{
 "paper": {
  "school": "Pei Chun",
  "year": 2023,
  "level": "P4",
  "label": "End of Year Exam",
  "source_prefix": "Pei Chun 2023 P4 End of Year Exam",
  "has_answer_key": true
 },
 "questions": [
  {
   "n": 1,
   "type_id": 1,
   "question": "The value of the digit 7 in 67 089 is [?].",
   "answer0": "70",
   "answer1": "700",
   "answer2": "7000",
   "answer3": "70 000",
   "correct_answer": 2,
   "skill_id": 105,
   "difficulty_id": 1,
   "explanation": "In 67 089 the digit 7 is in the thousands place, so its value is 7 × 1000 = 7000.",
   "hints": [
    "Identify the place value of the 7.",
    "67 089: the 7 sits in the thousands column."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q1",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: Q1 = option 3 (7000)."
  },
  {
   "n": 2,
   "type_id": 1,
   "question": "43 852 rounded to the nearest hundred is [?].",
   "answer0": "43 800",
   "answer1": "43 850",
   "answer2": "43 900",
   "answer3": "44 000",
   "correct_answer": 2,
   "skill_id": 109,
   "difficulty_id": 1,
   "explanation": "Look at the tens digit (5). Since 52 ≥ 50, round up: 43 852 → 43 900.",
   "hints": [
    "Find the hundreds digit and the digit after it.",
    "The number after the hundreds is 52, which is 50 or more, so round up."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q2",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: Q2 = option 3 (43 900)."
  },
  {
   "n": 3,
   "type_id": 1,
   "question": "In which of the following numbers does the digit 4 stand for 4 hundredths?",
   "answer0": "194.36",
   "answer1": "387.64",
   "answer2": "426.09",
   "answer3": "867.46",
   "correct_answer": 1,
   "skill_id": 123,
   "difficulty_id": 2,
   "explanation": "4 hundredths is the second place after the decimal point. In 387.64 the 4 is in the hundredths place.",
   "hints": [
    "Hundredths is the 2nd digit after the decimal point.",
    "Check each option: 387.64 has 4 in the hundredths place."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q3",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: Q3 = option 2 (387.64)."
  },
  {
   "n": 4,
   "type_id": 1,
   "question": "Express $$\\frac{53}{1000}$$ as a decimal.",
   "answer0": "0.53",
   "answer1": "0.503",
   "answer2": "0.053",
   "answer3": "0.0053",
   "correct_answer": 2,
   "skill_id": 127,
   "difficulty_id": 2,
   "explanation": "Thousandths take 3 decimal places. $$\\frac{53}{1000}$$ = 0.053.",
   "hints": [
    "A denominator of 1000 means 3 decimal places.",
    "53 thousandths = 0.053."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q4",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: Q4 = option 3 (0.053)."
  },
  {
   "n": 5,
   "type_id": 1,
   "question": "Which one of the following has $$\\frac{1}{6}$$ of the figure shaded?",
   "answer0": "Figure 1",
   "answer1": "Figure 2",
   "answer2": "Figure 3",
   "answer3": "Figure 4",
   "correct_answer": 1,
   "skill_id": 42,
   "difficulty_id": 2,
   "explanation": "A figure is $$\\frac{1}{6}$$ shaded when 1 of 6 equal parts is coloured. Figure 2 has 6 equal parts with exactly one shaded.",
   "hints": [
    "Count the total equal parts and the shaded parts.",
    "Look for 1 shaded part out of 6 equal parts."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q5",
   "image_needed": true,
   "image_options": true,
   "image_file": null,
   "notes": "Key: Q5 = option 2. Four option figures (rectangles divided into parts, some shaded) in a row across the page; crop each as q5_opt0..3.",
   "image_page": 4,
   "image_bbox": [
    0.18,
    0.15,
    0.78,
    0.27
   ],
   "image_loc": "row of four shaded-rectangle figures just below the question near top of page"
  },
  {
   "n": 6,
   "type_id": 1,
   "question": "Which of the following is not in its simplest form?",
   "answer0": "$$\\frac{2}{6}$$",
   "answer1": "$$\\frac{4}{7}$$",
   "answer2": "$$\\frac{5}{8}$$",
   "answer3": "$$\\frac{8}{9}$$",
   "correct_answer": 0,
   "skill_id": 78,
   "difficulty_id": 1,
   "explanation": "A fraction is in simplest form when numerator and denominator share no common factor besides 1. $$\\frac{2}{6}$$ can be simplified to $$\\frac{1}{3}$$, so it is not in simplest form.",
   "hints": [
    "Check if the top and bottom share a common factor.",
    "2 and 6 are both divisible by 2."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q6",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: Q6 = option 1 (2/6)."
  },
  {
   "n": 7,
   "type_id": 1,
   "question": "What is the length of the rectangle given its perimeter? Perimeter = 60 m, width 12 m.",
   "answer0": "5 m",
   "answer1": "15 m",
   "answer2": "18 m",
   "answer3": "24 m",
   "correct_answer": 2,
   "skill_id": 136,
   "difficulty_id": 2,
   "explanation": "Half the perimeter = length + width = 60 ÷ 2 = 30 m. Length = 30 − 12 = 18 m.",
   "hints": [
    "Perimeter = 2 × (length + width).",
    "60 ÷ 2 = 30; subtract the 12 m width."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q7",
   "image_needed": true,
   "image_options": false,
   "image_file": "q7.png",
   "notes": "Key: Q7 = option 3 (18 m). Rectangle diagram labelled '?', 'Perimeter = 60 m', '12 m'.",
   "image_page": 4,
   "image_bbox": [
    0.2,
    0.62,
    0.56,
    0.79
   ],
   "image_loc": "rectangle diagram with perimeter and width labels, middle of page below Q7"
  },
  {
   "n": 8,
   "type_id": 1,
   "question": "Which of the following figures has perpendicular lines?",
   "answer0": "Letter A",
   "answer1": "Letter N",
   "answer2": "Letter M",
   "answer3": "Letter E",
   "correct_answer": 3,
   "skill_id": 100,
   "difficulty_id": 1,
   "explanation": "Perpendicular lines meet at a right angle (90°). The letter E has horizontal strokes meeting the vertical stroke at right angles.",
   "hints": [
    "Perpendicular means meeting at 90°.",
    "Which letter has a right angle where two strokes meet? E does."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q8",
   "image_needed": true,
   "image_options": true,
   "image_file": null,
   "notes": "Key: Q8 = option 4 (letter E). Four letter drawings A, N, M, E stacked vertically; crop each as q8_opt0..3.",
   "image_page": 5,
   "image_bbox": [
    0.27,
    0.15,
    0.42,
    0.82
   ],
   "image_loc": "four large letter figures (A, N, M, E) stacked down the left-centre of the page"
  },
  {
   "n": 9,
   "type_id": 1,
   "question": "Which of the following figures is symmetrical?",
   "answer0": "Figure 1",
   "answer1": "Figure 2",
   "answer2": "Figure 3",
   "answer3": "Figure 4",
   "correct_answer": 0,
   "skill_id": 144,
   "difficulty_id": 2,
   "explanation": "A symmetrical figure can be folded so both halves match. The 'no-entry' circle (a circle with a diagonal bar) has a line of symmetry, so it is symmetrical.",
   "hints": [
    "A symmetrical figure has a fold line giving two matching halves.",
    "Test each: the circle-with-bar sign is symmetrical."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q9",
   "image_needed": true,
   "image_options": true,
   "image_file": null,
   "notes": "Key: Q9 = option 1. Four figures stacked vertically (no-entry sign, wavy band, four-leaf clover, rectangle with attached triangle); crop each as q9_opt0..3.",
   "image_page": 6,
   "image_bbox": [
    0.25,
    0.14,
    0.52,
    0.68
   ],
   "image_loc": "four option figures stacked vertically down the left-centre of the page"
  },
  {
   "n": 10,
   "type_id": 1,
   "question": "Jane completed her job at 01 20. She worked for 4 h 30 min. At what time did she start her job?",
   "answer0": "5.50 a.m.",
   "answer1": "8.50 a.m.",
   "answer2": "8.10 p.m.",
   "answer3": "8.50 p.m.",
   "correct_answer": 3,
   "skill_id": 135,
   "difficulty_id": 2,
   "explanation": "01 20 is 1.20 a.m. Going back 4 h 30 min: 01 20 − 4 h = 21 20 (the previous day) − 30 min = 20 50, i.e. 8.50 p.m.",
   "hints": [
    "Subtract the duration from the finishing time.",
    "01 20 minus 4 h 30 min lands in the previous evening: 20 50 = 8.50 p.m."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q10",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: Q10 = option 4 (8.50 p.m.)."
  },
  {
   "n": 11,
   "type_id": 1,
   "question": "Mr Ling sold 8 sofas and some carpets for $5928. The sofa cost $645 each. How much did the carpets cost?",
   "answer0": "$741",
   "answer1": "$768",
   "answer2": "$5160",
   "answer3": "$5283",
   "correct_answer": 1,
   "skill_id": 118,
   "difficulty_id": 2,
   "explanation": "8 sofas cost 8 × $645 = $5160. Carpets = $5928 − $5160 = $768.",
   "hints": [
    "Find the total cost of the sofas first.",
    "8 × $645 = $5160; subtract from $5928."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q11",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: Q11 = option 2 ($768)."
  },
  {
   "n": 12,
   "type_id": 1,
   "question": "Mandy and William had a total of 1712 stickers at first. After Mandy gave away 92 stickers, William had 5 times as many stickers as Mandy. How many stickers did Mandy have in the end?",
   "answer0": "270",
   "answer1": "324",
   "answer2": "362",
   "answer3": "1350",
   "correct_answer": 0,
   "skill_id": 118,
   "difficulty_id": 3,
   "explanation": "After Mandy gives away 92, the total left is 1712 − 92 = 1620. This is 5 + 1 = 6 units (William = 5 units, Mandy = 1 unit). 1 unit = 1620 ÷ 6 = 270, so Mandy had 270 in the end.",
   "hints": [
    "Subtract the 92 stickers given away from the total first.",
    "The remaining 1620 splits into 6 equal units (5 for William, 1 for Mandy)."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q12",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: Q12 = option 1 (270)."
  },
  {
   "n": 13,
   "type_id": 1,
   "question": "ABCD is a square. ∠ADF = 56° and ∠EDC = 75°. Find ∠EDF.",
   "answer0": "15°",
   "answer1": "19°",
   "answer2": "34°",
   "answer3": "41°",
   "correct_answer": 3,
   "skill_id": 230,
   "difficulty_id": 3,
   "explanation": "∠ADC of the square is 90°. ∠ADF + ∠EDF + ... overlap: ∠EDF = ∠ADF + ∠EDC − ∠ADC = 56° + 75° − 90° = 41°.",
   "hints": [
    "The corner angle ADC of a square is 90°.",
    "∠ADF and ∠EDC overlap; ∠EDF = 56° + 75° − 90°."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q13",
   "image_needed": true,
   "image_options": false,
   "image_file": "q13.png",
   "notes": "Key: Q13 = option 4 (41°). Square ABCD with E on AB, F on BC, lines from D, angles 56° and 75° marked at D.",
   "image_page": 7,
   "image_bbox": [
    0.32,
    0.5,
    0.62,
    0.72
   ],
   "image_loc": "square diagram with marked angles below the Q13 statement, centre of page"
  },
  {
   "n": 14,
   "type_id": 1,
   "question": "Jerry bought 3 apples and 1 orange. The cost of 3 apples was $5.25. An apple cost $0.60 less than an orange. What was the cost of an orange?",
   "answer0": "$1.15",
   "answer1": "$1.75",
   "answer2": "$2.35",
   "answer3": "$4.65",
   "correct_answer": 2,
   "skill_id": 131,
   "difficulty_id": 2,
   "explanation": "1 apple = $5.25 ÷ 3 = $1.75. An apple costs $0.60 less than an orange, so orange = $1.75 + $0.60 = $2.35.",
   "hints": [
    "Find the cost of 1 apple first.",
    "$5.25 ÷ 3 = $1.75; add $0.60 to get the orange."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q14",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: Q14 = option 3 ($2.35)."
  },
  {
   "n": 15,
   "type_id": 1,
   "question": "The original height of a plant was recorded at the start of week 1. The bar graph shows the increase in the height of the plant at the end of each week. The height of the plant was 22 cm by the end of week 4. What was the height of the plant by the end of week 2?",
   "answer0": "10 cm",
   "answer1": "14 cm",
   "answer2": "18 cm",
   "answer3": "28 cm",
   "correct_answer": 1,
   "skill_id": 104,
   "difficulty_id": 3,
   "explanation": "Total increase over 4 weeks (2 + 4 + 3 + 5 = 14 cm) means the original height = 22 − 14 = 8 cm. By end of week 2 the increase is 2 + 4 = 6 cm, so height = 8 + 6 = 14 cm.",
   "hints": [
    "Add all four weekly increases to find total growth, then the starting height.",
    "Original height = 22 − 14 = 8 cm; add the week 1 and week 2 increases (2 + 4)."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q15",
   "image_needed": true,
   "image_options": false,
   "image_file": "q15.png",
   "notes": "Key: Q15 = option 2 (14 cm). Bar graph: weeks 1-4 increases of 2, 4, 3, 5 cm.",
   "image_page": 8,
   "image_bbox": [
    0.18,
    0.38,
    0.8,
    0.6
   ],
   "image_loc": "bar graph of weekly height increase, middle of page below the Q15 text"
  },
  {
   "n": 16,
   "type_id": 2,
   "question": "What number is 100 more than 9997? [?]",
   "answer0": "10097",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 105,
   "difficulty_id": 1,
   "explanation": "9997 + 100 = 10 097.",
   "hints": [
    "Add 100 to 9997.",
    "Increase the hundreds place by 1."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q16",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: Q16 = 10097."
  },
  {
   "n": 17,
   "type_id": 2,
   "question": "Two factors of 21 are 1 and 21. What are the other two factors of 21? [?] and [?]",
   "answer0": "3",
   "answer1": "7",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 111,
   "difficulty_id": 1,
   "explanation": "The factors of 21 are 1, 3, 7 and 21. Besides 1 and 21, the other two factors are 3 and 7.",
   "hints": [
    "A factor divides 21 exactly.",
    "3 × 7 = 21."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q17",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: Q17 = 7 and 3 (order interchangeable)."
  },
  {
   "n": 18,
   "type_id": 2,
   "question": "Write $$3\\frac{5}{8}$$ as an improper fraction. [?]",
   "answer0": "29/8",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 119,
   "difficulty_id": 1,
   "explanation": "$$3\\frac{5}{8}$$ = $$\\frac{3 \\times 8 + 5}{8}$$ = $$\\frac{29}{8}$$.",
   "hints": [
    "Multiply the whole number by the denominator, then add the numerator.",
    "(3 × 8) + 5 = 29, over 8."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q18",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: Q18 = 29/8."
  },
  {
   "n": 19,
   "type_id": 2,
   "question": "Find the value of $$\\frac{7}{9}-\\frac{2}{3}$$. [?]",
   "answer0": "1/9",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 121,
   "difficulty_id": 2,
   "explanation": "Convert $$\\frac{2}{3}$$ to ninths: $$\\frac{2}{3}=\\frac{6}{9}$$. Then $$\\frac{7}{9}-\\frac{6}{9}=\\frac{1}{9}$$.",
   "hints": [
    "Make the denominators the same.",
    "2/3 = 6/9, then subtract from 7/9."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q19",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: Q19 = 1/9."
  },
  {
   "n": 20,
   "type_id": 2,
   "question": "Round 78.55 to the nearest whole number. [?]",
   "answer0": "79",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 128,
   "difficulty_id": 1,
   "explanation": "The tenths digit is 5, so round up: 78.55 → 79.",
   "hints": [
    "Look at the first decimal place.",
    "5 or more rounds up the whole number."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q20",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: Q20 = 79."
  },
  {
   "n": 21,
   "type_id": 2,
   "question": "Arrange the following fractions from the smallest to the greatest.<br>$$\\frac{5}{6}$$, $$\\frac{5}{12}$$, $$\\frac{11}{12}$$<br>[?], [?], [?]",
   "answer0": "5/12",
   "answer1": "5/6",
   "answer2": "11/12",
   "answer3": null,
   "correct_answer": null,
   "skill_id": 79,
   "difficulty_id": 2,
   "explanation": "Express in twelfths: $$\\frac{5}{6}=\\frac{10}{12}$$. Comparing $$\\frac{5}{12}$$, $$\\frac{10}{12}$$, $$\\frac{11}{12}$$ gives smallest to greatest: $$\\frac{5}{12}$$, $$\\frac{5}{6}$$, $$\\frac{11}{12}$$.",
   "hints": [
    "Convert all to a common denominator of 12.",
    "5/6 = 10/12, so order is 5/12, 10/12, 11/12."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q21",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key printed as '3/5, 3/5, 3/5' which is a typo/OCR artefact; the correct ordered answer for the stated fractions is 5/12, 5/6, 11/12 (solved/verified)."
  },
  {
   "n": 22,
   "type_id": 2,
   "question": "26.92 + 0.58 = [?]",
   "answer0": "27.50",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 129,
   "difficulty_id": 1,
   "explanation": "26.92 + 0.58 = 27.50.",
   "hints": [
    "Line up the decimal points.",
    "92 + 58 hundredths = 150 hundredths = 1.50."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q22",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: Q22 = 27.50."
  },
  {
   "n": 23,
   "type_id": 2,
   "question": "Find the value of 8.26 × 9. [?]",
   "answer0": "74.34",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 130,
   "difficulty_id": 2,
   "explanation": "8.26 × 9 = 74.34.",
   "hints": [
    "Multiply as 826 × 9 then place the decimal point.",
    "826 × 9 = 7434, so 8.26 × 9 = 74.34."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q23",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: Q23 = 74.34."
  },
  {
   "n": 24,
   "type_id": 2,
   "question": "In the figure, ABCD is a rectangle. Find the value of ∠y. [?]",
   "answer0": "18",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 230,
   "difficulty_id": 2,
   "explanation": "At corner B the right angle is 90°. The marked 72° and ∠y together with the line make 90°: ∠y = 90° − 72° = 18°.",
   "hints": [
    "Corner B of a rectangle is 90°.",
    "72° + ∠y = 90°."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q24",
   "image_needed": true,
   "image_options": false,
   "image_file": "q24.png",
   "notes": "Key: Q24 = 18 (degrees). Rectangle ABCD with a line from B to side DC making 72° at B and angle y below it.",
   "image_page": 11,
   "image_bbox": [
    0.2,
    0.72,
    0.52,
    0.85
   ],
   "image_loc": "rectangle ABCD diagram with 72° and y marked near corner B, below Q24"
  },
  {
   "n": 25,
   "type_id": 2,
   "question": "Measure and write down the size of ∠m. [?]",
   "answer0": "121",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 140,
   "difficulty_id": 2,
   "explanation": "Using a protractor, ∠m measures 121°.",
   "hints": [
    "Place the protractor centre on the angle vertex.",
    "Read the scale that starts from 0° along the base line."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q25",
   "image_needed": true,
   "image_options": false,
   "image_file": "q25.png",
   "notes": "Key: Q25(a) = 121°. Only part (a) is served — it has a definite value. Part (b) 'Draw ∠ABC = 83°' is a drawing task with no value answer and is omitted. Figure is an angle ∠m to measure.",
   "image_page": 12,
   "image_bbox": [
    0.25,
    0.15,
    0.58,
    0.29
   ],
   "image_loc": "single angle drawing labelled m near top of page for Q25(a)"
  },
  {
   "n": 26,
   "type_id": 2,
   "question": "State the time 36 min before midnight using the 24-hour clock. [?]<br>What is the duration from 10 35 to 13 08? [?] h [?] min",
   "answer0": "2324",
   "answer1": "2",
   "answer2": "33",
   "answer3": null,
   "correct_answer": null,
   "skill_id": 135,
   "difficulty_id": 2,
   "explanation": "(a) Midnight is 24 00; 36 min before is 24 00 − 36 min = 23 24. (b) From 10 35 to 13 08: 10 35 to 13 35 is 3 h, but 13 08 is 27 min short, so 3 h − 27 min = 2 h 33 min.",
   "hints": [
    "(a) Count back 36 min from 00 00 / 24 00.",
    "(b) Find whole hours first then adjust the minutes."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q26",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: Q26(a) = 2324; Q26(b) = 2 h 33 min."
  },
  {
   "n": 27,
   "type_id": 2,
   "question": "The perimeter of a square is 36 m. What is the area of the square? [?]",
   "answer0": "81",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 137,
   "difficulty_id": 2,
   "explanation": "Side = perimeter ÷ 4 = 36 ÷ 4 = 9 m. Area = 9 × 9 = 81 m².",
   "hints": [
    "A square has 4 equal sides.",
    "Side = 36 ÷ 4 = 9; area = side × side."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q27",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: Q27 = 81 m² (answer in m²)."
  },
  {
   "n": 28,
   "type_id": 2,
   "question": "Six landmarks on a map of a district are shown in the square grid.<br>(a) Which landmark is north-east of R and north of S? [?]<br>(b) Parvati is at one of the landmarks. She is facing U and needs to turn 45° clockwise to face P. Which landmark is Parvati at? [?]",
   "answer0": "P",
   "answer1": "T",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 142,
   "difficulty_id": 2,
   "explanation": "(a) The landmark that is both north-east of R and directly north of S is P. (b) Turning 45° clockwise from facing U to facing P places Parvati at T.",
   "hints": [
    "(a) Use the compass: north-east of R and directly above S.",
    "(b) A 45° clockwise turn changes the facing direction by one compass point."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q28",
   "image_needed": true,
   "image_options": false,
   "image_file": "q28.png",
   "notes": "Key: Q28(a) = P; Q28(b) = T. Square grid with landmarks P, Q, U, T, R, S and a North arrow.",
   "image_page": 13,
   "image_bbox": [
    0.24,
    0.36,
    0.74,
    0.66
   ],
   "image_loc": "square grid of six labelled landmarks with N arrow, middle of page"
  },
  {
   "n": 29,
   "type_id": 0,
   "question": "Shade three more squares in the figure so that CD is the line of symmetry.",
   "answer0": null,
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 145,
   "difficulty_id": 2,
   "explanation": "Reflect each already-shaded square across the diagonal CD and shade its mirror image so the pattern is symmetrical about CD.",
   "hints": [
    "CD is the diagonal mirror line.",
    "Each shaded square needs its reflection shaded on the other side of CD."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q29",
   "image_needed": true,
   "image_options": false,
   "image_file": "q29.png",
   "notes": "type_id 0 — interactive 'shade the squares' task, skipped on insert. Answer: shade the three squares that are the mirror images of the existing shaded squares across diagonal CD. Grid figure on page.",
   "image_page": 14,
   "image_bbox": [
    0.32,
    0.13,
    0.66,
    0.4
   ],
   "image_loc": "square grid with diagonal CD and some shaded squares, upper part of page"
  },
  {
   "n": 30,
   "type_id": 2,
   "question": "Rashid and Wen Long cycled a total distance of 8.34 km. Rashid cycled 3 times as far as Wen Long did. How far did Wen Long cycle? Give your answer correct to 2 decimal places. [?]",
   "answer0": "2.09",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 131,
   "difficulty_id": 2,
   "explanation": "Total is 3 + 1 = 4 units. 1 unit (Wen Long) = 8.34 ÷ 4 = 2.085 km ≈ 2.09 km (to 2 d.p.).",
   "hints": [
    "Wen Long is 1 unit, Rashid is 3 units, so 4 units in total.",
    "8.34 ÷ 4 = 2.085, round to 2 decimal places."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q30",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: Q30 = 2.085 km ≈ 2.09 km (answer in km, 2 d.p.)."
  },
  {
   "n": 31,
   "type_id": 2,
   "question": "Siva had some money. She bought 7 books for $8.65 and had $7.45 left. How much money did Siva have at first? [?]",
   "answer0": "16.10",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 83,
   "difficulty_id": 1,
   "explanation": "Money at first = money spent + money left = $8.65 + $7.45 = $16.10.",
   "hints": [
    "Add what she spent to what she had left.",
    "$8.65 + $7.45 = $16.10."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q31",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: Q31 = $16.10 (answer prefixed with $)."
  },
  {
   "n": 32,
   "type_id": 2,
   "question": "Mrs Chan had 5 $$l$$ of orange juice. Her daughter drank $$\\frac{3}{5}$$ $$l$$ of it. How much orange juice had Mrs Chan left? [?]",
   "answer0": "4 2/5",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 122,
   "difficulty_id": 2,
   "explanation": "5 − $$\\frac{3}{5}$$ = $$4\\frac{5}{5}-\\frac{3}{5}$$ = $$4\\frac{2}{5}$$ litres.",
   "hints": [
    "Borrow 1 whole from 5 as 5/5.",
    "5/5 − 3/5 = 2/5, leaving 4 wholes."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q32",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: Q32 = 4 2/5 litres. FIB answer kept plain as a mixed number '4 2/5'."
  },
  {
   "n": 33,
   "type_id": 2,
   "question": "Some pupils joined a survey to indicate their favourite ice-cream flavour. The bar graph shows the results of the survey. What was the total number of pupils who joined the survey? [?]",
   "answer0": "265",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 104,
   "difficulty_id": 2,
   "explanation": "Add all four bars: Vanilla 95 + Chocolate 70 + Strawberry 65 + Mango 35 = 265 pupils.",
   "hints": [
    "Read each bar's value.",
    "95 + 70 + 65 + 35 = 265."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q33",
   "image_needed": true,
   "image_options": false,
   "image_file": "q33.png",
   "notes": "Key: Q33 = 265. Bar graph of favourite ice-cream flavours (Vanilla 95, Chocolate 70, Strawberry 65, Mango 35).",
   "image_page": 15,
   "image_bbox": [
    0.16,
    0.37,
    0.78,
    0.6
   ],
   "image_loc": "bar graph of ice-cream flavours, middle of page below the Q33 text"
  },
  {
   "n": 34,
   "type_id": 2,
   "question": "At first, Mei Hua had $48 less than Celeste. Mei Hua then gave $36 to Celeste. How much more money did Celeste have than Mei Hua in the end? [?]",
   "answer0": "120",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 35,
   "difficulty_id": 2,
   "explanation": "At first the gap is $48. Giving $36 widens the gap by 2 × $36 = $72. New difference = $48 + $72 = $120.",
   "hints": [
    "A transfer changes the difference by twice the amount given.",
    "$48 + (2 × $36) = $120."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q34",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: Q34 = $120 (answer prefixed with $)."
  },
  {
   "n": 35,
   "type_id": 2,
   "question": "The figure is made up of 10 identical squares. The area of each square is 49 cm². What is the perimeter of the figure? [?]",
   "answer0": "140",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 138,
   "difficulty_id": 3,
   "explanation": "Side of each square = √49 = 7 cm. The outline of the figure is 20 square-sides long, so perimeter = 20 × 7 = 140 cm.",
   "hints": [
    "Find one square's side from its area (7 × 7 = 49).",
    "Count the unit sides on the outline (20), then multiply by 7."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q35",
   "image_needed": true,
   "image_options": false,
   "image_file": "q35.png",
   "notes": "Key: Q35 = 140 cm (answer in cm). Figure of 10 identical squares arranged in a staircase/offset shape.",
   "image_page": 16,
   "image_bbox": [
    0.22,
    0.5,
    0.5,
    0.64
   ],
   "image_loc": "arrangement of 10 identical squares, below the Q35 text upper-middle of page"
  },
  {
   "n": 36,
   "type_id": 2,
   "question": "The table shows the ticket prices to an amusement park during the weekdays and weekends.<br>Adult: weekdays $14.50 per ticket, weekend $31 for 2 tickets.<br>Child below 12 years old: weekdays $6.90 per ticket, weekend $8.90 per ticket.<br>(a) Mr Omar took his child, Suresh, to the park on Monday. Suresh was 6 years old. How much did Mr Omar pay for their tickets? [?]<br>(b) On Saturday, Mr and Mrs Johnson took their 3 children to the park. Their eldest child was 11 years old. How much did Mr Johnson pay for their tickets? [?]",
   "answer0": "21.40",
   "answer1": "57.70",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 148,
   "difficulty_id": 2,
   "explanation": "(a) Monday is a weekday: 1 adult $14.50 + 1 child $6.90 = $21.40. (b) Saturday is a weekend: 2 adults = $31 (2 for $31), 3 children at $8.90 = $26.70; total = $31 + $26.70 = $57.70.",
   "hints": [
    "(a) Use the weekday column for 1 adult + 1 child.",
    "(b) Weekend: 2 adults are $31 together; add 3 children at $8.90 each."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q36",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: Q36(a) = $21.40; Q36(b) = $57.70. Ticket-price table reproduced in the stem text rather than as an image."
  },
  {
   "n": 37,
   "type_id": 2,
   "question": "Shop Mobile had 80 mobile phones on Monday and started selling the mobile phones from Tuesday to Friday. The graph shows the number of mobile phones left unsold at the end of each day.<br>(a) How many mobile phones were sold on Tuesday? [?]<br>(b) By which day did Shop Mobile sell $$\\frac{7}{10}$$ of the mobile phones? [?]",
   "answer0": "8",
   "answer1": "Friday",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 147,
   "difficulty_id": 3,
   "explanation": "(a) On Tuesday the unsold count drops from 80 to 72, so 80 − 72 = 8 phones were sold. (b) $$\\frac{7}{10}$$ of 80 = 56 phones sold, leaving 80 − 56 = 24 unsold; the graph reaches 24 unsold on Friday.",
   "hints": [
    "(a) Read the line value on Monday and Tuesday and subtract.",
    "(b) 7/10 of 80 = 56 sold; find when only 24 remain."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q37",
   "image_needed": true,
   "image_options": false,
   "image_file": "q37.png",
   "notes": "Key: Q37(a) = 8; Q37(b) = Friday (when 56 of 80 sold, 24 left). Line graph of phones left unsold Mon-Sat.",
   "image_page": 18,
   "image_bbox": [
    0.12,
    0.18,
    0.8,
    0.45
   ],
   "image_loc": "line graph of mobile phones left unsold across the week, upper part of page"
  },
  {
   "n": 38,
   "type_id": 2,
   "question": "At a school activity, one teacher was needed to guide at most 8 pupils in a group. A total of 125 girls and 386 boys participated in the activity. The last group had fewer than 8 pupils.<br>(a) What was the least number of teachers needed to guide all the pupils? [?]<br>(b) How many pupils were there in the last group? [?]",
   "answer0": "64",
   "answer1": "7",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 117,
   "difficulty_id": 3,
   "explanation": "Total pupils = 386 + 125 = 511. 511 ÷ 8 = 63 remainder 7. (a) The remainder needs an extra group/teacher, so 63 + 1 = 64 teachers. (b) The last group has the remainder = 7 pupils.",
   "hints": [
    "Find the total number of pupils first.",
    "511 ÷ 8 = 63 R 7; the remainder needs one more group."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q38",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: Q38(a) = 64; Q38(b) = 7."
  },
  {
   "n": 39,
   "type_id": 2,
   "question": "The shaded figure (not drawn to scale) is made up of rectangles.<br>(a) Find the area of the shaded figure. [?]<br>(b) Find the perimeter of the shaded figure. [?]",
   "answer0": "122",
   "answer1": "54",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 138,
   "difficulty_id": 3,
   "explanation": "(a) Split into rectangles: top 6 × 10 = 60 m², a 3 × 6 = 18 m² piece, and a 4 × 11 = 44 m² leg; total area = 60 + 18 + 44 = 122 m². (b) Going round the outline: 10 + 12 + 3 + 5 + 4 + 11 + 3 + 6 = 54 m.",
   "hints": [
    "(a) Break the L/T-shape into rectangles and add their areas.",
    "(b) Add every side length around the boundary."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q39",
   "image_needed": true,
   "image_options": false,
   "image_file": "q39.png",
   "notes": "Key: Q39(a) = 122 m²; Q39(b) = 54 m. Shaded composite rectilinear figure with edge labels 10 m, 12 m, 17 m, 11 m, 3 m, 4 m.",
   "image_page": 20,
   "image_bbox": [
    0.16,
    0.14,
    0.6,
    0.43
   ],
   "image_loc": "black shaded composite rectangle figure with dimension labels, top-left of page"
  },
  {
   "n": 40,
   "type_id": 2,
   "question": "There are 36 pupils in a class. There are 12 boys in the class.<br>(a) What fraction of the class are girls? Express your answer in the simplest form. [?]<br>(b) $$\\frac{4}{9}$$ of the pupils in the class wear spectacles. How many pupils do not wear spectacles? [?]",
   "answer0": "2/3",
   "answer1": "20",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 120,
   "difficulty_id": 2,
   "explanation": "(a) Girls = 36 − 12 = 24. Fraction = $$\\frac{24}{36}=\\frac{2}{3}$$. (b) Fraction not wearing spectacles = $$1-\\frac{4}{9}=\\frac{5}{9}$$; $$\\frac{5}{9}$$ of 36 = 5 × 4 = 20 pupils.",
   "hints": [
    "(a) Girls = total − boys, then simplify the fraction.",
    "(b) 1 − 4/9 = 5/9; find 5/9 of 36."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q40",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: Q40(a) = 2/3; Q40(b) = 20. Part (a) FIB answer is a plain fraction '2/3'."
  },
  {
   "n": 41,
   "type_id": 2,
   "question": "An exercise book cost 4 times as much as a pencil. Paul paid $7.56 for 3 pencils and 1 exercise book.<br>(a) What was the cost of 1 pencil? [?]<br>(b) What was the cost of 1 exercise book? [?]",
   "answer0": "1.08",
   "answer1": "4.32",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 131,
   "difficulty_id": 3,
   "explanation": "1 exercise book = 4 pencils, so 3 pencils + 1 book = 3 + 4 = 7 pencils = $7.56. (a) 1 pencil = $7.56 ÷ 7 = $1.08. (b) 1 exercise book = 4 × $1.08 = $4.32.",
   "hints": [
    "Express everything in 'pencils': 3 pencils + 1 book = 7 pencils.",
    "$7.56 ÷ 7 = $1.08, then ×4 for the book."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q41",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: Q41(a) = $1.08; Q41(b) = $4.32."
  },
  {
   "n": 42,
   "type_id": 2,
   "question": "Mrs Koh had 90 candies and 72 jellies. She packed all of them into as many bags as possible. Each bag contained an equal number of candies. The total number of candies and jellies in each bag was also the same.<br>(a) How many bags of candies and jellies did Mrs Koh pack? [?]<br>(b) What was the total number of candies and jellies in each bag? [?]",
   "answer0": "18",
   "answer1": "9",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 113,
   "difficulty_id": 3,
   "explanation": "(a) Bags must divide both 90 and 72 — the common factors are 1, 2, 3, 6, 9, 18. The greatest (most bags possible) is 18 bags. (b) Each bag holds 90 ÷ 18 = 5 candies and 72 ÷ 18 = 4 jellies, total 5 + 4 = 9 per bag.",
   "hints": [
    "(a) Find the greatest common factor of 90 and 72.",
    "(b) Divide each quantity by the number of bags and add."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q42",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: Q42(a) = 18 (greatest common factor); Q42(b) = 9 (5 + 4)."
  },
  {
   "n": 43,
   "type_id": 2,
   "question": "Mike bought 5 pens and 2 erasers. Kelly bought 2 pens and 5 erasers. Mike paid $2.40 more than Kelly. An eraser cost $0.95.<br>(a) How much more does a pen cost than an eraser? [?]<br>(b) What was the cost of a pen? [?]",
   "answer0": "0.80",
   "answer1": "1.75",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 131,
   "difficulty_id": 3,
   "explanation": "The difference between the two buys is 3 pens − 3 erasers = $2.40. So 3 × (pen − eraser) = $2.40, giving pen − eraser = $0.80. (a) A pen costs $0.80 more than an eraser. (b) 1 pen = $0.80 + $0.95 = $1.75.",
   "hints": [
    "Compare the two purchases: the difference is 3 pens vs 3 erasers.",
    "3 × (pen − eraser) = $2.40, so pen − eraser = $0.80; add the eraser's $0.95."
   ],
   "source": "Pei Chun 2023 P4 End of Year Exam Q43",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: Q43(a) = $0.80; Q43(b) = $1.75."
  }
 ]
}