{
  "paper": {
    "school": "Nanyang",
    "year": 2022,
    "level": "P5",
    "label": "Weighted Assessment 1",
    "source_prefix": "Nanyang 2022 P5 Weighted Assessment 1",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "What is the value of \\(312\\,000 \\div 400\\)?",
      "answer0": "78",
      "answer1": "780",
      "answer2": "7800",
      "answer3": "78 000",
      "correct_answer": 1,
      "skill_id": 151,
      "difficulty_id": 1,
      "explanation": "Method: divide by tens/hundreds. \\(312\\,000 \\div 400 = 3120 \\div 4 = 780\\). Answer: 780.",
      "hints": ["Cancel the trailing zeros: \\(312\\,000 \\div 400 = 3120 \\div 4\\).", "\\(3120 \\div 4 = 780\\)."],
      "source": "Nanyang 2022 P5 Weighted Assessment 1 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option (2) = 780."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "What is the value of \\(16 + (39 - 7) \\div 4 \\times 2\\)?",
      "answer0": "20",
      "answer1": "24",
      "answer2": "32",
      "answer3": "48",
      "correct_answer": 2,
      "skill_id": 155,
      "difficulty_id": 2,
      "explanation": "Method: order of operations. \\(39 - 7 = 32\\); \\(32 \\div 4 = 8\\); \\(8 \\times 2 = 16\\); \\(16 + 16 = 32\\). Answer: 32.",
      "hints": ["Brackets first, then divide and multiply from left to right.", "\\(32 \\div 4 \\times 2 = 16\\), so \\(16 + 16 = 32\\)."],
      "source": "Nanyang 2022 P5 Weighted Assessment 1 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option (3) = 32."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "What is the value of \\(\\dfrac{2}{7} \\times \\dfrac{9}{5}\\)?",
      "answer0": "\\(\\dfrac{11}{35}\\)",
      "answer1": "\\(\\dfrac{18}{35}\\)",
      "answer2": "\\(\\dfrac{53}{35}\\)",
      "answer3": "\\(\\dfrac{73}{35}\\)",
      "correct_answer": 1,
      "skill_id": 161,
      "difficulty_id": 1,
      "explanation": "Method: multiply numerators and denominators. \\(\\dfrac{2}{7} \\times \\dfrac{9}{5} = \\dfrac{2 \\times 9}{7 \\times 5} = \\dfrac{18}{35}\\). Answer: \\(\\dfrac{18}{35}\\).",
      "hints": ["Multiply the numerators: \\(2 \\times 9 = 18\\).", "Multiply the denominators: \\(7 \\times 5 = 35\\)."],
      "source": "Nanyang 2022 P5 Weighted Assessment 1 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option (2) = 18/35."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Donna had 168 stamps. She gave \\(\\dfrac{2}{3}\\) of her stamps to 7 friends. Each friend received an equal number of stamps. How many stamps did each friend receive?",
      "answer0": "8",
      "answer1": "16",
      "answer2": "24",
      "answer3": "112",
      "correct_answer": 1,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "Method: find the fraction of the set, then divide. \\(\\dfrac{2}{3} \\times 168 = 112\\) stamps given away. \\(112 \\div 7 = 16\\) stamps per friend. Answer: 16.",
      "hints": ["First find \\(\\dfrac{2}{3}\\) of 168.", "Then share that total equally among 7 friends."],
      "source": "Nanyang 2022 P5 Weighted Assessment 1 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option (2) = 16. Working: 168 x 2/3 = 112; 112 / 7 = 16."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "A repeated pattern is formed using numbers 3, 2, 1 and 0. The first 18 numbers are shown.<br>3, 0, 2, 0, 1, 3, 0, 2, 0, 1, 3, 0, 2, 0, 1, 3, 0, 2, ...<br>Find the sum of the first 44 numbers.",
      "answer0": "55",
      "answer1": "54",
      "answer2": "53",
      "answer3": "48",
      "correct_answer": 2,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Method: identify the repeating block. The block is 3, 0, 2, 0, 1 (5 numbers, sum = 6). \\(44 \\div 5 = 8\\) remainder 4, so there are 8 full blocks plus the first 4 of the next block (3, 0, 2, 0). Sum \\(= 8 \\times 6 + (3 + 0 + 2 + 0) = 48 + 5 = 53\\). Answer: 53.",
      "hints": ["The repeating block is 3, 0, 2, 0, 1 with sum 6.", "\\(44 \\div 5 = 8\\) R \\(4\\): add 8 full blocks then the first 4 terms 3, 0, 2, 0."],
      "source": "Nanyang 2022 P5 Weighted Assessment 1 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option (3) = 53. Working: 8x6=48, plus 3+0+2+0 = 5 (the key writes 4x3+0+2+0=53 sequence working)."
    },
    {
      "n": 6,
      "type_id": 2,
      "question": "Write six million, twenty-seven thousand and nineteen in numerals.<br>[?]",
      "answer0": "6027019",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 149,
      "difficulty_id": 2,
      "explanation": "Method: place the digits by place value. Six million = 6 000 000; twenty-seven thousand = 27 000; nineteen = 19. Total = 6 027 019. Answer: 6 027 019.",
      "hints": ["Six million is 6 000 000.", "Add 27 000 and 19: 6 000 000 + 27 000 + 19 = 6 027 019."],
      "source": "Nanyang 2022 P5 Weighted Assessment 1 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 6 027 019."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "8 children shared 5 pizzas equally for lunch. What fraction of a pizza did each child get?",
      "answer0": "\\(\\dfrac{5}{8}\\)",
      "answer1": "\\(\\dfrac{8}{5}\\)",
      "answer2": "\\(\\dfrac{5}{13}\\)",
      "answer3": "\\(\\dfrac{3}{8}\\)",
      "correct_answer": 0,
      "skill_id": 157,
      "difficulty_id": 1,
      "explanation": "Method: associate division with a fraction. 5 pizzas shared among 8 children = \\(5 \\div 8 = \\dfrac{5}{8}\\). Each child gets \\(\\dfrac{5}{8}\\) of a pizza. Answer: \\(\\dfrac{5}{8}\\).",
      "hints": ["Divide the number of pizzas by the number of children.", "\\(5 \\div 8\\) written as a fraction is \\(\\dfrac{5}{8}\\)."],
      "source": "Nanyang 2022 P5 Weighted Assessment 1 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 5/8. Converted from FIB to MCQ because the answer is a fraction (FIB answers must be integer/decimal)."
    },
    {
      "n": 8,
      "type_id": 2,
      "question": "Express \\(3\\dfrac{2}{5}\\) as a decimal.<br>[?]",
      "answer0": "3.4",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 158,
      "difficulty_id": 1,
      "explanation": "Method: convert the fraction part to a decimal. \\(\\dfrac{2}{5} = \\dfrac{4}{10} = 0.4\\), so \\(3\\dfrac{2}{5} = 3 + 0.4 = 3.4\\). Answer: 3.4.",
      "hints": ["Convert \\(\\dfrac{2}{5}\\) to tenths: \\(\\dfrac{2}{5} = \\dfrac{4}{10}\\).", "\\(\\dfrac{4}{10} = 0.4\\), so the answer is 3.4."],
      "source": "Nanyang 2022 P5 Weighted Assessment 1 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 3.4. Decimal answer, so FIB is valid."
    },
    {
      "n": 9,
      "type_id": 2,
      "question": "Hui En bakes 420 cookies each day. She packs them into tins of 30 cookies. How many tins of cookies will she have in 9 days?<br>[?]",
      "answer0": "126",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "Method: find tins per day, then multiply by days. \\(420 \\div 30 = 14\\) tins per day. \\(14 \\times 9 = 126\\) tins in 9 days. Answer: 126.",
      "hints": ["Each day she makes \\(420 \\div 30 = 14\\) tins.", "Over 9 days: \\(14 \\times 9 = 126\\) tins."],
      "source": "Nanyang 2022 P5 Weighted Assessment 1 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 126 tins. Working: 420/30=14; 14x9=126."
    },
    {
      "n": 10,
      "type_id": 2,
      "question": "On Monday, Mr Yusof bought 4 tables. Each table cost $357. On Tuesday, he bought 6 identical chairs. The 6 chairs cost as much as the 4 tables. How much did each chair cost?<br>$[?]",
      "answer0": "238",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "Method: total cost of tables, then divide among chairs. 4 tables cost \\(4 \\times \\$357 = \\$1428\\). The 6 chairs cost the same total, so each chair costs \\(\\$1428 \\div 6 = \\$238\\). Answer: $238.",
      "hints": ["First find the total cost of the 4 tables: \\(4 \\times 357\\).", "Share that total equally among 6 chairs: \\(1428 \\div 6\\)."],
      "source": "Nanyang 2022 P5 Weighted Assessment 1 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: $238. Working: 4x357=1428; 1428/6=238. Answer entered as dollars only."
    },
    {
      "n": 11,
      "type_id": 2,
      "question": "Find the missing number in the box.<br>\\(\\dfrac{6}{7} \\times 35 = 3 \\times\\) [?]",
      "answer0": "10",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 161,
      "difficulty_id": 2,
      "explanation": "Method: evaluate the left side, then solve. \\(\\dfrac{6}{7} \\times 35 = 6 \\times 5 = 30\\). So \\(3 \\times ? = 30\\), giving \\(? = 30 \\div 3 = 10\\). Answer: 10.",
      "hints": ["Work out \\(\\dfrac{6}{7} \\times 35\\) first (35 divides by 7).", "\\(\\dfrac{6}{7} \\times 35 = 30\\), so \\(3 \\times ? = 30\\)."],
      "source": "Nanyang 2022 P5 Weighted Assessment 1 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 10. Working: 6/7 x 35 = 30; 30/3 = 10."
    },
    {
      "n": 12,
      "type_id": 2,
      "question": "Prisha had some stickers at first. She gave away \\(\\dfrac{1}{5}\\) of her stickers and bought another 372 stickers. In the end, she was left with 912 stickers. How many stickers did Prisha give away?<br>[?]",
      "answer0": "135",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Method: work backwards. After giving away \\(\\dfrac{1}{5}\\), the remaining \\(\\dfrac{4}{5}\\) plus 372 = 912. So \\(\\dfrac{4}{5}\\) of the original = \\(912 - 372 = 540\\). The full amount \\(= 540 \\div 4 \\times 5 = 675\\). Stickers given away = \\(\\dfrac{1}{5} \\times 675 = 135\\) (or \\(540 \\div 4 = 135\\)). Answer: 135.",
      "hints": ["Subtract the 372 she bought: \\(912 - 372 = 540\\) is the \\(\\dfrac{4}{5}\\) she kept.", "\\(\\dfrac{4}{5}\\) is 540, so 1 unit \\(\\left(\\dfrac{1}{5}\\right) = 540 \\div 4 = 135\\)."],
      "source": "Nanyang 2022 P5 Weighted Assessment 1 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 135. Working: 912-372=540 = 4 units; 540/4=135 = 1 unit (the amount given away)."
    },
    {
      "n": 13,
      "type_id": 2,
      "question": "Peter had a six-sided die. Each side had a number from 1 to 6. He rolled the die three times. Each time, he recorded the number he obtained. The product of the three numbers he obtained was 96. What were the three numbers he obtained?<br>[?] , [?] , [?]",
      "answer0": "4",
      "answer1": "4",
      "answer2": "6",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Method: factorise 96 into three factors each from 1 to 6. \\(96 = 2^5 \\times 3\\). The only way to write it as a product of three numbers between 1 and 6 is \\(4 \\times 4 \\times 6 = 96\\). Answer: 4, 4, 6.",
      "hints": ["Find three numbers, each from 1 to 6, that multiply to 96.", "\\(4 \\times 4 = 16\\) and \\(16 \\times 6 = 96\\)."],
      "source": "Nanyang 2022 P5 Weighted Assessment 1 Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 4, 4, 6 (any order accepted). The die photo is decorative; no figure needed to solve. Three answer blanks for the three recorded numbers."
    }
  ]
}