{
  "paper": {
    "school": "Methodist Girls' School (Primary)",
    "year": 2024,
    "level": "P5",
    "label": "Weighted Assessment 2",
    "source_prefix": "MGS 2024 P5 Weighted Assessment 2",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 2,
      "question": "Express \\(1\\dfrac{3}{7}\\) as a decimal. Round your answer to 2 decimal places. [?]",
      "answer0": "1.43",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 158,
      "difficulty_id": 1,
      "explanation": "Method: convert the fraction to a decimal. \\(1\\dfrac{3}{7}=1+3\\div7=1.428...\\). Rounded to 2 decimal places, \\(1.428 \\approx 1.43\\). Final answer: 1.43",
      "hints": ["Divide the numerator by the denominator: 3 ÷ 7.", "1 + 0.428... then round to 2 decimal places."],
      "source": "MGS 2024 P5 Weighted Assessment 2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Q1(a). Answer is a decimal -> FIB. Verified against key (1.428 ≈ 1.43)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Evaluate \\(4\\dfrac{1}{5} - 1\\dfrac{8}{9}\\). Express your answer as a mixed number.",
      "answer0": "\\(2\\dfrac{31}{45}\\)",
      "answer1": "\\(3\\dfrac{31}{45}\\)",
      "answer2": "\\(2\\dfrac{14}{45}\\)",
      "answer3": "\\(2\\dfrac{7}{45}\\)",
      "correct_answer": 0,
      "skill_id": 160,
      "difficulty_id": 2,
      "explanation": "Method: subtract mixed numbers using a common denominator. \\(4\\dfrac{1}{5}=4\\dfrac{9}{45}\\) and \\(1\\dfrac{8}{9}=1\\dfrac{40}{45}\\). \\(4\\dfrac{9}{45}-1\\dfrac{40}{45}=3\\dfrac{54}{45}-1\\dfrac{40}{45}=2\\dfrac{31}{45}\\). Final answer: \\(2\\dfrac{31}{45}\\)",
      "hints": ["Use a common denominator of 45.", "Regroup 1 whole from the 4 since 9/45 < 40/45."],
      "source": "MGS 2024 P5 Weighted Assessment 2 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Q1(b) in paper (part b of question 1). Answer is a mixed number -> MCQ. Verified against key: 2 31/45."
    },
    {
      "n": 3,
      "type_id": 2,
      "question": "12 : [?] = 9 : 24",
      "answer0": "32",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 181,
      "difficulty_id": 1,
      "explanation": "Method: find the missing term in equivalent ratios. 9 multiplied by what gives 12? Scale factor = 12 ÷ 9. Apply the same to 24: 24 × 12 ÷ 9 = 32. Check: 12 : 32 = 9 : 24 (both simplify to 3 : 8). Final answer: 32",
      "hints": ["The two ratios are equivalent.", "24 × (12 ÷ 9) = 32."],
      "source": "MGS 2024 P5 Weighted Assessment 2 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Q2 in paper: 'What is the missing number in the box? 12 : [?] = 9 : 24'. Answer is a whole number -> FIB. Verified against key: 32."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "There are 12 pink, 14 yellow and 10 green beads. Write the ratio of the number of pink beads to the total number of beads in its simplest form.",
      "answer0": "1 : 3",
      "answer1": "12 : 36",
      "answer2": "1 : 2",
      "answer3": "2 : 3",
      "correct_answer": 0,
      "skill_id": 179,
      "difficulty_id": 1,
      "explanation": "Method: total beads = 12 + 14 + 10 = 36. Ratio of pink to total = 12 : 36. Divide both by 12: 1 : 3. Final answer: 1 : 3",
      "hints": ["Find the total number of beads first.", "Simplify 12 : 36 by dividing both parts by 12."],
      "source": "MGS 2024 P5 Weighted Assessment 2 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Q3 in paper. Answer is a ratio -> MCQ. Verified against key: 1 : 3."
    },
    {
      "n": 5,
      "type_id": 2,
      "question": "A box contains 64 apples and oranges altogether. The number of apples to the number of oranges is in the ratio 3 : 5. How many apples are there? [?]",
      "answer0": "24",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 2,
      "explanation": "Method: total units = 3 + 5 = 8 units = 64. 1 unit = 64 ÷ 8 = 8. Apples = 3 units = 8 × 3 = 24. Final answer: 24",
      "hints": ["Add the ratio parts: 3 + 5 = 8 units make 64.", "Find 1 unit, then multiply by 3 for the apples."],
      "source": "MGS 2024 P5 Weighted Assessment 2 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Q4 in paper. Answer is a whole number -> FIB. Verified against key: 24 apples."
    },
    {
      "n": 6,
      "type_id": 2,
      "question": "There are some red marbles and blue marbles in a bottle. \\(\\dfrac{2}{7}\\) of the marbles are red and the rest are blue. There are 213 more blue marbles than red marbles. How many marbles are there altogether? [?]",
      "answer0": "497",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "Method: red = 2/7, so blue = 1 - 2/7 = 5/7. Difference between blue and red = 5/7 - 2/7 = 3/7 of the total = 3 units = 213. 1 unit = 213 ÷ 3 = 71. Total = 7 units = 71 × 7 = 497. Final answer: 497",
      "hints": ["Blue is 5/7 and red is 2/7; the difference is 3/7.", "3 units = 213, so 1 unit = 71. Total = 7 units."],
      "source": "MGS 2024 P5 Weighted Assessment 2 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Q5 in paper. Answer is a whole number -> FIB. Verified against key: 497 marbles."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "A vase holds blue, red and white roses. \\(\\dfrac{1}{9}\\) of the roses are blue. \\(\\dfrac{3}{4}\\) of the remaining roses are red and the rest are white. What fraction of the roses in the vase are white?",
      "answer0": "\\(\\dfrac{2}{9}\\)",
      "answer1": "\\(\\dfrac{1}{4}\\)",
      "answer2": "\\(\\dfrac{6}{9}\\)",
      "answer3": "\\(\\dfrac{1}{9}\\)",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "Method: blue = 1/9, so remaining = 8/9. Red = 3/4 of 8/9 = 6/9. Blue + red = 1/9 + 6/9 = 7/9. White = 1 - 7/9 = 2/9. Final answer: \\(\\dfrac{2}{9}\\)",
      "hints": ["After the blue roses, 8/9 remain.", "Red = 3/4 of 8/9 = 6/9; white is what is left of the whole."],
      "source": "MGS 2024 P5 Weighted Assessment 2 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Q6 in paper. Answer is a fraction -> MCQ. Verified against key: 2/9 (working 6/9 + 1/9 = 7/9; 1 - 7/9 = 2/9)."
    },
    {
      "n": 8,
      "type_id": 2,
      "question": "Alan had 30 stickers and Bala had 54 stickers. After Alan gave some stickers to Bala, the number of stickers Alan and Bala had was in the ratio 2 : 5. How many stickers did Alan give to Bala? [?]",
      "answer0": "6",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 2,
      "explanation": "Method: the total stays the same when stickers are passed between them. Total = 30 + 54 = 84. After, ratio is 2 : 5, so 7 units = 84, 1 unit = 84 ÷ 7 = 12. Alan now has 2 units = 24. Alan gave away 30 - 24 = 6 stickers. Final answer: 6",
      "hints": ["The total number of stickers does not change.", "Alan ends with 2 units = 24; he started with 30."],
      "source": "MGS 2024 P5 Weighted Assessment 2 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Q7 in paper. Answer is a whole number -> FIB. Key shows 7u=84, 1u=12; Alan ends with 2u=24, so gave 30-24=6."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "The figure is made up of 2 identical rectangles, ABCD and DCEF. ABCD is divided into 3 equal parts and DCEF is divided into 5 equal parts. What fraction of the figure is shaded?",
      "answer0": "\\(\\dfrac{8}{15}\\)",
      "answer1": "\\(\\dfrac{7}{15}\\)",
      "answer2": "\\(\\dfrac{1}{2}\\)",
      "answer3": "\\(\\dfrac{8}{16}\\)",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Method: take each rectangle as 1 whole. In DCEF (5 equal parts), 2 parts are shaded each worth 3 small units = 2 × 3 = 6. In ABCD (3 equal parts), 2 parts are shaded each worth 5 small units = 5 × 2 = 10. Total shaded = 10 + 6 = 16 small units. Each rectangle = 3 × 5 = 15 small units, so the whole figure = 30 small units. Shaded fraction = 16 ÷ 30 ÷ 2 ... simplify: 16/30 = 8/15. Final answer: \\(\\dfrac{8}{15}\\)",
      "hints": ["Split each rectangle into the same small units (15 each).", "Count shaded small units over the total small units, then simplify."],
      "source": "MGS 2024 P5 Weighted Assessment 2 Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q9.png",
      "image_page": 4,
      "image_bbox": [0.30, 0.55, 0.62, 0.69],
      "image_loc": "lower-middle of page 4, the two stacked rectangles labelled A B C D F E with shaded strips",
      "notes": "Q8 in paper. Answer is a fraction -> MCQ. Verified against key working: 5x2=10, 2x3=6, 10+6=16, /2 over /2 of 30 -> 8/15."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "Taylor used \\(2\\dfrac{1}{4}\\) m of fabric to make a dress and \\(\\dfrac{2}{5}\\) of the remaining fabric to sew a blouse. She had \\(4\\dfrac{1}{5}\\) m of fabric left. What was the length of fabric that she had at first?",
      "answer0": "\\(9\\dfrac{1}{4}\\) m",
      "answer1": "\\(7\\dfrac{1}{4}\\) m",
      "answer2": "\\(11\\dfrac{1}{4}\\) m",
      "answer3": "\\(6\\dfrac{9}{20}\\) m",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Method: after the dress, let the remaining fabric be 5 units. The blouse uses 2 units, so 3 units are left = \\(4\\dfrac{1}{5}\\) m. 1 unit = \\(4\\dfrac{1}{5} \\div 3 = 1\\dfrac{2}{5}\\) m. The remaining before the blouse = 5 units = \\(1\\dfrac{2}{5} \\times 5 = 7\\) m. At first = \\(7 + 2\\dfrac{1}{4} = 9\\dfrac{1}{4}\\) m. Final answer: \\(9\\dfrac{1}{4}\\) m",
      "hints": ["After the dress, 3/5 of the remaining fabric is left = 4 1/5 m.", "Find the full remaining (5 units), then add back the 2 1/4 m for the dress."],
      "source": "MGS 2024 P5 Weighted Assessment 2 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Q9 in paper. Answer is a mixed number -> MCQ. Verified against key: 3u = 4 1/5, 1u = 1 2/5, 5u = 7, +2 1/4 = 9 1/4 m."
    },
    {
      "n": 11,
      "type_id": 2,
      "question": "Adora had a bottle of apple juice. She drank 250 ml of it in the morning and \\(\\dfrac{4}{7}\\) of the remaining juice in the afternoon. After that, there was \\(\\dfrac{1}{3}\\) of the bottle of juice left. How much apple juice was there in the bottle at first? [?]",
      "answer0": "1125",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Method: let the bottle be 9 units (so the afternoon and the final 1/3 work out evenly). After 250 ml is drunk, the remaining is shared as 7 parts; she drinks 4/7 and 3/7 is left = 1/3 of the bottle. Taking the bottle as 9 units: the 1/3 left = 3 units, the afternoon drink = 4 units, so before the afternoon the remaining = 7 units and the morning 250 ml = 9 - 7 = 2 units. 2 units = 250 ml, 1 unit = 125 ml, bottle = 9 units = 125 × 9 = 1125 ml. Final answer: 1125 ml",
      "hints": ["Express everything in the same units (the bottle as 9 units).", "250 ml corresponds to 2 units; find 1 unit then the whole bottle."],
      "source": "MGS 2024 P5 Weighted Assessment 2 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Q10 in paper. Answer is a whole number (ml) -> FIB. Verified against key: 250ml = 9u - 7u = 2u; 1u = 125ml; 9u = 1125 ml."
    },
    {
      "n": 12,
      "type_id": 2,
      "question": "Mrs Tan bought some notebooks and pencils for her students. The ratio of number of notebooks to the number of pencils that she bought was 2 : 3. Each notebook cost $1.20 and each pencil cost $0.75. Altogether, she paid $83.70. How many notebooks did she buy? [?]",
      "answer0": "36",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "Method: for every group (2 notebooks + 3 pencils), cost = $1.20 × 2 + $0.75 × 3 = $2.40 + $2.25 = $4.65. Number of groups = $83.70 ÷ $4.65 = 18. Notebooks = 2 per group × 18 = 36. Final answer: 36",
      "hints": ["Find the cost of one group of 2 notebooks and 3 pencils.", "Divide the total by the group cost, then multiply by 2 for notebooks."],
      "source": "MGS 2024 P5 Weighted Assessment 2 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Q11 in paper. Answer is a whole number -> FIB. Verified against key: $1.2x2 + $0.75x3 = $4.65; 83.70/4.65 = 18; 2x18 = 36 notebooks."
    },
    {
      "n": 13,
      "type_id": 2,
      "question": "A rectangle is made up of four triangles, A, B, C and D. The area of triangle A is \\(\\dfrac{1}{4}\\) of the area of the rectangle while the area of triangle B is \\(\\dfrac{2}{9}\\) of the area of the rectangle. The total area of triangle A and B is 51 cm². Find the area of the rectangle. [?]",
      "answer0": "108",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Method: A + B as a fraction of the rectangle = \\(\\dfrac{1}{4} + \\dfrac{2}{9} = \\dfrac{9}{36} + \\dfrac{8}{36} = \\dfrac{17}{36}\\). So \\(\\dfrac{17}{36}\\) of the rectangle = 51 cm². \\(\\dfrac{1}{36}\\) = 51 ÷ 17 = 3 cm². Rectangle = 36 units = 3 × 36 = 108 cm². Final answer: 108 cm²",
      "hints": ["Add the two fractions of the rectangle that A and B take up.", "17/36 of the rectangle = 51 cm²; find 1/36 then the whole."],
      "source": "MGS 2024 P5 Weighted Assessment 2 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q13.png",
      "image_page": 7,
      "image_bbox": [0.28, 0.17, 0.66, 0.30],
      "image_loc": "upper-middle of page 7, rectangle divided into four triangles labelled A, B, C, D",
      "notes": "Q12(a) in paper. Answer is a whole number (cm2) -> FIB. Verified against key: 1/4+2/9 = 17/36; 51/17 = 3; 3x36 = 108 cm2."
    },
    {
      "n": 14,
      "type_id": 2,
      "question": "A rectangle is made up of four triangles, A, B, C and D. The area of triangle A is \\(\\dfrac{1}{4}\\) of the area of the rectangle while the area of triangle B is \\(\\dfrac{2}{9}\\) of the area of the rectangle. The total area of triangle A and B is 51 cm². The ratio of the length of the rectangle to its breadth is 3 : 1. Find the perimeter of the rectangle. [?]",
      "answer0": "48",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Method: from part (a) the rectangle area = 108 cm². With length : breadth = 3 : 1, area = length × breadth = 3b × b = 3b² = 108, so b² = 36 and b = 6 cm, length = 18 cm. Perimeter = 2 × (length + breadth) = 2 × (18 + 6) = 48 cm. Final answer: 48 cm",
      "hints": ["Use the area 108 cm² from part (a) with length = 3 × breadth.", "3b² = 108 gives breadth = 6 cm; perimeter = 2 × (length + breadth)."],
      "source": "MGS 2024 P5 Weighted Assessment 2 Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q14.png",
      "image_page": 7,
      "image_bbox": [0.28, 0.17, 0.66, 0.30],
      "image_loc": "upper-middle of page 7, rectangle divided into four triangles labelled A, B, C, D",
      "notes": "Q12(b) in paper. Answer is a whole number (cm) -> FIB. Verified against key: P = 2 x (6+18) = 48 cm. Length 18, breadth 6 from area 108 and ratio 3:1."
    }
  ]
}