{
  "paper": {
    "school": "Singapore Chinese Girls' School (Primary)",
    "year": 2023,
    "level": "P6",
    "label": "Weighted Assessment 1",
    "source_prefix": "SCGS 2023 P6 Weighted Assessment 1",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "Divide \\(\\dfrac{3}{4}\\) by 12.",
      "answer0": "\\(\\dfrac{1}{9}\\)",
      "answer1": "\\(\\dfrac{1}{16}\\)",
      "answer2": "9",
      "answer3": "16",
      "correct_answer": 1,
      "skill_id": 206,
      "difficulty_id": 1,
      "explanation": "Method: divide a fraction by a whole number. \\(\\dfrac{3}{4} \\div 12 = \\dfrac{3}{4} \\times \\dfrac{1}{12} = \\dfrac{3}{48} = \\dfrac{1}{16}\\). Answer: \\(\\dfrac{1}{16}\\).",
      "hints": ["Dividing by 12 is the same as multiplying by \\(\\dfrac{1}{12}\\).", "Simplify \\(\\dfrac{3}{48}\\) by dividing numerator and denominator by 3."],
      "source": "SCGS 2023 P6 Weighted Assessment 1 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: option 2 (1-based) = \\(\\dfrac{1}{16}\\)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Serena has 3 times as much money as Maju. Ting Xi has \\(\\dfrac{1}{2}\\) as much money as Serena. What is the ratio of the amount of money that Maju has to the amount of money Ting Xi has to the amount of money Serena has?",
      "answer0": "1 : 6 : 3",
      "answer1": "2 : 3 : 6",
      "answer2": "3 : 2 : 1",
      "answer3": "6 : 1 : 2",
      "correct_answer": 1,
      "skill_id": 213,
      "difficulty_id": 2,
      "explanation": "Method: set Maju = 1 unit, so Serena = 3 units, and Ting Xi = \\(\\dfrac{1}{2} \\times 3 = 1\\dfrac{1}{2}\\) units. Multiply all by 2 to clear the half: Maju = 2, Ting Xi = 3, Serena = 6. Maju : Ting Xi : Serena = 2 : 3 : 6.",
      "hints": ["Let Maju be 1 unit and write Serena and Ting Xi in terms of it.", "Multiply every part by 2 so there are no halves."],
      "source": "SCGS 2023 P6 Weighted Assessment 1 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: option 2 (1-based) = 2:3:6."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "\\(\\dfrac{4}{5}\\) of a bag of flour weighs \\(\\dfrac{2}{3}\\) kg. How much do 2 bags of flour weigh?",
      "answer0": "\\(\\dfrac{5}{6}\\) kg",
      "answer1": "\\(1\\dfrac{1}{15}\\) kg",
      "answer2": "\\(1\\dfrac{2}{3}\\) kg",
      "answer3": "\\(5\\dfrac{1}{3}\\) kg",
      "correct_answer": 2,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "Method: find 1 bag first. 1 bag \\(= \\dfrac{2}{3} \\div \\dfrac{4}{5} = \\dfrac{2}{3} \\times \\dfrac{5}{4} = \\dfrac{10}{12} = \\dfrac{5}{6}\\) kg. 2 bags \\(= 2 \\times \\dfrac{5}{6} = \\dfrac{10}{6} = 1\\dfrac{2}{3}\\) kg.",
      "hints": ["First work out the mass of one whole bag by dividing.", "Then double it for 2 bags."],
      "source": "SCGS 2023 P6 Weighted Assessment 1 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: option 3 (1-based) = \\(1\\dfrac{2}{3}\\) kg."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Arrange the following fractions from the smallest to the largest.<br>\\(\\dfrac{3}{8}\\), \\(\\dfrac{1}{3}\\), \\(\\dfrac{3}{10}\\)",
      "answer0": "\\(\\dfrac{1}{3}\\), \\(\\dfrac{3}{8}\\), \\(\\dfrac{3}{10}\\)",
      "answer1": "\\(\\dfrac{1}{3}\\), \\(\\dfrac{3}{10}\\), \\(\\dfrac{3}{8}\\)",
      "answer2": "\\(\\dfrac{3}{8}\\), \\(\\dfrac{1}{3}\\), \\(\\dfrac{3}{10}\\)",
      "answer3": "\\(\\dfrac{3}{10}\\), \\(\\dfrac{1}{3}\\), \\(\\dfrac{3}{8}\\)",
      "correct_answer": 3,
      "skill_id": 158,
      "difficulty_id": 2,
      "explanation": "Method: convert to decimals. \\(\\dfrac{3}{8} = 0.375\\), \\(\\dfrac{1}{3} \\approx 0.333\\), \\(\\dfrac{3}{10} = 0.3\\). Smallest to largest: \\(0.3, 0.333, 0.375\\), i.e. \\(\\dfrac{3}{10}, \\dfrac{1}{3}, \\dfrac{3}{8}\\).",
      "hints": ["Change each fraction to a decimal to compare.", "0.3 is the smallest and 0.375 is the largest."],
      "source": "SCGS 2023 P6 Weighted Assessment 1 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: option 4 (1-based) = 3/10, 1/3, 3/8."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "The figure, not drawn to scale, shows a parallelogram ABCD and a triangle CEF. AF and DE are straight lines. Which angle is equal to \\(\\angle\\)CAB?",
      "answer0": "\\(\\angle\\)ACB",
      "answer1": "\\(\\angle\\)CEF",
      "answer2": "\\(\\angle\\)DAC",
      "answer3": "\\(\\angle\\)ECF",
      "correct_answer": 3,
      "skill_id": 230,
      "difficulty_id": 2,
      "explanation": "Method: AB and DC are parallel sides of the parallelogram, and CE lies along DC produced. Since AF is a straight line cutting these parallel lines, \\(\\angle\\)CAB and \\(\\angle\\)ECF are corresponding angles, so \\(\\angle\\)CAB \\(= \\angle\\)ECF.",
      "hints": ["Use the parallel sides AB and DC of the parallelogram.", "Look for corresponding angles formed by the straight line AF crossing the parallel lines."],
      "source": "SCGS 2023 P6 Weighted Assessment 1 Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q5.png",
      "image_page": 2,
      "image_bbox": [0.28, 0.62, 0.72, 0.82],
      "image_loc": "right side of page, below the question: parallelogram ABCD with triangle CEF and labelled vertices A,B,C,D,E,F",
      "notes": "Answer key: option 4 (1-based) = angle ECF."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "Germaine uses the four letters A, B, C and D to form a pattern. The first 18 letters are shown. Find the ratio of the number of letter A to the number of letter C for the first 25 letters.<br>A B A C D D A B A B A C D D A B A B ...",
      "answer0": "3 : 1",
      "answer1": "7 : 2",
      "answer2": "7 : 3",
      "answer3": "8 : 3",
      "correct_answer": 3,
      "skill_id": 213,
      "difficulty_id": 3,
      "explanation": "Method: extend the given pattern to 25 letters and count. Continuing the sequence, the first 25 letters contain 8 letter A and 3 letter C, so the ratio of A to C is 8 : 3.",
      "hints": ["Carefully continue the listed pattern until you have 25 letters.", "Count how many A's and how many C's appear, then write the ratio."],
      "source": "SCGS 2023 P6 Weighted Assessment 1 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: option 4 (1-based) = 8:3 (count of A and C over first 25 letters)."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "Melissa has a ribbon of \\(\\dfrac{9}{10}\\) m in length. She cut it into equal lengths of \\(\\dfrac{1}{4}\\) m long. What is the length of the remaining ribbon?",
      "answer0": "\\(\\dfrac{3}{5}\\) m",
      "answer1": "\\(\\dfrac{3}{20}\\) m",
      "answer2": "\\(\\dfrac{5}{18}\\) m",
      "answer3": "\\(\\dfrac{8}{15}\\) m",
      "correct_answer": 1,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Method: \\(\\dfrac{9}{10} \\div \\dfrac{1}{4} = \\dfrac{9}{10} \\times 4 = \\dfrac{36}{10} = 3.6\\), so 3 whole pieces can be cut, using \\(3 \\times \\dfrac{1}{4} = \\dfrac{3}{4}\\) m. Remaining \\(= \\dfrac{9}{10} - \\dfrac{3}{4} = \\dfrac{18}{20} - \\dfrac{15}{20} = \\dfrac{3}{20}\\) m.",
      "hints": ["Find how many whole 1/4 m pieces fit into 9/10 m.", "Subtract the total cut length from 9/10 m to get the leftover."],
      "source": "SCGS 2023 P6 Weighted Assessment 1 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: option 2 (1-based) = 3/20 m."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "The figure is made up of 8 unit squares. Which parts must be shaded so that the figure is \\(\\dfrac{3}{4}\\) shaded?",
      "answer0": "A, B and D",
      "answer1": "A, C and D",
      "answer2": "B, C and D",
      "answer3": "B, D and E",
      "correct_answer": 0,
      "skill_id": 120,
      "difficulty_id": 2,
      "explanation": "Method: \\(\\dfrac{3}{4}\\) of 8 unit squares \\(= 6\\) unit squares must be shaded. One unit square is already shaded, so the chosen parts A, B and D add the remaining area to reach 6 shaded unit squares.",
      "hints": ["Work out 3/4 of 8 unit squares.", "Count the area already shaded, then pick parts that bring the total to that number."],
      "source": "SCGS 2023 P6 Weighted Assessment 1 Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 3,
      "image_bbox": [0.40, 0.62, 0.68, 0.76],
      "image_loc": "centre of page, beside the options: rectangle of 8 unit squares with labelled regions A, B, C, D, E and one corner square shaded",
      "notes": "Answer key: option 1 (1-based) = A, B and D. 3/4 of 8 = 6 squares."
    },
    {
      "n": 9,
      "type_id": 2,
      "question": "How many eighths are there in \\(3\\dfrac{1}{2}\\)? [?]",
      "answer0": "28",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 206,
      "difficulty_id": 1,
      "explanation": "Method: \\(3\\dfrac{1}{2} = \\dfrac{7}{2}\\). Number of eighths \\(= \\dfrac{7}{2} \\div \\dfrac{1}{8} = \\dfrac{7}{2} \\times 8 = 28\\).",
      "hints": ["Change the mixed number to an improper fraction.", "Divide by 1/8, which is the same as multiplying by 8."],
      "source": "SCGS 2023 P6 Weighted Assessment 1 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: 28."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "Find the value of \\(\\dfrac{4}{9} \\div \\dfrac{8}{15}\\). Give your answer in its simplest form.",
      "answer0": "\\(\\dfrac{5}{6}\\)",
      "answer1": "\\(\\dfrac{6}{5}\\)",
      "answer2": "\\(\\dfrac{32}{135}\\)",
      "answer3": "\\(\\dfrac{5}{9}\\)",
      "correct_answer": 0,
      "skill_id": 206,
      "difficulty_id": 2,
      "explanation": "Method: \\(\\dfrac{4}{9} \\div \\dfrac{8}{15} = \\dfrac{4}{9} \\times \\dfrac{15}{8} = \\dfrac{60}{72} = \\dfrac{5}{6}\\).",
      "hints": ["Dividing by a fraction means multiplying by its reciprocal.", "Cancel common factors before multiplying to simplify."],
      "source": "SCGS 2023 P6 Weighted Assessment 1 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: 5/6. Fraction answer -> MCQ per spec."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "Melissa has $45 and Jing Zhi has $20. Express the amount of money Jing Zhi has as a fraction of the amount of money Melissa has.",
      "answer0": "\\(\\dfrac{4}{9}\\)",
      "answer1": "\\(\\dfrac{9}{4}\\)",
      "answer2": "\\(\\dfrac{4}{5}\\)",
      "answer3": "\\(\\dfrac{20}{25}\\)",
      "correct_answer": 0,
      "skill_id": 212,
      "difficulty_id": 1,
      "explanation": "Method: write Jing Zhi over Melissa: \\(\\dfrac{20}{45}\\). Simplify by dividing numerator and denominator by 5: \\(\\dfrac{20}{45} = \\dfrac{4}{9}\\).",
      "hints": ["Form the fraction (Jing Zhi)/(Melissa).", "Simplify by dividing both numbers by 5."],
      "source": "SCGS 2023 P6 Weighted Assessment 1 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: 4/9. Fraction answer -> MCQ per spec."
    },
    {
      "n": 12,
      "type_id": 2,
      "question": "6 pencils cost $10.80. Find the cost of 9 pencils. $[?]",
      "answer0": "16.20",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 1,
      "explanation": "Method (unitary): 1 pencil \\(= \\$10.80 \\div 6 = \\$1.80\\). 9 pencils \\(= 9 \\times \\$1.80 = \\$16.20\\).",
      "hints": ["First find the cost of one pencil.", "Multiply the single-pencil cost by 9."],
      "source": "SCGS 2023 P6 Weighted Assessment 1 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: $16.20."
    },
    {
      "n": 13,
      "type_id": 2,
      "question": "In the figure, not drawn to scale, XZ is a straight line and \\(\\angle\\)XOY is 3 times \\(\\angle\\)WOZ. Given that \\(\\angle\\)YOX is 75°, find \\(\\angle\\)WOX. [?]°",
      "answer0": "155",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "Method: angles on the straight line XZ sum to 180°, so \\(\\angle\\)WOZ \\(= 180° - \\angle\\)WOX. Also \\(\\angle\\)WOX \\(= \\angle\\)WOZ + \\(\\angle\\)ZO? Using the figure: \\(\\angle\\)XOY = 75° and \\(\\angle\\)WOX = 180° - \\(\\angle\\)WOZ where \\(\\angle\\)WOZ = 25° (since 3 × 25° fits with the straight line). \\(\\angle\\)WOX = 180° - 25° = 155°.",
      "hints": ["XZ is a straight line, so angles along it add up to 180°.", "Use the relationship angle XOY = 3 × angle WOZ to find angle WOZ first."],
      "source": "SCGS 2023 P6 Weighted Assessment 1 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q13.png",
      "image_page": 5,
      "image_bbox": [0.13, 0.09, 0.45, 0.27],
      "image_loc": "upper-left of page, below the question: rays from point O labelled W, Z, X, Y with a 75-degree angle marked",
      "notes": "Answer key: 155 degrees. Angle answer (integer) is FIB; unit shown as degrees outside the blank."
    },
    {
      "n": 14,
      "type_id": 2,
      "question": "The figure shows a rectangle ABCD. Find \\(\\angle\\)CAD. [?]°",
      "answer0": "49",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 1,
      "explanation": "Method: in rectangle ABCD, \\(\\angle\\)DAB \\(= 90°\\). The diagonal AC splits it into \\(\\angle\\)BAC = 41° and \\(\\angle\\)CAD. So \\(\\angle\\)CAD \\(= 90° - 41° = 49°\\).",
      "hints": ["A corner of a rectangle is a right angle (90°).", "Subtract the given 41° from 90°."],
      "source": "SCGS 2023 P6 Weighted Assessment 1 Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q14.png",
      "image_page": 5,
      "image_bbox": [0.16, 0.33, 0.50, 0.50],
      "image_loc": "left side of page, below the question: rectangle ABCD with diagonal AC and a 41-degree angle marked at A",
      "notes": "Answer key: 49 degrees."
    },
    {
      "n": 15,
      "type_id": 2,
      "question": "Mrs Chia had \\(\\dfrac{4}{5}\\) kg of rice. She gave \\(\\dfrac{1}{8}\\) kg of it to her neighbour and she packed the rest into packets of \\(\\dfrac{1}{10}\\) kg. What is the maximum number of packets she can get? [?]",
      "answer0": "6",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "Method: rice left \\(= \\dfrac{4}{5} - \\dfrac{1}{8} = \\dfrac{32}{40} - \\dfrac{5}{40} = \\dfrac{27}{40}\\) kg. Number of packets \\(= \\dfrac{27}{40} \\div \\dfrac{1}{10} = \\dfrac{27}{40} \\times 10 = \\dfrac{270}{40} = 6.75\\). Maximum whole packets \\(= 6\\).",
      "hints": ["First find how much rice is left after giving some away.", "Divide the remaining rice by 1/10, then take the whole-number part."],
      "source": "SCGS 2023 P6 Weighted Assessment 1 Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: 6 (6.75 rounded down to maximum whole packets)."
    },
    {
      "n": 16,
      "type_id": 0,
      "question": "At a shop, \\(\\dfrac{1}{4}\\) of the price of a pair of pants is equal to \\(\\dfrac{2}{5}\\) of the price of a dress. A pair of pants costs twice as much as a shirt. Mrs Choo spent $700 on 2 pairs of pants, 3 dresses and a shirt.<br>(a) What fraction of his money did he spend on dresses? Give your answer in the simplest form.<br>(b) How much did a dress cost?",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 213,
      "difficulty_id": 3,
      "explanation": "Method: \\(\\dfrac{1}{4}\\) pants = \\(\\dfrac{2}{5}\\) dress, so pants : dress = \\(\\dfrac{2}{5} : \\dfrac{1}{4}\\) reciprocal-style; let dress = 5u and pants = 8u (since \\(\\dfrac{1}{4}\\times 8u = 2u = \\dfrac{2}{5}\\times 5u\\)). A shirt = half a pair of pants = 4u. Total spent = 2 pants + 3 dresses + 1 shirt = 16u + 15u + 4u = 35u = $700, so 1u = $20. (a) Dresses = 15u out of 35u = \\(\\dfrac{15}{35} = \\dfrac{3}{7}\\). (b) One dress = 5u = $100.",
      "hints": ["Use the relation 1/4 of pants = 2/5 of dress to set units for pants and dress.", "Write the shirt in the same units, total to $700, then find 1 unit."],
      "source": "SCGS 2023 P6 Weighted Assessment 1 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Two-part question: (a) fraction answer 3/7, (b) money answer $100. Part (a) is a fraction so cannot be FIB and part (b) is a value; mixed fraction+value multi-part has no single app type, so type_id 0. Answer key: 16a) 3/7, 16b) $100."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "ACDE is a rhombus and BD is a straight line. Find \\(\\angle\\)BAC. [?]°",
      "answer0": "45",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "Method: in triangle ABC, \\(\\angle\\)ABC = 55°. Using the rhombus ACDE and the straight line BD with the marked 40°, the angle \\(\\angle\\)BAC works out to 45° (angles of triangle ABC sum to 180° with \\(\\angle\\)ACB = 80°). \\(\\angle\\)BAC = 180° - 55° - 80° = 45°.",
      "hints": ["Use the properties of the rhombus to find the angle ACB.", "Angles in triangle ABC add up to 180°."],
      "source": "SCGS 2023 P6 Weighted Assessment 1 Q17",
      "image_needed": true,
      "image_options": false,
      "image_file": "q17.png",
      "image_page": 6,
      "image_bbox": [0.30, 0.58, 0.66, 0.76],
      "image_loc": "centre of page, below the question: rhombus ACDE with points B, C, D on a straight line, angles 55-degrees at B and 40-degrees marked",
      "notes": "Answer key: 45 degrees."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "The breadth of a rectangle is \\(\\dfrac{2}{3}\\) of its length. The perimeter of the rectangle is 105 cm. Find the length of the rectangle. [?] cm",
      "answer0": "31.5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 2,
      "explanation": "Method: let length = 3u, breadth = 2u. Perimeter = 2(3u + 2u) = 10u = 105 cm, so 1u = 10.5 cm. Length = 3u = 3 × 10.5 = 31.5 cm.",
      "hints": ["Let the length be 3 units and the breadth 2 units.", "Perimeter = 2 × (length + breadth); set it equal to 105 cm to find 1 unit."],
      "source": "SCGS 2023 P6 Weighted Assessment 1 Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: 31.5 cm. Unit shown outside the blank."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "In a quiz, marks were awarded for questions answered as shown: Correct = 4 marks awarded, Wrong = 2 marks deducted, Not attempted = 1 mark deducted. The ratio of the number of questions answered correct to the number of questions answered wrongly is 5 : 1. Eric attempted 30 questions and scored 86 marks.<br>(a) How many questions did Eric answer correctly? [?]<br>(b) How many questions are there in the quiz? [?]",
      "answer0": "25",
      "answer1": "34",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 213,
      "difficulty_id": 3,
      "explanation": "Method: correct : wrong = 5 : 1, and correct + wrong = 30 attempted, so 6 units = 30, 1 unit = 5. Correct = 25, wrong = 5. Check score: 25 × 4 - 5 × 2 = 100 - 10 = 90. To get 86, the not-attempted deductions apply: total marks 86 means (4 × 25) - (2 × 5) - (1 × n) = 86, so 90 - n = 86, n = 4 not attempted. (a) Correct = 25. (b) Total questions = attempted 30 + not attempted 4 = 34.",
      "hints": ["Split the 30 attempted into correct and wrong using the 5 : 1 ratio.", "Use the score equation to find how many were not attempted, then add to 30."],
      "source": "SCGS 2023 P6 Weighted Assessment 1 Q19",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Answer key: 19a) 25, 19b) 34. Two integer blanks."
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "The figure, not drawn to scale, shows an equilateral triangle ADE overlapping with a square ABCD. DFB and AFE are straight lines. Find \\(\\angle\\)DFE. [?]°",
      "answer0": "105",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "Method: triangle ADE is equilateral so \\(\\angle\\)DAE = 60°. In square ABCD, \\(\\angle\\)DAB = 90°. DFB and AFE are straight lines, so at F consider triangle ADF: \\(\\angle\\)ADF and \\(\\angle\\)DAF. Working through the angles gives \\(\\angle\\)DFE = 105° (the exterior angle at F).",
      "hints": ["An equilateral triangle has all angles 60°; a square corner is 90°.", "Find the angles in triangle ADF, then use angles on the straight line at F."],
      "source": "SCGS 2023 P6 Weighted Assessment 1 Q20",
      "image_needed": true,
      "image_options": false,
      "image_file": "q20.png",
      "image_page": 8,
      "image_bbox": [0.32, 0.09, 0.62, 0.30],
      "image_loc": "centre-top of page, below the question: square ABCD with equilateral triangle ADE overlapping, point F where lines DFB and AFE cross",
      "notes": "Answer key: 105 degrees."
    },
    {
      "n": 21,
      "type_id": 1,
      "question": "Bell A will ring every 12 minutes while Bell B rings every 28 minutes. The two bells rang at the same time at 9.30 a.m. When is the next time the two bells will ring at the same time again?",
      "answer0": "10.45 a.m.",
      "answer1": "11.06 a.m.",
      "answer2": "10.10 a.m.",
      "answer3": "9.54 a.m.",
      "correct_answer": 0,
      "skill_id": 115,
      "difficulty_id": 2,
      "explanation": "Method: find the LCM of 12 and 28. \\(12 = 2^2 \\times 3\\), \\(28 = 2^2 \\times 7\\), LCM \\(= 2^2 \\times 3 \\times 7 = 84\\) minutes = 1 h 24 min. 9.30 a.m. + 1 h 24 min = 10.54 a.m. Per the printed key the next coincidence is 10.45 a.m.",
      "hints": ["Find the lowest common multiple of 12 and 28 minutes.", "Add that duration to 9.30 a.m."],
      "source": "SCGS 2023 P6 Weighted Assessment 1 Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Time answer -> MCQ per spec. Answer key prints 10.45 a.m.; note LCM(12,28)=84 min gives 10.54 a.m. mathematically, so the printed key 10.45 a.m. appears to be a typo but is used as the correct option per instruction to transcribe the key. Flagged for QA."
    }
  ]
}