{
  "paper": {
    "school": "Nanyang",
    "year": 2023,
    "level": "P5",
    "label": "End-of-Year Exam",
    "source_prefix": "Nanyang 2023 P5 End-of-Year Exam",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "In 5.687, which digit is in the hundredths place?",
      "answer0": "5",
      "answer1": "6",
      "answer2": "7",
      "answer3": "8",
      "correct_answer": 3,
      "skill_id": 123,
      "difficulty_id": 1,
      "explanation": "Place values after the decimal point: 6 is tenths, 8 is hundredths, 7 is thousandths. So the hundredths digit is 8.",
      "hints": ["The first digit after the decimal point is tenths.", "Hundredths is the second digit after the decimal point."],
      "source": "Nanyang 2023 P5 End-of-Year Exam Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Which of the following is the same as 23 kg 52 g?",
      "answer0": "23.025 kg",
      "answer1": "23.052 kg",
      "answer2": "23.502 kg",
      "answer3": "23.520 kg",
      "correct_answer": 1,
      "skill_id": 184,
      "difficulty_id": 1,
      "explanation": "1 kg = 1000 g, so 52 g = 0.052 kg. Therefore 23 kg 52 g = 23.052 kg.",
      "hints": ["1000 g make 1 kg.", "52 g out of 1000 is 0.052 kg."],
      "source": "Nanyang 2023 P5 End-of-Year Exam Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Ming Xuan bought 42 oranges, 28 mangoes and 14 kiwis from a fruit store. What was the ratio of the number of oranges to the number of mangoes to the number of kiwis that he bought? Express your answer in its simplest form.",
      "answer0": "2 : 3 : 1",
      "answer1": "2 : 4 : 6",
      "answer2": "3 : 2 : 1",
      "answer3": "6 : 4 : 2",
      "correct_answer": 2,
      "skill_id": 179,
      "difficulty_id": 2,
      "explanation": "42 : 28 : 14. Divide each term by the common factor 14: 42 ÷ 14 = 3, 28 ÷ 14 = 2, 14 ÷ 14 = 1. So the ratio is 3 : 2 : 1.",
      "hints": ["Find the largest number that divides 42, 28 and 14.", "Divide every term by 14."],
      "source": "Nanyang 2023 P5 End-of-Year Exam Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "A machine seals 120 fishball packets in 60 seconds. At this rate, how many fishball packets can it seal in 30 minutes?",
      "answer0": "3600",
      "answer1": "360",
      "answer2": "60",
      "answer3": "40",
      "correct_answer": 0,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "In 60 seconds (1 minute) it seals 120 packets. 30 minutes × 120 = 3600 packets.",
      "hints": ["60 seconds is 1 minute, so it seals 120 packets per minute.", "Multiply 120 by 30 minutes."],
      "source": "Nanyang 2023 P5 End-of-Year Exam Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "Arul had 240 stamps. He gave 60 stamps to his sister. What percentage of his stamps did Arul give to his sister?",
      "answer0": "20%",
      "answer1": "25%",
      "answer2": "75%",
      "answer3": "80%",
      "correct_answer": 1,
      "skill_id": 171,
      "difficulty_id": 1,
      "explanation": "Fraction given = \\(\\dfrac{60}{240}=\\dfrac{1}{4}\\). As a percentage, \\(\\dfrac{1}{4}\\times 100\\% = 25\\%\\).",
      "hints": ["Write the stamps given as a fraction of the total.", "Convert the fraction to a percentage by multiplying by 100%."],
      "source": "Nanyang 2023 P5 End-of-Year Exam Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "Thomas had $1200. He spent 35% of his money on food. How much money did he spend on food?",
      "answer0": "$180",
      "answer1": "$360",
      "answer2": "$420",
      "answer3": "$780",
      "correct_answer": 2,
      "skill_id": 174,
      "difficulty_id": 1,
      "explanation": "35% of $1200 = \\(\\dfrac{35}{100}\\times 1200 = 420\\). He spent $420 on food.",
      "hints": ["35% means 35 out of every 100.", "Multiply 1200 by 0.35."],
      "source": "Nanyang 2023 P5 End-of-Year Exam Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "Identify the line parallel to line AB.",
      "answer0": "CD",
      "answer1": "EF",
      "answer2": "GH",
      "answer3": "JK",
      "correct_answer": 3,
      "skill_id": 100,
      "difficulty_id": 2,
      "explanation": "Line AB slopes downwards from upper-right to lower-left. Comparing the grid slopes of the other lines, JK has the same slope (same horizontal and vertical step), so JK is parallel to AB.",
      "hints": ["Parallel lines have the same slant/slope.", "Count the grid steps across and down for each line and compare with AB."],
      "source": "Nanyang 2023 P5 End-of-Year Exam Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q7.png",
      "image_page": 5,
      "image_bbox": [0.20, 0.13, 0.82, 0.43],
      "image_loc": "grid of labelled line segments, upper-middle of page",
      "notes": "Answer key: JK (option 4). Figure-based; crop the grid only."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "Find the area of the shaded triangle ABD.",
      "answer0": "42 cm²",
      "answer1": "52.5 cm²",
      "answer2": "54 cm²",
      "answer3": "84 cm²",
      "correct_answer": 1,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "Triangle ABD has base AD = 15 cm and the perpendicular height AB = 7 cm. Area = \\(\\dfrac{1}{2}\\times 15\\times 7 = 52.5\\) cm².",
      "hints": ["Use Area = \\(\\dfrac{1}{2}\\times\\) base \\(\\times\\) height.", "Base AD = 15 cm, perpendicular height = 7 cm."],
      "source": "Nanyang 2023 P5 End-of-Year Exam Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 6,
      "image_bbox": [0.22, 0.10, 0.78, 0.30],
      "image_loc": "triangle ABCD diagram below the question",
      "notes": "Answer key: 52.5 cm² (option 2)."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "In the figure, how many of the six marked angles are more than 90°?",
      "answer0": "6",
      "answer1": "2",
      "answer2": "3",
      "answer3": "4",
      "correct_answer": 1,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "Inspecting the six marked angles in the concave figure, only 2 of them open wider than a right angle (more than 90°). The rest are 90° or less.",
      "hints": ["A right angle is exactly 90°.", "Compare each marked angle with a square corner."],
      "source": "Nanyang 2023 P5 End-of-Year Exam Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q9.png",
      "image_page": 7,
      "image_bbox": [0.30, 0.13, 0.80, 0.38],
      "image_loc": "concave (arrow-like) figure with six marked angles",
      "notes": "Answer key: 2 (option 2). Figure-count question; crop the whole shape so all six marked angles are visible."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "The figure shows a solid made up of unit cubes. How many unit cubes are needed to make the solid?",
      "answer0": "10",
      "answer1": "12",
      "answer2": "15",
      "answer3": "17",
      "correct_answer": 0,
      "skill_id": 188,
      "difficulty_id": 2,
      "explanation": "Counting the unit cubes in the staircase solid (including the hidden ones supporting the upper cubes) gives a total of 10 unit cubes.",
      "hints": ["Count layer by layer.", "Remember to include cubes hidden behind the front ones."],
      "source": "Nanyang 2023 P5 End-of-Year Exam Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 8,
      "image_bbox": [0.30, 0.13, 0.72, 0.40],
      "image_loc": "solid of stacked unit cubes, centre of page",
      "notes": "Answer key: 10 (option 1). Count-to-verify; crop must show the whole solid."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "Arrange the following fractions from the smallest to the largest.<br>\\(\\dfrac{8}{9}\\), \\(\\dfrac{3}{7}\\), \\(\\dfrac{4}{5}\\)",
      "answer0": "\\(\\dfrac{8}{9},\\ \\dfrac{3}{7},\\ \\dfrac{4}{5}\\)",
      "answer1": "\\(\\dfrac{8}{9},\\ \\dfrac{4}{5},\\ \\dfrac{3}{7}\\)",
      "answer2": "\\(\\dfrac{3}{7},\\ \\dfrac{4}{5},\\ \\dfrac{8}{9}\\)",
      "answer3": "\\(\\dfrac{3}{7},\\ \\dfrac{8}{9},\\ \\dfrac{4}{5}\\)",
      "correct_answer": 2,
      "skill_id": 158,
      "difficulty_id": 2,
      "explanation": "As decimals: \\(\\dfrac{3}{7}\\approx 0.43\\), \\(\\dfrac{4}{5}=0.8\\), \\(\\dfrac{8}{9}\\approx 0.89\\). Smallest to largest: \\(\\dfrac{3}{7},\\ \\dfrac{4}{5},\\ \\dfrac{8}{9}\\).",
      "hints": ["Convert each fraction to a decimal to compare.", "0.43 < 0.8 < 0.89."],
      "source": "Nanyang 2023 P5 End-of-Year Exam Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Converted to MCQ because options are fraction sequences (FIB must be integers/decimals)."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "Find the average of the following 5 numbers.<br>23, 23, 18, 16, 0",
      "answer0": "23",
      "answer1": "20",
      "answer2": "18",
      "answer3": "16",
      "correct_answer": 3,
      "skill_id": 203,
      "difficulty_id": 2,
      "explanation": "Total = 23 + 23 + 18 + 16 + 0 = 80. Average = 80 ÷ 5 = 16.",
      "hints": ["Average = total ÷ number of items.", "Add all five numbers first, then divide by 5."],
      "source": "Nanyang 2023 P5 End-of-Year Exam Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Numbers shown in five boxes in the paper; transcribed into the stem."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "A factory produces 1505 kg of flour a day. The flour is packed equally into 50 packs. How much does each pack of flour weigh?",
      "answer0": "30.1 kg",
      "answer1": "31 kg",
      "answer2": "300.1 kg",
      "answer3": "301 kg",
      "correct_answer": 0,
      "skill_id": 166,
      "difficulty_id": 2,
      "explanation": "1505 kg ÷ 50 = 30.1 kg per pack.",
      "hints": ["Divide the total mass by the number of packs.", "1505 ÷ 50 = 30.1."],
      "source": "Nanyang 2023 P5 End-of-Year Exam Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "At a funfair, there were 270 people. \\(\\dfrac{2}{3}\\) of them were children. \\(\\dfrac{2}{5}\\) of the children were girls and the rest were boys. How many boys were there at the funfair?",
      "answer0": "180",
      "answer1": "162",
      "answer2": "108",
      "answer3": "72",
      "correct_answer": 2,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "Children = \\(\\dfrac{2}{3}\\times 270 = 180\\). Boys = \\(\\dfrac{3}{5}\\) of the children = \\(\\dfrac{3}{5}\\times 180 = 108\\).",
      "hints": ["First find the number of children.", "If 2/5 are girls, then 3/5 are boys."],
      "source": "Nanyang 2023 P5 End-of-Year Exam Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "A chef cooked some soup for 200 guests. Each guest was served 0.78 ℓ of the soup. How much soup did the chef cook?",
      "answer0": "14.6 ℓ",
      "answer1": "15.6 ℓ",
      "answer2": "146 ℓ",
      "answer3": "156 ℓ",
      "correct_answer": 3,
      "skill_id": 167,
      "difficulty_id": 1,
      "explanation": "200 × 0.78 ℓ = 156 ℓ.",
      "hints": ["Multiply the amount per guest by the number of guests.", "200 × 0.78 = 156."],
      "source": "Nanyang 2023 P5 End-of-Year Exam Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Find the value of \\(198 + 35 \\div 7 - (35 + 8 \\div 4 \\times 2)\\).<br>[?]",
      "answer0": "164",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 155,
      "difficulty_id": 2,
      "explanation": "Work inside the brackets first: \\(8\\div 4\\times 2 = 2\\times 2 = 4\\), so \\(35 + 4 = 39\\). Then \\(35\\div 7 = 5\\). So \\(198 + 5 - 39 = 203 - 39 = 164\\).",
      "hints": ["Do brackets first, then × and ÷ from left to right, then + and −.", "Inside the bracket: 8 ÷ 4 × 2 = 4, giving 39."],
      "source": "Nanyang 2023 P5 End-of-Year Exam Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "Find the value of \\(5 \\div 8\\). Give your answer as a decimal.<br>[?]",
      "answer0": "0.625",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 125,
      "difficulty_id": 2,
      "explanation": "\\(5 \\div 8 = 0.625\\).",
      "hints": ["Divide 5 by 8 using long division.", "5.000 ÷ 8 = 0.625."],
      "source": "Nanyang 2023 P5 End-of-Year Exam Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "What is the missing number in the box?<br>[?] : 5 = 24 : 40",
      "answer0": "3",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 181,
      "difficulty_id": 2,
      "explanation": "40 ÷ 5 = 8, so each term on the right is 8 times the left. 24 ÷ 8 = 3. The missing number is 3.",
      "hints": ["The two ratios are equivalent.", "5 × 8 = 40, so divide 24 by 8."],
      "source": "Nanyang 2023 P5 End-of-Year Exam Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "AOD and COF are straight lines. \\(\\angle BOC = 58°\\), \\(\\angle DOE = 76°\\), \\(\\angle AOB = 90°\\). Find \\(\\angle FOE\\).<br>[?]",
      "answer0": "72",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 194,
      "difficulty_id": 3,
      "explanation": "AOD is a straight line: \\(\\angle AOB + \\angle BOC + \\angle COD = 180°\\), so \\(\\angle COD = 180 - 90 - 58 = 32°\\). COF is a straight line: \\(\\angle COD + \\angle DOE + \\angle EOF = 180°\\), so \\(\\angle EOF = 180 - 32 - 76 = 72°\\).",
      "hints": ["Angles on a straight line add up to 180°.", "First use line AOD to find ∠COD, then use line COF."],
      "source": "Nanyang 2023 P5 End-of-Year Exam Q19",
      "image_needed": true,
      "image_options": false,
      "image_file": "q19.png",
      "image_page": 15,
      "image_bbox": [0.28, 0.14, 0.78, 0.40],
      "image_loc": "angle diagram with rays through point O (top half of page)",
      "notes": "Answer 72°. Units degrees (answer is the number)."
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "Measure and write down the size of \\(\\angle BAC\\).<br>[?]",
      "answer0": "72",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 140,
      "difficulty_id": 1,
      "explanation": "Using a protractor to measure \\(\\angle BAC\\) at vertex A of the triangle gives 72° (per the answer key).",
      "hints": ["Place the protractor centre on vertex A.", "Read the scale along arm AC starting from arm AB."],
      "source": "Nanyang 2023 P5 End-of-Year Exam Q20",
      "image_needed": true,
      "image_options": false,
      "image_file": "q20.png",
      "image_page": 15,
      "image_bbox": [0.30, 0.55, 0.78, 0.82],
      "image_loc": "triangle ABC in the lower half of the page",
      "notes": "Protractor-measure question; answer 72° per key (measured value may vary ±1°). Crop must preserve the angle accurately."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "ABCD is a rhombus. BCE is a straight line and \\(\\angle DCE = 134°\\). Find \\(\\angle ABD\\).<br>[?]",
      "answer0": "67",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 200,
      "difficulty_id": 3,
      "explanation": "BCE is a straight line, so \\(\\angle BCD = 180 - 134 = 46°\\). In a rhombus, opposite angles are equal and adjacent angles are supplementary, so \\(\\angle ABC = 180 - 46 = 134°\\). The diagonal BD bisects \\(\\angle ABC\\), so \\(\\angle ABD = 134 \\div 2 = 67°\\).",
      "hints": ["Angles on a straight line: ∠BCD = 180 − 134.", "A diagonal of a rhombus bisects the corner angles."],
      "source": "Nanyang 2023 P5 End-of-Year Exam Q21",
      "image_needed": true,
      "image_options": false,
      "image_file": "q21.png",
      "image_page": 16,
      "image_bbox": [0.30, 0.13, 0.72, 0.42],
      "image_loc": "rhombus ABCD with line BCE, upper part of page",
      "notes": "Answer 67°."
    },
    {
      "n": 22,
      "type_id": 1,
      "question": "Find the value of \\(\\dfrac{2}{3} \\times \\dfrac{5}{8}\\). Give your answer as a fraction in the simplest form.",
      "answer0": "\\(\\dfrac{5}{12}\\)",
      "answer1": "\\(\\dfrac{10}{24}\\)",
      "answer2": "\\(\\dfrac{7}{12}\\)",
      "answer3": "\\(\\dfrac{5}{24}\\)",
      "correct_answer": 0,
      "skill_id": 161,
      "difficulty_id": 2,
      "explanation": "\\(\\dfrac{2}{3}\\times\\dfrac{5}{8}=\\dfrac{10}{24}=\\dfrac{5}{12}\\) (dividing top and bottom by 2).",
      "hints": ["Multiply the numerators and the denominators.", "Simplify \\(\\dfrac{10}{24}\\) by dividing by 2."],
      "source": "Nanyang 2023 P5 End-of-Year Exam Q22",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Converted to MCQ because the answer is a fraction (FIB must be integers/decimals). Correct value 5/12."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "What is the volume of the cuboid shown?<br>[?]",
      "answer0": "690",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 190,
      "difficulty_id": 1,
      "explanation": "Volume of a cuboid = length × breadth × height = 23 × 6 × 5 = 690 cm³.",
      "hints": ["Volume = length × breadth × height.", "23 × 6 × 5 = 690."],
      "source": "Nanyang 2023 P5 End-of-Year Exam Q23",
      "image_needed": true,
      "image_options": false,
      "image_file": "q23.png",
      "image_page": 17,
      "image_bbox": [0.28, 0.12, 0.66, 0.27],
      "image_loc": "cuboid diagram (23 cm by 6 cm by 5 cm), upper part of page",
      "notes": "Answer 690 cm³ (answer entered in cm³)."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "The bar graph shows the group points scored by 3 groups. What is the difference in the group points between the highest score and the lowest score?<br>[?]",
      "answer0": "42",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 104,
      "difficulty_id": 2,
      "explanation": "Group X = 57, Group Y = 33, Group Z = 75. Highest = 75, lowest = 33. Difference = 75 − 33 = 42.",
      "hints": ["Read the height of each bar.", "Subtract the shortest bar's value from the tallest bar's value."],
      "source": "Nanyang 2023 P5 End-of-Year Exam Q24",
      "image_needed": true,
      "image_options": false,
      "image_file": "q24.png",
      "image_page": 18,
      "image_bbox": [0.14, 0.14, 0.92, 0.62],
      "image_loc": "bar graph of group points for Group X, Y, Z",
      "notes": "Answer 42 (highest 75 − lowest 33). Crop must include axis scale and bar labels."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "Sophia paid $87.40 for 3 identical pencils and 7 identical markers. The price of a marker is $1.20 more than the price of a pencil. Tim bought 10 such pencils. What was the amount of money he paid for 10 such pencils?<br>[?]",
      "answer0": "79",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Replace each marker with (pencil + $1.20): 3 pencils + 7 pencils + 7 × $1.20 = $87.40. So 10 pencils + $8.40 = $87.40, giving 10 pencils = $79.00. Tim paid $79 for 10 pencils.",
      "hints": ["A marker costs $1.20 more than a pencil; swap markers for pencils plus the extra.", "10 pencils + 7 × $1.20 = $87.40."],
      "source": "Nanyang 2023 P5 End-of-Year Exam Q25",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer entered in dollars: 79 (i.e. $79.00)."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "The product of 2 numbers is 3069. The smaller number is 9. Find the larger number. Round the answer to the nearest hundred.<br>[?]",
      "answer0": "300",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 150,
      "difficulty_id": 2,
      "explanation": "Larger number = 3069 ÷ 9 = 341. Rounded to the nearest hundred, 341 ≈ 300.",
      "hints": ["Divide the product by the smaller number to get the larger number.", "341 rounds down to 300 because 41 < 50."],
      "source": "Nanyang 2023 P5 End-of-Year Exam Q26",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "What is the price of the refrigerator after adding 8% GST? The price before GST is $2800.<br>[?]",
      "answer0": "3024",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 2,
      "explanation": "GST = 8% of $2800 = \\(\\dfrac{8}{100}\\times 2800 = 224\\). Price after GST = $2800 + $224 = $3024.",
      "hints": ["Find 8% of $2800 first.", "Add the GST to the original price (or multiply by 1.08)."],
      "source": "Nanyang 2023 P5 End-of-Year Exam Q27",
      "image_needed": true,
      "image_options": false,
      "image_file": "q27.png",
      "image_page": 20,
      "image_bbox": [0.38, 0.12, 0.62, 0.30],
      "image_loc": "refrigerator picture labelled $2800 (price before GST)",
      "notes": "Answer entered in dollars: 3024. '$2800 (price before GST)' is part of the figure; transcribed into the stem so the question is answerable."
    },
    {
      "n": 28,
      "type_id": 0,
      "question": "The figure shows a solid made up of 11 unit cubes. (a) Draw the side view of the solid on the grid. (b) Jun Wei painted the whole solid, including the base, green. How many of the 11 unit cubes had exactly three of their faces painted green?",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 231,
      "difficulty_id": 3,
      "explanation": "(a) Drawing task (no app input type). (b) A cube has exactly 3 faces painted when it sits at a corner of the solid with exactly 3 exposed faces. Counting these on the 11-cube solid gives the answer in the key.",
      "hints": ["A corner cube touching the outside on three sides has three painted faces.", "Check each cube's exposed faces, remembering the base is also painted."],
      "source": "Nanyang 2023 P5 End-of-Year Exam Q28",
      "image_needed": true,
      "image_options": false,
      "image_file": "q28.png",
      "image_page": 21,
      "image_bbox": [0.30, 0.08, 0.74, 0.27],
      "image_loc": "isometric solid of 11 unit cubes with Top/Side/Front view arrows",
      "notes": "type_id 0: part (a) is a draw-the-side-view task (no app input type), so this whole multi-part item is skipped on insert. Part (b) answer per key: 4 cubes (corner cubes with exactly three exposed faces)."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "ABCD and EFGH are 2 identical rectangles. Find the total area of the unshaded parts.<br>[?]",
      "answer0": "200",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Each rectangle has area 25 × 8 = 200 cm²; the two identical rectangles overlap. The shaded part is made of two triangles whose areas together equal one rectangle's worth of the figure, leaving the unshaded parts totalling 200 cm². (Total of both rectangles 400 cm² minus the shaded 200 cm² = 200 cm².)",
      "hints": ["Each rectangle is 25 cm by 8 cm, so its area is 200 cm².", "Total area of the two rectangles minus the shaded area gives the unshaded area."],
      "source": "Nanyang 2023 P5 End-of-Year Exam Q29",
      "image_needed": true,
      "image_options": false,
      "image_file": "q29.png",
      "image_page": 22,
      "image_bbox": [0.22, 0.10, 0.74, 0.36],
      "image_loc": "two overlapping rectangles ABCD and EFGH with shaded triangular parts",
      "notes": "Answer entered in cm²: 200 (per key). Composite-area figure question — crop the whole labelled figure including the 25 cm, 8 cm and 2 cm measurements."
    },
    {
      "n": 30,
      "type_id": 2,
      "question": "The table below shows the height of 3 boys, Abel, Bernard and Carl. Their heights are in whole numbers. They have an average height of 154 cm. Carl is taller than Bernard and Abel is the shortest. Part of the table is smeared with ink. What is the lowest possible height of Carl?<br>[?]",
      "answer0": "159",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 205,
      "difficulty_id": 3,
      "explanation": "Total height = 154 × 3 = 462 cm. Abel (the shortest) = 146 cm, so Bernard + Carl = 462 − 146 = 316 cm. Carl is taller than Bernard and both are whole numbers, so Carl must be more than half of 316, i.e. Carl ≥ 159 (with Bernard = 157). The lowest possible height of Carl is 159 cm.",
      "hints": ["Total = average × number of boys = 462 cm.", "Carl + Bernard = 316; for Carl to be the lowest while still taller than Bernard, split 316 as 159 and 157."],
      "source": "Nanyang 2023 P5 End-of-Year Exam Q30",
      "image_needed": true,
      "image_options": false,
      "image_file": "q30.png",
      "image_page": 23,
      "image_bbox": [0.30, 0.12, 0.74, 0.22],
      "image_loc": "name/height table with smeared (inked) entries for Bernard and Carl",
      "notes": "Answer entered in cm: 159. Abel's height reads 146 cm from the table; Bernard's and Carl's heights are smeared. Crop the table."
    },
    {
      "n": 31,
      "type_id": 1,
      "question": "Abdul bought \\(5\\dfrac{2}{5}\\) m of string. He used \\(1\\dfrac{3}{4}\\) m of it to tie a parcel and \\(\\dfrac{4}{10}\\) m of it to decorate a present. How many metres of string had he left? Give your answer as a mixed number.",
      "answer0": "\\(3\\dfrac{1}{4}\\)",
      "answer1": "\\(3\\dfrac{3}{4}\\)",
      "answer2": "\\(3\\dfrac{1}{2}\\)",
      "answer3": "\\(2\\dfrac{3}{4}\\)",
      "correct_answer": 0,
      "skill_id": 160,
      "difficulty_id": 3,
      "explanation": "\\(5\\dfrac{2}{5}=5.4\\), \\(1\\dfrac{3}{4}=1.75\\), \\(\\dfrac{4}{10}=0.4\\). Left = \\(5.4 - 1.75 - 0.4 = 3.25 = 3\\dfrac{1}{4}\\) m.",
      "hints": ["Add the two pieces used, then subtract from the total.", "5.4 − 1.75 − 0.4 = 3.25."],
      "source": "Nanyang 2023 P5 End-of-Year Exam P2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q1. Converted to MCQ because the answer is a mixed number (FIB must be integers/decimals). Correct value 3 1/4 m."
    },
    {
      "n": 32,
      "type_id": 1,
      "question": "A jug contains \\(1\\dfrac{7}{9}\\) litres of apple juice. How many litres of apple juice are there in 6 such jugs altogether?",
      "answer0": "\\(10\\dfrac{2}{3}\\)",
      "answer1": "\\(10\\dfrac{6}{9}\\)",
      "answer2": "\\(6\\dfrac{7}{9}\\)",
      "answer3": "\\(9\\dfrac{1}{3}\\)",
      "correct_answer": 0,
      "skill_id": 163,
      "difficulty_id": 2,
      "explanation": "\\(1\\dfrac{7}{9}=\\dfrac{16}{9}\\). \\(6\\times\\dfrac{16}{9}=\\dfrac{96}{9}=10\\dfrac{6}{9}=10\\dfrac{2}{3}\\) litres.",
      "hints": ["Change the mixed number to an improper fraction first.", "\\(\\dfrac{96}{9}\\) simplifies to \\(10\\dfrac{2}{3}\\)."],
      "source": "Nanyang 2023 P5 End-of-Year Exam P2 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q2. Converted to MCQ because the answer is a mixed number. Correct value 10 2/3 L. Options 1 and 2 are equal in value (10 2/3 = 10 6/9); option 1 is the simplest form requested."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "The average mass of 5 children is 48 kg. When Peter's mass is added, the average mass becomes 45 kg. What is Peter's mass?<br>[?]",
      "answer0": "30",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 204,
      "difficulty_id": 3,
      "explanation": "Total of 5 children = 5 × 48 = 240 kg. Total of 6 people = 6 × 45 = 270 kg. Peter's mass = 270 − 240 = 30 kg.",
      "hints": ["Total = average × number of people.", "Subtract the 5-child total from the 6-person total."],
      "source": "Nanyang 2023 P5 End-of-Year Exam P2 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q3. Answer entered in kg: 30."
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "ACE is a triangle. Triangle ABF and triangle FDE are isosceles triangles. Find the sum of \\(\\angle BAF\\) and \\(\\angle FED\\).<br>[?]",
      "answer0": "128",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "A, F and E lie on a straight line. At F, \\(\\angle AFB + \\angle BFD + \\angle DFE = 180°\\). Triangle ABF is isosceles (AB = BF) so \\(\\angle BAF = \\angle AFB\\); triangle FDE is isosceles (DF = DE) so \\(\\angle FED = \\angle DFE\\). With \\(\\angle BFD = 52°\\), \\(\\angle AFB + \\angle DFE = 180 - 52 = 128°\\). Therefore \\(\\angle BAF + \\angle FED = 128°\\).",
      "hints": ["In each isosceles triangle the two base angles are equal.", "A, F and E are in a straight line, so the three angles at F add up to 180°."],
      "source": "Nanyang 2023 P5 End-of-Year Exam P2 Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q34.png",
      "image_page": 28,
      "image_bbox": [0.30, 0.45, 0.72, 0.80],
      "image_loc": "triangle ACE with inner points B, D, F and a 52° angle at F",
      "notes": "Paper 2 Q4. Answer 128°. ∠BAF and ∠FED are the base angles of the two isosceles triangles; their sum = 180° − 52° = 128°. Crop must show the 52° mark and the equal-side tick marks."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "Mei Yan has a piece of yellow ribbon and red ribbon of the same length. She then cuts the yellow ribbon and the red ribbon into shorter pieces. If she gives a group of friends a shorter piece of yellow ribbon of length 1.4 m each, she will have 0.6 m of the yellow ribbon left. If she gives the same group of friends a shorter piece of red ribbon of length 1.8 m each, she will need an additional 2.2 m of the red ribbon. How many friends does Mei Yan have in this group?<br>[?]",
      "answer0": "7",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "Let the number of friends be n. Yellow length = 1.4n + 0.6. Red length = 1.8n − 2.2 (she is 2.2 m short). The ribbons are the same length: 1.4n + 0.6 = 1.8n − 2.2, so 0.6 + 2.2 = 0.4n, 2.8 = 0.4n, n = 7. Mei Yan has 7 friends.",
      "hints": ["Write the yellow ribbon length and the red ribbon length in terms of the number of friends.", "Set the two equal lengths equal and solve: 1.4n + 0.6 = 1.8n − 2.2."],
      "source": "Nanyang 2023 P5 End-of-Year Exam P2 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q5. Answer 7 friends."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "The total cost of 2 identical files and 3 identical markers was $15. The total cost of 5 such files and 6 such markers was $34.80. What was the cost of 1 such marker?<br>[?]",
      "answer0": "1.80",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "Double the first set: 4 files + 6 markers = $30. Compare with 5 files + 6 markers = $34.80. The difference is 1 file = $34.80 − $30 = $4.80. Then 2 × $4.80 + 3 markers = $15, so 3 markers = $15 − $9.60 = $5.40, and 1 marker = $1.80.",
      "hints": ["Make the number of markers the same in both statements by doubling the first.", "Subtracting gives the cost of one file, then back-substitute."],
      "source": "Nanyang 2023 P5 End-of-Year Exam P2 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q6. Answer entered in dollars: 1.80 ($1.80)."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "Team A played against Team B in a badminton match. 560 children watched the badminton match. 70% of the children were boys. (a) How many girls watched the badminton match? (b) 42 of the girls supported Team B and the rest of the girls supported Team A. What percentage of the girls supported Team A?<br>(a) [?]<br>(b) [?]",
      "answer0": "168",
      "answer1": "75",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 175,
      "difficulty_id": 3,
      "explanation": "(a) 70% were boys, so 30% were girls. Girls = \\(\\dfrac{30}{100}\\times 560 = 168\\). (b) Girls supporting Team A = 168 − 42 = 126. Percentage = \\(\\dfrac{126}{168}\\times 100\\% = 75\\%\\).",
      "hints": ["If 70% are boys, then 30% are girls.", "Find the girls supporting Team A, then write that as a percentage of all the girls."],
      "source": "Nanyang 2023 P5 End-of-Year Exam P2 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q7. Two blanks: (a) 168 girls; (b) 75 (percent)."
    },
    {
      "n": 38,
      "type_id": 0,
      "question": "A triangle ABC is drawn on a square grid inside a box. By joining dots on the grid with straight lines, (a) draw a rhombus with BC as one of the sides, with the rhombus and triangle ABC not overlapping; (b) draw parallelogram ACFG where the length of AB is twice the length of AG, with triangle ABC not overlapping parallelogram ACFG.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 201,
      "difficulty_id": 3,
      "explanation": "This is a construction (drawing) task: pupils draw a rhombus on side BC and parallelogram ACFG on the grid. There is no single value answer; it is marked by checking the drawn shapes.",
      "hints": ["A rhombus has all four sides equal; use the grid to keep side lengths equal to BC.", "For the parallelogram, AG must be half of AB; opposite sides ACFG are parallel and equal."],
      "source": "Nanyang 2023 P5 End-of-Year Exam P2 Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q38.png",
      "image_page": 32,
      "image_bbox": [0.16, 0.10, 0.86, 0.40],
      "image_loc": "dotted square grid with triangle ABC drawn inside a box",
      "notes": "type_id 0: draw-on-grid construction task with no value/sequence answer, so it is skipped on insert."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "Jason, Peter and Chris shared a sum of money in the ratio 5 : 9 : 2. The difference between Peter's share and Jason's share is $128. How much more money did Peter have than Chris?<br>[?]",
      "answer0": "224",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "Peter : Jason difference = 9 − 5 = 4 units = $128, so 1 unit = $32. Peter − Chris = 9 − 2 = 7 units = 7 × $32 = $224.",
      "hints": ["Find the value of 1 unit from the Peter–Jason difference.", "Peter − Chris is 7 units."],
      "source": "Nanyang 2023 P5 End-of-Year Exam P2 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q9. Answer entered in dollars: 224 ($224)."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "The average mark for a class of students in a quiz is 74. The top 3 students scored 87, 95 and 100. When the top 3 students were excluded in the calculation for the average, the average mark becomes 62. How many students were there in the class?<br>[?]",
      "answer0": "8",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 205,
      "difficulty_id": 3,
      "explanation": "Let there be n students. Total marks = 74n. Top 3 total = 87 + 95 + 100 = 282. The remaining (n − 3) students average 62: 74n − 282 = 62(n − 3). So 74n − 282 = 62n − 186, 12n = 96, n = 8.",
      "hints": ["Total marks = average × number of students.", "Set 74n − 282 = 62(n − 3) and solve for n."],
      "source": "Nanyang 2023 P5 End-of-Year Exam P2 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q10. Answer 8 students."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "Ravi baked 2535 cookies. \\(\\dfrac{1}{3}\\) of them were chocolate cookies, \\(\\dfrac{3}{5}\\) of the remaining cookies were vanilla cookies and the rest were strawberry cookies. (a) How many vanilla cookies did he bake? (b) Ravi packed all the vanilla cookies into large and small tins to sell. He filled each large tin with 30 cookies and each small tin with 12 cookies. All the tins were full and there were no cookies left over. What was the least number of tins used by Ravi?<br>(a) [?]<br>(b) [?]",
      "answer0": "1014",
      "answer1": "35",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "(a) Chocolate = \\(\\dfrac{1}{3}\\times 2535 = 845\\). Remaining = 2535 − 845 = 1690. Vanilla = \\(\\dfrac{3}{5}\\times 1690 = 1014\\). (b) 1014 = 30 × a + 12 × b. To use the fewest tins, fill as many large (30) tins as possible: 30 × 33 = 990, leaving 24 = 12 × 2. So 33 large + 2 small = 35 tins.",
      "hints": ["Find the chocolate cookies first, then take 3/5 of what remains.", "For the fewest tins, use as many 30-cookie tins as possible, then fill the rest with 12-cookie tins."],
      "source": "Nanyang 2023 P5 End-of-Year Exam P2 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q11. Two blanks: (a) 1014 vanilla cookies; (b) 35 tins (33 large + 2 small)."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "A rectangular tank measuring 19 cm by 14 cm by 15 cm is \\(\\dfrac{2}{3}\\)-filled with water. All the water is then poured into an empty cubical tank with sides measuring 15 cm each. (a) What is the volume of water in the rectangular tank at first? (b) How much more water has to be added so that the cubical tank is \\(\\dfrac{4}{5}\\)-filled with water? Give your answer in litres.<br>(a) [?]<br>(b) [?]",
      "answer0": "2660",
      "answer1": "0.04",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 193,
      "difficulty_id": 3,
      "explanation": "(a) Rectangular tank volume = 19 × 14 × 15 = 3990 cm³. Water = \\(\\dfrac{2}{3}\\times 3990 = 2660\\) cm³. (b) Cubical tank volume = 15 × 15 × 15 = 3375 cm³. \\(\\dfrac{4}{5}\\)-filled = \\(\\dfrac{4}{5}\\times 3375 = 2700\\) cm³. Extra water = 2700 − 2660 = 40 cm³ = 0.04 ℓ.",
      "hints": ["Volume = length × breadth × height; then take 2/3 for part (a).", "1000 cm³ = 1 ℓ, so 40 cm³ = 0.04 ℓ."],
      "source": "Nanyang 2023 P5 End-of-Year Exam P2 Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q42.png",
      "image_page": 36,
      "image_bbox": [0.22, 0.14, 0.78, 0.33],
      "image_loc": "rectangular tank (19 by 14 by 15 cm) and cubical tank (15 cm) diagrams",
      "notes": "Paper 2 Q12. Two blanks: (a) 2660 (cm³); (b) 0.04 (litres). Crop both tank diagrams."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "Keryn and Carol had an equal number of stickers at first. After Keryn used 352 stickers and Carol used 84 stickers, Carol had 5 times as many stickers as Keryn. (a) How many stickers did Keryn have left? (b) How many stickers did each girl have at first?<br>(a) [?]<br>(b) [?]",
      "answer0": "67",
      "answer1": "419",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Let each girl start with x stickers. Keryn left = x − 352, Carol left = x − 84, and Carol = 5 × Keryn: x − 84 = 5(x − 352). So x − 84 = 5x − 1760, 1676 = 4x, x = 419. (a) Keryn left = 419 − 352 = 67. (b) Each girl had 419 stickers at first.",
      "hints": ["They started equal; write each girl's leftover in terms of the same starting amount.", "Set Carol's leftover equal to 5 times Keryn's leftover."],
      "source": "Nanyang 2023 P5 End-of-Year Exam P2 Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q13. Two blanks: (a) 67 stickers; (b) 419 stickers."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "ABCD is a square. AB = 32 cm, DG = GC, AF = FE and DE = EB. (a) Find the area of the triangle BDG. (b) Find the area of the shaded parts.<br>(a) [?]<br>(b) [?]",
      "answer0": "256",
      "answer1": "512",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "(a) DG = GC means G is the midpoint of DC, so DG = 16 cm. Triangle BDG has base DG = 16 cm and height = side AB = 32 cm: area = \\(\\dfrac{1}{2}\\times 16\\times 32 = 256\\) cm². (b) Using the midpoints E (of diagonal DB) and F (where AF = FE), the two shaded triangles combine to 512 cm².",
      "hints": ["G is the midpoint of DC, so DG = 16 cm.", "For triangle BDG the height is the full side of the square, 32 cm."],
      "source": "Nanyang 2023 P5 End-of-Year Exam P2 Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q44.png",
      "image_page": 38,
      "image_bbox": [0.28, 0.10, 0.66, 0.40],
      "image_loc": "square ABCD with points F, E, G and shaded region",
      "notes": "Paper 2 Q14. Two blanks (cm²): (a) 256; (b) 512 (derived from the figure using E and F as midpoints — verify against printed key during QA). Crop the full labelled square."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "A piece of triangular paper is folded into a trapezium as shown. \\(\\angle ABO = 53°\\), \\(\\angle DCO = 50°\\) and \\(\\angle AOC = 127°\\). (a) Find \\(\\angle AOD\\). (b) Find \\(\\angle BAO\\).<br>(a) [?]<br>(b) [?]",
      "answer0": "77",
      "answer1": "74",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "B, O and C lie on a straight line, so \\(\\angle AOB = 180 - 127 = 53°\\). (a) On the straight line BOC, \\(\\angle AOB + \\angle AOD + \\angle DOC = 180°\\); since triangle DOC is isosceles from the fold, \\(\\angle DOC = \\angle DCO = 50°\\), so \\(\\angle AOD = 180 - 53 - 50 = 77°\\). (b) In triangle ABO, \\(\\angle BAO = 180 - \\angle ABO - \\angle AOB = 180 - 53 - 53 = 74°\\).",
      "hints": ["B, O, C are on a straight line, so ∠AOB = 180° − 127°.", "The three angles on the straight line at O add to 180°; use the angle sum of triangle ABO for part (b)."],
      "source": "Nanyang 2023 P5 End-of-Year Exam P2 Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q45.png",
      "image_page": 39,
      "image_bbox": [0.18, 0.13, 0.86, 0.50],
      "image_loc": "folded triangle/trapezium diagram with points A, B, C, D, O, X",
      "notes": "Paper 2 Q15. Two blanks (degrees): (a) 77; (b) 74 (computed from B-O-C straight line and triangle ABO angle sum; verify (b) against printed key during QA)."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "The table shows the parking charges at Value Shopping Mall: first hour or part thereof (9 a.m. to 5 p.m.) costs $1.20; every additional \\(\\dfrac{1}{2}\\) hour or part thereof costs $1.00; after 5 p.m. till next morning 9 a.m. costs $5.00 per entry. (a) Mrs Wee parked her car from 9.30 a.m. to 11.45 a.m. How much did she pay for her parking charges? (b) Mr Ong parked his car from 4.30 p.m. till the next morning 9 a.m. How much did he pay for his parking charges?<br>(a) [?]<br>(b) [?]",
      "answer0": "4.20",
      "answer1": "5.00",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 135,
      "difficulty_id": 3,
      "explanation": "(a) 9.30 a.m. to 11.45 a.m. = 2 h 15 min. First hour = $1.20. Remaining 1 h 15 min = 3 half-hour blocks (part thereof) × $1.00 = $3.00. Total = $1.20 + $3.00 = $4.20. (b) Parking from 4.30 p.m. till next morning 9 a.m. is charged the overnight flat rate of $5.00 per entry.",
      "hints": ["After the first hour, count each extra half hour (round any part up).", "An overnight stay past 5 p.m. is the $5.00 flat charge."],
      "source": "Nanyang 2023 P5 End-of-Year Exam P2 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q16(a)(b). Two blanks in dollars: (a) 4.20; (b) 5.00. Part (c) of this question (tick True/False/Not-possible table) is a separate non-standard item recorded as Q47."
    },
    {
      "n": 47,
      "type_id": 0,
      "question": "Using the parking charges at Value Shopping Mall, each statement below is either true, false or not possible to tell from the information given. For each statement, indicate true / false / not possible to tell: (i) Mr Lim paid $5 when he parked his car from 6 p.m. till next morning 8.45 a.m. (ii) Mr Tan paid $1.20 when he parked his car for 30 minutes. (iii) Some cars entered at 6 p.m. and exited at 6.50 p.m. on the same day. The parking charges for these cars were $7.20.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 135,
      "difficulty_id": 3,
      "explanation": "(i) True — parking from 6 p.m. overnight is the $5.00 flat rate. (ii) True — 30 minutes falls within the first hour, charged $1.20. (iii) False — a car entering after 5 p.m. is charged the $5.00 overnight flat rate, not $7.20.",
      "hints": ["Check each statement against the charge table.", "After 5 p.m. a single flat overnight rate applies, regardless of how long within that window."],
      "source": "Nanyang 2023 P5 End-of-Year Exam P2 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "type_id 0: tick-the-box True/False/Not-possible table has no app input type, so it is skipped on insert. Answers per key: (i) True, (ii) True, (iii) False. This is part (c) of Paper 2 Q16."
    },
    {
      "n": 48,
      "type_id": 2,
      "question": "Bryan uses grey and white squares to form figures that follow a pattern. For each figure the number of grey squares are 2, 5, 8, 13 for Figures 1 to 4; the number of white squares are 2, 4, 8, 12 for Figures 1 to 4; the total number of squares are 4, 9, 16, 25 for Figures 1 to 4. (a) Find the number of white squares in Figure 5. (b) Find the number of white squares in Figure 8. (c) Find the total number of squares in Figure 49.<br>(a) [?]<br>(b) [?]<br>(c) [?]",
      "answer0": "18",
      "answer1": "40",
      "answer2": "2500",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 108,
      "difficulty_id": 3,
      "explanation": "The total number of squares in Figure n is \\((n+1)^2\\): 4, 9, 16, 25, 36, ... (a) White squares increase by 2, 4, 4, 6, 6, ... : 2, 4, 8, 12, 18, so Figure 5 has 18 white squares. (b) Continuing 18, 24, 32, 40 gives Figure 8 = 40 white squares. (c) Figure 49 total = \\((49+1)^2 = 50^2 = 2500\\).",
      "hints": ["The total number of squares is a perfect square: Figure n has (n+1)² squares.", "Look at the differences between consecutive white-square counts to extend the pattern."],
      "source": "Nanyang 2023 P5 End-of-Year Exam P2 Q17",
      "image_needed": true,
      "image_options": false,
      "image_file": "q48.png",
      "image_page": 42,
      "image_bbox": [0.10, 0.10, 0.92, 0.27],
      "image_loc": "four pattern figures of grey and white squares (Figures 1 to 4)",
      "notes": "Paper 2 Q17. Three blanks: (a) 18 white squares (Fig 5); (b) 40 white squares (Fig 8); (c) 2500 total squares (Fig 49 = 50²). The first-four-figure counts are transcribed from the printed table so the question is answerable; crop shows the figure pictures."
    }
  ]
}