{
  "paper": {
    "school": "Ai Tong",
    "year": 2023,
    "level": "P6",
    "label": "Prelim",
    "source_prefix": "Ai Tong 2023 P6 Prelim",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "5 809 621 = 5 000 000 + ______ + 9000 + 600 + 20 + 1<br>What is the missing number in the blank?",
      "answer0": "800",
      "answer1": "8000",
      "answer2": "80 000",
      "answer3": "800 000",
      "correct_answer": 3,
      "skill_id": 149,
      "difficulty_id": 1,
      "explanation": "Method: read the place value of each part. 5 809 621 = 5 000 000 + 800 000 + 9000 + 600 + 20 + 1. The digit 8 is in the hundred-thousands place, so the missing number is 800 000. Final answer: 800 000.",
      "hints": ["Compare the expanded form to the original number, digit by digit.", "The 8 sits in the hundred-thousands place."],
      "source": "Ai Tong 2023 P6 Prelim Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 4 (800 000)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Which of the following numbers are common factors of 16 and 24?",
      "answer0": "8 and 12",
      "answer1": "2 and 3",
      "answer2": "4 and 6",
      "answer3": "4 and 8",
      "correct_answer": 3,
      "skill_id": 113,
      "difficulty_id": 1,
      "explanation": "Method: list factors of each number. Factors of 16: 1, 2, 4, 8, 16. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Common factors: 1, 2, 4, 8. The pair that are both common factors is 4 and 8. Final answer: 4 and 8.",
      "hints": ["A common factor must divide both 16 and 24 exactly.", "Check each option: do both numbers go into 16 AND 24?"],
      "source": "Ai Tong 2023 P6 Prelim Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 4 (4 and 8)."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Express 0.6 as a percentage.",
      "answer0": "0.006%",
      "answer1": "0.06%",
      "answer2": "6%",
      "answer3": "60%",
      "correct_answer": 3,
      "skill_id": 173,
      "difficulty_id": 1,
      "explanation": "Method: to convert a decimal to a percentage, multiply by 100. 0.6 × 100% = 60%. Final answer: 60%.",
      "hints": ["Multiply the decimal by 100 to get a percentage.", "0.6 = 60 hundredths = 60%."],
      "source": "Ai Tong 2023 P6 Prelim Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 4 (60%)."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Carol is 15 years old. She is $z$ years older than Abbie. How old is Abbie?",
      "answer0": "$(15 + z)$ years old",
      "answer1": "$(15 - z)$ years old",
      "answer2": "$(z - 15)$ years old",
      "answer3": "$(15z)$ years old",
      "correct_answer": 1,
      "skill_id": 238,
      "difficulty_id": 1,
      "explanation": "Method: Carol is z years older than Abbie, so Abbie is z years younger than Carol. Abbie's age = Carol's age − z = 15 − z. Final answer: (15 − z) years old.",
      "hints": ["If Carol is z years older, Abbie must be younger by z years.", "Subtract z from Carol's age of 15."],
      "source": "Ai Tong 2023 P6 Prelim Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 2 (15 - z)."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "Which of the following fractions has the largest value?",
      "answer0": "\\(\\dfrac{7}{9}\\)",
      "answer1": "\\(\\dfrac{5}{11}\\)",
      "answer2": "\\(\\dfrac{4}{7}\\)",
      "answer3": "\\(\\dfrac{1}{2}\\)",
      "correct_answer": 0,
      "skill_id": 79,
      "difficulty_id": 2,
      "explanation": "Method: compare each fraction to \\(\\dfrac{1}{2}\\) or convert to decimals. \\(\\dfrac{7}{9}\\approx0.78\\), \\(\\dfrac{5}{11}\\approx0.45\\), \\(\\dfrac{4}{7}\\approx0.57\\), \\(\\dfrac{1}{2}=0.5\\). The largest is \\(\\dfrac{7}{9}\\). Final answer: \\(\\dfrac{7}{9}\\).",
      "hints": ["Convert each fraction to a decimal to compare easily.", "Which value is closest to 1?"],
      "source": "Ai Tong 2023 P6 Prelim Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 1 (7/9)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "Ravi had 6 coins in his wallet. He took out only 4 coins to pay the exact amount for a bun. The coins are 5¢, 5¢, 10¢, 20¢, 50¢ and $1. Which of the following amounts is <b>not</b> a possible cost of the bun?",
      "answer0": "$1.65",
      "answer1": "$1.40",
      "answer2": "$1.35",
      "answer3": "$1.30",
      "correct_answer": 1,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Method: find which amount cannot be made with exactly 4 of the 6 coins {5¢, 5¢, 10¢, 20¢, 50¢, $1}. $1.65 = $1 + 50¢ + 10¢ + 5¢ (4 coins). $1.35 = $1 + 20¢ + 10¢ + 5¢ (4 coins). $1.30 = $1 + 20¢ + 5¢ + 5¢ (4 coins). $1.40 cannot be made with exactly 4 of these coins. Final answer: $1.40.",
      "hints": ["You must use exactly 4 of the 6 coins, each once.", "Try to build each amount; the impossible one is the answer."],
      "source": "Ai Tong 2023 P6 Prelim Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q6.png",
      "image_page": 4,
      "image_bbox": [0.16, 0.62, 0.82, 0.78],
      "image_loc": "row of 6 coin circles (5c, 5c, 10c, 20c, 50c, $1) in the middle of the page",
      "notes": "Answer key: option 2 ($1.40). Coin values transcribed into stem so question is solvable from text; image shows the coins."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "The average of 6 numbers is 14. When a 7th number is added, the average becomes 16. What is the 7th number?",
      "answer0": "30",
      "answer1": "28",
      "answer2": "14",
      "answer3": "12",
      "correct_answer": 1,
      "skill_id": 204,
      "difficulty_id": 2,
      "explanation": "Method: total = average × number of items. Total of 6 numbers = 14 × 6 = 84. Total of 7 numbers = 16 × 7 = 112. The 7th number = 112 − 84 = 28. Final answer: 28.",
      "hints": ["Total = average × count.", "Subtract the old total from the new total."],
      "source": "Ai Tong 2023 P6 Prelim Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 2 (28)."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "In the diagram, point A is north of point B and ∠ABC = 135°. In what direction is point C from point B?",
      "answer0": "North-East",
      "answer1": "North-West",
      "answer2": "South-East",
      "answer3": "South-West",
      "correct_answer": 3,
      "skill_id": 142,
      "difficulty_id": 2,
      "explanation": "Method: A is due north of B. Turning 135° from BA (north) towards C. The diagram shows C below and to the left of B. 135° from north (measured towards the west/left side) points between south and west. Final answer: South-West.",
      "hints": ["BA points due North; measure 135° from that direction.", "135° is past West-of-North; C lies in the lower-left quadrant."],
      "source": "Ai Tong 2023 P6 Prelim Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 5,
      "image_bbox": [0.55, 0.32, 0.88, 0.56],
      "image_loc": "diagram on the right showing A above B, C to the lower-left, angle 135 marked at B, and a North arrow",
      "notes": "Answer key: option 4 (South-West)."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "The pie chart shows what a group of children has chosen as their favourite colour. The same information is shown in a bar graph, but the names of the colours are not shown on the bar graph.<br>How many children chose yellow and red as their favourite colour?",
      "answer0": "20",
      "answer1": "40",
      "answer2": "44",
      "answer3": "46",
      "correct_answer": 2,
      "skill_id": 235,
      "difficulty_id": 3,
      "explanation": "Method: match pie-chart sectors to bar lengths. The pie chart shows Yellow is the largest sector, Green next, then Red, then Blue smallest. Bar lengths read off the graph: largest bar = 32 (Yellow), next = 20 (Green), then 12 (Red), smallest = 8 (Blue). Yellow + Red = 32 + 12 = 44. Final answer: 44.",
      "hints": ["Order the sectors by size, then match to the bar lengths in the same order.", "Add the Yellow bar value and the Red bar value."],
      "source": "Ai Tong 2023 P6 Prelim Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q9.png",
      "image_page": 6,
      "image_bbox": [0.14, 0.18, 0.92, 0.45],
      "image_loc": "pie chart (Blue/Green/Red/Yellow) on the left and a horizontal bar graph (axis 0 to 40) on the right",
      "notes": "Answer key: option 3 (44). Both pie chart and bar graph are needed to read off the values."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "There were 84 adults. 51 of them were men. What was the ratio of the number of women to the number of men?",
      "answer0": "11 : 17",
      "answer1": "17 : 28",
      "answer2": "17 : 11",
      "answer3": "28 : 17",
      "correct_answer": 0,
      "skill_id": 179,
      "difficulty_id": 1,
      "explanation": "Method: women = 84 − 51 = 33. Ratio women : men = 33 : 51. Divide both by 3: 33 ÷ 3 = 11, 51 ÷ 3 = 17, giving 11 : 17. Final answer: 11 : 17.",
      "hints": ["Find the number of women first: total − men.", "Simplify the ratio 33 : 51 by dividing by 3."],
      "source": "Ai Tong 2023 P6 Prelim Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 1 (11 : 17)."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "The solid is made up of 1-cm cubes. How many more 1-cm cubes are needed to build a cube of edge 4 cm?",
      "answer0": "28",
      "answer1": "36",
      "answer2": "49",
      "answer3": "53",
      "correct_answer": 2,
      "skill_id": 190,
      "difficulty_id": 2,
      "explanation": "Method: a 4 cm cube needs 4 × 4 × 4 = 64 unit cubes. Count the cubes in the given solid = 15. More cubes needed = 64 − 15 = 49. Final answer: 49.",
      "hints": ["Volume of a 4 cm cube = 4 × 4 × 4 = 64 unit cubes.", "Count the cubes shown, then subtract from 64."],
      "source": "Ai Tong 2023 P6 Prelim Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q11.png",
      "image_page": 7,
      "image_bbox": [0.25, 0.16, 0.72, 0.45],
      "image_loc": "3-D drawing of a solid built from 1-cm cubes, upper-middle of page",
      "notes": "Answer key: option 3 (49), so the solid contains 15 cubes (64 - 49 = 15). Verify count from the figure."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "The figure is made up of 2 identical quarter circles in a rectangle. Find the perimeter of the shaded part. (Take π = 3.14)",
      "answer0": "31.4 cm",
      "answer1": "35.7 cm",
      "answer2": "51.4 cm",
      "answer3": "78.5 cm",
      "correct_answer": 2,
      "skill_id": 221,
      "difficulty_id": 3,
      "explanation": "Method: the rectangle is 20 cm by 10 cm (two quarter circles of radius 10 cm fit side by side along a 20 cm top, height 10 cm). The shaded perimeter consists of the two quarter-circle arcs plus the straight sides. Two quarter-circle arcs (radius 10) = 2 × \\(\\dfrac{1}{4}\\) × 2 × 3.14 × 10 = 31.4 cm. Add the two vertical sides (10 + 10 = 20) gives 31.4 + 20 = 51.4 cm. Final answer: 51.4 cm.",
      "hints": ["The rectangle measures 20 cm by 10 cm; each quarter circle has radius 10 cm.", "Add the two arc lengths to the straight edges of the shaded region."],
      "source": "Ai Tong 2023 P6 Prelim Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q12.png",
      "image_page": 7,
      "image_bbox": [0.6, 0.66, 0.92, 0.80],
      "image_loc": "rectangle with two quarter circles forming a shaded V-shape at the top, height 10 cm marked, lower-right of page",
      "notes": "Answer key: option 3 (51.4 cm)."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "Which of the following is <b>not</b> 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": "Method: a valid cube net folds into a closed cube without overlapping faces. Mentally fold each net. Net 1 has an arrangement where two faces overlap when folded, so it cannot form a cube. The other three fold correctly. Final answer: Net 1.",
      "hints": ["A cube net has 6 squares that fold into a closed box.", "Try folding each one; the one where faces overlap is not a valid net."],
      "source": "Ai Tong 2023 P6 Prelim Q13",
      "image_needed": true,
      "image_options": true,
      "image_file": null,
      "image_page": 8,
      "image_bbox": [0.15, 0.16, 0.85, 0.48],
      "image_loc": "four candidate nets labelled (1)-(4), each a 6-square arrangement, in a 2x2 layout",
      "notes": "Answer key: option 1. image_options=true: each option is a picture of a net. Crop each option to q13_opt0.png .. q13_opt3.png."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "Meifang spent 20% of her money on a shirt. She used the rest of the money to buy a bag and a necklace. The bag cost $24 more than the shirt. The necklace cost $72. Find the cost of the bag.",
      "answer0": "$56",
      "answer1": "$48",
      "answer2": "$40",
      "answer3": "$32",
      "correct_answer": 0,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Method: let total money = T. Shirt = 20% of T = 0.2T. Bag + necklace = 80% of T = 0.8T. Bag = shirt + 24 = 0.2T + 24, necklace = 72. So 0.2T + 24 + 72 = 0.8T, i.e. 96 = 0.6T, T = 160. Shirt = 0.2 × 160 = 32; Bag = 32 + 24 = 56. Final answer: $56.",
      "hints": ["The shirt is 20% and the bag + necklace make up the other 80%.", "Set up: (shirt + $24) + $72 = 80% of total, and shirt = 20% of total."],
      "source": "Ai Tong 2023 P6 Prelim Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 1 ($56)."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "In the figure, ABCD is a square, EAFG is a rectangle and ∠EAB = 252°. Find ∠DAF.",
      "answer0": "108°",
      "answer1": "72°",
      "answer2": "45°",
      "answer3": "18°",
      "correct_answer": 1,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "Method: the reflex ∠EAB = 252°, so the interior ∠EAB = 360° − 252° = 108°. ∠DAB = 90° (square) and ∠EAF = 90° (rectangle). ∠EAB = ∠EAD + ∠DAB, but using the corner: ∠DAF = ∠EAB − ∠EAF − ∠... Working from the key: ∠DAF = 72°. (∠DAE = 108° − 90° = 18°; ∠DAF = ∠EAF − ∠DAE = 90° − 18° = 72°.) Final answer: 72°.",
      "hints": ["Reflex 252° means the interior angle ∠EAB = 360° − 252° = 108°.", "Use the 90° corners of the square and the rectangle to break up the angles at A."],
      "source": "Ai Tong 2023 P6 Prelim Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q15.png",
      "image_page": 9,
      "image_bbox": [0.28, 0.14, 0.68, 0.40],
      "image_loc": "square ABCD with a tilted rectangle EAFG overlapping at corner A, reflex angle 252 marked at A",
      "notes": "Answer key: option 2 (72°)."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "In the number line, what is the value represented by A?<br>[?]",
      "answer0": "31.18",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 124,
      "difficulty_id": 2,
      "explanation": "Method: the number line runs from 31 to 31.2 with the gap from 31.1 to 31.2 divided into equal small intervals. Each interval = 0.02. A is positioned 4 intervals past 31.1 (or read from the key as 31.18). Value at A = 31.18. Final answer: 31.18.",
      "hints": ["Work out the value of one small interval between 31.1 and 31.2.", "Count the intervals from 31.1 up to the arrow A."],
      "source": "Ai Tong 2023 P6 Prelim Q16",
      "image_needed": true,
      "image_options": false,
      "image_file": "q16.png",
      "image_page": 12,
      "image_bbox": [0.18, 0.22, 0.72, 0.38],
      "image_loc": "horizontal number line labelled 31, 31.1, 31.2 with an arrow A pointing to a tick near 31.2",
      "notes": "Answer key Q16: 31.18 (decimal, FIB)."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "7 men donated a total of $1435.<br>What is the average amount donated by each man?<br>$[?]",
      "answer0": "205",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 203,
      "difficulty_id": 1,
      "explanation": "Method: average = total ÷ number of items = $1435 ÷ 7 = $205. Final answer: $205.",
      "hints": ["Average = total amount ÷ number of men.", "Divide $1435 by 7."],
      "source": "Ai Tong 2023 P6 Prelim Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Q17: 205 (dollars)."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "GH and EF are straight lines. ∠GOE = 95° and ∠JOH = 32°. Find ∠FOJ.<br>[?]°",
      "answer0": "63",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "Method: ∠GOE = 95°, and ∠FOH is vertically opposite ∠GOE, so ∠FOH = 95°. ∠FOH = ∠FOJ + ∠JOH, so ∠FOJ = 95° − 32° = 63°. Final answer: 63°.",
      "hints": ["∠FOH is vertically opposite ∠GOE, so they are equal.", "Subtract ∠JOH from ∠FOH to get ∠FOJ."],
      "source": "Ai Tong 2023 P6 Prelim Q18",
      "image_needed": true,
      "image_options": false,
      "image_file": "q18.png",
      "image_page": 13,
      "image_bbox": [0.30, 0.14, 0.78, 0.40],
      "image_loc": "intersecting straight lines through point O with rays G,E,K,H,J,F and angles 95 and 32 marked",
      "notes": "Answer key Q18: 63 degrees (FIB)."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "Find the area of Triangle XYZ.<br>[?] cm²",
      "answer0": "36",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "Method: area of a triangle = \\(\\dfrac{1}{2}\\) × base × height. Take base YZ = 8 cm and the corresponding height = 9 cm (the vertical height from X to the line YW). Area = \\(\\dfrac{1}{2}\\) × 8 × 9 = 36 cm². Final answer: 36 cm².",
      "hints": ["Use base YZ = 8 cm.", "The perpendicular height to that base is 9 cm; area = ½ × base × height."],
      "source": "Ai Tong 2023 P6 Prelim Q19",
      "image_needed": true,
      "image_options": false,
      "image_file": "q19.png",
      "image_page": 13,
      "image_bbox": [0.30, 0.52, 0.82, 0.80],
      "image_loc": "triangle XYZ with measurements 15 cm, 6 cm, 9 cm, 8 cm, 4 cm and right-angle marks, lower part of page",
      "notes": "Answer key Q19: 36 cm² (FIB)."
    },
    {
      "n": 20,
      "type_id": 0,
      "question": "The figure is made up of identical squares. Shade three more squares to form a symmetric figure with XY as the line of symmetry.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 145,
      "difficulty_id": 2,
      "explanation": "Method: reflect each already-shaded square across the diagonal line XY. The three squares that have no mirror-image partner must be shaded to complete the symmetry. The answer key shows the three additional squares shaded (top-left region) to make the pattern symmetric about XY.",
      "hints": ["Reflect each shaded square across the dashed line XY.", "Shade the mirror-image of any square that does not yet have its reflection shaded."],
      "source": "Ai Tong 2023 P6 Prelim Q20",
      "image_needed": true,
      "image_options": false,
      "image_file": "q20.png",
      "image_page": 14,
      "image_bbox": [0.26, 0.18, 0.72, 0.52],
      "image_loc": "6x6 grid of squares with some shaded and a dashed diagonal line XY",
      "notes": "Interactive shade-the-grid task (type_id 0, skipped on insert). Answer key (Pg1) shows three more squares shaded to make the figure symmetric about diagonal XY."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "Candies were sold by mass: First 100 g costs $5, every additional 50 g costs $2. Rashid bought a packet of candies which weighed 250 g. How much did he pay?<br>$[?]",
      "answer0": "11",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "Method: first 100 g costs $5. Remaining mass = 250 g − 100 g = 150 g. 150 g ÷ 50 g = 3 lots of 50 g, each $2, so 3 × $2 = $6. Total = $5 + $6 = $11. Final answer: $11.",
      "hints": ["The first 100 g is a flat $5.", "Find how many 50 g lots are in the remaining 150 g, then charge $2 each."],
      "source": "Ai Tong 2023 P6 Prelim Q21",
      "image_needed": true,
      "image_options": false,
      "image_file": "q21.png",
      "image_page": 15,
      "image_bbox": [0.26, 0.17, 0.72, 0.30],
      "image_loc": "\"Candies for Sale!\" price box (First 100 g : $5, Every additional 50 g : $2) with a candy jar picture",
      "notes": "Answer key Q21: $11. Pricing transcribed into stem so solvable from text; image is the price sign."
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "In the figure, ABCD is a square. AB = EB and ∠BAE = 70°. Find ∠BCE.<br>[?]°",
      "answer0": "65",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "Method: in triangle ABE, AB = EB so it is isosceles with ∠BAE = ∠BEA = 70°, giving ∠ABE = 180° − 70° − 70° = 40°. Since ∠ABC = 90° (square), ∠CBE = 90° − 40° = 50°. AB = EB = BC (sides of square equal AB), so triangle BCE is isosceles with ∠BCE = ∠BEC = (180° − 50°) ÷ 2 = 65°. Final answer: 65°.",
      "hints": ["Triangle ABE is isosceles (AB = EB); find ∠ABE first.", "BC = AB = EB, so triangle BCE is isosceles too."],
      "source": "Ai Tong 2023 P6 Prelim Q22",
      "image_needed": true,
      "image_options": false,
      "image_file": "q22.png",
      "image_page": 15,
      "image_bbox": [0.46, 0.58, 0.78, 0.82],
      "image_loc": "square ABCD with point E inside, lines from A and B and C meeting at E, angle 70 marked at A",
      "notes": "Answer key Q22: 65 degrees (FIB)."
    },
    {
      "n": 23,
      "type_id": 1,
      "question": "A group of pupils volunteered at an old folks' home for 5 days. The line graph shows their attendance from Monday to Friday. All pupils turned up on Friday.<br>On which day were 30% of the pupils absent from the old folks' home?",
      "answer0": "Monday",
      "answer1": "Tuesday",
      "answer2": "Wednesday",
      "answer3": "Thursday",
      "correct_answer": 3,
      "skill_id": 147,
      "difficulty_id": 3,
      "explanation": "Method: all pupils turned up on Friday, so the total group size = Friday's attendance = 60. If 30% are absent, then 70% are present: 0.7 × 60 = 42 pupils present. Reading the graph, the day with 42 present is Thursday. Final answer: Thursday.",
      "hints": ["Friday's value is the full group size since everyone came.", "30% absent means 70% present; find the day matching that count."],
      "source": "Ai Tong 2023 P6 Prelim Q23",
      "image_needed": true,
      "image_options": false,
      "image_file": "q23.png",
      "image_page": 16,
      "image_bbox": [0.12, 0.16, 0.84, 0.52],
      "image_loc": "line graph of Number of Pupils (0-70) against Days Monday-Friday",
      "notes": "Answer key Q23: Thursday. Converted to MCQ (day name is a word answer); options are the 5 weekdays (Friday excluded as it is the full-attendance reference)."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "Find the value of $5 + 4a + 18 - 2a$ when $a = 8$.<br>[?]",
      "answer0": "39",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 240,
      "difficulty_id": 1,
      "explanation": "Method: substitute a = 8. 5 + 4(8) + 18 − 2(8) = 5 + 32 + 18 − 16 = 39. (Or simplify first: 5 + 18 + 2a = 23 + 2(8) = 23 + 16 = 39.) Final answer: 39.",
      "hints": ["Substitute a = 8 into each term.", "You can simplify 4a − 2a = 2a first, then add."],
      "source": "Ai Tong 2023 P6 Prelim Q24",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Q24: 39 (FIB)."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "A cuboid of height 12 cm has a square base of side 4 cm. What is its volume?<br>[?] cm³",
      "answer0": "192",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 190,
      "difficulty_id": 1,
      "explanation": "Method: volume of cuboid = length × breadth × height = 4 × 4 × 12 = 192 cm³. Final answer: 192 cm³.",
      "hints": ["The base is a 4 cm by 4 cm square.", "Volume = base area × height = (4 × 4) × 12."],
      "source": "Ai Tong 2023 P6 Prelim Q25",
      "image_needed": true,
      "image_options": false,
      "image_file": "q25.png",
      "image_page": 17,
      "image_bbox": [0.44, 0.42, 0.72, 0.72],
      "image_loc": "tall cuboid with height 12 cm and base width 4 cm labelled, middle-right of page",
      "notes": "Answer key Q25: 192 cm³ (printed as cm² in key, but volume is cm³). FIB."
    },
    {
      "n": 26,
      "type_id": 1,
      "question": "Lydia bought $3n$ packets of stickers. Each packet contained 8 stickers. She gave 25 stickers to her friends and divided the rest of the stickers equally into 7 boxes. How many stickers were there in each box? Give your answer in terms of $n$ in the simplest form.",
      "answer0": "\\(\\dfrac{24n - 25}{7}\\)",
      "answer1": "\\(\\dfrac{24n + 25}{7}\\)",
      "answer2": "\\(\\dfrac{8n - 25}{7}\\)",
      "answer3": "\\(24n - 25\\)",
      "correct_answer": 0,
      "skill_id": 241,
      "difficulty_id": 2,
      "explanation": "Method: total stickers = 3n × 8 = 24n. After giving away 25, stickers left = 24n − 25. Divided equally into 7 boxes: each box has \\(\\dfrac{24n - 25}{7}\\). Final answer: \\(\\dfrac{24n - 25}{7}\\).",
      "hints": ["Total = 3n packets × 8 stickers = 24n.", "Subtract 25, then divide the result by 7."],
      "source": "Ai Tong 2023 P6 Prelim Q26",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Q26: (24n - 25)/7. Algebraic fraction answer, so made MCQ; correct is option 1. Distractors are common errors."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "At first, the ratio of Weijie's savings to Lihua's savings was 5 : 4. After each of them spent $40, the ratio of Weijie's savings to Lihua's savings became 13 : 10. What was Lihua's savings at first?<br>$[?]",
      "answer0": "240",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "Method: the difference between Weijie's and Lihua's savings stays constant since both spend $40. Before, difference = 5u − 4u = 1u (in 5:4 units). After, difference = 13p − 10p = 3p (in 13:10 units). Make the difference equal: scale 5:4 to keep difference matching. From the key: 12u − 10u = 2u corresponds to $40, so 1u = $20; Lihua at first = 4 × (5:4 scaled) ... using key's units, Lihua at first = $20 × 12 = $240. Final answer: $240.",
      "hints": ["The difference in their savings does not change when both spend the same amount.", "Equate the difference in both ratios to find the value of one unit ($40 = 2 units)."],
      "source": "Ai Tong 2023 P6 Prelim Q27",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Q27: $240. Key working: 12u - 10u = 2u, $40/2 = $20, $20 x 12 = $240."
    },
    {
      "n": 28,
      "type_id": 1,
      "question": "The bar graph shows the number of printers sold by 4 shops in a month.<br>What fraction of the total number of printers was sold by Shop B? Give your answer in its simplest form.",
      "answer0": "\\(\\dfrac{13}{49}\\)",
      "answer1": "\\(\\dfrac{26}{98}\\)",
      "answer2": "\\(\\dfrac{13}{50}\\)",
      "answer3": "\\(\\dfrac{12}{49}\\)",
      "correct_answer": 0,
      "skill_id": 104,
      "difficulty_id": 2,
      "explanation": "Method: read the bar values: A = 24, B = 26, C = 18, D = 30 (in the graph's units). Total = 24 + 26 + 18 + 30 = 98. Fraction sold by B = \\(\\dfrac{26}{98}\\) = \\(\\dfrac{13}{49}\\) in simplest form. Final answer: \\(\\dfrac{13}{49}\\).",
      "hints": ["Read each shop's bar value and add for the total.", "Write B over the total, then simplify the fraction."],
      "source": "Ai Tong 2023 P6 Prelim Q28",
      "image_needed": true,
      "image_options": false,
      "image_file": "q28.png",
      "image_page": 19,
      "image_bbox": [0.18, 0.14, 0.78, 0.45],
      "image_loc": "vertical bar graph of Number of Printers Sold for Shops A, B, C, D",
      "notes": "Answer key Q28: 26/98 = 13/49. Fraction answer so made MCQ; correct option 1. Bar values A=24,B=26,C=18,D=30 per key."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "A total of 115 people stand in a queue for concert tickets. There are at least 3 men between any 2 women. What is the largest possible number of women in the queue?<br>[?]",
      "answer0": "29",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Method: to maximise women, place them as densely as allowed: a repeating block of 1 woman followed by 3 men = 4 people (W M M M). 115 ÷ 4 = 28 remainder 3. So 28 full blocks use 112 people (28 women), and the remaining 3 people can start a new block with 1 more woman (the trailing men are not required after the last woman). Largest number of women = 28 + 1 = 29. Final answer: 29.",
      "hints": ["Use a repeating pattern of 1 woman + 3 men (a block of 4).", "Divide 115 by 4; the remainder can hold one extra woman at the end."],
      "source": "Ai Tong 2023 P6 Prelim Q29",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Q29: 29 (FIB)."
    },
    {
      "n": 30,
      "type_id": 2,
      "question": "Hasnah had 5 boxes of identical erasers. At first, each of the boxes contained the same number of erasers. She took 21 erasers from each box. After that, the total number of erasers left in the 5 boxes was equal to the total number of erasers in 2 of the boxes at first. What was the number of erasers in each box at first?<br>[?]",
      "answer0": "35",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 3,
      "explanation": "Method: let each box have u erasers at first; total at first = 5u. She removes 21 from each of 5 boxes, removing 5 × 21 = 105. Total left = 5u − 105. This equals 2 boxes' original total = 2u. So 5u − 105 = 2u, giving 3u = 105, u = 35. Final answer: 35 erasers.",
      "hints": ["Let each box hold u erasers; total = 5u, and 21 × 5 = 105 are removed.", "Set 5u − 105 = 2u and solve for u."],
      "source": "Ai Tong 2023 P6 Prelim Q30",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Q30: 35 (FIB)."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "Use all the digits 9, 2, 0, 3 to form<br>(a) the greatest possible odd number [?]<br>(b) the number closest to 3000 [?]",
      "answer0": "9203",
      "answer1": "3029",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 150,
      "difficulty_id": 2,
      "explanation": "Method: (a) For the greatest odd 4-digit number using 9, 2, 0, 3, put the largest digit first and an odd digit last. Largest arrangement ending in an odd digit: 9203 (ends in 3, which is odd; 9 in thousands). (b) For the number closest to 3000, start with 3 in the thousands place and make the rest small: 3029 (which is 29 away from 3000, closer than 3092 or 2930). Final answers: (a) 9203, (b) 3029.",
      "hints": ["(a) Greatest odd number: biggest digit in front, an odd digit at the end.", "(b) Closest to 3000: put 3 first, then arrange the rest to stay just above 3000."],
      "source": "Ai Tong 2023 P6 Prelim Q31",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q1. Answer key: (a) 9203, (b) 3029. Two-part FIB, two blanks, two integer answers."
    },
    {
      "n": 32,
      "type_id": 2,
      "question": "A roll of ribbon is cut into three pieces in the ratio of 7 : 2 : 3. The shortest piece is 42 cm. What is the length of the longest piece of ribbon?<br>[?] cm",
      "answer0": "147",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 182,
      "difficulty_id": 2,
      "explanation": "Method: the ratio is 7 : 2 : 3, so the shortest piece is 2 units = 42 cm, meaning 1 unit = 21 cm. The longest piece is 7 units = 7 × 21 = 147 cm. Final answer: 147 cm.",
      "hints": ["The smallest number in the ratio (2) matches the shortest piece, 42 cm.", "Find 1 unit, then multiply by 7 for the longest piece."],
      "source": "Ai Tong 2023 P6 Prelim Q32",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q2. Answer key: 2u=42, 1u=21, 7u=147 cm (FIB)."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "Figure 1 shows a right-angled triangle. Figure 2 is made up of 4 such identical triangles and a square in the middle. Find the sum of ∠a, ∠b and ∠c.<br>[?]°",
      "answer0": "135",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "Method: from the answer key, ∠a = ∠c = 90° each is a right angle in the figure, and ∠b = 90° ÷ 2 = 45°. Sum ∠a + ∠b + ∠c = 90° + 45° = 135°. Final answer: 135°.",
      "hints": ["Identify the right angles formed by the identical right-angled triangles.", "Use the symmetry of the 4 identical triangles around the central square."],
      "source": "Ai Tong 2023 P6 Prelim Q33",
      "image_needed": true,
      "image_options": false,
      "image_file": "q33.png",
      "image_page": 23,
      "image_bbox": [0.16, 0.13, 0.78, 0.40],
      "image_loc": "Figure 1 (a right-angled triangle) and Figure 2 (4 triangles around a central square) with angles a, b, c marked",
      "notes": "Paper 2 Q3. Answer key: angle a + b + c = 90 + 45 = 135 degrees (FIB)."
    },
    {
      "n": 34,
      "type_id": 1,
      "question": "The table shows the grades of 120 students who joined a Mathematics competition. Grade A is the best grade and Grade E is the worst grade.<br>Grade: A, B, C, D, E<br>Number of students: 15, 27, 54, 18, 6<br>Only \\(\\dfrac{7}{20}\\) of the students made it through to the second round. What was the minimum grade required to go through to the second round?",
      "answer0": "Grade A",
      "answer1": "Grade B",
      "answer2": "Grade C",
      "answer3": "Grade D",
      "correct_answer": 1,
      "skill_id": 147,
      "difficulty_id": 2,
      "explanation": "Method: number through to round 2 = \\(\\dfrac{7}{20}\\) × 120 = 42 students. Starting from the best grade: A = 15, A + B = 15 + 27 = 42. So the top 42 students are exactly grades A and B; the minimum grade required is B. Final answer: Grade B.",
      "hints": ["Find how many students qualify: 7/20 of 120.", "Add up students from the best grade downwards until you reach that number."],
      "source": "Ai Tong 2023 P6 Prelim Q34",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q4. Answer key: 120 x 7/20 = 42; 15 + 27 = 42; min grade = B. Word/grade answer so made MCQ; correct option 2."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "The area of rectangle ABCD is 1728 cm². The length of FE is \\(\\dfrac{5}{6}\\) of the length of AD. What is the area of the triangle ABE?<br>[?] cm²",
      "answer0": "720",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 138,
      "difficulty_id": 3,
      "explanation": "Method: triangle ABE has base AB (the top side of the rectangle) and height FE (the perpendicular from E to AB). FE = \\(\\dfrac{5}{6}\\) of AD, and AD is the height of the rectangle. Area of triangle ABE = \\(\\dfrac{1}{2}\\) × AB × FE = \\(\\dfrac{1}{2}\\) × AB × \\(\\dfrac{5}{6}\\)AD = \\(\\dfrac{5}{12}\\) × (AB × AD) = \\(\\dfrac{5}{12}\\) × 1728. From the key: 1728 × \\(\\dfrac{5}{6}\\) = 1440, then ÷ 2 = 720 cm². Final answer: 720 cm².",
      "hints": ["The triangle's base is AB and its height is FE.", "FE = 5/6 of AD; area = ½ × AB × FE, and AB × AD = 1728."],
      "source": "Ai Tong 2023 P6 Prelim Q35",
      "image_needed": true,
      "image_options": false,
      "image_file": "q35.png",
      "image_page": 24,
      "image_bbox": [0.20, 0.14, 0.68, 0.32],
      "image_loc": "rectangle ABCD with F on top side AB, E below F inside, triangle ABE drawn, near top of page",
      "notes": "Paper 2 Q5. Answer key: 1728 x 5/6 = 1440; 1440 / 2 = 720 cm² (FIB)."
    },
    {
      "n": 36,
      "type_id": 1,
      "question": "The pie chart shows the CCAs of 300 students in school. The CCAs shown are Wushu 30%, Robotics 15%, Track and Field, Dance Club and Brownies.<br>What percentage of the students are in Dance Club and Brownies?",
      "answer0": "30%",
      "answer1": "45%",
      "answer2": "25%",
      "answer3": "55%",
      "correct_answer": 0,
      "skill_id": 236,
      "difficulty_id": 2,
      "explanation": "Method: the whole pie is 100%. Wushu = 30%, Robotics = 15%, and Track and Field appears as a quarter (right-angle marked) = 25%. So Dance Club + Brownies = 100% − 30% − 15% − 25% = 30%. Final answer: 30%.",
      "hints": ["All sectors add up to 100%.", "Track and Field is a right angle (quarter) = 25%; subtract the known sectors."],
      "source": "Ai Tong 2023 P6 Prelim Q36",
      "image_needed": true,
      "image_options": false,
      "image_file": "q36.png",
      "image_page": 25,
      "image_bbox": [0.28, 0.18, 0.70, 0.45],
      "image_loc": "pie chart with sectors Wushu 30%, Robotics 15%, Track and Field, Dance Club, Brownies",
      "notes": "Paper 2 Q6(a). Answer key: 100% - 15% - 30% - 25% = 30%. Made MCQ (percentage value). Track and Field = 25% (right-angle sector)."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "The pie chart shows the CCAs of 300 students in school (Wushu 30%, Robotics 15%, Track and Field 25%, Dance Club and Brownies together 30%). The ratio of the number of students in Dance Club to the number of students in Brownies is 3 : 2. How many students are in Brownies?<br>[?]",
      "answer0": "36",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 213,
      "difficulty_id": 2,
      "explanation": "Method: Dance Club + Brownies = 30% of students. Dance Club : Brownies = 3 : 2, so Brownies = \\(\\dfrac{2}{5}\\) of that 30% = \\(\\dfrac{2}{5}\\) × 30% = 12%. Number in Brownies = 12% × 300 = \\(\\dfrac{12}{100}\\) × 300 = 36. Final answer: 36 students.",
      "hints": ["Dance Club and Brownies together are 30%; split in the ratio 3 : 2.", "Brownies = 2/5 of 30% = 12%, then take 12% of 300."],
      "source": "Ai Tong 2023 P6 Prelim Q37",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q6(b). Answer key: 2/5 x 30% = 12%; 12/100 x 300 = 36 (FIB). Pie chart context only; no figure needed for this part."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "The figure shows an empty container. All edges meet at right angles. When the tap is turned on, water flows into the container at a rate of 2.01 litres per minute. How much time is needed to fill the container completely?<br>[?] min",
      "answer0": "14",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 193,
      "difficulty_id": 3,
      "explanation": "Method: split the L-shaped container into two cuboids. Lower full-width block: 24 × 20 × 14 = 6720 cm³ (the lower step) plus the tall left column: 85 × 14 × (42 − 24) = 85 × 14 × 18 = 21420 cm³. Total volume = 6720 + 21420 = 28140 cm³ = 28.14 litres. Time = 28.14 ÷ 2.01 = 14 min. Final answer: 14 min.",
      "hints": ["Break the L-shaped solid into two cuboids and add their volumes.", "Convert cm³ to litres (1000 cm³ = 1 litre), then divide by the flow rate 2.01 l/min."],
      "source": "Ai Tong 2023 P6 Prelim Q38",
      "image_needed": true,
      "image_options": false,
      "image_file": "q38.png",
      "image_page": 26,
      "image_bbox": [0.20, 0.18, 0.60, 0.52],
      "image_loc": "L-shaped container with a tap; dimensions 85 cm, 42 cm, 24 cm, 20 cm, 14 cm marked",
      "notes": "Paper 2 Q7. Answer key: 24x20x14 + 85x14x(42-24) = 28140 cm³ = 28.14 l; 28.14 / 2.01 = 14 min (FIB)."
    },
    {
      "n": 39,
      "type_id": 0,
      "question": "Trapezium T is drawn on the square grid. (a) In the square grid, draw a square with twice the area of Trapezium T. (b) In the square grid, draw a parallelogram with twice the perimeter of Trapezium T.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 201,
      "difficulty_id": 3,
      "explanation": "Method: (a) find the area of Trapezium T from the grid, double it, and draw a square of that area. (b) find the perimeter of Trapezium T, double it, and draw a parallelogram with that perimeter. The answer key shows a sample square (Q8a) and parallelogram (Q8b) drawn on the grid.",
      "hints": ["First measure Trapezium T's area and perimeter from the grid squares.", "Double each value, then construct the required shape."],
      "source": "Ai Tong 2023 P6 Prelim Q39",
      "image_needed": true,
      "image_options": false,
      "image_file": "q39.png",
      "image_page": 27,
      "image_bbox": [0.14, 0.13, 0.80, 0.27],
      "image_loc": "Trapezium T drawn on a square grid at the top of the page",
      "notes": "Paper 2 Q8. Construct-on-grid task (draw a square / parallelogram) = interactive, type_id 0, skipped on insert. Answer key shows sample drawings."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "There were 45 soccer balls, 30 basketballs and 68 ping pong balls in the PE room. After 80 balls were added, the number of soccer balls increased by 40% and the number of ping pong balls increased by 25%. What was the percentage increase in the number of basketballs?<br>[?] %",
      "answer0": "150",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 208,
      "difficulty_id": 3,
      "explanation": "Method: soccer balls added = 40% × 45 = 18. Ping pong balls added = 25% × 68 = 17. Total added = 80, so basketballs added = 80 − 18 − 17 = 45. Percentage increase in basketballs = \\(\\dfrac{45}{30}\\) × 100% = 150%. Final answer: 150%.",
      "hints": ["Find how many soccer and ping pong balls were added using their percentages.", "The rest of the 80 are basketballs; divide that by the original 30."],
      "source": "Ai Tong 2023 P6 Prelim Q40",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q9. Answer key: soccer +18, ping pong +17, basketball +45; 45/30 x 100% = 150% (FIB)."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "Both Farah and Jamil left their houses at the same time to go to the park. Farah travelled 20 km from her house to the park at an average speed of 30 km/h. Jamil travelled from his house at an average speed of 42 km/h and reached the park 15 minutes later than Farah. What was the distance between Jamil's home and the park?<br>[?] km",
      "answer0": "38.5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 219,
      "difficulty_id": 3,
      "explanation": "Method: time for Farah = distance ÷ speed = 20 ÷ 30 h = 40 min. Jamil arrived 15 min later, so Jamil's time = 40 + 15 = 55 min = \\(\\dfrac{55}{60}\\) h = \\(\\dfrac{11}{12}\\) h. Distance for Jamil = speed × time = 42 × \\(\\dfrac{11}{12}\\) = 38.5 km. Final answer: 38.5 km.",
      "hints": ["Find Farah's travel time first (20 km at 30 km/h).", "Add 15 minutes for Jamil, convert to hours, then multiply by 42 km/h."],
      "source": "Ai Tong 2023 P6 Prelim Q41",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q10. Answer key: Farah 40 min; Jamil 55 min = 11/12 h; 42 x 11/12 = 38.5 km (FIB)."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "STUV is a trapezium. UVWX is a rhombus. Find ∠y.<br>[?]°",
      "answer0": "224",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 200,
      "difficulty_id": 3,
      "explanation": "Method: in trapezium STUV, ST is parallel to VU, so ∠TUV and ∠STU are co-interior: ∠TUV = 180° − 122° = 58°. In rhombus UVWX, ∠VUX = ∠XWV (opposite angles equal) = 78°. ∠y is the reflex angle at U going around the outside = 360° − ∠VUX − ∠TUV = 360° − 78° − 58° = 224°. Final answer: 224°.",
      "hints": ["Use co-interior angles in the trapezium to find ∠TUV from 122°.", "In the rhombus, opposite angles are equal; ∠y is the reflex angle at U (360° minus the two angles)."],
      "source": "Ai Tong 2023 P6 Prelim Q42",
      "image_needed": true,
      "image_options": false,
      "image_file": "q42.png",
      "image_page": 30,
      "image_bbox": [0.20, 0.15, 0.60, 0.42],
      "image_loc": "trapezium STUV joined to rhombus UVWX; angles 122 at T, 78 at W, reflex y at U marked",
      "notes": "Paper 2 Q11. Answer key: angle TUV = 58, angle VUX = 78, y = 360 - 78 - 58 = 224 degrees (FIB)."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "There were a total of 2120 students at the school parade square at first. After 536 boys and \\(\\dfrac{1}{4}\\) of the girls left, the ratio of the number of boys to the number of girls became 4 : 9. How many more girls than boys were there at the parade square in the end?<br>[?]",
      "answer0": "495",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "Method: students remaining after some left = 2120 − 536 = 1584. Of the girls, \\(\\dfrac{1}{4}\\) left so \\(\\dfrac{3}{4}\\) remained; let remaining girls = 9u (from ratio 4 : 9). Then \\(\\dfrac{3}{4}\\) of original girls = 9u, so original girls = 12u. Remaining boys = 4u. Remaining total = 4u + 9u + (girls who left = 3u) ... using key: 12u + 4u = 1584, so 16u = 1584, 1u = 99. More girls than boys in the end = 9u − 4u = 5u = 5 × 99 = 495. Final answer: 495.",
      "hints": ["Total remaining after 536 boys left (before counting girls leaving) = 2120 − 536 = 1584.", "Remaining boys : girls = 4 : 9; the difference is 5 units. Find 1 unit, then 5 units."],
      "source": "Ai Tong 2023 P6 Prelim Q43",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q12. Answer key: 2120-536=1584; 12u+4u=1584; 1u=99; 5u=495 (FIB)."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "Charlie poured pancake mixture into two types of containers. The small container holds 75 ml and the big container holds 375 ml. He poured half the mixture into big containers and the other half into small containers. He filled the containers to the brim. Charlie used 24 more small containers than big containers.<br>(a) How many big containers did Charlie use? [?]<br>(b) How much pancake mixture was there? [?] ml",
      "answer0": "6",
      "answer1": "4500",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 193,
      "difficulty_id": 3,
      "explanation": "Method: each half of the mixture is the same volume. One big container (375 ml) holds the same as 375 ÷ 75 = 5 small containers. So for an equal half-volume, the number of small containers = 5 × the number of big containers. The difference = 5b − b = 4b = 24, so b = 6 big containers. (a) 6 big containers. (b) Volume of one half = 6 × 375 = 2250 ml; total mixture = 2 × 2250 = 4500 ml. Final answers: (a) 6, (b) 4500 ml.",
      "hints": ["A 375 ml big container equals five 75 ml small containers for the same volume.", "Small count = 5 × big count; the difference of 24 gives the number of big containers."],
      "source": "Ai Tong 2023 P6 Prelim Q44",
      "image_needed": true,
      "image_options": false,
      "image_file": "q44.png",
      "image_page": 32,
      "image_bbox": [0.30, 0.13, 0.58, 0.30],
      "image_loc": "two jars: a small jar labelled 75ml and a big jar labelled 375ml",
      "notes": "Paper 2 Q13. Answer key: (a) 375-75 leads to small=5x big; 24x75=1800, 1800/300=6 big; (b) 6 x 375 x 2 = 4500 ml. Two-part FIB, two blanks, two integer answers. Capacities transcribed into stem."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "A rectangular piece of paper RSVX is folded at two of its corners. After folding, VT = VU and ∠RXW = 18°.<br>(a) Find ∠VUT. [?]°<br>(b) Find ∠XWU. [?]°",
      "answer0": "45",
      "answer1": "54",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "Method: (a) The corner is folded so the right angle (90°) is split. With VT = VU, triangle VTU is isosceles and the right angle at the corner gives ∠VUT = (180° − 90°) ÷ 2 = 45°. (b) The other fold: ∠RWX (= ∠RXW reflected) means ∠RWX = 180° − 90° − 18° = 72° is the folded right angle minus 18°, so ∠XWU = (180° − 72°) ÷ 2 = 54°. Final answers: (a) 45°, (b) 54°.",
      "hints": ["A folded corner preserves the original 90°; use VT = VU (isosceles) for part (a).", "For (b), find ∠RWX using the 18° and the folded right angle, then use the isosceles fold."],
      "source": "Ai Tong 2023 P6 Prelim Q45",
      "image_needed": true,
      "image_options": false,
      "image_file": "q45.png",
      "image_page": 33,
      "image_bbox": [0.08, 0.15, 0.82, 0.36],
      "image_loc": "rectangle RSVX shown before folding (left) and after folding (right) with 18 degrees and labels W, X, V, U, T",
      "notes": "Paper 2 Q14. Answer key: (a) (180-90)/2 = 45; (b) angle RWX=180-90-18=72, XWU=(180-72)/2=54. Two-part FIB, two blanks."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "The figure is made up of a quadrant and a circle overlapping each other. The quadrant touches the circle at points F and G. The circle, with centre O, has a diameter of 24 cm. Find the area of the shaded parts. (Take π = 3.14)<br>[?] cm²",
      "answer0": "164.16",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 222,
      "difficulty_id": 3,
      "explanation": "Method: the big quadrant has radius equal to the circle's diameter, 24 cm. Area of quadrant = \\(\\dfrac{1}{4}\\)πr² = \\(\\dfrac{1}{4}\\) × 3.14 × 24² = 452.16 cm². The unshaded inner region AFBG has area 24 × 12 = 288 cm². Shaded area = 452.16 − 288 = 164.16 cm². Final answer: 164.16 cm².",
      "hints": ["The quadrant's radius is the circle's diameter, 24 cm.", "Shaded = area of the big quadrant − the unshaded inner region (24 × 12)."],
      "source": "Ai Tong 2023 P6 Prelim Q46",
      "image_needed": true,
      "image_options": false,
      "image_file": "q46.png",
      "image_page": 34,
      "image_bbox": [0.30, 0.18, 0.62, 0.40],
      "image_loc": "a quadrant and a circle (centre O) overlapping, touching at F and G, with shaded crescent regions",
      "notes": "Paper 2 Q15. Answer key: quadrant = 1/4 x 3.14 x 24^2 = 452.16; AFBG = 24 x 12 = 288; shaded = 164.16 cm² (FIB)."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "Ms Wong received $6120 from selling some bags and some dresses. She received $3240 more for the bags than the dresses. 4 times as many bags as dresses were sold. Each dress cost $15 more than each bag.<br>(a) How much did Ms Wong receive for the bags? $[?]<br>(b) How many dresses did Ms Wong sell? [?]",
      "answer0": "4680",
      "answer1": "18",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Method: (a) total = $6120; bags' amount is $3240 more than dresses'. Dresses' amount = (6120 − 3240) ÷ 2 = 2880 ÷ 2 = $1440; bags' amount = 1440 + 3240 = $4680. (b) Let each bag cost b; each dress = b + 15. Number of bags = 4 × number of dresses. Bags amount $4680 = 4d × b and dresses amount $1440 = d × (b+15). From the key: $4680 ÷ 4 = $1170 is the per-dress-equivalent for bags... $1440 − $1170 = $270; $270 ÷ 15 = 18 dresses. Final answers: (a) $4680, (b) 18.",
      "hints": ["(a) Bags = dresses + $3240 and bags + dresses = $6120; solve for each amount.", "(b) Use '4 times as many bags' and 'each dress costs $15 more than each bag' to find the number of dresses."],
      "source": "Ai Tong 2023 P6 Prelim Q47",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q16. Answer key: (a) (6120-3240)/2=1440; 1440+3240=$4680; (b) 4680/4=1170; 1440-1170=270; 270/15=18 dresses. Two-part FIB."
    },
    {
      "n": 48,
      "type_id": 1,
      "question": "Ali, Brandon, Carrie and Devi shared a sum of money equally at first. Ali gave \\(\\dfrac{2}{3}\\) of his money to Brandon. What fraction of the sum of money did Ali have in the end?",
      "answer0": "\\(\\dfrac{1}{12}\\)",
      "answer1": "\\(\\dfrac{1}{4}\\)",
      "answer2": "\\(\\dfrac{1}{3}\\)",
      "answer3": "\\(\\dfrac{2}{12}\\)",
      "correct_answer": 0,
      "skill_id": 161,
      "difficulty_id": 2,
      "explanation": "Method: the four share equally, so Ali had \\(\\dfrac{1}{4}\\) of the total. He gave away \\(\\dfrac{2}{3}\\) of his share, keeping \\(\\dfrac{1}{3}\\) of it. Ali's remaining fraction = \\(\\dfrac{1}{3}\\) × \\(\\dfrac{1}{4}\\) = \\(\\dfrac{1}{12}\\). Final answer: \\(\\dfrac{1}{12}\\).",
      "hints": ["Each person starts with 1/4 of the total.", "Ali keeps 1/3 of his 1/4 share."],
      "source": "Ai Tong 2023 P6 Prelim Q48",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q17(a). Answer key: total units 4x3=12u; Ali kept 1/12. Fraction answer so made MCQ; correct option 1."
    },
    {
      "n": 49,
      "type_id": 2,
      "question": "Ali, Brandon, Carrie and Devi shared a sum of money equally at first. Ali gave \\(\\dfrac{2}{3}\\) of his money to Brandon. Brandon then gave \\(\\dfrac{1}{5}\\) of his money to Carrie. Carrie then gave \\(\\dfrac{3}{8}\\) of her money and an additional $55 to Devi. Devi had $595 in the end. How much was the sum of money they shared?<br>$[?]",
      "answer0": "1440",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Method: work in units where each started with 3u (total 12u). Before: A:B:C:D = 1u:5u:3u:3u (Ali kept 1u after giving 2u to Brandon, so Brandon = 3u + 2u = 5u). After Brandon gave 1/5 of his 5u (= 1u) to Carrie: A:B:C:D = 1u:4u:4u:3u, scaled ×2 = 2u:8u:8u:6u. After Carrie gave 3/8 of her 8u (= 3u) plus $55 to Devi: Carrie = 8u−3u = 5u−$55... and Devi = 6u + 3u + $55 = 9u + $55. Devi's final = 9u + $55 = $595, so 9u = $540, 1u = $60. Total = 24u = 24 × $60 = $1440. Final answer: $1440.",
      "hints": ["Track each person in units, starting equal; scale up to keep whole numbers when fractions are taken.", "Devi ends with 9u + $55 = $595; solve for 1u, then the total is 24u."],
      "source": "Ai Tong 2023 P6 Prelim Q49",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q17(b). Answer key: 9u + $55 = $595; 9u = $540; 1u = $60; 24u = $1440 (FIB)."
    }
  ]
}