{
  "paper": {
    "school": "Raffles Girls' Primary School",
    "year": 2024,
    "level": "P6",
    "label": "Prelim",
    "source_prefix": "Raffles 2024 P6 Prelim",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "60 000 + 5000 + 400 + 3 =",
      "answer0": "65 430",
      "answer1": "65 403",
      "answer2": "65 043",
      "answer3": "60 543",
      "correct_answer": 1,
      "skill_id": 105,
      "difficulty_id": 1,
      "explanation": "Expanded form: 60 000 + 5000 + 400 + 3 = 65 403.",
      "hints": ["Add each place value separately.", "Ten thousands 6, thousands 5, hundreds 4, tens 0, ones 3."],
      "source": "Raffles 2024 P6 Prelim Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 2 (65 403)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "What is the missing number in the box?<br>\\(2\\dfrac{5}{6}=\\dfrac{[\\,]}{6}\\)",
      "answer0": "10",
      "answer1": "12",
      "answer2": "17",
      "answer3": "25",
      "correct_answer": 2,
      "skill_id": 119,
      "difficulty_id": 1,
      "explanation": "\\(2\\dfrac{5}{6}=\\dfrac{2\\times6+5}{6}=\\dfrac{17}{6}\\). Missing numerator = 17.",
      "hints": ["Convert the mixed number to an improper fraction.", "Numerator = whole number x denominator + numerator."],
      "source": "Raffles 2024 P6 Prelim Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 3 (17)."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Which number is the largest?",
      "answer0": "1.440",
      "answer1": "1.450",
      "answer2": "1.054",
      "answer3": "1.405",
      "correct_answer": 1,
      "skill_id": 124,
      "difficulty_id": 1,
      "explanation": "Compare decimals: 1.450 > 1.440 > 1.405 > 1.054. Largest is 1.450.",
      "hints": ["Line up the decimal points and compare digit by digit.", "Compare the tenths first."],
      "source": "Raffles 2024 P6 Prelim Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 2 (1.450). OCR showed superscripts on options 1 and 2; correct values are 1.440 and 1.450."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "What is the length of the bolt shown?",
      "answer0": "5.6 cm",
      "answer1": "5.8 cm",
      "answer2": "7.1 cm",
      "answer3": "7.2 cm",
      "correct_answer": 0,
      "skill_id": 85,
      "difficulty_id": 2,
      "explanation": "Bolt spans from the 1.5 cm mark to the 7.1 cm mark on the ruler: 7.1 - 1.5 = 5.6 cm.",
      "hints": ["Read the start and end positions of the bolt on the ruler.", "Length = end reading - start reading."],
      "source": "Raffles 2024 P6 Prelim Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q4.png",
      "image_page": 3,
      "image_bbox": [0.27, 0.13, 0.74, 0.27],
      "image_loc": "bolt on a cm ruler, upper-middle of page",
      "notes": "Key: option 1 (5.6 cm)."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "What is 5% of 2000?",
      "answer0": "10",
      "answer1": "100",
      "answer2": "1000",
      "answer3": "10 000",
      "correct_answer": 1,
      "skill_id": 174,
      "difficulty_id": 1,
      "explanation": "5% of 2000 = \\(\\dfrac{5}{100}\\times2000=100\\).",
      "hints": ["1% of 2000 = 20.", "Multiply by 5."],
      "source": "Raffles 2024 P6 Prelim Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 2 (100)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "Which of the following shows \\(\\dfrac{1}{5}\\) of the figure shaded?",
      "answer0": "Figure 1",
      "answer1": "Figure 2",
      "answer2": "Figure 3",
      "answer3": "Figure 4",
      "correct_answer": 3,
      "skill_id": 120,
      "difficulty_id": 2,
      "explanation": "Figure 4 (trapezium divided into 5 equal triangles with 1 shaded) shows exactly \\(\\dfrac{1}{5}\\) shaded.",
      "hints": ["Count the equal parts and how many are shaded.", "Look for 1 shaded part out of 5 equal parts."],
      "source": "Raffles 2024 P6 Prelim Q6",
      "image_needed": true,
      "image_options": true,
      "image_file": null,
      "image_page": 3,
      "image_bbox": [0.2, 0.7, 0.85, 0.85],
      "image_loc": "four shaded shape options across the lower third of the page",
      "notes": "Key: option 4. Image-option MCQ; crop each option to q6_opt0..q6_opt3."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "Which of the following is not a net of a cube?",
      "answer0": "Net 1",
      "answer1": "Net 2",
      "answer2": "Net 3",
      "answer3": "Net 4",
      "correct_answer": 0,
      "skill_id": 232,
      "difficulty_id": 2,
      "explanation": "Net 1 cannot fold into a cube (overlapping faces); the other three are valid cube nets.",
      "hints": ["Mentally fold each arrangement of 6 squares.", "A valid net has no overlapping faces."],
      "source": "Raffles 2024 P6 Prelim Q7",
      "image_needed": true,
      "image_options": true,
      "image_file": null,
      "image_page": 4,
      "image_bbox": [0.2, 0.12, 0.85, 0.24],
      "image_loc": "four cube-net options across the top of the page",
      "notes": "Key: option 1. Image-option MCQ; crop each option to q7_opt0..q7_opt3."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "Arrange these distances from the longest to the shortest.<br>2.25 km, 2 km 55 m, \\(2\\dfrac{1}{5}\\) km",
      "answer0": "2 km 55 m, \\(2\\dfrac{1}{5}\\) km, 2.25 km",
      "answer1": "2 km 55 m, 2.25 km, \\(2\\dfrac{1}{5}\\) km",
      "answer2": "\\(2\\dfrac{1}{5}\\) km, 2.25 km, 2 km 55 m",
      "answer3": "2.25 km, \\(2\\dfrac{1}{5}\\) km, 2 km 55 m",
      "correct_answer": 3,
      "skill_id": 184,
      "difficulty_id": 2,
      "explanation": "Convert all to km: 2.25 km, 2 km 55 m = 2.055 km, \\(2\\dfrac{1}{5}\\) km = 2.2 km. Longest to shortest: 2.25, 2.2, 2.055 = 2.25 km, \\(2\\dfrac{1}{5}\\) km, 2 km 55 m.",
      "hints": ["Convert every distance to kilometres in decimal form.", "55 m = 0.055 km; \\(\\dfrac{1}{5}\\) km = 0.2 km."],
      "source": "Raffles 2024 P6 Prelim Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 4. Options contain fractions so kept as MCQ."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "ACDF is a parallelogram and BED is an equilateral triangle. \\(\\angle AFE = 68^\\circ\\). Find \\(\\angle BDC\\).",
      "answer0": "44°",
      "answer1": "52°",
      "answer2": "56°",
      "answer3": "60°",
      "correct_answer": 1,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "In parallelogram ACDF, \\(\\angle FDC = \\angle AFE = 68^\\circ\\) (co-interior gives \\(\\angle ACD\\) etc.; \\(\\angle FDC=68^\\circ\\)). BED equilateral so \\(\\angle BDE = 60^\\circ\\). \\(\\angle BDC = 180^\\circ - 68^\\circ - 60^\\circ = 52^\\circ\\).",
      "hints": ["Equilateral triangle angles are all 60°.", "Use the parallelogram angle properties along line FED."],
      "source": "Raffles 2024 P6 Prelim Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q9.png",
      "image_page": 4,
      "image_bbox": [0.35, 0.66, 0.72, 0.82],
      "image_loc": "parallelogram ACDF with triangle BED, middle of page",
      "notes": "Key: option 2 (52°)."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "A group of senior citizens was asked in a survey to choose one game they enjoy from Uno, Chess, Toss-a-ring and Bingo. The table represents their choices.<br>Uno 5%, Chess 15%, Toss-a-ring 25%, Bingo ?<br>What percentage of the senior citizens chose Chess and Bingo?",
      "answer0": "15%",
      "answer1": "55%",
      "answer2": "70%",
      "answer3": "80%",
      "correct_answer": 2,
      "skill_id": 175,
      "difficulty_id": 2,
      "explanation": "Bingo = 100% - (5% + 15% + 25%) = 55%. Chess + Bingo = 15% + 55% = 70%.",
      "hints": ["All percentages add up to 100%.", "Find Bingo first, then add Chess."],
      "source": "Raffles 2024 P6 Prelim Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 3 (70%). Table data folded into stem; table image not needed."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "The choices enjoyed by the senior citizens were also represented by a pie chart but the names of the games were not shown. The number of senior citizens choosing one of the games was 30. How many senior citizens took part in the survey?",
      "answer0": "100",
      "answer1": "120",
      "answer2": "200",
      "answer3": "600",
      "correct_answer": 2,
      "skill_id": 236,
      "difficulty_id": 3,
      "explanation": "The 30 corresponds to the 15% sector (Chess). 15% -> 30, so 1% -> 2, 100% -> 200 senior citizens.",
      "hints": ["Match the 30 to its percentage sector in the pie chart.", "If 15% = 30, then 100% = 30 / 15 x 100."],
      "source": "Raffles 2024 P6 Prelim Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q11.png",
      "image_page": 5,
      "image_bbox": [0.38, 0.6, 0.65, 0.82],
      "image_loc": "pie chart with a 30 sector, lower half of page",
      "notes": "Key: option 3 (200)."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "Box A: 100 markers, 6% red. Box B: 200 markers, 9% red.<br>What is the ratio of the total number of red markers in Box A and B to the total number of markers in Box A and B?",
      "answer0": "1 : 3",
      "answer1": "1 : 20",
      "answer2": "2 : 3",
      "answer3": "2 : 25",
      "correct_answer": 3,
      "skill_id": 179,
      "difficulty_id": 2,
      "explanation": "Red = 6% of 100 + 9% of 200 = 6 + 18 = 24. Total markers = 300. Ratio 24 : 300 = 2 : 25.",
      "hints": ["Find the number of red markers in each box.", "Simplify the ratio red : total."],
      "source": "Raffles 2024 P6 Prelim Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 4 (2 : 25). Table data folded into stem."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "The figure is made up of 6 identical rectangles. Find the area of the shaded triangle.",
      "answer0": "72 cm²",
      "answer1": "96 cm²",
      "answer2": "144 cm²",
      "answer3": "192 cm²",
      "correct_answer": 1,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Base of triangle = 24 cm. Height = 2 rectangle-heights. 6 identical rectangles arranged 3 by 2 over a 24 cm width: each rectangle 8 cm by 4 cm, so height = 8 cm. Area = \\(\\dfrac{1}{2}\\times24\\times8 = 96\\) cm².",
      "hints": ["The base of the triangle is 24 cm.", "Work out the height from the rectangle arrangement, then use \\(\\dfrac{1}{2}\\times b\\times h\\)."],
      "source": "Raffles 2024 P6 Prelim Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q13.png",
      "image_page": 6,
      "image_bbox": [0.27, 0.5, 0.85, 0.68],
      "image_loc": "shaded triangle over a 24 cm-wide block of 6 rectangles, middle of page",
      "notes": "Key: option 2 (96 cm²)."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "ABCD is a rhombus and AEC is a straight line. Find \\(\\angle DEC\\).",
      "answer0": "130°",
      "answer1": "113°",
      "answer2": "102°",
      "answer3": "101°",
      "correct_answer": 3,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "Diagonal AC bisects the angles. \\(\\angle ADC = 50^\\circ\\times2 = ... \\) using triangle DEC: \\(\\angle EDC = 50^\\circ\\) (half of \\(\\angle ADC\\)) and \\(\\angle DCE = 29^\\circ\\) (half of \\(\\angle DCB = 180^\\circ-78^\\circ\\times... \\)). \\(\\angle DEC = 180^\\circ - 50^\\circ - 29^\\circ = 101^\\circ\\).",
      "hints": ["In a rhombus the diagonals bisect the corner angles.", "Use the angle sum of triangle DEC."],
      "source": "Raffles 2024 P6 Prelim Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q14.png",
      "image_page": 7,
      "image_bbox": [0.32, 0.11, 0.66, 0.28],
      "image_loc": "rhombus ABCD with diagonal AEC, top of page",
      "notes": "Key: option 4 (101°)."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "Figure 1 shows a parallelogram with a perimeter of 50 cm. Figure 2 is formed using 3 such parallelograms and it has a perimeter of 108 cm. Find the length of AB.",
      "answer0": "7 cm",
      "answer1": "9 cm",
      "answer2": "14 cm",
      "answer3": "42 cm",
      "correct_answer": 0,
      "skill_id": 199,
      "difficulty_id": 3,
      "explanation": "Let the parallelogram have sides AB and the longer side L, so 2(AB + L) = 50 -> AB + L = 25. Figure 2 perimeter = 6 long sides + 6 short sides - overlaps; solving with the 108 cm condition gives AB = 7 cm.",
      "hints": ["Use the single-parallelogram perimeter to relate the two side lengths.", "Set up the Figure 2 perimeter in terms of AB."],
      "source": "Raffles 2024 P6 Prelim Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q15.png",
      "image_page": 7,
      "image_bbox": [0.2, 0.5, 0.78, 0.75],
      "image_loc": "Figure 1 single parallelogram (AB marked) and Figure 2 pinwheel of 3 parallelograms, lower half of page",
      "notes": "Key: option 1 (7 cm)."
    },
    {
      "n": 16,
      "type_id": 1,
      "question": "Find the value of \\(\\dfrac{11}{12}\\div3\\).",
      "answer0": "\\(\\dfrac{11}{36}\\)",
      "answer1": "\\(\\dfrac{11}{4}\\)",
      "answer2": "\\(\\dfrac{33}{12}\\)",
      "answer3": "\\(\\dfrac{3}{11}\\)",
      "correct_answer": 0,
      "skill_id": 164,
      "difficulty_id": 1,
      "explanation": "\\(\\dfrac{11}{12}\\div3=\\dfrac{11}{12}\\times\\dfrac{1}{3}=\\dfrac{11}{36}\\).",
      "hints": ["Dividing by 3 is multiplying by \\(\\dfrac{1}{3}\\).", "Multiply the denominators."],
      "source": "Raffles 2024 P6 Prelim Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: \\(\\dfrac{11}{36}\\). Originally free-response; answer is a fraction so made MCQ per FIB rule."
    },
    {
      "n": 17,
      "type_id": 1,
      "question": "7 lines are drawn in the square grid. Name two lines that are parallel to each other.",
      "answer0": "CD and FE",
      "answer1": "AB and CD",
      "answer2": "AG and EF",
      "answer3": "BC and DE",
      "correct_answer": 0,
      "skill_id": 100,
      "difficulty_id": 2,
      "explanation": "On the square grid, lines CD and FE have the same slope (run and rise), so CD is parallel to FE.",
      "hints": ["Parallel lines have the same gradient on the grid.", "Compare how many squares across and up each line goes."],
      "source": "Raffles 2024 P6 Prelim Q17",
      "image_needed": true,
      "image_options": false,
      "image_file": "q17.png",
      "image_page": 9,
      "image_bbox": [0.18, 0.4, 0.82, 0.68],
      "image_loc": "square grid with 7 labelled line segments A-G, middle of page",
      "notes": "Key: CD and FE. Letter/line answer so made MCQ (not FIB)."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "In the programme guide shown, one movie leads to another without any break in between.<br>Start time 5.45 pm A Little Princess; 7.20 pm Wonder; 9.15 pm The Secret Garden.<br>What is the duration of the movie \"Wonder\"?<br>[?] h [?] min",
      "answer0": "1",
      "answer1": "55",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 93,
      "difficulty_id": 2,
      "explanation": "Wonder runs from 7.20 pm to 9.15 pm. 7.20 to 8.15 = 55 min; 8.15 to 9.15 = 1 h. Total = 1 h 55 min.",
      "hints": ["Wonder starts at 7.20 pm and the next movie starts at 9.15 pm.", "Find the time from 7.20 pm to 9.15 pm."],
      "source": "Raffles 2024 P6 Prelim Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 1 h 55 min. Two FIB blanks (hours, minutes). Table data folded into stem."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "Usual price of a toaster is $80 and the sale price is $56. What is the percentage discount for the toaster? [?]%",
      "answer0": "30",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 208,
      "difficulty_id": 2,
      "explanation": "Discount = $80 - $56 = $24. Percentage discount = \\(\\dfrac{24}{80}\\times100\\% = 30\\%\\).",
      "hints": ["Find the discount in dollars first.", "Discount % = discount / usual price x 100%."],
      "source": "Raffles 2024 P6 Prelim Q19",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 30%. Prices folded into stem; toaster picture decorative, not needed. Answer is whole number so FIB."
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "The bar graph shows the number of items sold in an electrical store in a month. How many more fans than washing machines were sold? [?]",
      "answer0": "55",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 104,
      "difficulty_id": 1,
      "explanation": "Fans = 95, Washing machines = 40. 95 - 40 = 55.",
      "hints": ["Read the bar heights for Fans and Washing machines.", "Subtract the smaller from the larger."],
      "source": "Raffles 2024 P6 Prelim Q20",
      "image_needed": true,
      "image_options": false,
      "image_file": "q20.png",
      "image_page": 11,
      "image_bbox": [0.2, 0.15, 0.85, 0.42],
      "image_loc": "bar graph of items sold (Fans, Ovens, Washing machines, Refrigerators), upper half of page",
      "notes": "Key: 55. Need bar graph to read values."
    },
    {
      "n": 21,
      "type_id": 1,
      "question": "Find the value of the following when \\(r=4\\): (a) \\(9r-2\\)  (b) \\(3r-\\dfrac{r}{9}\\)",
      "answer0": "(a) 34  (b) \\(11\\dfrac{5}{9}\\)",
      "answer1": "(a) 36  (b) \\(12\\dfrac{4}{9}\\)",
      "answer2": "(a) 34  (b) \\(12\\dfrac{4}{9}\\)",
      "answer3": "(a) 32  (b) \\(11\\dfrac{5}{9}\\)",
      "correct_answer": 0,
      "skill_id": 240,
      "difficulty_id": 2,
      "explanation": "(a) 9r - 2 = 9(4) - 2 = 36 - 2 = 34. (b) 3r - r/9 = 3(4) - 4/9 = 12 - 4/9 = \\(11\\dfrac{5}{9}\\).",
      "hints": ["Substitute r = 4 into each expression.", "For (b), 12 - 4/9 = 11 + 9/9 - 4/9."],
      "source": "Raffles 2024 P6 Prelim Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: (a) 34, (b) 11 5/9. Part (b) is a mixed number so the whole item is MCQ."
    },
    {
      "n": 22,
      "type_id": 1,
      "question": "(a) Round 32.047 to one decimal place.  (b) Write down one decimal between \\(\\dfrac{1}{10}\\) and \\(\\dfrac{1}{5}\\).",
      "answer0": "(a) 32.0  (b) 0.15",
      "answer1": "(a) 32.1  (b) 0.15",
      "answer2": "(a) 32.0  (b) 0.05",
      "answer3": "(a) 32.05  (b) 0.25",
      "correct_answer": 0,
      "skill_id": 128,
      "difficulty_id": 2,
      "explanation": "(a) 32.047 to 1 d.p.: the hundredths digit is 4, so round down to 32.0. (b) 1/10 = 0.1 and 1/5 = 0.2; a decimal between them is 0.15.",
      "hints": ["For (a) look at the second decimal place to decide rounding.", "For (b) convert the fractions to decimals first."],
      "source": "Raffles 2024 P6 Prelim Q22",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: (a) 32.0, (b) 0.15 (any decimal strictly between 0.1 and 0.2 accepted). Kept MCQ as (b) has many valid answers."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "A machine started packing snacks at 8 a.m. at the rate of 300 packets per hour. After every 8 hours, it was stopped for 2 hours. How many packets can it pack by 11 p.m. on the same day? [?]",
      "answer0": "3900",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "8 a.m. to 11 p.m. = 15 h. Works 8 h (8am-4pm), stops 2 h (4pm-6pm), then works 5 h (6pm-11pm). Total working time = 13 h. 300 x 8 = 2400; 300 x 5 = 1500; 2400 + 1500 = 3900 packets.",
      "hints": ["Find the total time from 8 a.m. to 11 p.m.", "Subtract the 2-hour stop, then multiply working hours by 300."],
      "source": "Raffles 2024 P6 Prelim Q23",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 3900."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "A swimmer has to swim a total of 3 races in a competition. The timings for Ryan's first two races are: 1st 4.6 min, 2nd 4.1 min, 3rd ?. Ryan's average timing is 4.3 min for the 3 races. What is the timing for his 3rd race? [?] min",
      "answer0": "4.2",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 204,
      "difficulty_id": 2,
      "explanation": "Total of 3 races = 4.3 x 3 = 12.9 min. First two = 4.6 + 4.1 = 8.7 min. 3rd race = 12.9 - 8.7 = 4.2 min.",
      "hints": ["Total time = average x number of races.", "Subtract the first two timings from the total."],
      "source": "Raffles 2024 P6 Prelim Q24",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 4.2 min. Table data folded into stem."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "The figure is made up of a square and 2 triangles. The area of the square is 100 cm². The total width across the top is 35 cm. Find the shaded area of the figure. [?] cm²",
      "answer0": "125",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Square area 100 cm² so side = 10 cm. The two shaded triangles share the same height 10 cm and their bases total 35 - 10 = 25 cm. Shaded area = \\(\\dfrac{1}{2}\\times25\\times10 = 125\\) cm².",
      "hints": ["Side of the square = \\(\\sqrt{100}\\) = 10 cm.", "Combined base of the triangles = 35 - 10; height = 10."],
      "source": "Raffles 2024 P6 Prelim Q25",
      "image_needed": true,
      "image_options": false,
      "image_file": "q25.png",
      "image_page": 14,
      "image_bbox": [0.25, 0.14, 0.82, 0.27],
      "image_loc": "central square flanked by two shaded triangles, total width 35 cm, top of page",
      "notes": "Key: 125 cm²."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "A pattern is formed using the letters B, C and D. The first 21 letters are: B B C B D D B B B C B D D B B B C B D D B. The letter D appears 50 times in the pattern. What is the smallest possible number of letter B appearing in the pattern? [?]",
      "answer0": "99",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "The repeating block (B B C B D D) has 2 D and 4 B... using the printed working: 50 D means 25 blocks (50 / 2 = 25). 25 x 4 = 100 B, then for the smallest possible count subtract the final unmatched letter: 100 - 1 = 99.",
      "hints": ["Find the repeating unit and how many D's it contains.", "Work out how many full blocks give 50 D's, then count the B's."],
      "source": "Raffles 2024 P6 Prelim Q26",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 99 (printed working: 50/2=25, 25x4=100, 100-1=99)."
    },
    {
      "n": 27,
      "type_id": 0,
      "question": "There are 6 shaded shapes in the square grid. Shade the least number of shapes such that AB is the line of symmetry.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 145,
      "difficulty_id": 3,
      "explanation": "Reflect each existing shaded shape across the diagonal line AB and shade its mirror image where not already shaded, adding the least number of new shapes to make AB a line of symmetry.",
      "hints": ["Reflect each shaded shape across line AB.", "Only shade the mirror images that are not already shaded."],
      "source": "Raffles 2024 P6 Prelim Q27",
      "image_needed": true,
      "image_options": false,
      "image_file": "q27.png",
      "image_page": 15,
      "image_bbox": [0.25, 0.13, 0.78, 0.5],
      "image_loc": "square grid with diagonal line AB and 6 shaded shapes, upper half of page",
      "notes": "type_id 0: interactive shading task, no value answer. Answer is a completed shaded grid (see key). Skipped on insert."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "Bala glued 7 unit cubes to form the solid shown. Bala painted the whole solid, including the base, green. How many of the 7 cubes had exactly four of their faces painted green? [?]",
      "answer0": "2",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 188,
      "difficulty_id": 3,
      "explanation": "Examining the solid, exactly 2 of the 7 cubes have four faces exposed (painted) and the remaining faces hidden by glued neighbours.",
      "hints": ["Count exposed faces for each cube, including the base.", "A cube touching others on 2 faces has 4 painted faces."],
      "source": "Raffles 2024 P6 Prelim Q28",
      "image_needed": true,
      "image_options": false,
      "image_file": "q28.png",
      "image_page": 16,
      "image_bbox": [0.3, 0.14, 0.6, 0.36],
      "image_loc": "isometric drawing of a solid made of 7 unit cubes with Top/Front/Side view arrows, upper third of page",
      "notes": "Key (part b): 2. Part (a) 'draw the side view' is interactive and omitted; only the value answer for (b) is captured."
    },
    {
      "n": 29,
      "type_id": 0,
      "question": "A parallelogram ABCD is drawn on a square grid. EF is one side of a triangle EFG. The sum of \\(\\angle EFG\\) and \\(\\angle ADC\\) is 180°. FG is twice as long as BC. Draw triangle EFG on the square grid with a pencil and label it clearly.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 201,
      "difficulty_id": 3,
      "explanation": "G is placed so that angle EFG is the supplement of angle ADC and FG runs twice the length of BC along the grid (see printed key for the drawn triangle EFG).",
      "hints": ["\\(\\angle EFG = 180^\\circ - \\angle ADC\\).", "Measure BC on the grid and make FG twice as long."],
      "source": "Raffles 2024 P6 Prelim Q29",
      "image_needed": true,
      "image_options": false,
      "image_file": "q29.png",
      "image_page": 17,
      "image_bbox": [0.2, 0.18, 0.8, 0.55],
      "image_loc": "square grid with parallelogram ABCD and segment EF, middle of page",
      "notes": "type_id 0: interactive draw-and-label task, no value answer. Skipped on insert."
    },
    {
      "n": 30,
      "type_id": 2,
      "question": "Aleemah had an album of local and foreign stamps in the ratio 3 : 4. She gave away an equal number of local and foreign stamps. The total number of stamps she gave away is 40. The ratio of the number of local stamps and foreign stamps left in the album became 4 : 7. How many local stamps did she have at first? [?]",
      "answer0": "36",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "She gave away 20 local and 20 foreign. Let first amounts be 3u local, 4u foreign. After: (3u - 20) : (4u - 20) = 4 : 7. From the printed working 9 - 4 = 5u and 12 - 7 = 5u give 5u = 20, 1u = 4, so local at first = 9u = 9 x 4 = 36.",
      "hints": ["Equal amounts given away means 20 local and 20 foreign.", "Set up the after-ratio and solve for one unit."],
      "source": "Raffles 2024 P6 Prelim Q30",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 36 local stamps (printed working: 5u = 20, 1u = 4, 9u = 36)."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "The graph shows the total volume of water that evaporated from a container over a period of 8 h.<br>(a) During which two-hour interval was there the most volume of water evaporated? Give the start time. [?]<br>(b) What was the total volume of water that evaporated from 11 00 to 15 00? [?] ml",
      "answer0": "1500",
      "answer1": "28",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 147,
      "difficulty_id": 2,
      "explanation": "(a) The steepest part of the graph is the 15 00 to 17 00 interval (key: 1300 to 1500 was the answer given... the printed key states 1300 to 1500). (b) Volume at 15 00 minus volume at 11 00 = 38 - 10 = 28 ml.",
      "hints": ["The most evaporation is where the graph is steepest.", "For (b) read the volume at 15 00 and at 11 00 and subtract."],
      "source": "Raffles 2024 P6 Prelim Paper 2 Q1",
      "image_needed": true,
      "image_options": false,
      "image_file": "q31.png",
      "image_page": 20,
      "image_bbox": [0.2, 0.25, 0.82, 0.52],
      "image_loc": "line graph of total volume of water evaporated vs time, upper half of page",
      "notes": "Key: (a) 1300 to 1500, (b) 28 ml. NOTE: answer0 holds the (a) start time '1300' but answer key prints the interval '1300 to 1500'; for FIB the (a) blank should accept the interval start. Flag: part (a) is an interval which is awkward for numeric FIB. Printed key: (a) 1300 to 1500, (b) 28."
    },
    {
      "n": 32,
      "type_id": 2,
      "question": "The table shows the number of books borrowed from a library by 4 friends in a month: Amanda 5, Bala 6, Cal 30, Dewi ?. Cal borrowed half of the total number of books borrowed by his 3 friends. How many books did Dewi borrow? [?]",
      "answer0": "49",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "Cal (30) = half of the total of Amanda, Bala and Dewi, so the 3 friends together borrowed 60. Dewi = 60 - 5 - 6 = 49.",
      "hints": ["If Cal is half the friends' total, the friends' total = 30 x 2.", "Subtract Amanda's and Bala's books from that total."],
      "source": "Raffles 2024 P6 Prelim Paper 2 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 49. Table data folded into stem."
    },
    {
      "n": 33,
      "type_id": 1,
      "question": "A car and a taxi travelled from point A to point B. When the car started the journey at 8 a.m., the taxi was 7.5 km ahead. The car travelled at 90 km/h and the taxi travelled at 75 km/h. Both went in the same direction and did not change their speeds throughout. At what time did the car and taxi pass each other?",
      "answer0": "8.30 a.m.",
      "answer1": "8.15 a.m.",
      "answer2": "8.45 a.m.",
      "answer3": "9.00 a.m.",
      "correct_answer": 0,
      "skill_id": 217,
      "difficulty_id": 3,
      "explanation": "Relative speed = 90 - 75 = 15 km/h. Time to close 7.5 km = 7.5 / 15 = 0.5 h = 30 min. 8 a.m. + 30 min = 8.30 a.m.",
      "hints": ["Find the speed difference between the car and taxi.", "Time = gap distance / relative speed."],
      "source": "Raffles 2024 P6 Prelim Paper 2 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 8.30 a.m. Time answer so made MCQ (not FIB)."
    },
    {
      "n": 34,
      "type_id": 0,
      "question": "The pupils at a camp are divided into Group A and Group B. \\(\\dfrac{3}{8}\\) of the pupils in Group A are girls. \\(\\dfrac{1}{6}\\) of the pupils in Group B are girls. There are 3 times as many pupils in Group B as in Group A. For each statement, decide if it is True, False or Not possible to tell.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Let Group A = 8u (so girls A = 3u, boys A = 5u) and Group B = 24u (girls B = 4u, boys B = 20u). (1) More girls in Group A than B: 3u vs 4u -> False. (2) Total boys = 5u + 20u = 25u, a multiple of 5 -> True. (3) There are 32 pupils in the camp: total = 32u which need not equal 32 -> Not possible to tell.",
      "hints": ["Use units: Group B = 3 x Group A.", "Compute girls and boys in each group in terms of units."],
      "source": "Raffles 2024 P6 Prelim Paper 2 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "type_id 0: tick True/False/Not-possible-to-tell table, no single value answer. Key: False; True; Not possible to tell. Skipped on insert."
    },
    {
      "n": 35,
      "type_id": 1,
      "question": "The square grid shows the position of eight points (A, B, C, D, F, G, H, J) with North marked upward. Athena walked directly from point B to point D in a straight line. In which direction did Athena walk?",
      "answer0": "South-east",
      "answer1": "South-west",
      "answer2": "North-east",
      "answer3": "North-west",
      "correct_answer": 0,
      "skill_id": 142,
      "difficulty_id": 2,
      "explanation": "From B to D the movement is downward (south) and to the right (east) along the grid, so the direction is south-east.",
      "hints": ["B is higher and to the left; D is lower and to the right.", "Combine the vertical (N/S) and horizontal (E/W) directions."],
      "source": "Raffles 2024 P6 Prelim Paper 2 Q5a",
      "image_needed": true,
      "image_options": false,
      "image_file": "q35.png",
      "image_page": 23,
      "image_bbox": [0.3, 0.1, 0.75, 0.34],
      "image_loc": "square grid of eight labelled points with North arrow, top of page",
      "notes": "Key: south-east. Direction answer so MCQ. (Part b 'list all possible points' kept as separate Q36.)"
    },
    {
      "n": 36,
      "type_id": 1,
      "question": "On the square grid of eight points, Kok Ming stood at one of the points facing H. After he turned 45°, he faced C. Write down all the possible points where Kok Ming could be standing.",
      "answer0": "A and F",
      "answer1": "A and G",
      "answer2": "F and J",
      "answer3": "G and J",
      "correct_answer": 0,
      "skill_id": 142,
      "difficulty_id": 3,
      "explanation": "A 45° turn between facing H and facing C is possible from the points where the directions to H and to C are 45° apart. These are points A and F.",
      "hints": ["The directions from the standing point to H and to C must differ by 45°.", "Check each point's bearings to H and C."],
      "source": "Raffles 2024 P6 Prelim Paper 2 Q5b",
      "image_needed": true,
      "image_options": false,
      "image_file": "q36.png",
      "image_page": 23,
      "image_bbox": [0.3, 0.1, 0.75, 0.34],
      "image_loc": "same square grid of eight labelled points with North arrow, top of page",
      "notes": "Key: A, F. Letter answer so MCQ. Same figure as Q35."
    },
    {
      "n": 37,
      "type_id": 1,
      "question": "The table shows the salary Sumin was paid for working at a café: Monday to Friday $3m per day, Saturday $(5m + 8), Sunday $(4m - 2). Sumin worked from Monday to Saturday in her first week. What was her total salary for the first week in terms of m? Give your answer in the simplest form.",
      "answer0": "$(20m + 8)",
      "answer1": "$(18m + 8)",
      "answer2": "$(15m + 8)",
      "answer3": "$(20m - 2)",
      "correct_answer": 0,
      "skill_id": 239,
      "difficulty_id": 2,
      "explanation": "Monday to Friday = 5 x 3m = 15m. Plus Saturday (5m + 8): 15m + 5m + 8 = 20m + 8.",
      "hints": ["Five weekdays at $3m each.", "Add the Saturday amount and simplify."],
      "source": "Raffles 2024 P6 Prelim Paper 2 Q6a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: $(20m + 8). Algebraic answer so MCQ. Table folded into stem."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "Using the café salary rates (Saturday $(5m + 8), Sunday $(4m - 2)), Sumin only worked on Saturday and Sunday in her second week. She was paid a total amount of $240 for both days. Find the value of m. [?]",
      "answer0": "26",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 2,
      "explanation": "(5m + 8) + (4m - 2) = 9m + 6 = 240. 9m = 234, m = 26.",
      "hints": ["Add the Saturday and Sunday expressions.", "Set the sum equal to 240 and solve."],
      "source": "Raffles 2024 P6 Prelim Paper 2 Q6b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: m = 26. Answer is whole number so FIB."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "The average height of 3 plants is 105 cm. Plant A is twice as tall as Plant B. Plant C is 0.65 m shorter than Plant A. What is the height of Plant C? [?] cm",
      "answer0": "87",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 205,
      "difficulty_id": 3,
      "explanation": "Total height = 105 x 3 = 315 cm. Let B = u, A = 2u, C = 2u - 65. u + 2u + (2u - 65) = 315 -> 5u = 380 -> u = 76. Plant C = 2(76) - 65 = 152 - 65 = 87 cm.",
      "hints": ["Total = average x 3 = 315 cm; convert 0.65 m to 65 cm.", "Let Plant B be 1 unit and write A and C in units."],
      "source": "Raffles 2024 P6 Prelim Paper 2 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 87 cm."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "Emily had a rectangular piece of paper. She folded it along lines BC and GF as shown. \\(\\angle DBC = 64^\\circ\\) and \\(\\angle GFE = 45^\\circ\\). Find \\(\\angle FEH\\). [?]°",
      "answer0": "38",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "Using the printed working: \\(\\angle GHB = 180^\\circ - 52^\\circ = 128^\\circ\\); \\(\\angle FHE = 360^\\circ - 128^\\circ - 90^\\circ - 90^\\circ = 52^\\circ\\); \\(\\angle FEH = 180^\\circ - 90^\\circ - 52^\\circ = 38^\\circ\\).",
      "hints": ["Folding preserves angles; mark equal angles from the folds.", "Use angle sums in the triangles and around point H."],
      "source": "Raffles 2024 P6 Prelim Paper 2 Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q40.png",
      "image_page": 25,
      "image_bbox": [0.22, 0.45, 0.65, 0.68],
      "image_loc": "folded rectangle with points A,B,C,D,E,F,G,H and angles 64° and 45°, middle of page",
      "notes": "Key: 38°."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "Figure 1 shows a rectangular wooden plank of length 0.3 m. A carpenter used a number of such identical rectangular planks to cover the floor of a square room. Figure 2 shows part of the arrangement. He used a total of 108 wooden planks. Find the area of the floor. [?] m²",
      "answer0": "3.24",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 138,
      "difficulty_id": 3,
      "explanation": "From the arrangement, plank width = 0.3 / 3 = 0.1 m, so each plank area = 0.3 x 0.1 = 0.03 m². Total floor area = 108 x 0.03 = 3.24 m².",
      "hints": ["Work out the width of one plank from the arrangement.", "Floor area = number of planks x area of one plank."],
      "source": "Raffles 2024 P6 Prelim Paper 2 Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q41.png",
      "image_page": 26,
      "image_bbox": [0.18, 0.18, 0.85, 0.52],
      "image_loc": "Figure 1 single plank (0.3 m) and Figure 2 square room tiling layout, upper half of page",
      "notes": "Key: 3.24 m²."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "Mrs Raja spent \\(\\dfrac{1}{3}\\) of her money on a bag and 2 identical belts. The bag cost twice as much as each belt. Mrs Raja spent \\(\\dfrac{3}{4}\\) of her remaining money on a shirt. She spent $58 more on the shirt than on the bag. How much money did Mrs Raja have at first? [?]",
      "answer0": "174",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Bag + 2 belts = 1/3 of money. Bag = 2 belts in value, so among bag(2 parts)+2 belts(1 part each)=4 parts; bag = half of the 1/3 = 1/6 of total. Remaining = 2/3; shirt = 3/4 x 2/3 = 1/2 of total. Shirt - bag = 1/2 - 1/6 = 1/3 of total = $58... using printed working 6u - 2u = 4u = 58, 1u = 14.50, total 12u = $174.",
      "hints": ["Express the bag and shirt as fractions of the total money.", "Set shirt - bag = $58 and solve for the total."],
      "source": "Raffles 2024 P6 Prelim Paper 2 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: $174 (printed: 6u-2u=4u=58, 1u=14.50, 12u=174)."
    },
    {
      "n": 43,
      "type_id": 1,
      "question": "Aminah and Serene had the same number of coins. They each had a mix of twenty-cent coins and fifty-cent coins. Aminah had 12 twenty-cent coins while Serene had 20 twenty-cent coins. Who had more money? How much more?",
      "answer0": "Serene, $2.40 more",
      "answer1": "Aminah, $2.40 more",
      "answer2": "Serene, $1.60 more",
      "answer3": "Aminah, $1.60 more",
      "correct_answer": 1,
      "skill_id": 49,
      "difficulty_id": 3,
      "explanation": "Same total coins. Aminah has 8 fewer fifty-cent coins than... compare by swapping: each twenty-cent coin Serene has instead of a fifty-cent coin is 30 cents less. Aminah has 8 fewer 20c coins, i.e. 8 more 50c coins, so Aminah has 8 x (50 - 20) = 8 x 30 = 240 cents = $2.40 more. Aminah has more.",
      "hints": ["They have equal coin counts; compare the mix.", "Each extra fifty-cent coin (instead of twenty-cent) is worth 30c more."],
      "source": "Raffles 2024 P6 Prelim Paper 2 Q11a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Aminah had more, $2.40 more (printed working: 8 x (50-20) cents = $2.40). Name+amount answer so MCQ."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "Aminah and Serene had the same number of coins (a mix of twenty-cent and fifty-cent coins). Aminah had 12 twenty-cent coins; Serene had 20 twenty-cent coins. Serene spent all her twenty-cent coins. How much must Aminah give to Serene so that they have the same amount of money? [?]",
      "answer0": "3.20",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 49,
      "difficulty_id": 3,
      "explanation": "Aminah: 12 x 20c + 8 x 50c = $2.40 + $4.00 = $6.40 (each has 20 coins; Serene's split is 20 twenty-cent so 0 fifty-cent, total 20 coins). After Serene spends her twenty-cent coins she has $0... combined the two amounts. Total = $6.40; to share equally each needs $6.40 / 2 = $3.20. Aminah gives Serene $3.20.",
      "hints": ["Find each person's total money after Serene spends her 20c coins.", "Equal share = total / 2; Aminah transfers the difference."],
      "source": "Raffles 2024 P6 Prelim Paper 2 Q11b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: $3.20 (printed: total $6.40 / 2 = $3.20). Money answer so FIB; stored as 3.20."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "ABEG and CDEF are rhombuses. \\(\\angle CDE = 72^\\circ\\). Find \\(\\angle AGE\\). [?]°",
      "answer0": "126",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "In rhombus CDEF, \\(\\angle CDE = 72^\\circ\\) so adjacent angle \\(\\angle DEF = 180^\\circ - 72^\\circ = 108^\\circ\\); the rhombus ABEG shares orientation, giving \\(\\angle AGE = 180^\\circ - 54^\\circ = 126^\\circ\\) (printed: 180 - 54 = 126°).",
      "hints": ["Adjacent angles of a rhombus are supplementary.", "Use the shared geometry of the two rhombuses."],
      "source": "Raffles 2024 P6 Prelim Paper 2 Q12a",
      "image_needed": true,
      "image_options": false,
      "image_file": "q45.png",
      "image_page": 29,
      "image_bbox": [0.25, 0.11, 0.75, 0.32],
      "image_loc": "two rhombuses ABEG and CDEF with 72° marked, top of page",
      "notes": "Key: 126°."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "ABEG and CDEF are rhombuses. \\(\\angle CDE = 72^\\circ\\). Find \\(\\angle AHC\\). [?]°",
      "answer0": "81",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "Printed working: 54 / 2 = 27; \\(\\angle AHC = 180^\\circ - 72^\\circ - 27^\\circ = 81^\\circ\\).",
      "hints": ["The diagonal bisects the rhombus angle.", "Use the angle sum in the triangle at H."],
      "source": "Raffles 2024 P6 Prelim Paper 2 Q12b",
      "image_needed": true,
      "image_options": false,
      "image_file": "q46.png",
      "image_page": 29,
      "image_bbox": [0.25, 0.11, 0.75, 0.32],
      "image_loc": "two rhombuses ABEG and CDEF with 72° marked, top of page (same figure as Q45)",
      "notes": "Key: 81°."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "The table shows the printing rate of 4 printers: A 50, B 60, C 80, D ? posters per hour. The pie chart shows the total number of posters printed by each printer on a particular day. All printers printed for 6 hours, except Printer C which broke down after some time. Printer D's sector is 35%. What percentage of the posters were printed by Printer B? [?]%",
      "answer0": "30",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 236,
      "difficulty_id": 3,
      "explanation": "Printer D printed 35% which equals 6 x D posters. Working backward (printed key): 1% -> 2, 100% -> 200 (total relation); B printed 60 x ... -> \\(\\dfrac{60}{200}\\times100\\% = 30\\%\\). Printer B printed 30% of the posters.",
      "hints": ["Use Printer A's right-angle sector (25%) as a reference.", "Express B's posters as a percentage of the total."],
      "source": "Raffles 2024 P6 Prelim Paper 2 Q13a",
      "image_needed": true,
      "image_options": false,
      "image_file": "q47.png",
      "image_page": 30,
      "image_bbox": [0.35, 0.32, 0.65, 0.55],
      "image_loc": "pie chart of posters by printers A,B,C,D with 35% on D, middle of page",
      "notes": "Key: 30% (printed: 1% -> 2, 60/200 x 100% = 30%)."
    },
    {
      "n": 48,
      "type_id": 2,
      "question": "The table shows the printing rate of 4 printers: A 50, B 60, C 80, D ? posters per hour. All printers printed for 6 hours except Printer C which broke down after some time. Printer D's sector on the pie chart is 35%. How many hours did Printer C print before breaking down? [?]",
      "answer0": "1.5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 236,
      "difficulty_id": 3,
      "explanation": "Printed working: A = 25%, D = 35%, B = 30%, so C = 100 - (25 + 30 + 35) = 10%. 10% x 1200 (total) = 120 posters by C. At 80 posters/hour: 120 / 80 = 1.5 hours.",
      "hints": ["Find Printer C's percentage of the pie (the remainder).", "Posters by C / rate (80 per hour) = hours."],
      "source": "Raffles 2024 P6 Prelim Paper 2 Q13b",
      "image_needed": true,
      "image_options": false,
      "image_file": "q48.png",
      "image_page": 30,
      "image_bbox": [0.35, 0.32, 0.65, 0.55],
      "image_loc": "pie chart of posters by printers A,B,C,D with 35% on D, middle of page (same figure as Q47)",
      "notes": "Key: 1.5 hours (printed: C = 10%, 10% x 1200 = 120, 120 / 80 = 1.5 h)."
    },
    {
      "n": 49,
      "type_id": 2,
      "question": "The first four rows of numbers are arranged in a pattern: Row 1 has 1 number (1), Row 2 has 3 numbers (2,3,4), Row 3 has 5 numbers (5..9), Row 4 has 7 numbers (10..16). Complete the table for Row 5: write the first number and the last number in Row 5. [?] and [?]",
      "answer0": "17",
      "answer1": "25",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 108,
      "difficulty_id": 2,
      "explanation": "Last number in row n = n². Row 4 last = 16, so Row 5 first = 17 and Row 5 last = 5² = 25.",
      "hints": ["The last number in each row is a perfect square (1, 4, 9, 16).", "The first number in a row is one more than the previous row's last number."],
      "source": "Raffles 2024 P6 Prelim Paper 2 Q14a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: first 17, last 25. Two FIB blanks."
    },
    {
      "n": 50,
      "type_id": 2,
      "question": "In the number pattern where the last number in row n is n², find the first number in Row 10. [?]",
      "answer0": "82",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 108,
      "difficulty_id": 2,
      "explanation": "Last number in Row 9 = 9² = 81. First number in Row 10 = 81 + 1 = 82. (Printed: 10 x 10 = 100, 100 - 18 = 82, since Row 10 has 19 numbers ending at 100.)",
      "hints": ["Row 10 ends at 10² = 100.", "Row 10 has 2(10) - 1 = 19 numbers; first = 100 - 18."],
      "source": "Raffles 2024 P6 Prelim Paper 2 Q14b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 82."
    },
    {
      "n": 51,
      "type_id": 2,
      "question": "In the number pattern where the last number in row n is n², find the average of the numbers in Row 10. [?]",
      "answer0": "91",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 203,
      "difficulty_id": 2,
      "explanation": "Row 10 runs from 82 to 100 (19 numbers). Average = (first + last) / 2 = (82 + 100) / 2 = 91. (Printed: 100 - 9 = 91.)",
      "hints": ["The numbers in a row are consecutive, so average = (first + last) / 2.", "Row 10 ends at 100 and has a middle term."],
      "source": "Raffles 2024 P6 Prelim Paper 2 Q14c",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 91."
    },
    {
      "n": 52,
      "type_id": 1,
      "question": "Megan had some lilies and carnations. After she sold 75% of the lilies and \\(\\dfrac{1}{5}\\) of the carnations, she had an equal number of lilies and carnations. What was the ratio of the number of lilies to the number of carnations Megan had at first? Give your answer in the simplest form.",
      "answer0": "16 : 5",
      "answer1": "5 : 16",
      "answer2": "4 : 5",
      "answer3": "3 : 4",
      "correct_answer": 0,
      "skill_id": 179,
      "difficulty_id": 3,
      "explanation": "Lilies left = 25% = 1/4 of lilies; carnations left = 4/5 of carnations. These are equal: \\(\\dfrac{1}{4}L = \\dfrac{4}{5}C\\) -> L : C = \\(\\dfrac{4}{5} : \\dfrac{1}{4}\\) = 16 : 5.",
      "hints": ["Lilies left = 25%; carnations left = 4/5.", "Set the two 'left' quantities equal and form the ratio."],
      "source": "Raffles 2024 P6 Prelim Paper 2 Q15a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 16 : 5. Ratio answer so MCQ."
    },
    {
      "n": 53,
      "type_id": 2,
      "question": "Megan had lilies and carnations in the ratio 16 : 5 at first. The number of lilies Megan had at first was more than 90. What was the smallest possible number of flowers Megan had at first? [?]",
      "answer0": "126",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "Lilies = 16u > 90, so 1u > 5.625, smallest whole u = 6. Total flowers = 21u = 21 x 6 = 126. (Printed: 16u = 91 -> 1u = 6, total 126.)",
      "hints": ["Lilies = 16 units must exceed 90.", "Find the smallest whole-number unit, then total = 21 units."],
      "source": "Raffles 2024 P6 Prelim Paper 2 Q15b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 126."
    },
    {
      "n": 54,
      "type_id": 2,
      "question": "Tank P (base 20 cm by 18 cm, height 30 cm) is filled to 24 cm at first. Raj poured \\(\\dfrac{1}{3}\\) of the water from tank P into tank Q (base 25 cm by 16 cm). Tank Q in the end has water 16.2 cm high. What was the height of the water level in Tank Q at first? [?] cm",
      "answer0": "9",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 191,
      "difficulty_id": 3,
      "explanation": "Water poured from P = 1/3 x (20 x 18 x 24) = 1/3 x 8640 = 2880 cm³. Height this adds to Q = 2880 / (25 x 16) = 7.2 cm. Q ends at 16.2 cm, so at first it was 16.2 - 7.2 = 9 cm.",
      "hints": ["Volume poured = 1/3 of the water in P.", "Subtract the added height from the final height in Q."],
      "source": "Raffles 2024 P6 Prelim Paper 2 Q16a",
      "image_needed": true,
      "image_options": false,
      "image_file": "q54.png",
      "image_page": 33,
      "image_bbox": [0.18, 0.13, 0.85, 0.36],
      "image_loc": "two rectangular tanks P (24/30 cm, 20 x 18) and Q (16.2 cm, 25 x 16), upper third of page",
      "notes": "Key: 9 cm."
    },
    {
      "n": 55,
      "type_id": 2,
      "question": "Tank P (base 20 cm by 18 cm) had water 24 cm high. Raj poured \\(\\dfrac{1}{3}\\) of P's water into tank Q (base 25 cm by 16 cm), which had water 9 cm high at first and 16.2 cm high in the end. What was the percentage increase in the volume of water in Tank Q? [?]%",
      "answer0": "80",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 208,
      "difficulty_id": 3,
      "explanation": "Water added = 2880 cm³. Original volume in Q = 25 x 16 x 9 = 3600 cm³. Percentage increase = \\(\\dfrac{2880}{3600}\\times100\\% = 80\\%\\).",
      "hints": ["Find the volume added and the original volume in Q.", "Percentage increase = added / original x 100%."],
      "source": "Raffles 2024 P6 Prelim Paper 2 Q16b",
      "image_needed": true,
      "image_options": false,
      "image_file": "q55.png",
      "image_page": 33,
      "image_bbox": [0.18, 0.13, 0.85, 0.36],
      "image_loc": "two rectangular tanks P and Q, upper third of page (same figure as Q54)",
      "notes": "Key: 80%."
    },
    {
      "n": 56,
      "type_id": 2,
      "question": "The diagram shows two identical semicircles and a quarter circle. The base width is 28 cm. (Take \\(\\pi=\\dfrac{22}{7}\\).) Find the area of the shaded figure. [?] cm²",
      "answer0": "616",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 221,
      "difficulty_id": 3,
      "explanation": "Printed working: quarter circle of radius 28 = \\(\\dfrac{1}{4}\\times\\dfrac{22}{7}\\times14\\times14 ... \\) the shaded area = \\(\\dfrac{22}{7}\\times\\dfrac{1}{2}\\times14\\times14 + 308 = 308 + 308 = 616\\) cm².",
      "hints": ["Use radius = 14 cm for the semicircles.", "Add the areas of the semicircles and quarter circle as shaded."],
      "source": "Raffles 2024 P6 Prelim Paper 2 Q17a",
      "image_needed": true,
      "image_options": false,
      "image_file": "q56.png",
      "image_page": 34,
      "image_bbox": [0.25, 0.14, 0.65, 0.34],
      "image_loc": "shaded figure of two semicircles and a quarter circle, 28 cm base, upper third of page",
      "notes": "Key: 616 cm² (printed: 308 + 308 = 616)."
    },
    {
      "n": 57,
      "type_id": 2,
      "question": "The diagram shows two identical semicircles and a quarter circle with base width 28 cm. (Take \\(\\pi=\\dfrac{22}{7}\\).) Find the perimeter of the shaded figure. [?] cm",
      "answer0": "132",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 221,
      "difficulty_id": 3,
      "explanation": "Printed working: quarter-circle arc \\(\\dfrac{22}{7}\\times\\dfrac{1}{4}\\times2\\times14 = ... = 88\\); semicircle arcs \\(\\dfrac{22}{7}\\times\\dfrac{1}{2}\\times14\\times2 = 44\\). Perimeter = 88 + 44 = 132 cm.",
      "hints": ["Perimeter is the sum of the arc lengths on the boundary.", "Arc of semicircle = \\(\\pi r\\); quarter-circle arc = \\(\\dfrac{1}{2}\\pi r\\)."],
      "source": "Raffles 2024 P6 Prelim Paper 2 Q17b",
      "image_needed": true,
      "image_options": false,
      "image_file": "q57.png",
      "image_page": 34,
      "image_bbox": [0.25, 0.14, 0.65, 0.34],
      "image_loc": "shaded figure of two semicircles and a quarter circle, 28 cm base, upper third of page (same as Q56)",
      "notes": "Key: 132 cm (printed: 88 + 44 = 132)."
    },
    {
      "n": 58,
      "type_id": 2,
      "question": "The shaded figure (two identical semicircles and a quarter circle, perimeter 132 cm) is used to form a repeated pattern printed at the bottom of a piece of cloth. 19 of such shaded figures were used. Find the length of the piece of cloth. [?] cm",
      "answer0": "546",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 222,
      "difficulty_id": 3,
      "explanation": "Printed working: one figure spans 14 + 28 + 14 = 56 cm of width; 19 figures overlapping in the repeated pattern give length = (9 x 56) + 42 = 504 + 42 = 546 cm.",
      "hints": ["Find the horizontal span contributed by each figure in the pattern.", "Account for the overlap between consecutive figures."],
      "source": "Raffles 2024 P6 Prelim Paper 2 Q17c",
      "image_needed": true,
      "image_options": false,
      "image_file": "q58.png",
      "image_page": 35,
      "image_bbox": [0.18, 0.18, 0.85, 0.32],
      "image_loc": "repeated wave pattern of shaded figures along a strip of cloth, upper third of page",
      "notes": "Key: 546 cm (printed: 14+28+14=56, (9 x 56) + 42 = 546)."
    }
  ]
}