{
  "paper": {
    "school": "Henry Park",
    "year": 2024,
    "level": "P5",
    "label": "Weighted Assessment 2",
    "source_prefix": "Henry Park 2024 P5 Weighted Assessment 2",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 2,
      "question": "Mary used 800 g of flour to make some muffins. Jane used 500 g more than Mary. Eileen used twice as much flour as Jane. How much flour did Eileen use? [?] kg",
      "answer0": "2.6",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 1,
      "explanation": "Jane used 800 + 500 = 1300 g. Eileen used twice Jane's amount: 1300 × 2 = 2600 g = 2.6 kg.",
      "hints": ["Find Jane's amount first: Mary's 800 g plus 500 g more.", "Eileen used twice Jane's amount, then convert 2600 g to kg by dividing by 1000."],
      "source": "Henry Park 2024 P5 Weighted Assessment 2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 2.6 kg."
    },
    {
      "n": 2,
      "type_id": 2,
      "question": "14 years ago, the ratio of Jack's age to Tom's age to Michael's age was 7 : 2 : 5. Michael is 54 years old now. What is Jack's age now? [?] years old",
      "answer0": "70",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 2,
      "explanation": "14 years ago Michael was 54 - 14 = 40. Michael was 5 units, so 1 unit = 40 ÷ 5 = 8. Jack was 7 units = 7 × 8 = 56. Jack now = 56 + 14 = 70 years old.",
      "hints": ["Work out everyone's age 14 years ago first (Michael was 54 - 14).", "Use Michael's 5 units to find 1 unit, then find Jack's 7 units, then add 14 years back."],
      "source": "Henry Park 2024 P5 Weighted Assessment 2 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 70 years old."
    },
    {
      "n": 3,
      "type_id": 2,
      "question": "The tank shown will be filled to its brim after 5 ℓ of water is added into it. What is the volume of water in the tank now? [?] cm³",
      "answer0": "4000",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 191,
      "difficulty_id": 2,
      "explanation": "5 ℓ = 5000 cm³. The empty height = 5000 ÷ (50 × 10) = 10 cm. Water height now = 18 - 10 = 8 cm. Volume of water = 8 × 50 × 10 = 4000 cm³.",
      "hints": ["1 litre = 1000 cm³, so 5 ℓ = 5000 cm³ is the empty space to be filled.", "Find the empty height (5000 ÷ base area), subtract from 18 cm to get the water height, then multiply by the base area."],
      "source": "Henry Park 2024 P5 Weighted Assessment 2 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q3.png",
      "image_page": 4,
      "image_bbox": [0.29, 0.15, 0.70, 0.30],
      "image_loc": "cuboid tank diagram near top of page, dimensions 50 cm by 10 cm by 18 cm",
      "notes": "Answer key: 4000 cm³. Tank base 50 cm × 10 cm, full height 18 cm."
    },
    {
      "n": 4,
      "type_id": 2,
      "question": "After John spent \\(\\dfrac{1}{3}\\) of his savings on a laptop and a tablet, he had $5460 left. Given that the laptop cost 4 times as much as the tablet, find the cost of the laptop. $[?]",
      "answer0": "2184",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "$5460 is the remaining \\(\\dfrac{2}{3}\\) of his savings, so \\(\\dfrac{1}{3}\\) (spent on laptop + tablet) = 5460 ÷ 2 = $2730. Laptop : tablet = 4 : 1, total 5 parts = 2730, so 1 part = 2730 ÷ 5 = 546. Laptop = 4 × 546 = $2184.",
      "hints": ["He spent 1/3, so the $5460 left is 2/3 of his savings; use that to find 1/3 (the amount spent).", "Split the amount spent into 5 equal parts (laptop 4 parts, tablet 1 part)."],
      "source": "Henry Park 2024 P5 Weighted Assessment 2 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: $2184."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "A pet shop has a total of 570 angelfish, goldfish and guppies. \\(\\dfrac{1}{5}\\) of the fish are angelfish, \\(\\dfrac{1}{6}\\) of the fish are guppies and the rest are goldfish. What fraction of the fish are goldfish?",
      "answer0": "\\(\\dfrac{19}{30}\\)",
      "answer1": "\\(\\dfrac{11}{30}\\)",
      "answer2": "\\(\\dfrac{2}{11}\\)",
      "answer3": "\\(\\dfrac{13}{30}\\)",
      "correct_answer": 0,
      "skill_id": 159,
      "difficulty_id": 1,
      "explanation": "Goldfish fraction = 1 - \\(\\dfrac{1}{5}\\) - \\(\\dfrac{1}{6}\\) = \\(\\dfrac{30}{30}\\) - \\(\\dfrac{6}{30}\\) - \\(\\dfrac{5}{30}\\) = \\(\\dfrac{19}{30}\\).",
      "hints": ["The three groups make 1 whole; subtract the angelfish and guppy fractions from 1.", "Use a common denominator of 30 for fifths and sixths."],
      "source": "Henry Park 2024 P5 Weighted Assessment 2 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Q5(a). Answer key: 19/30. Fraction answer, so MCQ. Q5(b) (247 more goldfish than angelfish) is split into Q5b below."
    },
    {
      "n": 6,
      "type_id": 2,
      "question": "A pet shop has a total of 570 angelfish, goldfish and guppies. \\(\\dfrac{1}{5}\\) of the fish are angelfish, \\(\\dfrac{1}{6}\\) of the fish are guppies and the rest are goldfish. How many more goldfish than angelfish are there? [?]",
      "answer0": "247",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "Goldfish are \\(\\dfrac{19}{30}\\) of the fish and angelfish are \\(\\dfrac{1}{5}=\\dfrac{6}{30}\\), so goldfish exceed angelfish by \\(\\dfrac{19}{30}-\\dfrac{6}{30}=\\dfrac{13}{30}\\) of the total. 1 unit = 570 ÷ 30 = 19. Difference = 19 × 13 = 247.",
      "hints": ["Find the fraction by which goldfish exceed angelfish (goldfish fraction minus angelfish fraction).", "Each thirtieth of the total is 570 ÷ 30 = 19 fish."],
      "source": "Henry Park 2024 P5 Weighted Assessment 2 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "This is Q5(b). Answer key: 247. Stem repeats Q5 context for standalone serving."
    },
    {
      "n": 7,
      "type_id": 2,
      "question": "On Friday, Nora walked 1.09 km. Each day, she walked 665 m more than the day before. What is the total distance she would have walked in 1 week? Express your answer as a decimal in kilometres. [?]",
      "answer0": "21.595",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "665 m = 0.665 km. Over 7 days the daily increase adds 0 + 1 + 2 + 3 + 4 + 5 + 6 = 21 times of 0.665 km. Base distance = 1.09 × 7 = 7.63 km. Total = 7.63 + 21 × 0.665 = 7.63 + 13.965 = 21.595 km.",
      "hints": ["Convert 665 m to km (0.665 km) and treat the 7 days as 7 lots of Friday's distance plus growing increments.", "The increments over 7 days total (0+1+2+3+4+5+6) = 21 lots of 0.665 km."],
      "source": "Henry Park 2024 P5 Weighted Assessment 2 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 21.595 km."
    },
    {
      "n": 8,
      "type_id": 2,
      "question": "The figure consists of 2 shaded triangles, BGF and BGC, and 2 identical squares, ABEF and BCDE. The perimeter of the rectangle ACDF is 120 cm. The length of BG is three times the length of GE.<br>(a) What is the length of GE? [?] cm<br>(b) What is the total area of the shaded triangles? [?] cm²",
      "answer0": "5",
      "answer1": "300",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "(a) The rectangle ACDF is made of 2 identical squares, so its perimeter = 6 sides of a square = 120 cm, giving square side = 120 ÷ 6 = 20 cm. BE = 20 cm and BG = 3 × GE, so BG + GE = 20, i.e. 4 × GE = 20, GE = 5 cm. (b) BG = 20 - 5 = 15 cm. Area of ΔBGF = \\(\\dfrac{1}{2}\\) × 15 × 20 = 150 cm²; area of ΔBGC = \\(\\dfrac{1}{2}\\) × 15 × 20 = 150 cm². Total = 150 + 150 = 300 cm².",
      "hints": ["The rectangle is two equal squares side by side, so its perimeter equals 6 square-sides.", "Each shaded triangle has base BG and height equal to the square's side (20 cm)."],
      "source": "Henry Park 2024 P5 Weighted Assessment 2 Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 7,
      "image_bbox": [0.16, 0.16, 0.82, 0.42],
      "image_loc": "rectangle ACDF with vertices A,B,C top and F,E,D bottom, two shaded triangles BGF and BGC, point G inside",
      "notes": "Answer key: (a) 5 cm, (b) 300 cm². Two-part question: answer0=GE, answer1=total area."
    },
    {
      "n": 9,
      "type_id": 2,
      "question": "The table shows the cost of red and blue coloured shirts. Red shirts cost $10 each and blue shirts cost $8 each. Mr Lim bought red and blue shirts in the ratio 7 : 4. He paid $306 for all the shirts. How many red shirts did he buy? [?]",
      "answer0": "21",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 2,
      "explanation": "For each ratio group: 7 red shirts cost 7 × $10 = $70 and 4 blue shirts cost 4 × $8 = $32, total $70 + $32 = $102 per group. Number of groups = 306 ÷ 102 = 3. Red shirts = 3 × 7 = 21.",
      "hints": ["Find the cost of one ratio group of 7 red and 4 blue shirts.", "Divide the total $306 by the cost of one group, then multiply by 7 for the red shirts."],
      "source": "Henry Park 2024 P5 Weighted Assessment 2 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 21 red shirts. Small cost table (Red $10, Blue $8) incorporated into the stem text rather than cropped."
    },
    {
      "n": 10,
      "type_id": 2,
      "question": "Alan has some packets of sugar and some packets of flour. He has 18 more packets of sugar than packets of flour. Each packet of sugar weighs 2.7 kg. Each packet of flour weighs 1.8 kg more than each packet of sugar. The total mass of all the packets of sugar and packets of flour is 343.8 kg. How many such packets of sugar does Alan have? [?]",
      "answer0": "59",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "Each flour packet = 2.7 + 1.8 = 4.5 kg. The 18 extra sugar packets weigh 2.7 × 18 = 48.6 kg; remove these so sugar and flour packets are equal in number: 343.8 - 48.6 = 295.2 kg. One sugar + one flour packet = 2.7 + 4.5 = 7.2 kg, so equal pairs = 295.2 ÷ 7.2 = 41. Sugar packets = 41 + 18 = 59.",
      "hints": ["Work out each flour packet's mass first (1.8 kg more than a sugar packet).", "Subtract the mass of the 18 extra sugar packets, then pair one sugar with one flour packet (7.2 kg each)."],
      "source": "Henry Park 2024 P5 Weighted Assessment 2 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 59 packets of sugar."
    }
  ]
}