{
  "paper": {
    "school": "Methodist Girls",
    "year": 2025,
    "level": "P6",
    "label": "Weighted Assessment 1",
    "source_prefix": "Methodist Girls 2025 P6 Weighted Assessment 1",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 2,
      "question": "Find the value of \\(\\dfrac{3}{5}+1\\dfrac{6}{7}\\). Express your answer as a decimal to the nearest tenth.<br>[?]",
      "answer0": "2.5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 160,
      "difficulty_id": 1,
      "explanation": "\\(\\dfrac{3}{5}+1\\dfrac{6}{7}=\\dfrac{21}{35}+1\\dfrac{30}{35}=2\\dfrac{16}{35}\\approx 2.45\\). Rounded to the nearest tenth, 2.45 = 2.5.",
      "hints": ["Add the fractions using a common denominator of 35.", "Convert to a decimal, then round to 1 decimal place."],
      "source": "Methodist Girls 2025 P6 Weighted Assessment 1 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key answer 2.5 (1 d.p.). Decimal answer so FIB."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Write a number between \\(1\\dfrac{1}{2}\\) and \\(1\\dfrac{5}{8}\\).",
      "answer0": "\\(1\\dfrac{9}{16}\\)",
      "answer1": "\\(1\\dfrac{3}{4}\\)",
      "answer2": "\\(1\\dfrac{2}{5}\\)",
      "answer3": "\\(1\\dfrac{7}{8}\\)",
      "correct_answer": 0,
      "skill_id": 159,
      "difficulty_id": 1,
      "explanation": "\\(1\\dfrac{1}{2}=1\\dfrac{8}{16}\\) and \\(1\\dfrac{5}{8}=1\\dfrac{10}{16}\\). A number between them is \\(1\\dfrac{9}{16}\\).",
      "hints": ["Express both fractions with a common denominator of 16.", "Find a fraction lying strictly between 8/16 and 10/16."],
      "source": "Methodist Girls 2025 P6 Weighted Assessment 1 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key answer 1 9/16 (one valid value). Fraction answer so rendered as MCQ; distractors lie outside the range."
    },
    {
      "n": 3,
      "type_id": 2,
      "question": "XY is a straight line. Find \\(\\angle a\\).<br>[?]",
      "answer0": "58",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 194,
      "difficulty_id": 1,
      "explanation": "Angles on a straight line XY: \\(\\angle a = 180\\degree - 90\\degree - 32\\degree = 58\\degree\\).",
      "hints": ["The three angles on the straight line XY add up to 180°.", "Subtract the right angle (90°) and 32°."],
      "source": "Methodist Girls 2025 P6 Weighted Assessment 1 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q3.png",
      "image_page": 1,
      "image_bbox": [0.14, 0.71, 0.50, 0.88],
      "image_loc": "straight line X to Y with a 32° angle and a right angle, ∠a marked at the vertex, lower-left of page",
      "notes": "Key answer 58°. Answer in degrees (unit shown after blank)."
    },
    {
      "n": 4,
      "type_id": 0,
      "question": "Mr Lim cut a wooden cube at 3 corners of the cube and painted a triangular face on Block B. Circle the words that describe the painted face: The triangular painted face in Block B is a / an ( scalene / isosceles / equilateral ) triangle as it has ( 0 / 2 / 3 ) equal sides.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 195,
      "difficulty_id": 2,
      "explanation": "Cutting a cube symmetrically at three corners makes a triangular face whose three sides are equal face-diagonals, so it is an equilateral triangle with 3 equal sides.",
      "hints": ["The three cut edges are equal diagonals of identical square faces.", "Three equal sides means equilateral."],
      "source": "Methodist Girls 2025 P6 Weighted Assessment 1 Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q4.png",
      "image_page": 2,
      "image_bbox": [0.14, 0.07, 0.80, 0.22],
      "image_loc": "three diagrams: a cube with cut lines, Block A and Block B (shaded triangular face), top of page",
      "notes": "Interactive circle-the-words task with no app question type — type_id 0, skipped on insert. Key: equilateral, 3 equal sides."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "Express 54 cm as a fraction of 2.5 m. Leave your answer in its simplest form.",
      "answer0": "\\(\\dfrac{27}{125}\\)",
      "answer1": "\\(\\dfrac{54}{250}\\)",
      "answer2": "\\(\\dfrac{27}{250}\\)",
      "answer3": "\\(\\dfrac{54}{125}\\)",
      "correct_answer": 0,
      "skill_id": 212,
      "difficulty_id": 1,
      "explanation": "2.5 m = 250 cm. \\(\\dfrac{54}{250}=\\dfrac{27}{125}\\) in simplest form.",
      "hints": ["Convert 2.5 m to centimetres first (250 cm).", "Simplify 54/250 by dividing both by 2."],
      "source": "Methodist Girls 2025 P6 Weighted Assessment 1 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key answer 27/125. Fraction answer so rendered as MCQ."
    },
    {
      "n": 6,
      "type_id": 2,
      "question": "LMN is an isosceles triangle. LM = LN. Find \\(\\angle b\\).<br>[?]",
      "answer0": "22",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 1,
      "explanation": "Since LM = LN, base angles are equal: \\(\\angle M = \\angle N = 79\\degree\\). \\(\\angle b = 180\\degree - (79\\degree \\times 2) = 22\\degree\\).",
      "hints": ["In an isosceles triangle the base angles are equal.", "Angle sum of a triangle is 180°."],
      "source": "Methodist Girls 2025 P6 Weighted Assessment 1 Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q6.png",
      "image_page": 2,
      "image_bbox": [0.14, 0.62, 0.42, 0.82],
      "image_loc": "isosceles triangle LMN with apex angle b at L and 79° at M, lower-left of page",
      "notes": "Key answer 22°. Answer in degrees."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "The figure is formed by 3 rectangles. BC : AC : DE : FG = 1 : 2 : 4 : 6. FY = DX = AW. What fraction of the figure is shaded? Give your answer in its simplest form.",
      "answer0": "\\(\\dfrac{1}{8}\\)",
      "answer1": "\\(\\dfrac{1}{6}\\)",
      "answer2": "\\(\\dfrac{3}{24}\\)",
      "answer3": "\\(\\dfrac{1}{12}\\)",
      "correct_answer": 0,
      "skill_id": 138,
      "difficulty_id": 3,
      "explanation": "The shaded region is a triangle of base spanning the figure with height BC. Its area = \\(\\dfrac{1}{2}\\times 6 \\times 1 = 3\\) units. The total figure area = 24 units. Shaded fraction = \\(\\dfrac{3}{24}=\\dfrac{1}{8}\\).",
      "hints": ["Set BC = 1 unit and use the ratio to size each rectangle.", "Shaded triangle area = 1/2 × base × height; divide by the total area."],
      "source": "Methodist Girls 2025 P6 Weighted Assessment 1 Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q7.png",
      "image_page": 3,
      "image_bbox": [0.18, 0.13, 0.45, 0.28],
      "image_loc": "three stepped rectangles with points A B C D E F G W X Y and a shaded thin triangle along the base, upper-left of page",
      "notes": "Key answer 1/8 (= 3/24). Fraction answer so rendered as MCQ."
    },
    {
      "n": 8,
      "type_id": 2,
      "question": "ABCD is a trapezium with AB parallel to DC and DC = DA. CDE is a straight line. \\(\\angle ADE = 88\\degree\\) and \\(\\angle ABC = 106\\degree\\). Find \\(\\angle BCA\\).<br>[?]",
      "answer0": "30",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 2,
      "explanation": "\\(\\angle ADC = 180\\degree - 88\\degree = 92\\degree\\) (angles on straight line CDE). Triangle ACD is isosceles (DC = DA), so \\(\\angle ACD = \\dfrac{180\\degree - 92\\degree}{2} = 44\\degree\\). AB is parallel to DC, so co-interior \\(\\angle BCD = 180\\degree - 106\\degree = 74\\degree\\). \\(\\angle BCA = 74\\degree - 44\\degree = 30\\degree\\).",
      "hints": ["Use the straight line CDE to find ∠ADC, then the isosceles triangle ACD.", "AB parallel to DC gives co-interior angles; subtract ∠ACD."],
      "source": "Methodist Girls 2025 P6 Weighted Assessment 1 Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 3,
      "image_bbox": [0.24, 0.46, 0.66, 0.62],
      "image_loc": "trapezium ABCD with diagonal AC, CDE straight line, angles 106° at B and 88° at D, middle of page",
      "notes": "Key working: ∠ACD = 88° ÷ 2 = 44°, ∠BCA = 180° − 106° − 44° = 30°. Key answer 30°."
    },
    {
      "n": 9,
      "type_id": 2,
      "question": "Norman has 14 kg of cashew nuts. He packs them into bags of \\(\\dfrac{3}{4}\\) kg and has some left. He sells each bag for $4.95.<br>(a) What is the greatest amount of money that Norman can get from selling all the \\(\\dfrac{3}{4}\\)-kg bags of cashew nuts? $[?]<br>(b) What is the mass of cashew nuts left? [?] g",
      "answer0": "89.10",
      "answer1": "500",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "(a) \\(\\dfrac{3}{4}\\) kg = 750 g. 14 kg ÷ 750 g = \\(18\\dfrac{2}{3}\\), so 18 full bags. 18 × $4.95 = $89.10. (b) 18 × 750 g = 13 500 g. Left = 14 000 g − 13 500 g = 500 g.",
      "hints": ["Find how many full 3/4-kg bags fit into 14 kg (whole bags only).", "Leftover mass = total − mass packed into full bags."],
      "source": "Methodist Girls 2025 P6 Weighted Assessment 1 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Two FIB blanks: (a) $89.10, (b) 500 g. Key answers match."
    },
    {
      "n": 10,
      "type_id": 2,
      "question": "AB and BC are straight lines drawn in a square grid. Measure and write down the size of \\(\\angle ABC\\).<br>[?]",
      "answer0": "135",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "Measuring with a protractor, \\(\\angle ABC = 135\\degree\\).",
      "hints": ["Use a protractor placed at vertex B.", "Read the angle between ray BA and ray BC."],
      "source": "Methodist Girls 2025 P6 Weighted Assessment 1 Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 5,
      "image_bbox": [0.20, 0.09, 0.74, 0.27],
      "image_loc": "square grid with straight lines from A up to B then down to C, top of page",
      "notes": "Served blank is part (a) ∠ABC = 135° (key). Part (b) 'Complete the drawing of trapezium ABCD and label D' is a draw task with no app question type — omitted from the served answer; recorded here in notes."
    },
    {
      "n": 11,
      "type_id": 2,
      "question": "Xinyu and Caitlyn had $708 altogether. Xinyu spent \\(\\dfrac{4}{7}\\) of her money and Caitlyn spent \\(\\dfrac{3}{8}\\) of her money. In the end, both girls had an equal amount of money left. How much money did Xinyu have at first?<br>$[?]",
      "answer0": "420",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Xinyu kept \\(\\dfrac{3}{7}\\); Caitlyn kept \\(\\dfrac{5}{8}\\). The 'left' amounts are equal. Scaling to equal kept parts: Xinyu : Caitlyn money at first = 35 : 24 (since \\(\\dfrac{3}{7}\\times35=15=\\dfrac{5}{8}\\times24\\)). Total = 35 + 24 = 59 units = $708, so 1 unit = $12. Xinyu = 35 units = 35 × $12 = $420.",
      "hints": ["Xinyu keeps 3/7 and Caitlyn keeps 5/8; set these 'left' amounts equal.", "Find a common kept value to get the ratio of their starting amounts, then split $708."],
      "source": "Methodist Girls 2025 P6 Weighted Assessment 1 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key working: Xinyu:Caitlyn at first = 35u:24u, total 59u = $708, 1u = $12, Xinyu = 35u = $420. Key answer $420."
    },
    {
      "n": 12,
      "type_id": 2,
      "question": "PTRU is a square. PTS and QRS are straight lines. \\(\\angle QPU = 8\\degree\\) and \\(\\angle PQR = 40\\degree\\).<br>(a) Find \\(\\angle PSR\\). [?]<br>(b) Find \\(\\angle PRQ\\). [?]",
      "answer0": "42",
      "answer1": "87",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "(a) \\(\\angle SPQ = \\angle UPT + \\angle QPU = 90\\degree + 8\\degree = 98\\degree\\). In triangle PQS, \\(\\angle PSR = 180\\degree - 98\\degree - 40\\degree = 42\\degree\\). (b) Diagonal PR bisects the square's right angle, so \\(\\angle SPR = 90\\degree \\div 2 = 45\\degree\\). In triangle PRS, \\(\\angle PRS = 180\\degree - 45\\degree - 42\\degree = 93\\degree\\), so \\(\\angle SRT = 93\\degree - 45\\degree = 48\\degree\\). \\(\\angle PRQ = 180\\degree - 45\\degree - 48\\degree = 87\\degree\\) (angles on straight line QRS at R).",
      "hints": ["∠SPQ is the square's right angle plus 8°; use the triangle PQS angle sum.", "The square's diagonal bisects the 90° corner; work through the angles at R."],
      "source": "Methodist Girls 2025 P6 Weighted Assessment 1 Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q12.png",
      "image_page": 6,
      "image_bbox": [0.18, 0.12, 0.66, 0.33],
      "image_loc": "square PTRU with straight lines PTS and QRS, angles 8° at P and 40° at Q, upper part of page",
      "notes": "Two FIB blanks: (a) ∠PSR = 42°, (b) ∠PRQ = 87°. Key answers match."
    },
    {
      "n": 13,
      "type_id": 2,
      "question": "Kirsten bought 3 pens and 4 erasers with \\(\\dfrac{2}{5}\\) of her money. Each pen cost 4 times as much as an eraser. She spent \\(\\dfrac{1}{4}\\) of her remaining money on a notebook. The notebook cost $2.20 more than a pen. How much did the notebook cost?<br>$[?]",
      "answer0": "6.60",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "3 pens + 4 erasers = 12 erasers + 4 erasers = 16 erasers cost \\(\\dfrac{2}{5}\\) of her money, so 1 eraser = \\(\\dfrac{2}{5}\\div16=\\dfrac{1}{40}\\) and 1 pen = \\(\\dfrac{4}{40}=\\dfrac{1}{10}\\) of her money. Remaining = \\(\\dfrac{3}{5}=\\dfrac{12}{20}\\); notebook = \\(\\dfrac{1}{4}\\) of that = \\(\\dfrac{3}{20}\\). Notebook − pen = \\(\\dfrac{3}{20}-\\dfrac{2}{20}=\\dfrac{1}{20}\\) of her money = $2.20, so \\(\\dfrac{1}{20}\\) of money = ... using key: 2u = $2.20, 1u = $1.10; pen 4u = $4.40; notebook = $4.40 + $2.20 = $6.60.",
      "hints": ["Convert 3 pens to erasers (1 pen = 4 erasers) to find the fraction per item.", "The notebook is 1/4 of the remaining 3/5; it costs $2.20 more than a pen — set up the unit equation."],
      "source": "Methodist Girls 2025 P6 Weighted Assessment 1 Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Served blank is part (b) notebook cost = $6.60 (key). Part (a) 'What fraction of her money did she spend on each pen?' = 1/10 — fraction answer, omitted from served FIB and recorded here in notes. Key answers (a) 1/10, (b) $6.60."
    }
  ]
}