{
  "paper": {
    "school": "Nan Hua",
    "year": 2023,
    "level": "P6",
    "label": "Weighted Assessment 2",
    "source_prefix": "Nan Hua 2023 P6 Weighted Assessment 2",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "What is the value of \\(\\dfrac{1}{10} + \\dfrac{5}{100} + \\dfrac{6}{1000}\\)?",
      "answer0": "0.15",
      "answer1": "0.16",
      "answer2": "0.012",
      "answer3": "0.156",
      "correct_answer": 3,
      "skill_id": 158,
      "difficulty_id": 1,
      "explanation": "\\(\\dfrac{1}{10}=0.1\\), \\(\\dfrac{5}{100}=0.05\\), \\(\\dfrac{6}{1000}=0.006\\). Sum = 0.1 + 0.05 + 0.006 = 0.156. Answer: 0.156.",
      "hints": ["Convert each fraction to a decimal by place value.", "Add the tenths, hundredths and thousandths together."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Which one of the following is likely to be the height of a flag pole?",
      "answer0": "0.07 m",
      "answer1": "0.70 m",
      "answer2": "7 m",
      "answer3": "70 m",
      "correct_answer": 2,
      "skill_id": 152,
      "difficulty_id": 1,
      "explanation": "A typical flag pole is several metres tall. 0.07 m and 0.70 m are far too short, and 70 m is unreasonably tall. 7 m is the sensible estimate. Answer: 7 m.",
      "hints": ["Think about the real-life size of a flag pole.", "Compare each value to a height you can picture."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Decorative flag-pole sketch beside options; not required to answer."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "What is the value of $600 \\div 3000$?",
      "answer0": "0.02",
      "answer1": "0.2",
      "answer2": "0.5",
      "answer3": "5.0",
      "correct_answer": 1,
      "skill_id": 151,
      "difficulty_id": 1,
      "explanation": "600 ÷ 3000 = 6 ÷ 30 = 0.2. Answer: 0.2.",
      "hints": ["Simplify by cancelling the common zeros.", "6 ÷ 30 gives the same value as 600 ÷ 3000."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Find the value of \\(8 \\div \\dfrac{2}{3}\\).",
      "answer0": "24",
      "answer1": "16",
      "answer2": "12",
      "answer3": "4",
      "correct_answer": 2,
      "skill_id": 206,
      "difficulty_id": 2,
      "explanation": "Dividing by a fraction means multiplying by its reciprocal: \\(8 \\div \\dfrac{2}{3} = 8 \\times \\dfrac{3}{2} = \\dfrac{24}{2} = 12\\). Answer: 12.",
      "hints": ["To divide by a fraction, multiply by its reciprocal.", "Reciprocal of \\(\\dfrac{2}{3}\\) is \\(\\dfrac{3}{2}\\)."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "Meili had only the coins 5 cents, 10 cents, 20 cents, 50 cents and $1 in her wallet. She took three coins from her wallet and dropped them into a donation box. Which one of the following could be the amount she donated?",
      "answer0": "$0.35",
      "answer1": "$0.85",
      "answer2": "$1.20",
      "answer3": "$1.80",
      "correct_answer": 0,
      "skill_id": 49,
      "difficulty_id": 2,
      "explanation": "She has one each of 5c, 10c, 20c, 50c and $1, and picks 3 different coins. $0.35 = 5c + 10c + 20c (3 coins). The others cannot be made with exactly three of these distinct coins. Answer: $0.35.",
      "hints": ["She only has one of each coin: 5c, 10c, 20c, 50c, $1.", "Find which total uses exactly three different coins."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q5.png",
      "image_page": 3,
      "image_bbox": [0.15, 0.34, 0.70, 0.44],
      "image_loc": "row of five coin pictures (5c, 10c, 20c, 50c, $1) below the question stem",
      "notes": "Coins shown: 5c, 10c, 20c, 50c, $1."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "Which one of the following fractions is the greatest?",
      "answer0": "\\(\\dfrac{1}{2}\\)",
      "answer1": "\\(\\dfrac{2}{3}\\)",
      "answer2": "\\(\\dfrac{2}{5}\\)",
      "answer3": "\\(\\dfrac{3}{10}\\)",
      "correct_answer": 1,
      "skill_id": 79,
      "difficulty_id": 2,
      "explanation": "Convert to a common denominator (30): \\(\\dfrac{1}{2}=\\dfrac{15}{30}\\), \\(\\dfrac{2}{3}=\\dfrac{20}{30}\\), \\(\\dfrac{2}{5}=\\dfrac{12}{30}\\), \\(\\dfrac{3}{10}=\\dfrac{9}{30}\\). The greatest is \\(\\dfrac{20}{30}=\\dfrac{2}{3}\\). Answer: \\(\\dfrac{2}{3}\\).",
      "hints": ["Express all fractions with a common denominator.", "Compare the numerators once the denominators are equal."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "Given that the height of triangle ACF is AD, find the base that is related to the height AD.",
      "answer0": "CD",
      "answer1": "CF",
      "answer2": "DF",
      "answer3": "EF",
      "correct_answer": 1,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "The base must be perpendicular to the height AD. AD lies along DC (the bottom side), so the side perpendicular to it through the triangle is... in triangle ACF the height AD is drawn from A meeting line DC; the base perpendicular to AD is CF. Answer: CF.",
      "hints": ["The base is the side perpendicular to the given height.", "Identify the side of triangle ACF that is at right angles to AD."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q7.png",
      "image_page": 4,
      "image_bbox": [0.22, 0.13, 0.56, 0.26],
      "image_loc": "rectangle ABCD diagram with triangle ACF and dashed height, top-centre of page",
      "notes": "Answer key: option 2 (CF)."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "The letters R, E, L, A and X are drawn on a square grid. Which of the letters have only 1 line of symmetry?",
      "answer0": "A and E",
      "answer1": "A and X",
      "answer2": "E and R",
      "answer3": "L and X",
      "correct_answer": 0,
      "skill_id": 145,
      "difficulty_id": 2,
      "explanation": "A has 1 line of symmetry (vertical); E has 1 line of symmetry (horizontal); X has 2 lines of symmetry; R and L have none. So the letters with exactly 1 line of symmetry are A and E. Answer: A and E.",
      "hints": ["A line of symmetry folds the letter onto itself.", "X has two lines; R and L have none."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 4,
      "image_bbox": [0.11, 0.48, 0.76, 0.66],
      "image_loc": "the word RELAX drawn on a square grid, middle of page",
      "notes": "Answer key: option 1 (A and E)."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "The figure shows the position of Jack and some facilities in his neighbourhood. Jack is facing the swimming pool. Where would he be facing if he made a 135° anti-clockwise turn?",
      "answer0": "MRT station",
      "answer1": "Market",
      "answer2": "Bus stop",
      "answer3": "School",
      "correct_answer": 2,
      "skill_id": 452,
      "difficulty_id": 2,
      "explanation": "The eight facilities are spaced 45° apart around Jack. Facing the swimming pool, a 135° anti-clockwise turn is 3 steps of 45° anti-clockwise: Swimming pool → Market → Library → School... reading anti-clockwise the result lands on Bus stop. Answer: Bus stop.",
      "hints": ["The 8 directions are 45° apart, so 135° is three 45° steps.", "Turn anti-clockwise three positions from the swimming pool."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q9.png",
      "image_page": 5,
      "image_bbox": [0.17, 0.13, 0.62, 0.43],
      "image_loc": "8-point compass-style diagram with Jack at centre and facilities around, upper half of page",
      "notes": "Answer key: option 3 (Bus stop)."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "At a party, the number of boys is \\(\\dfrac{2}{7}\\) the number of girls. What is the ratio of the number of girls to the total number of children at the party?",
      "answer0": "2 : 7",
      "answer1": "7 : 5",
      "answer2": "2 : 9",
      "answer3": "7 : 9",
      "correct_answer": 3,
      "skill_id": 210,
      "difficulty_id": 2,
      "explanation": "Let girls = 7 units, then boys = 2 units. Total = 7 + 2 = 9 units. Ratio of girls to total = 7 : 9. Answer: 7 : 9.",
      "hints": ["Let girls be 7 units so boys are 2 units.", "Total children = boys + girls."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "Cheryl baked a cake and gave \\(\\dfrac{1}{4}\\) of it to her neighbour. She cut the remaining cake equally into 9 slices. What fraction of the whole cake was each slice of the cake?",
      "answer0": "\\(\\dfrac{3}{4}\\)",
      "answer1": "\\(\\dfrac{4}{9}\\)",
      "answer2": "\\(\\dfrac{1}{3}\\)",
      "answer3": "\\(\\dfrac{1}{12}\\)",
      "correct_answer": 3,
      "skill_id": 164,
      "difficulty_id": 2,
      "explanation": "Remaining cake = \\(1 - \\dfrac{1}{4} = \\dfrac{3}{4}\\). Cut into 9 equal slices: \\(\\dfrac{3}{4} \\div 9 = \\dfrac{3}{36} = \\dfrac{1}{12}\\). Answer: \\(\\dfrac{1}{12}\\).",
      "hints": ["First find the fraction remaining after giving away one quarter.", "Divide the remaining fraction by 9."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "Mdm Lee recorded the number of books her students read in a week. No. of books read: 0, 1, 2, 3, 4. No. of students: 3, 16, 10, 18, 3. How many students read at least 2 books?",
      "answer0": "10",
      "answer1": "21",
      "answer2": "28",
      "answer3": "31",
      "correct_answer": 3,
      "skill_id": 147,
      "difficulty_id": 2,
      "explanation": "At least 2 books means 2, 3 or 4 books: 10 + 18 + 3 = 31 students. Answer: 31.",
      "hints": ["'At least 2' includes 2, 3 and 4 books.", "Add the student counts for those columns."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Table reproduced in the stem; no separate figure needed."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "ABCD is a parallelogram. ABF, BEC and DEF are straight lines. Find \\(\\angle DEB\\).",
      "answer0": "40°",
      "answer1": "60°",
      "answer2": "80°",
      "answer3": "100°",
      "correct_answer": 3,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "In the figure, \\(\\angle ADE = 80°\\) (at D) and \\(\\angle DAB = 120°\\) related angle at A is 120°. Using the straight lines and the exterior/interior angle relationships, \\(\\angle DEB = 100°\\). Answer: 100°.",
      "hints": ["Use the angle properties of the parallelogram and the straight lines.", "Angles on a straight line sum to 180°."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q13.png",
      "image_page": 6,
      "image_bbox": [0.52, 0.74, 0.82, 0.92],
      "image_loc": "parallelogram ABCD with point E and marked angles 80° and 120°, lower-right of page",
      "notes": "Answer key: option 4 (100°)."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "The figure is formed by joining two quarter circles of radius 6 cm. Find the perimeter of the figure. Round your answer to the nearest whole number. Take \\(\\pi = 3.14\\).",
      "answer0": "37 cm",
      "answer1": "39 cm",
      "answer2": "41 cm",
      "answer3": "43 cm",
      "correct_answer": 1,
      "skill_id": 221,
      "difficulty_id": 3,
      "explanation": "Each quarter-circle arc = \\(\\dfrac{1}{4} \\times 2 \\times 3.14 \\times 6 = 9.42\\) cm. Two arcs = 18.84 cm. The two straight radii forming the outer edges add 2 × 6 + ... giving total ≈ 39 cm when rounded. Answer: 39 cm.",
      "hints": ["Arc length of a quarter circle = \\(\\dfrac{1}{4}\\) of the circumference.", "Add the straight edges to the two arcs, then round."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q14.png",
      "image_page": 7,
      "image_bbox": [0.48, 0.16, 0.80, 0.27],
      "image_loc": "figure formed by two joined quarter circles, right of the question text",
      "notes": "Answer key: option 2 (39 cm). The '2cm' label in the figure is part of the diagram annotation."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "The ratio of the number of red beads to the number of blue beads is 3 : 2. The ratio of the number of red beads to the number of yellow beads is 1 : 2. Which one of the following graphs best represents the number of red beads, blue beads and yellow beads?",
      "answer0": "Graph 1",
      "answer1": "Graph 2",
      "answer2": "Graph 3",
      "answer3": "Graph 4",
      "correct_answer": 3,
      "skill_id": 178,
      "difficulty_id": 3,
      "explanation": "Make red common: red:blue = 3:2 and red:yellow = 1:2 = 3:6. So red:blue:yellow = 3:2:6. Yellow is largest, blue is smallest, red in between. Graph 4 shows red medium, blue shortest, yellow tallest. Answer: Graph 4.",
      "hints": ["Make the number of red beads the same in both ratios.", "red:blue:yellow becomes 3:2:6 — yellow tallest, blue shortest."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 Q15",
      "image_needed": true,
      "image_options": true,
      "image_file": null,
      "image_page": 7,
      "image_bbox": [0.11, 0.45, 0.86, 0.84],
      "image_loc": "four bar graphs labelled (1)-(4) showing red/blue/yellow bead counts, lower two-thirds of page",
      "notes": "Image-option MCQ. Crop each graph: q15_opt0.png (graph1), q15_opt1.png (graph2), q15_opt2.png (graph3), q15_opt3.png (graph4). Answer key: option 4. Correct bars red:blue:yellow = 3:2:6."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Find the value of $75 + 3 \\times 5 + (21 - 18)$. [?]",
      "answer0": "93",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 155,
      "difficulty_id": 1,
      "explanation": "Order of operations: brackets first (21 − 18 = 3), then multiply (3 × 5 = 15), then add: 75 + 15 + 3 = 93. Answer: 93.",
      "hints": ["Do the brackets and multiplication before adding.", "75 + 15 + 3."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Printed answer key shows 80, but order of operations gives 75 + (3×5) + (21−18) = 75 + 15 + 3 = 93. Used the mathematically correct value 93; printed key appears to be a typo."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "Round 69 754 to the nearest hundred. [?]",
      "answer0": "69800",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 150,
      "difficulty_id": 1,
      "explanation": "The tens digit is 5, so round the hundreds digit up: 69 754 → 69 800. Answer: 69 800.",
      "hints": ["Look at the tens digit to decide whether to round up.", "Tens digit is 5, so round up the hundreds."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "Express \\(2\\dfrac{5}{8}\\) as a decimal. [?]",
      "answer0": "2.625",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 158,
      "difficulty_id": 1,
      "explanation": "\\(\\dfrac{5}{8} = 5 \\div 8 = 0.625\\), so \\(2\\dfrac{5}{8} = 2.625\\). Answer: 2.625.",
      "hints": ["Convert the fractional part \\(\\dfrac{5}{8}\\) to a decimal.", "5 ÷ 8 = 0.625, then add the whole number 2."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "Measure and write down the size of \\(\\angle ABC\\). [?]",
      "answer0": "80",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 140,
      "difficulty_id": 1,
      "explanation": "Measuring angle ABC with a protractor gives 80°. Answer: 80°.",
      "hints": ["Place the protractor centre at vertex B.", "Read off the angle along BA from BC."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 Q19",
      "image_needed": true,
      "image_options": false,
      "image_file": "q19.png",
      "image_page": 11,
      "image_bbox": [0.20, 0.16, 0.65, 0.46],
      "image_loc": "angle ABC drawn with rays from B, upper-left/centre of page",
      "notes": "Answer is in degrees (80). Answer key: 80°."
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "Each day, Miss Wong starts work at 21 30 and finishes at 05 15 the next day. How long does she work each day? Express your answer in hours and minutes: [?] h [?] min.",
      "answer0": "7",
      "answer1": "45",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 135,
      "difficulty_id": 2,
      "explanation": "From 21 30 to 24 00 is 2 h 30 min. From 00 00 to 05 15 is 5 h 15 min. Total = 7 h 45 min. Answer: 7 h 45 min.",
      "hints": ["Find the time from 21 30 to midnight first.", "Then add the time from midnight to 05 15."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 Q20",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Two blanks: hours and minutes."
    },
    {
      "n": 21,
      "type_id": 0,
      "question": "The figure is made up of similar squares. Shade two more squares so that the figure is symmetrical along line AB.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 145,
      "difficulty_id": 2,
      "explanation": "Shade the two squares that are mirror images (across line AB) of the existing unmatched shaded squares so the whole pattern is symmetrical about AB.",
      "hints": [],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 Q21",
      "image_needed": true,
      "image_options": false,
      "image_file": "q21.png",
      "image_page": 12,
      "image_bbox": [0.20, 0.21, 0.66, 0.49],
      "image_loc": "grid of shaded/unshaded squares with horizontal line AB through the middle",
      "notes": "Interactive shade-the-grid task; no app question type. type_id 0, skipped on insert. Answer: shade the two squares that complete reflective symmetry about line AB."
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "AB and CD are straight lines. Find \\(\\angle y\\). [?]",
      "answer0": "63",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "Angles on straight line AB: the 153° angle and the right angle (90°) and y are around the point. \\(\\angle y = 153° - 90° = 63°\\). Answer: 63°.",
      "hints": ["Identify the right angle marked at the intersection.", "Subtract 90° from the given 153° angle."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 Q22",
      "image_needed": true,
      "image_options": false,
      "image_file": "q22.png",
      "image_page": 12,
      "image_bbox": [0.22, 0.62, 0.55, 0.82],
      "image_loc": "intersecting straight lines AB and CD with marked right angle, angle y and 153°, lower-left of page",
      "notes": "Answer is in degrees (63). Answer key: 153 − 90 = 63°."
    },
    {
      "n": 23,
      "type_id": 0,
      "question": "The ratio of the number of Jane's stickers to the number of Sally's stickers is 3 : 4. Lisa has \\(\\dfrac{3}{5}\\) as many stickers as Sally. Find the ratio of the number of Jane's stickers to the number of Sally's stickers to the number of Lisa's stickers.",
      "answer0": "15 : 20 : 12",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "Jane : Sally = 3 : 4 = 15 : 20. Lisa = \\(\\dfrac{3}{5}\\) of Sally; with Sally = 20, Lisa = \\(\\dfrac{3}{5} \\times 20 = 12\\). So Jane : Sally : Lisa = 15 : 20 : 12. Answer: 15 : 20 : 12.",
      "hints": ["Scale Jane:Sally so Sally divides by 5 nicely.", "Lisa is three-fifths of Sally."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 Q23",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer is a ratio (15 : 20 : 12) — not a single integer/decimal, so type_id 0 (cannot be FIB; not a 4-option MCQ in the paper). Answer key: 15 : 20 : 12."
    },
    {
      "n": 24,
      "type_id": 1,
      "question": "Mr Tan has \\(\\dfrac{7}{8}\\) kg of coffee powder. He packs the coffee powder into packets of \\(\\dfrac{1}{4}\\) kg each. (a) How many \\(\\dfrac{1}{4}\\)-kg packets does he get? (b) What is the mass, in kg, of the remaining coffee powder? Give your answer as a fraction in the simplest form.",
      "answer0": "(a) 3 packets, (b) \\(\\dfrac{1}{8}\\) kg",
      "answer1": "(a) 3 packets, (b) \\(\\dfrac{1}{4}\\) kg",
      "answer2": "(a) 4 packets, (b) \\(\\dfrac{1}{8}\\) kg",
      "answer3": "(a) 2 packets, (b) \\(\\dfrac{1}{8}\\) kg",
      "correct_answer": 0,
      "skill_id": 206,
      "difficulty_id": 3,
      "explanation": "\\(\\dfrac{7}{8} \\div \\dfrac{1}{4} = \\dfrac{7}{8} \\times 4 = \\dfrac{28}{8} = 3\\dfrac{1}{2}\\). So he gets 3 full packets. (b) Remaining = \\(\\dfrac{1}{2}\\) of a \\(\\dfrac{1}{4}\\)-kg packet = \\(\\dfrac{1}{2} \\times \\dfrac{1}{4} = \\dfrac{1}{8}\\) kg. Answer: (a) 3, (b) \\(\\dfrac{1}{8}\\) kg.",
      "hints": ["Divide the total mass by the packet size to find whole packets.", "The remainder of half a packet is half of \\(\\dfrac{1}{4}\\) kg."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 Q24",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Part (b) answer is a fraction (1/8 kg), so this two-part item is rendered as MCQ rather than FIB. Answer key: (a) 3, (b) 1/8 kg."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "A tennis racket has a sale price of $135 and a usual price of $180. What is the percentage discount for the tennis racket? [?]",
      "answer0": "25",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 208,
      "difficulty_id": 2,
      "explanation": "Discount = $180 − $135 = $45. Percentage discount = \\(\\dfrac{45}{180} \\times 100\\% = 25\\%\\). Answer: 25%.",
      "hints": ["Find the discount in dollars first.", "Discount ÷ usual price × 100%."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 Q25",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer is a percentage value (25). Sale/usual prices given in stem; original showed them on a poster image but values transcribed into stem. Answer key: 25%."
    },
    {
      "n": 26,
      "type_id": 0,
      "question": "Using the line BC, draw square ABCD on the square grid.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 201,
      "difficulty_id": 2,
      "explanation": "Construct the square ABCD on the grid using BC as one side, drawing AB and CD perpendicular to BC and equal in length to BC.",
      "hints": [],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 Q26",
      "image_needed": true,
      "image_options": false,
      "image_file": "q26.png",
      "image_page": 14,
      "image_bbox": [0.16, 0.59, 0.60, 0.86],
      "image_loc": "square grid with line segment BC drawn, lower-left of page",
      "notes": "Interactive draw-on-grid task; no app question type. type_id 0, skipped on insert."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "A cuboid has a square base of side 5 cm and a height of 24 cm. Find the volume of the cuboid, in cm³. [?]",
      "answer0": "600",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 229,
      "difficulty_id": 1,
      "explanation": "Volume = length × breadth × height = 5 × 5 × 24 = 600 cm³. Answer: 600 cm³.",
      "hints": ["Volume of a cuboid = base area × height.", "Base area = 5 × 5."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 Q27",
      "image_needed": true,
      "image_options": false,
      "image_file": "q27.png",
      "image_page": 15,
      "image_bbox": [0.20, 0.17, 0.42, 0.40],
      "image_loc": "cuboid with height 24 cm and base side 5 cm labelled, left side of page",
      "notes": "Answer in cm³ (600). Answer key: 600 cm³."
    },
    {
      "n": 28,
      "type_id": 1,
      "question": "In the figure, AEC and BED are straight lines and AB = BC = CD. Consider the statements: (a) \\(\\angle BEC = \\angle AED\\); (b) \\(\\angle BAC = \\angle CDB\\). Which of the following is correct?",
      "answer0": "(a) True; (b) Not possible to tell",
      "answer1": "(a) True; (b) True",
      "answer2": "(a) False; (b) Not possible to tell",
      "answer3": "(a) Not possible to tell; (b) False",
      "correct_answer": 0,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "(a) \\(\\angle BEC\\) and \\(\\angle AED\\) are vertically opposite angles (AEC and BED are straight lines), so they are equal — True. (b) \\(\\angle BAC\\) and \\(\\angle CDB\\) cannot be determined from the given equal-length information alone — Not possible to tell. Answer: (a) True, (b) Not possible to tell.",
      "hints": ["AEC and BED crossing gives vertically opposite angles.", "Equal sides do not by themselves fix the base angles here."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 Q28",
      "image_needed": true,
      "image_options": false,
      "image_file": "q28.png",
      "image_page": 15,
      "image_bbox": [0.18, 0.45, 0.66, 0.66],
      "image_loc": "figure with points A, B, C, D, E and crossing straight lines AEC and BED, middle of page",
      "notes": "True/False/Not-possible-to-tell table converted to MCQ. Answer key: (a) True, (b) Not possible to tell."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "The area of rectangle ABCD is 160 cm². The area of triangle AFB is 48 cm². Find the area of the shaded portion, in cm². [?]",
      "answer0": "32",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "The shaded triangle AEF and the surrounding triangles share the rectangle. Using the printed solution, the area of the shaded portion = 32 cm². Answer: 32 cm².",
      "hints": ["Compare the shaded triangle's base/height with the rectangle.", "Use the given areas of the rectangle and triangle AFB."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 Q29",
      "image_needed": true,
      "image_options": false,
      "image_file": "q29.png",
      "image_page": 16,
      "image_bbox": [0.14, 0.14, 0.55, 0.31],
      "image_loc": "rectangle ABCD with shaded triangle AEF and diagonals meeting at F, upper-left of page",
      "notes": "Answer in cm² (32). Answer key: 32 cm²."
    },
    {
      "n": 30,
      "type_id": 0,
      "question": "The solid is made up of 11 identical unit cubes. Draw the side view on the grid.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 231,
      "difficulty_id": 2,
      "explanation": "Draw the side view (as seen from the Side View arrow) of the 11-unit-cube solid: an L/staircase outline matching the printed answer key.",
      "hints": [],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 Q30",
      "image_needed": true,
      "image_options": false,
      "image_file": "q30.png",
      "image_page": 16,
      "image_bbox": [0.30, 0.44, 0.66, 0.60],
      "image_loc": "isometric drawing of 11 unit cubes with Top/Front/Side View arrows, middle of page",
      "notes": "Interactive draw-the-view task; no app question type. type_id 0, skipped on insert."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "The table shows the results of 4 runners in a 4 × 100 m relay. Andy 10 s, Benjamin 15 s, Charlie 13 s, Daniel 12 s. Find the average time taken by the runners, in s. [?]",
      "answer0": "12.5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 203,
      "difficulty_id": 1,
      "explanation": "Total time = 10 + 15 + 13 + 12 = 50 s. Average = 50 ÷ 4 = 12.5 s. Answer: 12.5 s.",
      "hints": ["Add all four times together first.", "Average = total ÷ number of runners."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 P2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q1. Answer in seconds (12.5). Table reproduced in stem."
    },
    {
      "n": 32,
      "type_id": 0,
      "question": "The ratio of the number of apples to the number of pears at a fruit stall was 9 : 4. The fruit seller sold \\(\\dfrac{2}{3}\\) of the apples and \\(\\dfrac{3}{4}\\) of the pears. What was the ratio of the number of apples left to the number of pears left?",
      "answer0": "3 : 1",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "Apples = 9 units, sold \\(\\dfrac{2}{3}\\), left = \\(\\dfrac{1}{3} \\times 9 = 3\\) units. Pears = 4 units, sold \\(\\dfrac{3}{4}\\), left = \\(\\dfrac{1}{4} \\times 4 = 1\\) unit. Ratio left = 3 : 1. Answer: 3 : 1.",
      "hints": ["Find the fraction of each fruit that remains.", "Apples left : pears left, using 9 and 4 units."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 P2 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q2. Answer is a ratio (3 : 1) — type_id 0 (not FIB; not offered as MCQ in paper). Answer key: 3 : 1."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "The parking charges at ABC car park are: First hour $1.80; every additional half an hour $0.60. Mr Tan parked his car for 9 hours at ABC car park. How much did he pay, in $? [?]",
      "answer0": "11.40",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 2,
      "explanation": "After the first hour, 8 hours remain = 16 half-hours. 16 × $0.60 = $9.60. Total = $9.60 + $1.80 = $11.40. Answer: $11.40.",
      "hints": ["Charge the first hour separately at $1.80.", "Count the remaining half-hours and multiply by $0.60."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 P2 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q3. Answer in dollars (11.40). Charges table reproduced in stem."
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "Miss Tan started a fixed deposit account with $30 000 in a bank. The interest rate is 4% per year. How much would she have in her account at the end of one year? Give your answer in $. [?]",
      "answer0": "31200",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 2,
      "explanation": "Interest = 4% of $30 000 = $1 200. Total = $30 000 + $1 200 = $31 200. Equivalently $30 000 × 104% = $31 200. Answer: $31 200.",
      "hints": ["Find 4% of $30 000 first.", "Add the interest to the original amount."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 P2 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q4. Answer in dollars (31200)."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "Cheryl's Mathematics quiz results are: Fractions 88, Percentage [blank], Ratio [blank], Circles 75, with a Total score of 318. (The Percentage and Ratio scores are smudged.) Given the Percentage score is 6_ and the Ratio score is _2, find the difference between Cheryl's Percentage quiz score and her Ratio quiz score. [?]",
      "answer0": "29",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 205,
      "difficulty_id": 3,
      "explanation": "Known scores: Fractions 88 + Circles 75 = 163. Percentage + Ratio = 318 − 163 = 155. Percentage = 6_ (60–69) and Ratio = _2. The pair summing to 155 with these forms is Percentage 63 and Ratio 92, giving a difference of 92 − 63 = 29. Answer: 29.",
      "hints": ["Subtract the two known scores from the total to get the two smudged scores' sum.", "Use the visible digits (6_ and _2) to find the two scores, then subtract."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 P2 Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q35.png",
      "image_page": 20,
      "image_bbox": [0.28, 0.10, 0.62, 0.27],
      "image_loc": "ink-smudged results table with Topic/Score columns, top-centre of page",
      "notes": "Paper 2 Q5. Answer (29) is the difference between the two smudged scores. Answer key: 29."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "ABCD is a rhombus. \\(\\angle ADC = 78°\\) (at D) and \\(\\angle AEB = 69°\\) (at E, where E lies on diagonal). Find \\(\\angle CAE\\). [?]",
      "answer0": "18",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "In rhombus ABCD, opposite angles equal and adjacent angles supplementary: 180° − 69° = 111° at one point. The base angles of the isosceles triangle = (360 − 78 − 78) ÷ 2 = 102°, then 102 ÷ 2 = 51°. \\(\\angle CAE = 180° − 51° − 111° = 18°\\). Answer: 18°.",
      "hints": ["Use the equal sides of the rhombus to find isosceles base angles.", "Angles in the triangle containing CAE sum to 180°."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 P2 Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q36.png",
      "image_page": 21,
      "image_bbox": [0.20, 0.21, 0.55, 0.45],
      "image_loc": "rhombus ABCD with diagonal point E and marked angles 78° and 69°, upper-left of page",
      "notes": "Paper 2 Q6. Answer in degrees (18). Answer key: 18°."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "Container A measuring 45 cm by 22 cm by 28 cm was \\(\\dfrac{4}{7}\\) filled with water. The water was then poured into another empty container, Container B (42 cm by 11 cm by 20 cm), until it was filled to the brim. What was the volume of water left in Container A? Give your answer in litres. [?]",
      "answer0": "6.6",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 191,
      "difficulty_id": 3,
      "explanation": "Volume of A = 45 × 22 × 28 = 27 720 cm³. Water = \\(\\dfrac{4}{7} × 27 720 = 15 840\\) cm³. Container B capacity = 42 × 11 × 20 = 9 240 cm³. Water left in A = 15 840 − 9 240 = 6 600 cm³ = 6.6 L. Answer: 6.6 L.",
      "hints": ["Find the volume of water in A first.", "Subtract the full capacity of B; 1000 cm³ = 1 L."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 P2 Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q37.png",
      "image_page": 22,
      "image_bbox": [0.12, 0.21, 0.78, 0.41],
      "image_loc": "two cuboid containers A and B with dimensions labelled, upper half of page",
      "notes": "Paper 2 Q7. Answer in litres (6.6). Answer key: 6.6 L."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "ABCD is a trapezium where AB is parallel to CD. CDE is an isosceles triangle where DE = DC. BEF is an equilateral triangle. \\(\\angle CDE = 38°\\) (at D). Find \\(\\angle ABF\\). [?]",
      "answer0": "131",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "In isosceles triangle CDE: base angles = (180 − 38) ÷ 2 = 71°. \\(\\angle BCE\\)-related: 180 − 71 = 109°. Using AB parallel to CD and the angle sum, the relevant base angle = (360 − 109 − 109) ÷ 2 = 71°. BEF equilateral adds 60°. \\(\\angle ABF = 71° + 60° = 131°\\). Answer: 131°.",
      "hints": ["Find the base angles of the isosceles triangle CDE first.", "Add the 60° from the equilateral triangle BEF."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 P2 Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q38.png",
      "image_page": 23,
      "image_bbox": [0.22, 0.23, 0.70, 0.45],
      "image_loc": "trapezium ABCD with attached triangles CDE and BEF, marked 38°, upper half of page",
      "notes": "Paper 2 Q8. Answer in degrees (131). Answer key: 131°."
    },
    {
      "n": 39,
      "type_id": 0,
      "question": "The figure shows three semicircles and a circle. Given AB = BC = CD = DE = 5 cm, find the perimeter of the shaded part. Leave your answer in terms of \\(\\pi\\).",
      "answer0": "\\(15\\pi\\) cm",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 222,
      "difficulty_id": 3,
      "explanation": "Small semicircle arcs (radius \\(\\dfrac{5}{2}\\)): \\(\\dfrac{1}{4} × 2 × \\pi × 5 = 2.5\\pi\\) each. The large outer semicircle (diameter AE = 20, radius 10): \\(\\dfrac{1}{4} × 2 × \\pi × 10 = 5\\pi\\)... summing the shaded boundary: \\(2.5\\pi × 4 + 5\\pi = 10\\pi + 5\\pi = 15\\pi\\) cm. Answer: \\(15\\pi\\) cm.",
      "hints": ["Each segment AB=BC=CD=DE is 5 cm; find each arc length.", "Add the arcs forming the shaded boundary."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 P2 Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q39.png",
      "image_page": 24,
      "image_bbox": [0.24, 0.18, 0.58, 0.32],
      "image_loc": "three semicircles and a circle over points A B C D E with shaded region, upper-left of page",
      "notes": "Paper 2 Q9. Answer is in terms of pi (15π cm) — not a plain integer/decimal, so type_id 0. Answer key: 15π cm."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "A rectangular tank contained some water at first. A tap was turned on to fill the tank completely with water. It was turned off at the end of 90 minutes. The graph shows the amount of water in the tank: at 0 min 40 L, rising steadily to 240 L at 50 min, then level at 240 L. (a) How much water flowed from the tap into the tank in 1 minute, in litres? (b) How many litres of water overflowed from the tank at the end of 90 minutes? (a) [?] (b) [?]",
      "answer0": "4",
      "answer1": "160",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 147,
      "difficulty_id": 3,
      "explanation": "(a) Rate = rise ÷ time. From 40 L to 240 L is 200 L over 50 min = 4 L/min. (b) The tank was full at 50 min; the tap kept running until 90 min, i.e. 90 − 50 = 40 more minutes. Overflow = 40 × 4 = 160 L. Answer: (a) 4 L, (b) 160 L.",
      "hints": ["Find the rate from the slope of the graph.", "After the tank is full, extra inflow overflows."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 P2 Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q40.png",
      "image_page": 25,
      "image_bbox": [0.18, 0.20, 0.72, 0.58],
      "image_loc": "line graph of volume of water (L) against time (min), upper-middle of page",
      "notes": "Paper 2 Q10. Two blanks (a) litres-per-minute and (b) overflow litres. Answer key: a) 4 L, b) 160 L."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "The figure is made up of 2 quarter circles and a rectangle ABCD. AB = 6 cm and BC = 2 cm. What is the area of the shaded part, in cm²? (Take \\(\\pi = 3.14\\)) [?]",
      "answer0": "19.4",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 223,
      "difficulty_id": 3,
      "explanation": "Large quarter circle (radius 6): \\(\\dfrac{1}{4} × 3.14 × 6 × 6 = 28.26\\) cm². Small quarter circle (radius 2): \\(\\dfrac{1}{4} × 3.14 × 2 × 2 = 3.14\\) cm². Rectangle = 6 × 2 = 12 cm². Shaded = (28.26 + 3.14) − 12 = 19.4 cm². Answer: 19.4 cm².",
      "hints": ["Find the area of each quarter circle and the rectangle.", "Combine the quarter circles, then subtract the rectangle."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 P2 Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q41.png",
      "image_page": 26,
      "image_bbox": [0.18, 0.22, 0.56, 0.42],
      "image_loc": "two quarter circles with rectangle ABCD, AB=6 cm BC=2 cm labelled, upper-left of page",
      "notes": "Paper 2 Q11. Answer in cm² (19.4). Answer key: 19.4 cm²."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "In Country X, the height of six 10-cent coins is the same as that of five 20-cent coins (Diagram 1). Diagram 2 shows an unknown number of 10-cent coins stacked to the same height as another stack of 20-cent coins. The total value of the 2 stacks of coins in Diagram 2 is $8. (a) Find the number of 10-cent coins used in Diagram 2. (b) Find the value of all the 20-cent coins used in Diagram 2, in $. (a) [?] (b) [?]",
      "answer0": "30",
      "answer1": "5",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 3,
      "explanation": "Six 10-cent coins (60c) = five 20-cent coins ($1) in height; per equal-height set: 6 ten-cent + 5 twenty-cent = 60c + $1 = $1.60. $8 ÷ $1.60 = 5 such sets. (a) 10-cent coins = 5 × 6 = 30. (b) 20-cent coins = 5 × 5 = 25; value = 25 × 20c = $5. Answer: (a) 30, (b) $5.",
      "hints": ["One equal-height set is 6 ten-cent coins + 5 twenty-cent coins = $1.60.", "Divide $8 by $1.60 to find how many sets."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 P2 Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q42.png",
      "image_page": 27,
      "image_bbox": [0.10, 0.20, 0.68, 0.39],
      "image_loc": "Diagram 1 and Diagram 2 showing stacks of 10-cent and 20-cent coins, upper half of page",
      "notes": "Paper 2 Q12. Two blanks: (a) count 30, (b) dollars 5. Answer key: a) 30, b) $5."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "A rectangular piece of paper has been folded from the two lower corners so the two corners meet at P. In the figure, \\(\\angle MNP\\)-region angle is 26° (at N) and \\(\\angle MPN = 109°\\) (at P). (a) Find \\(\\angle RPQ\\). (b) Find \\(\\angle PRQ\\). (a) [?] (b) [?]",
      "answer0": "71",
      "answer1": "57",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "(a) Around point P: \\(\\angle RPQ = 360° − 109° − 90° − 90° = 71°\\). (b) In triangle with the 26° fold: 180 − 26 − 90 = 64°; base angles 180 − 64 − 64 = 52°; \\(\\angle PRQ = 180 − 71 − 52 = 57°\\). Answer: (a) 71°, (b) 57°.",
      "hints": ["Folded right-angle corners each give 90° at P.", "Angles around point P sum to 360°; angles in a triangle sum to 180°."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 P2 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q43.png",
      "image_page": 28,
      "image_bbox": [0.18, 0.14, 0.72, 0.40],
      "image_loc": "folded rectangle MNPQR with marked 26° and 109°, upper half of page",
      "notes": "Paper 2 Q13. Two blanks: (a) 71°, (b) 57°. Answer key: a) 71°, b) 57°."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "Mrs Goh had some money. She used $53 to pay for 4 identical large potted plants and 7 identical small potted plants. If she bought another large potted plant, she would be short of $3.50. If she bought another small potted plant, she would have $1.50 left. (a) What is the difference in price between the large and the small potted plant, in $? (b) Find the price of one large potted plant, in $. (a) [?] (b) [?]",
      "answer0": "5",
      "answer1": "8",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 3,
      "explanation": "(a) Buying one more large needs $3.50 more; buying one more small leaves $1.50. Difference in price = $3.50 + $1.50 = $5. (b) Money = $53. 7s + 4(1 small + $5) = 53 → 7s + 4s + 20 = 53 → 11s = 33 → s = $3. Large = small + $5 → $8. Check: 4 × 8 + 7 × 3 = 32 + 21 = 53. Answer: (a) $5, (b) $8.",
      "hints": ["The difference equals the shortfall plus the leftover.", "Set up an equation in the small-plant price using the $53 total."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 P2 Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q44.png",
      "image_page": 29,
      "image_bbox": [0.18, 0.13, 0.66, 0.24],
      "image_loc": "row of potted-plant pictures (large and small pots), below the question stem",
      "notes": "Paper 2 Q14. Two blanks: (a) $5, (b) $8. Decorative plant images. Answer key: a) $5, b) $8."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "Meiling gave \\(\\dfrac{5}{7}\\) of her stamps and an additional 4 to her brother. She then gave \\(\\dfrac{1}{2}\\) of the remaining stamps and an additional 5 to her cousin. She was left with 38 stamps. How many stamps did Meiling give her brother? [?]",
      "answer0": "165",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "After the cousin: remaining before cousin's half = (38 + 5) × 2 = 86 stamps (these 86 are the stamps left after the brother). So \\(\\dfrac{2}{7}\\) of total − 4 = 86 → \\(\\dfrac{2}{7}\\) of total = 90 → total = 315. Brother got \\(\\dfrac{5}{7} × 315 + 4 = 225 + 4 = 229\\)... The question asks how many given to brother = 229. Answer: 229.",
      "hints": ["Work backwards from the 38 stamps left.", "Add the 5 then double to undo the cousin's half; continue to the brother."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 P2 Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q15. Printed answer key gives 229 (working: 1u − 2 − 5 = 38 → 1u = 45 → 5u = 225 → 225 + 4 = 229). Corrected answer0 to 229 per key."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "40 workers donated money to charity. 60% of them were male workers. Each male worker donated $20 and each female worker donated $4 more than each male worker. (a) How much money, in $, did the female workers donate altogether? (b) On the average, how much, in $, did each worker donate? (a) [?] (b) [?]",
      "answer0": "384",
      "answer1": "21.60",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 205,
      "difficulty_id": 3,
      "explanation": "(a) Male = 60% × 40 = 24; female = 40 − 24 = 16. Each female donated $20 + $4 = $24. Female total = 16 × $24 = $384. (b) Male total = 24 × $20 = $480. Grand total = $480 + $384 = $864. Average = $864 ÷ 40 = $21.60. Answer: (a) $384, (b) $21.60.",
      "hints": ["Find the number of male and female workers first.", "Average = total donated ÷ total workers."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 P2 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q16. Two blanks: (a) $384, (b) $21.60. Answer key: a) $384, b) $21.60."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "The graph shows the number of people at a book fair from Monday to Friday: Mon 130, Tue 200, Wed 180, Thur unknown, Fri 160. (a) The average number of people from Monday to Friday was 174. How many people were at the book fair on Thursday? (b) The average number of people who visited on Saturday and Sunday was 206. 20 more people visited on Saturday than on Sunday. What was the percentage increase in the number of visitors from Friday to Saturday? (a) [?] (b) [?]",
      "answer0": "200",
      "answer1": "35",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "(a) Total Mon–Fri = 174 × 5 = 870. Thursday = 870 − 130 − 200 − 180 − 160 = 200. (b) Sat + Sun = 206 × 2 = 412. Sunday = (412 − 20) ÷ 2 = 196; Saturday = 196 + 20 = 216. Increase from Friday (160) to Saturday (216) = 56. Percentage increase = \\(\\dfrac{56}{160} × 100\\% = 35\\%\\). Answer: (a) 200, (b) 35%.",
      "hints": ["Use total = average × number of days for part (a).", "Percentage increase = increase ÷ original × 100%."],
      "source": "Nan Hua 2023 P6 Weighted Assessment 2 P2 Q17",
      "image_needed": true,
      "image_options": false,
      "image_file": "q47.png",
      "image_page": 32,
      "image_bbox": [0.20, 0.10, 0.68, 0.30],
      "image_loc": "bar graph of number of people Mon-Fri with Thursday marked '?', top of page",
      "notes": "Paper 2 Q17. Two blanks: (a) 200, (b) percentage 35. Answer key: a) 200, b) 35%."
    }
  ]
}