{
  "paper": {
    "school": "Nan Hua",
    "year": 2024,
    "level": "P6",
    "label": "Non-Weighted Assessment 2",
    "source_prefix": "Nan Hua 2024 P6 Non-Weighted Assessment 2",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "Which of the following is thirty-eight thousand and thirty in numerals?",
      "answer0": "3830",
      "answer1": "38 030",
      "answer2": "38 300",
      "answer3": "380 030",
      "correct_answer": 1,
      "skill_id": 2,
      "difficulty_id": 1,
      "explanation": "Thirty-eight thousand = 38 000; plus thirty = 38 030.",
      "hints": ["38 thousands means 38 000.", "Add 30 to 38 000."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: (2)"
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "What are the common factors of 18 and 81?",
      "answer0": "3 and 6",
      "answer1": "3 and 9",
      "answer2": "6 and 18",
      "answer3": "9 and 18",
      "correct_answer": 1,
      "skill_id": 2,
      "difficulty_id": 1,
      "explanation": "Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 81: 1, 3, 9, 27, 81. Common factors: 1, 3, 9. Among the options, 3 and 9.",
      "hints": ["List the factors of each number.", "Pick the numbers that divide both 18 and 81."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: (2)"
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "I am a multiple of 6 and a factor of 24. What number am I?",
      "answer0": "8",
      "answer1": "2",
      "answer2": "3",
      "answer3": "12",
      "correct_answer": 3,
      "skill_id": 2,
      "difficulty_id": 1,
      "explanation": "Multiples of 6: 6, 12, 18, 24, ... Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. The number that is both is 12 (also 6 and 24, but among options only 12 fits).",
      "hints": ["List multiples of 6.", "Which of those also divides 24 exactly?"],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: (4)"
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Arrange the following numbers from the largest to the smallest.<br>8.03, 8.3, 8",
      "answer0": "8, 8.03, 8.3",
      "answer1": "8.3, 8, 8.03",
      "answer2": "8.3, 8.03, 8",
      "answer3": "8.03, 8.3, 8",
      "correct_answer": 2,
      "skill_id": 2,
      "difficulty_id": 1,
      "explanation": "Compare: 8.3 > 8.03 > 8. So largest to smallest is 8.3, 8.03, 8.",
      "hints": ["Compare the tenths digit first.", "8.3 has 3 tenths; 8.03 has 0 tenths."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: (3). Options list order Largest/Smallest columns."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "$7 + \\dfrac{7}{10} + \\dfrac{7}{1000} =$ ____________ .",
      "answer0": "7.07",
      "answer1": "7.077",
      "answer2": "7.707",
      "answer3": "7.77",
      "correct_answer": 2,
      "skill_id": 2,
      "difficulty_id": 2,
      "explanation": "\\(\\dfrac{7}{10}=0.7\\), \\(\\dfrac{7}{1000}=0.007\\). So 7 + 0.7 + 0.007 = 7.707.",
      "hints": ["Convert each fraction to a decimal.", "Tenths go in the 1st place, thousandths in the 3rd place."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: (3)"
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "Express \\(8\\dfrac{3}{50}\\) as a decimal.",
      "answer0": "8.03",
      "answer1": "8.06",
      "answer2": "8.3",
      "answer3": "8.6",
      "correct_answer": 1,
      "skill_id": 2,
      "difficulty_id": 1,
      "explanation": "\\(\\dfrac{3}{50}=\\dfrac{6}{100}=0.06\\). So \\(8\\dfrac{3}{50}=8.06\\).",
      "hints": ["Make the denominator 100.", "3/50 = 6/100."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: (2)"
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "Which figure has only one line of symmetry?",
      "answer0": "Pac-man / quarter-cut circle",
      "answer1": "Wavy flag shape",
      "answer2": "Square (concentric squares)",
      "answer3": "Sun with rays",
      "correct_answer": 0,
      "skill_id": 6,
      "difficulty_id": 2,
      "explanation": "The pac-man / quarter-cut circle shape has exactly one line of symmetry. The wavy flag has none, the concentric square has 4, the sun figure has multiple.",
      "hints": ["A line of symmetry folds the figure onto itself.", "Count the fold lines for each shape."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Q7",
      "image_needed": true,
      "image_options": true,
      "image_file": null,
      "notes": "Key: (1). Image-option MCQ: crop each option shape to q7_opt0..3. Opt0=quarter-cut circle, opt1=wavy flag, opt2=nested square, opt3=sun. Page 4."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "Given that the base of triangle ABC is BC, find the height that is related to the base BC.",
      "answer0": "CE",
      "answer1": "AD",
      "answer2": "AC",
      "answer3": "AB",
      "correct_answer": 1,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "The height to base BC is the perpendicular distance from vertex A to the line containing BC. AD is perpendicular to BC extended, so AD is the height.",
      "hints": ["Height is perpendicular to the chosen base.", "Which segment is perpendicular to BC and reaches the opposite vertex A?"],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 4,
      "image_bbox": [0.30, 0.52, 0.85, 0.74],
      "image_loc": "triangle ABC with dashed CE and AD perpendiculars, right of the question text",
      "notes": "Key: (2)"
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "What is the missing number in the box?<br>\\(\\dfrac{8}{12}=\\dfrac{[\\,\\,]}{9}\\)",
      "answer0": "6",
      "answer1": "5",
      "answer2": "3",
      "answer3": "4",
      "correct_answer": 0,
      "skill_id": 2,
      "difficulty_id": 1,
      "explanation": "\\(\\dfrac{8}{12}=\\dfrac{2}{3}\\). To get denominator 9, multiply by 3: \\(\\dfrac{2\\times3}{3\\times3}=\\dfrac{6}{9}\\). Missing numerator = 6.",
      "hints": ["Simplify 8/12 first.", "Scale up so the denominator is 9."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: (1). Equivalent-fraction with a box numerator; rendered inline."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "Mary bought a pizza. She ate \\(\\dfrac{1}{4}\\) of the pizza and her brother ate \\(\\dfrac{1}{12}\\) of the pizza. What fraction of the pizza was left?",
      "answer0": "\\(\\dfrac{1}{6}\\)",
      "answer1": "\\(\\dfrac{1}{3}\\)",
      "answer2": "\\(\\dfrac{2}{3}\\)",
      "answer3": "\\(\\dfrac{3}{4}\\)",
      "correct_answer": 2,
      "skill_id": 206,
      "difficulty_id": 2,
      "explanation": "Eaten = \\(\\dfrac{1}{4}+\\dfrac{1}{12}=\\dfrac{3}{12}+\\dfrac{1}{12}=\\dfrac{4}{12}=\\dfrac{1}{3}\\). Left = \\(1-\\dfrac{1}{3}=\\dfrac{2}{3}\\).",
      "hints": ["Use a common denominator of 12.", "Subtract the total eaten from 1 whole."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: (3). Fraction answer -> MCQ."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "Ken used \\(\\dfrac{4}{7}\\) of his money to buy 8 donuts and 4 pies. The cost of 4 donuts was the same as that of 2 pies. What was the most number of pies that Ken could buy with the amount of money he had left?",
      "answer0": "8",
      "answer1": "2",
      "answer2": "6",
      "answer3": "4",
      "correct_answer": 2,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "4 donuts = 2 pies, so 1 donut = 0.5 pie. 8 donuts = 4 pies. So 8 donuts + 4 pies = 8 pies' worth, costing 4/7 of his money. So 8 pies = 4/7 of money, 1 pie = 1/14 of money. Money left = 3/7 = 6/14 of money = 6 pies.",
      "hints": ["Convert all donuts into equivalent pies.", "8 donuts + 4 pies = 8 pies cost 4/7 of his money.", "Find what 3/7 (the remainder) buys."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: (3)"
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "Zach kept his red and blue marbles in two boxes. The ratio of the number of red marbles to blue marbles in the first box was 1 : 5 and it was 1 : 2 in the second box. The two boxes contained the same number of marbles.<br>What fraction of Zach's marbles were red marbles?",
      "answer0": "\\(\\dfrac{2}{7}\\)",
      "answer1": "\\(\\dfrac{1}{3}\\)",
      "answer2": "\\(\\dfrac{1}{4}\\)",
      "answer3": "\\(\\dfrac{3}{4}\\)",
      "correct_answer": 2,
      "skill_id": 210,
      "difficulty_id": 3,
      "explanation": "Make each box total the same. Box 1 (1:5) has 6 parts; Box 2 (1:2) has 3 parts. LCM of totals = 6: Box1 = 6 units (red 1, blue 5); Box2 scaled to 6 units (red 2, blue 4). Total marbles = 12, red = 1 + 2 = 3. Fraction red = 3/12 = 1/4.",
      "hints": ["Equalise the two box totals.", "Scale the ratios so both boxes have the same number of marbles.", "Add the red parts over the grand total."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: (3)"
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "\\(\\dfrac{4}{9}\\) of the people at a carnival were adults and the rest were children. The number of boys was twice the number of girls. What was the ratio of the number of boys to the number of adults?",
      "answer0": "1 : 2",
      "answer1": "2 : 1",
      "answer2": "6 : 5",
      "answer3": "5 : 6",
      "correct_answer": 3,
      "skill_id": 210,
      "difficulty_id": 3,
      "explanation": "Adults = 4/9, children = 5/9. Take total 9 units: adults 4, children 5. Boys : girls = 2 : 1, so boys = 2/3 of children = 2/3 x 5 = 10/3 units. Boys : adults = (10/3) : 4 = 10 : 12 = 5 : 6.",
      "hints": ["Split into adults 4/9 and children 5/9.", "Boys are 2/3 of the children.", "Form the ratio boys : adults and simplify."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: (4)"
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "Container A has 200 markers with 6% blue. Container B has 400 markers with 12% blue. What percentage of the total number of markers in container A and B are blue?",
      "answer0": "6%",
      "answer1": "10%",
      "answer2": "12%",
      "answer3": "18%",
      "correct_answer": 1,
      "skill_id": 209,
      "difficulty_id": 2,
      "explanation": "Blue in A = 6% of 200 = 12. Blue in B = 12% of 400 = 48. Total blue = 60 out of 600 markers. 60/600 = 10%.",
      "hints": ["Find the actual number of blue markers in each container.", "Total blue / total markers x 100%."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: (2). Table data transcribed into stem (no figure needed)."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "The figure shows part of a circle of radius 8 cm. Find the perimeter of the figure. Leave your answer in terms of \\(\\pi\\).",
      "answer0": "\\((6\\pi+16)\\) cm",
      "answer1": "\\((12\\pi+16)\\) cm",
      "answer2": "\\((16\\pi+16)\\) cm",
      "answer3": "\\((48\\pi+16)\\) cm",
      "correct_answer": 1,
      "skill_id": 221,
      "difficulty_id": 3,
      "explanation": "Figure is a three-quarter circle (radius 8). Arc = 3/4 of circumference = 3/4 x 2 x pi x 8 = 12pi. Two radii bound the missing quarter: 8 + 8 = 16. Perimeter = (12pi + 16) cm.",
      "hints": ["The shape is 3/4 of a full circle.", "Arc length = 3/4 of the circumference.", "Add the two straight radii (8 + 8)."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q15.png",
      "image_page": 7,
      "image_bbox": [0.33, 0.46, 0.66, 0.62],
      "image_loc": "three-quarter circle with right-angle marker and an 8 cm radius arrow, centre of page",
      "notes": "Key: (2)"
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Find the value of \\(7.5\\div30\\). [?]",
      "answer0": "0.25",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 2,
      "difficulty_id": 1,
      "explanation": "7.5 ÷ 30 = 7.5 ÷ 10 ÷ 3 = 0.75 ÷ 3 = 0.25.",
      "hints": ["Divide by 10 first, then by 3.", "0.75 ÷ 3 = 0.25."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 0.25 (decimal -> FIB)."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "Write down the common multiple of 6 and 8 that is smaller than 40. [?]",
      "answer0": "24",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 2,
      "difficulty_id": 1,
      "explanation": "Multiples of 6: 6, 12, 18, 24, ... Multiples of 8: 8, 16, 24, ... Common multiple below 40 is 24.",
      "hints": ["The LCM of 6 and 8 is 24.", "List multiples of each and find the shared one under 40."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 24 (integer -> FIB)."
    },
    {
      "n": 18,
      "type_id": 1,
      "question": "Find the value of \\(12\\times\\dfrac{8}{9}\\). Leave your answer as a mixed number in its simplest form.",
      "answer0": "\\(10\\dfrac{2}{3}\\)",
      "answer1": "\\(10\\dfrac{6}{9}\\)",
      "answer2": "\\(9\\dfrac{2}{3}\\)",
      "answer3": "\\(\\dfrac{96}{9}\\)",
      "correct_answer": 0,
      "skill_id": 206,
      "difficulty_id": 2,
      "explanation": "\\(12\\times\\dfrac{8}{9}=\\dfrac{96}{9}=\\dfrac{32}{3}=10\\dfrac{2}{3}\\).",
      "hints": ["Multiply 12 by the numerator, keep denominator 9.", "Convert 96/9 to a mixed number and simplify."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 10 2/3. Mixed-number answer -> MCQ."
    },
    {
      "n": 19,
      "type_id": 1,
      "question": "Find the value of \\(\\dfrac{3}{4}\\div12\\). Leave your answer in its simplest form.",
      "answer0": "\\(\\dfrac{1}{16}\\)",
      "answer1": "\\(\\dfrac{1}{9}\\)",
      "answer2": "9",
      "answer3": "\\(\\dfrac{3}{48}\\)",
      "correct_answer": 0,
      "skill_id": 206,
      "difficulty_id": 2,
      "explanation": "\\(\\dfrac{3}{4}\\div12=\\dfrac{3}{4}\\times\\dfrac{1}{12}=\\dfrac{3}{48}=\\dfrac{1}{16}\\).",
      "hints": ["Dividing by 12 = multiplying by 1/12.", "Simplify 3/48."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Q19",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 1/16. Fraction answer -> MCQ."
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "Find the value of \\(22-12\\div(4+2)\\times4\\). [?]",
      "answer0": "14",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 2,
      "difficulty_id": 2,
      "explanation": "Brackets first: 4 + 2 = 6. Then 12 ÷ 6 = 2; 2 x 4 = 8. Finally 22 - 8 = 14.",
      "hints": ["Do the brackets first.", "Division and multiplication left to right, then subtract."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Q20",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 14 (integer -> FIB)."
    },
    {
      "n": 21,
      "type_id": 0,
      "question": "Using the line AB provided, construct \\(\\angle BAC = 80^\\circ\\).",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 201,
      "difficulty_id": 2,
      "explanation": "Using a protractor, place the centre at A on line AB, measure 80 degrees from AB, and draw ray AC. Answer key shows the constructed 80 degrees angle at A.",
      "hints": [],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Construction/drawing task — no app question type. Answer: draw 80 deg angle BAC at A. type_id 0, skipped on insert."
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "The solid is made of 1-cm cubes. What is the volume of the solid? [?] cm³",
      "answer0": "9",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 190,
      "difficulty_id": 2,
      "explanation": "Each cube is 1 cm³. Counting the cubes in the solid gives 9 cubes, so volume = 9 x 1 = 9 cm³.",
      "hints": ["Each small cube is 1 cm³.", "Count all the cubes, including hidden ones."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Q22",
      "image_needed": true,
      "image_options": false,
      "image_file": "q22.png",
      "image_page": 12,
      "image_bbox": [0.34, 0.40, 0.52, 0.52],
      "image_loc": "stacked 1-cm unit-cube solid below the question text",
      "notes": "Key: 9 cm³ (count of cubes = 9). Answer unit cm³ in stem."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "6000 ml of juice was poured into 8 identical bottles equally. How much juice was there in one bottle? [?] ml",
      "answer0": "750",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 192,
      "difficulty_id": 1,
      "explanation": "6000 ml ÷ 8 = 750 ml per bottle. (Key writes 6000 ml = 6 L; 6 L ÷ 8 = 0.75 L = 750 ml.)",
      "hints": ["Divide the total volume by the number of bottles.", "6000 ÷ 8 = 750."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Q23",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 0.75 L = 750 ml. Used ml so answer is integer 750."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "The grid squares are 1 cm by 1 cm.<br>(a) What is the area of triangle BEF? [?] cm²<br>(b) Which triangle has an area twice the area of triangle BEF? Triangle [?]",
      "answer0": "4",
      "answer1": "BCF",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "(a) Triangle BEF: base EF = 2 cm, height = 4 cm. Area = 1/2 x 2 x 4 = 4 cm². (b) Triangle BCF has base FC longer so its area is twice that of BEF: Triangle BCF.",
      "hints": ["Area of triangle = 1/2 x base x height.", "Use the grid to read off base EF and the height.", "(b) Look for a triangle on the same height with double the base."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Q24",
      "image_needed": true,
      "image_options": false,
      "image_file": "q24.png",
      "image_page": 13,
      "image_bbox": [0.38, 0.05, 0.62, 0.22],
      "image_loc": "square grid with points A B at top and F E D C at bottom, lines from B",
      "notes": "Key: (a) 4 cm² (b) Triangle BCF. answer1 is a letter label (triangle name); kept as FIB per the printed single-word answer."
    },
    {
      "n": 25,
      "type_id": 0,
      "question": "The figure is made up of identical squares and identical triangles. Shade 4 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": 6,
      "difficulty_id": 2,
      "explanation": "Reflect the already-shaded cells across the vertical line AB and shade the 4 missing mirror-image squares so the whole figure is symmetric about AB. Answer key shows the completed symmetric shading.",
      "hints": [],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Q25",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Shade-to-complete-symmetry task — interactive, no app type. type_id 0, skipped on insert."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "The figure is made up of an equilateral triangle ABC and a right-angled triangle CDE. ACE and BCD are straight lines. \\(\\angle ABC = 60^\\circ\\) and the right angle is at E. Find \\(\\angle CDE\\). [?]°",
      "answer0": "30",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 2,
      "explanation": "In equilateral triangle ABC each angle = 60 degrees, so angle ACB = 60. angle DCE is vertically opposite angle ACB = 60. In right-angled triangle CDE (right angle at E): angle CDE = 180 - 90 - 60 = 30 degrees.",
      "hints": ["Each angle of an equilateral triangle is 60 degrees.", "angle DCE equals angle ACB (vertically opposite).", "Angle sum of triangle CDE is 180 degrees."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Q26",
      "image_needed": true,
      "image_options": false,
      "image_file": "q26.png",
      "image_page": 14,
      "image_bbox": [0.20, 0.10, 0.78, 0.33],
      "image_loc": "equilateral triangle ABC joined to right-angled triangle CDE, lines ACE and BCD",
      "notes": "Key: angle CDE = 180 - 90 - 60 = 30°. Answer unit deg in stem."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "Ivan started revising for a test at 8.05 a.m. while Kevin started 10 minutes later. Ivan completed 25 minutes earlier than Kevin who completed it at 9.20 a.m. How much more time did Kevin spend on his revision than Ivan? [?] min",
      "answer0": "15",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 204,
      "difficulty_id": 2,
      "explanation": "Ivan: 8.05 a.m. to (9.20 - 25 min) = 8.55 a.m., duration 50 min. Kevin: started 8.15 a.m., ended 9.20 a.m., duration 65 min. Difference = 65 - 50 = 15 min.",
      "hints": ["Find each person's start and end time.", "Ivan ended 25 minutes before Kevin's 9.20 a.m.", "Subtract the two durations."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Q27",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 15 min. Time-duration word problem -> integer FIB."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "A pattern is formed using the letters A, B and N: A, B, A, N, A, A, B, A, N, A, A, B, A, N, A, ... The letter A appears 23 times in the pattern. What is the greatest possible number of letters in the pattern? [?]",
      "answer0": "39",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 6,
      "difficulty_id": 3,
      "explanation": "The repeating block of 5 letters (A,B,A,N,A) contains 3 A's. 23 ÷ 3 = 7 remainder 2, so 7 complete blocks use 21 A's (35 letters), and 2 more A's appear in the next block. The greatest possible length keeps the most non-A letters before the 23rd A: 35 + 4 = 39 letters.",
      "hints": ["Each block of 5 letters has 3 A's.", "23 = 3 x 7 + 2.", "Take 7 full blocks (35 letters) then add up to 4 more to reach the 23rd A."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Q28",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 23÷3 = 7 R2; 7x5 = 35; 35 + 4 = 39. Pattern transcribed into stem."
    },
    {
      "n": 29,
      "type_id": 0,
      "question": "A rectangle Y is drawn by joining dots on the square grid with four straight lines. Lines must meet at the dots in the given grid. Draw a rectangle, with the same area as Y, that gives the largest possible perimeter. Label the rectangle R.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 223,
      "difficulty_id": 3,
      "explanation": "Rectangle Y has a fixed area. The largest perimeter for the same area on the grid is the longest, thinnest rectangle (1 unit wide x area-units long). Draw a 1-by-(area) rectangle on the grid and label it R. Answer key shows R drawn as a long thin rectangle of the same area.",
      "hints": [],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Q29",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Draw-on-grid task — interactive, no app type. type_id 0, skipped on insert."
    },
    {
      "n": 30,
      "type_id": 0,
      "question": "ABCD is a rhombus and triangle CDE is an isosceles triangle. \\(\\angle BCE = 145^\\circ\\). For each statement, indicate True, False, or Not possible to tell: (i) \\(\\angle BAD + \\angle DEC = 145^\\circ\\); (ii) \\(\\angle ABC = 125^\\circ\\).",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 200,
      "difficulty_id": 3,
      "explanation": "Angles around: in quadrilateral-plus-triangle, 360 + 180 = 540; 540 - 145 - 145 = 250 = angle ABC + angle ADC + angle DEC. (i) Cannot be determined / depends; (ii) Since angle ABC = angle ADC in the rhombus, angle ABC cannot be 125 (False). Answer key reasons angle ABC cannot be 125 deg.",
      "hints": [],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Q30",
      "image_needed": true,
      "image_options": false,
      "image_file": "q30.png",
      "image_page": 16,
      "image_bbox": [0.22, 0.10, 0.70, 0.28],
      "image_loc": "rhombus ABCD with isosceles triangle CDE attached at side DC, angle 145 at C",
      "notes": "True/False/Not-possible tick-table — interactive, no app type. type_id 0, skipped on insert. Key reasoning: 540-145-145=250; angle ABC cannot be 125 deg."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "The rate for parcel postage at a post office is: not over 100 g = $2.50; not over 250 g = $3.90; not over 500 g = $5.20; every additional 100 g = $1. Alice posted a parcel that weighed 660 g. How much did she pay for the postage? [?]",
      "answer0": "7.20",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 22,
      "difficulty_id": 2,
      "explanation": "660 g = first 500 g ($5.20) + 160 g above 500 g. 160 g counts as 2 additional 100-g steps = 2 x $1 = $2. Total = $5.20 + $2 = $7.20.",
      "hints": ["First 500 g costs $5.20.", "Each extra 100 g (or part) costs $1.", "160 g over = 2 steps = $2."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Paper 2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q1. Key: $7.20. Money answer -> FIB (7.20). Table data transcribed into stem."
    },
    {
      "n": 32,
      "type_id": 2,
      "question": "The box is filled with some 1-cm cubes. The box is a cube. What is the volume of the box? [?] cm³",
      "answer0": "125",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 190,
      "difficulty_id": 2,
      "explanation": "The bottom row shows 5 cubes along one edge, so each edge = 5 cm. Volume of cube = 5 x 5 x 5 = 125 cm³.",
      "hints": ["The base edge is 5 cubes long.", "Volume of a cube = side x side x side."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Paper 2 Q2",
      "image_needed": true,
      "image_options": false,
      "image_file": "q32.png",
      "image_page": 18,
      "image_bbox": [0.20, 0.62, 0.45, 0.84],
      "image_loc": "outline cube with a row of 1-cm cubes along the bottom front edge",
      "notes": "Paper 2 Q2. Key: 125 cm³. Answer unit cm³ in stem."
    },
    {
      "n": 33,
      "type_id": 0,
      "question": "The line graph shows the amount of money Siti had in her bank on the last day of every month (Jan to Jun). Every month, Siti tried to deposit some money into the bank without making any withdrawal.<br>(a) In which month did she not make any deposit?<br>(b) In which month did she deposit the most amount of money?",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 461,
      "difficulty_id": 2,
      "explanation": "(a) The month where the graph is flat (no increase) is the month with no deposit: April. (b) The steepest upward segment is the largest deposit: March. Answer key: (a) April, (b) March.",
      "hints": [],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Paper 2 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q33.png",
      "image_page": 19,
      "image_bbox": [0.22, 0.13, 0.72, 0.42],
      "image_loc": "line graph of amount of money ($) vs month Jan-Jun",
      "notes": "Paper 2 Q3. Answers are month names (word answers) for a two-part graph-reading question. Set type_id 0 (word answers, would need two separate MCQs); answers (a) April (b) March. Skipped on insert."
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "The average mass of 3 girls is 28 kg. A fourth girl joined the group and the average mass becomes 29 kg. What is the mass of the fourth girl? [?] kg",
      "answer0": "32",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 205,
      "difficulty_id": 2,
      "explanation": "Total of 3 girls = 28 x 3 = 84 kg. Total of 4 girls = 29 x 4 = 116 kg. Fourth girl = 116 - 84 = 32 kg.",
      "hints": ["Total = average x number of items.", "Find both totals and subtract."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Paper 2 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q4. Key: 32 kg. Answer unit kg in stem."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "In the figure, AB, CD and EF are straight lines. \\(\\angle AOC = 60^\\circ\\). \\(\\angle BOE\\) is twice of \\(\\angle FOD\\). What is \\(\\angle FOD\\)? [?]°",
      "answer0": "40",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 194,
      "difficulty_id": 3,
      "explanation": "angle FOD = angle COE (vertically opposite). angle BOE = 2 x angle FOD. On straight line through O: angle AOC + angle COE + angle BOE = 180. So 60 + angle COE + 2(angle COE) = 180 -> 3 x angle COE = 120 -> angle COE = 40. Therefore angle FOD = 40 degrees.",
      "hints": ["angle FOD and angle COE are vertically opposite (equal).", "angle AOC + angle COE + angle BOE = 180 deg (straight line).", "Let angle FOD = x and solve 60 + x + 2x = 180."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Paper 2 Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q35.png",
      "image_page": 20,
      "image_bbox": [0.18, 0.45, 0.62, 0.78],
      "image_loc": "three straight lines AB, CD, EF crossing at point O with 60 deg marked",
      "notes": "Paper 2 Q5. Key: 40°. Answer unit deg in stem."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "Bala had some muffins for sale. In the morning, he sold \\(\\dfrac{1}{3}\\) of the muffins. In the afternoon, he sold \\(\\dfrac{2}{5}\\) of the remaining muffins. After that, there were 42 muffins left. How many muffins did Bala have at first? [?]",
      "answer0": "105",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Afternoon sold = 2/5 of remaining 2/3 = 2/5 x 2/3 = 4/15. Fraction left = 1 - 1/3 - 4/15 = 5/15 - ... = 1 - 5/15 - 4/15 = 6/15. So 6/15 of total = 42 muffins -> 1/15 = 7 -> total = 15 x 7 = 105 muffins.",
      "hints": ["After morning, 2/3 remain.", "Afternoon sold 2/5 x 2/3 = 4/15 of the original.", "The 42 left equal 6/15 of the original."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Paper 2 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q6. Key: 105 muffins."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "Ivan and Helen shared a sum of money in the ratio of 3 : 2. When Ivan gave $21 to Helen, the ratio of Ivan's amount of money to Helen's amount of money became 2 : 13. How much money did Ivan have at first? [?]",
      "answer0": "27",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "Total stays constant. Before 3 : 2 = 9 : 6 (total 15). After 2 : 13 (total 15). So Ivan went from 9 units to 2 units, a drop of 7 units = $21, so 1 unit = $3. Ivan at first = 9 units = $27.",
      "hints": ["The total amount does not change.", "Make both ratios have the same total (15).", "Ivan's drop of 7 units equals $21."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Paper 2 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q7. Key: $27."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "Karen paid $54 for 15 cupcakes after a 25% discount. How many cupcakes could she have bought with the same amount of money without the discount? [?]",
      "answer0": "11",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "$54 is 75% of the original price of 15 cupcakes, so original price = 54 ÷ 0.75 = $72 for 15 cupcakes; 1 cupcake = $72 ÷ 15 = $4.80. Without discount, $54 ÷ $4.80 = 11.25, so she could buy 11 cupcakes.",
      "hints": ["$54 is 75% of the full price of 15 cupcakes.", "Full price of 15 = $72, so 1 cupcake = $4.80.", "$54 ÷ $4.80 = 11.25, round down to 11."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Paper 2 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q8. Key: 11 cupcakes."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "The bar graph shows the number of visitors to an art gallery (Mon to Fri).<br>(a) There were 56 more visitors on Monday than Tuesday. How many visitors were there at the art gallery on Monday? [?]<br>(b) The average number of visitors from Wednesday to Friday was 75. There were more visitors on Wednesday than on Thursday. Given that the difference between the number of visitors on Wednesday and Thursday was the smallest possible number, what was the number of visitors on Thursday? [?]",
      "answer0": "124",
      "answer1": "52",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 461,
      "difficulty_id": 3,
      "explanation": "(a) From the graph Tuesday is read off; Monday = Tuesday + 56 = 124. (Key: 56 ÷ 14 scaling gives Monday = 4 x 31 = 124.) (b) Wed+Thu+Fri = 75 x 3 = 225. Friday = 120 (from graph). Wed + Thu = 105. With Wed > Thu and smallest difference, Wed = 53, Thu = 52. Number on Thursday = 52.",
      "hints": ["(a) Monday = Tuesday's bar + 56.", "(b) Total Wed-Fri = 75 x 3 = 225; subtract Friday.", "Split the remainder into two near-equal numbers with Wed larger."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Paper 2 Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q39.png",
      "image_page": 23,
      "image_bbox": [0.20, 0.06, 0.62, 0.30],
      "image_loc": "bar graph number of visitors Mon-Fri to an art gallery",
      "notes": "Paper 2 Q9. Key: (a) 124, (b) 52. Two integer FIB blanks. Graph values needed from figure (Fri=120 per key working)."
    },
    {
      "n": 40,
      "type_id": 0,
      "question": "The bar graph shows the sales of four food items at a fun fair (Burgers $240, Hot dogs $225, Chicken pies $300, Waffles $300). Prices: Burger $5, Hot dog $3, Chicken pie $4, Waffles $3.<br>(a) Find the number of hot dogs sold.<br>(b) The total number sold for two of the food items was the same. Which were the two food items?",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 461,
      "difficulty_id": 3,
      "explanation": "(a) Hot dogs = $225 ÷ $3 = 75. (b) Burgers = 240÷5 = 48; Hot dogs = 75; Chicken pies = 300÷4 = 75; Waffles = 300÷3 = 100. Chicken pie (75) and hot dog (75) sold the same number. Answer key: (a) 75; (b) chicken pie and hot dog.",
      "hints": [],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Paper 2 Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q40.png",
      "image_page": 24,
      "image_bbox": [0.18, 0.05, 0.66, 0.30],
      "image_loc": "bar graph sales collected ($) for Burgers, Hot dogs, Chicken pies, Waffles",
      "notes": "Paper 2 Q10. (a) is integer 75 but (b) answer is two food-item names (word answers). Whole question set type_id 0 (mixed numeric + word two-item answer); answers (a) 75 (b) chicken pie and hot dog. Skipped on insert."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "Tom had a square piece of paper with an area of 64 cm². He cut out one quarter circle and three identical semicircles from it. The quarter circle had the same radius as each semicircle. (Take \\(\\pi = 3.14\\))<br>(a) What is the radius of the quarter circle? [?] cm<br>(b) What is the area of the remaining piece of paper? [?] cm²",
      "answer0": "2",
      "answer1": "42.02",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 222,
      "difficulty_id": 3,
      "explanation": "(a) Square area 64 cm² so side = 8 cm. Along one side there are 4 radii (quarter + semicircles spanning the side): radius = 8 ÷ 4 = 2 cm. (b) One quarter circle + three semicircles = 1/4 + 3/2 = 1.75 full circles of radius 2. Area cut out = 1.75 x 3.14 x 2 x 2 = 21.98 cm². Remaining = 64 - 21.98 = 42.02 cm².",
      "hints": ["Side of square = sqrt(64) = 8 cm.", "Four radii fit along a side, so radius = 8 ÷ 4 = 2 cm.", "Cut area = (1/4 + 3 x 1/2) circles = 1.75 circles of radius 2."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Paper 2 Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q41.png",
      "image_page": 25,
      "image_bbox": [0.28, 0.13, 0.66, 0.43],
      "image_loc": "tilted square with a quarter circle and three semicircles cut from its edges",
      "notes": "Paper 2 Q11. Key: (a) 2 cm, (b) 42.02 cm². Both decimal/integer -> FIB."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "Pop-its cost $4.50 for one set of 4 pop-its. Unicorn soft toys cost $18 for a set of 5 soft toys. The items are sold only in sets.<br>(a) If Ms Chou wants to buy 18 pop-its and 22 unicorn soft toys, what is the least amount of money that she needs to spend on both items? $[?]<br>(b) She is given a 10% discount for all the items bought. How much will she pay? $[?]",
      "answer0": "112.50",
      "answer1": "101.25",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 208,
      "difficulty_id": 3,
      "explanation": "(a) Pop-its: 18 ÷ 4 = 4.5 -> need 5 sets = 5 x $4.50 = $22.50. Unicorns: 22 ÷ 5 = 4.4 -> need 5 sets = 5 x $18 = $90. Total = $22.50 + $90 = $112.50. (b) With 10% discount, pay 90% x $112.50 = $101.25.",
      "hints": ["Items sold only in whole sets — round the number of sets up.", "5 pop-it sets + 5 unicorn sets.", "10% discount means pay 90% of the total."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Paper 2 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q12. Key: (a) $112.50, (b) $101.25. Money -> FIB. Set images are decorative (prices in stem), no figure needed."
    },
    {
      "n": 43,
      "type_id": 0,
      "question": "A, B, C, D, E, F, G are points on the square grid. North is straight up.<br>(a)(i) Which one of the points is south-east of point B?<br>(a)(ii) Which direction is Point B from Point D?<br>(b) Gabriel stands at a point facing Point E. He makes a 135°-turn anti-clockwise and faces Point A. Which Point is he standing on?",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 6,
      "difficulty_id": 3,
      "explanation": "(a)(i) South-east of B is the point below and to the right: G. (a)(ii) From D, point B is directly to the left, i.e. West. (b) Facing E then turning 135 deg anti-clockwise to face A places Gabriel at point G. Answer key: (a)(i) F (a)(ii) West (b) G. (Note: key states (i) F.)",
      "hints": [],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Paper 2 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q43.png",
      "image_page": 27,
      "image_bbox": [0.22, 0.06, 0.62, 0.34],
      "image_loc": "square grid with labelled points A B C D E F G and a North arrow",
      "notes": "Paper 2 Q13. Direction/compass + point-label word answers — interactive/word, no app type. type_id 0. Answer key: (a)(i) F, (a)(ii) West, (b) G. Skipped on insert."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "ABCD is a square. BFE and AFC are straight lines. BC = BE and \\(\\angle EAF = 18^\\circ\\).<br>(a) Find \\(\\angle ABE\\). [?]°<br>(b) Find \\(\\angle BEC\\). [?]°",
      "answer0": "54",
      "answer1": "72",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "(a) AFC is a diagonal of the square so angle BAC = 45 deg; angle EAF = 18 deg. In triangle ABE-related working, angle ABE = 180 - 2(45 + 18) = 180 - 126 = 54 deg. (b) angle EBC = 90 - 54 = 36 deg. Triangle BEC is isosceles (BC = BE), so angle BEC = (180 - 36) ÷ 2 = 72 deg.",
      "hints": ["The diagonal AC makes a 45 deg angle at A.", "(a) angle ABE = 180 - 2(45 + 18).", "(b) Triangle BEC is isosceles with BC = BE; use angle EBC = 90 - 54."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Paper 2 Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q44.png",
      "image_page": 28,
      "image_bbox": [0.34, 0.08, 0.66, 0.25],
      "image_loc": "square ABCD with diagonals/lines BFE and AFC meeting at F, point E inside",
      "notes": "Paper 2 Q14. Key: (a) 54°, (b) 72°. Two integer FIB blanks (degrees)."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "Peter and John were paid a total of $3390 for the work they did. Peter was paid $1830 more than John.<br>(a) How much was Peter paid? $[?]<br>(b) Peter and John were paid based on the number of days they worked. Peter worked 3 times as many days as John. Peter was paid $5 more than John per day. How many days did Peter work? [?]",
      "answer0": "2610",
      "answer1": "54",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 3,
      "explanation": "(a) (3390 - 1830) ÷ 2 = 1560 ÷ 2 = 780 = John; Peter = 780 + 1830 = $2610. (b) John = $780, Peter = $2610. Peter worked 3x John's days. If John's daily rate is r, John days d, John pay = rd = 780. Peter days = 3d, Peter rate = r+5, Peter pay = 3d(r+5) = 2610. Using key method: had they been paid the same per day, Peter would get 780 x 3 = $2340; the extra $5/day over 3d days gives 2610 - 2340 = $270; $270 ÷ $5 = 54 = Peter's days.",
      "hints": ["(a) Difference method: (total - difference) ÷ 2 = John's share.", "(b) At equal pay-rate Peter would earn 3 x John = $2340.", "The extra $270 comes from $5 per day over Peter's days: 270 ÷ 5 = 54."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Paper 2 Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q15. Key: (a) $2610, (b) 54 days. Two FIB blanks."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "In the figure, QM is the arc of a quarter circle, MNP is a triangle and MN is perpendicular to SN. SN = 7 cm and MN = 19 cm. (Take \\(\\pi = \\dfrac{22}{7}\\))<br>(a) Find the total area of the shaded parts. [?] cm²<br>(b) The perimeter of the unshaded triangle is 43.5 cm. Find the perimeter of the shaded parts. [?] cm",
      "answer0": "56",
      "answer1": "54.5",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 222,
      "difficulty_id": 3,
      "explanation": "(a) Total shaded = rectangle + quarter circle - unshaded triangle. Rectangle = 12 x 7 = 84 (MN split: 19 - 7 = 12 for the rectangle height). Quarter circle (radius 7) = 1/4 x 22/7 x 7 x 7 = 38.5. Total = 84 + 38.5 = 122.5. Unshaded triangle = 1/2 x 19 x 7 = 66.5. Shaded = 122.5 - 66.5 = 56 cm². (b) Arc (quarter, radius 7) = 1/4 x 22/7 x 14 = 11; plus 12 + 7 (straight sides) + (43.5 - 19) = shaded perimeter = 11 + 12 + 7 + 24.5 = 54.5 cm.",
      "hints": ["Shaded area = rectangle + quarter circle - unshaded triangle.", "Quarter-circle radius is 7 cm; use pi = 22/7.", "(b) Arc = 1/4 x circumference; add the relevant straight edges."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Paper 2 Q16",
      "image_needed": true,
      "image_options": false,
      "image_file": "q46.png",
      "image_page": 30,
      "image_bbox": [0.10, 0.10, 0.45, 0.36],
      "image_loc": "quarter-circle arc QM with triangle MNP, SN = 7 cm and MN = 19 cm marked",
      "notes": "Paper 2 Q16. Key: (a) 56 cm², (b) 54.5 cm. Two FIB blanks."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "The charges for water consumption are: Up to 40 m³ = 117 cents per m³; Above 40 m³ = 140 cents per m³.<br>(a) John's family used 32 m³ of water in March. How much did his family pay? $[?]<br>(b) Simon's family spent $66.40 on water consumption in April. How much water did his family use? Give your answer in m³. [?] m³",
      "answer0": "37.44",
      "answer1": "54",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 22,
      "difficulty_id": 3,
      "explanation": "(a) 32 m³ is within the first 40 m³, so charge = $1.17 x 32 = $37.44. (b) First 40 m³ cost $1.17 x 40 = $46.80. Remaining $66.40 - $46.80 = $19.60 charged at $1.40/m³ -> 19.60 ÷ 1.40 = 14 m³. Total water = 40 + 14 = 54 m³.",
      "hints": ["117 cents = $1.17 per m³ for the first 40 m³.", "(b) Subtract the cost of the first 40 m³, then divide the rest by $1.40.", "Add the 40 m³ back to the extra m³."],
      "source": "Nan Hua 2024 P6 Non-Weighted Assessment 2 Paper 2 Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q17. Key: (a) $37.44, (b) 54 m³. Two FIB blanks (money + integer m³). Table data transcribed into stem."
    }
  ]
}