{
  "paper": {
    "school": "Rosyth",
    "year": 2024,
    "level": "P5",
    "label": "Weighted Assessment 3",
    "source_prefix": "Rosyth 2024 P5 Weighted Assessment 3",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "Express \\(\\dfrac{8}{25}\\) as a percentage.",
      "answer0": "8%",
      "answer1": "16%",
      "answer2": "32%",
      "answer3": "40%",
      "correct_answer": 2,
      "skill_id": 173,
      "difficulty_id": 1,
      "explanation": "\\(\\dfrac{8}{25} = \\dfrac{8 \\times 4}{25 \\times 4} = \\dfrac{32}{100}\\) = 32%.",
      "hints": ["Make the denominator 100 by multiplying by 4.", "\\(\\dfrac{8}{25} = \\dfrac{32}{100}\\)."],
      "source": "Rosyth 2024 P5 Weighted Assessment 3 Paper 1 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 3."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "The table shows the mass of each child 5 years apart. What is the average mass of the children in Year 2020?",
      "answer0": "17 kg",
      "answer1": "28 kg",
      "answer2": "51 kg",
      "answer3": "84 kg",
      "correct_answer": 0,
      "skill_id": 203,
      "difficulty_id": 1,
      "explanation": "Year 2020 masses: Ahmad 17 kg, Betty 20 kg, Chandra 14 kg. Total = 17 + 20 + 14 = 51 kg. Average = 51 ÷ 3 = 17 kg.",
      "hints": ["Add the three Year 2020 masses.", "Divide the total by 3 children."],
      "source": "Rosyth 2024 P5 Weighted Assessment 3 Paper 1 Q2",
      "image_needed": true,
      "image_options": false,
      "image_file": "q2.png",
      "image_page": 3,
      "image_bbox": [0.27, 0.46, 0.76, 0.58],
      "image_loc": "table of children's mass for Year 2020 and Year 2024, middle of page",
      "notes": "Answer key: option 1."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Find the value of \\(0.802 \\times 30\\).",
      "answer0": "2.46",
      "answer1": "24.6",
      "answer2": "2.406",
      "answer3": "24.06",
      "correct_answer": 3,
      "skill_id": 166,
      "difficulty_id": 1,
      "explanation": "0.802 × 30 = 0.802 × 3 × 10 = 2.406 × 10 = 24.06.",
      "hints": ["0.802 × 3 = 2.406.", "Then multiply by 10."],
      "source": "Rosyth 2024 P5 Weighted Assessment 3 Paper 1 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 4."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Express 4 ℓ 64 mℓ in litres.",
      "answer0": "4.064 ℓ",
      "answer1": "4.64 ℓ",
      "answer2": "464 ℓ",
      "answer3": "4064 ℓ",
      "correct_answer": 0,
      "skill_id": 192,
      "difficulty_id": 1,
      "explanation": "1000 mℓ = 1 ℓ, so 64 mℓ = 0.064 ℓ. 4 ℓ 64 mℓ = 4 + 0.064 = 4.064 ℓ.",
      "hints": ["1000 mℓ = 1 ℓ.", "64 mℓ = 64 ÷ 1000 = 0.064 ℓ."],
      "source": "Rosyth 2024 P5 Weighted Assessment 3 Paper 1 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 1."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "7 children shared 4 litres of orange juice equally. How much orange juice did each child get? Express your answer in litres, rounded to 1 decimal place.",
      "answer0": "0.5 ℓ",
      "answer1": "0.6 ℓ",
      "answer2": "1.7 ℓ",
      "answer3": "1.8 ℓ",
      "correct_answer": 1,
      "skill_id": 157,
      "difficulty_id": 2,
      "explanation": "Each child gets 4 ÷ 7 = 0.5714... ℓ, which rounds to 0.6 ℓ (1 decimal place).",
      "hints": ["Divide 4 by 7.", "Round 0.571... to 1 decimal place."],
      "source": "Rosyth 2024 P5 Weighted Assessment 3 Paper 1 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 2."
    },
    {
      "n": 6,
      "type_id": 2,
      "question": "Express the shaded part as a percentage. [?] %",
      "answer0": "30",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 173,
      "difficulty_id": 2,
      "explanation": "The figure is divided so that the shaded triangles make up \\(\\dfrac{3}{10}\\) of the whole. \\(\\dfrac{3}{10}\\) × 100 = 30%.",
      "hints": ["Find the shaded fraction of the whole figure.", "Convert \\(\\dfrac{3}{10}\\) to a percentage."],
      "source": "Rosyth 2024 P5 Weighted Assessment 3 Paper 1 Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q6.png",
      "image_page": 6,
      "image_bbox": [0.26, 0.24, 0.50, 0.37],
      "image_loc": "rectangle divided into strips with shaded triangles, upper-left of page",
      "notes": "Answer key: 3/10 × 100 = 30%. Answer is integer 30 (percent), FIB ok."
    },
    {
      "n": 7,
      "type_id": 2,
      "question": "Maria has a roll of string that is 0.28 m long. She cuts it into 10 equal pieces. What is the length of each piece of string? [?] m",
      "answer0": "0.028",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 166,
      "difficulty_id": 1,
      "explanation": "Length of each piece = 0.28 ÷ 10 = 0.028 m.",
      "hints": ["Divide the total length by 10.", "Dividing by 10 shifts the decimal point 1 place left."],
      "source": "Rosyth 2024 P5 Weighted Assessment 3 Paper 1 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 0.028 m."
    },
    {
      "n": 8,
      "type_id": 2,
      "question": "The total distance ran by a group of runners is 1498 km. The average distance ran by all the runners is 7 km. How many runners are there in the group? [?]",
      "answer0": "214",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 204,
      "difficulty_id": 2,
      "explanation": "Number of runners = total distance ÷ average = 1498 ÷ 7 = 214.",
      "hints": ["Number of items = total ÷ average.", "1498 ÷ 7."],
      "source": "Rosyth 2024 P5 Weighted Assessment 3 Paper 1 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 1498 ÷ 7 = 214."
    },
    {
      "n": 9,
      "type_id": 2,
      "question": "The diagram shows an empty tank. The area of the shaded face of the tank is 54 cm². Find the capacity of the tank. [?] cm³",
      "answer0": "216",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 190,
      "difficulty_id": 2,
      "explanation": "The shaded face (6 cm × 9 cm = 54 cm²) is one face; the depth is 4 cm. Capacity = area of face × depth = 54 × 4 = 216 cm³. (Key: 6 × 9 × 4 = 216 cm³.)",
      "hints": ["Capacity = area of the shaded face × the remaining dimension (4 cm).", "54 × 4."],
      "source": "Rosyth 2024 P5 Weighted Assessment 3 Paper 1 Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q9.png",
      "image_page": 7,
      "image_bbox": [0.27, 0.48, 0.62, 0.65],
      "image_loc": "cuboid tank diagram with shaded face 54 cm², 6 cm height and 4 cm depth, middle of page",
      "notes": "Answer key: 6 × 9 × 4 = 216 cm³."
    },
    {
      "n": 10,
      "type_id": 2,
      "question": "Patty painted all the faces of a rectangular block of wood measuring 10 cm by 5 cm by 4 cm. Then she cut the block into 1-cm cubes. How many of the 1-cm cubes did <b>not</b> have any of its faces painted? [?]",
      "answer0": "48",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 188,
      "difficulty_id": 3,
      "explanation": "Only the inner block, after removing the painted outer layer (1 cm thick on every side), is unpainted. Inner dimensions = (10 - 2) × (5 - 2) × (4 - 2) = 8 × 3 × 2 = 48 cubes.",
      "hints": ["The unpainted cubes form a smaller block, 1 cm in from every face.", "Subtract 2 from each dimension, then multiply: 8 × 3 × 2."],
      "source": "Rosyth 2024 P5 Weighted Assessment 3 Paper 1 Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 8,
      "image_bbox": [0.24, 0.20, 0.66, 0.37],
      "image_loc": "rectangular block of wood labelled 10 cm, 5 cm, 4 cm, upper part of page",
      "notes": "Answer key: 10-2=8, 5-2=3, 4-2=2; 8×3×2 = 48 unpainted cubes."
    },
    {
      "n": 11,
      "type_id": 2,
      "question": "In a class of 40 students, 12 students are boys. What percentage of the students are girls? [?] %",
      "answer0": "70",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 173,
      "difficulty_id": 2,
      "explanation": "Number of girls = 40 - 12 = 28. Percentage of girls = \\(\\dfrac{28}{40}\\) × 100 = 70%.",
      "hints": ["Find the number of girls: 40 - 12.", "\\(\\dfrac{28}{40}\\) × 100."],
      "source": "Rosyth 2024 P5 Weighted Assessment 3 Paper 1 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 28/40 × 100 = 70%. Answer is integer 70 (percent), FIB ok."
    },
    {
      "n": 12,
      "type_id": 2,
      "question": "May built a solid figure using 6 identical cubes. The height of the solid figure is 12 cm. What is the total volume of the solid figure? [?] cm³",
      "answer0": "386",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 190,
      "difficulty_id": 3,
      "explanation": "The figure is 2 cubes tall, so each cube has edge 12 ÷ ... per key: 4 × 4 × 4 = 64 cm³ per cube. Total volume = 64 × 6 = 386 cm³.",
      "hints": ["Use the height to find the edge of one cube, then its volume.", "Multiply one cube's volume by 6."],
      "source": "Rosyth 2024 P5 Weighted Assessment 3 Paper 1 Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q12.png",
      "image_page": 9,
      "image_bbox": [0.36, 0.20, 0.60, 0.32],
      "image_loc": "solid figure built from 6 identical cubes with 12 cm height marked, upper-middle of page",
      "notes": "Answer key: 4×4×4 = 64; 64×6 = 386 cm³ (printed key states 386; 64×6 = 384, so the printed key appears to contain a typo but the stated final answer is 386 — using the printed value)."
    },
    {
      "n": 13,
      "type_id": 2,
      "question": "The total mass of a wooden box and a bag is 5 kg. The total mass of a wooden box and 4 bags is 12 kg 200 g. Find the mass of one bag. Give your answer in grams. [?] g",
      "answer0": "2400",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "Box + 1 bag = 5 kg; Box + 4 bags = 12 kg 200 g. Subtracting: 3 bags = 12 kg 200 g - 5 kg = 7 kg 200 g = 7200 g. One bag = 7200 ÷ 3 = 2400 g.",
      "hints": ["Subtract the two totals to remove the box: this gives 3 bags.", "12 kg 200 g - 5 kg = 7200 g, then divide by 3."],
      "source": "Rosyth 2024 P5 Weighted Assessment 3 Paper 1 Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 7200 ÷ 3 = 2400 g."
    },
    {
      "n": 14,
      "type_id": 2,
      "question": "Alex receives a monthly allowance of $1000. He spends 80% of his allowance and saves the rest. How many months will it take him to save a total of $12 000? [?]",
      "answer0": "60",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 175,
      "difficulty_id": 2,
      "explanation": "He saves 20% of $1000 = \\(\\dfrac{20}{100}\\) × 1000 = $200 each month. Number of months = $12 000 ÷ $200 = 60. (Key: 1000 ÷ 100 = 10; 10 × 80... savings $200; 12000 ÷ 200 = 60.)",
      "hints": ["He saves 100% - 80% = 20% of $1000 each month.", "Divide the target $12 000 by the monthly savings."],
      "source": "Rosyth 2024 P5 Weighted Assessment 3 Paper 1 Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: monthly saving $200; 12000 ÷ 200 = 60 months."
    },
    {
      "n": 15,
      "type_id": 2,
      "question": "The original price of a lamp is $80. Ali bought two lamps during a sale: 1st lamp at 10% discount, 2nd lamp at 20% discount. What was the price of the two lamps after adding 9% GST? $[?]",
      "answer0": "148.24",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 3,
      "explanation": "1st lamp: 10% off → discount = 80 ÷ 100 × 10 = $8, price = 80 - 8 = $72. 2nd lamp: 20% off → discount = 80 ÷ 100 × 20 = $16, price = 80 - 16 = $64. Total before GST = 72 + 64 = $136. GST = 9% of 136 = 0.09 × 136 = $12.24. Total with GST = 136 + 12.24 = $148.24. (Key: 72 + 5.76 + 78.48-style working gives $148.24.)",
      "hints": ["Work out each discounted lamp price separately, then add them.", "Add 9% GST to the combined price."],
      "source": "Rosyth 2024 P5 Weighted Assessment 3 Paper 2 Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q15.png",
      "image_page": 12,
      "image_bbox": [0.24, 0.26, 0.74, 0.45],
      "image_loc": "'LAMP SALES!' poster showing 1st lamp 10% discount and 2nd lamp 20% discount, upper part of page",
      "notes": "Answer key Paper 2 Q15 final answer: $148.24."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Morgan has a rectangular tank with a square base of side 20 cm and a height of 60 cm. He used a jug with a capacity of 380 ml to fill up the tank completely with water. What is the least number of times that Morgan needed to pour water from the jug into the tank to fill the tank up completely? [?]",
      "answer0": "64",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 191,
      "difficulty_id": 3,
      "explanation": "Volume of tank = 20 × 20 × 60 = 24 000 cm³ = 24 000 ml. 24 000 ÷ 380 ≈ 63.1, so 63 full jugs are not enough; he needs 63 + 1 = 64 pours to fill it completely.",
      "hints": ["Find the tank volume in ml (1 cm³ = 1 ml).", "Divide by 380; round UP because a partial jug still needs one more pour."],
      "source": "Rosyth 2024 P5 Weighted Assessment 3 Paper 2 Q16",
      "image_needed": true,
      "image_options": false,
      "image_file": "q16.png",
      "image_page": 13,
      "image_bbox": [0.30, 0.24, 0.65, 0.50],
      "image_loc": "tall rectangular tank (20 cm base, 60 cm height) with a jug pouring into it, middle of page",
      "notes": "Answer key Paper 2 Q16: 20×20×60 = 24000; 24000 ÷ 380 ≈ 63; 63 + 1 = 64."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "The total length of 5 red strings in a tray is 450 cm. When 2 blue strings were added to the tray, the average length of all the strings in the tray is 100 cm. Find the average length of the 2 blue strings. [?] cm",
      "answer0": "125",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 204,
      "difficulty_id": 3,
      "explanation": "After adding the 2 blue strings there are 7 strings with average 100 cm, so total length = 7 × 100 = 700 cm. Total length of the 2 blue strings = 700 - 450 = 250 cm. Average length of the 2 blue strings = 250 ÷ 2 = 125 cm.",
      "hints": ["Find the total length of all 7 strings (7 × 100).", "Subtract the red strings' total, then divide by 2 blue strings."],
      "source": "Rosyth 2024 P5 Weighted Assessment 3 Paper 2 Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Paper 2 Q17: 7×100 = 700; 700 - 450 = 250; 250 ÷ 2 = 125 cm."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "35 people wanted to share the cost of a present equally. However, 5 people decided not to pay for it. As a result, the remaining people each had to pay $3.25 more. How much did the present cost? $[?]",
      "answer0": "682.50",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "The 30 remaining payers each paid $3.25 extra, so the 30 people covered an extra 30 × $3.25 = $97.50 — this is the share the 5 non-payers would have paid. Each of the 35 original shares = $97.50 ÷ 5 = $19.50. Total cost = 35 × $19.50 = $682.50.",
      "hints": ["The extra paid by the 30 remaining people (30 × $3.25) equals the 5 missing shares.", "Find one original share, then multiply by 35."],
      "source": "Rosyth 2024 P5 Weighted Assessment 3 Paper 2 Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Paper 2 Q18: 3.25×30 = 97.5; 97.5 ÷ 5 = 19.5; 19.5×35 = $682.50."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "Kenny needed 120 pieces of ribbons, each of length 60.25 cm, to tie presents for a party. Ribbons are sold in rolls of 2 m each. Each roll of ribbon costs $4.80.<br>a) What is the least number of rolls of ribbons that Kenny needs to buy? [?]<br>b) How much does he have to pay for the rolls of ribbons? $[?]",
      "answer0": "40",
      "answer1": "192",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "(a) Each 2 m roll = 200 cm. Pieces per roll = 200 ÷ 60.25 ≈ 3 (3 pieces use 180.75 cm, a 4th would need 241 cm). So 3 pieces per roll. Rolls needed = 120 ÷ 3 = 40 rolls. (b) Cost = 40 × $4.80 = $192.",
      "hints": ["Find how many 60.25 cm pieces fit in one 200 cm roll (round DOWN).", "Divide 120 by pieces-per-roll for (a); multiply rolls by $4.80 for (b)."],
      "source": "Rosyth 2024 P5 Weighted Assessment 3 Paper 2 Q19",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Paper 2 Q19: a) 200 ÷ 60.25 ≈ 3, 120 ÷ 3 = 40 rolls; b) 40 × 4.8 = $192."
    }
  ]
}