{
  "paper": {
    "school": "ACS Primary",
    "year": 2023,
    "level": "P5",
    "label": "Weighted Assessment 2",
    "source_prefix": "ACS Primary 2023 P5 Weighted Assessment 2",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "Find the value of \\(\\dfrac{3}{4} \\times \\dfrac{6}{9}\\).",
      "answer0": "\\(\\dfrac{1}{2}\\)",
      "answer1": "\\(\\dfrac{1}{4}\\)",
      "answer2": "\\(\\dfrac{1}{18}\\)",
      "answer3": "\\(\\dfrac{9}{13}\\)",
      "correct_answer": 0,
      "skill_id": 161,
      "difficulty_id": 1,
      "explanation": "\\(\\dfrac{3}{4} \\times \\dfrac{6}{9} = \\dfrac{18}{36} = \\dfrac{1}{2}\\). Answer: \\(\\dfrac{1}{2}\\) (option 1).",
      "hints": ["Multiply numerators together and denominators together.", "Simplify \\(\\dfrac{18}{36}\\) by dividing both by 18."],
      "source": "ACS Primary 2023 P5 Weighted Assessment 2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Fraction answer -> MCQ. Key: option 1."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Andrew drew a house using circles, triangles and rectangles. What is the ratio of the number of circles to the number of triangles to the total number of circles, triangles and rectangles?",
      "answer0": "1 : 1 : 3",
      "answer1": "1 : 1 : 7",
      "answer2": "2 : 2 : 3",
      "answer3": "2 : 2 : 7",
      "correct_answer": 3,
      "skill_id": 180,
      "difficulty_id": 2,
      "explanation": "The house figure has 2 circles, 2 triangles (the roof triangle and the small triangle on the door) and 3 rectangles (the body, the window strip and the door). Total shapes = 2 + 2 + 3 = 7. Ratio circles : triangles : total = 2 : 2 : 7. Answer: option 4.",
      "hints": ["Count each type of shape in the figure.", "The last term is the TOTAL number of all three shapes, not just rectangles."],
      "source": "ACS Primary 2023 P5 Weighted Assessment 2 Q2",
      "image_needed": true,
      "image_options": false,
      "image_file": "q2.png",
      "image_page": 3,
      "image_bbox": [0.36, 0.55, 0.66, 0.74],
      "notes": "Ratio answer -> MCQ. Key: option 4 (2:2:7). Figure = house drawn from circles/triangles/rectangles, middle of page below the question."
    },
    {
      "n": 3,
      "type_id": 2,
      "question": "In the figure, the length of the rectangle is 16 cm and its height is 6 cm. The length of AD is 10 cm and CD = DE. Find the area of the shaded triangle.<br>Area = [?] cm²",
      "answer0": "24",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "EC is the base of the rectangle = 16 cm, so CD = DE = 8 cm. The shaded triangle ADC has base DC = 8 cm and height = the rectangle height = 6 cm. Area = \\(\\dfrac{1}{2} \\times 8 \\times 6 = 24\\) cm². Answer: 24 cm².",
      "hints": ["CD = DE means D is the midpoint of EC, so DC = 16 ÷ 2 = 8 cm.", "Area of a triangle = \\(\\dfrac{1}{2} \\times \\text{base} \\times \\text{height}\\); the height equals the rectangle's height of 6 cm."],
      "source": "ACS Primary 2023 P5 Weighted Assessment 2 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q3.png",
      "image_page": 4,
      "image_bbox": [0.22, 0.24, 0.66, 0.40],
      "notes": "Key: option 1 = 24 cm². Decimal/integer answer -> FIB. Rectangle ABCE with shaded triangle, labels A B (16 cm) top, 6 cm right, 10 cm slant, E D C bottom."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "The rectangle is made up of 8 identical squares. The height of the rectangle is \\(\\dfrac{1}{3}\\) m. Find the area of the rectangle. Give your answer as a fraction in its simplest form.",
      "answer0": "\\(\\dfrac{2}{9}\\) m²",
      "answer1": "\\(\\dfrac{1}{3}\\) m²",
      "answer2": "\\(\\dfrac{2}{3}\\) m²",
      "answer3": "\\(\\dfrac{8}{9}\\) m²",
      "correct_answer": 0,
      "skill_id": 161,
      "difficulty_id": 2,
      "explanation": "The 8 squares form a 4-wide by 2-tall grid, so the rectangle is 4 squares wide and 2 squares tall. Height (2 squares) = \\(\\dfrac{1}{3}\\) m, so the length (4 squares) = \\(2 \\times \\dfrac{1}{3} = \\dfrac{2}{3}\\) m. Area = \\(\\dfrac{1}{3} \\times \\dfrac{2}{3} = \\dfrac{2}{9}\\) m². Answer: \\(\\dfrac{2}{9}\\) m².",
      "hints": ["The 8 squares are arranged 4 across and 2 down; the height of 1/3 m covers 2 squares, the length covers 4 squares.", "Length = 2 × (1/3) = 2/3 m, then Area = length × height."],
      "source": "ACS Primary 2023 P5 Weighted Assessment 2 Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q4.png",
      "image_page": 5,
      "image_bbox": [0.20, 0.30, 0.45, 0.40],
      "notes": "Fraction answer -> MCQ. Key: 2/9 m². Figure = rectangle of 8 identical squares (4 by 2) with 1/3 m height bracket on the left."
    },
    {
      "n": 5,
      "type_id": 2,
      "question": "There are some apples in a box. For every 5 good apples, there are 2 rotten ones. There are 55 good apples in the box. Find the total number of apples in the box.<br>[?]",
      "answer0": "77",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 2,
      "explanation": "Good : rotten = 5 : 2. 55 good apples ÷ 5 = 11 units. Rotten = 11 × 2 = 22. Total = 55 + 22 = 77 apples. Answer: 77.",
      "hints": ["Find how many units 55 good apples represent: 55 ÷ 5 = 11.", "Rotten apples = 11 × 2; total = good + rotten."],
      "source": "ACS Primary 2023 P5 Weighted Assessment 2 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 77."
    },
    {
      "n": 6,
      "type_id": 2,
      "question": "The square is made up of 8 identical rectangles and 8 identical shaded triangles. The side of the square is 16 cm. Find the total area of the shaded triangles.<br>Area = [?] cm²",
      "answer0": "128",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "The 16 cm square is divided so each small unit is 16 ÷ 2 = 8 cm. The 8 shaded triangles together make up half of the square's area. Area of square = 16 × 16 = 256 cm². Total shaded = 256 ÷ 2 = 128 cm². (Key working: 16 ÷ 2 = 8; 8 × 16 = 128 cm².) Answer: 128 cm².",
      "hints": ["The shaded triangles together cover exactly half of the whole square.", "Square area = 16 × 16; take half for the shaded part."],
      "source": "ACS Primary 2023 P5 Weighted Assessment 2 Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q6.png",
      "image_page": 6,
      "image_bbox": [0.21, 0.24, 0.46, 0.42],
      "notes": "Key: 128 cm². Figure = 16 cm square containing a shaded hexagon/diamond pattern (8 rectangles + 8 shaded triangles), with 16 cm width bracket on top."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "A box contained some potatoes. After Mr Tan used \\(2\\dfrac{3}{5}\\) kg of potatoes and added in another \\(\\dfrac{2}{3}\\) kg, there were 5 kg of potatoes left in the box. What was the mass of the potatoes in the box at first?",
      "answer0": "\\(6\\dfrac{14}{15}\\) kg",
      "answer1": "\\(7\\dfrac{4}{15}\\) kg",
      "answer2": "\\(6\\dfrac{1}{15}\\) kg",
      "answer3": "\\(3\\dfrac{4}{15}\\) kg",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "Work backwards. Before adding \\(\\dfrac{2}{3}\\) kg there was \\(5 - \\dfrac{2}{3} = 4\\dfrac{1}{3}\\) kg. Before using \\(2\\dfrac{3}{5}\\) kg there was \\(4\\dfrac{1}{3} + 2\\dfrac{3}{5} = 6\\dfrac{14}{15}\\) kg. (\\(\\dfrac{1}{3} + \\dfrac{3}{5} = \\dfrac{5}{15} + \\dfrac{9}{15} = \\dfrac{14}{15}\\).) Answer: \\(6\\dfrac{14}{15}\\) kg.",
      "hints": ["Work backwards from the 5 kg left: first undo the adding, then undo the using.", "5 − 2/3 = 4 1/3, then add back 2 3/5."],
      "source": "ACS Primary 2023 P5 Weighted Assessment 2 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Mixed-number answer -> MCQ. Key: 6 14/15 kg."
    },
    {
      "n": 8,
      "type_id": 2,
      "question": "A piece of ribbon was cut into three pieces in the ratio 3 : 4 : 7. The longest piece is 112 cm longer than the shortest piece. Find the original length of the piece of ribbon. Give your answer in centimetres.<br>[?] cm",
      "answer0": "392",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 2,
      "explanation": "Difference between longest and shortest = 7u − 3u = 4u = 112 cm, so 1u = 28 cm. Total units = 3 + 4 + 7 = 14u. Original length = 14 × 28 = 392 cm. Answer: 392 cm.",
      "hints": ["The difference 112 cm equals 7 − 3 = 4 units.", "Find 1 unit, then multiply by the total 14 units."],
      "source": "ACS Primary 2023 P5 Weighted Assessment 2 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 392 cm."
    },
    {
      "n": 9,
      "type_id": 2,
      "question": "Two big triangles BFG and DFG are drawn in rectangle AEFG. The total area of triangle BCG and triangle CDF is 127.6 cm². The height of the rectangle is 14 cm and the base GF is 22 cm. Find the area of triangle CFG.<br>Area = [?] cm²",
      "answer0": "40.2",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Area of triangle DFG = \\(\\dfrac{1}{2} \\times 22 \\times 14 = 154\\) cm² (= area of triangle BFG by symmetry). The total of triangles BCG and CDF is 127.6 cm², so each is 127.6 ÷ 2 = 63.8 cm². Triangle CFG = triangle DFG − triangle CDF = 154 − 63.8 = 40.2 cm². Answer: 40.2 cm².",
      "hints": ["Area of triangle DFG = 1/2 × base × height = 1/2 × 22 × 14 = 154 cm².", "Triangle CFG = triangle DFG minus triangle CDF, where CDF is half of the given 127.6 cm²."],
      "source": "ACS Primary 2023 P5 Weighted Assessment 2 Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q9.png",
      "image_page": 11,
      "image_bbox": [0.24, 0.20, 0.60, 0.36],
      "notes": "Key: 40.2 cm². Figure = rectangle AEFG with two crossing triangles BFG and DFG meeting at C, 14 cm right side, 22 cm bottom (GF), '?' marking triangle CFG."
    },
    {
      "n": 10,
      "type_id": 2,
      "question": "Adele had 3 identical boxes, Box A, Box B and Box C. Box A contained 65 cubes. The ratio of the number of cubes in Box A to the number of cubes in Box B was 5 : 3.<br>(a) Find the number of cubes in Box B. [?]<br>(b) After Adele took some cubes out of Box A, the ratio of the number of cubes in Box A to the number of cubes in Box C became 5 : 6. The number of cubes in Box C was more than 50 and less than 60. How many cubes were left in Box A in the end? [?]",
      "answer0": "39",
      "answer1": "45",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "(a) A : B = 5 : 3 and A = 65, so 5u = 65, 1u = 13. Box B = 3u = 3 × 13 = 39 cubes. (b) A : C = 5 : 6. Box C is between 50 and 60 and must be a multiple of 6, so Box C = 54 (54 ÷ 6 = 9 per unit). Box A = 5 × 9 = 45 cubes. Answer: (a) 39, (b) 45.",
      "hints": ["(a) 65 cubes equals 5 units, so 1 unit = 13.", "(b) Box C is a multiple of 6 between 50 and 60 → 54; then Box A = 5 parts when 6 parts = 54."],
      "source": "ACS Primary 2023 P5 Weighted Assessment 2 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Two-part: (a) 39, (b) 45. Both integer -> FIB with 2 blanks."
    },
    {
      "n": 11,
      "type_id": 2,
      "question": "The figure is made up of a big square and 2 small identical squares. The side of the big square is 20 cm and the side of the small square is 14 cm. BCD is a straight line.<br>(a) Find the area of triangle ACD. [?] cm²<br>(b) Find the area of triangle ABC. [?] cm²",
      "answer0": "336",
      "answer1": "144",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Small square area = 14 × 14 = 196 cm², so a small-square triangle (half) = 98 cm². (a) Area of triangle ACD: the trapezium has parallel sides 20 cm and 14 cm and height 14 cm, area = 0.5 × (20 + 14) × 14 = 238 cm²; subtract the 98 cm² triangle to get 238 − 98 = 336 cm². (b) Triangle ABC: 0.5 × 20 × 48 = 480 cm² for the large triangle, then 480 − 336 = 144 cm². Answer: (a) 336 cm², (b) 144 cm².",
      "hints": ["Small square area = 14 × 14 = 196; half of it = 98 cm².", "Use the trapezium area 0.5 × (20 + 14) × 14 = 238, then subtract 98 for part (a)."],
      "source": "ACS Primary 2023 P5 Weighted Assessment 2 Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q11.png",
      "image_page": 13,
      "image_bbox": [0.20, 0.24, 0.62, 0.40],
      "notes": "Two-part: (a) 336 cm², (b) 144 cm². Both integer -> FIB with 2 blanks. Figure = big square (20 cm) with 2 small squares (14 cm), shaded triangle ABC, points A B C D, BCD straight line, 14 cm right, 20 cm bottom bracket."
    },
    {
      "n": 12,
      "type_id": 2,
      "question": "Anan and Jia Qi had the same amount of money at first. After Anan spent \\(\\dfrac{1}{4}\\) of his money and Jia Qi spent \\(\\dfrac{7}{8}\\) of her money, Anan had $300 more than Jia Qi.<br>(a) How much money did Anan have left? $[?]<br>(b) Anan gave \\(\\dfrac{2}{5}\\) of the money he had left to his mother and \\(\\dfrac{1}{3}\\) of the remainder to his father. How much money did Anan give to his father? $[?]",
      "answer0": "360",
      "answer1": "72",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Let the starting amount be 8 units. Anan kept \\(\\dfrac{3}{4}\\) = 6 units; Jia Qi kept \\(\\dfrac{1}{8}\\) = 1 unit. Difference = 6u − 1u = 5u = $300, so 1u = $60. (a) Anan left = 6u = $360. (b) Anan gave \\(\\dfrac{2}{5}\\) of $360 to mother = $144, leaving remainder $360 − $144 = $216; he gave \\(\\dfrac{1}{3}\\) of $216 to father = $72. Answer: (a) $360, (b) $72.",
      "hints": ["Use 8 units for the start; Anan keeps 6 units (3/4), Jia Qi keeps 1 unit (1/8); the difference of 5 units = $300.", "(b) Mother gets 2/5 of $360; the remainder is then split, with father getting 1/3 of it."],
      "source": "ACS Primary 2023 P5 Weighted Assessment 2 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Two-part: (a) $360, (b) $72. Both money/integer -> FIB with 2 blanks."
    }
  ]
}