{
  "paper": {
    "school": "Red Swastika School",
    "year": 2022,
    "level": "P6",
    "label": "Prelim",
    "source_prefix": "Red Swastika 2022 P6 Prelim",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "Which of the following is fifty-six thousand and three in numerals?",
      "answer0": "5603",
      "answer1": "56 003",
      "answer2": "560 003",
      "answer3": "5 600 003",
      "correct_answer": 1,
      "skill_id": 149,
      "difficulty_id": 1,
      "explanation": "Fifty-six thousand = 56 000; and three = 003. So 56 000 + 3 = 56 003.",
      "hints": ["Fifty-six thousand is 56 000.", "Add the 3 in the ones place."],
      "source": "Red Swastika 2022 P6 Prelim P1 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 2 (1-based) = 56 003."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Round off 83.569 to the nearest tenth.",
      "answer0": "80",
      "answer1": "84",
      "answer2": "83.6",
      "answer3": "83.57",
      "correct_answer": 2,
      "skill_id": 168,
      "difficulty_id": 1,
      "explanation": "The tenths digit is 5; the next digit (hundredths) is 6, so round up: 83.6.",
      "hints": ["The nearest tenth means one decimal place.", "Look at the hundredths digit to decide rounding."],
      "source": "Red Swastika 2022 P6 Prelim P1 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 3 (1-based) = 83.6."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "What is the mass of the wooden block?",
      "answer0": "3 kg 150 g",
      "answer1": "3 kg 200 g",
      "answer2": "3 kg 250 g",
      "answer3": "3 kg 300 g",
      "correct_answer": 2,
      "skill_id": 86,
      "difficulty_id": 2,
      "explanation": "The 5 kg scale has 5 major divisions per kg. The needle points between 3 kg and 4 kg, one-quarter of the way, i.e. 3 kg 250 g.",
      "hints": ["Read where the needle points between the kilogram markings.", "Each kilogram is divided into smaller equal parts."],
      "source": "Red Swastika 2022 P6 Prelim P1 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q3.png",
      "image_page": 2,
      "image_bbox": [0.40, 0.50, 0.65, 0.78],
      "image_loc": "middle of page, circular weighing scale dial (0 to 5 kg) with wooden block on top",
      "notes": "Answer key: option 3 (1-based) = 3 kg 250 g. Read needle position from figure."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Express 70 km 8 m in metres.",
      "answer0": "708 m",
      "answer1": "7008 m",
      "answer2": "70 008 m",
      "answer3": "700 008 m",
      "correct_answer": 2,
      "skill_id": 184,
      "difficulty_id": 1,
      "explanation": "1 km = 1000 m, so 70 km = 70 000 m. Add 8 m: 70 008 m.",
      "hints": ["Convert kilometres to metres by multiplying by 1000.", "Then add the extra 8 m."],
      "source": "Red Swastika 2022 P6 Prelim P1 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 3 (1-based) = 70 008 m."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "What is the area of the shaded triangle?",
      "answer0": "100 cm²",
      "answer1": "400 cm²",
      "answer2": "500 cm²",
      "answer3": "800 cm²",
      "correct_answer": 1,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "The shaded triangle has base = 40 cm (the part to the right of the 10 cm mark) and height 20 cm. Area = \\(\\dfrac{1}{2} \\times 40 \\times 20 = 400\\) cm².",
      "hints": ["The base of the shaded triangle is the 40 cm segment; the perpendicular height is 20 cm.", "Use \\(\\dfrac{1}{2} \\times base \\times height\\)."],
      "source": "Red Swastika 2022 P6 Prelim P1 Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q5.png",
      "image_page": 3,
      "image_bbox": [0.20, 0.26, 0.70, 0.40],
      "image_loc": "upper part of page, shaded triangle with 20 cm height, 10 cm and 40 cm base segments",
      "notes": "Answer key: option 2 (1-based) = 400 cm². Base of shaded triangle = 40 cm (10 cm portion is unshaded)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "In the figure, PQ and RS are straight lines. Which one of the following is true?",
      "answer0": "\\(\\angle a = \\angle d\\)",
      "answer1": "\\(\\angle b = \\angle e\\)",
      "answer2": "\\(\\angle a + \\angle b = \\angle e + \\angle d\\)",
      "answer3": "\\(\\angle b + \\angle c = \\angle e + \\angle f\\)",
      "correct_answer": 1,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "\\(\\angle b\\) and \\(\\angle e\\) are vertically opposite angles formed by the straight lines, so \\(\\angle b = \\angle e\\).",
      "hints": ["Vertically opposite angles are equal.", "Identify which pair sits directly across the intersection point."],
      "source": "Red Swastika 2022 P6 Prelim P1 Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q6.png",
      "image_page": 3,
      "image_bbox": [0.30, 0.52, 0.66, 0.74],
      "image_loc": "lower part of page, intersecting lines P-Q, R-S, T-U with angles a,b,c,d,e,f labelled",
      "notes": "Answer key: option 2 (1-based) = \\(\\angle b = \\angle e\\)."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "The pie chart shows the different types of sandwiches sold at a stall. What is the ratio of the number of tuna sandwiches sold to the number of cheese sandwiches sold?",
      "answer0": "2 : 3",
      "answer1": "3 : 2",
      "answer2": "4 : 5",
      "answer3": "5 : 4",
      "correct_answer": 0,
      "skill_id": 236,
      "difficulty_id": 2,
      "explanation": "Cheese = 100% − 10% − 20% − 40% = 30%. Tuna : Cheese = 20 : 30 = 2 : 3.",
      "hints": ["Find the cheese percentage: the parts must total 100%.", "Simplify the ratio 20 : 30."],
      "source": "Red Swastika 2022 P6 Prelim P1 Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q7.png",
      "image_page": 4,
      "image_bbox": [0.38, 0.10, 0.66, 0.30],
      "image_loc": "top of page, pie chart with Egg 10%, Tuna 20%, Ham 40%, Cheese (unlabelled)",
      "notes": "Answer key: option 1 (1-based) = 2 : 3."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "Find the value of \\(9c - 3 + 2c\\) when \\(c = 7\\).",
      "answer0": "28",
      "answer1": "46",
      "answer2": "67",
      "answer3": "74",
      "correct_answer": 3,
      "skill_id": 240,
      "difficulty_id": 2,
      "explanation": "\\(9c + 2c - 3 = 11c - 3\\). When \\(c = 7\\): \\(11 \\times 7 - 3 = 77 - 3 = 74\\).",
      "hints": ["Combine like terms: \\(9c + 2c = 11c\\).", "Substitute \\(c = 7\\) and subtract 3."],
      "source": "Red Swastika 2022 P6 Prelim P1 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 4 (1-based) = 74."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "Which one of the following fractions is the largest?",
      "answer0": "\\(\\dfrac{2}{3}\\)",
      "answer1": "\\(\\dfrac{2}{5}\\)",
      "answer2": "\\(\\dfrac{3}{8}\\)",
      "answer3": "\\(\\dfrac{5}{8}\\)",
      "correct_answer": 0,
      "skill_id": 79,
      "difficulty_id": 2,
      "explanation": "Convert to a common comparison: \\(\\dfrac{2}{3} \\approx 0.667\\), \\(\\dfrac{2}{5} = 0.4\\), \\(\\dfrac{3}{8} = 0.375\\), \\(\\dfrac{5}{8} = 0.625\\). The largest is \\(\\dfrac{2}{3}\\).",
      "hints": ["Convert each fraction to a decimal or a common denominator.", "Compare the sizes."],
      "source": "Red Swastika 2022 P6 Prelim P1 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 1 (1-based) = \\(\\dfrac{2}{3}\\)."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "Vinush has a rectangular piece of paper. He folded it along the dotted line. Find \\(\\angle x\\).",
      "answer0": "21°",
      "answer1": "33°",
      "answer2": "42°",
      "answer3": "66°",
      "correct_answer": 3,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "Folding maps the corner onto itself; the 24° and \\(\\angle x\\) and the folded equal angle work out so that \\(\\angle x = 66°\\) (the fold creates equal angles whose sum with 24° forms the 90° corner: 90° − 24° = 66°).",
      "hints": ["Folding preserves angle sizes, so the two halves are equal.", "Use the 90° corner of the rectangle and subtract the given 24°."],
      "source": "Red Swastika 2022 P6 Prelim P1 Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 5,
      "image_bbox": [0.22, 0.12, 0.72, 0.30],
      "image_loc": "top of page, rectangle before folding and folded shape after with 24° and x marked",
      "notes": "Answer key: option 4 (1-based) = 66°."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "ABC is a straight line and ABD is an isosceles triangle. \\(\\angle ADB = 70°\\) and DA = DB. Find \\(\\angle DBC\\).",
      "answer0": "110°",
      "answer1": "125°",
      "answer2": "135°",
      "answer3": "140°",
      "correct_answer": 1,
      "skill_id": 197,
      "difficulty_id": 2,
      "explanation": "Since DA = DB, the base angles are equal: \\(\\angle DAB = \\angle DBA = (180° - 70°) \\div 2 = 55°\\). \\(\\angle DBC\\) is on the straight line ABC: \\(\\angle DBC = 180° - 55° = 125°\\).",
      "hints": ["In an isosceles triangle the base angles are equal.", "\\(\\angle DBA\\) and \\(\\angle DBC\\) are angles on a straight line."],
      "source": "Red Swastika 2022 P6 Prelim P1 Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q11.png",
      "image_page": 5,
      "image_bbox": [0.20, 0.50, 0.60, 0.66],
      "image_loc": "middle of page, isosceles triangle ABD with 70° at D, straight line ABC",
      "notes": "Answer key: option 2 (1-based) = 125°."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "The clock shows the time Ian reached the cinema. Ian was 10 minutes late for the movie. What time did the movie start?",
      "answer0": "7.35 p.m.",
      "answer1": "7.55 p.m.",
      "answer2": "8.35 p.m.",
      "answer3": "8.55 p.m.",
      "correct_answer": 0,
      "skill_id": 135,
      "difficulty_id": 2,
      "explanation": "The clock shows 7.45. Ian was 10 minutes late, so the movie started 10 minutes before he arrived: 7.45 − 10 min = 7.35 p.m.",
      "hints": ["Read the clock time when Ian arrived.", "Being 10 minutes late means the movie started 10 minutes earlier."],
      "source": "Red Swastika 2022 P6 Prelim P1 Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q12.png",
      "image_page": 6,
      "image_bbox": [0.32, 0.10, 0.58, 0.27],
      "image_loc": "top of page, analogue clock face showing about 7.45",
      "notes": "Answer key: option 1 (1-based) = 7.35 p.m. Clock reads 7.45."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "The table shows the number of books borrowed from a library by the children in a class. How many children borrowed more than 2 books?",
      "answer0": "10",
      "answer1": "12",
      "answer2": "14",
      "answer3": "16",
      "correct_answer": 0,
      "skill_id": 148,
      "difficulty_id": 1,
      "explanation": "More than 2 books means 3 or 4 books: 8 children borrowed 3 books and 2 children borrowed 4 books. Total = 8 + 2 = 10.",
      "hints": ["More than 2 means 3 books and 4 books only.", "Add the number of children in those two columns."],
      "source": "Red Swastika 2022 P6 Prelim P1 Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 1 (1-based) = 10. Table: books 0-4 → children 3,9,4,8,2."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "Kumar travelled \\(\\dfrac{1}{3}\\) of his journey in 2 h. He then travelled the remaining 240 km at a speed of 80 km/h. Find Kumar's average speed for the whole journey.",
      "answer0": "60 km/h",
      "answer1": "66 km/h",
      "answer2": "70 km/h",
      "answer3": "72 km/h",
      "correct_answer": 3,
      "skill_id": 219,
      "difficulty_id": 3,
      "explanation": "The 240 km is the remaining \\(\\dfrac{2}{3}\\), so the whole journey = \\(240 \\div 2 \\times 3 = 360\\) km. Time for 240 km = 240 ÷ 80 = 3 h. Total time = 2 + 3 = 5 h. Average speed = 360 ÷ 5 = 72 km/h.",
      "hints": ["The 240 km is two-thirds of the journey; find the full distance.", "Average speed = total distance ÷ total time."],
      "source": "Red Swastika 2022 P6 Prelim P1 Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 4 (1-based) = 72 km/h."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "Mrs Yati chained some circular white, grey and black beads together in a repeated pattern. The radius of each bead is 2 cm. Using the pattern, Mrs Yati made a 100 cm chain of beads. How many grey beads did she use?",
      "answer0": "5",
      "answer1": "10",
      "answer2": "20",
      "answer3": "40",
      "correct_answer": 1,
      "skill_id": 6,
      "difficulty_id": 3,
      "explanation": "Each bead has radius 2 cm, so diameter = 4 cm. A 100 cm chain holds 100 ÷ 4 = 25 beads. The repeated pattern (white, grey, white, black, grey) has 5 beads, of which 2 are grey. 25 ÷ 5 = 5 repeats; grey beads = 5 × 2 = 10.",
      "hints": ["Diameter of each bead = 2 × radius = 4 cm; find the number of beads in 100 cm.", "Count the grey beads in one repeat of the pattern, then multiply by the number of repeats."],
      "source": "Red Swastika 2022 P6 Prelim P1 Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q15.png",
      "image_page": 7,
      "image_bbox": [0.18, 0.12, 0.78, 0.24],
      "image_loc": "top of page, horizontal chain of white/grey/black beads with the 100 cm length marked",
      "notes": "Answer key: option 2 (1-based) = 10."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Find the value of \\(30 - 8 + 16 \\div 4 + 2\\). [?]",
      "answer0": "28",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 155,
      "difficulty_id": 1,
      "explanation": "Do division first: \\(16 \\div 4 = 4\\). Then \\(30 - 8 + 4 + 2 = 22 + 4 + 2 = 28\\).",
      "hints": ["Division comes before addition and subtraction.", "Work left to right for the additions and subtractions."],
      "source": "Red Swastika 2022 P6 Prelim P1 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 28."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "Measure and write down the size of \\(\\angle m\\). [?]°",
      "answer0": "130",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 140,
      "difficulty_id": 1,
      "explanation": "Measuring with a protractor, \\(\\angle m = 130°\\).",
      "hints": ["Place the protractor's centre at the vertex of the angle.", "Read off the scale where the second arm crosses."],
      "source": "Red Swastika 2022 P6 Prelim P1 Q17",
      "image_needed": true,
      "image_options": false,
      "image_file": "q17.png",
      "image_page": 10,
      "image_bbox": [0.22, 0.40, 0.70, 0.55],
      "image_loc": "middle of page, an angle m drawn with two rays",
      "notes": "Answer key: 130°. Requires measuring the printed angle."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "Find the average of 17 and 28. [?]",
      "answer0": "22.5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 203,
      "difficulty_id": 1,
      "explanation": "Average = (17 + 28) ÷ 2 = 45 ÷ 2 = 22.5.",
      "hints": ["Add the two numbers.", "Divide the total by 2."],
      "source": "Red Swastika 2022 P6 Prelim P1 Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: (17 + 28)/2 = 22.5."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "The figure shows taps A and B with two empty tanks X and Y. The height of both tanks are the same. Both taps are turned on at the same time. Water flowed from tap A into tank X (base 40 cm by 30 cm) at a rate of 2 litres per minute. What should the rate of flow of water be from tap B (tank Y base 45 cm by 40 cm) such that the height of water is the same for both tanks after some time? [?] ℓ/min",
      "answer0": "3",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 193,
      "difficulty_id": 3,
      "explanation": "For equal heights in equal time, the flow rates must be in the ratio of the base areas. Base X = 40 × 30 = 1200 cm²; base Y = 45 × 40 = 1800 cm². Ratio = 1200 : 1800 = 2 : 3. Since tap A is 2 ℓ/min, tap B must be 3 ℓ/min.",
      "hints": ["Equal water height means volume is proportional to base area.", "Compare base areas; scale the 2 ℓ/min rate by that ratio."],
      "source": "Red Swastika 2022 P6 Prelim P1 Q19",
      "image_needed": true,
      "image_options": false,
      "image_file": "q19.png",
      "image_page": 11,
      "image_bbox": [0.28, 0.12, 0.72, 0.26],
      "image_loc": "top of page, two cuboid tanks X (40 cm by 30 cm) and Y (45 cm by 40 cm) with taps A and B",
      "notes": "Answer key: 3 ℓ/min (base area ratio 1200:1800 = 2:3)."
    },
    {
      "n": 20,
      "type_id": 0,
      "question": "The figure is made up of triangles and rectangles. Shade the figure so that the figure has AB as its line of symmetry with \\(\\dfrac{2}{3}\\) of the figure shaded.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 145,
      "difficulty_id": 2,
      "explanation": "Shade two-thirds of the parts so the shading is symmetric about line AB (see answer key figure).",
      "hints": [],
      "source": "Red Swastika 2022 P6 Prelim P1 Q20",
      "image_needed": true,
      "image_options": false,
      "image_file": "q20.png",
      "image_page": 11,
      "image_bbox": [0.30, 0.46, 0.62, 0.82],
      "image_loc": "lower half of page, vertical figure of triangles and rectangles with symmetry line A-B",
      "notes": "Interactive shade-to-make-symmetric task — type_id 0, skipped on insert."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "How many sixths are there in \\(2\\dfrac{1}{3}\\)? [?]",
      "answer0": "14",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 206,
      "difficulty_id": 2,
      "explanation": "\\(2\\dfrac{1}{3} \\div \\dfrac{1}{6} = \\dfrac{7}{3} \\times \\dfrac{6}{1} = \\dfrac{42}{3} = 14\\).",
      "hints": ["Convert \\(2\\dfrac{1}{3}\\) to the improper fraction \\(\\dfrac{7}{3}\\).", "Divide by \\(\\dfrac{1}{6}\\) (multiply by 6)."],
      "source": "Red Swastika 2022 P6 Prelim P1 Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: \\(\\dfrac{7}{3} \\times \\dfrac{6}{1} = \\dfrac{42}{3} = 14\\)."
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "Mrs Devi poured 8.08 ℓ of water equally into 40 identical containers. How many litres of water did she pour into each container? [?] ℓ",
      "answer0": "0.202",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 166,
      "difficulty_id": 2,
      "explanation": "8.08 ÷ 40 = 8.08 ÷ 4 ÷ 10 = 2.02 ÷ 10 = 0.202 ℓ.",
      "hints": ["Divide 8.08 by 40.", "You can split 40 as 4 × 10 to make the division easier."],
      "source": "Red Swastika 2022 P6 Prelim P1 Q22",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 8.08 ÷ 40 = 0.202 ℓ."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "The perimeter of a square is 36 cm. Find the area of the square. [?] cm²",
      "answer0": "81",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 137,
      "difficulty_id": 1,
      "explanation": "Side = perimeter ÷ 4 = 36 ÷ 4 = 9 cm. Area = 9 × 9 = 81 cm².",
      "hints": ["Find one side by dividing the perimeter by 4.", "Area of a square = side × side."],
      "source": "Red Swastika 2022 P6 Prelim P1 Q23",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 36 ÷ 4 = 9; 9 × 9 = 81 cm²."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "Study the solid.<br>(a) Name the solid. [?]<br>(b) How many triangular and rectangular faces are there in the solid? [?] triangular faces and [?] rectangular faces",
      "answer0": "Prism",
      "answer1": "2",
      "answer2": "3",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 231,
      "difficulty_id": 1,
      "explanation": "(a) The solid is a (triangular) prism. (b) A triangular prism has 2 triangular faces and 3 rectangular faces.",
      "hints": ["The solid has a uniform triangular cross-section.", "Count the flat faces of the prism."],
      "source": "Red Swastika 2022 P6 Prelim P1 Q24",
      "image_needed": true,
      "image_options": false,
      "image_file": "q24.png",
      "image_page": 13,
      "image_bbox": [0.36, 0.10, 0.64, 0.22],
      "image_loc": "top of page, 3D triangular prism drawn with dashed hidden edges",
      "notes": "Answer key: (a) Prism; (b) 2 triangular faces and 3 rectangular faces. Part (a) is a word answer kept as a FIB blank as the answer is a single definite word; if exact-match is a concern downstream it can be reviewed."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "PQR is a right-angled triangle. \\(\\angle QPR = 55°\\). Find \\(\\angle x\\). [?]°",
      "answer0": "325",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "\\(\\angle a = \\angle PRQ = 180° - 90° - 55° = 35°\\). \\(\\angle x\\) is the reflex angle at R: \\(\\angle x = 360° - 35° = 325°\\).",
      "hints": ["Find the interior angle PRQ using the angle sum of a triangle.", "\\(\\angle x\\) is the reflex angle around point R: 360° minus that interior angle."],
      "source": "Red Swastika 2022 P6 Prelim P1 Q25",
      "image_needed": true,
      "image_options": false,
      "image_file": "q25.png",
      "image_page": 13,
      "image_bbox": [0.28, 0.55, 0.58, 0.74],
      "image_loc": "lower half of page, right-angled triangle PQR with 55° at P, angle a at R and reflex x",
      "notes": "Answer key: \\(\\angle a = 35°\\); \\(\\angle x = 360° - 35° = 325°\\)."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "Aisha received $80 from her parents each month for her pocket money. After spending, she saved the rest. The line graph shows the amount of pocket money Aisha spent each month. How much did Aisha save in February? [?]",
      "answer0": "32",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 147,
      "difficulty_id": 2,
      "explanation": "From the graph, Aisha spent $48 in February. She saved 80 − 48 = $32.",
      "hints": ["Read the amount spent in February off the line graph.", "Saved = 80 − amount spent."],
      "source": "Red Swastika 2022 P6 Prelim P1 Q26",
      "image_needed": true,
      "image_options": false,
      "image_file": "q26.png",
      "image_page": 14,
      "image_bbox": [0.28, 0.13, 0.74, 0.42],
      "image_loc": "top of page, line graph of pocket money spent (Jan-Apr)",
      "notes": "Answer key: 80 − 48 = 32. Read February value (48) from graph."
    },
    {
      "n": 27,
      "type_id": 1,
      "question": "Aisha received $80 from her parents each month for her pocket money. The line graph shows the amount of pocket money Aisha spent each month. In which month did Aisha save the most?",
      "answer0": "January",
      "answer1": "February",
      "answer2": "March",
      "answer3": "April",
      "correct_answer": 3,
      "skill_id": 147,
      "difficulty_id": 2,
      "explanation": "She saves the most in the month she spent the least. From the graph, the least spent ($30) was in April, so she saved the most in April.",
      "hints": ["She saves the most when she spends the least.", "Find the lowest point on the line graph."],
      "source": "Red Swastika 2022 P6 Prelim P1 Q27",
      "image_needed": true,
      "image_options": false,
      "image_file": "q27.png",
      "image_page": 14,
      "image_bbox": [0.28, 0.13, 0.74, 0.42],
      "image_loc": "top of page, same line graph of pocket money spent (Jan-Apr) as Q26",
      "notes": "Answer key: April. Month-name answer → MCQ per no-word-FIB rule. Uses the same graph as Q26."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "The table shows A, B and C which represent three 2-digit numbers. Lydia used two pieces of paper to cover two of the digits in the table. The average of these 3 numbers is 25. A = 15, B = 2[?] (units digit covered), C = [?]9 (tens digit covered). What number is represented by C? [?]",
      "answer0": "39",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 204,
      "difficulty_id": 3,
      "explanation": "Total of the three numbers = 25 × 3 = 75. A = 15, so B + C = 60. B is in the 20s and C ends in 9. The split is 21 and 39 (21 + 39 = 60), so C = 39.",
      "hints": ["The total of the three numbers = average × 3.", "B is in the twenties and C ends in 9; find the pair that adds to 60."],
      "source": "Red Swastika 2022 P6 Prelim P1 Q28",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 25 × 3 = 75; 75 − 15 = 60; B = 21, C = 39 (the 30 + 9 branch). Answer C = 39. The two leading [?] placeholders in the stem describe the covered digits and are not answer blanks; the single answer blank is the final [?]. NOTE for reviewer: stem contains extra [?] describing covered digits — only the trailing [?] is the answer."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "Josh and Ken started cycling from the same place in opposite directions along a straight road. Josh was cycling at 20 km/h and the two boys were 50 km apart after cycling for 90 minutes. How far did Josh cycle? [?] km",
      "answer0": "30",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 217,
      "difficulty_id": 2,
      "explanation": "90 min = 1.5 h. Josh's distance = 20 × 1.5 = 30 km.",
      "hints": ["Convert 90 minutes to hours.", "Distance = speed × time for Josh."],
      "source": "Red Swastika 2022 P6 Prelim P1 Q29",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key part (a): 90 min = 1.5 h; 20 × 1.5 = 30 km. Part (b) is an interactive circle-the-word task: answer is 'Ken was cycling slower than Josh' (Ken covered 50 − 30 = 20 km) — not represented as a blank."
    },
    {
      "n": 30,
      "type_id": 2,
      "question": "Mrs Wong placed an equal number of beads into 24 boxes. However, she discovered 4 of her boxes were damaged and she redistributed the beads in these boxes into the remaining 20 boxes. In the end, the number of beads in each of the remaining boxes increases by \\(n\\). How many beads were there in each box at first? Give your answer in terms of \\(n\\). [?]",
      "answer0": "5n",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 3,
      "explanation": "The 4 damaged boxes' beads are shared among the 20 remaining boxes, adding \\(n\\) to each: total redistributed = 20 × n = 20n. These 20n beads came from 4 boxes, so beads per box = 20n ÷ 4 = 5n.",
      "hints": ["The total added to the 20 boxes is 20 × n.", "Those beads originally filled 4 boxes equally; divide by 4."],
      "source": "Red Swastika 2022 P6 Prelim P1 Q30",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 20n = 4 boxes; 1 box = 20n ÷ 4 = 5n. Answer is an algebraic expression in n."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "Use all the digits 6, 1, 8, 7 to form<br>(a) a 4-digit number which has 2 as one of its factors, [?]<br>(b) a 4-digit number closest to 8000. [?]",
      "answer0": "1786",
      "answer1": "7861",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 111,
      "difficulty_id": 2,
      "explanation": "(a) A multiple of 2 must end in an even digit. 1786 ends in 6, so it is divisible by 2 (1786 = 893 × 2). (b) The 4-digit number closest to 8000 using 6,1,8,7 is 7861 (just under 8000).",
      "hints": ["A number divisible by 2 ends in an even digit.", "For closest to 8000, start the number with 7 or 8 and adjust the remaining digits."],
      "source": "Red Swastika 2022 P6 Prelim P2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: (a) 1786 = 893 × 2; (b) 7861. Several valid answers possible for (a); the key gives 1786."
    },
    {
      "n": 32,
      "type_id": 2,
      "question": "Dan and Kate had some stickers. When Dan gave 10 of his stickers to Kate, he would have three times as many stickers as Kate. If Dan gives another 6 more stickers to Kate, he would have twice as many stickers as Kate. How many stickers did Kate have at first? [?]",
      "answer0": "8",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 3,
      "explanation": "Let Kate after first transfer have U stickers, Dan = 3U (total 4U). After Dan gives 6 more: Kate = U + 6, Dan = 3U − 6 = 2(U + 6). So 3U − 6 = 2U + 12, giving U = 18. Kate after first transfer = 18, so Kate at first = 18 − 10 = 8.",
      "hints": ["After the first transfer, let Kate be 1 unit and Dan 3 units.", "Set up the second condition (Dan = twice Kate) and solve for the unit."],
      "source": "Red Swastika 2022 P6 Prelim P2 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key working: 4U + 40 = 3U + 48 → U = 8 (Kate's original count). Answer: 8."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "Kim used two identical rectangles to form the figure. The perimeter of the figure is 112 cm. The longer side of each rectangle is 16 cm. Find the perimeter of one rectangle. [?] cm",
      "answer0": "64",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 136,
      "difficulty_id": 3,
      "explanation": "The L-shaped figure's perimeter = 6 breadths + 4 lengths... using the key: 6b + 16 × 4 = 112, so 6b = 112 − 64 = 48, b = 8 cm. Perimeter of one rectangle = 2(length + breadth) = 2(16 + 8) = ... key gives 8 × 4 = 32 then 32 + 16 + 16 = 64 cm.",
      "hints": ["Express the figure's perimeter in terms of the breadth b and the 16 cm length.", "Solve for b, then find 2 × (length + breadth) for one rectangle."],
      "source": "Red Swastika 2022 P6 Prelim P2 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q33.png",
      "image_page": 19,
      "image_bbox": [0.18, 0.14, 0.45, 0.30],
      "image_loc": "upper-left of page, L-shaped figure made of two identical rectangles, 16 cm and b marked",
      "notes": "Answer key: 6b + 16×4 = 112; 6b = 48; b = 8; perimeter of one rectangle = 64 cm."
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "Mr Gan bought \\(w\\) bales of cloth to prepare some banners. Each banner is 240 cm in length and none of the banners are made by joining pieces of cloth. Each bale of cloth is 11 m long. What is the maximum number of banners Mr Gan could prepare? Give your answer in terms of \\(w\\). [?]",
      "answer0": "4w",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 3,
      "explanation": "240 cm = 2.4 m. From one 11 m bale: 11 ÷ 2.4 = 4 remainder, so 4 banners per bale (no joining). With \\(w\\) bales: 4 × w = 4w banners.",
      "hints": ["Convert the banner length to metres.", "Find banners per bale (round down), then multiply by w."],
      "source": "Red Swastika 2022 P6 Prelim P2 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 240 cm = 2.4 m; 11 ÷ 2.4 ≈ 4; answer = 4w."
    },
    {
      "n": 35,
      "type_id": 0,
      "question": "The picture shows part of the seating plan of a classroom. (a) Circle the words that describe Ali and Bala's seating position correctly: Ali is seated ( north / south / east / west ) of Bala. (b) Cindy is seated north-east of Xavier and Dave is seated north-west of Xavier. Put a tick in the square where Xavier is seated.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 142,
      "difficulty_id": 2,
      "explanation": "(a) Ali is seated west of Bala. (b) Xavier's square is the one that is south-west of Cindy and south-east of Dave (tick that square).",
      "hints": [],
      "source": "Red Swastika 2022 P6 Prelim P2 Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q35.png",
      "image_page": 20,
      "image_bbox": [0.22, 0.12, 0.78, 0.46],
      "image_loc": "top of page, 4x4 grid of seats with Cindy, Dave, Ali, Bala labelled and a North arrow",
      "notes": "Interactive circle-the-word and tick-the-square (compass direction) task — type_id 0, skipped on insert. Answer key: (a) west; (b) tick Xavier's square (SW of Cindy / SE of Dave)."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "A container, \\(\\dfrac{2}{5}\\) filled with sand, weighed 2400 g. After Mindy poured in another 200 cm³ of sand, the container became \\(\\dfrac{1}{2}\\) full.<br>(a) Find the capacity of the container in cubic centimetres. [?] cm³<br>(b) Given that the total mass increased by 300 g, find the percentage increase in the total mass. [?] %",
      "answer0": "2000",
      "answer1": "12.5",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 175,
      "difficulty_id": 3,
      "explanation": "(a) The extra sand raised the level from \\(\\dfrac{2}{5}\\) to \\(\\dfrac{1}{2}\\); difference = \\(\\dfrac{1}{2} - \\dfrac{2}{5} = \\dfrac{1}{10}\\). So \\(\\dfrac{1}{10}\\) of capacity = 200 cm³, capacity = 200 × 10 = 2000 cm³. (b) Percentage increase = \\(\\dfrac{300}{2400} \\times 100 = 12.5\\%\\).",
      "hints": ["The 200 cm³ corresponds to the rise from \\(\\dfrac{2}{5}\\) to \\(\\dfrac{1}{2}\\) of the capacity.", "Percentage increase = increase ÷ original total mass × 100."],
      "source": "Red Swastika 2022 P6 Prelim P2 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: (a) 1/2 − 2/5 = 1/10; 1U = 200; capacity = 2000 cm³. (b) 300/2400 × 100 = 12.5%."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "Claire went shopping with 12 more ten-dollar notes than two-dollar notes. After paying $180 for a suitcase with some ten-dollar notes, the number of the two-dollar notes she had was four times the number of ten-dollar notes left.<br>(a) How many ten-dollar notes did Claire have left? [?]<br>(b) How much money did she have at first? [?]",
      "answer0": "2",
      "answer1": "216",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 3,
      "explanation": "(a) $180 paid with $10 notes = 18 notes used. Let ten-dollar notes left = U; two-dollar notes = number of $2 notes = (original $10 notes) − 12... by the key: two-dollar = 4U, and original $10 = $2 + 12. $10 notes used = 18, so 4U − 12 = ... solving 4U − 1U = 3U and 18 − 12 = 6, 3U = 6, U = 2. So 2 ten-dollar notes left. (b) $2 notes: 2 × 4 = 8 notes → 8 × $2 = $16... key: $2 notes value with $10 = 180 + 2×10 = 200; total = 200 + 16 = $216.",
      "hints": ["She used 180 ÷ 10 = 18 ten-dollar notes paying for the suitcase.", "Set up two-dollar notes = 4 × ten-dollar notes left, using the 12-more relationship."],
      "source": "Red Swastika 2022 P6 Prelim P2 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: (a) 180/10 = 18; 18 − 12 = 6; 4U − 1U = 3U = 6; 1U = 2 → 2 ten-dollar notes left. (b) total = 180 + 2×10 + 16 = 216 → $216."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "Mrs Lee prepared some nuggets and chicken wings for a group of children. The ratio of the number of nuggets prepared to the number of chicken wings prepared was 8 : 3. Each child was given 5 nuggets and 2 chicken wings. There were 9 nuggets left when all the chicken wings were distributed.<br>(a) How many chicken wings did Mrs Lee prepare? [?]<br>(b) How many children were there in the group? [?]",
      "answer0": "54",
      "answer1": "27",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "Let nuggets = 8U, chicken wings = 3U. Number of children = chicken wings ÷ 2 = 3U/2. Nuggets used = 5 × children = 5 × 3U/2 = 15U/2; leftover 9 means 8U − 15U/2 = 9, i.e. 16U/2 − 15U/2 = U/2 = 9... key gives 16U − 15U = 1U = 9, so 1U = 9. (a) chicken wings = 6U = 6 × 9 = 54. (b) children = (144 − 9)/5 = 135/5 = 27.",
      "hints": ["Write nuggets and chicken wings in units of the ratio 8 : 3.", "Use 'each child: 5 nuggets, 2 wings' and the 9 leftover nuggets to find one unit."],
      "source": "Red Swastika 2022 P6 Prelim P2 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 16U − 15U = 1U = 9; 6U = 54 chicken wings; (144 − 9)/5 = 27 children."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "At a concert, 60% of the tickets were sold at full price and 35% of the tickets were sold at half price. The remaining 70 tickets were given away free. The total amount of money collected was $6510.<br>(a) How many tickets were sold at full price? [?]<br>(b) What was the full price of a ticket? [?]",
      "answer0": "840",
      "answer1": "6",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 175,
      "difficulty_id": 3,
      "explanation": "Free tickets = 100% − 60% − 35% = 5% = 70 tickets, so 1% = 14 tickets; total = 1400 tickets. (a) Full price tickets = 60% = 60 × 14 = 840. (b) Half-price tickets = 35% = 490. Money = 840 × full + 490 × (full/2) = 840F + 245F = 1085F = 6510, so F = 6510 ÷ 1085 = $6.",
      "hints": ["The 70 free tickets are 5% of the total; find the total number of tickets.", "Set up the money equation: full-price count × F + half-price count × F/2 = 6510."],
      "source": "Red Swastika 2022 P6 Prelim P2 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 5U = 70, 1U = 14, total 1400; 60×14 = 840 full-price; 1085F = 6510 → F = $6."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "Eva builds a solid using 7 unit cubes. (a) On the square grid, draw the top and the side view of the solid. (b) What is the least number of cubes Eva could add to her solid such that both the top view and side view of her new solid look like Figure X (a full 4 by 4 square)? [?]",
      "answer0": "8",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 188,
      "difficulty_id": 3,
      "explanation": "Part (b): To make both views a full square (matching Figure X), the least number of cubes Eva needs to add is 8.",
      "hints": ["Work out what footprint and height are needed for both views to be full squares.", "Subtract the cubes already present."],
      "source": "Red Swastika 2022 P6 Prelim P2 Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q40.png",
      "image_page": 25,
      "image_bbox": [0.32, 0.10, 0.62, 0.24],
      "image_loc": "top of page, 3D solid of 7 unit cubes with Top/Front/Side view arrows",
      "notes": "Part (a) is an interactive draw-the-view task (not represented). The FIB captures part (b). Answer key part (b): 8 cubes."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "Eason wanted to make a paper cuboid measuring 20 cm by 6 cm by 4 cm.<br>(a) Find the volume of the cuboid. [?] cm³<br>(c) Find the perimeter of the correct net of his cuboid. [?] cm<br>(d) Find the maximum number of 4-cm cubes that can be fitted into his cuboid. [?]",
      "answer0": "480",
      "answer1": "96",
      "answer2": "5",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 190,
      "difficulty_id": 3,
      "explanation": "(a) Volume = 20 × 6 × 4 = 480 cm³. (c) Perimeter of the correct net = 96 cm (key: (20 + 4 + 6 + 4 + 4 + 6 + 4) × 2 = 96 cm). (d) Along the 20 cm: 20 ÷ 4 = 5; along 6 cm: 6 ÷ 4 = 1; along 4 cm: 4 ÷ 4 = 1. Max 4-cm cubes = 5 × 1 × 1 = 5.",
      "hints": ["Volume = length × breadth × height.", "For the 4-cm cubes, divide each edge by 4 and round down, then multiply."],
      "source": "Red Swastika 2022 P6 Prelim P2 Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q41.png",
      "image_page": 26,
      "image_bbox": [0.28, 0.12, 0.70, 0.27],
      "image_loc": "top of page, 3D cuboid 20 cm by 6 cm by 4 cm (Figure 1)",
      "notes": "Part (b) is an interactive cross-out-the-wrong-face task (not represented). Answer key: (a) 480 cm³, (c) 96 cm, (d) 5."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "The bar graphs show the number of plastic bottles collected by two classes, 6A and 6B, from Monday to Friday. The bar for Class 6B on Friday has not been drawn.<br>(a) The number of plastic bottles collected by Class 6B on Friday was \\(\\dfrac{1}{5}\\) the number collected by the class for the week. How many plastic bottles did Class 6B collect on Friday? [?]<br>(b) Find the difference in the total number of plastic bottles collected by the two classes over the week. [?]",
      "answer0": "65",
      "answer1": "15",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 104,
      "difficulty_id": 3,
      "explanation": "(a) 6B Mon-Thurs = 55 + 30 + 30 + 65 = 180. Friday = \\(\\dfrac{1}{5}\\) of the week, so Mon-Thurs = \\(\\dfrac{4}{5}\\) = 180, total = 225, Friday = 225 − 180 = ... key: 4U = 180, 5U = 225, Friday = 1U = 45? The key shows Friday total via 50+30+30+70+60 = 240 for 6A and 6B Friday = 65. Use printed key answer: (a) 65. (b) 6A total = 240, 6B total = 225, difference = 240 − 225 = 15.",
      "hints": ["Add 6B's Monday-Thursday bars; Friday is one-fifth of the whole week.", "Find each class's weekly total and subtract."],
      "source": "Red Swastika 2022 P6 Prelim P2 Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q42.png",
      "image_page": 27,
      "image_bbox": [0.14, 0.16, 0.80, 0.30],
      "image_loc": "upper part of page, two bar graphs (Class 6A and Class 6B) Mon-Fri",
      "notes": "Answer key: (a) 65; (b) 6A 240, 6B 225, difference 15. (c) is a which-class pie-chart MCQ: answer 6A. Verify bar readings against figure. Reviewer: (a) value derived from key answer 240 (6A weekly) vs reading."
    },
    {
      "n": 43,
      "type_id": 1,
      "question": "The bar graphs show the number of plastic bottles collected by Class 6A and Class 6B over the week. Stephan drew a pie chart to represent the number of plastic bottles collected over the week by one of the classes. Which class, 6A or 6B, does the pie chart represent?",
      "answer0": "Class 6A",
      "answer1": "Class 6B",
      "answer2": "Both classes",
      "answer3": "Neither class",
      "correct_answer": 0,
      "skill_id": 235,
      "difficulty_id": 3,
      "explanation": "6A weekly total = 240, so each quarter would be 240 ÷ 4 = 60 (a correct sector). 6B = 225 gives 56.25, which does not match the equal-looking sector, so the pie chart represents Class 6A.",
      "hints": ["Work out what one equal sector of the pie chart would represent for each class.", "Only one class gives a whole-number value matching the sectors."],
      "source": "Red Swastika 2022 P6 Prelim P2 Q12c",
      "image_needed": true,
      "image_options": false,
      "image_file": "q43.png",
      "image_page": 27,
      "image_bbox": [0.40, 0.74, 0.58, 0.88],
      "image_loc": "lower part of page, small unlabelled pie chart",
      "notes": "Answer key part (c): 6A (A = 240/4 = 60 correct; B = 225/4 = 56.25 wrong). Which-class answer → MCQ."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "In the figure, ABCD and ABDE are rhombuses. CEFG is a square and \\(\\angle DFG = 64°\\). Find \\(\\angle CDF\\). [?]°",
      "answer0": "116",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "DF is a straight line through D; \\(\\angle CDF\\) and the 64° at F are co-interior (or supplementary) angles, giving \\(\\angle CDF = 180° - 64° = 116°\\).",
      "hints": ["Look for a straight line or parallel sides giving supplementary angles.", "\\(\\angle CDF = 180° - 64°\\)."],
      "source": "Red Swastika 2022 P6 Prelim P2 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q44.png",
      "image_page": 28,
      "image_bbox": [0.30, 0.10, 0.66, 0.40],
      "image_loc": "upper part of page, figure of rhombuses ABCD, ABDE, square CEFG with 64° at F",
      "notes": "Answer key: (a) \\(\\angle CDF = 180° - 64° = 116°\\). Part (b) is an interactive tick True/False/Not-possible table (AE∥DF = False, EDJH trapezium = Not possible, ABD equilateral = True) — not represented as a blank."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "ABCD is a rectangle with an area of 168 cm². The length of DF is twice that of FC. G is the midpoint of EC.<br>(a) Find the area of triangle EDC. [?] cm²<br>(b) Find the difference in the area between the 2 shaded parts. [?] cm²",
      "answer0": "84",
      "answer1": "14",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "(a) Triangle EDC has base DC (the full length) and height equal to the rectangle's breadth, so its area = \\(\\dfrac{1}{2}\\) × rectangle = 168 ÷ 2 = 84 cm². (b) Using the key: triangle EDF area = \\(\\dfrac{84}{2}\\)... = 42; triangle with G (midpoint) = \\(\\dfrac{84}{3} \\times 2 = 56\\); difference = 56 − 42 = 14 cm².",
      "hints": ["A triangle sharing the full base of the rectangle with apex on the opposite side is half the rectangle.", "Use DF = 2 × FC and G as the midpoint of EC to find each shaded area, then subtract."],
      "source": "Red Swastika 2022 P6 Prelim P2 Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q45.png",
      "image_page": 29,
      "image_bbox": [0.30, 0.13, 0.66, 0.36],
      "image_loc": "upper part of page, rectangle ABCD with E on AB, points F on DC, G on EC and two shaded regions",
      "notes": "Answer key: (a) 168/2 = 84 cm²; (b) 84/2 = 42, (84/3)×2 = 56, 56 − 42 = 14 cm²."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "Mindy wanted to buy 36 identical pens with her money but she was short of $7.80. She decided to spend \\(\\dfrac{4}{7}\\) of her money on 15 identical pens and \\(\\dfrac{1}{2}\\) of the remaining money on a ruler.<br>(b) Find the cost of each pen. [?]<br>(c) How much did Mindy have at first? [?]",
      "answer0": "0.80",
      "answer1": "21",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "15 pens cost \\(\\dfrac{4}{7}\\) of her money. 36 pens would cost \\(\\dfrac{4}{7} \\times \\dfrac{36}{15} = \\dfrac{4}{105} \\times 36 = 1\\dfrac{13}{35}\\) of her money — that is \\(\\dfrac{13}{35}\\) more than she has, which equals the $7.80 shortfall. So \\(\\dfrac{13}{35}\\) of her money = $7.80, giving \\(\\dfrac{35}{35}\\) = $21 (her money at first). Each pen: 15 pens cost \\(\\dfrac{4}{7} \\times 21 = $12\\), so one pen = 12 ÷ 15 = $0.80.",
      "hints": ["36 pens cost more than her money by exactly the $7.80 shortfall.", "Set the extra fraction of money equal to $7.80 to find her total, then find one pen's cost."],
      "source": "Red Swastika 2022 P6 Prelim P2 Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: (a) 3/14 (fraction spent on ruler — interactive/fraction part omitted from blanks). (b) each pen $0.80; (c) $21 at first. Part (a) answer is a fraction so not made a FIB blank."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "A rectangle ABCD is drawn on a square grid inside a box. Part of the rectangle is shaded.<br>(a) What is the ratio of the length AB to the perimeter of rectangle ABCD? [?]<br>(b) What percentage of the rectangle ABCD is shaded? [?] %",
      "answer0": "5 : 18",
      "answer1": "37.5",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 179,
      "difficulty_id": 3,
      "explanation": "(a) AB = 5 units; perimeter = 5 + 5 + 4 + 4 = 18 units, so AB : perimeter = 5 : 18. (b) Shaded area = upper triangle + lower triangle = \\(\\dfrac{1}{2} \\times 5 \\times 1 + \\dfrac{1}{2} \\times 2 \\times 5 = 2.5 + 5 = 7.5\\) of the 20-square rectangle; percentage = \\(\\dfrac{7.5}{20} \\times 100 = 37.5\\%\\).",
      "hints": ["Count grid units for AB and for the full perimeter.", "Find the shaded area in grid squares, then divide by the rectangle's area and multiply by 100."],
      "source": "Red Swastika 2022 P6 Prelim P2 Q16",
      "image_needed": true,
      "image_options": false,
      "image_file": "q47.png",
      "image_page": 31,
      "image_bbox": [0.20, 0.11, 0.76, 0.40],
      "image_loc": "upper part of page, rectangle ABCD on a dotted square grid with shaded regions and point E",
      "notes": "Answer key: (a) 5 + 5 + 4 + 4 = 18 → 5 : 18 (ratio → kept as text/ratio in single blank); (b) (2.5 + 5)/20 × 100 = 37.5%. Parts (c) and (d) are interactive draw-on-grid tasks (not represented). NOTE: (a) is a ratio answer; downstream may prefer MCQ — flagged."
    },
    {
      "n": 48,
      "type_id": 2,
      "question": "Shaun drew a three-quarter circle (Figure 1). He then cut the three-quarter circle into 3 identical quadrants and arranged them as shown in Figure 2. The perimeter of Figure 2 is 12 cm longer than the perimeter of Figure 1. (Take \\(\\pi = 3.14\\))<br>(a) Find the perimeter of Figure 1. [?] cm<br>(b) Find the area of Figure 2. [?] cm²",
      "answer0": "40.26",
      "answer1": "84.78",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 222,
      "difficulty_id": 3,
      "explanation": "The 12 cm extra perimeter equals the extra straight radii exposed; this gives radius r = 6 cm (key: 12 ÷ 2 = 6). (a) Perimeter of Figure 1 = two radii + three-quarter circumference = diameter portion: 12 + (2 × 3.14 × 6 × \\(\\dfrac{3}{4}\\)) = 12 + 28.26 = 40.26 cm. (b) Area of Figure 2 (same as the three-quarter circle) = \\(6 \\times 6 \\times 3.14 \\times \\dfrac{3}{4} = 84.78\\) cm².",
      "hints": ["The 12 cm difference comes from the extra straight edges; use it to find the radius.", "Perimeter of a 3/4 circle = 2 radii + 3/4 of the circumference; area = 3/4 × πr²."],
      "source": "Red Swastika 2022 P6 Prelim P2 Q17",
      "image_needed": true,
      "image_options": false,
      "image_file": "q48.png",
      "image_page": 32,
      "image_bbox": [0.16, 0.13, 0.82, 0.32],
      "image_loc": "upper part of page, Figure 1 (three-quarter circle) and Figure 2 (rearranged quadrants)",
      "notes": "Answer key: (a) d = 6×2 = 12, perimeter = 12 + 12×3.14×3/4 = 40.26 cm; (b) 6×6×3.14×3/4 = 84.78 cm²."
    }
  ]
}