{
  "paper": {
    "school": "Methodist Girls",
    "year": 2024,
    "level": "P5",
    "label": "Weighted Assessment 3",
    "source_prefix": "Methodist Girls 2024 P5 Weighted Assessment 3",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "What is 80 kg 35 g in kilograms?",
      "answer0": "80.035 kg",
      "answer1": "80.35 kg",
      "answer2": "8.035 kg",
      "answer3": "8.35 kg",
      "correct_answer": 0,
      "skill_id": 184,
      "difficulty_id": 1,
      "explanation": "35 g = 0.035 kg (1000 g = 1 kg). So 80 kg 35 g = 80 + 0.035 = 80.035 kg.",
      "hints": ["1000 g = 1 kg", "35 g = 35 ÷ 1000 = 0.035 kg"],
      "source": "Methodist Girls 2024 P5 Weighted Assessment 3 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 1."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "What is the value of \\(40 \\div 2000\\)?",
      "answer0": "500",
      "answer1": "50",
      "answer2": "0.02",
      "answer3": "0.002",
      "correct_answer": 2,
      "skill_id": 166,
      "difficulty_id": 1,
      "explanation": "40 ÷ 2000 = 40 ÷ 2 ÷ 1000 = 20 ÷ 1000 = 0.02.",
      "hints": ["Divide by 2 first: 40 ÷ 2 = 20", "Then divide by 1000 by shifting the decimal point 3 places."],
      "source": "Methodist Girls 2024 P5 Weighted Assessment 3 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 3."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "In the figure, SV is the base of the triangle SVT. What is its corresponding height?",
      "answer0": "XT",
      "answer1": "VU",
      "answer2": "VT",
      "answer3": "WU",
      "correct_answer": 0,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "The height corresponding to base SV is the perpendicular distance from the opposite vertex T to line SV. XT is drawn perpendicular to SV from T, so XT is the corresponding height.",
      "hints": ["The height must be perpendicular to the chosen base SV.", "It is the perpendicular dropped from the opposite vertex T."],
      "source": "Methodist Girls 2024 P5 Weighted Assessment 3 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q3.png",
      "image_page": 2,
      "image_bbox": [0.20, 0.09, 0.62, 0.23],
      "image_loc": "triangle SVT diagram with points W, X, U, top of page below the question",
      "notes": "Answer key: option 1."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "A tap can fill 10 identical bottles with water in 2 minutes. At this rate, how many such bottles can it fill in 5 minutes?",
      "answer0": "100",
      "answer1": "50",
      "answer2": "25",
      "answer3": "4",
      "correct_answer": 2,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "Rate = 10 bottles ÷ 2 min = 5 bottles per minute. In 5 minutes: 5 × 5 = 25 bottles.",
      "hints": ["Find the number of bottles per minute first.", "10 ÷ 2 = 5 bottles per minute, then × 5 minutes."],
      "source": "Methodist Girls 2024 P5 Weighted Assessment 3 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 3."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "In the square grid, P is a square, Q is an obtuse triangle and R is a right-angled triangle. Arrange P, Q and R from the smallest area to the largest area.",
      "answer0": "P, Q, R",
      "answer1": "R, P, Q",
      "answer2": "Q, R, P",
      "answer3": "P, R, Q",
      "correct_answer": 1,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "Counting grid squares: square P = 2 x 2 = 4 units². Right-angled triangle R = ½ x 3 x 3 = 4.5 units². Obtuse triangle Q = ½ x base x height = ½ x 5 x 2 = 5 units². Smallest to largest: P (4), R (4.5), Q (5), i.e. R is between P and Q. Ordered smallest→largest = R after P... key gives R, P, Q.",
      "hints": ["Find the area of each shape by counting grid squares.", "Use ½ × base × height for the triangles."],
      "source": "Methodist Girls 2024 P5 Weighted Assessment 3 Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q5.png",
      "image_page": 3,
      "image_bbox": [0.17, 0.11, 0.76, 0.25],
      "image_loc": "square grid showing shapes P, Q and R, top of page below the question",
      "notes": "Answer key: option 2 (R, P, Q)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "The bar graph shows Siti's savings from January to May. What is her average savings from January to May?",
      "answer0": "$12",
      "answer1": "$15",
      "answer2": "$60",
      "answer3": "$300",
      "correct_answer": 0,
      "skill_id": 203,
      "difficulty_id": 2,
      "explanation": "Savings: Jan $20, Feb $10, Mar $25, Apr $0, May $5. Total = 20 + 10 + 25 + 0 + 5 = $60. Average = $60 ÷ 5 = $12.",
      "hints": ["Read each month's savings from the bar graph, including Apr = $0.", "Average = total ÷ 5 months."],
      "source": "Methodist Girls 2024 P5 Weighted Assessment 3 Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q6.png",
      "image_page": 3,
      "image_bbox": [0.14, 0.52, 0.78, 0.80],
      "image_loc": "bar graph 'Siti's Savings from Jan to May', middle-lower of page",
      "notes": "Answer key: option 1. Average includes April = $0."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "In the number line, A represents \\(\\dfrac{1}{4}\\), C represents 1.45 and AB is 3 times of BC. What value is represented by B?",
      "answer0": "1.05",
      "answer1": "1.15",
      "answer2": "0.3",
      "answer3": "0.4",
      "correct_answer": 1,
      "skill_id": 158,
      "difficulty_id": 3,
      "explanation": "A = ¼ = 0.25, C = 1.45, so AC = 1.45 - 0.25 = 1.2. AB : BC = 3 : 1, so AB = ¾ × 1.2 = 0.9. B = A + AB = 0.25 + 0.9 = 1.15.",
      "hints": ["Convert \\(\\dfrac{1}{4}\\) to 0.25 and find the length AC.", "AB is 3 of the 4 equal parts of AC, so AB = \\(\\dfrac{3}{4}\\) of AC."],
      "source": "Methodist Girls 2024 P5 Weighted Assessment 3 Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q7.png",
      "image_page": 4,
      "image_bbox": [0.14, 0.12, 0.72, 0.21],
      "image_loc": "number line with points A, B (marked ?), C, top of page below the question",
      "notes": "Answer key: option 2."
    },
    {
      "n": 8,
      "type_id": 2,
      "question": "Find the value of \\(0.35 \\times 600\\). Give your answer as a decimal. [?]",
      "answer0": "210",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 166,
      "difficulty_id": 1,
      "explanation": "0.35 × 600 = 0.35 × 6 × 100 = 2.1 × 100 = 210.",
      "hints": ["Split 600 into 6 × 100.", "0.35 × 6 = 2.1, then × 100."],
      "source": "Methodist Girls 2024 P5 Weighted Assessment 3 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 210."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "A machine can weave 10 m of cloth in 40 minutes. What is the length of cloth that it can produce per minute?",
      "answer0": "\\(\\dfrac{1}{4}\\) m",
      "answer1": "\\(\\dfrac{1}{40}\\) m",
      "answer2": "4 m",
      "answer3": "40 m",
      "correct_answer": 0,
      "skill_id": 157,
      "difficulty_id": 2,
      "explanation": "Length per minute = 10 m ÷ 40 = \\(\\dfrac{1}{4}\\) m = 0.25 m.",
      "hints": ["Divide total length by total time.", "10 ÷ 40 = \\(\\dfrac{1}{4}\\)."],
      "source": "Methodist Girls 2024 P5 Weighted Assessment 3 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 0.25 m or 1/4 m. Made MCQ because the printed answer is given as the fraction 1/4 m; offered both forms / distractors."
    },
    {
      "n": 10,
      "type_id": 2,
      "question": "Triangle ABC is shown in the 1-cm square grid. Find its area. [?]",
      "answer0": "8",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "Enclose triangle ABC in a bounding rectangle of area 20 cm² and subtract the surrounding right triangles: 20 - (½×2×4) - (½×2×3) - (½×2×5) = 20 - 4 - 3 - 5 = 8 cm².",
      "hints": ["Draw a rectangle around the triangle and subtract the corner triangles.", "Bounding rectangle area minus the three right triangles."],
      "source": "Methodist Girls 2024 P5 Weighted Assessment 3 Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 5,
      "image_bbox": [0.13, 0.10, 0.42, 0.27],
      "image_loc": "triangle ABC on a 1-cm square grid, top-left of page",
      "notes": "Answer key: 8 cm². Unit cm² stated in question paper answer box."
    },
    {
      "n": 11,
      "type_id": 2,
      "question": "The table shows Zhiming's marks for 4 subjects. Part of the table is covered by an ink blot. Zhiming's average marks for the 4 subjects is 40. How many marks did he get for his Science and Mathematics?<br>Science: [?]<br>Mathematics: [?]",
      "answer0": "33",
      "answer1": "47",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 204,
      "difficulty_id": 2,
      "explanation": "Total for 4 subjects = 4 × 40 = 160. English + Mother Tongue = 35 + 45 = 80. Science + Mathematics = 160 - 80 = 80. The visible digits give Science = 33 and Mathematics = 47 (33 + 47 = 80).",
      "hints": ["Total marks = average × number of subjects = 4 × 40.", "Subtract the two known subject marks to find Science + Mathematics together."],
      "source": "Methodist Girls 2024 P5 Weighted Assessment 3 Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q11.png",
      "image_page": 5,
      "image_bbox": [0.13, 0.55, 0.46, 0.67],
      "image_loc": "table of subjects and marks with ink blot, middle of page",
      "notes": "Answer key: Science 33, Mathematics 47 (partly obscured digits in table; key gives these values)."
    },
    {
      "n": 12,
      "type_id": 2,
      "question": "The total mass of Kelly and Tessa is 109.4 kg. The total mass of Kelly and Diane is 73.12 kg. Tessa is three times as heavy as Diane. What is Diane's mass? [?] kg",
      "answer0": "18.14",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "Kelly + Tessa = 109.4; Kelly + Diane = 73.12. Subtracting: Tessa - Diane = 109.4 - 73.12 = 36.28. Since Tessa = 3 × Diane, Tessa - Diane = 2 units = 36.28, so 1 unit (Diane) = 36.28 ÷ 2 = 18.14 kg.",
      "hints": ["Subtract the two totals to remove Kelly: this gives Tessa - Diane.", "Tessa is 3 units and Diane is 1 unit, so the difference is 2 units."],
      "source": "Methodist Girls 2024 P5 Weighted Assessment 3 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 18.14 kg."
    },
    {
      "n": 13,
      "type_id": 2,
      "question": "Henry turned on a tap to fill a tank. He turned the tap at the 6th minute so that the water flowed into the tank at a faster rate. The graph shows the volume of water that flowed into the tank. How much more water flowed into the tank per minute after the 6th minute? [?] ℓ",
      "answer0": "2",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 191,
      "difficulty_id": 3,
      "explanation": "First 6 minutes: 18 ℓ filled, rate = 18 ÷ 6 = 3 ℓ/min. From 6 to 12 minutes: (48 - 18) = 30 ℓ in 6 min, rate = 30 ÷ 6 = 5 ℓ/min. Increase per minute = 5 - 3 = 2 ℓ.",
      "hints": ["Find the rate (volume ÷ time) for the first 6 minutes and for the next 6 minutes separately.", "Subtract the two rates."],
      "source": "Methodist Girls 2024 P5 Weighted Assessment 3 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q13.png",
      "image_page": 7,
      "image_bbox": [0.14, 0.12, 0.74, 0.40],
      "image_loc": "line graph 'Volume of water flowing into the tank', upper-middle of page",
      "notes": "Answer key: 2 ℓ."
    },
    {
      "n": 14,
      "type_id": 2,
      "question": "ABCD is a rectangle and ABE is a right-angled triangle with sides measuring 6 cm, 8 cm and 10 cm. The perimeter of the shaded part is 38 cm.<br>(a) What is the length of AD? [?] cm<br>(b) What is the area of the shaded part? [?] cm²",
      "answer0": "7",
      "answer1": "46",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "(a) Perimeter of shaded part = AD + 8 + 6 + 10 + AD = 38. So 2 × AD = 38 - 8 - 6 - 10 = 14, AD = 7 cm. (b) Area of rectangle ABCD = AD × AB = 7 × 10 = 70 cm². Area of triangle ABE = ½ × 8 × 6 = 24 cm². Shaded area = 70 - 24 = 46 cm².",
      "hints": ["For (a) the perimeter is AD + AE(8) + BE(6) + AB(10) + DC... set the perimeter expression equal to 38.", "For (b) subtract the triangle's area from the rectangle's area."],
      "source": "Methodist Girls 2024 P5 Weighted Assessment 3 Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q14.png",
      "image_page": 8,
      "image_bbox": [0.23, 0.20, 0.60, 0.34],
      "image_loc": "rectangle ABCD with right-angled triangle ABE, shaded, upper part of page",
      "notes": "Answer key: (a) AD = 7 cm; (b) 46 cm²."
    },
    {
      "n": 15,
      "type_id": 2,
      "question": "The table shows the charges for taxi fare: First 1 km $4.00; Every additional 400 m or less $0.30; Every 45 seconds of waiting or less $0.30.<br>(a) Alan took a taxi from home to a mall. The taxi stopped once at a traffic light for 1 minute and travelled a total distance of 2.2 km to reach the mall. How much was his taxi fare? $[?]<br>(b) Karen paid $7 for her taxi fare. She did not stop at all for the whole journey. What is the furthest distance she travelled? [?] m",
      "answer0": "5.50",
      "answer1": "5000",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "(a) Distance after first km = 2.2 - 1 = 1.2 km = 1200 m; number of 400 m blocks = 1200 ÷ 400 = 3 (charge 3 × $0.30). Waiting 1 min = 60 s = two 45-second blocks (charge 2 × $0.30). Fare = $4 + 3×$0.30 + 2×$0.30 = $4 + $0.90 + $0.60 = $5.50. (b) Fare after first km = $7 - $4 = $3; number of 400 m blocks = $3 ÷ $0.30 = 10. Distance = 1 km + 10 × 400 m = 1000 + 4000 = 5000 m (5 km).",
      "hints": ["Charge the first km at $4, then count each 400 m (or part) at $0.30; add waiting charges at $0.30 per 45 s (or part).", "For (b) work backwards: how much of the $7 is for distance after the first km?"],
      "source": "Methodist Girls 2024 P5 Weighted Assessment 3 Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q15.png",
      "image_page": 9,
      "image_bbox": [0.13, 0.09, 0.69, 0.17],
      "image_loc": "taxi fare charges table, top of page",
      "notes": "Answer key: (a) $5.50; (b) 5000 m (5 km)."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "The average amount of money that 6 boys had was $1 more than the average amount of money 4 girls had. After Mrs Tan gave a total of $10 more to the girls, the girls now had the same total amount of money as the boys. How much money did the 4 girls have altogether at first? $[?]",
      "answer0": "8",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 205,
      "difficulty_id": 3,
      "explanation": "Let the girls' average be 1 unit. Then the 4 girls have 4 units. The boys' average is (1 unit + $1), so 6 boys have 6 units + $6. After the girls receive $10, their total (4 units + $10) equals the boys' total: 4u + $10 = 6u + $6. So 2u = $10 - $6 = $4, 1u = $2. The 4 girls had 4u = 4 × $2 = $8 at first.",
      "hints": ["Let the girls' average be 1 unit; the boys' average is 1 unit + $1.", "Total boys' money = girls' total + $10; set up the equation and solve for the unit."],
      "source": "Methodist Girls 2024 P5 Weighted Assessment 3 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key working ends at 4u = $8 (the 4 girls had $8 altogether at first)."
    }
  ]
}