{
  "paper": {
    "school": "Nan Hua",
    "year": 2022,
    "level": "P5",
    "label": "Weighted Assessment 1",
    "source_prefix": "Nan Hua 2022 P5 Weighted Assessment 1",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "The figure is made up of 10 identical rectangles. What fraction of the figure is shaded? Leave your answer as a fraction in the simplest form.",
      "answer0": "\\(\\dfrac{2}{5}\\)",
      "answer1": "\\(\\dfrac{4}{5}\\)",
      "answer2": "\\(\\dfrac{1}{5}\\)",
      "answer3": "\\(\\dfrac{3}{10}\\)",
      "correct_answer": 0,
      "skill_id": 157,
      "difficulty_id": 2,
      "explanation": "The shaded triangle covers an area equal to half of the 6 rectangles it spans (half of 6 = 3) plus 1 full rectangle, giving 1 + 3 = 4 shaded rectangles out of 10. \\(\\dfrac{4}{10} = \\dfrac{2}{5}\\).",
      "hints": ["The triangle's area equals half the base-times-height region it covers.", "Count whole-rectangle equivalents shaded, then simplify the fraction out of 10."],
      "source": "Nan Hua 2022 P5 Weighted Assessment 1 Q1",
      "image_needed": true,
      "image_options": false,
      "image_file": "q1.png",
      "image_page": 1,
      "image_bbox": [0.24, 0.49, 0.55, 0.66],
      "image_loc": "left side of page, grid of 10 rectangles with a shaded triangle, below the question",
      "notes": "Fraction answer 2/5 so rendered as MCQ. Printed key: 4/10 = 2/5."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "2 \\(\\ell\\) of fruit juice was shared equally among 14 children. How many litres of fruit juice would each child receive? Leave your answer as a fraction in the simplest form.",
      "answer0": "\\(\\dfrac{1}{7}\\)",
      "answer1": "\\(\\dfrac{2}{14}\\)",
      "answer2": "\\(\\dfrac{1}{14}\\)",
      "answer3": "\\(\\dfrac{2}{7}\\)",
      "correct_answer": 0,
      "skill_id": 164,
      "difficulty_id": 1,
      "explanation": "Each child gets \\(2 \\div 14 = \\dfrac{2}{14} = \\dfrac{1}{7}\\) litre.",
      "hints": ["Divide the total 2 litres by 14 children.", "Simplify the resulting fraction."],
      "source": "Nan Hua 2022 P5 Weighted Assessment 1 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Fraction answer 1/7 so rendered as MCQ. Printed key: 2/14 = 1/7."
    },
    {
      "n": 3,
      "type_id": 2,
      "question": "Find the area of the rectangle with sides \\(\\dfrac{9}{5}\\) m and \\(\\dfrac{3}{10}\\) m. Express your answer as a decimal. [?] m²",
      "answer0": "0.54",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 161,
      "difficulty_id": 2,
      "explanation": "Area = length × breadth = \\(\\dfrac{9}{5} \\times \\dfrac{3}{10} = \\dfrac{27}{50}\\). As a decimal, \\(\\dfrac{27}{50} = 0.54\\) m².",
      "hints": ["Multiply the two side lengths together.", "Convert the resulting fraction 27/50 to a decimal."],
      "source": "Nan Hua 2022 P5 Weighted Assessment 1 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q3.png",
      "image_page": 2,
      "image_bbox": [0.18, 0.16, 0.50, 0.28],
      "image_loc": "upper-left of page, rectangle labelled 9/5 m (bottom) and 3/10 m (right side)",
      "notes": "Decimal answer so FIB. Printed key: 27/50 = 0.54 m²."
    },
    {
      "n": 4,
      "type_id": 2,
      "question": "\\(\\dfrac{7}{10} - \\dfrac{1}{6} = \\dfrac{[?]}{15}\\)",
      "answer0": "8",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 159,
      "difficulty_id": 2,
      "explanation": "\\(\\dfrac{7}{10} - \\dfrac{1}{6} = \\dfrac{21}{30} - \\dfrac{5}{30} = \\dfrac{16}{30} = \\dfrac{8}{15}\\). So the missing numerator is 8.",
      "hints": ["Find a common denominator for 10 and 6 (use 30).", "Simplify the result and compare with the /15 form."],
      "source": "Nan Hua 2022 P5 Weighted Assessment 1 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Missing numerator is an integer (8) over the printed denominator 15, so FIB. Printed key: 8."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "Leon's baby brother weighs \\(7\\dfrac{2}{5}\\) kg. Leon weighs 4 times as heavy as his baby brother. What is Leon's mass?",
      "answer0": "\\(29\\dfrac{3}{5}\\)",
      "answer1": "\\(28\\dfrac{2}{5}\\)",
      "answer2": "\\(29\\dfrac{2}{5}\\)",
      "answer3": "\\(30\\dfrac{3}{5}\\)",
      "correct_answer": 0,
      "skill_id": 163,
      "difficulty_id": 2,
      "explanation": "\\(7\\dfrac{2}{5} = \\dfrac{37}{5}\\). Leon's mass = \\(\\dfrac{37}{5} \\times 4 = \\dfrac{148}{5} = 29\\dfrac{3}{5}\\) kg.",
      "hints": ["Convert the mixed number to an improper fraction first.", "Multiply by 4, then convert back to a mixed number."],
      "source": "Nan Hua 2022 P5 Weighted Assessment 1 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Mixed-number answer so MCQ. Printed key: 148/5 = 29 3/5 kg."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "Mrs Lum bought \\(3\\dfrac{1}{2}\\) m of cloth. She used \\(1\\dfrac{1}{3}\\) m of cloth to make some cushion covers. How much cloth was left?",
      "answer0": "\\(2\\dfrac{1}{6}\\)",
      "answer1": "\\(2\\dfrac{1}{5}\\)",
      "answer2": "\\(1\\dfrac{5}{6}\\)",
      "answer3": "\\(2\\dfrac{5}{6}\\)",
      "correct_answer": 0,
      "skill_id": 160,
      "difficulty_id": 2,
      "explanation": "\\(3\\dfrac{1}{2} - 1\\dfrac{1}{3} = 3\\dfrac{3}{6} - 1\\dfrac{2}{6} = 2\\dfrac{1}{6}\\) m.",
      "hints": ["Convert both fractional parts to a common denominator of 6.", "Subtract the whole numbers and the fractions separately."],
      "source": "Nan Hua 2022 P5 Weighted Assessment 1 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Mixed-number answer so MCQ. Printed key: 2 1/6 m."
    },
    {
      "n": 7,
      "type_id": 2,
      "question": "Joan had twice as many beads as Germaine. After Joan gave away \\(\\dfrac{5}{12}\\) of her beads and Germaine bought another 25 beads, they had the same number of beads. How many beads did Joan have at first? [?]",
      "answer0": "300",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Let Germaine have 1 unit, so Joan has 2 units. Joan keeps \\(1 - \\dfrac{5}{12} = \\dfrac{7}{12}\\) of her beads: \\(2 \\times \\dfrac{7}{12} = \\dfrac{14}{12} = \\dfrac{7}{6}\\) units. Germaine then has \\(1\\) unit + 25. Setting equal: \\(\\dfrac{7}{6}\\) units = 1 unit + 25, so \\(\\dfrac{1}{6}\\) unit = 25, 1 unit = 150. Joan = 2 units = 300 beads.",
      "hints": ["Let Germaine = 1 unit and Joan = 2 units, then find the fraction Joan keeps.", "Set Joan's remaining beads equal to Germaine's new total and solve for one unit."],
      "source": "Nan Hua 2022 P5 Weighted Assessment 1 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Integer answer so FIB. Printed key working confirms Joan had 300 beads at first (12u = 300, Germaine 150)."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "Justin spent \\(\\dfrac{3}{8}\\) of his money on books and \\(\\dfrac{2}{5}\\) of his remaining money on toys. What fraction of his money did Justin spend on toys?",
      "answer0": "\\(\\dfrac{1}{4}\\)",
      "answer1": "\\(\\dfrac{2}{5}\\)",
      "answer2": "\\(\\dfrac{3}{20}\\)",
      "answer3": "\\(\\dfrac{1}{5}\\)",
      "correct_answer": 0,
      "skill_id": 161,
      "difficulty_id": 2,
      "explanation": "Remaining after books = \\(1 - \\dfrac{3}{8} = \\dfrac{5}{8}\\). Spent on toys = \\(\\dfrac{5}{8} \\times \\dfrac{2}{5} = \\dfrac{10}{40} = \\dfrac{1}{4}\\) of his money.",
      "hints": ["First find the fraction of money left after buying books.", "Multiply that remaining fraction by 2/5."],
      "source": "Nan Hua 2022 P5 Weighted Assessment 1 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Fraction answer 1/4 so MCQ. Printed key: 5/8 × 2/5 = 1/4."
    },
    {
      "n": 9,
      "type_id": 2,
      "question": "Lucas and James had the same number of stickers. Lucas gave away \\(\\dfrac{3}{4}\\) of his stickers. James gave away \\(\\dfrac{1}{8}\\) of his stickers. James has 75 more stickers than Lucas left. How many stickers did Lucas and James each have at first? [?]",
      "answer0": "120",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Lucas has \\(1 - \\dfrac{3}{4} = \\dfrac{1}{4}\\) left; James has \\(1 - \\dfrac{1}{8} = \\dfrac{7}{8}\\) left. Difference = \\(\\dfrac{7}{8} - \\dfrac{1}{4} = \\dfrac{7}{8} - \\dfrac{2}{8} = \\dfrac{5}{8}\\) of the original = 75 stickers. So original = \\(75 \\div \\dfrac{5}{8} = 75 \\times \\dfrac{8}{5} = 120\\). Each had 120 stickers at first.",
      "hints": ["Find the fraction of stickers each boy has left.", "The difference of those fractions equals 75 stickers; solve for the original amount."],
      "source": "Nan Hua 2022 P5 Weighted Assessment 1 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Integer answer (same for both) so FIB with single blank. Printed key: 120 each."
    },
    {
      "n": 10,
      "type_id": 2,
      "question": "Charles, Danny and Emily used \\(8\\dfrac{3}{4}\\) kg of flour to bake some cakes. Danny used \\(\\dfrac{1}{4}\\) kg of flour more than Charles. Emily used twice as much flour as Danny. How much flour did Charles use? [?] kg",
      "answer0": "2",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Let Charles = 1 unit. Danny = 1 unit + \\(\\dfrac{1}{4}\\). Emily = 2 × Danny = 2 units + \\(\\dfrac{1}{2}\\). Total = 4 units + \\(\\dfrac{3}{4}\\) = \\(8\\dfrac{3}{4}\\). So 4 units = \\(8\\dfrac{3}{4} - \\dfrac{3}{4} = 8\\), 1 unit = 2 kg. Charles used 2 kg.",
      "hints": ["Express Danny and Emily in terms of Charles' amount.", "Add them to 8 3/4, subtract the constant 3/4, then divide by the number of units."],
      "source": "Nan Hua 2022 P5 Weighted Assessment 1 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Integer answer so FIB. Printed key: 4u = 8, 1u = 2 kg (Charles)."
    },
    {
      "n": 11,
      "type_id": 2,
      "question": "Liling had some money. She spent $14 on a story book, \\(\\dfrac{3}{7}\\) of the remainder on a school bag and saved the rest. She saved $28. How much money did Liling have at first? [?]",
      "answer0": "63",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "After the story book, \\(\\dfrac{3}{7}\\) of the remainder went to the bag, so \\(\\dfrac{4}{7}\\) of the remainder was saved = $28. Remainder = \\(28 \\div \\dfrac{4}{7} = 28 \\times \\dfrac{7}{4} = 49\\). At first = $49 + $14 = $63.",
      "hints": ["The saved $28 is the fraction of the remainder NOT spent on the bag.", "Find the remainder after the book, then add back the $14."],
      "source": "Nan Hua 2022 P5 Weighted Assessment 1 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Money answer so FIB. Printed key: 28 ÷ 4 × 7 = 49, $49 + $14 = $63."
    }
  ]
}