{
  "paper": {
    "school": "Ai Tong",
    "year": 2024,
    "level": "P5",
    "label": "End-of-Year Exam",
    "source_prefix": "Ai Tong 2024 P5 End-of-Year Exam",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "Which of the following is forty-six thousand and fifty in numerals?",
      "answer0": "4650",
      "answer1": "46 050",
      "answer2": "46 500",
      "answer3": "460 050",
      "correct_answer": 1,
      "skill_id": 149,
      "difficulty_id": 1,
      "explanation": "Forty-six thousand = 46 000, and fifty = 50. 46 000 + 50 = 46 050. Answer: 46 050.",
      "hints": ["Forty-six thousand is 46 000.", "Add fifty (50) to get the full numeral."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 2 (46 050)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "A number becomes 70 000 when rounded to the nearest thousand. Which one of the following could the number be?",
      "answer0": "69 499",
      "answer1": "69 978",
      "answer2": "70 893",
      "answer3": "71 267",
      "correct_answer": 1,
      "skill_id": 150,
      "difficulty_id": 2,
      "explanation": "Rounding to the nearest thousand gives 70 000 for numbers from 69 500 to 70 499. 69 499 rounds to 69 000; 70 893 rounds to 71 000; 71 267 rounds to 71 000. Only 69 978 rounds to 70 000. Answer: 69 978.",
      "hints": ["The number must lie between 69 500 and 70 499.", "Check which option falls inside that range."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 2 (69 978)."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Which of the following has the same value as \\(\\dfrac{2}{3} \\times 4\\)?",
      "answer0": "\\(\\dfrac{1}{3} \\times 2\\)",
      "answer1": "\\(\\dfrac{2 \\times 4}{3 \\times 4}\\)",
      "answer2": "\\(\\dfrac{2}{3} \\times \\dfrac{2}{3} \\times \\dfrac{2}{3} \\times \\dfrac{2}{3}\\)",
      "answer3": "\\(\\dfrac{2}{3} + \\dfrac{2}{3} + \\dfrac{2}{3} + \\dfrac{2}{3}\\)",
      "correct_answer": 3,
      "skill_id": 163,
      "difficulty_id": 2,
      "explanation": "Multiplying a fraction by 4 means adding it 4 times: \\(\\dfrac{2}{3} \\times 4 = \\dfrac{2}{3} + \\dfrac{2}{3} + \\dfrac{2}{3} + \\dfrac{2}{3}\\). Answer: option 4.",
      "hints": ["Multiplying by a whole number is repeated addition.", "\\(\\dfrac{2}{3}\\) added 4 times equals \\(\\dfrac{2}{3} \\times 4\\)."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 4."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Which of the following is equal to \\(4\\dfrac{5}{7}\\)?",
      "answer0": "\\(\\dfrac{20}{7}\\)",
      "answer1": "\\(\\dfrac{27}{7}\\)",
      "answer2": "\\(\\dfrac{33}{7}\\)",
      "answer3": "\\(\\dfrac{39}{7}\\)",
      "correct_answer": 2,
      "skill_id": 158,
      "difficulty_id": 1,
      "explanation": "Convert the mixed number to an improper fraction: \\(4\\dfrac{5}{7} = \\dfrac{4 \\times 7 + 5}{7} = \\dfrac{33}{7}\\). Answer: \\(\\dfrac{33}{7}\\).",
      "hints": ["Multiply the whole number by the denominator, then add the numerator.", "\\(4 \\times 7 + 5 = 33\\)."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 3 (33/7)."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "What is the value of \\(40 + \\dfrac{4}{10} + \\dfrac{4}{100}\\)?",
      "answer0": "44.04",
      "answer1": "40.44",
      "answer2": "40.404",
      "answer3": "40.044",
      "correct_answer": 1,
      "skill_id": 123,
      "difficulty_id": 2,
      "explanation": "\\(\\dfrac{4}{10} = 0.4\\) (tenths) and \\(\\dfrac{4}{100} = 0.04\\) (hundredths). So 40 + 0.4 + 0.04 = 40.44. Answer: 40.44.",
      "hints": ["\\(\\dfrac{4}{10}\\) is 4 tenths = 0.4.", "\\(\\dfrac{4}{100}\\) is 4 hundredths = 0.04."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 2 (40.44)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "Arrange the following from the heaviest to the lightest.<br>7.25 kg , 7 kg 55 g , \\(7\\dfrac{1}{3}\\) kg",
      "answer0": "\\(7\\dfrac{1}{3}\\) kg , 7.25 kg , 7 kg 55 g",
      "answer1": "\\(7\\dfrac{1}{3}\\) kg , 7 kg 55 g , 7.25 kg",
      "answer2": "7.25 kg , \\(7\\dfrac{1}{3}\\) kg , 7 kg 55 g",
      "answer3": "7 kg 55 g , 7.25 kg , \\(7\\dfrac{1}{3}\\) kg",
      "correct_answer": 0,
      "skill_id": 184,
      "difficulty_id": 2,
      "explanation": "Convert to kg: 7.25 kg; 7 kg 55 g = 7.055 kg; \\(7\\dfrac{1}{3}\\) kg \\(\\approx\\) 7.333 kg. Heaviest to lightest: 7.333 > 7.25 > 7.055, i.e. \\(7\\dfrac{1}{3}\\) kg, 7.25 kg, 7 kg 55 g. Answer: option 1.",
      "hints": ["Express every mass in kilograms first.", "55 g = 0.055 kg and \\(\\dfrac{1}{3} \\approx 0.333\\)."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 1. Mixed-number/compound-unit comparison so kept as MCQ."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "In the number line, what is the mixed number represented by Y?",
      "answer0": "\\(2\\dfrac{2}{3}\\)",
      "answer1": "\\(2\\dfrac{3}{4}\\)",
      "answer2": "\\(2\\dfrac{5}{7}\\)",
      "answer3": "\\(2\\dfrac{5}{8}\\)",
      "correct_answer": 3,
      "skill_id": 158,
      "difficulty_id": 2,
      "explanation": "The interval from 2 to 3 is divided into 8 equal parts. Y is at the 5th mark after 2, so Y = \\(2\\dfrac{5}{8}\\). Answer: \\(2\\dfrac{5}{8}\\).",
      "hints": ["Count the number of equal parts between 2 and 3.", "Y sits 5 small marks past 2 out of 8 parts."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q7.png",
      "image_page": 5,
      "image_bbox": [0.46, 0.12, 0.88, 0.22],
      "image_loc": "number line from 2 to 3 with arrow marked Y, right of the options",
      "notes": "Key: option 4 (2 5/8). Number line divided into 8 parts, Y at 5th mark."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "Nora is facing the park after she made a 225° turn in a clockwise direction. Which landmark was she facing at first?",
      "answer0": "Fire station",
      "answer1": "Library",
      "answer2": "School",
      "answer3": "Cinema",
      "correct_answer": 2,
      "skill_id": 452,
      "difficulty_id": 3,
      "explanation": "A 225° clockwise turn ends facing the park. To find the start, turn 225° anticlockwise from the park. The 8-point compass has landmarks 45° apart; 225° is 5 steps of 45°. Counting back 5 positions clockwise-to-anticlockwise from Park lands on School. Answer: School.",
      "hints": ["Each landmark is 45° apart on the 8-point diagram.", "225° = 5 × 45°; turn back 5 positions from the Park."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 5,
      "image_bbox": [0.22, 0.42, 0.72, 0.66],
      "image_loc": "8-point compass diagram with Nora at centre and 8 landmarks",
      "notes": "Key: option 3 (School)."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "In the figure, EF and GH are straight lines. \\(\\angle EOH = 134°\\) and \\(\\angle JOF = 63°\\). Find \\(\\angle GOJ\\).",
      "answer0": "71°",
      "answer1": "67°",
      "answer2": "63°",
      "answer3": "54°",
      "correct_answer": 0,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "\\(\\angle GOE\\) and \\(\\angle EOH\\) are angles on a straight line GH: \\(\\angle GOE = 180° - 134° = 46°\\). On straight line EF, \\(\\angle GOE + \\angle GOJ + \\angle JOF = 180°\\), so \\(\\angle GOJ = 180° - 46° - 63° = 71°\\). Answer: 71°.",
      "hints": ["Angles on a straight line add up to 180°.", "First find \\(\\angle GOE\\) using line GH."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q9.png",
      "image_page": 6,
      "image_bbox": [0.48, 0.10, 0.95, 0.35],
      "image_loc": "intersecting lines diagram with point O, rays to E F G H J, angles 134° and 63°",
      "notes": "Key: option 1 (71°)."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "What is the area of triangle XYZ?",
      "answer0": "15 cm²",
      "answer1": "21 cm²",
      "answer2": "25 cm²",
      "answer3": "35 cm²",
      "correct_answer": 1,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "The base ZY = 10 cm + 4 cm = 14 cm and the perpendicular height from X is 3 cm. Area = \\(\\dfrac{1}{2} \\times 14 \\times 3 = 21\\) cm². Answer: 21 cm².",
      "hints": ["The full base ZY is 10 + 4 = 14 cm.", "Area of a triangle = \\(\\dfrac{1}{2} \\times \\text{base} \\times \\text{height}\\)."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 6,
      "image_bbox": [0.16, 0.45, 0.78, 0.62],
      "image_loc": "triangle XYZ with base split 10 cm and 4 cm, height 3 cm, side 5 cm",
      "notes": "Key: option 2 (21 cm²). Base = 14 cm, height = 3 cm."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "The sides of a triangle are in the ratio 3 : 4 : 5. The longest side of the triangle is 40 cm. What is the length of the shortest side?",
      "answer0": "12 cm",
      "answer1": "16 cm",
      "answer2": "24 cm",
      "answer3": "32 cm",
      "correct_answer": 2,
      "skill_id": 182,
      "difficulty_id": 2,
      "explanation": "The longest side corresponds to 5 units = 40 cm, so 1 unit = 8 cm. The shortest side is 3 units = 3 × 8 = 24 cm. Answer: 24 cm.",
      "hints": ["The longest side is the 5-unit part.", "Find the value of 1 unit, then multiply by 3 for the shortest side."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 3 (24 cm)."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "The sum of 4 numbers is 960. One of the numbers is 150. What is the average of the other 3 numbers?",
      "answer0": "90",
      "answer1": "170",
      "answer2": "270",
      "answer3": "510",
      "correct_answer": 2,
      "skill_id": 203,
      "difficulty_id": 2,
      "explanation": "Sum of the other 3 numbers = 960 - 150 = 810. Average = 810 ÷ 3 = 270. Answer: 270.",
      "hints": ["Subtract 150 from the total first.", "Average = total of the 3 numbers ÷ 3."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 3 (270)."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "In the figure, CEF is an isosceles triangle and DEF is a straight line. Find \\(\\angle FCE\\).",
      "answer0": "54°",
      "answer1": "63°",
      "answer2": "65°",
      "answer3": "79°",
      "correct_answer": 0,
      "skill_id": 458,
      "difficulty_id": 3,
      "explanation": "In triangle CDE, exterior angle \\(\\angle CEF = \\angle CDE + \\angle DCE = 38° + 25° = 63°\\). Since CEF is isosceles with CE = CF, base angles \\(\\angle CEF = \\angle CFE = 63°\\). So \\(\\angle FCE = 180° - 63° - 63° = 54°\\). Answer: 54°.",
      "hints": ["The exterior angle \\(\\angle CEF\\) equals 38° + 25°.", "Base angles of an isosceles triangle are equal; angles of a triangle sum to 180°."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q13.png",
      "image_page": 7,
      "image_bbox": [0.22, 0.55, 0.70, 0.80],
      "image_loc": "isosceles triangle CEF with D on straight line DEF, angles 25° at C and 38° at D",
      "notes": "Key: option 1 (54°)."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "Marcus had $120. He spent $24. What percentage of his money did he spend?",
      "answer0": "20%",
      "answer1": "25%",
      "answer2": "60%",
      "answer3": "80%",
      "correct_answer": 0,
      "skill_id": 171,
      "difficulty_id": 1,
      "explanation": "Percentage spent = \\(\\dfrac{24}{120} \\times 100\\% = 20\\%\\). Answer: 20%.",
      "hints": ["Write the amount spent as a fraction of the total.", "\\(\\dfrac{24}{120} = \\dfrac{1}{5} = 20\\%\\)."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 1 (20%)."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "The figure has 9 unit cubes which are glued together to form a solid. The solid, including the base, is then painted red. How many of the 9 cubes have exactly four of their faces painted red?",
      "answer0": "5",
      "answer1": "2",
      "answer2": "3",
      "answer3": "4",
      "correct_answer": 2,
      "skill_id": 188,
      "difficulty_id": 3,
      "explanation": "Counting the exposed faces of each cube in the solid (including the base), exactly 3 of the 9 cubes have four faces painted red. Answer: 3.",
      "hints": ["Count how many faces of each cube are on the outside, including the bottom.", "Cubes with two adjacent neighbours have fewer exposed faces."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q15.png",
      "image_page": 8,
      "image_bbox": [0.32, 0.34, 0.58, 0.48],
      "image_loc": "stacked solid of 9 unit cubes",
      "notes": "Key: option 3 (answer value 3). Per printed key Q15 = 3 (option 3)."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "There were 700 people in a concert hall. 25% of the people left the concert hall during the interval. How many people left the concert hall? [?]",
      "answer0": "175",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 174,
      "difficulty_id": 1,
      "explanation": "25% of 700 = \\(\\dfrac{25}{100} \\times 700 = 175\\). 175 people left the concert hall.",
      "hints": ["Find 1% of 700 first.", "25% = \\(\\dfrac{25}{100} \\times 700\\)."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 175."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "Find the value of \\(376.2 \\div 90\\). Express your answer as a decimal. [?]",
      "answer0": "4.18",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 166,
      "difficulty_id": 2,
      "explanation": "\\(376.2 \\div 90 = 376.2 \\div 9 \\div 10 = 41.8 \\div 10 = 4.18\\). Answer: 4.18.",
      "hints": ["Divide by 9 first, then by 10.", "\\(376.2 \\div 9 = 41.8\\)."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 4.18."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "Find the value of \\(16 + 32 \\div (2 \\times 4)\\). [?]",
      "answer0": "20",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 155,
      "difficulty_id": 2,
      "explanation": "Work out the bracket first: \\(2 \\times 4 = 8\\). Then \\(32 \\div 8 = 4\\). Finally \\(16 + 4 = 20\\). Answer: 20.",
      "hints": ["Do the operation inside the brackets first.", "Then divide before adding (order of operations)."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 20."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "The usual price of a vacuum cleaner was $3100. During a sale, it was sold at a discount of 20%. What was the price of the vacuum cleaner during the sale?<br>Ans: $ [?]",
      "answer0": "2480",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 2,
      "explanation": "Discount = 20% of $3100 = \\(\\dfrac{20}{100} \\times 3100 = $620\\). Sale price = 3100 - 620 = $2480. Answer: $2480.",
      "hints": ["Find 20% of $3100 for the discount.", "Subtract the discount from the usual price."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Q19",
      "image_needed": true,
      "image_options": false,
      "image_file": "q19.png",
      "image_page": 10,
      "image_bbox": [0.56, 0.12, 0.92, 0.33],
      "image_loc": "On Sale! box showing vacuum cleaner, Usual Price $3100, Discount 20%",
      "notes": "Key: $2480. Figure is a promo box; answer entered as a number."
    },
    {
      "n": 20,
      "type_id": 1,
      "question": "9 boys shared 6 pizzas equally. What fraction of a pizza did each boy get? Express your answer in its simplest form.",
      "answer0": "\\(\\dfrac{2}{3}\\)",
      "answer1": "\\(\\dfrac{6}{9}\\)",
      "answer2": "\\(\\dfrac{3}{2}\\)",
      "answer3": "\\(\\dfrac{1}{6}\\)",
      "correct_answer": 0,
      "skill_id": 157,
      "difficulty_id": 1,
      "explanation": "Each boy gets \\(6 \\div 9 = \\dfrac{6}{9} = \\dfrac{2}{3}\\) of a pizza. Answer: \\(\\dfrac{2}{3}\\).",
      "hints": ["Sharing 6 pizzas among 9 boys means \\(6 \\div 9\\).", "Simplify \\(\\dfrac{6}{9}\\) by dividing top and bottom by 3."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Q20",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 2/3. Fraction answer so made MCQ."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "The figure is made up of 2 squares. The perimeter of the smaller square is 20 cm. The area of the shaded part is 39 cm². Find the length of one side of the bigger square.<br>Ans: [?] cm",
      "answer0": "8",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 137,
      "difficulty_id": 3,
      "explanation": "Side of smaller square = 20 ÷ 4 = 5 cm, so its area = 5 × 5 = 25 cm². Area of bigger square = shaded part + smaller square = 39 + 25 = 64 cm². Since 8 × 8 = 64, the side of the bigger square = 8 cm.",
      "hints": ["Find the side of the small square from its perimeter.", "Big square area = shaded area + small square area."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Q21",
      "image_needed": true,
      "image_options": false,
      "image_file": "q21.png",
      "image_page": 11,
      "image_bbox": [0.57, 0.26, 0.86, 0.48],
      "image_loc": "shaded larger square with unshaded smaller square inside, top side marked ?",
      "notes": "Key: 8 cm."
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "The ratio of the number of blue pens to the number of green pens is 8 : 3. There are 48 blue pens. Find the total number of pens. [?]",
      "answer0": "66",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 182,
      "difficulty_id": 2,
      "explanation": "8 units = 48 blue pens, so 1 unit = 6. Total = 8 + 3 = 11 units = 11 × 6 = 66 pens. Answer: 66.",
      "hints": ["Blue pens are 8 units = 48, so 1 unit = 6.", "Total units = 8 + 3 = 11."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Q22",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 66."
    },
    {
      "n": 23,
      "type_id": 0,
      "question": "The solid is made up of 11 unit cubes. Draw the front view and the top view of the solid on the grids.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 231,
      "difficulty_id": 2,
      "explanation": "Front view and top view are to be drawn on the dot grids (the printed key shows the shaded front and top views of the 11-cube solid). This is a draw-on-grid task.",
      "hints": [],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Q23",
      "image_needed": true,
      "image_options": false,
      "image_file": "q23.png",
      "image_page": 12,
      "image_bbox": [0.34, 0.12, 0.62, 0.33],
      "image_loc": "isometric solid of 11 unit cubes with Top/Front/Side view arrows",
      "notes": "Drawing task (draw front + top views on grid) — no app question type, type_id 0, skipped on insert. Answer: front and top views drawn per key."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "Mengxuan studied from 10.50 a.m. to 1.35 p.m. How much time did Mengxuan spend studying? Give your answer in h and min.<br>Ans: [?] h [?] min",
      "answer0": "2",
      "answer1": "45",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 92,
      "difficulty_id": 2,
      "explanation": "From 10.50 a.m. to 12.50 p.m. is 2 h; from 12.50 p.m. to 1.35 p.m. is 45 min. Total = 2 h 45 min.",
      "hints": ["Count whole hours from 10.50 a.m. first.", "Then add the remaining minutes to 1.35 p.m."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Q24",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 2 h 45 min. Two answer blanks (h and min)."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "In the figure, find \\(\\angle y\\).<br>Ans: [?]°",
      "answer0": "114",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "Angles at a point add to 360°. The given angles are 57°, 99° and a right angle (90°). So \\(\\angle y = 360° - 99° - 90° - 57° = 114°\\). Answer: 114°.",
      "hints": ["Angles at a point add up to 360°.", "Subtract the 57°, 90° and 99° angles from 360°."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Q25",
      "image_needed": true,
      "image_options": false,
      "image_file": "q25.png",
      "image_page": 13,
      "image_bbox": [0.14, 0.55, 0.42, 0.78],
      "image_loc": "two lines crossing with angles y, 57° and 99° marked at the point",
      "notes": "Key: 114° (360 - 99 - 90 - 57). The 90° comes from a right angle in the figure."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "A shop baked 120 tarts. \\(\\dfrac{3}{4}\\) of them were fruit tarts. After some fruit tarts were sold, there were 38 fruit tarts left. How many fruit tarts were sold? [?]",
      "answer0": "52",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "Fruit tarts = \\(\\dfrac{3}{4} \\times 120 = 90\\). Fruit tarts sold = 90 - 38 = 52. Answer: 52.",
      "hints": ["Find \\(\\dfrac{3}{4}\\) of 120 to get the number of fruit tarts.", "Subtract the 38 left from the total fruit tarts."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Q26",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 52."
    },
    {
      "n": 27,
      "type_id": 0,
      "question": "The table shows the number of pets each student had in a group. Part of the table is covered by an ink blot. There were 40 students who had at least 2 pets. Each statement is either true, false or not possible to tell from the information given.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 147,
      "difficulty_id": 3,
      "explanation": "At least 2 pets means 2, 3 and 4 pets total 40, so students with 3 or 4 pets = 40 - 12 = 28. (1) 'There were 50 students with at least 1 pet' → True (10 + 40 = 50). (2) 'There were 77 students in the group' → False (15 + 50 = 65, not 77). (3) 'The number of students with 3 pets equalled the number with 4 pets' → Not possible to tell (28 split is unknown).",
      "hints": [],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Q27",
      "image_needed": true,
      "image_options": false,
      "image_file": "q27.png",
      "image_page": 14,
      "image_bbox": [0.18, 0.46, 0.88, 0.56],
      "image_loc": "pets table: 0 pets=15, 1 pet=10, 2 pets=12, 3 and 4 pets under ink blot",
      "notes": "Tick-table (True / False / Not possible to tell) — no app question type, type_id 0, skipped on insert. Key: True, False, Not possible to tell."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "Jasper wrote the number 3691847652 on a strip of paper. He cut the strip of paper twice and obtained 3 different numbers. He then added the 3 different numbers. What was the smallest possible sum he could get from the 3 different numbers? [?]",
      "answer0": "2868",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "To make the sum smallest, keep the high place-value digits in short numbers. Splitting 3691847652 into 369, 1847 and 652 gives 369 + 1847 + 652 = 2868, the smallest possible sum. Answer: 2868.",
      "hints": ["Make the numbers have as few digits in high place values as possible.", "The printed key uses 1847 + 652 + 369."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Q28",
      "image_needed": true,
      "image_options": false,
      "image_file": "q28.png",
      "image_page": 15,
      "image_bbox": [0.32, 0.12, 0.66, 0.21],
      "image_loc": "boxed number 3691847652 with scissors below",
      "notes": "Key: 1847 + 652 + 369 = 2868. Number is shown in a box on the strip."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "In the figure, QRST is a trapezium. QR is parallel to TS and \\(\\angle TRS = 46°\\). Find \\(\\angle QRT\\).<br>Ans: [?]°",
      "answer0": "44",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 200,
      "difficulty_id": 2,
      "explanation": "\\(\\angle QRS = 90°\\) (right angle at R, from the figure). \\(\\angle QRT = \\angle QRS - \\angle TRS = 90° - 46° = 44°\\). Answer: 44°.",
      "hints": ["The angle at R (\\(\\angle QRS\\)) is a right angle, 90°.", "\\(\\angle QRT = 90° - 46°\\)."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Q29",
      "image_needed": true,
      "image_options": false,
      "image_file": "q29.png",
      "image_page": 15,
      "image_bbox": [0.14, 0.55, 0.52, 0.80],
      "image_loc": "trapezium QRST with diagonal TR, angle 46° marked at R",
      "notes": "Key: 180 - 90 = 90; 90 - 46 = 44°."
    },
    {
      "n": 30,
      "type_id": 2,
      "question": "A square WXYZ is divided into 7 identical small squares and 3 triangles. The area of each small square is 16 cm². What is the total area of the shaded triangles?<br>Ans: [?] cm²",
      "answer0": "72",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Each small square has area 16 cm², so its side = 4 cm. The big square WXYZ has side 3 small squares = 12 cm. The shaded triangles together form a triangle of base 12 cm and height 12 cm: area = \\(\\dfrac{1}{2} \\times 12 \\times 12 = 72\\) cm². Answer: 72 cm².",
      "hints": ["Side of one small square = \\(\\sqrt{16} = 4\\) cm.", "The big square side = 12 cm; shaded area = \\(\\dfrac{1}{2} \\times 12 \\times 12\\)."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Q30",
      "image_needed": true,
      "image_options": false,
      "image_file": "q30.png",
      "image_page": 16,
      "image_bbox": [0.33, 0.15, 0.62, 0.36],
      "image_loc": "square WXYZ divided into 7 small squares and 3 shaded triangles",
      "notes": "Key: 12 × 12 × 1/2 = 72 cm²."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "Meiling had 3.75 m of ribbon at first. She used 48 cm of it. How many metres of ribbon had she left? [?]",
      "answer0": "3.27",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 184,
      "difficulty_id": 2,
      "explanation": "48 cm = 0.48 m. Ribbon left = 3.75 - 0.48 = 3.27 m. Answer: 3.27 m.",
      "hints": ["Convert 48 cm to metres (0.48 m) first.", "Subtract from 3.75 m."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Paper 2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q1. Key: 3.27 m (375 - 48 = 327 cm = 3.27 m)."
    },
    {
      "n": 32,
      "type_id": 1,
      "question": "Mrs Tan bought \\(\\dfrac{5}{7}\\) kg of onions. She used \\(\\dfrac{3}{4}\\) of them. How many kilograms of onions did Mrs Tan use?",
      "answer0": "\\(\\dfrac{15}{28}\\)",
      "answer1": "\\(\\dfrac{8}{11}\\)",
      "answer2": "\\(\\dfrac{15}{11}\\)",
      "answer3": "\\(\\dfrac{20}{21}\\)",
      "correct_answer": 0,
      "skill_id": 161,
      "difficulty_id": 2,
      "explanation": "Onions used = \\(\\dfrac{3}{4} \\times \\dfrac{5}{7} = \\dfrac{15}{28}\\) kg. Answer: \\(\\dfrac{15}{28}\\) kg.",
      "hints": ["'\\(\\dfrac{3}{4}\\) of \\(\\dfrac{5}{7}\\)' means \\(\\dfrac{3}{4} \\times \\dfrac{5}{7}\\).", "Multiply numerators and denominators."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Paper 2 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q2. Key: 15/28 kg. Fraction answer so made MCQ."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "A tap takes 3 min to fill 9 identical bottles. At the same rate, how long will it take to fill 153 such bottles?<br>Ans: [?] min",
      "answer0": "51",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "9 bottles take 3 min, so 1 bottle takes \\(\\dfrac{3}{9}\\) min. 153 bottles take \\(\\dfrac{3}{9} \\times 153 = 51\\) min. Answer: 51 min.",
      "hints": ["Find the time for 1 bottle: \\(3 \\div 9\\) min.", "Multiply by 153."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Paper 2 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q3. Key: 51 min."
    },
    {
      "n": 34,
      "type_id": 1,
      "question": "The parking charges at a mall are: First Hour $2.50; Every additional half hour or part thereof $1.30. Josh paid $9 for parking at the shopping mall. At most, how long did he park his car there?",
      "answer0": "\\(3\\dfrac{1}{2}\\) h",
      "answer1": "3 h",
      "answer2": "4 h",
      "answer3": "\\(4\\dfrac{1}{2}\\) h",
      "correct_answer": 0,
      "skill_id": 93,
      "difficulty_id": 3,
      "explanation": "After the first hour ($2.50), the remaining money is 9 - 2.50 = $6.50. Each additional half hour costs $1.30; $6.50 ÷ 1.30 = 5 half-hours = 2.5 h. Total = 1 h + 2.5 h = \\(3\\dfrac{1}{2}\\) h. Answer: \\(3\\dfrac{1}{2}\\) h.",
      "hints": ["Pay $2.50 for the first hour, then see how much is left.", "Each $1.30 buys another half hour."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Paper 2 Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q34.png",
      "image_page": 19,
      "image_bbox": [0.14, 0.13, 0.74, 0.22],
      "image_loc": "PARKING CHARGES table: First Hour $2.50, additional half hour $1.30",
      "notes": "Paper 2 Q4. Key: 3 1/2 h. Mixed-number answer so made MCQ."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "The table shows the number of people who signed up for a cooking class — May: 64, June: 0, July: 82, August: 78. What was the average number of people who signed up the cooking class from May to August? [?]",
      "answer0": "56",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 203,
      "difficulty_id": 2,
      "explanation": "Total = 64 + 0 + 82 + 78 = 224. Average = 224 ÷ 4 = 56. Answer: 56.",
      "hints": ["Add all four months' figures (June is 0).", "Divide the total by 4 months."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Paper 2 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q5. Key: 56. Table values stated in stem."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "An equilateral triangular piece of paper was folded along the dotted line. Find \\(\\angle x\\).<br>Ans: [?]°",
      "answer0": "102",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "Each angle of the equilateral triangle is 60°. After folding, the folded-over angle is 24°, so the remaining angle at the apex is 60° - 24° = 36°, which splits into two equal parts of 36° ÷ 2 = 18°. Then \\(\\angle x = 180° - 60° - 18° = 102°\\). Answer: 102°.",
      "hints": ["Every angle of an equilateral triangle is 60°.", "Use 60 - 24 = 36, then halve it before applying the 180° angle sum."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Paper 2 Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q36.png",
      "image_page": 20,
      "image_bbox": [0.24, 0.25, 0.78, 0.46],
      "image_loc": "equilateral triangle with fold along dotted line and result showing 24° and x",
      "notes": "Paper 2 Q6. Key: 60 - 24 = 36; 36 ÷ 2 = 18; 180 - 60 - 18 = 102°."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "The mass of a crate when filled with 50 apples was 15 kg. The mass of the same crate when filled with 20 apples was 9 kg. What was the mass of the empty crate?<br>Ans: [?] kg",
      "answer0": "5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "The difference of 50 - 20 = 30 apples accounts for 15 - 9 = 6 kg, so 30 apples = 6 kg and 10 apples = 2 kg, hence 20 apples = 4 kg. Empty crate = 9 - 4 = 5 kg. Answer: 5 kg.",
      "hints": ["The extra 30 apples add 6 kg of mass.", "Find the mass of 20 apples, then subtract from 9 kg."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Paper 2 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q7. Key: 5 kg."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "\\(\\dfrac{3}{5}\\) of Patrick's money is equal to \\(\\dfrac{1}{3}\\) of Joe's money. Patrick has $2472 less than Joe. How much money do they have altogether?<br>Ans: $ [?]",
      "answer0": "8652",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "\\(\\dfrac{3}{5}P = \\dfrac{1}{3}J\\) means \\(P : J = 5 : 9\\) (since \\(\\dfrac{3}{5} \\times 5 = 3\\) and \\(\\dfrac{1}{3} \\times 9 = 3\\)). The difference 9 - 5 = 4 units = $2472, so 1 unit = $618. Total = 5 + 9 = 14 units = 14 × 618 = $8652. Answer: $8652.",
      "hints": ["Make the two expressions equal to find the ratio P : J = 5 : 9.", "The 4-unit difference equals $2472."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Paper 2 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q8. Key: 4u = 2472, 1u = 618, total 14u = $8652."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "In the figure, EF is 34 cm. Find the area of the shaded part.<br>Ans: [?] cm²",
      "answer0": "1146",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "The big triangle has base 54 cm and height 84 cm: area = \\(\\dfrac{1}{2} \\times 54 \\times 84 = 2268\\) cm². The two unshaded triangles each have base 17 cm (half of EF = 34) and height (84 - 18) = 66 cm... Per the printed key: \\(\\dfrac{1}{2} \\times 54 \\times 84 = 2268\\); the unshaded pieces total \\(56.1 \\times 2 = 1122\\); shaded = 2268 - 1122 = 1146 cm². Answer: 1146 cm².",
      "hints": ["Find the area of the whole big triangle (base 54, height 84).", "Subtract the two unshaded inner triangles."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Paper 2 Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q39.png",
      "image_page": 22,
      "image_bbox": [0.30, 0.13, 0.72, 0.45],
      "image_loc": "large triangle with EF=34 cm midway, height 84 cm, base 54 cm, inner height 18 cm, shaded region",
      "notes": "Paper 2 Q9. Key: 2268 - 1122 = 1146 cm²."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "At 8 a.m., Machine A started printing stickers. Machine B started printing 1 minute later than Machine A. For every minute, Machine B printed 30 fewer stickers than Machine A. Both machines stopped printing at 8.05 a.m. A total of 600 stickers were printed. How many stickers did Machine A print? [?]",
      "answer0": "400",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Machine A ran 5 min, Machine B ran 4 min. Per the printed key: 600 ÷ 120 = 5 (i.e. each 'minute-unit' = 5 stickers across the combined 9 minute-runs adjusted for the 30 fewer), giving Machine A's rate, then A printed 80 per minute × 5 = 400. Answer: 400.",
      "hints": ["Machine A prints for 5 minutes; Machine B for 4 minutes.", "Set up the total: 5 minutes of A + 4 minutes of (A - 30) = 600."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Paper 2 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q10. Key: 600 ÷ 120 = ...; 720 ÷ 9 = 80; 80 × 5 = 400."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "In the figure, DE is parallel to GF and DE = EG = EF. \\(\\angle EDG = 61°\\). Find \\(\\angle GEF\\). [?]",
      "answer0": "64",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "Triangle DEG is isosceles (DE = EG) with base angles \\(\\angle EDG = \\angle EGD = 61°\\)... Per the printed key: angle \\(\\angle DEG = 180° - 61° - 61° = 58°\\), and using the parallel lines and EG = EF, \\(\\angle GEF = 180° - 58° - 58° = 64°\\). Answer: 64°.",
      "hints": ["DE = EG makes triangle DEG isosceles with two 61° angles.", "Use parallel lines (DE // GF) and EG = EF to find \\(\\angle GEF\\)."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Paper 2 Q11a",
      "image_needed": true,
      "image_options": false,
      "image_file": "q41.png",
      "image_page": 24,
      "image_bbox": [0.24, 0.10, 0.66, 0.30],
      "image_loc": "parallelogram-like figure DEFG with diagonal EG, angle 61° at D",
      "notes": "Paper 2 Q11(a). Key: 180 - 58 - 58 = 64°. Part (b) 'is/is not rhombus' is a circle-the-word task, not ingested."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "The line graph shows the number of bags sold each month from January to June. 224 bags were sold in February. How many bags were sold in April? [?]",
      "answer0": "168",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 147,
      "difficulty_id": 3,
      "explanation": "From the line graph, February = 8 units = 224 bags, so 1 unit = 28 bags. April = 6 units = 6 × 28 = 168 bags. Answer: 168.",
      "hints": ["Find the value of 1 grid unit from February (8 units = 224).", "Read April's height in units and multiply."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Paper 2 Q12c",
      "image_needed": true,
      "image_options": false,
      "image_file": "q42.png",
      "image_page": 25,
      "image_bbox": [0.20, 0.12, 0.74, 0.32],
      "image_loc": "line graph of bags sold Jan-Jun",
      "notes": "Paper 2 Q12(c). Key: 8u = 224, 1u = 28, 6u = 168. Parts (a) May & June and (b) Feb are word answers, not ingested separately."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "A rectangular tank measuring 150 cm by 120 cm by 50 cm was completely filled with water. What is the capacity of the rectangular tank?<br>Ans: [?] cm³",
      "answer0": "900000",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 190,
      "difficulty_id": 2,
      "explanation": "Capacity = length × breadth × height = 150 × 120 × 50 = 900 000 cm³. Answer: 900 000 cm³.",
      "hints": ["Volume of a cuboid = length × breadth × height.", "150 × 120 × 50."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Paper 2 Q13a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q13(a). Key: 900000 cm³."
    },
    {
      "n": 44,
      "type_id": 1,
      "question": "A rectangular tank measuring 150 cm by 120 cm by 50 cm was completely filled with water. Sam drained out the water from the tank at a rate of 12 litres per minute. At 11.45 am, Sam found that there were only 420 litres of water left in the tank. At what time would the tank be \\(\\dfrac{1}{5}\\) full?",
      "answer0": "12.05 pm",
      "answer1": "11.55 am",
      "answer2": "12.15 pm",
      "answer3": "12.00 pm",
      "correct_answer": 0,
      "skill_id": 193,
      "difficulty_id": 3,
      "explanation": "Capacity = 900 000 cm³ = 900 L. \\(\\dfrac{1}{5}\\) full = 180 L. Water to drain from 420 L down to 180 L = 240 L; at 12 L/min that takes 240 ÷ 12 = 20 min. From 11.45 am + 20 min = 12.05 pm. Answer: 12.05 pm.",
      "hints": ["\\(\\dfrac{1}{5}\\) of 900 L is 180 L.", "Time to drain (420 - 180) L at 12 L/min, added to 11.45 am."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Paper 2 Q13b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q13(b). Key: 12.05 pm. Time-of-day answer so made MCQ."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "Some lamp posts were placed in a straight row at equal distances apart. The distance between the 1st and the 6th lamp post was 90.5 m. The distance between the 2nd and the last lamp post was 307.7 m. How many lamp posts were there altogether? [?]",
      "answer0": "19",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "From the 1st to the 6th post there are 5 gaps: 1 gap = 90.5 ÷ 5 = 18.1 m. From the 2nd to the last post is 307.7 m, which is 307.7 ÷ 18.1 = 17 gaps, so the last post is the (2 + 17) = 19th. There were 19 lamp posts altogether. Answer: 19.",
      "hints": ["1st to 6th post = 5 equal gaps, so find one gap.", "Count the gaps from the 2nd post to the last, then add."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Paper 2 Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q14. Key: 1u = 18.1; 307.7 ÷ 18.1 = 17; 17 + 2 = 19."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "Tim had a total of 1648 blue and red paper cranes. He had 132 more blue than red paper cranes. He gave away half of his blue paper cranes and folded more red paper cranes. After that, he had four times as many red paper cranes as blue paper cranes. How many red paper cranes did Tim have at first? [?]",
      "answer0": "758",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Blue + Red = 1648 and Blue - Red = 132. Adding: 2 × Blue = 1648 + 132 = 1780... using the printed key: blue at first = (1648 + 132) ÷ 2 = 1516 ÷ 2 is for red. Red at first = (1648 - 132) ÷ 2 = 758. Answer: 758.",
      "hints": ["Use total = 1648 and difference = 132.", "Red = (1648 - 132) ÷ 2."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Paper 2 Q15a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q15(a). Key prints 1648+132=1516 then /2=758 for red at first."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "Tim had a total of 1648 blue and red paper cranes. He had 132 more blue than red paper cranes. He gave away half of his blue paper cranes and folded more red paper cranes. After that, he had four times as many red paper cranes as blue paper cranes. How many more red paper cranes did Tim fold? [?]",
      "answer0": "1022",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Blue at first = 1648 - 758 = 890. After giving away half, blue = 890 ÷ 2 = 445. Red after = 4 × 445 = 1780. Red folded = 1780 - 758 = 1022. Answer: 1022.",
      "hints": ["Blue left after giving away half = 890 ÷ 2.", "New red = 4 × (blue left); subtract red at first."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Paper 2 Q15b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q15(b). Key: 890÷2=445; 445×4=1780; 1780-758=1022."
    },
    {
      "n": 48,
      "type_id": 2,
      "question": "Weili spent \\(\\dfrac{3}{7}\\) of her money on 6 stalks of roses and 6 stalks of tulips. She spent \\(\\dfrac{1}{4}\\) of her remaining money on 10 stalks of daisies. Each stalk of tulip cost 7 times as much as each stalk of rose. Each stalk of daisy cost $0.30 more than each stalk of rose. How much did each stalk of tulip cost?<br>Ans: $ [?]",
      "answer0": "3.50",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Per the printed key: each rose cost $0.50 and each tulip cost 7 times as much, so each tulip = $0.50 × 7 = $3.50. Answer: $3.50.",
      "hints": ["Each tulip costs 7 times a rose.", "Once you find the rose price ($0.50), multiply by 7."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Paper 2 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q16. Key: $0.50 (rose) × 7 = $3.50 per tulip."
    },
    {
      "n": 49,
      "type_id": 2,
      "question": "Esther spent $558 on 4 similar skirts and 3 similar dresses. She wanted to buy another similar dress but she was short of $53. In the end, she bought another similar skirt and had $28 left. How much more did each dress cost than each skirt?<br>Ans: $ [?]",
      "answer0": "81",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "After spending $558 she was short $53 for a dress but had $28 left after buying a skirt instead. The difference between a dress and a skirt = 53 + 28 = $81. Answer: $81.",
      "hints": ["She was $53 short for a dress but had $28 spare after a skirt.", "Dress - skirt = 53 + 28."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Paper 2 Q17a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q17(a). Key: 53 + 28 = $81."
    },
    {
      "n": 50,
      "type_id": 2,
      "question": "Esther spent $558 on 4 similar skirts and 3 similar dresses. She wanted to buy another similar dress but she was short of $53. In the end, she bought another similar skirt and had $28 left. How much money did Esther have at first?<br>Ans: $ [?]",
      "answer0": "631",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Each dress costs $81 more than each skirt. 3 dresses = 3 × 81 = $243 more than 3 skirts, so 4 skirts + 3 dresses ($558) gives the skirt price; one skirt = (558 - 243) ÷ 7 = $45. She had at first = 558 + 45 (another skirt) + 28 left = $631. Answer: $631.",
      "hints": ["Find one skirt's price: (558 - 3×81) ÷ 7 = $45.", "At first = $558 + one more skirt + $28 left."],
      "source": "Ai Tong 2024 P5 End-of-Year Exam Paper 2 Q17b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q17(b). Key: 81×3=243; 558-243=315; 315÷7=45; 558+45+28=$631."
    }
  ]
}