{
 "paper": {
  "school": "Paya Lebar Methodist Girls' School (Primary)",
  "year": 2025,
  "level": "P4",
  "label": "End-of-Year Exam",
  "source_prefix": "PLMGS 2025 P4 End-of-Year Exam",
  "has_answer_key": true
 },
 "questions": [
  {
   "n": 1,
   "type_id": 1,
   "question": "The value of the digit 2 in 42 513 is ____________.",
   "answer0": "20",
   "answer1": "200",
   "answer2": "2000",
   "answer3": "20 000",
   "correct_answer": 2,
   "skill_id": 105,
   "difficulty_id": 1,
   "explanation": "The digit 2 in 42 513 is in the thousands place, so its value is 2 × 1000 = 2000.",
   "hints": [
    "Identify the place of the digit 2: ten thousands, thousands, hundreds, tens or ones.",
    "The 2 sits in the thousands column, so its value is 2 thousands = 2000."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q1",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key Q1 = option 3 (2000)."
  },
  {
   "n": 2,
   "type_id": 1,
   "question": "In 57.92, the digit ____________ is in the tenths place.",
   "answer0": "9",
   "answer1": "2",
   "answer2": "7",
   "answer3": "5",
   "correct_answer": 0,
   "skill_id": 123,
   "difficulty_id": 1,
   "explanation": "In 57.92 the first digit after the decimal point is the tenths place. That digit is 9.",
   "hints": [
    "The first digit after the decimal point is the tenths place.",
    "57.9 2 — the 9 is right after the point."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q2",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key Q2 = option 1 (9)."
  },
  {
   "n": 3,
   "type_id": 1,
   "question": "Which of the following is <b>not</b> an equivalent fraction of $$\\frac{1}{4}$$?",
   "answer0": "$$\\frac{3}{12}$$",
   "answer1": "$$\\frac{4}{16}$$",
   "answer2": "$$\\frac{6}{24}$$",
   "answer3": "$$\\frac{7}{32}$$",
   "correct_answer": 3,
   "skill_id": 77,
   "difficulty_id": 2,
   "explanation": "$$\\frac{1}{4}$$ equals 3/12, 4/16 and 6/24 (each numerator is one-quarter of the denominator). $$\\frac{7}{32}$$ is not, since 7 × 4 = 28 ≠ 32. So $$\\frac{7}{32}$$ is not equivalent.",
   "hints": [
    "A fraction equals $$\\frac{1}{4}$$ only if the numerator × 4 = denominator.",
    "Check 7 × 4 = 28, but the denominator is 32, so $$\\frac{7}{32}$$ is the odd one out."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q3",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key Q3 = option 4 (7/32)."
  },
  {
   "n": 4,
   "type_id": 1,
   "question": "2 and 3 are factors of ____________.",
   "answer0": "10",
   "answer1": "18",
   "answer2": "27",
   "answer3": "29",
   "correct_answer": 1,
   "skill_id": 111,
   "difficulty_id": 1,
   "explanation": "A number with both 2 and 3 as factors must be divisible by 6. Among the options, 18 = 6 × 3 is divisible by both 2 and 3.",
   "hints": [
    "The number must be divisible by both 2 and 3 (so by 6).",
    "18 ÷ 2 = 9 and 18 ÷ 3 = 6, so 18 works."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q4",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key Q4 = option 2 (18)."
  },
  {
   "n": 5,
   "type_id": 1,
   "question": "$$6\\frac{3}{8}$$ = $$\\frac{\\Box}{8}$$<br>What is the missing number in the box?",
   "answer0": "51",
   "answer1": "48",
   "answer2": "26",
   "answer3": "18",
   "correct_answer": 0,
   "skill_id": 119,
   "difficulty_id": 2,
   "explanation": "Convert the mixed number to an improper fraction: $$6\\frac{3}{8}$$ = (6 × 8 + 3)/8 = (48 + 3)/8 = $$\\frac{51}{8}$$. The missing number is 51.",
   "hints": [
    "Multiply the whole number by the denominator, then add the numerator.",
    "6 × 8 = 48, and 48 + 3 = 51."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q5",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key Q5 = option 1 (51)."
  },
  {
   "n": 6,
   "type_id": 1,
   "question": "Write $$7\\frac{9}{25}$$ as a decimal.",
   "answer0": "7.9",
   "answer1": "7.09",
   "answer2": "7.36",
   "answer3": "7.036",
   "correct_answer": 2,
   "skill_id": 127,
   "difficulty_id": 2,
   "explanation": "Make the denominator 100: $$\\frac{9}{25}$$ = $$\\frac{36}{100}$$ = 0.36. So $$7\\frac{9}{25}$$ = 7.36.",
   "hints": [
    "Convert $$\\frac{9}{25}$$ to hundredths by multiplying numerator and denominator by 4.",
    "$$\\frac{36}{100}$$ = 0.36, so the answer is 7.36."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q6",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key Q6 = option 3 (7.36)."
  },
  {
   "n": 7,
   "type_id": 1,
   "question": "The table shows the number of burgers and muffins sold by Mr Loh for 5 days.<br>How many more burgers than muffins were sold on Thursday?",
   "answer0": "1",
   "answer1": "5",
   "answer2": "3",
   "answer3": "8",
   "correct_answer": 3,
   "skill_id": 147,
   "difficulty_id": 1,
   "explanation": "On Thursday, burgers sold = 30 and muffins sold = 22. Difference = 30 − 22 = 8.",
   "hints": [
    "Read the Thursday row: burgers = 30, muffins = 22.",
    "30 − 22 = 8."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q7",
   "image_needed": true,
   "image_page": 4,
   "image_bbox": [
    0.14,
    0.2,
    0.78,
    0.34
   ],
   "image_loc": "table of burgers and muffins sold Mon-Fri, upper portion of page",
   "image_options": false,
   "image_file": "q7.png",
   "notes": "Shared table for Q7 and Q8. Key Q7 = option 4 (8)."
  },
  {
   "n": 8,
   "type_id": 1,
   "question": "The table shows the number of burgers and muffins sold by Mr Loh for 5 days.<br>On which two days did Mr Loh sell the same total number of burgers and muffins?",
   "answer0": "Monday and Wednesday",
   "answer1": "Monday and Friday",
   "answer2": "Tuesday and Wednesday",
   "answer3": "Tuesday and Friday",
   "correct_answer": 0,
   "skill_id": 148,
   "difficulty_id": 2,
   "explanation": "Daily totals: Mon = 25+30 = 55, Tue = 24+24 = 48, Wed = 28+27 = 55, Thu = 30+22 = 52, Fri = 26+21 = 47. Monday and Wednesday both total 55.",
   "hints": [
    "Add burgers + muffins for each day.",
    "Monday = 55 and Wednesday = 55 — these match."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q8",
   "image_needed": true,
   "image_page": 4,
   "image_bbox": [
    0.14,
    0.2,
    0.78,
    0.34
   ],
   "image_loc": "table of burgers and muffins sold Mon-Fri, upper portion of page",
   "image_options": false,
   "image_file": "q8.png",
   "notes": "Shared table for Q7 and Q8. Key Q8 = option 1 (Monday and Wednesday)."
  },
  {
   "n": 9,
   "type_id": 1,
   "question": "Which of the following figures is a net of a cuboid?",
   "answer0": "Figure 1",
   "answer1": "Figure 2",
   "answer2": "Figure 3",
   "answer3": "Figure 4",
   "correct_answer": 3,
   "skill_id": 232,
   "difficulty_id": 2,
   "explanation": "A valid net of a cuboid folds into a closed box with six rectangular faces. Figure 4 is the only arrangement that folds correctly into a cuboid.",
   "hints": [
    "Mentally fold each net and check it makes a closed box with no overlaps or gaps.",
    "Only Figure 4 forms a proper cuboid."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q9",
   "image_needed": true,
   "image_options": true,
   "image_page": 5,
   "image_bbox": [
    0.15,
    0.13,
    0.4,
    0.58
   ],
   "image_loc": "four candidate nets stacked vertically, options 1-4, left side of page",
   "image_file": null,
   "notes": "Image-option MCQ: each option is a net drawing. Crop q9_opt0.png..q9_opt3.png. Key Q9 = option 4 (Figure 4)."
  },
  {
   "n": 10,
   "type_id": 1,
   "question": "Valerie mixed 17.82 $$l$$ of water and 5.18 $$l$$ of orange syrup to make some orange juice. She poured the orange juice equally into 8 similar jugs. How much orange juice did she pour into each jug? Round your answer to the nearest tenth.",
   "answer0": "2.8 $$l$$",
   "answer1": "2.9 $$l$$",
   "answer2": "2.87 $$l$$",
   "answer3": "2.88 $$l$$",
   "correct_answer": 1,
   "skill_id": 131,
   "difficulty_id": 2,
   "explanation": "Total juice = 17.82 + 5.18 = 23 l. Each jug = 23 ÷ 8 = 2.875 l. Rounded to the nearest tenth = 2.9 l.",
   "hints": [
    "Add the two volumes first, then divide by 8.",
    "23 ÷ 8 = 2.875, which rounds to 2.9 to the nearest tenth."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q10",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key Q10 = option 2 (2.9 l)."
  },
  {
   "n": 11,
   "type_id": 1,
   "question": "Amy took $$\\frac{7}{12}$$ h to fix a jigsaw puzzle. Jenny took $$\\frac{2}{3}$$ h slower to fix the same jigsaw puzzle. How long did Jenny take to fix the puzzle? Express your answer in the simplest form.",
   "answer0": "$$\\frac{1}{12}$$ h",
   "answer1": "$$\\frac{3}{5}$$ h",
   "answer2": "$$1\\frac{1}{4}$$ h",
   "answer3": "$$1\\frac{5}{6}$$ h",
   "correct_answer": 2,
   "skill_id": 122,
   "difficulty_id": 2,
   "explanation": "Jenny = $$\\frac{7}{12}$$ + $$\\frac{2}{3}$$. Change $$\\frac{2}{3}$$ to $$\\frac{8}{12}$$: $$\\frac{7}{12}$$ + $$\\frac{8}{12}$$ = $$\\frac{15}{12}$$ = $$1\\frac{3}{12}$$ = $$1\\frac{1}{4}$$ h.",
   "hints": [
    "'Slower' means Jenny's time is longer, so add the two fractions.",
    "$$\\frac{7}{12}$$ + $$\\frac{8}{12}$$ = $$\\frac{15}{12}$$ = $$1\\frac{1}{4}$$ h."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q11",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key Q11 = option 3 (1 1/4 h)."
  },
  {
   "n": 12,
   "type_id": 1,
   "question": "The figure is a garden made up of 2 square plots, Plot X and Plot Y. The total area of the garden is 52 m². The area of Plot Y is 16 m². What is the length of Plot X?",
   "answer0": "36 m",
   "answer1": "24 m",
   "answer2": "6 m",
   "answer3": "4 m",
   "correct_answer": 2,
   "skill_id": 137,
   "difficulty_id": 2,
   "explanation": "Area of Plot X = 52 − 16 = 36 m². Plot X is a square, so its side = the number that multiplies by itself to give 36, which is 6 m.",
   "hints": [
    "Subtract Plot Y's area from the total to get Plot X's area.",
    "Plot X is a square of area 36 m², and 6 × 6 = 36, so its length is 6 m."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q12",
   "image_needed": true,
   "image_page": 6,
   "image_bbox": [
    0.34,
    0.46,
    0.6,
    0.62
   ],
   "image_loc": "two adjoining squares Plot X (larger, with '?' on top) and Plot Y, middle of page",
   "image_options": false,
   "image_file": "q12.png",
   "notes": "Key Q12 = option 3 (6 m)."
  },
  {
   "n": 13,
   "type_id": 1,
   "question": "The pie chart shows the different ways 162 students go to school.<br>How many students go to school by car?",
   "answer0": "6",
   "answer1": "18",
   "answer2": "36",
   "answer3": "54",
   "correct_answer": 1,
   "skill_id": 236,
   "difficulty_id": 2,
   "explanation": "Bus = $$\\frac{1}{3}$$ and Walk = $$\\frac{5}{9}$$. Fraction for car = 1 − $$\\frac{1}{3}$$ − $$\\frac{5}{9}$$ = $$\\frac{9}{9}$$ − $$\\frac{3}{9}$$ − $$\\frac{5}{9}$$ = $$\\frac{1}{9}$$. Car = $$\\frac{1}{9}$$ × 162 = 18 students.",
   "hints": [
    "Find the fraction for Car: 1 minus the Bus and Walk fractions.",
    "$$\\frac{1}{9}$$ of 162 = 18."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q13",
   "image_needed": true,
   "image_page": 7,
   "image_bbox": [
    0.28,
    0.12,
    0.55,
    0.34
   ],
   "image_loc": "pie chart with sectors Car, Bus (1/3) and Walk (5/9), upper part of page",
   "image_options": false,
   "image_file": "q13.png",
   "notes": "Key Q13 = option 2 (18)."
  },
  {
   "n": 14,
   "type_id": 1,
   "question": "The perimeter of the rectangle is 42 cm. What is the length of the rectangle?",
   "answer0": "28 cm",
   "answer1": "21 cm",
   "answer2": "14 cm",
   "answer3": "6 cm",
   "correct_answer": 2,
   "skill_id": 136,
   "difficulty_id": 2,
   "explanation": "Perimeter = 2 × (length + breadth). Length + breadth = 42 ÷ 2 = 21 cm. Breadth = 7 cm, so length = 21 − 7 = 14 cm.",
   "hints": [
    "Half the perimeter equals length + breadth.",
    "21 − 7 = 14 cm."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q14",
   "image_needed": true,
   "image_page": 7,
   "image_bbox": [
    0.34,
    0.58,
    0.6,
    0.72
   ],
   "image_loc": "rectangle with '?' on top edge and 7 cm on right side, middle of page",
   "image_options": false,
   "image_file": "q14.png",
   "notes": "Key Q14 = option 3 (14 cm)."
  },
  {
   "n": 15,
   "type_id": 1,
   "question": "Which of the following letters has at least one line of symmetry?",
   "answer0": "G",
   "answer1": "C",
   "answer2": "N",
   "answer3": "K",
   "correct_answer": 1,
   "skill_id": 144,
   "difficulty_id": 1,
   "explanation": "The letter C has a horizontal line of symmetry (top and bottom halves mirror each other). G, N and K have no line of symmetry.",
   "hints": [
    "A line of symmetry folds the letter so both halves match exactly.",
    "C folds along a horizontal line into matching halves."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q15",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Options are plain letters G/C/N/K — text options, not pictures. Key Q15 = option 2 (C)."
  },
  {
   "n": 16,
   "type_id": 1,
   "question": "Bala is arranging stickers on a display board. He has more than 20 stickers but fewer than 50 stickers. When he arranges them in rows of 6, there are 4 stickers left over. When he arranges them in rows of 8, there are 2 stickers left over. How many stickers does Bala have?",
   "answer0": "48",
   "answer1": "40",
   "answer2": "34",
   "answer3": "24",
   "correct_answer": 2,
   "skill_id": 118,
   "difficulty_id": 3,
   "explanation": "Need a number 20–50 that leaves remainder 4 when divided by 6 and remainder 2 when divided by 8. Check 34: 34 ÷ 6 = 5 r4 ✓ and 34 ÷ 8 = 4 r2 ✓. So Bala has 34 stickers.",
   "hints": [
    "Test each option against both conditions.",
    "34 ÷ 6 leaves 4 and 34 ÷ 8 leaves 2 — both match."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q16",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key Q16 = option 3 (34)."
  },
  {
   "n": 17,
   "type_id": 2,
   "question": "Write twenty thousand and forty-one in numerals.<br>Ans: [?]",
   "answer0": "20041",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 106,
   "difficulty_id": 1,
   "explanation": "Twenty thousand = 20 000, and forty-one = 41. Combine: 20 000 + 41 = 20 041.",
   "hints": [
    "Twenty thousand is 20 000.",
    "Add forty-one: 20 000 + 41 = 20 041."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q17",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key 17) 20041."
  },
  {
   "n": 18,
   "type_id": 2,
   "question": "Arrange these fractions from the smallest to the greatest.<br>$$\\frac{8}{11}$$ , $$\\frac{1}{2}$$ , $$\\frac{5}{11}$$<br>Ans: [?] (smallest) , [?] , [?] (greatest)",
   "answer0": "5/11",
   "answer1": "1/2",
   "answer2": "8/11",
   "answer3": null,
   "correct_answer": null,
   "skill_id": 79,
   "difficulty_id": 2,
   "explanation": "Compare: $$\\frac{5}{11}$$ ≈ 0.45, $$\\frac{1}{2}$$ = 0.5, $$\\frac{8}{11}$$ ≈ 0.73. From smallest to greatest: $$\\frac{5}{11}$$, $$\\frac{1}{2}$$, $$\\frac{8}{11}$$.",
   "hints": [
    "$$\\frac{1}{2}$$ = $$\\frac{5.5}{11}$$, so it sits between $$\\frac{5}{11}$$ and $$\\frac{8}{11}$$.",
    "Order: $$\\frac{5}{11}$$, $$\\frac{1}{2}$$, $$\\frac{8}{11}$$."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q18",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key 18) 5/11, 1/2, 8/11 (smallest to greatest). FIB fraction answers kept plain a/b."
  },
  {
   "n": 19,
   "type_id": 2,
   "question": "Round 18 430 to the nearest hundred.<br>Ans: [?]",
   "answer0": "18400",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 109,
   "difficulty_id": 1,
   "explanation": "Look at the tens digit of 18 430, which is 3. Since 3 < 5, round down: 18 430 → 18 400.",
   "hints": [
    "Check the tens digit to decide rounding to the nearest hundred.",
    "Tens digit is 3 (< 5), so round down to 18 400."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q19",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key 19) 18400."
  },
  {
   "n": 20,
   "type_id": 2,
   "question": "Rectangle PQRS is made up of 8 unit squares. What fraction of rectangle PQRS is shaded?<br>Ans: [?]",
   "answer0": "3/8",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 120,
   "difficulty_id": 2,
   "explanation": "Each unit square is split into triangles; the shaded triangles add up to 3 whole unit squares out of the 8 unit squares. So the shaded fraction is $$\\frac{3}{8}$$.",
   "hints": [
    "Combine the shaded triangle halves into whole squares.",
    "3 squares' worth are shaded out of 8, giving $$\\frac{3}{8}$$."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q20",
   "image_needed": true,
   "image_page": 11,
   "image_bbox": [
    0.2,
    0.18,
    0.45,
    0.3
   ],
   "image_loc": "rectangle PQRS divided into 8 unit squares with shaded triangles, top-left below the question",
   "image_options": false,
   "image_file": "q20.png",
   "notes": "Key 20) 3/8. FIB fraction answer kept plain 3/8."
  },
  {
   "n": 21,
   "type_id": 2,
   "question": "Express 0.6 as a fraction.<br>Ans: [?]",
   "answer0": "6/10",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 126,
   "difficulty_id": 1,
   "explanation": "0.6 means 6 tenths, which is written as $$\\frac{6}{10}$$.",
   "hints": [
    "The digit after the decimal point is in the tenths place.",
    "0.6 = 6 tenths = $$\\frac{6}{10}$$."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q21",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key 21) 6/10 (not simplified — accepting key's answer). FIB fraction answer kept plain."
  },
  {
   "n": 22,
   "type_id": 0,
   "question": "Name the two angles that are smaller than 90°.",
   "answer0": null,
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 140,
   "difficulty_id": 2,
   "explanation": "Angles a and d in the figure are each smaller than a right angle (acute), so the two angles smaller than 90° are angle a and angle d.",
   "hints": [
    "An angle smaller than 90° looks 'sharper' than a square corner.",
    "Angles a and d are the two acute ones."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q22",
   "image_needed": true,
   "image_page": 11,
   "image_bbox": [
    0.3,
    0.62,
    0.62,
    0.82
   ],
   "image_loc": "irregular pentagon with labelled angles a, b, c, d, e, lower-middle of page",
   "image_options": false,
   "image_file": "q22.png",
   "notes": "Key 22) angle a and angle d. type_id 0: answer depends on identifying labelled angles in a figure (no clean value/sequence input). SKIPPED on insert."
  },
  {
   "n": 23,
   "type_id": 2,
   "question": "What is the remainder when 2503 is divided by 4?<br>Ans: [?]",
   "answer0": "3",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 117,
   "difficulty_id": 1,
   "explanation": "2503 ÷ 4 = 625 remainder 3, since 625 × 4 = 2500 and 2503 − 2500 = 3.",
   "hints": [
    "Find the largest multiple of 4 not exceeding 2503.",
    "625 × 4 = 2500, so the remainder is 2503 − 2500 = 3."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q23",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key 23) 3."
  },
  {
   "n": 24,
   "type_id": 2,
   "question": "Write the decimal represented by A.<br>Ans: [?]",
   "answer0": "1.57",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 123,
   "difficulty_id": 2,
   "explanation": "Between 1.5 and 1.6 the number line is divided into 10 equal parts, each worth 0.01. Arrow A points to the 7th mark after 1.5, which is 1.50 + 0.07 = 1.57.",
   "hints": [
    "Each small interval between 1.5 and 1.6 is one hundredth (0.01).",
    "A is 7 marks past 1.5, so it reads 1.57."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q24",
   "image_needed": true,
   "image_page": 12,
   "image_bbox": [
    0.18,
    0.34,
    0.55,
    0.46
   ],
   "image_loc": "number line marked 1.5 and 1.6 with arrow A pointing upward, upper-middle of page",
   "image_options": false,
   "image_file": "q24.png",
   "notes": "Key 24) 1.57."
  },
  {
   "n": 25,
   "type_id": 2,
   "question": "ABCD is a rectangle. Find $$\\angle x$$.<br>Ans: [?]°",
   "answer0": "56",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 230,
   "difficulty_id": 2,
   "explanation": "Corner A of the rectangle is a right angle (90°). The 34° is part of that corner, so $$\\angle x$$ = 90° − 34° = 56°.",
   "hints": [
    "Each corner of a rectangle is 90°.",
    "$$\\angle x$$ = 90° − 34° = 56°."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q25",
   "image_needed": true,
   "image_page": 12,
   "image_bbox": [
    0.2,
    0.55,
    0.6,
    0.74
   ],
   "image_loc": "rectangle ABCD with diagonal from A to side BC, marking 34° and x at corner A, lower-middle of page",
   "image_options": false,
   "image_file": "q25.png",
   "notes": "Key 25) 56°."
  },
  {
   "n": 26,
   "type_id": 0,
   "question": "Complete the drawing of Square WXYZ and label Point Z.",
   "answer0": null,
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 143,
   "difficulty_id": 2,
   "explanation": "Given points W, X and Y, the fourth vertex Z completes the square. Z is placed so WXYZ forms a square (Z below X, opposite to the WY span), drawn on the grid.",
   "hints": [
    "WXYZ is a square, so the fourth vertex is the mirror of X across the line WY.",
    "Plot Z so all four sides are equal and the corners are right angles."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q26",
   "image_needed": true,
   "image_page": 13,
   "image_bbox": [
    0.27,
    0.16,
    0.62,
    0.44
   ],
   "image_loc": "square grid with W, X, Y marked and lines WX, XY drawn, upper-middle of page",
   "image_options": false,
   "image_file": "q26.png",
   "notes": "type_id 0: a draw-and-label task (complete the square on a grid), no value/sequence answer. Key shows the completed square diagram. SKIPPED on insert."
  },
  {
   "n": 27,
   "type_id": 2,
   "question": "Janice bought a roll of ribbon, 3 m long, to wrap some presents. She cut the roll of ribbon into 7 equal pieces. What is the length of each piece of ribbon? Round your answer to the nearest hundredth.<br>Ans: [?] m",
   "answer0": "0.43",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 125,
   "difficulty_id": 2,
   "explanation": "Each piece = 3 ÷ 7 = 0.428... m. Rounded to the nearest hundredth (2 decimal places) = 0.43 m.",
   "hints": [
    "Divide the total length by the number of pieces.",
    "3 ÷ 7 = 0.4285..., which rounds to 0.43 m."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q27",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key 27) 0.43 m."
  },
  {
   "n": 28,
   "type_id": 2,
   "question": "The bar graph shows the number of students who borrowed books from the school library from January to April.<br>a) In which month did the least number of students borrow books?<br>Ans: [?]<br>b) How many fewer students borrowed books in March than in April?<br>Ans: [?]",
   "answer0": "March",
   "answer1": "700",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 104,
   "difficulty_id": 2,
   "explanation": "a) The shortest bar is March, so the least number of students borrowed in March. b) March ≈ 1100 students and April ≈ 1800 students, so 1800 − 1100 = 700 fewer in March than April.",
   "hints": [
    "The least is the shortest bar; for the difference, subtract the two bar heights.",
    "March is shortest; April − March = 1800 − 1100 = 700."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q28",
   "image_needed": true,
   "image_page": 14,
   "image_bbox": [
    0.2,
    0.18,
    0.78,
    0.42
   ],
   "image_loc": "bar graph of students borrowing books Jan-Apr, upper portion of page",
   "image_options": false,
   "image_file": "q28.png",
   "notes": "Two-part FIB: a) month (word answer March), b) 700. Key 28) a) March b) 700."
  },
  {
   "n": 29,
   "type_id": 2,
   "question": "Gladys jogged a distance of $$\\frac{2}{3}$$ km. She jogged $$\\frac{1}{5}$$ km more than the distance jogged by Ben. What was the total distance Gladys and Ben jogged? Give your answer as a mixed number.<br>Ans: [?] km",
   "answer0": "1 2/15",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 122,
   "difficulty_id": 3,
   "explanation": "Ben = Gladys − $$\\frac{1}{5}$$ = $$\\frac{2}{3}$$ − $$\\frac{1}{5}$$ = $$\\frac{10}{15}$$ − $$\\frac{3}{15}$$ = $$\\frac{7}{15}$$ km. Total = $$\\frac{2}{3}$$ + $$\\frac{7}{15}$$ = $$\\frac{10}{15}$$ + $$\\frac{7}{15}$$ = $$\\frac{17}{15}$$ = $$1\\frac{2}{15}$$ km.",
   "hints": [
    "Find Ben's distance first by subtracting $$\\frac{1}{5}$$ from Gladys' $$\\frac{2}{3}$$.",
    "Add Gladys + Ben: $$\\frac{10}{15}$$ + $$\\frac{7}{15}$$ = $$\\frac{17}{15}$$ = $$1\\frac{2}{15}$$ km."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q29",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key 29) 1 2/15. FIB mixed-number answer kept plain '1 2/15'."
  },
  {
   "n": 30,
   "type_id": 0,
   "question": "Measure and write down the size of $$\\angle$$AOB.",
   "answer0": null,
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 140,
   "difficulty_id": 2,
   "explanation": "Using a protractor on the printed figure, $$\\angle$$AOB measures 126°.",
   "hints": [
    "Place the protractor centre on O along ray OA.",
    "Read where ray OB crosses the scale: 126°."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q30",
   "image_needed": true,
   "image_page": 15,
   "image_bbox": [
    0.18,
    0.5,
    0.62,
    0.74
   ],
   "image_loc": "angle AOB with ray OA horizontal and ray OB rising to the right, lower portion of page",
   "image_options": false,
   "image_file": "q30.png",
   "notes": "type_id 0: requires physically measuring the printed angle with a protractor — not solvable from text and depends on exact print scale (answer 126°). SKIPPED on insert."
  },
  {
   "n": 31,
   "type_id": 2,
   "question": "In the figure, PQRS is a rectangle with an area of 144 cm² and PS = 9 cm. X and Y are identical squares. Find the length of one side of square Y.<br>Ans: [?] cm",
   "answer0": "5",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 137,
   "difficulty_id": 3,
   "explanation": "PQ (length of rectangle) = 144 ÷ 9 = 16 cm. Along SR the gaps total 2 + 2 + 2 = 6 cm, leaving 16 − 6 = 10 cm shared by the two identical squares X and Y. Each side = 10 ÷ 2 = 5 cm.",
   "hints": [
    "Find PQ first: area ÷ PS = 144 ÷ 9 = 16 cm.",
    "Subtract the three 2 cm gaps (16 − 6 = 10) and split between two equal squares: 10 ÷ 2 = 5 cm."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q31",
   "image_needed": true,
   "image_page": 16,
   "image_bbox": [
    0.28,
    0.17,
    0.6,
    0.3
   ],
   "image_loc": "rectangle PQRS with two small squares X and Y inside along base, with 9 cm and three 2 cm labels, upper-middle of page",
   "image_options": false,
   "image_file": "q31.png",
   "notes": "Key 31) 10 ÷ 2 = 5 cm."
  },
  {
   "n": 32,
   "type_id": 2,
   "question": "In the figure, a rectangular piece of paper ABCD was folded along BD. Find $$\\angle a$$.<br>Ans: [?]°",
   "answer0": "14",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 230,
   "difficulty_id": 3,
   "explanation": "Corner A (= folded corner) is a right angle, 90°. The corner is split by the fold into the 38° angle and angle a, with a third part equal to 38° by the fold symmetry. So 90° = 38° + 38° + a, giving a = 90° − 76° = 14°.",
   "hints": [
    "The right angle at the folded corner is 90° and the fold makes two equal 38° angles.",
    "a = 90° − 38° − 38° = 14°."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q32",
   "image_needed": true,
   "image_page": 16,
   "image_bbox": [
    0.26,
    0.52,
    0.58,
    0.72
   ],
   "image_loc": "folded rectangle ABCD showing triangle with angle a and 38° at vertex D, lower-middle of page",
   "image_options": false,
   "image_file": "q32.png",
   "notes": "Key 32) 14°."
  },
  {
   "n": 33,
   "type_id": 2,
   "question": "Figures J, K, L and M are geometric figures. Identify the geometric figures. Write the letter representing the figure.<br>pyramid: [?] and [?]<br>prism: [?] and [?]",
   "answer0": "K",
   "answer1": "L",
   "answer2": "J",
   "answer3": "M",
   "correct_answer": null,
   "skill_id": 231,
   "difficulty_id": 2,
   "explanation": "Pyramids have a base and triangular faces meeting at an apex: Figures K and L. Prisms have two identical parallel ends joined by rectangles: Figures J and M.",
   "hints": [
    "A pyramid narrows to a single point (apex); a prism has two matching parallel ends.",
    "Pyramids: K and L. Prisms: J and M."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q33",
   "image_needed": true,
   "image_page": 17,
   "image_bbox": [
    0.18,
    0.14,
    0.65,
    0.45
   ],
   "image_loc": "four 3-D solids labelled Figure J, K, L, M in a 2x2 layout, upper portion of page",
   "image_options": false,
   "image_file": "q33.png",
   "notes": "Two-part FIB: pyramid = K, L; prism = J, M. Order within each pair not graded as fixed but stored K,L,J,M. Key 33) a) K and L b) J and M."
  },
  {
   "n": 34,
   "type_id": 2,
   "question": "The line graph shows the number of customers in a restaurant at different times in a day. During which 1-hour interval was the increase in the number of customers in the restaurant the greatest?<br>Ans: [?] to [?]",
   "answer0": "1100",
   "answer1": "1200",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 147,
   "difficulty_id": 2,
   "explanation": "Hourly increases: 0900→1000 falls; 1000→1100 rises from ~12 to ~19 (+7); 1100→1200 rises from ~19 to ~38 (+19); 1200→1300 falls. The steepest rise is 1100 to 1200.",
   "hints": [
    "Look for the steepest upward segment of the line.",
    "From 1100 to 1200 the line climbs the most (about 19 to 38)."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q34",
   "image_needed": true,
   "image_page": 18,
   "image_bbox": [
    0.22,
    0.2,
    0.78,
    0.44
   ],
   "image_loc": "line graph of number of customers vs time 0900-1400, upper-middle of page",
   "image_options": false,
   "image_file": "q34.png",
   "notes": "Shared line graph for Q34 and Q35. Two-blank time interval. Key 34) 1100 to 1200."
  },
  {
   "n": 35,
   "type_id": 2,
   "question": "The line graph shows the number of customers in a restaurant at different times in a day. What was the decrease in the number of customers from 12 00 to 14 00?<br>Ans: [?]",
   "answer0": "30",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 148,
   "difficulty_id": 2,
   "explanation": "At 1200 there were about 38 customers (the peak) and at 1400 about 8 customers. Decrease = 38 − 8 = 30 (reading the graph: 1200 = 37/38, 1400 = 7/8, difference 30).",
   "hints": [
    "Read the customer values at 1200 and at 1400, then subtract.",
    "Peak at 1200 minus the value at 1400 gives a decrease of 30."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q35",
   "image_needed": true,
   "image_page": 18,
   "image_bbox": [
    0.22,
    0.2,
    0.78,
    0.44
   ],
   "image_loc": "line graph of number of customers vs time 0900-1400, upper-middle of page",
   "image_options": false,
   "image_file": "q35.png",
   "notes": "Shared line graph for Q34 and Q35. Key 35) 30."
  },
  {
   "n": 36,
   "type_id": 2,
   "question": "In the figure, ABCD is made up of 7 identical rectangles. BC = 27 cm. Find the perimeter of the figure.<br>Ans: [?] cm",
   "answer0": "180",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 138,
   "difficulty_id": 3,
   "explanation": "BC = 27 cm is the height, made of 3 rectangle widths stacked, so each rectangle is 27 ÷ 3 = 9 cm wide. The figure's length AB = 27 + 27 = 54 cm (two rectangle lengths of 27). Perimeter = AB + DC + the two heights + the inner step edges: 54 + 54 + 27 + 27 + 9 + 9 = 180 cm.",
   "hints": [
    "The height BC = 27 cm splits into 3 equal rectangle widths of 9 cm each.",
    "Add all outer edges: 54 + 54 + 27 + 27 + 9 + 9 = 180 cm."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q36",
   "image_needed": true,
   "image_page": 19,
   "image_bbox": [
    0.32,
    0.18,
    0.62,
    0.3
   ],
   "image_loc": "figure ABCD made of 7 identical rectangles with 27 cm marked on right side BC, upper portion of page",
   "image_options": false,
   "image_file": "q36.png",
   "notes": "Key 36) 54 + 54 + 27 + 27 + 9 + 9 = 180 cm."
  },
  {
   "n": 37,
   "type_id": 2,
   "question": "Weiling bought 24 packets of sweets. There were 32 sweets in each packet. She gave 12 sweets to each of her 40 classmates.<br>(a) How many sweets did Weiling buy altogether?<br>Ans: (a) [?]<br>(b) How many sweets were left?<br>Ans: (b) [?]",
   "answer0": "768",
   "answer1": "288",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 118,
   "difficulty_id": 2,
   "explanation": "(a) Total bought = 24 × 32 = 768 sweets. (b) Sweets given away = 12 × 40 = 480. Sweets left = 768 − 480 = 288.",
   "hints": [
    "(a) Multiply packets by sweets per packet: 24 × 32.",
    "(b) Subtract sweets given (12 × 40 = 480) from 768: 768 − 480 = 288."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q37",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Two-part. Key 37) a) 24×32 = 768; b) 768−480 = 288."
  },
  {
   "n": 38,
   "type_id": 2,
   "question": "Farid baked some cookies. He gave away $$\\frac{3}{10}$$ of his cookies to his friends and gave away $$\\frac{1}{2}$$ of his cookies to his siblings. He had 50 cookies left.<br>(a) What fraction of Farid's cookies was left?<br>Ans: (a) [?]<br>(b) How many cookies did Farid bake?<br>Ans: (b) [?]",
   "answer0": "2/10",
   "answer1": "250",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 122,
   "difficulty_id": 3,
   "explanation": "(a) Given away = $$\\frac{3}{10}$$ + $$\\frac{1}{2}$$ = $$\\frac{3}{10}$$ + $$\\frac{5}{10}$$ = $$\\frac{8}{10}$$. Fraction left = $$\\frac{10}{10}$$ − $$\\frac{8}{10}$$ = $$\\frac{2}{10}$$. (b) $$\\frac{2}{10}$$ → 50 cookies, so $$\\frac{1}{10}$$ → 25, and $$\\frac{10}{10}$$ → 25 × 10 = 250 cookies.",
   "hints": [
    "(a) Add the two fractions given away, then subtract from 1 (= $$\\frac{10}{10}$$).",
    "(b) $$\\frac{2}{10}$$ of the cookies is 50, so 1 unit ($$\\frac{1}{10}$$) = 25 and the whole = 250."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q38",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Two-part. Key 38) a) 2/10; b) 250. FIB fraction answer kept plain 2/10 (key leaves it unsimplified)."
  },
  {
   "n": 39,
   "type_id": 2,
   "question": "The figure is made up of 3 rectangles, A, B and C, and Square D. Rectangle A and Rectangle B are identical. Rectangle B has a breadth of 5 cm. The area of Square D is 49 cm².<br>(a) What is the length of Rectangle B?<br>Ans: (a) [?] cm<br>(b) What is the total area of the figure?<br>Ans: (b) [?] cm²",
   "answer0": "12",
   "answer1": "204",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 138,
   "difficulty_id": 3,
   "explanation": "Square D has area 49 cm², so its side = 7 cm (7 × 7 = 49). The length of Rectangle B = side of C + side of D = 7 + 5 = 12 cm. (b) The figure is a large rectangle of length 12 cm and height (5 + 7 = 12 cm wait) — total height = breadth of B (5) + side of D (7) = 12 cm; total area = 12 × 17... using key: total area = 17 × 12 = 204 cm².",
   "hints": [
    "(a) Square D's side = 7 cm (since 7 × 7 = 49); add the 5 cm to reach B's length: 7 + 5 = 12 cm.",
    "(b) Total area = 17 × 12 = 204 cm²."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q39",
   "image_needed": true,
   "image_page": 22,
   "image_bbox": [
    0.33,
    0.18,
    0.62,
    0.34
   ],
   "image_loc": "figure of rectangles A, B, C and square D with 5 cm and '?' labels, upper-middle of page",
   "image_options": false,
   "image_file": "q39.png",
   "notes": "Two-part. Key 39) a) 7+5 = 12 m (key writes '7×5=12 m' — a typo for 7+5; length B = 12); b) 17×12 = 204 cm²."
  },
  {
   "n": 40,
   "type_id": 2,
   "question": "Siti used white squares and black dots to form figures that follow a pattern. The first four figures are shown.<br>(a) Complete the table for Figure 5: white squares [?], total number of white squares and black dots [?].<br>(b) What is the total number of white squares and black dots used to form Figure 24?<br>Ans: (b) [?]",
   "answer0": "5",
   "answer1": "15",
   "answer2": "72",
   "answer3": null,
   "correct_answer": null,
   "skill_id": 108,
   "difficulty_id": 2,
   "explanation": "Pattern: Figure n has n white squares, 2n black dots, total 3n. (a) Figure 5: white squares = 5; total = 3 × 5 = 15. (b) Figure 24 total = 3 × 24 = 72.",
   "hints": [
    "Each figure adds 1 white square and 2 black dots; total = 3 × figure number.",
    "(a) Figure 5: 5 white, total 15. (b) Figure 24: 3 × 24 = 72."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q40",
   "image_needed": true,
   "image_page": 23,
   "image_bbox": [
    0.2,
    0.15,
    0.78,
    0.24
   ],
   "image_loc": "row of pattern Figures 1-4 made of white squares and black dots, upper portion of page",
   "image_options": false,
   "image_file": "q40.png",
   "notes": "Multi-blank: 5(a) white squares = 5, total = 15; (b) Figure 24 total = 72. Key 40) a) 5, 15 (key lists '10, 15' for black dots & total — black dots for Fig5 = 10, total = 15; white squares blank = 5); b) 24×2=48, 48+24=72."
  },
  {
   "n": 41,
   "type_id": 2,
   "question": "Sarah had twice as many blue beads as red beads. She had 3 times as many green beads as blue beads. She had a total of 1728 blue and green beads.<br>(a) How many green beads did Sarah have?<br>Ans: (a) [?]<br>(b) How many fewer red beads than green beads did Sarah have?<br>Ans: (b) [?]",
   "answer0": "1296",
   "answer1": "1080",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 118,
   "difficulty_id": 3,
   "explanation": "Let red = 1 unit. Blue = 2 units, green = 3 × blue = 6 units. Blue + green = 2 + 6 = 8 units = 1728, so 1 unit = 1728 ÷ 8 = 216. (a) Green = 6 units = 6 × 216 = 1296. (b) Red = 1 unit = 216, so green − red = 1296 − 216 = 1080.",
   "hints": [
    "Set red = 1 unit; blue = 2 units; green = 6 units. Blue + green = 8 units = 1728.",
    "1 unit = 216. Green = 6 × 216 = 1296; fewer red = 1296 − 216 = 1080."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q41",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Two-part. Key 41) a) 1728÷8=216, 216×6=1296; b) 1296−216=1080."
  },
  {
   "n": 42,
   "type_id": 2,
   "question": "The total mass of 3 identical tables and 5 identical stools is 173.1 kg. The total mass of 1 such table and 3 such stools is 65.3 kg.<br>(a) What is the total mass of a table and a stool?<br>Ans: (a) [?] kg<br>(b) What is the mass of 4 stools?<br>Ans: (b) [?] kg",
   "answer0": "53.9",
   "answer1": "22.8",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 131,
   "difficulty_id": 3,
   "explanation": "(a) 3 tables + 5 stools = 173.1; 1 table + 3 stools = 65.3. Tripling the second: 3 tables + 9 stools = 195.9. Subtract the first: 4 stools = 195.9 − 173.1 = 22.8 kg, so 1 stool = 5.7 kg. From the second: 1 table = 65.3 − 3 × 5.7 = 65.3 − 17.1 = 48.2 kg. Table + stool = 48.2 + 5.7 = 53.9 kg. (b) 4 stools = 4 × 5.7 = 22.8 kg.",
   "hints": [
    "Eliminate one item: scale the equations so the tables (or stools) match, then subtract.",
    "1 stool = 5.7 kg; table + stool = 53.9 kg; 4 stools = 22.8 kg."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q42",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Two-part. Key 42) a) 53.9 kg; b) 4 stools = 22.8 kg. (Key's working uses 173.1−53.9 route but lands a)=53.9, b)=22.8.)"
  },
  {
   "n": 43,
   "type_id": 2,
   "question": "Andy has a rectangular piece of paper measuring 40 cm by 20 cm as shown in Figure 1. He cuts out a square from the paper and shifts it to the side to create a new figure as shown in Figure 2. There is no overlapping of the 2 pieces of paper. Figure 2 has a perimeter of 160 cm.<br>(a) What is the perimeter of Figure 1?<br>Ans: (a) [?] cm<br>(b) What is the area of the square that was cut out?<br>Ans: (b) [?] cm²",
   "answer0": "120",
   "answer1": "100",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 138,
   "difficulty_id": 3,
   "explanation": "(a) Perimeter of Figure 1 = 2 × (40 + 20) = 2 × 60 = 120 cm. (b) Shifting the cut square adds extra edges equal to 4 square sides to the perimeter: 160 − 120 = 40 cm of extra edges = 4 sides, so each side = 40 ÷ 4 = 10 cm. Area of square = 10 × 10 = 100 cm².",
   "hints": [
    "(a) Perimeter of a rectangle = 2 × (length + breadth) = 2 × 60 = 120 cm.",
    "(b) The extra perimeter (160 − 120 = 40) equals 4 square sides, so side = 10 cm and area = 100 cm²."
   ],
   "source": "PLMGS 2025 P4 End-of-Year Exam Q43",
   "image_needed": true,
   "image_page": 26,
   "image_bbox": [
    0.18,
    0.22,
    0.78,
    0.38
   ],
   "image_loc": "Figure 1 (40 cm by 20 cm rectangle) and Figure 2 (step shape) side by side, upper-middle of page",
   "image_options": false,
   "image_file": "q43.png",
   "notes": "Two-part. Key 43) a) 20+40=60, 60×2=120 cm; b) 160−120=40, 40÷4=10, 10×10=100 cm²."
  }
 ]
}