{
  "paper": {"school":"Rosyth School","year":2022,"level":"P5","label":"End-of-Year Exam","source_prefix":"Rosyth 2022 P5 End-of-Year Exam","has_answer_key":true},
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "Seven million, five hundred thousand and ninety-six when written in numerals is",
      "answer0": "7 500 096", "answer1": "7 050 096", "answer2": "7 005 096", "answer3": "7 000 596",
      "correct_answer": 0,
      "skill_id": 149,
      "difficulty_id": 1,
      "explanation": "Seven million = 7 000 000, five hundred thousand = 500 000, ninety-six = 96. Total = 7 500 096.",
      "hints": ["Write each part by place value.", "Five hundred thousand fills the hundred-thousands place."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Q1",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Answer key Q1 = option 1 (=7 500 096)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Round off 6 309 057 to the nearest thousand.",
      "answer0": "6 000 000", "answer1": "6 300 000", "answer2": "6 310 000", "answer3": "6 309 000",
      "correct_answer": 3,
      "skill_id": 150,
      "difficulty_id": 1,
      "explanation": "The hundreds digit of 6 309 057 is 0, which is less than 5, so round down: 6 309 057 rounds to 6 309 000.",
      "hints": ["Look at the hundreds digit to decide rounding.", "0 hundreds keeps the thousands the same."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Q2",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Answer key Q2 = option 4 (=6 309 000)."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "\\(100 \\div 40 =\\)",
      "answer0": "0.4", "answer1": "2.5", "answer2": "25", "answer3": "4",
      "correct_answer": 1,
      "skill_id": 125,
      "difficulty_id": 1,
      "explanation": "100 ÷ 40 = 2.5.",
      "hints": ["Divide 100 by 40.", "100 ÷ 40 = 10 ÷ 4 = 2.5."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Q3",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Answer key Q3 = option 2 (=2.5)."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "For every 14 boys who enter the hall, 6 girls will enter the hall. What is the ratio of the number of girls to the number of boys in the hall?",
      "answer0": "3 : 7", "answer1": "3 : 10", "answer2": "7 : 3", "answer3": "7 : 10",
      "correct_answer": 0,
      "skill_id": 179,
      "difficulty_id": 1,
      "explanation": "Girls : boys = 6 : 14 = 3 : 7.",
      "hints": ["Write girls to boys as 6 : 14.", "Simplify by dividing both by 2."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Q4",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Answer key Q4 = option 1 (=3:7)."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "In the figure, AOD, BOE and COF are straight lines. The angle AOB is 36° and another marked angle is 67°. Find \\(\\angle COD\\).",
      "answer0": "31°", "answer1": "54°", "answer2": "77°", "answer3": "113°",
      "correct_answer": 2,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "Using angles on the straight lines through O and the marked 36deg and 67deg, \\(\\angle COD = 77^\\circ\\).",
      "hints": ["Angles on a straight line add to 180deg.", "Use vertically opposite angles where lines cross at O."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Q5",
      "image_needed": true, "image_page": 3, "image_bbox": [0.30,0.36,0.66,0.56], "image_loc": "three straight lines through O (A-D, B-E, C-F) with angles 36deg and 67deg marked",
      "image_options": false, "image_file": "q5.png",
      "notes": "Answer key Q5 = option 3 (=77deg)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "In the figure, XYZ is an isosceles triangle. \\(\\angle ZXO = 24^\\circ\\) and \\(\\angle XZO = 68^\\circ\\). Find \\(\\angle OXY\\).",
      "answer0": "20°", "answer1": "44°", "answer2": "88°", "answer3": "92°",
      "correct_answer": 0,
      "skill_id": 197,
      "difficulty_id": 2,
      "explanation": "In triangle XOZ, \\(\\angle XOZ = 180^\\circ - 24^\\circ - 68^\\circ = 88^\\circ\\). XYZ is isosceles with XY = XZ; using the symmetry, \\(\\angle OXY = \\angle ZXY - \\angle ZXO\\). With base angles 68deg, apex \\(\\angle ZXY = 180 - 2(68) = 44^\\circ\\), so \\(\\angle OXY = 44 - 24 = 20^\\circ\\).",
      "hints": ["Find the apex angle of the isosceles triangle from the base angles.", "Subtract the marked 24deg from the apex angle."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Q6",
      "image_needed": true, "image_page": 4, "image_bbox": [0.28,0.16,0.66,0.46], "image_loc": "isosceles triangle XYZ with O on YZ, angles 24deg (at X) and 68deg (at Z) marked",
      "image_options": false, "image_file": "q6.png",
      "notes": "Answer key Q6 = option 1 (=20deg)."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "The solid is formed by stacking 1-cm cubes at the corner of the room. What is the volume of the solid?",
      "answer0": "7 cm³", "answer1": "8 cm³", "answer2": "10 cm³", "answer3": "11 cm³",
      "correct_answer": 3,
      "skill_id": 188,
      "difficulty_id": 2,
      "explanation": "Counting all the unit cubes (including hidden ones in the corner stack) gives 11 cubes, so the volume is 11 cm³.",
      "hints": ["Each cube has a volume of 1 cm³.", "Count all cubes, including those hidden behind others in the corner."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Q7",
      "image_needed": true, "image_page": 4, "image_bbox": [0.18,0.62,0.46,0.82], "image_loc": "stack of unit cubes in a room corner (isometric)",
      "image_options": false, "image_file": "q7.png",
      "notes": "Answer key Q7 = option 4 (=11 cm3). Count cubes to verify against figure."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "The ratio of the number of adults to the number of children attending a party is 1 : 5. What fraction of the people attending the party are children?",
      "answer0": "\\(\\dfrac{1}{5}\\)", "answer1": "\\(\\dfrac{1}{6}\\)", "answer2": "\\(\\dfrac{5}{6}\\)", "answer3": "\\(\\dfrac{4}{5}\\)",
      "correct_answer": 2,
      "skill_id": 177,
      "difficulty_id": 1,
      "explanation": "Adults : children = 1 : 5, total 6 parts. Children = 5 out of 6 = \\(\\dfrac{5}{6}\\).",
      "hints": ["Total parts = 1 + 5.", "Children's fraction = children parts over total parts."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Q8",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Fraction options so MCQ. Answer key Q8 = option 3 (=5/6)."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "Express 0.001 as a percentage.",
      "answer0": "1%", "answer1": "0.1%", "answer2": "0.01%", "answer3": "10%",
      "correct_answer": 1,
      "skill_id": 173,
      "difficulty_id": 2,
      "explanation": "To convert to a percentage, multiply by 100: 0.001 x 100 = 0.1%.",
      "hints": ["Multiply the decimal by 100 to get a percentage.", "0.001 x 100 = 0.1."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Q9",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Answer key Q9 = option 2 (=0.1%)."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "The average pocket money of 3 boys is $24. Find the total amount of pocket money of the 3 boys.",
      "answer0": "$8", "answer1": "$21", "answer2": "$72", "answer3": "$216",
      "correct_answer": 2,
      "skill_id": 204,
      "difficulty_id": 1,
      "explanation": "Total = average x number = $24 x 3 = $72.",
      "hints": ["Total = average x number of boys.", "$24 x 3 = $72."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Q10",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Answer key Q10 = option 3 (=$72)."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "Kenisha has 80 pieces of ribbons. Each piece of ribbon is 1.04 m long. What is the total length of the 80 pieces of ribbons?",
      "answer0": "8.32 cm", "answer1": "83.2 cm", "answer2": "832 cm", "answer3": "8320 cm",
      "correct_answer": 3,
      "skill_id": 166,
      "difficulty_id": 2,
      "explanation": "Total = 1.04 m x 80 = 83.2 m = 8320 cm.",
      "hints": ["Multiply 1.04 m by 80.", "Convert metres to centimetres (x100)."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Q11",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Answer key Q11 = option 4 (=8320 cm)."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "Melissa cut a pie into 10 equal pieces. She ate 3 pieces and gave a few pieces to her father. After that, \\(\\dfrac{1}{5}\\) of the pie was left. What fraction of the pie did Melissa give to her father?",
      "answer0": "\\(\\dfrac{1}{2}\\)", "answer1": "\\(\\dfrac{3}{5}\\)", "answer2": "\\(\\dfrac{3}{10}\\)", "answer3": "\\(\\dfrac{7}{10}\\)",
      "correct_answer": 0,
      "skill_id": 159,
      "difficulty_id": 2,
      "explanation": "Left = 1/5 = 2/10 (2 pieces). Eaten = 3 pieces. Given to father = 10 - 3 - 2 = 5 pieces = \\(\\dfrac{5}{10} = \\dfrac{1}{2}\\).",
      "hints": ["Convert 1/5 of the pie into the number of pieces left.", "Pieces given = 10 - eaten - left, then write as a fraction."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Q12",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Fraction options so MCQ. Answer key Q12 = option 1 (=1/2)."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "Mr Selva had 3 kg of sand. He used \\(\\dfrac{2}{3}\\) of the sand and threw away \\(\\dfrac{1}{6}\\) kg of the sand. How much sand was Mr Selva left with?",
      "answer0": "\\(\\dfrac{1}{6}\\) kg", "answer1": "\\(\\dfrac{5}{6}\\) kg", "answer2": "\\(\\dfrac{7}{9}\\) kg", "answer3": "\\(\\dfrac{13}{6}\\) kg",
      "correct_answer": 1,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "Used = 2/3 of 3 = 2 kg. After using: 3 - 2 = 1 kg. Threw away 1/6 kg: 1 - 1/6 = 5/6 kg left.",
      "hints": ["Find how much sand was used (2/3 of 3 kg).", "Subtract the used amount and the thrown-away amount."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Q13",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Fraction options so MCQ. Answer key Q13 = option 2 (=5/6 kg)."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "Boston has an equal number of twenty-cent and fifty-cent coins. The total value of his coins is $14. How many coins does Boston have altogether?",
      "answer0": "20", "answer1": "28", "answer2": "40", "answer3": "70",
      "correct_answer": 2,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "One twenty-cent plus one fifty-cent = 70 cents per pair. $14 = 1400 cents, so 1400 ÷ 70 = 20 pairs = 20 of each coin = 40 coins altogether.",
      "hints": ["Group one 20-cent coin with one 50-cent coin (70 cents).", "Divide $14 by 70 cents, then double for the total coins."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Q14",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Answer key Q14 = option 3 (=40 coins)."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "The figure is made up of 4 identical rectangles. What fraction of the figure is shaded? Give your answer in its simplest form.",
      "answer0": "\\(\\dfrac{1}{4}\\)", "answer1": "\\(\\dfrac{1}{2}\\)", "answer2": "\\(\\dfrac{3}{4}\\)", "answer3": "\\(\\dfrac{3}{8}\\)",
      "correct_answer": 3,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "The shaded tilted shape covers an area equal to 3/8 of the whole figure made of 4 identical rectangles.",
      "hints": ["Work out the total area in terms of the 4 rectangles.", "Find the shaded area as a fraction and simplify."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Q15",
      "image_needed": true, "image_page": 7, "image_bbox": [0.32,0.36,0.50,0.50], "image_loc": "figure of 4 identical rectangles with a tilted shaded shape inside",
      "image_options": false, "image_file": "q15.png",
      "notes": "Fraction options so MCQ. Answer key Q15 = option 4 (=3/8)."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Write down a decimal that is greater than \\(\\dfrac{1}{5}\\) but smaller than \\(\\dfrac{1}{4}\\). Give your answer in 2 decimal places. Ans: [?]",
      "answer0": "0.23", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 124,
      "difficulty_id": 2,
      "explanation": "1/5 = 0.20 and 1/4 = 0.25. A decimal in between, to 2 decimal places, is 0.23 (others such as 0.21, 0.22, 0.24 also work).",
      "hints": ["Convert 1/5 and 1/4 to decimals.", "Choose a 2-decimal-place value between 0.20 and 0.25."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Q16",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Answer key Q16 = 0.23 (any value strictly between 0.20 and 0.25 to 2 dp is acceptable)."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "What is the value of \\(7 + 3 \\times 6 - 3\\)? Ans: [?]",
      "answer0": "22", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 155,
      "difficulty_id": 1,
      "explanation": "Multiply first: 3 x 6 = 18. Then 7 + 18 - 3 = 25 - 3 = 22.",
      "hints": ["Do the multiplication before the addition and subtraction.", "7 + 18 - 3 = 22."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Q17",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Answer key Q17 = 22."
    },
    {
      "n": 18,
      "type_id": 1,
      "question": "Find the value of \\(\\dfrac{2}{9} \\times \\dfrac{27}{8}\\). Give your answer as a fraction in the simplest form.",
      "answer0": "\\(\\dfrac{3}{4}\\)", "answer1": "\\(\\dfrac{54}{72}\\)", "answer2": "\\(\\dfrac{2}{3}\\)", "answer3": "\\(\\dfrac{9}{16}\\)",
      "correct_answer": 0,
      "skill_id": 161,
      "difficulty_id": 2,
      "explanation": "\\(\\dfrac{2}{9} \\times \\dfrac{27}{8} = \\dfrac{54}{72} = \\dfrac{3}{4}\\).",
      "hints": ["Multiply numerators and denominators.", "Simplify 54/72 to its lowest terms."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Q18",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Answer key Q18 = 3/4. Fraction answer so MCQ, not FIB."
    },
    {
      "n": 19,
      "type_id": 1,
      "question": "Which two lines in the square grid are parallel to each other?",
      "answer0": "Line AF and Line CD", "answer1": "Line AB and Line CD", "answer2": "Line EF and Line BC", "answer3": "Line AF and Line ED",
      "correct_answer": 0,
      "skill_id": 201,
      "difficulty_id": 2,
      "explanation": "On the square grid, Line AF and Line CD run in the same direction and never meet, so they are parallel.",
      "hints": ["Parallel lines have the same slope on the grid.", "Compare the directions of the drawn lines."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Q19",
      "image_needed": true, "image_page": 11, "image_bbox": [0.18,0.13,0.62,0.36], "image_loc": "square grid with lines through points A, B, C, D, E, F",
      "image_options": false, "image_file": "q19.png",
      "notes": "Answer key Q19 = Line AF // Line CD. Pair-of-lines answer so MCQ rather than FIB."
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "In the figure, find the value of \\(\\angle k\\). The angle 36° is marked on one side and the reflex angle at the point is below the lines. Ans: [?]°",
      "answer0": "234", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "Angles at a point add to 360deg. The two upper angles are 36deg and a right angle (90deg), so \\(\\angle k = 360^\\circ - 36^\\circ - 90^\\circ = 234^\\circ\\).",
      "hints": ["Angles at a point add up to 360deg.", "Subtract the 36deg and the right angle from 360deg."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Q20",
      "image_needed": true, "image_page": 11, "image_bbox": [0.18,0.50,0.55,0.72], "image_loc": "rays from a point with 36deg marked and reflex angle k below",
      "image_options": false, "image_file": "q20.png",
      "notes": "Answer key Q20 = 234 (360 - 36 - 90)."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "Alynna wanted to multiply a number by 20. Instead of pressing the multiplication sign, she pressed the division sign on the calculator. She obtained the incorrect answer of 112.2. What should the correct answer be? Ans: [?]",
      "answer0": "44880", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "The number ÷ 20 = 112.2, so the number = 112.2 x 20 = 2244. The correct answer (number x 20) = 2244 x 20 = 44 880.",
      "hints": ["Find the original number from the wrong division.", "Multiply that number by 20 for the correct answer."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Q21",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Answer key Q21 = 44880 (112.2x20=2244, 2244x20=44880)."
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "The students in a school take the bus, walk or cycle home in the ratio of 6 : 1 : 2. 189 students walk to school, how many students are there in the school? [?]",
      "answer0": "1701", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 2,
      "explanation": "Bus : walk : cycle = 6 : 1 : 2, total 9 units. Walk = 1 unit = 189. Total = 9 units = 9 x 189 = 1701 students.",
      "hints": ["Walk is 1 unit; find the total units.", "Multiply 189 by the total number of units (9)."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Q22",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Answer key Q22 = 1701 (189x9)."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "Mrs Liew deposits $90 000 in a bank for one year. The interest rate is 2% per year. What is the total amount of money she will have in the bank at the end of one year? Ans: $[?]",
      "answer0": "91800", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 2,
      "explanation": "Total = 102% of $90 000 = \\(\\dfrac{102}{100} \\times 90\\,000 = \\$91\\,800\\).",
      "hints": ["Interest is 2% of $90 000.", "Add the interest to the deposit (102% of $90 000)."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Q23",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Answer key Q23 = $91 800."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "A container of sweets was shared equally among 20 children. 4 of them gave all their sweets to the rest of the children. As a result, the rest of the children received 160 more sweets altogether. How many sweets were there in the container at first? [?]",
      "answer0": "800", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "The 4 children gave away their sweets, and these 160 sweets came from those 4 children: each child had 160 ÷ 4 = 40 sweets. Total = 20 x 40 = 800 sweets.",
      "hints": ["The 160 extra sweets came from the 4 children who gave theirs away.", "Find sweets per child, then multiply by 20."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Q24",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Answer key Q24 = 800 (160÷4=40 each, 20x40=800)."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "Measure and write down the size of \\(\\angle y\\). Ans: [?]°",
      "answer0": "43", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 140,
      "difficulty_id": 2,
      "explanation": "Measuring the marked angle y with a protractor gives 43deg.",
      "hints": ["Use a protractor to measure the angle.", "Read the angle to the nearest degree."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Q25",
      "image_needed": true, "image_page": 14, "image_bbox": [0.18,0.13,0.52,0.30], "image_loc": "a horizontal line and a slanted line meeting, with angle y marked",
      "image_options": false, "image_file": "q25.png",
      "notes": "Answer key Q25 = 43 degrees. Angle must be measured from the figure."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "In the figure, PRS and QRT are triangles. RTS is a straight line and QT = QR. \\(\\angle QTR = 64^\\circ\\), \\(\\angle QRP = 27^\\circ\\) and \\(\\angle PST = 77^\\circ\\). Find \\(\\angle SPR\\). Ans: [?]°",
      "answer0": "66", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "In triangle QRT (QT = QR isosceles), \\(\\angle QTR = \\angle QRT = 64^\\circ\\)... \\(\\angle PRS = 64 - 27 = 37^\\circ\\). In triangle PRS: \\(\\angle SPR = 180^\\circ - 77^\\circ - 37^\\circ = 66^\\circ\\).",
      "hints": ["Use the isosceles triangle QRT (QT = QR).", "In triangle PRS use the angle sum 180deg."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Q26",
      "image_needed": true, "image_page": 14, "image_bbox": [0.14,0.50,0.55,0.72], "image_loc": "two triangles PRS and QRT sharing straight line RTS, angles 77deg, 64deg, 27deg marked",
      "image_options": false, "image_file": "q26.png",
      "notes": "Answer key Q26 = 66 (PRS:64-27=37, SPR:180-77-37=66)."
    },
    {
      "n": 27,
      "type_id": 0,
      "question": "The bar graph shows the daily pocket money some students receive from their parents. \\(\\dfrac{1}{5}\\) of these students receive $2.50 for their pocket money daily. Draw the bar that shows the number of students who receive $2.50 for their pocket money daily.",
      "answer0": null, "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 147,
      "difficulty_id": 2,
      "explanation": "Find the total number of students from the existing bars, take 1/5 of it, and draw a bar of that height at $2.50. See the answer-key diagram.",
      "hints": ["Add up the students shown on the other bars.", "1/5 of the total gives the height of the $2.50 bar."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Q27",
      "image_needed": true, "image_page": 15, "image_bbox": [0.14,0.22,0.66,0.48], "image_loc": "bar graph of number of students vs daily pocket money ($2, $2.50, $3, $3.50) with $2.50 bar missing",
      "image_options": false, "image_file": "q27.png",
      "notes": "Interactive 'draw the bar' task - no value answer, so type_id 0 (skipped on insert)."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "The figure is made up of square ABEF and rectangle BCDE. FD = 20 cm and AF = 8 cm. Find the area of the shaded triangle ADE. Ans: [?] cm²",
      "answer0": "48", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "AF = 8 cm so the square ABEF has side 8 cm, meaning FE = 8 cm and ED = FD - FE = 20 - 8 = 12 cm. Triangle ADE has base ED = 12 cm and height 8 cm: area = 1/2 x 12 x 8 = 48 cm².",
      "hints": ["Find ED using FD - FE (FE equals the square's side).", "Area of triangle ADE = 1/2 x ED x height."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Q28",
      "image_needed": true, "image_page": 16, "image_bbox": [0.22,0.16,0.62,0.30], "image_loc": "square ABEF and rectangle BCDE joined, FD = 20 cm, AF = 8 cm, shaded triangle ADE",
      "image_options": false, "image_file": "q28.png",
      "notes": "Answer key Q28 = 48 cm2 (ED=20-8=12, 1/2 x 12 x 8 = 48)."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "A rectangular container measuring 20 cm by 10 cm is filled with water to a depth of 14 cm. Hannah pours another 1.05 litres of water into the container. How much water is there in the container in the end? Express your answer in litres and millilitres. Ans: [?] ℓ [?] mℓ",
      "answer0": "3", "answer1": "850",
      "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 191,
      "difficulty_id": 3,
      "explanation": "Water at first = 20 x 10 x 14 = 2800 cm³ = 2800 ml = 2.8 ℓ. Add 1.05 ℓ: 2.8 + 1.05 = 3.85 ℓ = 3 ℓ 850 mℓ.",
      "hints": ["Find the starting volume of water (length x breadth x depth) in ml.", "Add 1.05 ℓ and express as litres and millilitres."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Q29",
      "image_needed": true, "image_page": 16, "image_bbox": [0.18,0.50,0.52,0.72], "image_loc": "rectangular container with water depth 14 cm, base 20 cm by 10 cm",
      "image_options": false, "image_file": "q29.png",
      "notes": "Answer key Q29 = 3 ℓ 850 mℓ. Base dimensions (20 cm, 10 cm) and depth (14 cm) shown in figure."
    },
    {
      "n": 30,
      "type_id": 2,
      "question": "A rectangular piece of paper was folded as shown. The angle 70° and a right angle are marked, with equal folded angles y and angle x. Find \\(\\angle x\\). Ans: [?]°",
      "answer0": "50", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 144,
      "difficulty_id": 3,
      "explanation": "The angle y = 180deg - 70deg - 90deg = 20deg. Then \\(\\angle x = 90^\\circ - 20^\\circ - 20^\\circ = 50^\\circ\\) (the fold creates two equal y angles).",
      "hints": ["Find y first using the 70deg and the right angle.", "x = 90deg minus the two equal folded angles."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Q30",
      "image_needed": true, "image_page": 17, "image_bbox": [0.18,0.16,0.55,0.40], "image_loc": "folded rectangular paper with 70deg, right angle, angles y and x marked",
      "image_options": false, "image_file": "q30.png",
      "notes": "Answer key Q30 = 50 (y=180-70-90=20, x=90-20-20=50)."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "A shaded triangle is drawn inside a rectangle 45 cm + 25 cm wide (total 70 cm) and 26 cm + 14 cm tall (total 40 cm). Find the area of the shaded triangle. Ans: [?] cm²",
      "answer0": "1085", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Rectangle area = (45 + 25) x (26 + 14) = 70 x 40 = 2800 cm². The three corner triangles: A = 1/2 x 45 x 40 = 900, B = 1/2 x 25 x 26 = 325, C = 1/2 x 14 x (25 + 45) = 490. Shaded triangle = 2800 - 900 - 325 - 490 = 1085 cm².",
      "hints": ["Find the area of the whole rectangle.", "Subtract the three unshaded corner triangles."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Paper2 Q1",
      "image_needed": true, "image_page": 20, "image_bbox": [0.18,0.28,0.52,0.46], "image_loc": "rectangle with a shaded triangle inside, labelled 45 cm, 25 cm, 26 cm, 14 cm",
      "image_options": false, "image_file": "q31.png",
      "notes": "Paper 2 Q1. Answer key: 2800 - 900 - 325 - 490 = 1085 cm2."
    },
    {
      "n": 32,
      "type_id": 2,
      "question": "The table shows the parking charges at a shopping mall: 1st hour or part thereof costs $2.80; subsequent 30 minutes or part thereof costs $0.90. Mr Wong parked his car from 5.45 p.m. to 7.55 p.m. How much was his parking charges? Ans: $[?]",
      "answer0": "5.50", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "Duration = 5.45 p.m. to 7.55 p.m. = 2 h 10 min. First hour = $2.80. Remaining 1 h 10 min = 3 blocks of 30 min (or part thereof) = 3 x $0.90 = $2.70. Total = 2.80 + 2.70 = $5.50.",
      "hints": ["Find the parking duration.", "First hour is $2.80; charge each 30 min (round up) at $0.90."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Paper2 Q2",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Paper 2 Q2. Answer key: 2.80 + 1.80 + 0.90 = $5.50. Charge table given in text."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "Sam had $340 more than John. Daniel had twice as much money as Sam. The total amount of money that Sam and Daniel had was $1230. How much money did John have? Ans: $[?]",
      "answer0": "70", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Sam + Daniel = Sam + 2 x Sam = 3 units = $1230, so Sam = $410. John = Sam - $340 = 410 - 340 = $70.",
      "hints": ["Daniel = 2 x Sam, so Sam + Daniel = 3 units.", "Find Sam, then subtract $340 for John."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Paper2 Q3",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Paper 2 Q3. Answer key: 1230÷3=410 (Sam), John = 410-340 = $70."
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "Daryl and James spent an average of $12.20 on their dinner. Daryl spent $2.40 less than James, how much did James spend on his dinner? Ans: $[?]",
      "answer0": "13.40", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 204,
      "difficulty_id": 2,
      "explanation": "Total = $12.20 x 2 = $24.40. Daryl + James = 24.40 and James - Daryl = 2.40, so 2 x James = 24.40 + 2.40 = 26.80... James = (24.40 + 2.40) ÷ 2 = $13.40.",
      "hints": ["Total of both = average x 2.", "James = (total + difference) ÷ 2."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Paper2 Q4",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Paper 2 Q4. Answer key: total 24.40, James = 11+2.40 = $13.40."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "The figure is made up of 3 triangles. The angle 73° is marked at the centre. Find the sum of \\(\\angle a + \\angle b + \\angle c + \\angle d\\). Ans: [?]°",
      "answer0": "394", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 196,
      "difficulty_id": 3,
      "explanation": "Angles a + b are in a triangle with the 73deg, so a + b = 180 - 73 = 107deg. Angles c and d are around the point with the 73deg: c + d = 360 - 73 = 287deg. Total = 107 + 287 = 394deg.",
      "hints": ["Use the triangle angle sum for a and b.", "Use angles at a point for c and d, then add."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Paper2 Q5",
      "image_needed": true, "image_page": 22, "image_bbox": [0.18,0.50,0.52,0.74], "image_loc": "figure of 3 triangles with angles a, b, c, d and 73deg marked",
      "image_options": false, "image_file": "q35.png",
      "notes": "Paper 2 Q5. Answer key: a+b=107, c+d=287, total=394 degrees."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "Mdm Ong had some sugar. She used \\(\\dfrac{3}{7}\\) of it to make lollipops. She then used \\(\\dfrac{2}{5}\\) of the remainder to make muffins. 210 kg of the sugar was left. What was the amount of sugar that she had at first? Ans: [?] kg",
      "answer0": "612.5", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "After lollipops, remainder = 1 - 3/7 = 4/7. After muffins (2/5 of remainder), left = 3/5 of 4/7 = 12/35 of the total = 210 kg. So 1 unit (1/35) = 210 ÷ 12 = 17.5 kg, and total = 35 x 17.5 = 612.5 kg.",
      "hints": ["Find the fraction of sugar left after both uses.", "Set that fraction equal to 210 kg and scale to the whole."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Paper2 Q6",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Paper 2 Q6. Answer key: 210÷3=70? Key working: u:210÷3=70, 5u=350, u:350÷4=87.5, 7u:87.5x7=612.5 kg."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "The figure is made up of 3 different triangles, ADE, ABD and BCD. ADE and BCD are isosceles triangles. \\(\\angle DAE = 37^\\circ\\), \\(\\angle BAD = 63^\\circ\\) and \\(\\angle BCD = 52^\\circ\\). EDC is a straight line. Find \\(\\angle ABD\\). Ans: [?]°",
      "answer0": "60.5", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "Triangle ADE is isosceles with \\(\\angle DAE = 37^\\circ\\), so its base angles = (180 - 37) ÷ 2 = 71.5deg, giving \\(\\angle ADE = 71.5^\\circ\\). Triangle BCD isosceles: \\(\\angle BDC = 180 - 52 - 71.5 = 56.5^\\circ\\). In triangle ABD: \\(\\angle ABD = 180 - 63 - 56.5 = 60.5^\\circ\\).",
      "hints": ["Use the isosceles triangle ADE to find its base angle.", "Use the straight line EDC and triangle ABD's angle sum."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Paper2 Q7",
      "image_needed": true, "image_page": 23, "image_bbox": [0.18,0.58,0.52,0.80], "image_loc": "three triangles ADE, ABD, BCD with straight line EDC, angles 63deg, 37deg, 52deg marked",
      "image_options": false, "image_file": "q37.png",
      "notes": "Paper 2 Q7. Answer key: X=(180-37)÷2=71.5, Y=180-52-71.5=56.5, ABD=180-63-56.5 = 60.5 degrees."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "At a funfair, the ratio of the number of children to the number of adults was 4 : 9. The ratio of the number of boys to the number of girls was 3 : 4. There was a total of 64 girls. How many adults were there altogether? [?]",
      "answer0": "252", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "Boys : girls = 3 : 4, total children = 7 parts; girls = 4 parts = 64, so 1 part = 16 and children = 7 x 16 = 112. Children : adults = 4 : 9, so 1 child-unit = 112 ÷ 4 = 28, and adults = 9 x 28 = 252.",
      "hints": ["Find the total number of children from the boy:girl ratio and 64 girls.", "Use the children:adults ratio to find the adults."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Paper2 Q8",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Paper 2 Q8. Answer key: children=112, u=64÷16=4, adults=63x4=252."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "A box with 9 identical ring files has a mass of 2 kg 2 g. The same box with 14 such ring files has a mass of 2642 g. What is the mass of the box? Give your answer in kg. Ans: [?] kg",
      "answer0": "0.85", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 184,
      "difficulty_id": 3,
      "explanation": "9 files + box = 2002 g; 14 files + box = 2642 g. The extra 5 files = 2642 - 2002 = 640 g, so 1 file = 128 g and 9 files = 1152 g. Box = 2002 - 1152 = 850 g = 0.85 kg.",
      "hints": ["Subtract to find the mass of the extra 5 files.", "Find one file's mass, then the box = total - 9 files."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Paper2 Q9",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Paper 2 Q9. Answer key: 5 files=640g, 1 file=128g, box=2002-1152=850g=0.85 kg. (2 kg 2 g = 2002 g.)"
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "4 identical right-angled triangles were cut out from a piece of square paper with area 64 cm². The 4 triangles were used to form a shape with a shaded rectangle inside. The perimeter of the shaded rectangle formed is 20 cm. Find the area of the shaded rectangle. Ans: [?] cm²",
      "answer0": "24", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 138,
      "difficulty_id": 3,
      "explanation": "Square side = sqrt(64) = 8 cm, so each triangle's legs sum to 8 cm. The rectangle's length + breadth = 20 ÷ 2 = 10 cm. Using length + breadth = 10 and length - breadth = 8 - ... by the key: length + breadth = 10, length 6 and breadth 4, area = 6 x 4 = 24 cm².",
      "hints": ["The square's side is the square root of 64 (= 8 cm).", "Use the rectangle's half-perimeter (10 cm) with the triangle legs to get length and breadth."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Paper2 Q10",
      "image_needed": true, "image_page": 25, "image_bbox": [0.14,0.20,0.66,0.40], "image_loc": "square paper with 4 right-angled triangles and the formed shape with shaded rectangle",
      "image_options": false, "image_file": "q40.png",
      "notes": "Paper 2 Q10. Answer key: 64=8x8, L+b=10, length=6, breadth=4, 6x4 = 24 cm2."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "James had a rectangular container measuring 55 cm by 28 cm by 24 cm. It was \\(\\dfrac{5}{8}\\) filled with water. James then poured out \\(\\dfrac{1}{4}\\) of the water. How much water remained in the container? Leave your answer in litres and millilitres. Ans: [?] ℓ [?] mℓ",
      "answer0": "17", "answer1": "325",
      "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 191,
      "difficulty_id": 3,
      "explanation": "Container volume = 55 x 28 x 24 = 36 960... actually 55 x 28 x 24 = 36 960 cm³. Water at 5/8 = 5/8 x 36 960 = 23 100 cm³. Remaining after pouring 1/4 out = 3/4 of 23 100 = 17 325 cm³ = 17 325 mℓ = 17 ℓ 325 mℓ.",
      "hints": ["Find the volume of water (5/8 of the container).", "Keep 3/4 of it after pouring out 1/4; convert to ℓ and mℓ."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Paper2 Q11",
      "image_needed": true, "image_page": 26, "image_bbox": [0.18,0.22,0.52,0.40], "image_loc": "cuboid container 55 cm by 28 cm by 24 cm",
      "image_options": false, "image_file": "q41.png",
      "notes": "Paper 2 Q11. Answer key: volume of water = 23100, remaining = 23100 x 3/4 = 17325 ml = 17 ℓ 325 mℓ. Dimensions given in text."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "Ahmad spent $112 for 5 identical books and 5 identical pens. The cost of 4 pens is the same as 3 books. What is the cost of 1 pen? Ans: $[?]",
      "answer0": "9.60", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "4 pens = 3 books, so 1 book = 4/3 pens. 5 books + 5 pens = 5(4/3 pens) + 5 pens = 20/3 + 5 = 35/3 pens... cost: 1 book = $112 ÷ (8 3/4) = $12.80, 3 books = $38.40, 1 pen = $38.40 ÷ 4 = $9.60.",
      "hints": ["Convert books to pens using 4 pens = 3 books.", "Express the $112 in terms of one unit, then find one pen."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Paper2 Q12",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Paper 2 Q12. Answer key: 1 book=112÷8.75=12.80, 3 books=38.40, 1 pen=38.40÷4 = $9.60."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "Elena bought many types of toys at an average cost of $12. She then bought one of each of two more toys costing $28 and $10, and the average cost of all her toys became $14.<br>(a) How many toys did she buy in total? [?]<br>(b) What was the total cost of all her toys that she bought? Ans: $[?]",
      "answer0": "7", "answer1": "98",
      "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 204,
      "difficulty_id": 3,
      "explanation": "Let the first number of toys be n. Total before = 12n. After adding $28 and $10 (2 toys), total = 12n + 38 and count = n + 2, with average 14: 12n + 38 = 14(n + 2) = 14n + 28, so 10 = 2n, n = 5. Total toys = 5 + 2 = 7. (b) Total cost = 14 x 7 = $98.",
      "hints": ["Set up the average equation before and after the two new toys.", "Total cost = final average x total number of toys."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Paper2 Q13",
      "image_needed": true, "image_page": 28, "image_bbox": [0.18,0.22,0.72,0.40], "image_loc": "two toys with price tags $28 and $10",
      "image_options": false, "image_file": "q43.png",
      "notes": "Paper 2 Q13 (a)&(b). Answer key: (a) 7 toys, (b) 14x7 = $98. Prices $28 and $10 shown in figures."
    },
    {
      "n": 44,
      "type_id": 1,
      "question": "There were 25 similar cones placed at equal distance along a straight road. The 1st cone is at the start and the 25th cone is at the end of the road. The base of each cone is 0.3 m and the distance between 2 cones (gap) is 8 m.<br>(a) Find the length of the road. (b) 4 of the cones were removed and the rest rearranged at equal distance with the first cone at the start and the last cone at the end. What was the new distance between each of the cones?",
      "answer0": "199.5 m (road); 9.66 m (new gap)", "answer1": "192 m (road); 8 m (new gap)", "answer2": "199.5 m (road); 8.32 m (new gap)", "answer3": "200 m (road); 9.5 m (new gap)",
      "correct_answer": 0,
      "skill_id": 184,
      "difficulty_id": 3,
      "explanation": "(a) 25 cones have 24 gaps of 8 m = 192 m, plus 25 cone-bases of 0.3 m = 7.5 m, so road = 192 + 7.5 = 199.5 m. (b) After removing 4 cones, 21 cones remain with 20 gaps. Total gap length = 199.5 - (21 x 0.3) = 193.2 m, so new distance = 193.2 ÷ 20 = 9.66 m.",
      "hints": ["Road = total gaps + total cone-base widths.", "After removal, recompute the gap length and divide by the number of new gaps."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Paper2 Q14",
      "image_needed": true, "image_page": 29, "image_bbox": [0.14,0.20,0.66,0.36], "image_loc": "row of cones along a road, base 0.3 m, gap 8 m, 1st to 25th cone",
      "image_options": false, "image_file": "q44.png",
      "notes": "Paper 2 Q14 (a)&(b). Answer key: (a) 199.5 m, (b) 9.66 m. Combined two decimal/measurement answers into one MCQ (option 1)."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "There are some red, green and black beans in a tin. 28% of the beans in the tin are red. The ratio of the number of green beans to the number of black beans is 8 : 1. There are 468 more green beans than red beans. How many red beans are there? [?]",
      "answer0": "364", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "Red = 28% of total. Green + black = 72%, with green : black = 8 : 1, so green = 8/9 of 72% = 64% and black = 8%. Green - red = 64% - 28% = 36% = 468 beans, so 1% = 13 beans. Red = 28% = 28 x 13 = 364.",
      "hints": ["Split the non-red 72% in the ratio 8 : 1 to find green's percentage.", "Use green - red = 36% = 468 to find 1%, then red = 28%."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Paper2 Q15",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Paper 2 Q15. Answer key: green=64%, difference 36%=468, 1u=13, red=13x28 = 364."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "Two companies show delivery fees. Fast Express: service fee $9, first 5 km $1.20 per km or part thereof, above 5 km $0.70 per km or part thereof. SaSamoveit: service fee $12, first 3 km $1 per km or part thereof, above 3 km $0.45 per km or part thereof.<br>(a) Mr Lee wants to send a parcel from RH School to NR School which is 4.4 km away. What is the delivery fee he needs to pay if he uses SaSamoveit? Ans: $[?]<br>(b)(ii) Mrs Wen wants to send a parcel 8.7 km away to the cheaper company. How much will she save when she uses the cheaper company? Ans: $[?]",
      "answer0": "15.90", "answer1": "0.10",
      "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "(a) SaSamoveit for 4.4 km: service $12 + first 3 km (3 x $1 = $3) + above 3 km (1.4 km -> 2 km at $0.45 = $0.90) = 12 + 3 + 0.90 = $15.90. (b)(ii) For 8.7 km: Fast Express = 9 + (5 x 1.20) + (3.7 km -> 4 x 0.70 = 2.80) = 9 + 6 + 2.80 = $17.80; SaSamoveit = 12 + 3 + (5.7 km -> 6 x 0.45 = 2.70) = $17.70. Saving = 17.80 - 17.70 = $0.10 (SaSamoveit is cheaper).",
      "hints": ["Charge the service fee, then per-km in whole-km blocks (round up).", "For (b) work out both companies' fees and subtract."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Paper2 Q16",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Paper 2 Q16. Answer key: (a) $15.90, (b)(i) SaSamoveit cheaper (a draw/circle part, omitted), (b)(ii) $0.10. Fee tables given in text. Part (b)(i) 'circle the company' is interactive and not represented as a separate answer."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "Eddie had some engine oil. He sold \\(\\dfrac{2}{3}\\) of his engine oil on Monday. He then sold \\(\\dfrac{4}{9}\\) of the remainder and an extra 340 litres on Tuesday. On Wednesday, he sold \\(\\dfrac{1}{2}\\) of the remainder and an extra 200 litres. Eddie then kept the remaining 1260 litres for himself. How much engine oil did he have at first? Ans: [?] ℓ",
      "answer0": "17604", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Work backwards. Before Wednesday's '+200' and '1/2': 1/2 remainder = 1260 + 200 = 1460, so start of Wednesday = 2920. Before Tuesday's '+340' and '4/9': after selling 4/9, 5/9 of the Tuesday remainder = 2920 + 340 = 3260, so start of Tuesday = 3260 x 9/5 = 5868. This is the 1/3 left after Monday, so total = 5868 x 3 = 17 604 ℓ.",
      "hints": ["Work backwards from the final 1260 litres.", "Undo each day's fraction and extra litres in reverse order."],
      "source": "Rosyth 2022 P5 End-of-Year Exam Paper2 Q17",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Paper 2 Q17. Answer key: 1/2:1260+200=1460, Wed start 2920, +340=3260, Tue start 3260x9/5=5868, total 5868x3 = 17604 ℓ."
    }
  ]
}