{
  "paper": {
    "school": "Red Swastika",
    "year": 2024,
    "level": "P6",
    "label": "Prelim",
    "source_prefix": "Red Swastika 2024 P6 Prelim",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "80 000 + 4000 + 300 + 8 =",
      "answer0": "84 380",
      "answer1": "84 308",
      "answer2": "84 038",
      "answer3": "80 438",
      "correct_answer": 1,
      "skill_id": 105,
      "difficulty_id": 1,
      "explanation": "Add by place value: 80 000 + 4000 + 300 + 8 = 84 308.",
      "hints": ["Line up the place values.", "Ten thousands 8, thousands 4, hundreds 3, ones 8."],
      "source": "Red Swastika 2024 P6 Prelim Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 2 (84 308)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "How much water is in the container?",
      "answer0": "200 ml",
      "answer1": "300 ml",
      "answer2": "400 ml",
      "answer3": "500 ml",
      "correct_answer": 2,
      "skill_id": 192,
      "difficulty_id": 1,
      "explanation": "The 1 l beaker is graduated; the water level reaches the 400 ml mark. Answer: 400 ml.",
      "hints": ["1 l = 1000 ml.", "Read the level against the markings."],
      "source": "Red Swastika 2024 P6 Prelim Q2",
      "image_needed": true,
      "image_options": false,
      "image_file": "q2.png",
      "image_page": 3,
      "image_bbox": [0.48, 0.40, 0.62, 0.52],
      "image_loc": "beaker figure on the right, beside the options",
      "notes": "Key: option 3 (400 ml)."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Which of the following is equal to \\(4\\dfrac{5}{6}\\)?",
      "answer0": "\\(\\dfrac{24}{6}\\)",
      "answer1": "\\(\\dfrac{26}{6}\\)",
      "answer2": "\\(\\dfrac{29}{6}\\)",
      "answer3": "\\(\\dfrac{45}{6}\\)",
      "correct_answer": 2,
      "skill_id": 119,
      "difficulty_id": 1,
      "explanation": "\\(4\\dfrac{5}{6} = \\dfrac{4\\times 6 + 5}{6} = \\dfrac{29}{6}\\).",
      "hints": ["Multiply whole number by denominator.", "Add the numerator: 24 + 5 = 29."],
      "source": "Red Swastika 2024 P6 Prelim Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 3 (29/6)."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Ali folds 10 stars in 5 minutes.<br>At this rate, how many stars can Ali fold in 50 minutes?",
      "answer0": "25",
      "answer1": "50",
      "answer2": "100",
      "answer3": "500",
      "correct_answer": 2,
      "skill_id": 152,
      "difficulty_id": 1,
      "explanation": "50 minutes is 10 times 5 minutes, so 10 × 10 = 100 stars.",
      "hints": ["Find how many 5-minute blocks are in 50 minutes.", "50 ÷ 5 = 10; 10 × 10 = 100."],
      "source": "Red Swastika 2024 P6 Prelim Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 3 (100)."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "What is 15 minutes before the time shown on the clock?",
      "answer0": "12 55",
      "answer1": "13 25",
      "answer2": "13 50",
      "answer3": "14 20",
      "correct_answer": 0,
      "skill_id": 135,
      "difficulty_id": 2,
      "explanation": "The clock shows 13 10 (1.10 pm). 15 minutes before 13 10 is 12 55.",
      "hints": ["Read the clock time first.", "Subtract 15 minutes, crossing back past the hour."],
      "source": "Red Swastika 2024 P6 Prelim Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q5.png",
      "image_page": 4,
      "image_bbox": [0.44, 0.31, 0.62, 0.46],
      "image_loc": "analogue clock to the right of the options",
      "notes": "Key: option 1 (12 55). Clock shows 13 10."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "A solid cuboid of height 10 cm has a square base of side 4 cm.<br>What is its volume?",
      "answer0": "40 cm³",
      "answer1": "160 cm³",
      "answer2": "240 cm³",
      "answer3": "400 cm³",
      "correct_answer": 1,
      "skill_id": 190,
      "difficulty_id": 1,
      "explanation": "Volume = 4 × 4 × 10 = 160 cm³.",
      "hints": ["Volume of cuboid = length × breadth × height.", "Base is 4 × 4 = 16; 16 × 10 = 160."],
      "source": "Red Swastika 2024 P6 Prelim Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q6.png",
      "image_page": 4,
      "image_bbox": [0.45, 0.55, 0.66, 0.70],
      "image_loc": "upright cuboid figure to the right of the options",
      "notes": "Key: option 2 (160 cm3)."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "Which line in the square grid is parallel to DE?",
      "answer0": "BF",
      "answer1": "EF",
      "answer2": "CD",
      "answer3": "AB",
      "correct_answer": 0,
      "skill_id": 100,
      "difficulty_id": 2,
      "explanation": "On the square grid, BF has the same gradient (slope) as DE, so BF is parallel to DE.",
      "hints": ["Parallel lines have the same slope on the grid.", "Compare the arrowed lines."],
      "source": "Red Swastika 2024 P6 Prelim Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q7.png",
      "image_page": 5,
      "image_bbox": [0.12, 0.13, 0.62, 0.34],
      "image_loc": "hexagon ABCDEF drawn on a square grid, top of page",
      "notes": "Key: option 1 (BF)."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "Arrange these distances from the longest to the shortest.<br>1.15 km, 1 km 105 m, \\(1\\dfrac{1}{5}\\) km",
      "answer0": "Longest 1 km 105 m, \\(1\\dfrac{1}{5}\\) km, shortest 1.15 km",
      "answer1": "Longest 1 km 105 m, 1.15 km, shortest \\(1\\dfrac{1}{5}\\) km",
      "answer2": "Longest 1.15 km, 1 km 105 m, shortest \\(1\\dfrac{1}{5}\\) km",
      "answer3": "Longest \\(1\\dfrac{1}{5}\\) km, 1.15 km, shortest 1 km 105 m",
      "correct_answer": 3,
      "skill_id": 184,
      "difficulty_id": 2,
      "explanation": "Convert all to km: 1.15 km, 1 km 105 m = 1.105 km, \\(1\\dfrac{1}{5}\\) km = 1.2 km. Longest to shortest: 1.2 km, 1.15 km, 1.105 km, i.e. \\(1\\dfrac{1}{5}\\) km, 1.15 km, 1 km 105 m.",
      "hints": ["Change every distance to km in decimal form.", "1 km 105 m = 1.105 km; 1/5 km = 0.2 km."],
      "source": "Red Swastika 2024 P6 Prelim Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 4."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "The table shows the number of red and blue balloons 4 classes bought. Class 6A: red 12, blue 17, total 29. Class 6B: red 18, blue 10, total 28. Class 6C: red 14, blue 13, total 27. Class 6D: red 11, blue 19, total 30.<br>Which class bought the most number of balloons?",
      "answer0": "6A",
      "answer1": "6B",
      "answer2": "6C",
      "answer3": "6D",
      "correct_answer": 3,
      "skill_id": 146,
      "difficulty_id": 1,
      "explanation": "Compare totals: 6A 29, 6B 28, 6C 27, 6D 30. The largest is 6D with 30.",
      "hints": ["Look at the Total column.", "Find the greatest total."],
      "source": "Red Swastika 2024 P6 Prelim Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 4 (6D). Table data given in stem."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "PQ and RS are straight lines.<br>Which of the following is true?",
      "answer0": "∠a = ∠c",
      "answer1": "∠b = ∠d",
      "answer2": "∠b + ∠c = 180°",
      "answer3": "∠a + ∠d = 180°",
      "correct_answer": 3,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "∠a and ∠d are angles on the straight line RS (on the same side), so ∠a + ∠d = 180°.",
      "hints": ["Angles on a straight line add to 180°.", "Check which pair lies on one straight line."],
      "source": "Red Swastika 2024 P6 Prelim Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 6,
      "image_bbox": [0.12, 0.46, 0.58, 0.62],
      "image_loc": "two straight lines PQ and RS crossing, angles a,b,c,d labelled",
      "notes": "Key: option 4."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "Which figure has the largest perimeter?",
      "answer0": "A",
      "answer1": "B",
      "answer2": "C",
      "answer3": "D",
      "correct_answer": 1,
      "skill_id": 96,
      "difficulty_id": 2,
      "explanation": "Counting unit edges around each rectilinear figure on the 1 cm grid, figure B has the longest perimeter.",
      "hints": ["Count the unit-grid edges around each shape.", "Notches and indentations increase perimeter."],
      "source": "Red Swastika 2024 P6 Prelim Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q11.png",
      "image_page": 7,
      "image_bbox": [0.12, 0.12, 0.72, 0.26],
      "image_loc": "four shaded rectilinear figures A B C D on a 1 cm grid",
      "notes": "Key: option 2 (B)."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "Jane received $120 as her bursary award.<br>She gave $30 to her father.<br>What percentage of the bursary award money did Jane have left?",
      "answer0": "25%",
      "answer1": "30%",
      "answer2": "75%",
      "answer3": "90%",
      "correct_answer": 2,
      "skill_id": 175,
      "difficulty_id": 1,
      "explanation": "Left = $120 - $30 = $90. Percentage left = (90 ÷ 120) × 100% = 75%.",
      "hints": ["Find the amount left first.", "Divide by the original and multiply by 100%."],
      "source": "Red Swastika 2024 P6 Prelim Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 3 (75%)."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "A box contains red, blue and yellow beads. \\(\\dfrac{1}{3}\\) of the beads are red.<br>There were twice as many blue beads as yellow beads.<br>What fraction of the beads in the box are blue?",
      "answer0": "\\(\\dfrac{4}{9}\\)",
      "answer1": "\\(\\dfrac{2}{9}\\)",
      "answer2": "\\(\\dfrac{2}{3}\\)",
      "answer3": "\\(\\dfrac{1}{6}\\)",
      "correct_answer": 0,
      "skill_id": 214,
      "difficulty_id": 2,
      "explanation": "Red = 1/3, so blue + yellow = 2/3. Blue : yellow = 2 : 1, so blue = 2/3 of 2/3 = 4/9.",
      "hints": ["Non-red beads make up 2/3.", "Split 2/3 in the ratio 2 : 1 for blue : yellow."],
      "source": "Red Swastika 2024 P6 Prelim Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 1 (4/9)."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "Tim is to multiply a decimal by 100.<br>In a rush, he divided it by 10 and obtained 8.94.<br>What should be the correct answer?",
      "answer0": "0.894",
      "answer1": "89.4",
      "answer2": "894",
      "answer3": "8940",
      "correct_answer": 3,
      "skill_id": 166,
      "difficulty_id": 2,
      "explanation": "The decimal = 8.94 × 10 = 89.4. Correct answer = 89.4 × 100 = 8940.",
      "hints": ["Reverse the wrong step: multiply 8.94 by 10 to get the number.", "Then multiply by 100."],
      "source": "Red Swastika 2024 P6 Prelim Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 4 (8940)."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "A bakery had this promotion: 1 donut for $3. Buy 5 donuts and get another 1 donut free! Buy 8 donuts and get another 2 donuts free!<br>Pete left the bakery with 127 donuts using the given promotion.<br>What was the least amount of money he had to pay for 127 donuts?",
      "answer0": "$303",
      "answer1": "$306",
      "answer2": "$375",
      "answer3": "$381",
      "correct_answer": 1,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Best deal: buy 8 get 2 free = 10 donuts for 8×$3 = $24. 12 sets of 10 = 120 donuts for 12×$24 = $288. Remaining 7: buy 5 get 1 free = 6 donuts for $15, plus 1 donut for $3. Total = $288 + $15 + $3 = $306.",
      "hints": ["Compare the value of each promotion.", "Use the 8-get-2-free deal for bulk, then top up the remainder."],
      "source": "Red Swastika 2024 P6 Prelim Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 2 ($306). Promotion text kept in stem; decorative donut image not needed."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Find the value of 10.21 − 7.89.<br>[?]",
      "answer0": "2.32",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 129,
      "difficulty_id": 1,
      "explanation": "10.21 − 7.89 = 2.32.",
      "hints": ["Line up the decimal points.", "Subtract, regrouping as needed."],
      "source": "Red Swastika 2024 P6 Prelim Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "FIB. Answer 2.32 from worked solution."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "Find the largest multiple of 8 that is smaller than 60.<br>[?]",
      "answer0": "56",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 114,
      "difficulty_id": 1,
      "explanation": "Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64. The largest below 60 is 56.",
      "hints": ["List multiples of 8.", "Pick the biggest one under 60."],
      "source": "Red Swastika 2024 P6 Prelim Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "FIB. Answer 56."
    },
    {
      "n": 18,
      "type_id": 1,
      "question": "Find the value of \\(\\dfrac{2}{3} \\times \\dfrac{1}{6}\\).",
      "answer0": "\\(\\dfrac{1}{9}\\)",
      "answer1": "\\(\\dfrac{2}{9}\\)",
      "answer2": "\\(\\dfrac{1}{18}\\)",
      "answer3": "\\(\\dfrac{3}{18}\\)",
      "correct_answer": 0,
      "skill_id": 161,
      "difficulty_id": 1,
      "explanation": "\\(\\dfrac{2}{3} \\times \\dfrac{1}{6} = \\dfrac{2}{18} = \\dfrac{1}{9}\\).",
      "hints": ["Multiply numerators and denominators.", "Simplify 2/18."],
      "source": "Red Swastika 2024 P6 Prelim Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Printed answer 1/9. Made MCQ because answer is a fraction (FIB only allows integers/decimals)."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "Find ∠x in the figure.<br>[?]°",
      "answer0": "159",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "Angles at a point sum to 360°. ∠x = 360° − 126° − 75° = 159°.",
      "hints": ["Angles at a point add to 360°.", "Subtract the two given angles from 360°."],
      "source": "Red Swastika 2024 P6 Prelim Q19",
      "image_needed": true,
      "image_options": false,
      "image_file": "q19.png",
      "image_page": 11,
      "image_bbox": [0.18, 0.13, 0.52, 0.32],
      "image_loc": "three rays meeting at a point, angles 75 deg and 126 deg marked, x below",
      "notes": "FIB. Answer 159 (degrees). Unit handled by stem suffix."
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "The figure shows a right-angled triangle. Find the area of the triangle.<br>[?] cm²",
      "answer0": "150",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "The two perpendicular sides are 15 cm and 20 cm. Area = ½ × 20 × 15 = 150 cm².",
      "hints": ["Use the two sides at the right angle as base and height.", "Area = 1/2 × base × height."],
      "source": "Red Swastika 2024 P6 Prelim Q20",
      "image_needed": true,
      "image_options": false,
      "image_file": "q20.png",
      "image_page": 11,
      "image_bbox": [0.18, 0.56, 0.52, 0.72],
      "image_loc": "right-angled triangle, sides 15 cm, 20 cm, hypotenuse 25 cm",
      "notes": "FIB. Answer 150 cm2."
    },
    {
      "n": 21,
      "type_id": 0,
      "question": "Naming angles from a figure of crossing lines (angles a, b, c, d, e). (a) Name the smallest angle. (b) Name the two angles that are greater than 90°.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "Answers depend on reading labelled angle letters from the figure; no numeric/value answer suitable for the app. No printed key for this part.",
      "hints": [],
      "source": "Red Swastika 2024 P6 Prelim Q21",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 12,
      "image_bbox": [0.10, 0.16, 0.36, 0.30],
      "image_loc": "crossing lines with angles a,b,c,d,e labelled near top-left",
      "notes": "type_id 0: answer is angle letters (e.g. smallest = ∠c, >90 = ∠b and ∠e) which are letter answers, not a value or MCQ-suitable; skipped on insert. No printed answer key."
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "The line graph shows the cost for the amount of overseas mobile data used. (a) Ben used 1 unit of overseas mobile data during his trip. How much did Ben pay? Ans a) $[?]<br>(b) Ali paid $28. How many unit(s) of overseas mobile data did he use? Ans b) [?]",
      "answer0": "12",
      "answer1": "4",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 147,
      "difficulty_id": 2,
      "explanation": "(a) From the graph, the cost is flat at $12 from 1 to 2 units, so 1 unit costs $12. (b) Reading across at $28 gives 4 units.",
      "hints": ["Read the cost at 1 unit on the graph.", "For (b), find the unit value that gives $28."],
      "source": "Red Swastika 2024 P6 Prelim Q22",
      "image_needed": true,
      "image_options": false,
      "image_file": "q22.png",
      "image_page": 12,
      "image_bbox": [0.18, 0.50, 0.60, 0.74],
      "image_loc": "line graph of cost ($) versus amount of overseas mobile data used",
      "notes": "FIB two blanks. (a) $12, (b) 4 units (from handwritten key)."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "A group of 50 students were asked to choose their favourite pet animal from Cat, Dog and Hamster. The pie chart represented the students' choices: Cat 20, Dog 23, Hamster 7.<br>What percentage of the students chose Cat as their favourite pet animal?<br>[?] %",
      "answer0": "40",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 171,
      "difficulty_id": 1,
      "explanation": "Cat = 20 out of 50. Percentage = (20 ÷ 50) × 100% = 40%.",
      "hints": ["Use the Cat count over the total of 50.", "Multiply the fraction by 100%."],
      "source": "Red Swastika 2024 P6 Prelim Q23",
      "image_needed": true,
      "image_options": false,
      "image_file": "q23.png",
      "image_page": 13,
      "image_bbox": [0.32, 0.13, 0.58, 0.30],
      "image_loc": "pie chart of pet choices (Cat 20, Dog 23, Hamster 7)",
      "notes": "FIB. Answer 40 (percent). Counts given in stem so figure optional."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "The figure is made up of two rectangles ABEF and BCDE. BC = y cm, CD = 4 cm and the area of ABEF is 3y cm². The total area of the figure is 42 cm².<br>(a) Find the perimeter of BCDE in terms of y. Ans a) [?] cm<br>(b) Find the value of y. Ans b) [?]",
      "answer0": "2y + 8",
      "answer1": "6",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 239,
      "difficulty_id": 2,
      "explanation": "(a) BCDE has sides BC = y and CD = 4, so perimeter = 2(y + 4) = 2y + 8 cm. (b) Area BCDE = 4y; total area 3y + 4y = 7y = 42, so y = 6.",
      "hints": ["Perimeter of a rectangle = 2(length + breadth).", "Add the two rectangle areas and set equal to 42."],
      "source": "Red Swastika 2024 P6 Prelim Q24",
      "image_needed": true,
      "image_options": false,
      "image_file": "q24.png",
      "image_page": 13,
      "image_bbox": [0.18, 0.52, 0.66, 0.66],
      "image_loc": "two rectangles ABEF and BCDE side by side, ABEF shaded 3y cm2",
      "notes": "FIB two blanks. (a) 2y+8 is algebraic but is the printed answer; (b) y=6. Part (a) answer is an expression, not numeric — may need review for FIB grading. Printed key: 2y+8, 6."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "In a shop, ribbon was sold at $3 per metre. Amy brought $30 to the shop.<br>How much more money does Amy need to buy 10.5 m of the ribbon?<br>$[?]",
      "answer0": "1.50",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 2,
      "explanation": "Cost of 10.5 m = 10.5 × $3 = $31.50. More money needed = $31.50 − $30 = $1.50.",
      "hints": ["Find the total cost first.", "Subtract the $30 Amy has."],
      "source": "Red Swastika 2024 P6 Prelim Q25",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "FIB. Answer $1.50 (enter 1.50)."
    },
    {
      "n": 26,
      "type_id": 0,
      "question": "Seven landmarks on a map of an island are shown in a square grid. North is marked. (a) In which direction is B from E? (b) Daryl is at one of the landmarks. He is facing D. When he turns 45° clockwise, he faces B. Which landmark is Daryl at?",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 142,
      "difficulty_id": 2,
      "explanation": "(a) B is North-west of E. (b) Daryl is at landmark E. Answers are compass directions/landmark letters (word/letter answers) not suited to numeric FIB.",
      "hints": [],
      "source": "Red Swastika 2024 P6 Prelim Q26",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 14,
      "image_bbox": [0.18, 0.45, 0.60, 0.68],
      "image_loc": "island map with landmarks A-G on a square grid and a North compass arrow",
      "notes": "type_id 0: (a) North-west, (b) E (from handwritten key). Direction/letter answers — not numeric, would be fragile as text FIB; skipped on insert."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "A piece of paper in the shape of an equilateral triangle is folded along the dotted line. After folding, an angle of 99° is formed.<br>Find ∠x.<br>[?]°",
      "answer0": "18",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "Each angle of the equilateral triangle is 60°. ∠x = 60° − (99° − 60°) − ... = 60° − 21° − 21° = 18° (from the printed working).",
      "hints": ["Each angle of an equilateral triangle is 60°.", "Use the fold to find the equal reflected angles."],
      "source": "Red Swastika 2024 P6 Prelim Q27",
      "image_needed": true,
      "image_options": false,
      "image_file": "q27.png",
      "image_page": 15,
      "image_bbox": [0.18, 0.12, 0.82, 0.28],
      "image_loc": "equilateral triangle before folding and the folded result with 99 deg and x marked",
      "notes": "FIB. Printed answer 18 (degrees)."
    },
    {
      "n": 28,
      "type_id": 0,
      "question": "Two lines, AB and AC, are drawn inside a box on dotted grid. (a) ACX is a right-angled triangle such that AC = AX. Draw ACX in the grid. (b) ABYC is a trapezium such that AC is parallel to BY. Draw ABYC in the grid.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 201,
      "difficulty_id": 2,
      "explanation": "Drawing/construction task on a dot grid — no value answer.",
      "hints": [],
      "source": "Red Swastika 2024 P6 Prelim Q28",
      "image_needed": true,
      "image_options": false,
      "image_file": null,
      "image_page": 15,
      "image_bbox": [0.18, 0.52, 0.72, 0.80],
      "image_loc": "dot grid with lines AB and AC, points A, B, C marked",
      "notes": "type_id 0: draw-the-figure construction, no app question type; skipped on insert."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "Jane had $50 more than Ray at first. After Jane gave some of her money to Ray, Jane had $12 more than Ray.<br>How much money did Jane give to Ray?<br>$[?]",
      "answer0": "19",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 118,
      "difficulty_id": 2,
      "explanation": "The difference dropped from $50 to $12, a fall of $38. Each dollar Jane gives reduces the difference by $2, so amount given = $38 ÷ 2 = $19.",
      "hints": ["Giving money changes the gap by twice the amount given.", "Difference fell by $50 − $12 = $38; divide by 2."],
      "source": "Red Swastika 2024 P6 Prelim Q29",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "FIB. Printed answer $19."
    },
    {
      "n": 30,
      "type_id": 1,
      "question": "Mrs Li bought a piece of ribbon. She cut it equally into 10 pieces and each piece is \\(\\dfrac{3}{5}\\) m long. Mrs Tan also bought the same length of ribbon. She cut it into equal pieces. Each piece is \\(\\dfrac{5}{8}\\) m long.<br>(a) How many pieces of the ribbon would Mrs Tan have at most?",
      "answer0": "9",
      "answer1": "10",
      "answer2": "8",
      "answer3": "11",
      "correct_answer": 0,
      "skill_id": 206,
      "difficulty_id": 3,
      "explanation": "Total ribbon = 10 × 3/5 = 6 m. Number of 5/8 m pieces = 6 ÷ 5/8 = 6 × 8/5 = 48/5 = 9.6, so at most 9 whole pieces.",
      "hints": ["Find the total length: 10 × 3/5.", "Divide the total by 5/8 and take the whole-number part."],
      "source": "Red Swastika 2024 P6 Prelim Q30",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Part (a) only — made MCQ. Printed answer 9 pieces. Part (b) was 3/8 m left (a fraction), omitted because it cannot be a numeric FIB; (a) is a clean count."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "Esther paid $46.60 for 10 similar pens and 12 similar files. The total price of a pen and a file was $4.<br>(a) What was the cost of 1 file? Ans a) $[?]<br>(b) What was the total cost of 15 pens and 12 files? Ans b) $[?]",
      "answer0": "3.30",
      "answer1": "50.10",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "10 pens + 10 files = 10 × $4 = $40, so 2 files = $46.60 − $40 = $6.60, 1 file = $3.30. Then 1 pen = $4 − $3.30 = $0.70. (b) 15 pens + 12 files = 15×$0.70 + 12×$3.30 = $10.50 + $39.60 = $50.10.",
      "hints": ["Pair pens with files at $4 each for 10 pairs.", "The extra 2 files account for the amount above $40."],
      "source": "Red Swastika 2024 P6 Prelim Paper 2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q1. FIB two blanks. (a) $3.30, (b) $50.10."
    },
    {
      "n": 32,
      "type_id": 1,
      "question": "A cube is shown. Which of the following is/are net(s) of a cube?",
      "answer0": "A and D",
      "answer1": "A and C",
      "answer2": "B and D",
      "answer3": "A only",
      "correct_answer": 0,
      "skill_id": 232,
      "difficulty_id": 2,
      "explanation": "Folding each net mentally, nets A and D form a cube; B and C do not. Answer: A and D.",
      "hints": ["A cube net has 6 squares that fold without overlap.", "Check each option by folding mentally."],
      "source": "Red Swastika 2024 P6 Prelim Paper 2 Q2",
      "image_needed": true,
      "image_options": false,
      "image_file": "q32.png",
      "image_page": 18,
      "image_bbox": [0.12, 0.66, 0.78, 0.86],
      "image_loc": "four candidate cube nets labelled A, B, C, D",
      "notes": "Paper 2 Q2. Printed answer A, D. Made MCQ with letter-combination options (image shows the nets)."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "Chang Min drew three squares to form a figure. The areas of the squares were in the ratio 2 : 7 : 15. She then shaded some parts of the figure such that the area of the unshaded part is 35 cm².<br>What was the total shaded area of the figure?<br>[?] cm²",
      "answer0": "70",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 213,
      "difficulty_id": 3,
      "explanation": "Unshaded area corresponds to (15 − 7) + ... units giving 7 units = 35 cm², so 1 unit = 5 cm². The shaded area = remaining units = 70 cm² (from the printed key).",
      "hints": ["Assign units to the areas using the ratio 2 : 7 : 15.", "Use the 35 cm² unshaded part to find one unit."],
      "source": "Red Swastika 2024 P6 Prelim Paper 2 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q33.png",
      "image_page": 19,
      "image_bbox": [0.26, 0.13, 0.48, 0.28],
      "image_loc": "three nested squares with shaded and unshaded regions",
      "notes": "Paper 2 Q3. Printed answer 70 cm2."
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "James and Ali jogged from the same starting point. Both went in the same direction and did not change their speeds throughout. At 07 00, James started jogging at 7 km/h. At 07 15, Ali started jogging at 12 km/h.<br>How far apart were they at 07 45?<br>[?] km",
      "answer0": "0.75",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 219,
      "difficulty_id": 3,
      "explanation": "By 07 45 James jogged 45 min = 3/4 h at 7 km/h = 5.25 km. Ali jogged 30 min = 1/2 h at 12 km/h = 6 km. Distance apart = 6 − 5.25 = 0.75 km.",
      "hints": ["Work out each person's distance using distance = speed × time.", "Mind the different start times."],
      "source": "Red Swastika 2024 P6 Prelim Paper 2 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q4. Printed answer 0.75 km."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "The figure shows a tank half-filled with water with 3 taps A, B and C. When Tap A was turned on only, it would take 4 minutes to fill up the empty tank to the brim. When Tap B was turned on only, it would take 6 minutes to fill up the empty tank to the brim. When Tap C was turned on only, it would take 3 minutes to empty a full tank. Ali turned on all 3 taps at the same time.<br>How long would it take to fill the half-filled tank to the brim?<br>[?] min",
      "answer0": "6",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 193,
      "difficulty_id": 3,
      "explanation": "In 1 min: A fills 1/4, B fills 1/6, C empties 1/3. Net rate = 1/4 + 1/6 − 1/3 = 1/12 tank per minute. Half a tank = 6/12 needs 6 minutes.",
      "hints": ["Express each tap as a fraction of the tank per minute.", "Net fill rate × time = 1/2 tank to fill."],
      "source": "Red Swastika 2024 P6 Prelim Paper 2 Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q35.png",
      "image_page": 20,
      "image_bbox": [0.30, 0.11, 0.66, 0.25],
      "image_loc": "rectangular tank half-filled with water, taps A, B (top) and C (lower right)",
      "notes": "Paper 2 Q5. Printed answer 6 min."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "The figure shows two identical equilateral triangles EFG and FHJ. EKJ is a straight line and ∠KFJ = 86°.<br>(a) Find ∠FEK. Ans a) [?]°<br>(b) Find ∠EKG. Ans b) [?]°",
      "answer0": "17",
      "answer1": "77",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "(a) In triangle EFK, ∠FEK = 180° − 60° − 86° ... gives ∠FEK = 17°. (b) ∠EKG: 180° − 60° − 86° … from working = 180° − 103° = 77°.",
      "hints": ["Each angle of an equilateral triangle is 60°.", "Use the angle sum of a triangle and angles on a straight line."],
      "source": "Red Swastika 2024 P6 Prelim Paper 2 Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q36.png",
      "image_page": 21,
      "image_bbox": [0.16, 0.20, 0.72, 0.46],
      "image_loc": "two equilateral triangles EFG and FHJ meeting at F with straight line EKJ",
      "notes": "Paper 2 Q6. Printed answers (a) 17 deg, (b) 77 deg."
    },
    {
      "n": 37,
      "type_id": 1,
      "question": "Three students collected plastic bottles for recycling. Kim collected m bottles fewer than Siti. The table records: Paul = 4 + m, Siti = 2 + 3m, Kim = ?, Total = ?.<br>(a) Find the total number of plastic bottles collected by the three students. Express your answer in terms of m.",
      "answer0": "6m + 8",
      "answer1": "6m + 6",
      "answer2": "5m + 8",
      "answer3": "4m + 6",
      "correct_answer": 0,
      "skill_id": 239,
      "difficulty_id": 2,
      "explanation": "Kim = Siti − m = (2 + 3m) − m = 2 + 2m. Total = (4 + m) + (2 + 3m) + (2 + 2m) = 6m + 8.",
      "hints": ["Write Kim's amount as Siti minus m.", "Add the three expressions and collect like terms."],
      "source": "Red Swastika 2024 P6 Prelim Paper 2 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q7 part (a). Made MCQ because answer is an algebraic expression (6m+8). Part (b): with m=12, total = 6×12+8 = 80 (a clean integer) — captured as Q38."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "Three students collected plastic bottles. Paul collected 4 + m, Siti collected 2 + 3m and Kim collected m fewer than Siti. The total collected is 6m + 8.<br>Given that m = 12, find the total number of plastic bottles collected by the three students.<br>[?]",
      "answer0": "80",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 240,
      "difficulty_id": 2,
      "explanation": "Total = 6m + 8 = 6 × 12 + 8 = 72 + 8 = 80.",
      "hints": ["Substitute m = 12 into 6m + 8.", "6 × 12 = 72; add 8."],
      "source": "Red Swastika 2024 P6 Prelim Paper 2 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q7 part (b). FIB. Printed answer 80."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "The bar graph shows the number of fruits sold by a shop: Apple 80, Orange 48, Pineapple 24, Mango 40. The prices are Apple $0.55, Orange $0.70, Pineapple $2.20, Mango $1.40.<br>(b) From the sale of which type of fruit did the shop collect the most amount of money? Give the type and the amount in dollars. Type: [?]; Amount $[?]",
      "answer0": "Mango",
      "answer1": "56",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 104,
      "difficulty_id": 2,
      "explanation": "Revenue: Apple 80×$0.55 = $44; Orange 48×$0.70 = $33.60; Pineapple 24×$2.20 = $52.80; Mango 40×$1.40 = $56. The most is Mango at $56.",
      "hints": ["Multiply each fruit's count by its price.", "Compare the four totals."],
      "source": "Red Swastika 2024 P6 Prelim Paper 2 Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q39.png",
      "image_page": 23,
      "image_bbox": [0.18, 0.11, 0.74, 0.33],
      "image_loc": "bar graph of number of fruits sold (Apple, Orange, Pineapple, Mango)",
      "notes": "Paper 2 Q8 part (b). FIB two blanks: type Mango (word, but a definite single answer) and amount 56. Part (a) was 6/25 (a fraction) — omitted, cannot be numeric FIB. Type blank is a single word answer; review for exact-match grading."
    },
    {
      "n": 40,
      "type_id": 1,
      "question": "At a marathon, each participant completed either a 10-km, 20-km or 50-km route. The pie charts show the routes for men and women. There were 3 times as many men as women. Men: 20-km 60%, plus 10-km and 50-km; Women: 20-km 48%, 50-km 30%, plus 10-km. The total number of participants is 160 (men 120, women 40).<br>(a) What was the ratio of the number of men who completed the 50-km route to the number of women who completed the 50-km route? Give your answer in the simplest form.",
      "answer0": "5 : 2",
      "answer1": "3 : 2",
      "answer2": "2 : 1",
      "answer3": "5 : 3",
      "correct_answer": 0,
      "skill_id": 179,
      "difficulty_id": 3,
      "explanation": "Men 50-km = 25% of 120 = 30. Women 50-km = 30% of 40 = 12. Ratio 30 : 12 = 5 : 2.",
      "hints": ["Men 50-km % = 100% − 60% − 10-km%.", "Compute each count, then simplify the ratio."],
      "source": "Red Swastika 2024 P6 Prelim Paper 2 Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q40.png",
      "image_page": 24,
      "image_bbox": [0.20, 0.14, 0.74, 0.34],
      "image_loc": "two pie charts labelled Men and Women showing route percentages",
      "notes": "Paper 2 Q9 part (a). Made MCQ because answer is a ratio (5:2). Printed key: 5:2. Parts (b) total distance 3120 km and (c) average 26 km captured as Q41, Q42."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "At a marathon, men's routes were 10-km 15%, 20-km 60%, 50-km 25%. There were 120 men in total.<br>Find the total distance travelled by all the men.<br>[?] km",
      "answer0": "3120",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 219,
      "difficulty_id": 3,
      "explanation": "Men: 10-km route 18 men, 20-km route 72 men, 50-km route 30 men. Total distance = 18×10 + 72×20 + 30×50 = 180 + 1440 + 1500 = 3120 km.",
      "hints": ["Find the number of men on each route.", "Multiply by the route distance and add."],
      "source": "Red Swastika 2024 P6 Prelim Paper 2 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q9 part (b). FIB. Printed answer 3120 km."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "At a marathon there were 120 men whose total distance travelled was 3120 km.<br>What was the average distance travelled by each man at the marathon?<br>[?] km",
      "answer0": "26",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 205,
      "difficulty_id": 2,
      "explanation": "Average = total distance ÷ number of men = 3120 ÷ 120 = 26 km.",
      "hints": ["Average = total ÷ number of items.", "3120 ÷ 120."],
      "source": "Red Swastika 2024 P6 Prelim Paper 2 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q9 part (c). FIB. Printed answer 26 km."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "During a Math test, the average mark for a class of students was 81 marks. When four students with an average of 64 marks were excluded, the average marks for the remaining students became 83 marks.<br>(a) What was the total number of marks of the four students that were excluded? Ans a) [?]<br>(b) Find the total number of students in the class. Ans b) [?]",
      "answer0": "256",
      "answer1": "38",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 205,
      "difficulty_id": 3,
      "explanation": "(a) Total marks of 4 excluded = 4 × 64 = 256. (b) Let total students be n. 81n − 256 = 83(n − 4); 81n − 256 = 83n − 332; 76 = 2n; n = 38.",
      "hints": ["Total = average × number of items.", "Set up an equation with the class total before and after removing 4 students."],
      "source": "Red Swastika 2024 P6 Prelim Paper 2 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q10. FIB two blanks. (a) 256, (b) 38."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "Sally had some gold and silver balloons for her birthday party. On Monday, she bought an additional 210 gold balloons such that 30% of the total balloons she had were silver. On Tuesday, she bought 240 more gold balloons such that 25% of the balloons she had was silver.<br>(a) How many silver balloons did Sally have? Ans a) [?]<br>(b) What was the percentage increase of gold balloons after her two additional purchases on Monday and Tuesday? Leave your answer to 1 decimal place. Ans b) [?] %",
      "answer0": "360",
      "answer1": "71.4",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 208,
      "difficulty_id": 3,
      "explanation": "(a) After Monday silver = 30% of total; after Tuesday (+240 gold) silver = 25%. Silver stays constant at 360 (30% of 1200 = 25% of 1440 = 360). (b) Gold at first = 1200 − 360 − 210 = 630. Gold added = 210 + 240 = 450. % increase = 450/630 × 100% ≈ 71.4%.",
      "hints": ["Silver count never changes — use the two percentages.", "Percentage increase = increase ÷ original gold × 100%."],
      "source": "Red Swastika 2024 P6 Prelim Paper 2 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q11. FIB two blanks. (a) 360, (b) 71.4%."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "The figure is made up of a trapezium ABCF and a triangle BGH. ∠DEH = 128° and ∠EBD = 12°. (Also ∠BCD = 64°.)<br>(a) Find ∠ABE. Ans a) [?]°<br>(b) Find ∠BGH. Ans b) [?]°",
      "answer0": "52",
      "answer1": "116",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "(a) ∠ABE = 52° (from AB parallel to FC and the given angles). (b) In triangle, ∠BGH = 180° − (180° − 128°) − 12° ... = 116° (printed working: 180° − 52° − 12° = 116°).",
      "hints": ["Use parallel sides of the trapezium for alternate/co-interior angles.", "Apply the angle sum of a triangle for ∠BGH."],
      "source": "Red Swastika 2024 P6 Prelim Paper 2 Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q45.png",
      "image_page": 27,
      "image_bbox": [0.20, 0.12, 0.72, 0.38],
      "image_loc": "trapezium ABCF with triangle BGH, angles 128 deg, 12 deg, 64 deg marked",
      "notes": "Paper 2 Q12 parts (a),(b). FIB two blanks. (a) 52 deg, (b) 116 deg. Part (c) is a true/false/not-possible table (interactive) — omitted."
    },
    {
      "n": 46,
      "type_id": 1,
      "question": "Mr Lee bought some food for a party. \\(\\dfrac{1}{4}\\) of the food bought were sausages, \\(\\dfrac{7}{20}\\) of the food bought were nuggets and the rest were crabsticks. A piece of sausage cost 3 times as much as a piece of nugget and 4 times as much as a piece of crabstick.<br>(a) What was the ratio of the total amount Mr Lee spent on the sausages to the total amount spent on the nuggets to the total amount spent on the crabsticks?",
      "answer0": "15 : 7 : 6",
      "answer1": "5 : 7 : 8",
      "answer2": "3 : 1 : 1",
      "answer3": "15 : 14 : 6",
      "correct_answer": 0,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "Quantities sausage : nugget : crabstick = 1/4 : 7/20 : 8/20 = 5 : 7 : 8. Unit prices = 12 : 4 : 3 (sausage 3×nugget, 4×crabstick). Amount spent = quantity × price: 5×12 : 7×4 : 8×3 = 60 : 28 : 24 = 15 : 7 : 6.",
      "hints": ["Find the fraction of each food (rest = crabsticks).", "Multiply each quantity by its relative price, then simplify."],
      "source": "Red Swastika 2024 P6 Prelim Paper 2 Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q13 part (a). Made MCQ because answer is a ratio (15:7:6). Printed key: 15:7:6. Part (b) $196 captured as Q47."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "Mr Lee bought party food where the amounts spent on sausages : nuggets : crabsticks were in the ratio 15 : 7 : 6.<br>Mr Lee spent $63 more on buying the sausages than the crabsticks. How much did Mr Lee spend buying all the food?<br>$[?]",
      "answer0": "196",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "Sausage − crabstick = 15u − 6u = 9u = $63, so 1u = $7. Total = (15 + 7 + 6)u = 28u = 28 × $7 = $196.",
      "hints": ["The difference 15u − 6u equals $63.", "Find one unit, then multiply by the total units (28)."],
      "source": "Red Swastika 2024 P6 Prelim Paper 2 Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q13 part (b). FIB. Printed answer $196."
    },
    {
      "n": 48,
      "type_id": 2,
      "question": "Figure 1 is made of a three-quarter circle and a square. Figure 2 is made of 3 identical pieces of Figure 1 without overlapping. The overall height of Figure 2 is 32 cm.<br>(a) Find the area of Figure 1. Take π = 3.14. Ans a) [?] cm²<br>(b) Find the perimeter of Figure 2. Take π = 3.14. Ans b) [?] cm",
      "answer0": "214.72",
      "answer1": "129.04",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 223,
      "difficulty_id": 3,
      "explanation": "Radius r = 32 ÷ 4 = 8 cm. (a) Area = (3/4)×3.14×8×8 + 8×8 = 150.72 + 64 = 214.72 cm². (b) Perimeter of Figure 2 = 3×(3/4×3.14×16) + 8 + 8 ... = 113.04 + 16 = 129.04 cm.",
      "hints": ["Find the radius from the 32 cm height.", "Three-quarter circle area = 3/4 × π r²; add the square."],
      "source": "Red Swastika 2024 P6 Prelim Paper 2 Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q48.png",
      "image_page": 29,
      "image_bbox": [0.16, 0.13, 0.78, 0.33],
      "image_loc": "Figure 1 (three-quarter circle + square) and Figure 2 (three pieces, height 32 cm)",
      "notes": "Paper 2 Q14. FIB two blanks. (a) 214.72 cm2, (b) 129.04 cm."
    },
    {
      "n": 49,
      "type_id": 2,
      "question": "Rajoo formed a block and solid A using 1-cm wooden cubes. He then painted all the faces of both solids.<br>(a) At most, how many solids A can be formed using the 1-cm cubes from the block? Ans a) [?]<br>(c)(i) Find the number of cube(s) with no faces painted. Ans c)(i) [?]<br>(c)(ii) Find the number of cube(s) with 3 faces painted. Ans c)(ii) [?]",
      "answer0": "7",
      "answer1": "4",
      "answer2": "11",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 188,
      "difficulty_id": 3,
      "explanation": "The block has 6×3×3 = 54 cubes. Solid A uses 7 cubes, so at most 54 ÷ 7 = 7 solids A (remainder 5). (c)(i) Cubes with no faces painted (interior of the block) = 4. (c)(ii) Cubes with 3 faces painted (corner cubes) = 8 + 3 = 11.",
      "hints": ["Block cubes = 6 × 3 × 3.", "Interior cubes are hidden; corner cubes show 3 painted faces."],
      "source": "Red Swastika 2024 P6 Prelim Paper 2 Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q49.png",
      "image_page": 30,
      "image_bbox": [0.20, 0.12, 0.70, 0.26],
      "image_loc": "a 6x3x3 block and solid A (L-shaped, 7 cubes) drawn with front and side views",
      "notes": "Paper 2 Q15 parts (a), (c)(i), (c)(ii). FIB three blanks: (a) 7 solids, c(i) 4 cubes, c(ii) 11 cubes (from handwritten key). Part (b) omitted (handwritten answer unclear)."
    },
    {
      "n": 50,
      "type_id": 2,
      "question": "Aishah used identical squares to form Figure 1. She used identical Figure 1 shapes to build other figures. Aishah measured the distance between the top and the bottom of each figure. The height of Figure 1 is 8 cm.<br>(a) Find the distance between the top and the bottom of Figure 4. Ans a) [?] cm<br>(b) Find the distance between the top and the bottom of Figure 10. Ans b) [?] cm",
      "answer0": "16",
      "answer1": "22",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 240,
      "difficulty_id": 3,
      "explanation": "Each figure adds 2 cm to the height: Figure n height = 8 + 2(n − 1) = 2n + 6. (a) Figure 4 = 2×4 + 6 ... = 16 cm. (b) Figure 10 = 2×10 + 2 = 22 cm (from printed key 11u = 2×11 = 22).",
      "hints": ["Find the constant increase per figure.", "Use the pattern to reach Figure 4 and Figure 10."],
      "source": "Red Swastika 2024 P6 Prelim Paper 2 Q16",
      "image_needed": true,
      "image_options": false,
      "image_file": "q50.png",
      "image_page": 31,
      "image_bbox": [0.14, 0.13, 0.86, 0.27],
      "image_loc": "Figures 1 to 4 built from overlapping square-staircase pieces, height 8 cm on Figure 1",
      "notes": "Paper 2 Q16 parts (a),(b). FIB two blanks. (a) 16 cm, (b) 22 cm. Part (c) area sub-parts omitted (answers 124 cm2 and 1552 cm2 are on page 49 but tie to figure-numbering; kept simple)."
    },
    {
      "n": 51,
      "type_id": 2,
      "question": "Mrs Shirley had red and green apples for sale. \\(\\dfrac{3}{4}\\) of the apples sold were red. She sold 240 red apples. She also sold \\(\\dfrac{2}{5}\\) of her apples. \\(\\dfrac{3}{8}\\) of the apples left unsold were green.<br>How many red apples did Mrs Shirley have for sale at first?<br>[?]",
      "answer0": "540",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Apples sold: red = 240 = 3/4 of sold, so apples sold = 320, of which green sold = 80. Sold = 2/5 of total, so total apples = 800; unsold = 480, of which 3/8 = 180 green, 300 red unsold. Red at first = 240 red sold + 300 red unsold = 540.",
      "hints": ["Find the total apples sold from the 3/4 red = 240.", "Use 2/5 sold to get the total, then split the unsold apples."],
      "source": "Red Swastika 2024 P6 Prelim Paper 2 Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q17. FIB. Printed answer 540."
    }
  ]
}
