{
  "paper": {
    "school": "Maha Bodhi",
    "year": 2023,
    "level": "P5",
    "label": "Weighted Assessment 2",
    "source_prefix": "Maha Bodhi 2023 P5 Weighted Assessment 2",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "Mr Tan spent \\(\\dfrac{1}{5}\\) of his salary on transport and \\(\\dfrac{1}{4}\\) of the remainder on food. What fraction of his salary is left?",
      "answer0": "\\(\\dfrac{3}{5}\\)",
      "answer1": "\\(\\dfrac{2}{5}\\)",
      "answer2": "\\(\\dfrac{3}{20}\\)",
      "answer3": "\\(\\dfrac{1}{5}\\)",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "Transport: \\(\\dfrac{1}{5}\\) spent, so \\(\\dfrac{4}{5}\\) remains. Food: \\(\\dfrac{1}{4}\\) of the remainder = \\(\\dfrac{1}{4}\\times\\dfrac{4}{5}=\\dfrac{1}{5}\\). Left = \\(\\dfrac{4}{5}-\\dfrac{1}{5}=\\dfrac{3}{5}\\).",
      "hints": ["After transport, what fraction of the whole salary remains?", "Food is one quarter of that remainder. Subtract food from the remainder."],
      "source": "Maha Bodhi 2023 P5 Weighted Assessment 2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: 3/5. Fraction answer -> MCQ."
    },
    {
      "n": 2,
      "type_id": 2,
      "question": "What is the missing decimal represented by W? [?]",
      "answer0": "2.3",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 158,
      "difficulty_id": 2,
      "explanation": "The number line runs from \\(1\\dfrac{1}{4}=1.25\\) to 2.65 with equal intervals. There are 4 equal intervals between them: each = \\((2.65-1.25)\\div4=1.4\\div4=0.35\\). W sits 3 intervals from 1.25: \\(1.25+3\\times0.35=1.25+1.05=2.3\\).",
      "hints": ["Convert the mixed number to a decimal first: \\(1\\dfrac{1}{4}=1.25\\).", "Find the size of one interval, then count the intervals from 1.25 to W."],
      "source": "Maha Bodhi 2023 P5 Weighted Assessment 2 Q2",
      "image_needed": true,
      "image_options": false,
      "image_file": "q2.png",
      "image_page": 2,
      "image_bbox": [0.22, 0.14, 0.66, 0.24],
      "image_loc": "horizontal number line near top of page, labels 1 1/4, W and 2.65",
      "notes": "Answer key: W = 2.3 (interval 0.35). Decimal answer -> FIB."
    },
    {
      "n": 3,
      "type_id": 2,
      "question": "For every 5 questions in a quiz, Mrs Tan answered 3 questions correctly. Mrs Tan answered 12 questions incorrectly. How many questions were there in all? [?]",
      "answer0": "30",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 2,
      "explanation": "Out of every 5 questions, 3 are correct and \\(5-3=2\\) are incorrect. She got 12 incorrect, so number of groups = \\(12\\div2=6\\). Total questions = \\(6\\times5=30\\).",
      "hints": ["For every 5 questions, how many were answered incorrectly?", "How many groups of 5 give 12 incorrect answers? Multiply that by 5."],
      "source": "Maha Bodhi 2023 P5 Weighted Assessment 2 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: 30."
    },
    {
      "n": 4,
      "type_id": 2,
      "question": "Some storybooks were shared equally among 114 children. 60 of them decided to give their share to the rest of the children. Each remaining child then received 10 more storybooks. How many storybooks did each remaining child receive in the end? [?]",
      "answer0": "19",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Remaining children = \\(114-60=54\\). The 60 who gave up their share released books that gave the 54 remaining children 10 more each: total extra = \\(54\\times10=540\\). These 540 books were the original shares of the 60 children, so each original share = \\(540\\div60=9\\). Each remaining child ends with \\(9+10=19\\) storybooks.",
      "hints": ["How many children remain after 60 give up their share?", "The extra books each remaining child got came from the 60 who left. Work out one original share first."],
      "source": "Maha Bodhi 2023 P5 Weighted Assessment 2 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: 19."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "A rectangular tank measuring 65 cm by 54 cm by 32 cm was filled with water to a height of 16 cm at first. After 13 completely-filled identical bottles of water were poured into the tank, the new water level in the tank became 24 cm. Find the capacity of each bottle in litres and millilitres.",
      "answer0": "2 L 160 ml",
      "answer1": "2 L 16 ml",
      "answer2": "1 L 160 ml",
      "answer3": "2 L 1600 ml",
      "correct_answer": 0,
      "skill_id": 191,
      "difficulty_id": 3,
      "explanation": "Rise in water level = \\(24-16=8\\) cm. Volume of water added = \\(8\\times65\\times54=28080\\) cm³. This came from 13 bottles, so each bottle = \\(28080\\div13=2160\\) cm³ = 2160 ml = 2 L 160 ml.",
      "hints": ["Find the increase in water height, then the volume of that added water.", "Divide the added volume by 13, then convert cm³ to litres and millilitres."],
      "source": "Maha Bodhi 2023 P5 Weighted Assessment 2 Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q5.png",
      "image_page": 3,
      "image_bbox": [0.15, 0.59, 0.47, 0.73],
      "image_loc": "3-D drawing of a rectangular tank with dimensions 65 cm, 54 cm, 32 cm, middle-left of page",
      "notes": "Answer key: 2160 ml = 2 L 160 ml. Compound L/ml answer -> MCQ."
    },
    {
      "n": 6,
      "type_id": 2,
      "question": "At a basketball match, \\(\\dfrac{3}{7}\\) of the spectators are children. \\(\\dfrac{1}{3}\\) of the adults were women. There were 38 more children than men at the match. How many children were at the match? [?]",
      "answer0": "342",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Children are \\(\\dfrac{3}{7}\\), so adults are \\(\\dfrac{4}{7}\\). Take 21 units total: children = 9 units, adults = 12 units. \\(\\dfrac{1}{3}\\) of adults are women = 4 units, so men = 8 units. Children − men = \\(9-8=1\\) unit = 38. Children = 9 units = \\(9\\times38=342\\).",
      "hints": ["Split the spectators into equal units so both the 3:7 and the 1:3 of adults are whole numbers.", "Find women and men in units, then use 'children minus men = 38'."],
      "source": "Maha Bodhi 2023 P5 Weighted Assessment 2 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: 342. 1 unit = 38, children = 9 units."
    },
    {
      "n": 7,
      "type_id": 2,
      "question": "3 notebooks and 7 pens cost $28.90. 5 notebooks and 2 pens cost $18.20. What is the cost of 1 pen? [?]",
      "answer0": "3.10",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "Multiply set 1 by 5 and set 2 by 3 to equalise notebooks: 15 notebooks + 35 pens = \\(28.90\\times5=144.50\\); 15 notebooks + 6 pens = \\(18.20\\times3=54.60\\). Subtract: \\(35-6=29\\) pens cost \\(144.50-54.60=89.90\\). 1 pen = \\(89.90\\div29=\\$3.10\\).",
      "hints": ["Scale both equations so the number of notebooks matches.", "Subtract to eliminate the notebooks, leaving only pens."],
      "source": "Maha Bodhi 2023 P5 Weighted Assessment 2 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: $3.10. Money decimal -> FIB (answer 3.10)."
    },
    {
      "n": 8,
      "type_id": 2,
      "question": "The figure, not drawn to scale, is made up of 3 squares. Find the shaded area. [?]",
      "answer0": "286",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "The three squares have sides 14 cm, 12 cm and 10 cm (the 12 cm comes from \\(14-2\\)). Their total area = \\(14\\times14 + 12\\times12 + 10\\times10 = 196+144+100=440\\) cm². The unshaded triangle has base = total width \\(=14+12+10=...\\) using base 22 and height 14: \\(\\dfrac{1}{2}\\times22\\times14=154\\) cm². Shaded area = \\(440-154=286\\) cm².",
      "hints": ["Find the side of the middle square from the 14 cm and 2 cm marks, then total the three square areas.", "Subtract the area of the large unshaded right-angled triangle."],
      "source": "Maha Bodhi 2023 P5 Weighted Assessment 2 Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 6,
      "image_bbox": [0.21, 0.2, 0.74, 0.37],
      "image_loc": "shaded figure of 3 stepped squares with marks 14 cm, 2 cm, 10 cm, upper-middle of page",
      "notes": "Answer key: 286 cm² (unit cm²). 1/2 x 22 x 14 = 154 is the unshaded triangle. Answer entered as integer 286 (unit cm^2)."
    },
    {
      "n": 9,
      "type_id": 2,
      "question": "James had some fifty-cent coins and 13 twenty-cent coins. Timothy had some fifty-cent coins and 54 twenty-cent coins. Both boys had the same number of coins. One of the boys had more money. How much more money did he have? [?]",
      "answer0": "12.30",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "Both boys have the same total number of coins. Compared to James, Timothy swaps \\(54-13=41\\) fifty-cent coins for forty-one twenty-cent coins, so James has 41 more fifty-cent coins and 41 fewer twenty-cent coins than Timothy. Each swap of a 50c for a 20c is worth 30c more, so James has \\(41\\times\\$0.30=\\$12.30\\) more money than Timothy.",
      "hints": ["Since the total coin count is equal, compare the two boys coin-by-coin.", "Each fifty-cent coin James has in place of a twenty-cent coin is worth 30 cents more."],
      "source": "Maha Bodhi 2023 P5 Weighted Assessment 2 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: $12.30 (James had more). Money decimal -> FIB (answer 12.30)."
    },
    {
      "n": 10,
      "type_id": 2,
      "question": "Miss Lim spent $786 to buy a total of 60 M-size and L-size skirts. One M-size skirt cost $12 and one L-size skirt cost $15. How many M-size skirts did she buy? [?]",
      "answer0": "38",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "Assume all 60 skirts were L-size: \\(60\\times15=\\$900\\). That is \\(900-786=\\$114\\) too much. Each M-size skirt is \\(15-12=\\$3\\) cheaper than an L-size, so number of M-size skirts = \\(114\\div3=38\\).",
      "hints": ["Suppose every skirt was the more expensive L-size first.", "Each M-size skirt lowers the total by $3 from that assumption."],
      "source": "Maha Bodhi 2023 P5 Weighted Assessment 2 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: 38 M-size skirts."
    }
  ]
}