\(\\dfrac{4}{9}\\)",
      "correct_answer": 0,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "(a) Shaded triangle area = 1/2 x 2 x 1 = 1 unit; EBCF = 3 x 1 = 3 units, so 1/3. (b) Shaded = 1 + 1 = 2 + ... per key: shaded = 4 units of ABCD = 9 units, so 4/9.",
      "hints": ["Set the small square's side as 1 unit and the big square's as 2 units.", "Find the shaded triangle areas as fractions of each whole."],
      "source": "Red Swastika 2023 P6 Prelim Q28",
      "image_needed": true,
      "image_options": false,
      "image_file": "q28.png",
      "image_page": 15,
      "image_bbox": [0.34, 0.40, 0.64, 0.57],
      "image_loc": "square ABCD with E on top edge and F on bottom edge, shaded V-shape inside",
      "notes": "Key: a) 1/3, b) 4/9. Fraction answers, so MCQ per spec. Carries 2 marks."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "A group of students had an average of $10. Three students with a sum of $57 joined the group and the average amount of each student increased by $3. How many students were there in the group at first? [?]",
      "answer0": "6",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 205,
      "difficulty_id": 3,
      "explanation": "The 3 new students bring $57; their fair share at the new average $13 is 3 x 13 = $39, so the extra $57 - $39 = $18 raises the original group by $3 each: 18 ÷ 3 = 6 students at first. Check: 6 x 10 = 60; (60 + 57) ÷ 9 = 13 ✓.",
      "hints": ["The new average is $10 + $3 = $13.", "Excess money from the new students raises each original member by $3."],
      "source": "Red Swastika 2023 P6 Prelim Q29",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key working: 10x3=30; 27÷3=9; 9-3=6. Answer 6 students. Carries 2 marks."
    },
    {
      "n": 30,
      "type_id": 0,
      "question": "In the figure, ABC and DEF are right-angled triangles. The base of triangle DEF is twice as long as the base of triangle ABC. The height of triangle DEF is also twice as long as the height of triangle ABC. The difference in the area between the 2 unshaded parts is 18 cm². For each statement, indicate True, False or Not possible to tell.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Statement 1 (AF:AB = 1:2): Not possible to tell. Statement 2 (area DEF is twice area ABC): False (it is 4 times). Statement 3 (area EFD is 24 cm²): True.",
      "hints": ["DEF has base and height both doubled, so its area is 4x ABC.", "Use the 18 cm² difference between the unshaded parts."],
      "source": "Red Swastika 2023 P6 Prelim Q30",
      "image_needed": true,
      "image_options": false,
      "image_file": "q30.png",
      "image_page": 16,
      "image_bbox": [0.28, 0.36, 0.78, 0.56],
      "image_loc": "two overlapping right-angled triangles ABC and DEF sharing region near F/B with shaded overlap",
      "notes": "Interactive tick-table (True/False/Not possible). type_id 0 (skipped on insert). Key: S1 Not possible to tell, S2 False, S3 True (24 cm²)."
    },
    {
      "n": 101,
      "type_id": 1,
      "question": "(a) Write down all the common factors of 4 and 6. (b) What is the largest common multiple of 4 and 6 that is smaller than 50?",
      "answer0": "(a) 1, 2; (b) 48",
      "answer1": "(a) 1, 2, 4; (b) 48",
      "answer2": "(a) 1, 2; (b) 36",
      "answer3": "(a) 2; (b) 24",
      "correct_answer": 0,
      "skill_id": 113,
      "difficulty_id": 2,
      "explanation": "(a) Factors of 4: 1,2,4; factors of 6: 1,2,3,6; common factors are 1 and 2. (b) Common multiples of 4 and 6 are multiples of 12: 12, 24, 36, 48; the largest below 50 is 48.",
      "hints": ["List the factors of each number and find the shared ones.", "Common multiples of 4 and 6 are multiples of 12."],
      "source": "Red Swastika 2023 P6 Prelim P2-Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q1. Key: a) 1, 2; b) 48. List-style answer rendered as MCQ. Carries 2 marks."
    },
    {
      "n": 102,
      "type_id": 2,
      "question": "Mrs Devi had 2.5 m of ribbon at first. She used 8 cm of it.<br>(a) Find the length of ribbon she had left in metres. [?] m<br>(b) Mrs Devi then cut the remaining length into two equal pieces. Find the length of each piece in centimetres. [?] cm",
      "answer0": "2.42",
      "answer1": "121",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 184,
      "difficulty_id": 2,
      "explanation": "(a) 2.5 m = 250 cm; 250 - 8 = 242 cm = 2.42 m. (b) 242 cm ÷ 2 = 121 cm.",
      "hints": ["Convert 2.5 m to cm before subtracting 8 cm.", "Divide the remaining length by 2."],
      "source": "Red Swastika 2023 P6 Prelim P2-Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q2. Key: a) 2.42 m, b) 121 cm. Two decimal/whole answers. Carries 2 marks."
    },
    {
      "n": 103,
      "type_id": 1,
      "question": "In the circle, O is the centre and AOB is a straight line.<br>(a) Measure and write down the diameter of the circle in cm. (b) Using your answer in (a), find the circumference of the circle. Leave your answer in terms of \\(\\pi\\).",
      "answer0": "(a) 4.5 cm, (b) \\(4.5\\pi\\) cm",
      "answer1": "(a) 4.5 cm, (b) \\(2.25\\pi\\) cm",
      "answer2": "(a) 9 cm, (b) \\(9\\pi\\) cm",
      "answer3": "(a) 4.5 cm, (b) \\(9\\pi\\) cm",
      "correct_answer": 0,
      "skill_id": 220,
      "difficulty_id": 2,
      "explanation": "(a) The measured diameter is 4.5 cm. (b) Circumference = πd = π x 4.5 = 4.5π cm.",
      "hints": ["The diameter passes through the centre O.", "Circumference = π × diameter."],
      "source": "Red Swastika 2023 P6 Prelim P2-Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q3.png",
      "image_page": 20,
      "image_bbox": [0.33, 0.13, 0.66, 0.31],
      "image_loc": "circle with centre O, straight line AOB, and points C, D on the circle",
      "notes": "Paper 2 Q3. Key: a) 4.5 cm, b) 4.5π cm. (b) has a pi/fraction answer, so MCQ per spec; both parts combined. Carries 2 marks."
    },
    {
      "n": 104,
      "type_id": 2,
      "question": "The average of two different 3-digit numbers is 104. Write down one possible set of values for the two numbers. [?] and [?]",
      "answer0": "100",
      "answer1": "108",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 204,
      "difficulty_id": 2,
      "explanation": "Total = 104 x 2 = 208. Choose two different 3-digit numbers summing to 208, e.g. 100 and 108.",
      "hints": ["The two numbers add up to 104 × 2 = 208.", "Pick any two different 3-digit numbers with that sum."],
      "source": "Red Swastika 2023 P6 Prelim P2-Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q4. Key: 100, 108 (any pair summing to 208 of two different 3-digit numbers). Carries 2 marks. Open answer - key's sample used."
    },
    {
      "n": 105,
      "type_id": 2,
      "question": "Vinesh has a rectangular piece of paper. He folded it along the dotted lines without overlapping. In the folded figure one angle is 62°. Find \\(\\angle x\\). [?]",
      "answer0": "31",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 194,
      "difficulty_id": 3,
      "explanation": "2x = 180 - 28 - 90 = 62, so x = 62 ÷ 2 = 31°.",
      "hints": ["Folding creates equal angles; use the right angle of the paper.", "2x = 180 - 28 - 90."],
      "source": "Red Swastika 2023 P6 Prelim P2-Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q5.png",
      "image_page": 21,
      "image_bbox": [0.18, 0.13, 0.82, 0.31],
      "image_loc": "rectangle 'Before folding' with dotted fold lines and 'After folding' triangular prism shape with angles x and 62 degrees",
      "notes": "Paper 2 Q5. Key: x = 31° (answer 31). Answer in degrees, integer. Carries 2 marks."
    },
    {
      "n": 106,
      "type_id": 2,
      "question": "The total mass of three parcels was 13.8 kg. Parcel B was 1.2 kg heavier than Parcel A while Parcel C was 1.2 kg lighter than Parcel A.<br>(a) How much heavier was Parcel B than Parcel C? Give your answer in kg. [?] kg<br>(b) Find the mass of Parcel A in kg. [?] kg",
      "answer0": "2.4",
      "answer1": "4.6",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "(a) B - C = 1.2 + 1.2 = 2.4 kg. (b) A + B + C = 13.8; with B = A+1.2 and C = A-1.2, 3A = 13.8, so A = 4.6 kg.",
      "hints": ["B is 1.2 above A and C is 1.2 below A.", "The total is 3 equal A-parts since the +1.2 and -1.2 cancel."],
      "source": "Red Swastika 2023 P6 Prelim P2-Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q6. Key: a) 2.4 kg, b) 4.6 kg. Decimal answers. Carries 3 marks."
    },
    {
      "n": 107,
      "type_id": 0,
      "question": "Ian drew a triangle ABX in a square grid. (a) ABCD is a rectangle with the same area as triangle ABX. Draw ABCD on the grid such that ABCD does not overlap with ABX. (b) ABR is a right-angled triangle. The area of triangle BXR is the same as the area of triangle ABX. Draw ABR such that ABR does not overlap with ABCD. (c) Ian drew another triangle Y on a grid. Draw a parallelogram with the same perimeter as Y and label it P.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 201,
      "difficulty_id": 3,
      "explanation": "Drawing/construction task on a grid; the marker's solution sheet shows the rectangle, triangle and parallelogram drawn on the grids.",
      "hints": ["A rectangle with the same area as a triangle uses half the height for equal base.", "Match the parallelogram's perimeter to triangle Y's side lengths."],
      "source": "Red Swastika 2023 P6 Prelim P2-Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q7.png",
      "image_page": 23,
      "image_bbox": [0.28, 0.10, 0.78, 0.36],
      "image_loc": "square grid with triangle ABX (A, B on top, X below); second grid lower down with triangle Y",
      "notes": "Interactive draw-on-grid task. type_id 0 (skipped on insert). Carries 3 marks."
    },
    {
      "n": 108,
      "type_id": 2,
      "question": "In the figure, ABCD is a rhombus and AB = AE. \\(\\angle\\)EBC = 29° and \\(\\angle\\)BCE = 80°.<br>(a) Find \\(\\angle\\)BAE in degrees. [?]<br>(b) Find \\(\\angle\\)ADE in degrees. [?]",
      "answer0": "38",
      "answer1": "69",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "(a) ∠ABC = 180 - 80 = 100° (co-interior in rhombus). ∠ABE = 100 - 29 = 71°. Since AB = AE, triangle ABE is isosceles: ∠BAE = 180 - 71 - 71 = 38°. (b) ∠EAD = 80 - 38 = 42°. AD = AE so ∠ADE = (180 - 42) ÷ 2 = 69°.",
      "hints": ["Opposite angles of a rhombus are equal; adjacent angles sum to 180°.", "AB = AE makes triangle ABE isosceles."],
      "source": "Red Swastika 2023 P6 Prelim P2-Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q8.png",
      "image_page": 24,
      "image_bbox": [0.30, 0.12, 0.72, 0.37],
      "image_loc": "rhombus ABCD with diagonal point E inside, angles 29 degrees at B and 80 degrees at C marked",
      "notes": "Paper 2 Q8. Key: a) 38°, b) 69°. Integer-degree answers. Carries 4 marks."
    },
    {
      "n": 109,
      "type_id": 2,
      "question": "Jill glued 12 cubes of side 1 cm to form a solid. (a) Draw the top view of the solid on the square grid. (b) Jill painted the whole solid, including the base. How many cubes would have only two painted faces? [?] (c) What was the total painted area of the solid in cm²? [?] cm²",
      "answer0": "2",
      "answer1": "42",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 190,
      "difficulty_id": 3,
      "explanation": "(b) Counting cube positions, 2 cubes have exactly two painted faces. (c) The total exposed surface = 42 unit faces, so 42 x 1 = 42 cm².",
      "hints": ["A cube with two painted faces sits along an edge with two exposed sides.", "Count every exposed unit square, including the base."],
      "source": "Red Swastika 2023 P6 Prelim P2-Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q9.png",
      "image_page": 25,
      "image_bbox": [0.34, 0.12, 0.70, 0.31],
      "image_loc": "isometric drawing of a solid made of 12 unit cubes with top/side/front view labels",
      "notes": "Paper 2 Q9. Part (a) is a draw-the-top-view task (not served). Served parts: b) 2 cubes, c) 42 cm². Two blanks, two answers. Carries 3 marks."
    },
    {
      "n": 110,
      "type_id": 2,
      "question": "ABC is a triangle, BFC is a straight line and \\(\\angle\\)DEF is a right angle. \\(\\angle\\)BAC = 61°, \\(\\angle\\)EDC = 122° (exterior), \\(\\angle\\)ABC = 58°. Find \\(\\angle\\)BEF in degrees. [?]",
      "answer0": "29",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "∠ACF = 180 - 61 - 58 = 61°. ∠AEF region: ∠BEF = 180 - 61 - 90 = 29°.",
      "hints": ["Angle sum of triangle ABC is 180°.", "∠DEF = 90°, so use the straight line at E."],
      "source": "Red Swastika 2023 P6 Prelim P2-Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q10.png",
      "image_page": 26,
      "image_bbox": [0.28, 0.10, 0.66, 0.32],
      "image_loc": "triangle ABC with E and D on the sides, F on base BC, angles 61, 122 and 58 degrees marked",
      "notes": "Paper 2 Q10. Only part (a) ∠BEF served (= 29°). Part (b) is a circle-the-words task (not served). Carries 2 marks for served part."
    },
    {
      "n": 111,
      "type_id": 2,
      "question": "At first, 80% of a tank was filled with water. Chris turned on Tap A to let water out. 4 minutes later he turned on Tap B to let water in. After a while both taps were turned off. The graph shows the amount of water in the tank over 12 minutes.<br>(a) Find the capacity of the tank in litres. [?] l<br>(b) How much water flowed out of the tank from Tap A in 1 minute? [?] l<br>(c) How much water flowed into the tank from Tap B in 1 minute? [?] l",
      "answer0": "43.75",
      "answer1": "3.75",
      "answer2": "1.25",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 191,
      "difficulty_id": 3,
      "explanation": "(a) At first the tank is 80% full = 35 l, so capacity = 35 ÷ 0.8 = 43.75 l. (b) In the first 4 min level drops 35 to 20, i.e. 15 l over 4 min = 3.75 l/min out. (c) After Tap B on, net change: 3.75 x 4 = 15 out, 15 - 10 = 5 over 4 min = 1.25 l/min in.",
      "hints": ["35 l is 80% of the capacity.", "Use the slope of each part of the graph for the flow rates."],
      "source": "Red Swastika 2023 P6 Prelim P2-Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q11.png",
      "image_page": 27,
      "image_bbox": [0.14, 0.18, 0.82, 0.46],
      "image_loc": "tank diagram with Tap A and Tap B on left; volume-vs-time line graph on right",
      "notes": "Paper 2 Q11. Key written as 35/80x100=43.79 (typo); correct value is 43.75 l. b) 3.75 l, c) 1.25 l. Three decimal answers. Carries 4 marks. Flagged key arithmetic typo per spec."
    },
    {
      "n": 112,
      "type_id": 1,
      "question": "Sam had a bag of red, blue and green marbles. The ratio of red to blue marbles was 2 : 1. The ratio of blue to green marbles was 5 : 3.<br>(a) What fraction of Sam's marbles was green? (b) Sam removed 4 red and 3 blue marbles each round. After a few rounds there were 18 red and 1 blue marble left. How many red marbles were there at first?",
      "answer0": "(a) \\(\\dfrac{1}{6}\\), (b) 50",
      "answer1": "(a) \\(\\dfrac{3}{18}\\), (b) 40",
      "answer2": "(a) \\(\\dfrac{1}{5}\\), (b) 50",
      "answer3": "(a) \\(\\dfrac{1}{6}\\), (b) 46",
      "correct_answer": 0,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "(a) Make blue common: R:B:G = 10:5:3, total 18 parts; green = 3/18 = 1/6. (b) Working back from 18 red and 1 blue with the 4-red/3-blue removals gives 50 red marbles at first.",
      "hints": ["Combine the two ratios so blue is the same in both.", "Work backwards from the ending counts, adding back what was removed."],
      "source": "Red Swastika 2023 P6 Prelim P2-Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q12. Key: a) 1/6, b) 50. Part (a) is a fraction, so MCQ per spec; parts combined. Carries 3 marks."
    },
    {
      "n": 113,
      "type_id": 2,
      "question": "Janice sold 80 cakes in January. In February she sold 30 more such cakes than in January.<br>(a) What was the percentage increase in the number of cakes sold from January to February? [?] %<br>(b) The number of cakes sold in March was a 100% increase from February. How many cakes were sold in March? [?]<br>(c) The number sold in April was a 40% decrease from January. The total sold in April and May was 200 when rounded to the nearest hundred. What was the greatest possible number of cakes sold in May? [?]",
      "answer0": "37.5",
      "answer1": "220",
      "answer2": "201",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "(a) 30/80 x 100 = 37.5%. (b) Feb = 80 + 30 = 110; March = 110 x 200/100 = 220. (c) April = 80 x 60/100 = 48. April+May rounds to 200, so max total is 249; May = 249 - 48 = 201.",
      "hints": ["Percentage increase = increase ÷ original × 100.", "Numbers that round to 200 (nearest hundred) range from 150 to 249."],
      "source": "Red Swastika 2023 P6 Prelim P2-Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q13. Key: a) 37.5%, b) 220, c) 201. Three answers (decimal/whole). Carries 4 marks."
    },
    {
      "n": 114,
      "type_id": 2,
      "question": "A market and a stadium are 240 m apart, located between Paul's and Rani's houses. The market is exactly half-way between the two houses. One morning Paul and Rani started cycling from their houses at the same time and arrived at the stadium together. Rani cycled at 100 m/min while Paul cycled 15 m/min faster than Rani.<br>(a) How much further did Paul cycle than Rani? Give your answer in m. [?] m<br>(b) How far was Rani's house from the stadium? Give your answer in m. [?] m",
      "answer0": "480",
      "answer1": "3200",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 219,
      "difficulty_id": 3,
      "explanation": "(a) The market is half-way, and the stadium is 240 m past the market towards Rani, so Paul cycles 240 + 240 = 480 m further than Rani. (b) Paul's extra 480 m at the 15 m/min speed difference takes 480 ÷ 15 = 32 min; Rani's distance = 100 x 32 = 3200 m.",
      "hints": ["The market is half-way, so Paul's house is 240 m further from the stadium than Rani's, plus the 240 m gap.", "Use the time = extra distance ÷ speed difference."],
      "source": "Red Swastika 2023 P6 Prelim P2-Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q14.png",
      "image_page": 30,
      "image_bbox": [0.10, 0.16, 0.86, 0.27],
      "image_loc": "horizontal line: Paul's house --- Market --- Stadium (240 m) --- Rani's house",
      "notes": "Paper 2 Q14. Key: a) 480 m, b) 3200 m. Whole-number answers. Carries 4 marks."
    },
    {
      "n": 115,
      "type_id": 2,
      "question": "Shermaine used rectangular blocks (length 2 cm, breadth 1 cm) to form figures following a pattern. The table shows blocks used per figure: Fig1=4, Fig2=7, Fig3=13, Fig4=16, Fig5=19, Fig6=23.<br>(a) Complete the table for Figure 7: number of blocks used. [?]<br>(b) How many rectangular blocks were used in Figure 123? [?]",
      "answer0": "26",
      "answer1": "413",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 108,
      "difficulty_id": 3,
      "explanation": "(a) The pattern adds in a repeating +3/+6 manner; Figure 7 uses 26 blocks (height 16 cm). (b) Figure 123: 123 ÷ 3 = 41 sets of 10; 40 x 10 = 400, plus 13 = 413 blocks.",
      "hints": ["Look at the differences between consecutive figures.", "Group the figures in sets of 3 to spot the +10 per set pattern."],
      "source": "Red Swastika 2023 P6 Prelim P2-Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q15.png",
      "image_page": 31,
      "image_bbox": [0.16, 0.13, 0.86, 0.27],
      "image_loc": "Figures 1 to 6 made of rectangular blocks, in a row with a height arrow h on Figure 1",
      "notes": "Paper 2 Q15. Key: a) Fig7 = 26 blocks (16 cm); b) 413. Only the block-count blanks served (height column is part-table). Carries 3 marks."
    },
    {
      "n": 116,
      "type_id": 2,
      "question": "Leon designed a logo made up of two identical small semi-circles, a circle and a big quadrant. YZ is the diameter of the circle and O is its centre. X is the centre of the big quadrant and XY = XZ. The radius of the small semi-circle is 7 cm. (Take \\(\\pi = \\dfrac{22}{7}\\).)<br>(a) Find the length of YZ in cm. [?] cm<br>(b) Find the area of triangle XYZ in cm². [?] cm²<br>(c) Find the total area of the shaded parts of Leon's logo in cm². [?] cm²",
      "answer0": "28",
      "answer1": "196",
      "answer2": "462",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 222,
      "difficulty_id": 3,
      "explanation": "(a) Small diameter = 7 x 2 = 14 cm; YZ = big circle diameter = 14 x 2 = 28 cm. (b) XY = XZ and the right angle at X give area = 1/2 x 14 x 28 = 196 cm². (c) Quadrant area 1/4 x 22/7 x 28 x 28 = 616; circle 1/2... shaded total = 616 - 154 = 462 cm² per the key.",
      "hints": ["The small semi-circle's diameter helps find the big circle's diameter.", "Use π = 22/7 and combine quadrant, circle and semi-circle areas."],
      "source": "Red Swastika 2023 P6 Prelim P2-Q16",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q16.png",
      "image_page": 32,
      "image_bbox": [0.28, 0.16, 0.74, 0.38],
      "image_loc": "heart-like logo of a big quadrant with two small semi-circles and a circle, labelled Y, O, Z, X, 7 cm",
      "notes": "Paper 2 Q16. Key: a) YZ = 28 cm, b) 196 cm², c) 462 cm². Three whole-number answers. Carries 5 marks."
    },
    {
      "n": 117,
      "type_id": 2,
      "question": "In a bakery, donuts and cupcakes are sold only in boxes. A box of 8 donuts costs $15 and a box of 5 cupcakes costs $7. Alice and Ben were given a sum of money. Alice needed 20 donuts and 3 cupcakes for her party. After buying, Alice passed the rest of the money to Ben.<br>(a) What was the least amount of money Alice spent? Give your answer in dollars. $[?]<br>(c) Ben spent \\(\\dfrac{4}{7}\\) of the rest of the money and had \\(\\dfrac{1}{3}\\) of the sum left. How many donuts and how many cupcakes did Ben buy? Donuts: [?], Cupcakes: [?]",
      "answer0": "52",
      "answer1": "48",
      "answer2": "10",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "(a) 20 donuts need 3 boxes (24 donuts) = 3 x $15 = $45; 3 cupcakes need 1 box (5) = $7; least = $45 + $7 = $52. (c) Ben spent 4/7 of the rest; donuts: 6 x 8 = 48, cupcakes: 2 x 5 = 10.",
      "hints": ["Donuts and cupcakes only come in full boxes, so round up the boxes needed.", "Find the boxes Ben buys from the fraction of money he spent."],
      "source": "Red Swastika 2023 P6 Prelim P2-Q17",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q17.png",
      "image_page": 33,
      "image_bbox": [0.22, 0.13, 0.80, 0.28],
      "image_loc": "a box of 8 donuts ($15) and a box of 5 cupcakes ($7) drawings side by side",
      "notes": "Paper 2 Q17. Part (b) was a fraction question (Alice spent 2/9) - kept in original but the served blanks here cover (a) $52 and (c) Donuts 48, Cupcakes 10. Key: a) $52, c) Donuts 6 boxes = 48, Cupcakes 2 boxes = 10. Carries 3 marks. Part (b) 2/9 omitted from blanks as it is a fraction answer."
    }
  ]
}