{
  "paper": {
    "school": "Nan Hua",
    "year": 2022,
    "level": "P5",
    "label": "Semestral Assessment 2",
    "source_prefix": "Nan Hua 2022 P5 Semestral Assessment 2",
    "has_answer_key": true,
    "notes": "The .url labels this SA2; the paper itself is printed as 'End of Year Examination 2022'. Following the specified source_prefix. Paper 1 = Q1-30 (MCQ Q1-15, FIB/short Q16-30), Paper 2 = Q1-17. To keep unique sequential ids, n runs 1-47; source uses the paper-faithful label (P1/P2) per question."
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "In 527.196, which digit is in the hundredths place?",
      "answer0": "1",
      "answer1": "5",
      "answer2": "6",
      "answer3": "9",
      "correct_answer": 3,
      "skill_id": 166,
      "difficulty_id": 1,
      "explanation": "Place values after the decimal: tenths (1), hundredths (9), thousandths (6). So the hundredths digit is 9. Answer: 9.",
      "hints": ["The first digit after the decimal point is tenths.", "The second digit after the decimal point is hundredths."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P1 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: option (4) = 9."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Find the value of $3 + 4 \\times 12 - 8$.",
      "answer0": "19",
      "answer1": "28",
      "answer2": "43",
      "answer3": "76",
      "correct_answer": 2,
      "skill_id": 155,
      "difficulty_id": 1,
      "explanation": "Order of operations: multiply first. $4 \\times 12 = 48$. Then $3 + 48 - 8 = 43$. Answer: 43.",
      "hints": ["Do multiplication before addition and subtraction.", "$4 \\times 12 = 48$."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P1 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: option (3) = 43."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "200 students went to a concert. 120 of the students are male. What is the ratio of the number of female students to the number of male students?",
      "answer0": "2 : 3",
      "answer1": "2 : 5",
      "answer2": "3 : 2",
      "answer3": "5 : 3",
      "correct_answer": 0,
      "skill_id": 179,
      "difficulty_id": 1,
      "explanation": "Female = 200 - 120 = 80. Ratio female : male = 80 : 120 = 2 : 3. Answer: 2 : 3.",
      "hints": ["Number of female = total - male.", "Simplify the ratio by dividing both parts by 40."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P1 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: option (1) = 2 : 3."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Find the value of $0.015 \\times 4000$.",
      "answer0": "0.6",
      "answer1": "6",
      "answer2": "60",
      "answer3": "600",
      "correct_answer": 2,
      "skill_id": 166,
      "difficulty_id": 1,
      "explanation": "$0.015 \\times 4000 = 0.015 \\times 4 \\times 1000 = 0.06 \\times 1000 = 60$. Answer: 60.",
      "hints": ["$0.015 \\times 4 = 0.06$.", "Then multiply by 1000."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P1 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: option (3) = 60."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "A picture is drawn on a square grid. What percentage of the square grid is not shaded?",
      "answer0": "8%",
      "answer1": "17%",
      "answer2": "32%",
      "answer3": "68%",
      "correct_answer": 3,
      "skill_id": 171,
      "difficulty_id": 2,
      "explanation": "The 5-by-5 grid has 25 squares. The shaded picture (triangle + stem) covers 8 squares' worth of area, so 25 - 8 = 17 squares are unshaded? The printed key gives (4) 68%. Of the 25 squares, the shaded area equals 8 squares, leaving 17 squares (68%) unshaded. $17 \\div 25 = 0.68 = 68\\%$. Answer: 68%.",
      "hints": ["Count the unshaded area in whole and half squares.", "Express the unshaded squares as a fraction of 25, then convert to a percentage."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P1 Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q5.png",
      "image_page": 3,
      "image_bbox": [0.22, 0.33, 0.55, 0.60],
      "image_loc": "5x5 square grid with shaded triangle and rectangular stem (arrow-like figure), below the question",
      "notes": "Key: option (4) = 68%. Figure required to count shaded vs unshaded squares."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "Bala receives a weekly allowance of $60. He saves $12 each week. What percentage of Bala's allowance did he spend?",
      "answer0": "12%",
      "answer1": "20%",
      "answer2": "48%",
      "answer3": "80%",
      "correct_answer": 3,
      "skill_id": 175,
      "difficulty_id": 1,
      "explanation": "He spends $60 - $12 = $48. Percentage spent = $48 \\div 60 \\times 100\\% = 80\\%$. Answer: 80%.",
      "hints": ["Amount spent = allowance - savings.", "Percentage = spent / allowance x 100%."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P1 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: option (4) = 80%."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "Mr Tan drove for 4h 35min and reached Malacca at 02 45. What time did Mr Tan start driving?",
      "answer0": "6.20 a.m.",
      "answer1": "6.20 p.m.",
      "answer2": "10.10 a.m.",
      "answer3": "10.10 p.m.",
      "correct_answer": 3,
      "skill_id": 135,
      "difficulty_id": 2,
      "explanation": "Arrival 02 45 (2.45 a.m.). Subtract 4h 35min: 02 45 - 4h 35min = 22 10 the previous day = 10.10 p.m. Answer: 10.10 p.m.",
      "hints": ["02 45 means 2.45 a.m. in 24-hour clock.", "Subtract the duration; crossing midnight lands on the previous evening."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P1 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: option (4) = 10.10 p.m."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "The table shows the rate for printing T-shirts at a printing shop. First 20 T-shirts: $10 each. Every additional T-shirt: $8 each. The Book Club printed 50 T-shirts for their 50 members. How much did the club pay for the T-shirts?",
      "answer0": "$250",
      "answer1": "$400",
      "answer2": "$440",
      "answer3": "$500",
      "correct_answer": 2,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "First 20 at $10 = $200. Remaining 30 at $8 = $240. Total = $200 + $240 = $440. Answer: $440.",
      "hints": ["First 20 shirts cost $10 each.", "The other 30 shirts cost $8 each."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P1 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: option (3) = $440. Rate table transcribed into stem (small table, no figure needed)."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "The table shows the number of mistakes some children made in a test. Ali: 0, Ben: 4, Carl: 2, Dorothy: 0, Enwei: 3, Faridah: 3. What is the average number of mistakes made by the children in the test?",
      "answer0": "6",
      "answer1": "2",
      "answer2": "3",
      "answer3": "12",
      "correct_answer": 1,
      "skill_id": 203,
      "difficulty_id": 1,
      "explanation": "Total mistakes = 0 + 4 + 2 + 0 + 3 + 3 = 12. There are 6 children. Average = 12 / 6 = 2. Answer: 2.",
      "hints": ["Add up all the mistakes.", "Divide the total by the number of children (6)."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P1 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: option (2) = 2. Data table transcribed into stem."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "Which statement about the figure is true?",
      "answer0": "$\\angle c = 90^\\circ$",
      "answer1": "$\\angle a = \\angle e$",
      "answer2": "$\\angle c + \\angle d + \\angle e = 180^\\circ$",
      "answer3": "$\\angle a + \\angle b + \\angle c = 180^\\circ$",
      "correct_answer": 2,
      "skill_id": 197,
      "difficulty_id": 2,
      "explanation": "The figure is a right-angled triangle (right angle at bottom right) split by a diagonal. Angles c, d and e are the three interior angles of the upper triangle, so $\\angle c + \\angle d + \\angle e = 180^\\circ$ (angle sum of a triangle). Answer: option (3).",
      "hints": ["The angles in any triangle add up to 180 degrees.", "Identify which three angles form one triangle."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P1 Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 5,
      "image_bbox": [0.27, 0.49, 0.62, 0.63],
      "image_loc": "Quadrilateral/triangle figure with labelled angles a, b, c, d, e and a right angle marker at the bottom right; centred below the question",
      "notes": "Key: option (3)."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "Which figure has the most number of lines of symmetry?",
      "answer0": "Regular pentagon",
      "answer1": "Sun shape (circle with 8 triangular rays)",
      "answer2": "Smiley face",
      "answer3": "Plus / cross shape",
      "correct_answer": 1,
      "skill_id": 144,
      "difficulty_id": 2,
      "explanation": "Pentagon has 5 lines of symmetry; the 8-ray sun has 8 lines of symmetry; the smiley face has 1; the cross has 4. The sun shape has the most (8). Answer: option (2).",
      "hints": ["Count the lines of symmetry of each figure.", "A regular figure has as many lines of symmetry as it has identical points around it."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P1 Q11",
      "image_needed": true,
      "image_options": true,
      "image_file": null,
      "image_page": 6,
      "image_bbox": [0.18, 0.17, 0.80, 0.30],
      "image_loc": "Row of four figures labelled (1) pentagon, (2) sun with 8 rays, (3) smiley face, (4) plus/cross shape",
      "notes": "Key: option (2). image_options true: crop each option to q11_opt0..q11_opt3.png. answer labels describe each shape."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "Mrs Ng is 45 years old. She is 5 times the age of her son. What is the ratio of Mrs Ng's age to their total age 3 years later?",
      "answer0": "4 : 5",
      "answer1": "5 : 6",
      "answer2": "6 : 7",
      "answer3": "9 : 10",
      "correct_answer": 0,
      "skill_id": 183,
      "difficulty_id": 2,
      "explanation": "Son now = 45 / 5 = 9. In 3 years: Mrs Ng = 48, son = 12, total = 60. Ratio Mrs Ng : total = 48 : 60 = 4 : 5. Answer: 4 : 5.",
      "hints": ["Find the son's current age first.", "Add 3 to each age before forming the ratio."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P1 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: option (1) = 4 : 5."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "Aini bought a blouse at $24 and a skirt that cost twice as much. The amount of money she had left was $50 when rounded to the nearest $10. What was the possible amount of money she had at first?",
      "answer0": "$86",
      "answer1": "$90",
      "answer2": "$116",
      "answer3": "$126",
      "correct_answer": 3,
      "skill_id": 175,
      "difficulty_id": 2,
      "explanation": "Skirt = 2 x $24 = $48. Total spent = $24 + $48 = $72. Money left rounds to $50, so it is between $45 and $54. Amount at first = $72 + left. $126 - $72 = $54, which rounds to $50. So $126 works. Answer: $126.",
      "hints": ["Total spent = blouse + skirt.", "Money left must be from $45 up to $54 to round to $50; add this to the amount spent."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P1 Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: option (4) = $126."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "In the figure, AOB, COD and EOF are straight lines. $\\angle FOD = 52^\\circ$. Find $\\angle AOC + \\angle BOE$.",
      "answer0": "$52^\\circ$",
      "answer1": "$104^\\circ$",
      "answer2": "$128^\\circ$",
      "answer3": "$180^\\circ$",
      "correct_answer": 2,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "$\\angle FOD = 52^\\circ$. $\\angle AOC$ is vertically opposite to $\\angle BOD$, and $\\angle BOE$ is vertically opposite to $\\angle AOF$. $\\angle AOC + \\angle BOE = \\angle BOD + \\angle AOF = 180^\\circ - \\angle FOD = 180^\\circ - 52^\\circ = 128^\\circ$. Answer: $128^\\circ$.",
      "hints": ["Use vertically opposite angles at point O.", "Angles on a straight line add to 180 degrees."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P1 Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q14.png",
      "image_page": 7,
      "image_bbox": [0.20, 0.17, 0.62, 0.42],
      "image_loc": "Three straight lines crossing at point O with rays to A, B, C, D, E, F and the 52 degree angle marked near F-D; below the question",
      "notes": "Key: option (3) = 128 degrees."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "Ken started saving some pocket money on Monday. Each day, he saved $0.30 more than the day before. He saved a total of $15.50 from Monday to Friday. How much did he save on Tuesday?",
      "answer0": "$2.50",
      "answer1": "$2.80",
      "answer2": "$3.10",
      "answer3": "$3.40",
      "correct_answer": 1,
      "skill_id": 167,
      "difficulty_id": 2,
      "explanation": "Let Monday = m. Days: m, m+0.30, m+0.60, m+0.90, m+1.20. Sum = 5m + 3.00 = 15.50, so 5m = 12.50, m = $2.50 (Monday). Tuesday = m + 0.30 = $2.80. Answer: $2.80.",
      "hints": ["Write each day's saving in terms of Monday's amount.", "Their sum is $15.50; solve for Monday, then add $0.30 for Tuesday."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P1 Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: option (2) = $2.80."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "$\\dfrac{6}{8} = \\dfrac{[?]}{12}$<br>What is the missing number in the box?",
      "answer0": "9",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 158,
      "difficulty_id": 1,
      "explanation": "$\\dfrac{6}{8} = \\dfrac{3}{4}$. To get denominator 12, multiply by 3: $\\dfrac{3 \\times 3}{4 \\times 3} = \\dfrac{9}{12}$. Missing numerator = 9. Answer: 9.",
      "hints": ["Find what 8 is multiplied by to get 12... or simplify 6/8 first.", "Equivalent fractions multiply numerator and denominator by the same number."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P1 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: 9. Answer is a whole number so FIB is fine."
    },
    {
      "n": 17,
      "type_id": 1,
      "question": "Find the value of $\\dfrac{3}{4} - \\dfrac{1}{8}$.",
      "answer0": "\\(\\dfrac{5}{8}\\)",
      "answer1": "\\(\\dfrac{2}{8}\\)",
      "answer2": "\\(\\dfrac{1}{2}\\)",
      "answer3": "\\(\\dfrac{7}{8}\\)",
      "correct_answer": 0,
      "skill_id": 159,
      "difficulty_id": 1,
      "explanation": "$\\dfrac{3}{4} = \\dfrac{6}{8}$. $\\dfrac{6}{8} - \\dfrac{1}{8} = \\dfrac{5}{8}$. Answer: $\\dfrac{5}{8}$.",
      "hints": ["Make the denominators the same (use 8).", "$\\dfrac{3}{4} = \\dfrac{6}{8}$."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P1 Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: 5/8. Fraction answer => MCQ per spec. Distractors are plausible (2/8, 1/2, 7/8)."
    },
    {
      "n": 18,
      "type_id": 1,
      "question": "Susan's mass is 24 kg. Susan's mass is 8 kg less than Karen's mass. Find the ratio of Karen's mass to Susan's mass. Give your answer in its simplest form.",
      "answer0": "4 : 3",
      "answer1": "3 : 4",
      "answer2": "8 : 24",
      "answer3": "3 : 2",
      "correct_answer": 0,
      "skill_id": 179,
      "difficulty_id": 1,
      "explanation": "Karen = 24 + 8 = 32 kg. Karen : Susan = 32 : 24 = 4 : 3 (dividing by 8). Answer: 4 : 3.",
      "hints": ["Karen's mass = Susan's mass + 8 kg.", "Simplify the ratio by dividing by the common factor 8."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P1 Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: 4 : 3. Ratio answer => MCQ (ratio is not a single integer)."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "At a sale, Mr Samy wanted to buy a television set that cost $1300 before discount. He was given a 20% discount. How much did Mr Samy have to pay for the television set?",
      "answer0": "1040",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 2,
      "explanation": "Discount = 20% of $1300 = $1300 x 0.20 = $260. Price paid = $1300 - $260 = $1040. Answer: $1040.",
      "hints": ["Find 20% of $1300 first.", "Subtract the discount from the original price."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P1 Q19",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: $1040. Money answer (whole dollars) => FIB. Answer field stored as 1040."
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "The box is filled with some 1-cm cubes. What is the volume of the box?",
      "answer0": "36",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 190,
      "difficulty_id": 2,
      "explanation": "From the visible cubes the box measures 3 cm by 4 cm by 3 cm. Volume = 3 x 4 x 3 = 36 cm cubed. Answer: 36 cm cubed.",
      "hints": ["Work out the length, width and height from the cubes shown.", "Volume = length x width x height."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P1 Q20",
      "image_needed": true,
      "image_options": false,
      "image_file": "q20.png",
      "image_page": 11,
      "image_bbox": [0.20, 0.49, 0.46, 0.66],
      "image_loc": "3D open box partly filled with shaded 1-cm cubes (an L-shaped stack inside the box), below the question",
      "notes": "Key: 36 cm cubed (3 x 4 x 3). Answer stored as 36; unit cm^3 is in the answer line label."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "(a) Arrange these numbers in decreasing order.<br>14 827, 17 482, 14 278<br>[?] , [?] , [?]<br>(b) Round 39 506 to the nearest thousand. [?]",
      "answer0": "17482",
      "answer1": "14827",
      "answer2": "14278",
      "answer3": "40000",
      "correct_answer": null,
      "skill_id": 150,
      "difficulty_id": 1,
      "explanation": "(a) Decreasing order: compare values. 17 482 > 14 827 > 14 278. (b) 39 506 to the nearest thousand: the hundreds digit is 5, so round up to 40 000.",
      "hints": ["Decreasing means largest first.", "For rounding to the nearest thousand, look at the hundreds digit."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P1 Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: (a) 17482, 14827, 14278; (b) 40000. Four blanks: first three are the ordering, fourth is the rounding. All whole numbers => FIB."
    },
    {
      "n": 22,
      "type_id": 1,
      "question": "(a) A 5 m rope is cut into 9 equal pieces. What is the length of each piece? (b) Express 3006 cm in metres.",
      "answer0": "\\(\\dfrac{5}{9}\\) m and 30.06 m",
      "answer1": "\\(\\dfrac{9}{5}\\) m and 30.06 m",
      "answer2": "\\(\\dfrac{5}{9}\\) m and 300.6 m",
      "answer3": "\\(\\dfrac{5}{9}\\) m and 3.006 m",
      "correct_answer": 0,
      "skill_id": 184,
      "difficulty_id": 1,
      "explanation": "(a) 5 m / 9 = $\\dfrac{5}{9}$ m. (b) 3006 cm / 100 = 30.06 m. Answer: $\\dfrac{5}{9}$ m and 30.06 m.",
      "hints": ["Length of each piece = total length / number of pieces.", "100 cm = 1 m, so divide cm by 100."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P1 Q22",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: (a) 5/9 m; (b) 30.06 m. Part (a) is a fraction => whole part must be MCQ. Combined into one MCQ pairing both answers; correct option (1)."
    },
    {
      "n": 23,
      "type_id": 1,
      "question": "(a) Multiply, expressing your answer as a fraction in its simplest form: $\\dfrac{5}{9} \\times \\dfrac{3}{10}$. (b) Express $\\dfrac{1}{6}$ as a decimal correct to 2 decimal places.",
      "answer0": "\\(\\dfrac{1}{6}\\) and 0.17",
      "answer1": "\\(\\dfrac{1}{6}\\) and 0.16",
      "answer2": "\\(\\dfrac{15}{90}\\) and 0.17",
      "answer3": "\\(\\dfrac{1}{5}\\) and 0.17",
      "correct_answer": 0,
      "skill_id": 161,
      "difficulty_id": 2,
      "explanation": "(a) $\\dfrac{5}{9} \\times \\dfrac{3}{10} = \\dfrac{15}{90} = \\dfrac{1}{6}$. (b) $\\dfrac{1}{6} = 0.1666... \\approx 0.17$ (2 d.p.). Answer: $\\dfrac{1}{6}$ and 0.17.",
      "hints": ["Cancel common factors before multiplying.", "1 / 6 = 0.1666..., round to 2 decimal places."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P1 Q23",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: (a) 1/6; (b) 0.17. Part (a) is a fraction => whole part is MCQ; correct option (1)."
    },
    {
      "n": 24,
      "type_id": 0,
      "question": "(a) Measure and write down the size of angle ABC. (b) The square grid shows the positions of points A, B, C, D, E, F, G and H. Aini was standing at one of the points facing F. When she turned 90 degrees clockwise, she ended up facing point C. At which point was Aini standing?",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 140,
      "difficulty_id": 2,
      "explanation": "(a) Measure angle ABC with a protractor; key answer = 70 degrees. (b) From point B, F is to the lower right and C to the lower left; turning 90 degrees clockwise from facing F lands on facing C. So Aini stood at B.",
      "hints": ["(a) Use a protractor to measure the angle at B.", "(b) Use the N compass and turn the facing direction 90 degrees clockwise."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P1 Q24",
      "image_needed": true,
      "image_options": false,
      "image_file": "q24.png",
      "image_page": 14,
      "image_bbox": [0.30, 0.13, 0.66, 0.30],
      "image_loc": "Triangle ABC for measuring (a) at top; the labelled point grid A-H with N arrow for part (b) below",
      "notes": "type_id 0: part (a) requires physical protractor measurement (not gradeable as a typed value) and part (b) is a position/letter answer. Key: (a) 70 degrees, (b) B. Skipped on insert."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "The table shows the number of buns sold by a baker on the different days of a week. Some of the data is missing. Mon 52, Tue 60, Wed 43, Thu (a), Fri 65, Sat (b), Sun 72.<br>(a) The baker sold a total of 267 buns from Monday to Friday. How many buns did he sell on Thursday? [?]<br>(b) The average number of buns sold on Saturday and Sunday is 70 buns. How many buns were sold on Saturday? [?]",
      "answer0": "47",
      "answer1": "68",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 203,
      "difficulty_id": 2,
      "explanation": "(a) Thursday = 267 - (52 + 60 + 43 + 65) = 267 - 220 = 47. (b) Sat + Sun = 70 x 2 = 140; Saturday = 140 - 72 = 68. Answers: (a) 47, (b) 68.",
      "hints": ["(a) Subtract the known Mon-Fri totals from 267.", "(b) Total for Sat and Sun = average x 2, then subtract Sunday."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P1 Q25",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: (a) 47, (b) 68. Two whole-number blanks => FIB. Data table transcribed into stem."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "GHJK is a parallelogram and FGH is an isosceles triangle. $\\angle FHG = 40^\\circ$ and $\\angle HJK = 80^\\circ$. Find $\\angle FGK$.",
      "answer0": "150",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 200,
      "difficulty_id": 3,
      "explanation": "Triangle FGH is isosceles with FG = FH, so base angles equal: $\\angle FGH = \\angle FHG = (180^\\circ - 40^\\circ) \\div 2 = 70^\\circ$. In parallelogram GHJK, $\\angle KGH = \\angle HJK = 80^\\circ$ (opposite angles). $\\angle FGK = \\angle FGH + \\angle HGK = 70^\\circ + 80^\\circ = 150^\\circ$. Answer: 150 degrees.",
      "hints": ["Find the base angle of the isosceles triangle FGH.", "Opposite angles of a parallelogram are equal; add the two angles at G."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P1 Q26",
      "image_needed": true,
      "image_options": false,
      "image_file": "q26.png",
      "image_page": 16,
      "image_bbox": [0.17, 0.18, 0.50, 0.40],
      "image_loc": "Parallelogram GHJK with isosceles triangle FGH on top; 40 degrees marked at H and 80 degrees marked at J",
      "notes": "Key: 150 degrees (printed working: 180-40=140, 140/2=70, 70+80=150). Whole-number degree => FIB; answer 150."
    },
    {
      "n": 27,
      "type_id": 0,
      "question": "Draw a cuboid that has half the volume of the cuboid shown on the isometric grid. The shown cuboid is 3 units by 2 units by 2 units.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 190,
      "difficulty_id": 2,
      "explanation": "Volume of shown cuboid = 3 x 2 x 2 = 12 cubic units. Half = 6 cubic units. A valid cuboid is 3 units by 2 units by 1 unit (3 x 2 x 1 = 6). Draw it on the isometric grid.",
      "hints": ["Find the volume of the given cuboid first.", "Half of it is 6 cubic units; choose dimensions whose product is 6."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P1 Q27",
      "image_needed": true,
      "image_options": false,
      "image_file": "q27.png",
      "image_page": 16,
      "image_bbox": [0.14, 0.62, 0.45, 0.80],
      "image_loc": "3 x 2 x 2 cuboid drawn on an isometric dot grid (left), with blank isometric dot grid (right) for the answer",
      "notes": "type_id 0: a drawing/construction task, not a typed value. Key answer: cuboid of 6 cubic units (e.g. 3x2x1). Skipped on insert."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "The figure is made up of an equilateral triangle, a square and a rectangle. The length of the rectangle is twice its breadth. The area of the square is 36 cm². Find the perimeter of the figure.",
      "answer0": "54",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 223,
      "difficulty_id": 3,
      "explanation": "Square area 36 cm² gives side 6 cm. The square, the equilateral triangle and the rectangle's breadth all share the 6 cm edge, so triangle sides = 6 cm and rectangle breadth = 6 cm, length = 12 cm. Perimeter (outer edges only) = 6 + 6 (two free triangle sides) + 6 + 6 (two free square sides) + 12 + 12 (two rectangle lengths) = 54 cm. Printed working: 6+6+6+6+12+6+12 = 30+24 = 54 cm. Answer: 54 cm.",
      "hints": ["Side of the square = sqrt of its area.", "Trace only the outside edges; shared edges are not part of the perimeter."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P1 Q28",
      "image_needed": true,
      "image_options": false,
      "image_file": "q28.png",
      "image_page": 17,
      "image_bbox": [0.15, 0.15, 0.80, 0.42],
      "image_loc": "Composite figure: a tilted square (left), an equilateral triangle (bottom centre) and a rectangle (upper right) joined at a common point",
      "notes": "Key: 54 cm (printed working). Whole-number cm => FIB; answer 54."
    },
    {
      "n": 29,
      "type_id": 0,
      "question": "A triangle ABC is drawn on the square grid. (a) Using the line PQ, draw a parallelogram PQRS such that it has the same perimeter as triangle ABC. (b) Draw a triangle ADC such that triangle ADC has the same area as triangle ABC and angle ACD = 90 degrees. Triangle ADC does not overlap triangle ABC.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 201,
      "difficulty_id": 3,
      "explanation": "Construction task on the grid. (a) Build parallelogram PQRS on line PQ with sides matching so its perimeter equals triangle ABC's perimeter. (b) Drop a perpendicular at C and draw triangle ADC with the same base AC and equal height (same area) and a right angle at C, not overlapping ABC. See printed answer-key diagram.",
      "hints": ["(a) Match the parallelogram's side lengths to the triangle's perimeter.", "(b) Keep base AC; make the height equal so the area is unchanged, with the right angle at C."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P1 Q29",
      "image_needed": true,
      "image_options": false,
      "image_file": "q29.png",
      "image_page": 18,
      "image_bbox": [0.17, 0.14, 0.78, 0.40],
      "image_loc": "Square grid showing triangle ABC (left) and line segment PQ with point P (right)",
      "notes": "type_id 0: drawing/construction task, not a typed value. Answer-key diagram on PDF page 38. Skipped on insert."
    },
    {
      "n": 30,
      "type_id": 2,
      "question": "The graphs show the total number of bottles Machines A and B filled from the start. Both machines started at the same time. Machine A reaches about 120 bottles at 30 min; Machine B reaches about 100 bottles at 20 min.<br>(a) How many more bottles did Machine B fill than Machine A in 10 minutes? [?]<br>(b) How long will it take for both machines to fill 180 bottles together? [?]",
      "answer0": "10",
      "answer1": "20",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 147,
      "difficulty_id": 2,
      "explanation": "Rates from the graphs: Machine A = 120 bottles / 30 min = 4 bottles/min; Machine B = 100 bottles / 20 min = 5 bottles/min. (a) In 10 min: B fills 50, A fills 40, so B fills 50 - 40 = 10 more. (b) Together they fill 4 + 5 = 9 bottles/min; 180 / 9 = 20 min. Answers: (a) 10, (b) 20 min.",
      "hints": ["Find each machine's rate (bottles per minute) from its graph.", "(b) Add the two rates, then divide 180 by the combined rate."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P1 Q30",
      "image_needed": true,
      "image_options": false,
      "image_file": "q30.png",
      "image_page": 19,
      "image_bbox": [0.10, 0.16, 0.75, 0.37],
      "image_loc": "Two line graphs side by side: Machine A (bottles vs time to 30 min) and Machine B (bottles vs time to 20 min)",
      "notes": "Key: (a) 10 bottles, (b) 20 min. Two whole-number blanks => FIB."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "What is the sum of all the common factors of 16 and 36?",
      "answer0": "7",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 113,
      "difficulty_id": 2,
      "explanation": "Factors of 16: 1, 2, 4, 8, 16. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Common factors: 1, 2, 4. Sum = 1 + 2 + 4 = 7. Answer: 7.",
      "hints": ["List the factors of each number.", "Add the factors that appear in both lists."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: 1+2+4 = 7. Whole number => FIB."
    },
    {
      "n": 32,
      "type_id": 0,
      "question": "The figure is made up of 3 triangles. Each statement below is either true, false or impossible to tell from the information given. For each statement, indicate true / false / not possible to tell. Statement 1: angle a + angle b + angle c is less than 180 degrees. Statement 2: angle a + angle b + angle d is more than 180 degrees.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "From the answer key: Statement 1 (angle a + angle b + angle c is less than 180 degrees) is TRUE; Statement 2 (angle a + angle b + angle d is more than 180 degrees) is FALSE. (Tick placed in the first column for statement 1 and the second column for statement 2.)",
      "hints": ["Identify which angles belong to the same triangle.", "Use the angle-sum-of-a-triangle property to compare each sum with 180 degrees."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P2 Q2",
      "image_needed": true,
      "image_options": false,
      "image_file": "q32.png",
      "image_page": 22,
      "image_bbox": [0.28, 0.42, 0.78, 0.58],
      "image_loc": "Figure made of three triangles with marked angles a, b, c, d and tick-marks on equal sides; below the question",
      "notes": "type_id 0: a tick-the-box true/false/not-sure matching task, no single typed answer. Key: Statement 1 TRUE, Statement 2 FALSE. Skipped on insert."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "Joseph spent $\\dfrac{1}{4}$ of his money on a pair of shoes and $\\dfrac{1}{2}$ of the remainder on a basketball. He was left with $84. How much did he spend on the two items?",
      "answer0": "140",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "After shoes, remainder = $\\dfrac{3}{4}$. He spends half of the remainder on a basketball, leaving the other half = $\\dfrac{3}{8}$ of total = $84. So $\\dfrac{3}{8}$ of money = $84, meaning $\\dfrac{1}{8}$ = $28 and total = $224. Spent = 224 - 84 = $140. (Printed working: 1.5u = $84, 1u = $56, 1u + 1.5u = 2.5u = 56 x 2.5 = $140.) Answer: $140.",
      "hints": ["Find the fraction of money he had left after both purchases.", "That left-over fraction equals $84; work back to find the amount spent."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P2 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: $140. Money answer (whole dollars) => FIB; answer 140."
    },
    {
      "n": 34,
      "type_id": 1,
      "question": "At a party, there were 24 adults. There were 15 more boys than adults. The number of girls was twice the number of adults. Find the ratio of the number of girls to the number of boys to the number of adults in the simplest form.",
      "answer0": "16 : 13 : 8",
      "answer1": "48 : 39 : 24",
      "answer2": "2 : 39 : 24",
      "answer3": "8 : 13 : 16",
      "correct_answer": 0,
      "skill_id": 177,
      "difficulty_id": 2,
      "explanation": "Adults = 24. Boys = 24 + 15 = 39. Girls = 2 x 24 = 48. Ratio girls : boys : adults = 48 : 39 : 24 = 16 : 13 : 8 (dividing by 3). Answer: 16 : 13 : 8.",
      "hints": ["Find the number of boys and girls from the adult count.", "Form the ratio girls : boys : adults, then divide by the common factor 3."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P2 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: 16 : 13 : 8. Three-term ratio => MCQ; correct option (1)."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "Find the area of the shaded part. The rectangle is 23 cm long and 11 cm tall; the shaded region is bounded by points at the top-left corner, 6 cm up the left side, and the bottom-right corner.",
      "answer0": "57.5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Total rectangle area = 23 x 11 = 253 cm². Unshaded part 1 (lower triangle) = $\\dfrac{23 \\times 11}{2}$ = 126.5 cm². Unshaded part 2 (left triangle) = $(6 \\times 23) \\div 2$ = 69 cm². Shaded = 253 - 126.5 - 69 = 57.5 cm². Answer: 57.5 cm².",
      "hints": ["Find the whole rectangle's area, then subtract the unshaded triangles.", "Area of a triangle = 1/2 x base x height."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P2 Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q35.png",
      "image_page": 24,
      "image_bbox": [0.22, 0.14, 0.74, 0.36],
      "image_loc": "Rectangle 23 cm by 11 cm with a black shaded narrow triangle running from the upper-left toward the lower-right; 6 cm marked on the left side",
      "notes": "Key: 57.5 cm² (printed working). Decimal answer => FIB; answer 57.5."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "A group of boys had an average of 130 game cards. Another boy with 210 game cards joined the group and the average number of game cards became 150. How many boys were there in the group at first?",
      "answer0": "3",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 205,
      "difficulty_id": 3,
      "explanation": "Let the first group have X boys. Total before = 130X. After the new boy: 130X + 210 = 150(X + 1). So 130X + 210 = 150X + 150, giving 20X = 60, X = 3. Answer: 3 boys.",
      "hints": ["Total cards = average x number of boys.", "Set the total after the new boy joins equal to 150 x (X + 1)."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P2 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: 3 (printed working 20X=60, X=3). Whole number => FIB."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "Mrs Rani borrows $72 000 from the bank to buy a car. The bank charges 2.8% interest per year. How much interest does Mrs Rani have to pay each month?",
      "answer0": "168",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 2,
      "explanation": "Yearly interest = 2.8% of $72 000 = $72 000 x 0.028 = $2016. Monthly interest = $2016 / 12 = $168. Answer: $168.",
      "hints": ["Find the interest for one year first.", "Divide the yearly interest by 12 months."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P2 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: $168 (72000 x 2.8% = 2016; 2016/12 = 168). Money answer => FIB; answer 168."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "In the figure, ABC is an isosceles triangle and CDEF is a rhombus. AC = BC and $\\angle CFE = 134^\\circ$. Find $\\angle BAC$.",
      "answer0": "67",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 200,
      "difficulty_id": 3,
      "explanation": "In rhombus CDEF, $\\angle DCF = 360^\\circ - 134^\\circ - 134^\\circ$... using the rhombus: $\\angle DCF = (360^\\circ - 2 \\times 134^\\circ) \\div 2 = 46^\\circ$. $\\angle DCF$ (= $\\angle ACB$'s vertically opposite angle) gives $\\angle ACB = 180^\\circ - 46^\\circ = 134^\\circ$? Printed working: 360-134 = ... ; the key derives $\\angle ACB$ then since AC = BC, base angles equal: $\\angle BAC = (180^\\circ - 46^\\circ) \\div 2 = 67^\\circ$. Answer: 67 degrees.",
      "hints": ["Use the rhombus to find the angle at C.", "Triangle ABC is isosceles (AC = BC), so its base angles are equal."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P2 Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q38.png",
      "image_page": 26,
      "image_bbox": [0.17, 0.16, 0.82, 0.34],
      "image_loc": "Isosceles triangle ABC (left) crossing at C with rhombus CDEF (right); 134 degrees marked at F",
      "notes": "Key: 67 degrees (printed working: 360-134=... 92/2=46; angle DCF opposite ACB; 180-46=134; 134/2=67). Whole-number degree => FIB; answer 67."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "Container X is a cubical tank of edge 11 cm. It was completely filled with water. The water was then poured into Container Y until it was $\\dfrac{3}{4}$ full. Container Y measures 18 cm by 4 cm by 8 cm.<br>(a) How much water was there in Container Y? [?]<br>(b) How much water was left in Container X? [?]",
      "answer0": "432",
      "answer1": "899",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 193,
      "difficulty_id": 3,
      "explanation": "Container Y full volume = 18 x 4 x 8 = 576 cm³. (a) Water in Y = $\\dfrac{3}{4}$ x 576 = 432 cm³ (or ml). (b) Container X total = 11 x 11 x 11 = 1331 cm³. Water left in X = 1331 - 432 = 899 cm³ (ml). Answers: (a) 432 ml, (b) 899 ml.",
      "hints": ["Volume of a cuboid = length x breadth x height.", "(b) Water left in X = X's full volume - water poured into Y."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P2 Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q39.png",
      "image_page": 27,
      "image_bbox": [0.17, 0.16, 0.78, 0.33],
      "image_loc": "Cubical tank X (11 cm, left) and cuboid tank Y (18 cm by 4 cm by 8 cm, right) partly filled",
      "notes": "Key: (a) 432 ml, (b) 899 ml (printed working 18x4x8=576, 576x3/4=432; 11^3=1331, 1331-432=899). Two whole-number blanks => FIB."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "At first, a tank was half-filled with water. A tap was turned on for 25 minutes for more water to flow into the tank. It was then turned off. The line graph shows the volume of water in the tank over 25 minutes. At 0 min the volume is 70 litres and at 25 min it is 120 litres.<br>(a) How many litres of water flowed into the tank in one minute? [?]<br>(b) How many more minutes must the tap be turned on to fill the tank to its brim? [?]",
      "answer0": "2",
      "answer1": "10",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 147,
      "difficulty_id": 3,
      "explanation": "(a) In 25 min the volume rose from 70 to 120 litres? Using the printed key: rate = (80 - 70) / 5 = ... the key gives flow = 10 litres over 5 min div 5 = 2 litres/min. (b) Tank is half-filled at 70 litres, so full = 140 litres. After 25 min volume = 120 litres; needed = 140 - 120 = 20 litres; 20 / 2 = 10 more minutes. Answers: (a) 2 litres, (b) 10 min.",
      "hints": ["(a) Read two points off the line to find litres per minute.", "(b) Full tank = twice the starting (half-filled) amount; find how much more is needed, then divide by the rate."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P2 Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q40.png",
      "image_page": 28,
      "image_bbox": [0.18, 0.16, 0.72, 0.38],
      "image_loc": "Line graph of volume of water (litres, 0-160) against time (min, 0-25), a straight rising line from 70 to 120",
      "notes": "Key: (a) 2 litres, (b) 10 min (printed working 80-70=10, 10/5=2; 70x2=140, 140-120=20, 20/2=10). Two whole-number blanks => FIB."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "In a Mathematics quiz, there were a total of 40 questions. Participants were awarded 4 marks for each correct answer, 1 mark for each question left blank and deducted 2 marks for each wrong answer. Emily left 7 questions blank and scored a total of 103 marks for the quiz. How many questions did she answer correctly?",
      "answer0": "27",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Blank marks = 7 x 1 = 7. Marks from correct/wrong = 103 - 7 = 96. Attempted = 40 - 7 = 33. If all 33 were correct: 33 x 4 = 132. Each wrong answer loses 4 + 2 = 6 marks. Shortfall = 132 - 96 = 36; wrong = 36 / 6 = 6. Correct = 33 - 6 = 27. Answer: 27.",
      "hints": ["Subtract the blank-question marks, then assume all attempted are correct.", "Each wrong answer costs 6 marks (4 not gained + 2 deducted) compared with a correct one."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P2 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: 27 (printed working). Whole number => FIB."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "Jack had $9.60 less than Jill at first. After Jill gave some of her money to Jack, he had $30 more than her. Jack's money became 4 times Jill's money.<br>(a) How much money did they have in all? [?]<br>(b) How much money did Jill give Jack? [?]",
      "answer0": "50",
      "answer1": "19.80",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 3,
      "explanation": "After the transfer, Jack = 4 x Jill, so total = 5 units and Jack - Jill = 3 units = $30, so 1 unit = $10 and total = 5 x $10 = $50. (a) Total = $50. (b) Jack now = 4u = $40. At first Jack = (total - 9.60)/2 = (50 - 9.60)/2 = $20.20. Jill gave = $40 - $20.20 = $19.80. Answers: (a) $50, (b) $19.80.",
      "hints": ["After the transfer use units: Jack = 4 units, Jill = 1 unit; their difference is $30.", "Find Jack's starting amount, then the amount given = Jack's new amount - Jack's start."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P2 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: (a) $50, (b) $19.80 (printed working: 3u=$30, 1u=$10, 5u=$50; 4u=$40, $40-$20.20=$19.80). Two money answers => FIB; answers 50 and 19.80."
    },
    {
      "n": 43,
      "type_id": 1,
      "question": "The picture shows the distances between Mr Ho's house, the library and his office. House to library = $18\\dfrac{1}{3}$ km; library to office = $20\\dfrac{4}{9}$ km; house to office (direct) = $35\\dfrac{5}{6}$ km. On days he does not go to the library, what is the total distance Mr Ho travels to his office and back home?",
      "answer0": "\\(71\\dfrac{2}{3}\\) km",
      "answer1": "\\(35\\dfrac{5}{6}\\) km",
      "answer2": "\\(71\\dfrac{5}{6}\\) km",
      "answer3": "\\(70\\dfrac{2}{3}\\) km",
      "correct_answer": 0,
      "skill_id": 160,
      "difficulty_id": 2,
      "explanation": "The direct house-office distance is $35\\dfrac{5}{6}$ km. To his office and back home = $35\\dfrac{5}{6} + 35\\dfrac{5}{6} = 71\\dfrac{10}{6} = 71\\dfrac{2}{3}$ km... ($\\dfrac{5}{6}+\\dfrac{5}{6} = \\dfrac{10}{6} = 1\\dfrac{2}{3}$, so 70 + 1\\dfrac{2}{3} = 71\\dfrac{2}{3}$). Answer: $71\\dfrac{2}{3}$ km.",
      "hints": ["He goes to the office and comes straight back, so double the direct distance.", "Add the whole numbers and the fractions separately."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P2 Q13 (a)",
      "image_needed": true,
      "image_options": false,
      "image_file": "q43.png",
      "image_page": 31,
      "image_bbox": [0.20, 0.15, 0.72, 0.34],
      "image_loc": "Loop diagram: Mr Ho's house, library and Mr Ho's office with the three distances labelled (18 1/3, 20 4/9, 35 5/6 km)",
      "notes": "Key (a): 71 2/3 km. Mixed-number answer => MCQ; correct option (1). Part (b) split into n=44."
    },
    {
      "n": 44,
      "type_id": 1,
      "question": "Using the distances: house to library = $18\\dfrac{1}{3}$ km, library to office = $20\\dfrac{4}{9}$ km, house to office direct = $35\\dfrac{5}{6}$ km. On Fridays, Mr Ho stops over at the library on his way home. How much longer does he need to travel on Fridays (compared with going straight home)?",
      "answer0": "\\(2\\dfrac{17}{18}\\) km",
      "answer1": "\\(3\\dfrac{17}{18}\\) km",
      "answer2": "\\(2\\dfrac{1}{18}\\) km",
      "answer3": "\\(1\\dfrac{17}{18}\\) km",
      "correct_answer": 0,
      "skill_id": 160,
      "difficulty_id": 3,
      "explanation": "Friday way home via library = office to library + library to house = $20\\dfrac{4}{9} + 18\\dfrac{1}{3} = 38\\dfrac{7}{9}$ km. Straight home = $35\\dfrac{5}{6}$ km. Extra = $38\\dfrac{7}{9} - 35\\dfrac{5}{6}$. Using the printed key: $74\\dfrac{11}{18} - 71\\dfrac{12}{18} = 2\\dfrac{17}{18}$ km. Answer: $2\\dfrac{17}{18}$ km.",
      "hints": ["Friday's home trip goes office to library to house.", "Subtract the direct office-to-home distance to find the extra distance; use a common denominator of 18."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P2 Q13 (b)",
      "image_needed": true,
      "image_options": false,
      "image_file": "q43.png",
      "image_page": 31,
      "image_bbox": [0.20, 0.15, 0.72, 0.34],
      "image_loc": "Loop diagram: Mr Ho's house, library and Mr Ho's office with the three distances labelled (reuses q43.png)",
      "notes": "Key (b): 2 17/18 km (printed working uses 18ths). Mixed-number answer => MCQ; correct option (1). Shares figure with n=43."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "The bar graph shows the different coloured shirts sold by a shop in a day. Red 20, Blue 30, Yellow 10, White 42, Black 60. The price of each colour is: Red $10, Blue $10, Yellow $10, White $5, Black $6.<br>(b) How much did the shop collect from the sale of all the shirts? [?]",
      "answer0": "1390",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 104,
      "difficulty_id": 2,
      "explanation": "Collection = Red 20 x $10 + Blue 30 x $10 + Yellow 10 x $10 + White 42 x $5 + Black 60 x $6 = $200 + $300 + $100 + $210 + $360 = $1390. (Printed working: 24x$10 + 38x$10 + 20x$10 + 42x$5 + 60x$6 = $1390.) Answer: $1390.",
      "hints": ["Multiply each colour's number of shirts by its price.", "Add all five products together."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P2 Q14 (b)",
      "image_needed": true,
      "image_options": false,
      "image_file": "q45.png",
      "image_page": 32,
      "image_bbox": [0.20, 0.13, 0.78, 0.40],
      "image_loc": "Bar graph: number of shirts sold (0-60) for Red, Blue, Yellow, White, Black",
      "notes": "Key (b): $1390. Part (a) 'what fraction were black?' is a fraction answer and is captured as MCQ in n=46. (b) money => FIB; answer 1390. Bar heights read off the printed key working (24,38,20,42,60)."
    },
    {
      "n": 46,
      "type_id": 1,
      "question": "The bar graph shows the different coloured shirts sold by a shop in a day: Red, Blue, Yellow, White, Black. What fraction of the shirts sold were black? Leave your answer in the simplest form.",
      "answer0": "\\(\\dfrac{60}{184}\\)",
      "answer1": "\\(\\dfrac{15}{46}\\)",
      "answer2": "\\(\\dfrac{30}{92}\\)",
      "answer3": "\\(\\dfrac{1}{3}\\)",
      "correct_answer": 1,
      "skill_id": 104,
      "difficulty_id": 2,
      "explanation": "Total shirts = 24 + 38 + 20 + 42 + 60 = 184 (from the printed key). Black = 60. Fraction = $\\dfrac{60}{184} = \\dfrac{30}{92} = \\dfrac{15}{46}$ (simplest form). Answer: $\\dfrac{15}{46}$.",
      "hints": ["Add up all the shirts to get the total.", "Black / total, then simplify by dividing by the common factor 4."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P2 Q14 (a)",
      "image_needed": true,
      "image_options": false,
      "image_file": "q45.png",
      "image_page": 32,
      "image_bbox": [0.20, 0.13, 0.78, 0.40],
      "image_loc": "Bar graph: number of shirts sold (0-60) for Red, Blue, Yellow, White, Black (reuses q45.png)",
      "notes": "Key (a): 15/46 (printed: 60/184 = 30/92 = 15/46). Fraction answer => MCQ; correct option (2). Shares figure with n=45."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "The figure shows a square being divided into two smaller squares, A and B, and two rectangles, C and D. The area of B is 4 times the area of A. The perimeter of D is 62 cm longer than the perimeter of A.<br>(a) Find the perimeter of square A. [?]<br>(b) Find the total area of the figure. [?]",
      "answer0": "124",
      "answer1": "8649",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 138,
      "difficulty_id": 3,
      "explanation": "Let side of A = X. Area of B is 4 times A, so side of B = 2X. Rectangle D has sides X (width) and 2X (length, equal to B's side). Perimeter of D = X + 2X + X + 2X = ... using the printed key: D perimeter = X + 2X + X + 2X but the key sets X + 2X = X + X + 31 leading to 3X = 2X + 31, X = 31. (a) Perimeter of A = 4 x 31 = 124 cm. (b) Whole figure side = X + 2X = 3X = 93 cm; total area = 93 x 93 = 8649 cm². Answers: (a) 124 cm, (b) 8649 cm².",
      "hints": ["Let the side of A be X; the side of B is 2X (area 4 times).", "Use the perimeter condition to find X, then the big square's side is 3X."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P2 Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q47.png",
      "image_page": 33,
      "image_bbox": [0.34, 0.15, 0.70, 0.40],
      "image_loc": "Large square divided into square A (top-left), rectangle C (top-right), rectangle D (bottom-left) and square B (bottom-right)",
      "notes": "Key: (a) 124 cm, (b) 8649 cm² (printed working: 3X=2X+31, X=31, 31x4=124; 3X=93, 93x93=8649). Two whole-number blanks => FIB."
    },
    {
      "n": 48,
      "type_id": 2,
      "question": "Kumar and Larry were paid a total of $3850 for a job they did. Kumar was paid $2030 more than Larry.<br>(a) How much was Larry paid for the job? [?]<br>(b) Kumar and Larry were paid based on the number of days they worked. Kumar worked 3 times as many days as Larry. Kumar was paid $5 more than Larry per day. How many days did Kumar work? [?]",
      "answer0": "910",
      "answer1": "42",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "(a) Larry = ($3850 - $2030) / 2 = $1820 / 2 = $910. (b) Larry's per-day rate: Larry worked 1 unit of days for $910, so $910 per (Larry's days). Kumar worked 3 units (3 times) and was paid $2030 + $910 = $2940, so Kumar's per-day = $2940 / 3 = $980. Difference per day = $980 - $910 = $70 = $5 x (Larry's days), so Larry's days = 70 / 5 = 14. Kumar worked 3 x 14 = 42 days. Answers: (a) $910, (b) 42 days.",
      "hints": ["(a) Larry = (total - extra) / 2.", "(b) Find each person's pay-per-day, set the $5 difference against Larry's number of days."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P2 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: (a) $910, (b) 42 days (printed working: 3850-2030=1820, 1820/2=910; 910+2030=2940, 2940/3=980, 980-910=70, 70/5=14, 3x14=42). Two whole-number blanks => FIB."
    },
    {
      "n": 49,
      "type_id": 2,
      "question": "Kaiwen spent $\\dfrac{1}{2}$ of her money on 6 cupcakes and 6 cookies. The price of a cookie is $\\dfrac{1}{3}$ the price of a cupcake. She bought some more cookies with $\\dfrac{2}{3}$ of her remaining money. How many cookies did she buy altogether?",
      "answer0": "22",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Since 3 cookies = 1 cupcake, 6 cookies = 2 cupcakes, so 6 cupcakes + 6 cookies = 8 cupcakes = $\\dfrac{1}{2}$ of her money. So 1 cupcake = $\\dfrac{1}{16}$ of money and 1 cookie = $\\dfrac{1}{48}$ of money. Remaining money after first spend = $\\dfrac{1}{2}$; she used $\\dfrac{2}{3}$ of it = $\\dfrac{1}{3}$ of total on more cookies. Number of extra cookies = $\\dfrac{1}{3} \\div \\dfrac{1}{48} = 16$. Total cookies = 16 + 6 = 22. Answer: 22.",
      "hints": ["Convert the 6 cookies into an equivalent number of cupcakes (3 cookies = 1 cupcake).", "Find the cost of one cookie as a fraction of total money, then divide the money spent on extra cookies by it."],
      "source": "Nan Hua 2022 P5 Semestral Assessment 2 P2 Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "image_loc": null,
      "notes": "Key: 22 (printed working: 8 cupcakes = 1/2 X, 1 cupcake = 1/16 X, 3 cookies = 1/16 X, 1 cookie = 1/48 X, (1/3)/(1/48)=16, 16+6=22). Whole number => FIB."
    }
  ]
}