{
  "paper": {
    "school": "Nan Hua",
    "year": 2022,
    "level": "P6",
    "label": "Prelim",
    "source_prefix": "Nan Hua 2022 P6 Prelim",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "Round 56 354 to the nearest 1000.",
      "answer0": "56 000",
      "answer1": "56 300",
      "answer2": "56 400",
      "answer3": "57 000",
      "correct_answer": 0,
      "skill_id": 13,
      "difficulty_id": 1,
      "explanation": "The hundreds digit is 3 (less than 5), so round down. 56 354 rounds to 56 000.",
      "hints": ["Look at the hundreds digit to decide whether to round up or down.", "354 is less than 500, so the thousands digit stays the same."],
      "source": "Nan Hua 2022 P6 Prelim Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 1"
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "In 18.624, which digit is in the tenths place?",
      "answer0": "1",
      "answer1": "2",
      "answer2": "6",
      "answer3": "8",
      "correct_answer": 2,
      "skill_id": 13,
      "difficulty_id": 1,
      "explanation": "The first digit after the decimal point is the tenths place. In 18.624 that is 6.",
      "hints": ["The tenths place is immediately after the decimal point.", "18.6|2|4 — the 6 is in the tenths place."],
      "source": "Nan Hua 2022 P6 Prelim Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 3"
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Arrange the following numbers from the smallest to the largest.<br>7, 7.3, 7.03",
      "answer0": "7, 7.03, 7.3",
      "answer1": "7.3, 7, 7.03",
      "answer2": "7.3, 7.03, 7",
      "answer3": "7.03, 7.3, 7",
      "correct_answer": 0,
      "skill_id": 13,
      "difficulty_id": 1,
      "explanation": "Compare: 7 = 7.00, 7.03, 7.3 = 7.30. In order smallest to largest: 7, 7.03, 7.3.",
      "hints": ["Write each number with the same number of decimal places: 7.00, 7.30, 7.03.", "Then compare the tenths, then hundredths."],
      "source": "Nan Hua 2022 P6 Prelim Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 1. The boxed numbers 7, 7.3, 7.03 are the given set, folded into the stem."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Express \\(\\dfrac{1}{8}\\) as a decimal.",
      "answer0": "0.125",
      "answer1": "1.25",
      "answer2": "12.5",
      "answer3": "125",
      "correct_answer": 0,
      "skill_id": 13,
      "difficulty_id": 1,
      "explanation": "1 ÷ 8 = 0.125.",
      "hints": ["Divide 1 by 8.", "1 ÷ 8 gives 0.125."],
      "source": "Nan Hua 2022 P6 Prelim Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 1"
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "In a marathon, there are 40 Malay participants, 70 Chinese participants and 30 Indian participants. What is the ratio of the number of Malay participants to the total number of Chinese and Indian participants?",
      "answer0": "2 : 5",
      "answer1": "2 : 7",
      "answer2": "4 : 3",
      "answer3": "4 : 7",
      "correct_answer": 0,
      "skill_id": 210,
      "difficulty_id": 2,
      "explanation": "Chinese + Indian = 70 + 30 = 100. Ratio Malay : (Chinese + Indian) = 40 : 100 = 2 : 5.",
      "hints": ["First add the Chinese and Indian participants.", "Simplify 40 : 100 by dividing both by 20."],
      "source": "Nan Hua 2022 P6 Prelim Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 1"
    },
    {
      "n": 6,
      "type_id": 2,
      "question": "John is thinking of a number. 40% of the number is 36. What is the number?",
      "answer0": "90",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 207,
      "difficulty_id": 2,
      "explanation": "40% of the number is 36, so 1% is 36 ÷ 40 = 0.9, and 100% is 0.9 × 100 = 90.",
      "hints": ["40% → 36, so find what 1% is.", "Multiply 1% by 100 to get the whole number."],
      "source": "Nan Hua 2022 P6 Prelim Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 4 (=90). Answer is a whole number, converted to FIB."
    },
    {
      "n": 7,
      "type_id": 2,
      "question": "Aini spent $40 in school in January. In February, she spent $32 in school. Find the percentage decrease in her spending.",
      "answer0": "20",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 208,
      "difficulty_id": 2,
      "explanation": "Decrease = 40 − 32 = 8. Percentage decrease = 8/40 × 100% = 20%.",
      "hints": ["Find the amount of the decrease first.", "Percentage decrease = decrease ÷ original × 100%."],
      "source": "Nan Hua 2022 P6 Prelim Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 2 (=20%). Answer in percent (whole number), FIB; the % sign is in the stem wording."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "Simplify $9 + 5d - 3d + 4$.",
      "answer0": "$5 + 2d$",
      "answer1": "$5 + 8d$",
      "answer2": "$13 + 2d$",
      "answer3": "$13 + 8d$",
      "correct_answer": 2,
      "skill_id": 239,
      "difficulty_id": 1,
      "explanation": "Combine like terms: 9 + 4 = 13 and 5d − 3d = 2d, giving 13 + 2d.",
      "hints": ["Add the number terms: 9 + 4.", "Combine the d terms: 5d − 3d."],
      "source": "Nan Hua 2022 P6 Prelim Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 3"
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "Which of the following is the most likely mass of a calculator?",
      "answer0": "5 g",
      "answer1": "15 g",
      "answer2": "150 g",
      "answer3": "1500 g",
      "correct_answer": 2,
      "skill_id": 13,
      "difficulty_id": 1,
      "explanation": "A typical handheld calculator has a mass of about 150 g. 5 g and 15 g are too light; 1500 g is too heavy.",
      "hints": ["Think about how heavy a small calculator feels in your hand.", "150 g is about the mass of a calculator."],
      "source": "Nan Hua 2022 P6 Prelim Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q9.png",
      "image_page": 5,
      "image_bbox": [0.55, 0.55, 0.68, 0.72],
      "image_loc": "small calculator picture on the right side of the page, beside the options",
      "notes": "Key: option 3. Figure is a small calculator image."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "Which of the following is the same as 8050 cm?",
      "answer0": "8 m 5 cm",
      "answer1": "8 m 50 cm",
      "answer2": "80 m 5 cm",
      "answer3": "80 m 50 cm",
      "correct_answer": 3,
      "skill_id": 13,
      "difficulty_id": 1,
      "explanation": "8050 cm = 8000 cm + 50 cm = 80 m + 50 cm = 80 m 50 cm (since 100 cm = 1 m).",
      "hints": ["100 cm = 1 m.", "8050 cm = 80 m and 50 cm left over."],
      "source": "Nan Hua 2022 P6 Prelim Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 4"
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "These are the operating hours of ABC Dental Clinic.<br>Opens Monday to Friday, Closed on weekends<br>8.30 a.m. to 12.30 p.m.<br>2.30 p.m. to 4.30 p.m.<br>7 p.m. to 9.15 p.m.<br>How long is the clinic open on Wednesday?",
      "answer0": "9 h 15 min",
      "answer1": "8 h 15 min",
      "answer2": "7 h 15 min",
      "answer3": "6 h 15 min",
      "correct_answer": 3,
      "skill_id": 13,
      "difficulty_id": 2,
      "explanation": "Morning: 8.30 a.m. to 12.30 p.m. = 4 h. Afternoon: 2.30 p.m. to 4.30 p.m. = 2 h. Evening: 7 p.m. to 9.15 p.m. = 2 h 15 min. Total = 4 h + 2 h + 2 h 15 min = 8 h 15 min.",
      "hints": ["Find the length of each opening session separately.", "Add up the three durations."],
      "source": "Nan Hua 2022 P6 Prelim Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 2 (=8 h 15 min). The opening-hours sign content is folded into the stem text, so no image needed."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "The figure shows a circle inside a square of side 14 cm. Find the area and perimeter of the circle. Take \\(\\pi=\\dfrac{22}{7}\\).",
      "answer0": "Area 154 cm², Perimeter 44 cm",
      "answer1": "Area 154 cm², Perimeter 22 cm",
      "answer2": "Area 44 cm², Perimeter 154 cm",
      "answer3": "Area 22 cm², Perimeter 154 cm",
      "correct_answer": 0,
      "skill_id": 220,
      "difficulty_id": 2,
      "explanation": "Diameter = 14 cm, radius = 7 cm. Area = \\(\\pi r^2\\) = 22/7 × 7 × 7 = 154 cm². Perimeter (circumference) = \\(\\pi d\\) = 22/7 × 14 = 44 cm.",
      "hints": ["The circle fits the square, so the diameter equals the side, 14 cm.", "Area = πr² and circumference = πd."],
      "source": "Nan Hua 2022 P6 Prelim Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q12.png",
      "image_page": 7,
      "image_bbox": [0.28, 0.16, 0.55, 0.34],
      "image_loc": "circle inscribed in a square labelled 14 cm, upper-middle of the page",
      "notes": "Key: option 1"
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "Mrs Lim had \\(\\dfrac{1}{10}\\) ℓ of syrup. She mixed the syrup with \\(\\dfrac{4}{5}\\) ℓ of water to make fruit punch. The fruit punch was poured into bottles, each containing \\(\\dfrac{1}{5}\\) ℓ. How much fruit punch was left?",
      "answer0": "\\(\\dfrac{1}{10}\\) ℓ",
      "answer1": "\\(\\dfrac{1}{2}\\) ℓ",
      "answer2": "\\(\\dfrac{7}{10}\\) ℓ",
      "answer3": "\\(\\dfrac{4}{5}\\) ℓ",
      "correct_answer": 0,
      "skill_id": 62,
      "difficulty_id": 2,
      "explanation": "Total punch = 1/10 + 4/5 = 1/10 + 8/10 = 9/10 ℓ. Each bottle holds 1/5 = 2/10 ℓ. 9/10 ÷ 2/10 = 4 full bottles (8/10 ℓ) with 1/10 ℓ left over.",
      "hints": ["Add the syrup and water amounts using a common denominator of 10.", "See how many 1/5 ℓ (=2/10 ℓ) bottles fit, then find the remainder."],
      "source": "Nan Hua 2022 P6 Prelim Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "ERRATA version (page 11) replaces the original Q13: syrup 1/10 ℓ, water 4/5 ℓ. Key: option 1 (=1/10 ℓ). Fraction options → MCQ."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "The graph shows the number of books that the students in Class 6A read in a week. Find the total number of books read by students who read more than 2 books.",
      "answer0": "19",
      "answer1": "25",
      "answer2": "64",
      "answer3": "76",
      "correct_answer": 2,
      "skill_id": 202,
      "difficulty_id": 2,
      "explanation": "More than 2 books means 3 books and 4 books. From the graph: 12 students read 3 books (12 × 3 = 36) and 7 students read 4 books (7 × 4 = 28). Total = 36 + 28 = 64.",
      "hints": ["\"More than 2\" means the 3-book and 4-book bars only.", "Multiply each number of books by its number of students, then add."],
      "source": "Nan Hua 2022 P6 Prelim Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q14.png",
      "image_page": 8,
      "image_bbox": [0.18, 0.15, 0.78, 0.46],
      "image_loc": "horizontal bar graph of number of books vs number of students, upper part of the page",
      "notes": "Key: option 3 (=64). Bar graph required."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "Halim's result slip was accidentally torn. His average mark for 4 subjects is 78. Part of his Mathematics and Science marks are missing. What is the greatest possible difference between Halim's Mathematics and Science mark?",
      "answer0": "19",
      "answer1": "16",
      "answer2": "10",
      "answer3": "4",
      "correct_answer": 1,
      "skill_id": 205,
      "difficulty_id": 3,
      "explanation": "Total of 4 subjects = 78 × 4 = 312. English 80 + Chinese 76 = 156, so Mathematics + Science = 312 − 156 = 156. Maths starts with 8_ (80–89) and Science with 7_ (70–79). For the greatest difference, take Maths as large and Science as small. Maths 89 + Science 67 = 156 → difference 22 (but 67 starts with 6, not allowed). Valid: Maths must be 8_, Science 7_ summing to 156. Largest Maths = 86 (Science 70) gives difference 16; Maths 89 needs Science 67 (invalid). So greatest valid difference = 86 − 70 = 16.",
      "hints": ["Total marks = average × number of subjects = 78 × 4.", "Maths is in the 80s and Science in the 70s; they must add to 156. Maximise Maths and minimise Science within those tens."],
      "source": "Nan Hua 2022 P6 Prelim Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q15.png",
      "image_page": 9,
      "image_bbox": [0.22, 0.18, 0.52, 0.40],
      "image_loc": "torn result-slip showing English 80, Chinese 76, Mathematics 8_, Science 7_, Average 78",
      "notes": "Key: option 2 (=16). The torn-slip figure (with partly missing Maths 8_ and Science 7_ digits) is essential to the problem."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Measure and write down the size of \\(\\angle ABC\\).",
      "answer0": "127",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 1,
      "explanation": "Using a protractor on the figure, \\(\\angle ABC = 127°\\) (accept 126°–128°).",
      "hints": ["Place the protractor centre at vertex B.", "Measure the angle between BA and BC."],
      "source": "Nan Hua 2022 P6 Prelim Q16",
      "image_needed": true,
      "image_options": false,
      "image_file": "q16.png",
      "image_page": 15,
      "image_bbox": [0.10, 0.17, 0.72, 0.38],
      "image_loc": "triangle with vertices A (top-left), B (bottom-left), C (right)",
      "notes": "Key: 127 ± 1°. Measurement question — figure required."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "The volume of the cuboid is 96 cm³. The area of the shaded face is 8 cm². Find the height of the cuboid.",
      "answer0": "12",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 226,
      "difficulty_id": 2,
      "explanation": "Volume = base area × height. Height = volume ÷ base area = 96 ÷ 8 = 12 cm.",
      "hints": ["Volume = base area × height.", "Divide the volume by the shaded face area."],
      "source": "Nan Hua 2022 P6 Prelim Q17",
      "image_needed": true,
      "image_options": false,
      "image_file": "q17.png",
      "image_page": 15,
      "image_bbox": [0.13, 0.55, 0.36, 0.80],
      "image_loc": "tall cuboid with a shaded top face and the height marked '? cm'",
      "notes": "Key: 12 (cm). Answer in cm."
    },
    {
      "n": 18,
      "type_id": 1,
      "question": "Figure A and Figure B are nets of solids. Which statement correctly describes them?",
      "answer0": "Figure A is a net of a prism; Figure B is a net of a pyramid.",
      "answer1": "Figure A is a net of a pyramid; Figure B is a net of a prism.",
      "answer2": "Both Figure A and Figure B are nets of prisms.",
      "answer3": "Both Figure A and Figure B are nets of pyramids.",
      "correct_answer": 0,
      "skill_id": 230,
      "difficulty_id": 1,
      "explanation": "Figure A (rectangles with two triangular ends) folds into a triangular prism. Figure B (a polygon base with triangles meeting at an apex) folds into a pyramid.",
      "hints": ["A prism net has two identical end-faces joined by rectangles.", "A pyramid net has one base with triangular faces meeting at a point."],
      "source": "Nan Hua 2022 P6 Prelim Q18",
      "image_needed": true,
      "image_options": false,
      "image_file": "q18.png",
      "image_page": 16,
      "image_bbox": [0.18, 0.12, 0.70, 0.30],
      "image_loc": "two nets side by side, Figure A (left) and Figure B (right)",
      "notes": "Key: Figure A → prism, Figure B → pyramid. Original is a circle-the-word task; converted to MCQ describing both. Figure required."
    },
    {
      "n": 19,
      "type_id": 0,
      "question": "There are 4 shaded squares in the figure. Shade 3 more squares to form a symmetric figure with AB as the line of symmetry.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 2,
      "explanation": "Reflect each of the 4 already-shaded squares across diagonal AB; the 3 squares that do not yet have their mirror image shaded must be shaded (the answer-key figure on page 45 shows the completed symmetric pattern).",
      "hints": ["Diagonal AB is the line of symmetry.", "Each shaded square needs its mirror image across AB shaded too."],
      "source": "Nan Hua 2022 P6 Prelim Q19",
      "image_needed": true,
      "image_options": false,
      "image_file": "q19.png",
      "image_page": 16,
      "image_bbox": [0.30, 0.55, 0.62, 0.82],
      "image_loc": "5x5 grid with diagonal AB and 4 shaded squares",
      "notes": "Interactive shade-the-grid task — type_id 0, skipped on insert. Answer key: see completed symmetric grid on page 45."
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "ABCD is a trapezium with AB parallel to DC. Find \\(\\angle y\\).",
      "answer0": "33",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 2,
      "explanation": "AB is parallel to DC, so \\(\\angle BAC = \\angle ACD\\) (alternate angles). At vertex A, \\(\\angle DAC = 85°\\) is split; with \\(\\angle ADC = 62°\\), in triangle ADC: \\(\\angle ACD = 180° - 85° - 62° = 33°\\). By alternate angles, \\(\\angle y = \\angle ACD = 33°\\) wait — y is the angle at A between AB and AC. Since AB∥DC, \\(\\angle y\\) (between AB and AC) = \\(\\angle ACD\\) (between CD and CA) = 33°.",
      "hints": ["AB is parallel to DC — look for alternate (Z) angles.", "Use the 85° and 62° angles in triangle ADC to find ∠ACD first."],
      "source": "Nan Hua 2022 P6 Prelim Q20",
      "image_needed": true,
      "image_options": false,
      "image_file": "q20.png",
      "image_page": 17,
      "image_bbox": [0.14, 0.14, 0.60, 0.34],
      "image_loc": "trapezium ABCD with diagonal AC, angle 85° and y at A, 62° at D",
      "notes": "Key: 33 (°). Answer in degrees."
    },
    {
      "n": 21,
      "type_id": 1,
      "question": "Find the value of \\(\\dfrac{2}{7}\\div 4\\). Give your answer as a fraction in the simplest form.",
      "answer0": "\\(\\dfrac{1}{14}\\)",
      "answer1": "\\(\\dfrac{2}{28}\\)",
      "answer2": "\\(\\dfrac{1}{7}\\)",
      "answer3": "\\(\\dfrac{8}{7}\\)",
      "correct_answer": 0,
      "skill_id": 62,
      "difficulty_id": 1,
      "explanation": "2/7 ÷ 4 = 2/7 × 1/4 = 2/28 = 1/14.",
      "hints": ["Dividing by 4 is the same as multiplying by 1/4.", "Simplify 2/28 by dividing top and bottom by 2."],
      "source": "Nan Hua 2022 P6 Prelim Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key (part a): 1/14. Fraction answer → MCQ. Only part (a) of Q21 (part b is the separate decimal item Q21b, recorded as Q31 below)."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "Find the value of $2\\div 9$. Give your answer correct to 1 decimal place.",
      "answer0": "0.2",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 62,
      "difficulty_id": 1,
      "explanation": "2 ÷ 9 = 0.222..., which rounds to 0.2 (1 decimal place).",
      "hints": ["Divide 2 by 9 to get a recurring decimal.", "Round 0.222... to 1 decimal place."],
      "source": "Nan Hua 2022 P6 Prelim Q21b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "This is Q21 part (b). Decimal answer → FIB. Numbered 31 to keep n unique; source preserves the printed Q21(b) label."
    },
    {
      "n": 22,
      "type_id": 1,
      "question": "Which fraction is smaller, \\(\\dfrac{4}{9}\\) or \\(\\dfrac{2}{3}\\)?",
      "answer0": "\\(\\dfrac{4}{9}\\)",
      "answer1": "\\(\\dfrac{2}{3}\\)",
      "answer2": "They are equal",
      "answer3": "Cannot be determined",
      "correct_answer": 0,
      "skill_id": 62,
      "difficulty_id": 1,
      "explanation": "Convert to ninths: 2/3 = 6/9. Compare 4/9 and 6/9 → 4/9 is smaller.",
      "hints": ["Make the denominators the same (use 9).", "2/3 = 6/9, so compare 4/9 with 6/9."],
      "source": "Nan Hua 2022 P6 Prelim Q22",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key (part a): 4/9. Original part (a). Fraction answer → MCQ. Part (b) is the separate ordering item Q32 below."
    },
    {
      "n": 32,
      "type_id": 1,
      "question": "Arrange \\(\\dfrac{5}{9}\\), \\(\\dfrac{2}{3}\\), \\(\\dfrac{9}{8}\\) in decreasing order.",
      "answer0": "\\(\\dfrac{9}{8}\\), \\(\\dfrac{2}{3}\\), \\(\\dfrac{5}{9}\\)",
      "answer1": "\\(\\dfrac{5}{9}\\), \\(\\dfrac{2}{3}\\), \\(\\dfrac{9}{8}\\)",
      "answer2": "\\(\\dfrac{2}{3}\\), \\(\\dfrac{9}{8}\\), \\(\\dfrac{5}{9}\\)",
      "answer3": "\\(\\dfrac{9}{8}\\), \\(\\dfrac{5}{9}\\), \\(\\dfrac{2}{3}\\)",
      "correct_answer": 0,
      "skill_id": 62,
      "difficulty_id": 2,
      "explanation": "9/8 = 1.125 (greater than 1). 2/3 ≈ 0.667 and 5/9 ≈ 0.556. Decreasing order: 9/8, 2/3, 5/9.",
      "hints": ["9/8 is more than 1, so it is the largest.", "Compare 2/3 and 5/9 by converting to a common denominator (e.g. 18): 12/18 vs 10/18."],
      "source": "Nan Hua 2022 P6 Prelim Q22b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "This is Q22 part (b). Key: 9/8, 2/3, 5/9. Fraction sequence → MCQ (FIB cannot hold fractions). Numbered 32 for uniqueness; source keeps printed Q22(b)."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "The square grid shows the positions of points A, B, C, D, E, F, G and H.<br>(a) In which direction is point A from point D?<br>(b) Winnie is at point B facing East at first. She turns 135° clockwise. Which point is she facing after the turn?",
      "answer0": "North-West",
      "answer1": "C",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 2,
      "explanation": "(a) A is directly above and to the left of D, so A is North-West of D. (b) Facing East and turning 135° clockwise points to the South-West; from B that direction reaches point C.",
      "hints": ["Use the North arrow to read directions; A is up-and-left of D.", "From East, a 90° clockwise turn faces South; another 45° (135° total) faces South-West."],
      "source": "Nan Hua 2022 P6 Prelim Q23",
      "image_needed": true,
      "image_options": false,
      "image_file": "q23.png",
      "image_page": 20,
      "image_bbox": [0.30, 0.10, 0.72, 0.30],
      "image_loc": "square grid with plotted points A,B,C,D,E(F),G,H and a North arrow to the right",
      "notes": "Key: (a) North-West, (b) C. Two-blank FIB: answer0=direction, answer1=point label. Grid figure required."
    },
    {
      "n": 24,
      "type_id": 1,
      "question": "A box contains red, green, blue and black markers. \\(\\dfrac{3}{8}\\) of the markers are red. \\(\\dfrac{3}{10}\\) of the remaining markers are green. The number of blue and black markers are equal. What fraction of the markers in the box are blue?",
      "answer0": "\\(\\dfrac{7}{32}\\)",
      "answer1": "\\(\\dfrac{7}{16}\\)",
      "answer2": "\\(\\dfrac{3}{16}\\)",
      "answer3": "\\(\\dfrac{5}{8}\\)",
      "correct_answer": 0,
      "skill_id": 62,
      "difficulty_id": 3,
      "explanation": "Red = 3/8, so remaining = 5/8. Green = 3/10 of 5/8 = 3/16. Blue + black = 5/8 − 3/16 = 10/16 − 3/16 = 7/16. Blue = black, so blue = 7/16 ÷ 2 = 7/32.",
      "hints": ["After removing red (3/8), 5/8 remains.", "Subtract the green fraction, then halve the rest because blue = black."],
      "source": "Nan Hua 2022 P6 Prelim Q24",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 7/32. Fraction answer → MCQ."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "John is $t$ years old. His mother is 25 years older than him.<br>(a) How old is John's mother? Express your answer in terms of $t$.<br>(b) What is their total age when $t=10$?",
      "answer0": "$t+25$",
      "answer1": "45",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 238,
      "difficulty_id": 2,
      "explanation": "(a) Mother's age = (t + 25) years old. (b) When t = 10: John = 10, mother = 10 + 25 = 35, total = 10 + 35 = 45 years.",
      "hints": ["\"25 years older\" means add 25 to t.", "For (b), substitute t = 10 and add John's and mother's ages."],
      "source": "Nan Hua 2022 P6 Prelim Q25",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: (a) t+25, (b) 45. Two-blank FIB: answer0=algebraic expression, answer1=45 (years)."
    },
    {
      "n": 26,
      "type_id": 0,
      "question": "Draw the following cuboid (3 units by 2 units by 2 units) on the isometric grid.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 2,
      "explanation": "Draw a 3 × 2 × 2 unit cuboid on the isometric dot grid (see the answer-key drawing on page 46).",
      "hints": ["Use the isometric dots to mark the 3-unit, 2-unit and 2-unit edges.", "Draw the visible front, top and side faces."],
      "source": "Nan Hua 2022 P6 Prelim Q26",
      "image_needed": true,
      "image_options": false,
      "image_file": "q26.png",
      "image_page": 22,
      "image_bbox": [0.12, 0.13, 0.74, 0.36],
      "image_loc": "cuboid (3 units x 2 units x 2 units) on the left and a blank isometric dot grid on the right",
      "notes": "Interactive drawing task — type_id 0, skipped on insert. Answer key drawing on page 46."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "The figure shows a rectangular glass box filled with unit cubes. How many more unit cubes are needed to fill the box completely?",
      "answer0": "49",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 229,
      "difficulty_id": 2,
      "explanation": "The box holds 5 × 4 × 3 = 60 unit cubes when full. There are already 11 cubes inside. More needed = 60 − 11 = 49.",
      "hints": ["Find the full capacity: length × width × height in cubes.", "Subtract the cubes already in the box."],
      "source": "Nan Hua 2022 P6 Prelim Q27",
      "image_needed": true,
      "image_options": false,
      "image_file": "q27.png",
      "image_page": 22,
      "image_bbox": [0.14, 0.56, 0.42, 0.74],
      "image_loc": "open rectangular box partly filled with unit cubes, lower-left of the page",
      "notes": "Key: 49 (60 capacity − 11 present). Figure required to count present cubes (11) and box dimensions (5x4x3)."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "In the figure, ABCD is a square. BCE is an equilateral triangle. Find \\(\\angle AEB\\).",
      "answer0": "75",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "Each angle of equilateral triangle BCE is 60°, so \\(\\angle EBC = 60°\\) and \\(\\angle ABE = 90° - 60° = 30°\\). Triangle ABE is isosceles (AB = BE), so \\(\\angle AEB = (180° - 30°) ÷ 2 = 75°\\).",
      "hints": ["Equilateral triangle angles are 60°, so find ∠ABE inside the square.", "AB = BC = BE makes triangle ABE isosceles; use base angles."],
      "source": "Nan Hua 2022 P6 Prelim Q28",
      "image_needed": true,
      "image_options": false,
      "image_file": "q28.png",
      "image_page": 23,
      "image_bbox": [0.22, 0.16, 0.56, 0.40],
      "image_loc": "square ABCD with equilateral triangle BCE inside; E near the left side, lines to A and C marked",
      "notes": "Key: 75 (°). Working on page 46: 90−60=30, (180−30)÷2=75. Answer in degrees."
    },
    {
      "n": 29,
      "type_id": 0,
      "question": "A triangle ABC is drawn on a square grid.<br>(a) Using triangle ABC, draw rhombus ABCD.<br>(b) Draw a triangle ACE such that area of ABC is \\(\\dfrac{1}{3}\\) of the area of ACE. Triangle ACE must not overlap with triangle ABC.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "(a) Add point D so that ABCD is a rhombus (D placed so all four sides equal and ABCD is a parallelogram). (b) Draw triangle ACE sharing base AC with three times the area of ABC, on the opposite side so it does not overlap. See the answer-key drawing on page 47.",
      "hints": ["For a rhombus, all four sides must be equal; place D opposite B.", "For 3× the area on the same base AC, the height of ACE must be 3× the height of ABC."],
      "source": "Nan Hua 2022 P6 Prelim Q29",
      "image_needed": true,
      "image_options": false,
      "image_file": "q29.png",
      "image_page": 24,
      "image_bbox": [0.24, 0.12, 0.66, 0.36],
      "image_loc": "square grid showing triangle ABC (A lower-left, B above A, C upper-right)",
      "notes": "Interactive drawing task — type_id 0, skipped on insert. Answer key drawing on page 47."
    },
    {
      "n": 30,
      "type_id": 2,
      "question": "The figure is made up of 3 identical squares, ABCD, BEFG and BHJK. \\(\\angle ABG=40°\\) and \\(\\angle HBE=30°\\). Find \\(\\angle KBC\\).",
      "answer0": "20",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "Each square has a 90° corner at B. \\(\\angle GBK = \\angle HBE = 30°\\) (matching angles between identical squares). \\(\\angle KBC = 90° - \\angle ABG - \\angle GBK = 90° - 40° - 30° = 20°\\).",
      "hints": ["The full corner angle of a square at B is 90°.", "Subtract the 40° and the 30° angles from 90° to find ∠KBC."],
      "source": "Nan Hua 2022 P6 Prelim Q30",
      "image_needed": true,
      "image_options": false,
      "image_file": "q30.png",
      "image_page": 25,
      "image_bbox": [0.14, 0.16, 0.66, 0.42],
      "image_loc": "three overlapping squares meeting at B, with 40° and 30° angles marked at B",
      "notes": "Key: 20 (°). Working on page 47: ∠GBK=∠HBE=30°, ∠KBC=90−40−30=20°. Answer in degrees."
    }
  ]
}