{
  "paper": {
    "school": "Nanyang",
    "year": 2022,
    "level": "P5",
    "label": "Semestral Assessment 2",
    "source_prefix": "Nanyang 2022 P5 Semestral Assessment 2",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "In 742.896, which digit is in the hundredths place?",
      "answer0": "6",
      "answer1": "7",
      "answer2": "8",
      "answer3": "9",
      "correct_answer": 3,
      "skill_id": 149,
      "difficulty_id": 1,
      "explanation": "Place values after the decimal point: 8 is tenths, 9 is hundredths, 6 is thousandths. So the digit in the hundredths place is 9.",
      "hints": ["Tenths is the first digit after the decimal point.", "Hundredths is the second digit after the decimal point."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: (4)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Which of the following is the same as 20 ml?",
      "answer0": "2 ℓ",
      "answer1": "0.2 ℓ",
      "answer2": "0.02 ℓ",
      "answer3": "0.002 ℓ",
      "correct_answer": 2,
      "skill_id": 192,
      "difficulty_id": 1,
      "explanation": "1 ℓ = 1000 ml, so 20 ml = 20 ÷ 1000 = 0.02 ℓ.",
      "hints": ["1 litre = 1000 millilitres.", "Divide the millilitres by 1000 to get litres."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: (3)."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "There are 30 chocolate cookies, 18 raisin cookies and 48 butter cookies. What is the ratio of the number of chocolate cookies to the number of raisin cookies to the number of butter cookies?",
      "answer0": "5 : 3 : 8",
      "answer1": "3 : 5 : 8",
      "answer2": "5 : 3 : 6",
      "answer3": "6 : 3 : 8",
      "correct_answer": 0,
      "skill_id": 179,
      "difficulty_id": 1,
      "explanation": "30 : 18 : 48, divide each term by the common factor 6: 30÷6 : 18÷6 : 48÷6 = 5 : 3 : 8.",
      "hints": ["Find the largest number that divides all three quantities.", "Divide each quantity by that common factor."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: (1)."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Sindri worked for 30 hours. He was paid $600. How much was he paid per hour?",
      "answer0": "$5",
      "answer1": "$2",
      "answer2": "$20",
      "answer3": "$50",
      "correct_answer": 2,
      "skill_id": 152,
      "difficulty_id": 1,
      "explanation": "Pay per hour = total pay ÷ number of hours = $600 ÷ 30 = $20.",
      "hints": ["Divide the total amount by the number of hours.", "$600 ÷ 30."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: (3)."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "Shahul had $2500. He spent $2000. What percentage of his money did he spend?",
      "answer0": "20%",
      "answer1": "25%",
      "answer2": "80%",
      "answer3": "125%",
      "correct_answer": 2,
      "skill_id": 171,
      "difficulty_id": 1,
      "explanation": "Percentage spent = \\(\\dfrac{2000}{2500}\\times 100\\% = \\dfrac{80}{100}\\times 100\\% = 80\\%\\).",
      "hints": ["Write the amount spent as a fraction of the total.", "Multiply the fraction by 100% to convert to a percentage."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: (3)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "There were 960 people in a concert. 60% of them were adults. How many adults were there at the concert?",
      "answer0": "384",
      "answer1": "576",
      "answer2": "588",
      "answer3": "768",
      "correct_answer": 1,
      "skill_id": 174,
      "difficulty_id": 2,
      "explanation": "60% of 960 = \\(\\dfrac{60}{100}\\times 960\\) = 9.6 × 60 = 576 adults.",
      "hints": ["1% of 960 = 960 ÷ 100 = 9.6.", "Multiply 9.6 by 60 to find 60%."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: (2)."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "Which line in the square grid is perpendicular to AB?",
      "answer0": "DE",
      "answer1": "EF",
      "answer2": "CD",
      "answer3": "FG",
      "correct_answer": 0,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "AB runs at a diagonal of 1 unit across to 2 units down (gradient). A line perpendicular to AB has the opposite reciprocal gradient. Line DE meets AB at right angles, so DE is perpendicular to AB.",
      "hints": ["Perpendicular lines meet at a right angle (90°).", "Compare the slope of each line on the grid against AB."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q7.png",
      "image_page": 5,
      "image_bbox": [0.24, 0.16, 0.78, 0.47],
      "image_loc": "square grid with lines AB, CD, DE, EF, FG below the question",
      "notes": "Answer key: (1) DE."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "ABCD is a rectangle. E is a point on BC. BE is half the length of BC, DC = 20 cm and AD = 14 cm. Find the area of triangle BDE.",
      "answer0": "35 cm²",
      "answer1": "70 cm²",
      "answer2": "140 cm²",
      "answer3": "280 cm²",
      "correct_answer": 1,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "BC = AD = 14 cm, so BE = 14 ÷ 2 = 7 cm. Base BE = 7 cm and height = DC = 20 cm. Area of triangle BDE = \\(\\dfrac{1}{2}\\times 20\\times 7\\) = 70 cm².",
      "hints": ["BE is half of BC, and BC equals AD = 14 cm.", "Area of triangle = ½ × base × height."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 6,
      "image_bbox": [0.24, 0.24, 0.64, 0.46],
      "image_loc": "rectangle ABCD with shaded triangle BDE, 14 cm and 20 cm labelled",
      "notes": "Answer key: (2) 70 cm²."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "Which of the following triangles is an equilateral triangle?",
      "answer0": "Triangle (1)",
      "answer1": "Triangle (2)",
      "answer2": "Triangle (3)",
      "answer3": "Triangle (4)",
      "correct_answer": 0,
      "skill_id": 195,
      "difficulty_id": 1,
      "explanation": "An equilateral triangle has all three angles equal to 60°. Triangle (1) shows two 60° angles, so the third is also 180° − 60° − 60° = 60°, making it equilateral.",
      "hints": ["All angles of an equilateral triangle are 60°.", "The angles in a triangle add up to 180°."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q9",
      "image_needed": true,
      "image_options": true,
      "image_file": null,
      "image_page": 6,
      "image_bbox": [0.1, 0.69, 0.78, 0.83],
      "image_loc": "four triangles labelled (1)-(4) with angle markings 60°, 110°, right-angle, 80°",
      "notes": "Answer key: (1). Image options: crop each triangle to q9_opt0.png..q9_opt3.png."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "The solid is formed by unit cubes. How many unit cubes are there?",
      "answer0": "12",
      "answer1": "17",
      "answer2": "18",
      "answer3": "26",
      "correct_answer": 1,
      "skill_id": 188,
      "difficulty_id": 2,
      "explanation": "Counting the cubes by layers: the staircase solid is made of 9 + 3 + 5 = 17 unit cubes.",
      "hints": ["Count the cubes layer by layer, including hidden ones.", "Add the cubes in each step of the staircase."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 7,
      "image_bbox": [0.22, 0.18, 0.62, 0.43],
      "image_loc": "staircase solid made of unit cubes below the question",
      "notes": "Answer key: (2) 17 (9+3+5=17). Count to verify: 17 cubes."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "Which one of the following fractions is closest to 2?",
      "answer0": "\\(2\\dfrac{2}{3}\\)",
      "answer1": "\\(2\\dfrac{1}{4}\\)",
      "answer2": "\\(1\\dfrac{1}{6}\\)",
      "answer3": "\\(1\\dfrac{7}{8}\\)",
      "correct_answer": 3,
      "skill_id": 160,
      "difficulty_id": 2,
      "explanation": "Distance from 2: \\(2\\dfrac{2}{3}\\) is \\(\\dfrac{2}{3}\\) away; \\(2\\dfrac{1}{4}\\) is \\(\\dfrac{1}{4}\\) away; \\(1\\dfrac{1}{6}\\) is \\(\\dfrac{5}{6}\\) away; \\(1\\dfrac{7}{8}\\) is \\(\\dfrac{1}{8}\\) away. The smallest distance is \\(\\dfrac{1}{8}\\), so \\(1\\dfrac{7}{8}\\) is closest to 2.",
      "hints": ["Find how far each number is from 2.", "The closest one has the smallest difference."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: (4) 1 7/8. Mixed-number options rendered inline."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "Jasmine scored an average of 70 marks for a Mathematics test and a Science test. She scored 68 marks for the Mathematics test. How many marks did she score for the Science test?",
      "answer0": "66",
      "answer1": "69",
      "answer2": "72",
      "answer3": "138",
      "correct_answer": 2,
      "skill_id": 152,
      "difficulty_id": 1,
      "explanation": "Total marks for both tests = average × 2 = 70 × 2 = 140. Science marks = 140 − 68 = 72.",
      "hints": ["Total = average × number of tests.", "Subtract the Mathematics marks from the total."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: (3) 72."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "Mandy had 408 ℓ of milk. She poured all the milk into 400 bottles. Each bottle contained the same amount of milk. How many litres of milk did each bottle contain?",
      "answer0": "1.02",
      "answer1": "1.2",
      "answer2": "10.2",
      "answer3": "12",
      "correct_answer": 0,
      "skill_id": 167,
      "difficulty_id": 1,
      "explanation": "Milk per bottle = 408 ÷ 400 = 1.02 ℓ.",
      "hints": ["Divide the total volume by the number of bottles.", "408 ÷ 400."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: (1) 1.02."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "Noah bought \\(\\dfrac{7}{8}\\) kg of grapes. He ate \\(\\dfrac{1}{3}\\) of it. How many kilograms of grapes had he left?",
      "answer0": "\\(\\dfrac{5}{12}\\)",
      "answer1": "\\(\\dfrac{7}{12}\\)",
      "answer2": "\\(\\dfrac{7}{24}\\)",
      "answer3": "\\(\\dfrac{13}{24}\\)",
      "correct_answer": 1,
      "skill_id": 161,
      "difficulty_id": 2,
      "explanation": "Fraction left = \\(1-\\dfrac{1}{3}=\\dfrac{2}{3}\\). Grapes left = \\(\\dfrac{2}{3}\\times\\dfrac{7}{8}=\\dfrac{14}{24}=\\dfrac{7}{12}\\) kg.",
      "hints": ["He has 1 − 1/3 = 2/3 of the grapes left.", "Multiply 2/3 by 7/8."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: (2) 7/12. Fraction options rendered inline."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "Mrs Tan cooks 0.35 kg of rice every day. How many kilograms of rice does she cook in 60 days?",
      "answer0": "2.1",
      "answer1": "3.5",
      "answer2": "18",
      "answer3": "21",
      "correct_answer": 3,
      "skill_id": 166,
      "difficulty_id": 1,
      "explanation": "Rice in 60 days = 0.35 × 60 = 0.35 × 10 × 6 = 3.5 × 6 = 21 kg.",
      "hints": ["Multiply the daily amount by the number of days.", "0.35 × 60."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: (4) 21."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Find the value of 14 + (30 − 18) ÷ 6 × 2. [?]",
      "answer0": "18",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 155,
      "difficulty_id": 1,
      "explanation": "14 + (30 − 18) ÷ 6 × 2 = 14 + 12 ÷ 6 × 2 = 14 + 2 × 2 = 14 + 4 = 18.",
      "hints": ["Work out the brackets first.", "Do division and multiplication from left to right before adding."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 18."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "Find the value of 923 ÷ 4. Express your answer as a decimal. [?]",
      "answer0": "230.75",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 1,
      "explanation": "923 ÷ 4 = 230 remainder 3; 3 ÷ 4 = 0.75, so 923 ÷ 4 = 230.75.",
      "hints": ["Divide 923 by 4 using long division.", "The remainder of 3 ÷ 4 = 0.75."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 230.75."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "What is the missing number in the box?<br>4 : 7 = 32 : [?]",
      "answer0": "56",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 181,
      "difficulty_id": 1,
      "explanation": "4 × 8 = 32, so the ratio is multiplied by 8. Missing number = 7 × 8 = 56.",
      "hints": ["Find what 4 was multiplied by to get 32 (32 ÷ 4 = 8).", "Multiply 7 by the same number."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 56."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "JKL and MKN are straight lines. ∠NKP = 90° and ∠JKN = 130°. Find ∠PKL. [?]",
      "answer0": "40",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "∠NKL = 180° − ∠JKN = 180° − 130° = 50° (angles on straight line JKL). ∠PKL = ∠NKP − ∠NKL = 90° − 50° = 40°.",
      "hints": ["Angles on a straight line add up to 180°.", "∠PKL = ∠NKP − ∠NKL."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q19",
      "image_needed": true,
      "image_options": false,
      "image_file": "q19.png",
      "image_page": 13,
      "image_bbox": [0.2, 0.25, 0.66, 0.45],
      "image_loc": "intersecting lines JKL and MKN with rays KP, KN, 130° marked at K",
      "notes": "Answer key: 40 (degrees)."
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "QRS is a triangle. ∠QSR = 10° and ∠QRS = 25°. Find ∠SQR. [?]",
      "answer0": "145",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 196,
      "difficulty_id": 2,
      "explanation": "Angle sum of a triangle = 180°. ∠SQR = 180° − ∠QSR − ∠QRS = 180° − 10° − 25° = 145°.",
      "hints": ["The three angles of a triangle add up to 180°.", "Subtract the two given angles from 180°."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q20",
      "image_needed": true,
      "image_options": false,
      "image_file": "q20.png",
      "image_page": 13,
      "image_bbox": [0.26, 0.62, 0.62, 0.74],
      "image_loc": "triangle QRS with 10° at S and 25° at R",
      "notes": "Answer key: 145 (degrees)."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "WXYZ is a trapezium. WX // ZY, ∠ZWY = 95° and ∠WZY = 65°. Find ∠YWX. [?]",
      "answer0": "20",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 200,
      "difficulty_id": 2,
      "explanation": "Since WX // ZY, ∠ZWX + ∠WZY = 180° (interior angles). So ∠ZWX = 180° − 65° = 115°. Wait — use: ∠ZWY = 95°; ∠YWX = ∠ZWX − ∠ZWY. ∠ZWX = 180° − ∠WZY = 180° − 65° = 115°. Hmm, key uses 95° + 65° = 160°, ∠YWX = 180° − 160° = 20°. Method: ∠WYZ = 180° − 95° − 65° = 20° (angle sum of triangle WZY); since WX // ZY, ∠YWX = ∠WYZ = 20° (alternate angles).",
      "hints": ["In triangle WZY, the three angles add to 180°.", "WX is parallel to ZY, so use alternate angles."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q21",
      "image_needed": true,
      "image_options": false,
      "image_file": "q21.png",
      "image_page": 14,
      "image_bbox": [0.26, 0.28, 0.78, 0.42],
      "image_loc": "trapezium WXYZ with diagonal WY, 95° at W and 65° at Z",
      "notes": "Answer key: 20 (degrees). Key working: 95+65=160, 180-160=20."
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "Mrs Tan had some money at first. She spent \\(\\dfrac{2}{3}\\) of her money on a watch and \\(\\dfrac{1}{5}\\) of her money on food. She had $100 left. How much did she have at first? $[?]",
      "answer0": "750",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "Fraction left = \\(1-\\dfrac{2}{3}-\\dfrac{1}{5}=1-\\dfrac{10}{15}-\\dfrac{3}{15}=\\dfrac{2}{15}\\). \\(\\dfrac{2}{15}\\) of the money = $100, so \\(\\dfrac{1}{15}\\) = $50 and total = $50 × 15 = $750.",
      "hints": ["Find the fraction of money left as a single fraction.", "If 2/15 = $100, find 1/15 then the whole."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q22",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: $750."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "What is the volume of the cuboid? [?] cm³",
      "answer0": "84000",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 190,
      "difficulty_id": 1,
      "explanation": "Volume = length × breadth × height = 40 × 30 × 70 = 1200 × 70 = 84 000 cm³.",
      "hints": ["Volume of a cuboid = length × breadth × height.", "Multiply 40 × 30 × 70."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q23",
      "image_needed": true,
      "image_options": false,
      "image_file": "q23.png",
      "image_page": 15,
      "image_bbox": [0.3, 0.16, 0.52, 0.33],
      "image_loc": "cuboid labelled 70 cm, 30 cm and 40 cm",
      "notes": "Answer key: 84 000 cm³."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "Find the average cost of the 3 items. $[?]",
      "answer0": "36",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 1,
      "explanation": "Total cost = $36 + $29.50 + $42.50 = $108. Average cost = $108 ÷ 3 = $36.",
      "hints": ["Add the three prices together.", "Divide the total by 3."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q24",
      "image_needed": true,
      "image_options": false,
      "image_file": "q24.png",
      "image_page": 15,
      "image_bbox": [0.12, 0.55, 0.72, 0.66],
      "image_loc": "three clothing items priced $36, $29.50 and $42.50",
      "notes": "Answer key: $36. Prices given in question text; figure is decorative."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "The mass of a book is 3.08 kg. Find the total mass of 6 such books. [?] kg",
      "answer0": "18.48",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 166,
      "difficulty_id": 1,
      "explanation": "Total mass = 3.08 × 6 = 18.48 kg.",
      "hints": ["Multiply the mass of one book by 6.", "3.08 × 6."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q25",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 18.48 kg."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "The drink stall sold 2651 packet drinks in January. The number of packet drinks sold in February was 44 more than the number of packet drinks sold in January. How many packet drinks were sold in February? Round your answer to the nearest ten. [?]",
      "answer0": "2700",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 150,
      "difficulty_id": 1,
      "explanation": "February = 2651 + 44 = 2695. Rounded to the nearest ten, 2695 ≈ 2700.",
      "hints": ["First add 44 to 2651.", "Round 2695 to the nearest ten (5 rounds up)."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q26",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 2700."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "Mrs Singh deposits $15 000 in the bank for one year. The bank offers an interest of 4% per year. How much will Mrs Singh have in her bank at the end of one year? $[?]",
      "answer0": "15600",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 2,
      "explanation": "Interest = 4% of $15 000 = \\(\\dfrac{4}{100}\\times 15000\\) = $600. Total at year end = $15 000 + $600 = $15 600.",
      "hints": ["Find 4% of $15 000.", "Add the interest to the original deposit."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q27",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: $15 600."
    },
    {
      "n": 28,
      "type_id": 0,
      "question": "Nana stacked 10 unit cubes and glued them together to form the solid. Draw the top view and the side view of the solid on the grids.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 187,
      "difficulty_id": 2,
      "explanation": "Draw the top view and side view of the 10-cube solid. Top view: an L-shape / 3-by-2 footprint matching the base layer; side view: the stepped profile of the stacked cubes (per the answer key sketches).",
      "hints": ["Top view is what you see looking straight down.", "Side view is what you see looking from the side."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q28",
      "image_needed": true,
      "image_options": false,
      "image_file": "q28.png",
      "image_page": 17,
      "image_bbox": [0.3, 0.25, 0.66, 0.42],
      "image_loc": "isometric solid of 10 unit cubes with Top/Front/Side View arrows",
      "notes": "Drawing task (draw top & side view) — no app question type, SKIPPED on insert. Answer is a drawing."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "WXYZ is a rectangle. The area of rectangle WXYZ is 552 cm². C and D are points on WX. E and F are points on ZY. Find the total area of the shaded parts. [?] cm²",
      "answer0": "276",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "Each shaded triangle has its base on one side of the rectangle and its apex on the opposite side, so the combined bases equal the full length and the height equals the rectangle's width. The shaded triangles total half the rectangle's area = 552 ÷ 2 = 276 cm².",
      "hints": ["The shaded triangles all have the same height as the rectangle's width.", "Their bases add up to the full length, giving half the rectangle's area."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q29",
      "image_needed": true,
      "image_options": false,
      "image_file": "q29.png",
      "image_page": 18,
      "image_bbox": [0.2, 0.2, 0.74, 0.33],
      "image_loc": "rectangle WXYZ with three shaded triangles to points C, D on WX and E, F on ZY",
      "notes": "Answer key: 276 cm² (552 ÷ 2)."
    },
    {
      "n": 30,
      "type_id": 2,
      "question": "The average mass of Mei Mei and her cousins was 45 kg. Mei Mei's mass was 53 kg. The average mass of her cousins was 43 kg. How many cousins did Mei Mei have? [?]",
      "answer0": "4",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Mei Mei is 53 − 45 = 8 kg above the group average. Each cousin is 45 − 43 = 2 kg below the group average. To balance Mei Mei's +8 kg, the cousins must total −8 kg, so number of cousins = 8 ÷ 2 = 4.",
      "hints": ["Find how much Mei Mei is above the overall average.", "Each cousin is below the average; balance the surplus."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q30",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 4. Working: 53-45=8, 45-43=2, 8÷2=4."
    },
    {
      "n": 31,
      "type_id": 1,
      "question": "Sarah spent \\(1\\dfrac{1}{4}\\) h in the morning to complete her Science project. She spent \\(1\\dfrac{7}{10}\\) h in the afternoon to complete her Chinese project. What was the total amount of time she spent on completing both her Science and Chinese projects?",
      "answer0": "\\(2\\dfrac{19}{20}\\) h",
      "answer1": "\\(2\\dfrac{8}{14}\\) h",
      "answer2": "\\(3\\dfrac{1}{20}\\) h",
      "answer3": "\\(2\\dfrac{1}{2}\\) h",
      "correct_answer": 0,
      "skill_id": 160,
      "difficulty_id": 2,
      "explanation": "\\(1\\dfrac{1}{4}+1\\dfrac{7}{10}=1\\dfrac{5}{20}+1\\dfrac{14}{20}=2\\dfrac{19}{20}\\) h.",
      "hints": ["Use a common denominator of 20 for the fractions.", "Add the whole numbers and the fractions separately."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q31",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q1. Answer key: 2 19/20 h. Made MCQ as answer is a mixed number; distractors are plausible miscalculations."
    },
    {
      "n": 32,
      "type_id": 1,
      "question": "The side of a square is \\(6\\dfrac{2}{5}\\) cm. What is the perimeter of the square?",
      "answer0": "\\(25\\dfrac{3}{5}\\) cm",
      "answer1": "\\(12\\dfrac{4}{5}\\) cm",
      "answer2": "\\(24\\dfrac{2}{5}\\) cm",
      "answer3": "\\(26\\dfrac{2}{5}\\) cm",
      "correct_answer": 0,
      "skill_id": 163,
      "difficulty_id": 1,
      "explanation": "Perimeter = 4 × side = \\(6\\dfrac{2}{5}\\times 4=\\dfrac{32}{5}\\times 4=\\dfrac{128}{5}=25\\dfrac{3}{5}\\) cm.",
      "hints": ["A square has 4 equal sides; perimeter = 4 × side.", "Convert to an improper fraction before multiplying."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q32",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q2. Answer key: 25 3/5 cm. Made MCQ as answer is a mixed number."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "The table shows the number of books sold in Everygreen bookshop from January to May.<br>January: 88, February: 75, March: 82, April: 69, May: 71.<br>What was the average number of books sold from January to May? [?]",
      "answer0": "77",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 1,
      "explanation": "Total = 88 + 75 + 82 + 69 + 71 = 385. Average = 385 ÷ 5 = 77 books.",
      "hints": ["Add up all five monthly totals.", "Divide the total by 5 (the number of months)."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q33",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q3. Table data placed in question text. Answer key: 77."
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "ABC is a right-angled triangle. D is a point on AC. ∠BAC = 23°, ∠ABC = 90° and BC = BD. Find ∠BDA. [?]",
      "answer0": "113",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "∠ACB = 180° − 90° − 23° = 67°. Since BC = BD, triangle BDC is isosceles, so ∠BDC = ∠BCD = 67°. ∠BDA = 180° − ∠BDC = 180° − 67° = 113°.",
      "hints": ["First find ∠ACB using the angle sum of triangle ABC.", "BD = BC makes triangle BDC isosceles; ∠BDA is on a straight line with ∠BDC."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q34",
      "image_needed": true,
      "image_options": false,
      "image_file": "q34.png",
      "image_page": 21,
      "image_bbox": [0.24, 0.5, 0.66, 0.66],
      "image_loc": "right-angled triangle ABC with D on AC, 23° at A, equal marks on BD and BC",
      "notes": "Paper 2 Q4. Answer key: 113 (degrees)."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "Junie bought a book from ABC Bookshop. She had forgotten how much she paid for the book. However, she remembered that the book cost $30 when rounded to the nearest dollar. She remembered the following about the cost of the book:<br>- It showed 2 decimal places.<br>- All the digits are different.<br>- The digits she saw in the tenths and hundredths places are 1, 4 or 5.<br>How many possible costs of the book are there? [?]",
      "answer0": "6",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 150,
      "difficulty_id": 3,
      "explanation": "Rounded to nearest dollar = $30, so the cost is $29.50 to $30.49. Tenths and hundredths digits come from {1,4,5} and must differ. Possible costs: $29.51, $29.54, $30.14, $30.15, $30.41, $30.45 — and all digits in the whole number must also differ. The valid costs total 6.",
      "hints": ["The cost must round to $30, so it lies between $29.50 and $30.49.", "List the tenths/hundredths pairs from {1,4,5} with different digits."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q35",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q5. Book-cover figure is decorative (not needed). Answer key lists $29.51, $29.54, $30.14, $30.15, $30.41, $30.45 = 6."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "Anna and James had the same amount of money at first. Anna bought some pens and had $4.30 left. James wanted to buy highlighters only. The number of highlighters that James wanted to buy was the same as the number of pens Anna bought. However, he was short of $8.70. Each pen cost $1.20 and each highlighter cost $2.50. How much money did Anna have at first? $[?]",
      "answer0": "16.30",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "The difference in money James would need versus Anna's leftover = $4.30 + $8.70 = $13 (this is the extra cost of buying highlighters instead of pens). Each highlighter costs $2.50 − $1.20 = $1.30 more than a pen. Number bought = $13 ÷ $1.30 = 10. Anna spent on pens = 10 × $1.20 = $12, so she had $12 + $4.30 = $16.30 at first.",
      "hints": ["The total gap is $4.30 + $8.70 = $13.", "Each highlighter costs $1.30 more than a pen; divide $13 by $1.30 for the count."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q36",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q6. Answer key: $16.30."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "The Art Museum offers tickets on discount. Usual price: $16 per ticket. Buy 1 ticket at 10% discount. Buy 2 or more tickets at 20% discount.<br>(a) Mr Lim bought 1 ticket. How much did he pay? $[?]<br>(b) Mr Tan bought 3 tickets. What was the least amount of money he paid? $[?]",
      "answer0": "14.40",
      "answer1": "38.40",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 2,
      "explanation": "(a) 1 ticket at 10% discount: pay 90% of $16 = \\(\\dfrac{90}{100}\\times 16\\) = $14.40. (b) 3 tickets qualify for 20% discount: each costs 80% of $16 = \\(\\dfrac{80}{100}\\times 16\\) = $12.80, so 3 × $12.80 = $38.40.",
      "hints": ["10% off means paying 90%; 20% off means paying 80%.", "Buying 3 tickets gets the 20% discount on each."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q37",
      "image_needed": true,
      "image_options": false,
      "image_file": "q37.png",
      "image_page": 24,
      "image_bbox": [0.24, 0.18, 0.72, 0.37],
      "image_loc": "Art Museum ticket sale flyer stating usual price $16 and discount terms",
      "notes": "Paper 2 Q7, 2 parts. Answer key: (a) $14.40, (b) $38.40. Prices restated in text; flyer figure is supportive."
    },
    {
      "n": 38,
      "type_id": 0,
      "question": "In the square grid, JK and JN are straight lines. (a) JK and JN form two sides of a square JKLN. Complete the drawing of the square JKLN. (b) JK and JN form two sides of a trapezium JKMN. KM is parallel to JN. Complete the drawing of trapezium JKMN such that the area of JKMN is \\(1\\dfrac{1}{2}\\) times the area of JKLN.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 201,
      "difficulty_id": 2,
      "explanation": "(a) Complete square JKLN by drawing the two remaining sides equal and perpendicular to JK and JN. (b) Make KM parallel to JN and extend so the trapezium's area is 1½ × the square's area (per the answer-key drawing, M is placed so the perpendicular distance gives the required area).",
      "hints": ["A square has four equal sides meeting at right angles.", "KM // JN; choose the length so the trapezium area is 1.5× the square."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q38",
      "image_needed": true,
      "image_options": false,
      "image_file": "q38.png",
      "image_page": 25,
      "image_bbox": [0.24, 0.36, 0.62, 0.66],
      "image_loc": "square grid with line segments JK and JN drawn from J",
      "notes": "Paper 2 Q8 — drawing/construction task, no app question type, SKIPPED on insert."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "Chin Lee is 12 years older than Ming Shi. In 5 years' time, the ratio of Ming Shi's age to Chin Lee's age will be 5 : 9. How old is Chin Lee now? [?]",
      "answer0": "22",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "In 5 years the age difference is still 12. Ratio 5 : 9 means difference is 9 − 5 = 4 units = 12, so 1 unit = 3. Chin Lee in 5 years = 9 units = 9 × 3 = 27. Chin Lee now = 27 − 5 = 22 years old.",
      "hints": ["The age difference stays the same (12 years).", "The difference in ratio units (9 − 5 = 4) equals 12."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q39",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q9. Answer key: 22."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "The average of 8 numbers is 45. When 2 of the numbers are removed, the average of the remaining numbers is 32. The difference between the 2 numbers that are removed is 6.<br>(a) Find the sum of the remaining numbers. [?]<br>(b) What are the 2 numbers that are removed? [?] and [?]",
      "answer0": "192",
      "answer1": "87",
      "answer2": "81",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "(a) 8 − 2 = 6 numbers remain; sum = 32 × 6 = 192. (b) Sum of all 8 = 45 × 8 = 360. Sum of the 2 removed = 360 − 192 = 168. They differ by 6: larger = (168 + 6) ÷ 2 = 87, smaller = 87 − 6 = 81.",
      "hints": ["Sum = average × count.", "The two removed numbers sum to 168 and differ by 6."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q40",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q10, 2 parts. Answer key: (a) 192, (b) 87 and 81. answer0=part(a); answer1,answer2=the two removed numbers."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "Farhana baked some cupcakes. \\(\\dfrac{1}{5}\\) of the cupcakes were chocolate cupcakes and the rest were banana cupcakes. She sold \\(\\dfrac{4}{7}\\) of the chocolate cupcakes and 51 banana cupcakes. She then had \\(\\dfrac{2}{5}\\) of the cupcakes left.<br>(a) How many chocolate cupcakes did she sell? [?]<br>(b) How many cupcakes did she bake in all? [?]",
      "answer0": "12",
      "answer1": "105",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Let total = T. Chocolate = \\(\\dfrac{1}{5}T\\), banana = \\(\\dfrac{4}{5}T\\). She sold \\(\\dfrac{4}{7}\\) of chocolate, so chocolate left = \\(\\dfrac{3}{7}\\times\\dfrac{1}{5}T=\\dfrac{3}{35}T\\). Cupcakes left = \\(\\dfrac{2}{5}T=\\dfrac{14}{35}T\\), so banana left = \\(\\dfrac{14}{35}T-\\dfrac{3}{35}T=\\dfrac{11}{35}T\\). Banana sold = \\(\\dfrac{4}{5}T-\\dfrac{11}{35}T=\\dfrac{28-11}{35}T=\\dfrac{17}{35}T=51\\), so \\(\\dfrac{1}{35}T=3\\) and T = 105. (a) Chocolate sold = \\(\\dfrac{4}{7}\\times\\dfrac{1}{5}\\times105=\\dfrac{4}{35}\\times105=12\\). (b) Total = 105.",
      "hints": ["Express chocolate and banana amounts as fractions of the total.", "The 17/35 of total that are banana sold equals 51."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q41",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q11, 2 parts. Answer key: (a) 12, (b) 105."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "A tank measuring 40 cm by 14 cm by 18 cm was \\(\\dfrac{3}{4}\\)-filled with water. All the water in the tank was poured into a cubical container of sides 20 cm.<br>(a) How much water was in the tank at first? [?] cm³<br>(b) How many more litres of water are needed to fill the cubical container to the brim? [?]",
      "answer0": "7560",
      "answer1": "0.44",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 193,
      "difficulty_id": 3,
      "explanation": "(a) Water = \\(\\dfrac{3}{4}\\times 40\\times 14\\times 18\\) = \\(\\dfrac{3}{4}\\times 10080\\) = 7560 cm³. (b) Cube volume = 20 × 20 × 20 = 8000 cm³. More water needed = 8000 − 7560 = 440 cm³ = 440 ÷ 1000 = 0.44 ℓ.",
      "hints": ["Water volume = 3/4 of the tank's full volume.", "1000 cm³ = 1 litre; subtract the water already poured in."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q42",
      "image_needed": true,
      "image_options": false,
      "image_file": "q42.png",
      "image_page": 28,
      "image_bbox": [0.18, 0.23, 0.74, 0.37],
      "image_loc": "rectangular tank (40 by 14 by 18 cm) with water, arrow to a 20 cm cube",
      "notes": "Paper 2 Q12, 2 parts. Answer key: (a) 7560 cm³, (b) 0.44 ℓ."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "Kean Yew had 7200 shuttlecocks. He packed the shuttlecocks into as many bags of 7 shuttlecocks as possible and had some shuttlecocks left unpacked. He sold all his shuttlecocks and received $3608. Each bag of shuttlecocks was sold at $3.50.<br>(a) How many shuttlecocks were left unpacked? [?]<br>(b) Each of the shuttlecocks left unpacked was sold at the same price. How much did each of the shuttlecocks left unpacked sell at? $[?]",
      "answer0": "4",
      "answer1": "2.50",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "(a) 7200 ÷ 7 = 1028 remainder 4, so 4 shuttlecocks were left unpacked. (b) Money from bags = 1028 × $3.50 = $3598. Money from unpacked = $3608 − $3598 = $10. Each unpacked = $10 ÷ 4 = $2.50.",
      "hints": ["Divide 7200 by 7; the remainder is the unpacked shuttlecocks.", "Subtract the bag sales from the total to find unpacked sales."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q43",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q13, 2 parts. Answer key: (a) 4, (b) $2.50."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "The figure shows a right-angled triangle AFG and a square ABCD overlapping each other. ADG is a straight line. ∠AGF = 90°, DC = GF and EC = 7 cm. The length of AB is twice the length of EC. Triangle AFG has the same area as square ABCD.<br>(a) What is the area of square ABCD? [?] cm²<br>(b) Find the shaded area DEFG. [?] cm²",
      "answer0": "196",
      "answer1": "147",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "(a) AB = 2 × EC = 2 × 7 = 14 cm. Area of square ABCD = 14 × 14 = 196 cm². (b) Triangle ADE has base DE and is the unshaded part of triangle AFG inside the square: area of △ADE = \\(\\dfrac{1}{2}\\times 7\\times 14\\) = 49 cm². Shaded DEFG = area of △AFG − △ADE = 196 − 49 = 147 cm².",
      "hints": ["AB is twice EC; the square's area = side × side.", "Triangle AFG and square ABCD have equal areas; subtract triangle ADE."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q44",
      "image_needed": true,
      "image_options": false,
      "image_file": "q44.png",
      "image_page": 30,
      "image_bbox": [0.32, 0.22, 0.6, 0.48],
      "image_loc": "square ABCD overlapping right-angled triangle AFG, shaded region DEFG, EC = 7 cm",
      "notes": "Paper 2 Q14, 2 parts. Answer key: (a) 196 cm², (b) 147 cm²."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "In the figure, NQRT is a parallelogram. P is a point on NQ and PTS is a straight line. ∠NTP = 33°, ∠PNT = 105° and ∠TRS = 21°. Find ∠RST. [?]",
      "answer0": "21",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 200,
      "difficulty_id": 3,
      "explanation": "In triangle NPT, ∠PTR exterior or ∠NTP region: ∠PTR = 180° − 105° − 33° = 42° (in triangle, but here ∠NTR computation). ∠PTR = 180° − ∠NTP − ∠PNT = 180° − 105° − 33° = 42°. Then ∠STR = 180° − 42° = 138° (angles on straight line PTS). In triangle RST, ∠RST = 180° − ∠STR − ∠TRS = 180° − 138° − 21° = 21°.",
      "hints": ["Find ∠PTR using the angle sum of triangle NPT.", "PTS is a straight line, so ∠STR = 180° − ∠PTR; then use triangle RST."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q45",
      "image_needed": true,
      "image_options": false,
      "image_file": "q45.png",
      "image_page": 31,
      "image_bbox": [0.2, 0.2, 0.78, 0.4],
      "image_loc": "parallelogram NQRT with P on NQ, line PTS, angles 105°, 33°, 21° marked",
      "notes": "Paper 2 Q15(a). Answer key: 21 (degrees). Part (b) is a circle-the-words task (interactive) — omitted; answer was 'is not' / 'is not' (RT is not equal to ST, so RTS is not isosceles)."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "Cindy had a piece of ribbon. She used \\(\\dfrac{2}{7}\\) of the ribbon to make 15 small identical bows and 7 large identical bows. The length of ribbon used for 3 large bows was the same as the length of ribbon used for 5 small bows.<br>(a) How many large bows can she make with the same length of ribbon used for 15 small bows? [?]<br>(b) How many small bows can she make with \\(\\dfrac{3}{10}\\) of the remaining ribbon? [?]",
      "answer0": "9",
      "answer1": "20",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "(a) 3 large = 5 small, so 1 small = \\(\\dfrac{3}{5}\\) large. 15 small = 15 ÷ 5 × 3 = 9 large bows. (b) \\(\\dfrac{2}{7}\\) made 15 small + 7 large = (9 + 7) = 16 large-equivalents, so \\(\\dfrac{1}{7}\\) = 16 ÷ 2 = 8 large; \\(\\dfrac{2}{7}\\) = 16 large. Remaining ribbon = \\(\\dfrac{5}{7}\\). \\(\\dfrac{3}{10}\\) of remaining = \\(\\dfrac{3}{10}\\times\\dfrac{5}{7}=\\dfrac{3}{14}\\) of whole. Since \\(\\dfrac{1}{14}\\) = 4 large, \\(\\dfrac{3}{14}\\) = 12 large = 12 × (5/3) small = 20 small bows.",
      "hints": ["3 large bows use the same ribbon as 5 small bows.", "Convert all bows to one type to compare lengths."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q46",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q16, 2 parts. Answer key: (a) 9, (b) 20."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "Hon Lee formed some figures using squares and circles. In Figure 1 there is 1 circle and 2 squares; Figure 2 has 4 circles and 6 squares; Figure 3 has 9 circles and 12 squares; Figure 4 has 16 circles and 20 squares.<br>(a) Find the number of circles in Figure 8. [?]<br>(b) Which figure in the pattern has 930 squares? Figure [?]<br>(c) Find the total number of circles and squares in Figure 15. [?]",
      "answer0": "64",
      "answer1": "30",
      "answer2": "465",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Number of circles in Figure n = n × n. Number of squares in Figure n = n × (n + 1). (a) Figure 8 circles = 8 × 8 = 64. (b) Squares = n(n+1) = 930; 30 × 31 = 930, so Figure 30. (c) Figure 15: circles = 15 × 15 = 225, squares = 15 × 16 = 240, total = 225 + 240 = 465.",
      "hints": ["Circles follow the square numbers: 1, 4, 9, 16 = n².", "Squares follow n × (n + 1)."],
      "source": "Nanyang 2022 P5 Semestral Assessment 2 Q47",
      "image_needed": true,
      "image_options": false,
      "image_file": "q47.png",
      "image_page": 33,
      "image_bbox": [0.16, 0.18, 0.82, 0.31],
      "image_loc": "Figures 1-4 made of circles and squares in triangular arrangements",
      "notes": "Paper 2 Q17, 3 parts. Pattern data given in text. Answer key: (a) 64, (b) Figure 30, (c) 465."
    }
  ]
}