{
 "paper": {
  "school": "Raffles Girls' Primary School",
  "year": 2024,
  "level": "P4",
  "label": "End-of-Year Exam",
  "source_prefix": "Raffles 2024 P4 End-of-Year Exam",
  "has_answer_key": true
 },
 "questions": [
  {
   "n": 1,
   "type_id": 1,
   "question": "The value of the digit 7 in 37 892 is [?].",
   "answer0": "70",
   "answer1": "700",
   "answer2": "7000",
   "answer3": "70 000",
   "correct_answer": 2,
   "skill_id": 105,
   "difficulty_id": 1,
   "explanation": "The digit 7 is in the thousands place, so its value is 7 × 1000 = 7000.",
   "hints": [
    "Identify which place the digit 7 sits in.",
    "37 892: 3 ten-thousands, 7 thousands, 8 hundreds, 9 tens, 2 ones."
   ],
   "source": "Raffles 2024 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": "In which of the following are the numbers arranged from the smallest to the greatest?",
   "answer0": "6830, 6803, 6083",
   "answer1": "6083, 6830, 6803",
   "answer2": "6830, 6083, 6803",
   "answer3": "6083, 6803, 6830",
   "correct_answer": 3,
   "skill_id": 107,
   "difficulty_id": 1,
   "explanation": "Order ascending: 6083 < 6803 < 6830. That is option 4.",
   "hints": [
    "Compare the thousands and hundreds digits.",
    "All start with 6; compare the hundreds digit next."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q2",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key Q2 = option 4."
  },
  {
   "n": 3,
   "type_id": 1,
   "question": "Which fraction is in its simplest form?",
   "answer0": "$$\\frac{5}{7}$$",
   "answer1": "$$\\frac{6}{9}$$",
   "answer2": "$$\\frac{3}{6}$$",
   "answer3": "$$\\frac{4}{10}$$",
   "correct_answer": 0,
   "skill_id": 78,
   "difficulty_id": 1,
   "explanation": "$$\\frac{5}{7}$$ has no common factor between 5 and 7, so it is already in simplest form. The others simplify: $$\\frac{6}{9}=\\frac{2}{3}$$, $$\\frac{3}{6}=\\frac{1}{2}$$, $$\\frac{4}{10}=\\frac{2}{5}$$.",
   "hints": [
    "A fraction is in simplest form when numerator and denominator share no common factor besides 1.",
    "Check each option for a common factor."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q3",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key Q3 = option 1 (5/7)."
  },
  {
   "n": 4,
   "type_id": 1,
   "question": "What fraction of the shapes are hearts?",
   "answer0": "$$\\frac{5}{6}$$",
   "answer1": "$$\\frac{5}{11}$$",
   "answer2": "$$\\frac{6}{5}$$",
   "answer3": "$$\\frac{6}{11}$$",
   "correct_answer": 3,
   "skill_id": 120,
   "difficulty_id": 1,
   "explanation": "There are 11 shapes in total: 5 pentagons and 6 hearts. The fraction that are hearts is $$\\frac{6}{11}$$.",
   "hints": [
    "Count the total number of shapes.",
    "Count how many are hearts, then write hearts over total."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q4",
   "image_needed": true,
   "image_options": false,
   "image_file": "q4.png",
   "image_page": 4,
   "image_bbox": [
    0.19,
    0.15,
    0.64,
    0.27
   ],
   "image_loc": "boxed row of pentagons and hearts below the question",
   "notes": "Count to verify: 5 pentagons + 6 hearts = 11 shapes; hearts = 6/11. Key Q4 = option 4."
  },
  {
   "n": 5,
   "type_id": 1,
   "question": "In the number 93.25, the digit [?] is in the tenths place.",
   "answer0": "5",
   "answer1": "2",
   "answer2": "3",
   "answer3": "9",
   "correct_answer": 1,
   "skill_id": 123,
   "difficulty_id": 1,
   "explanation": "In 93.25, the first digit after the decimal point is the tenths digit, which is 2.",
   "hints": [
    "The tenths place is the first digit to the right of the decimal point.",
    "93.25 → 2 is tenths, 5 is hundredths."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q5",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key Q5 = option 2 (2)."
  },
  {
   "n": 6,
   "type_id": 1,
   "question": "Which of the following decimals is the greatest?",
   "answer0": "0.369",
   "answer1": "0.192",
   "answer2": "0.346",
   "answer3": "0.129",
   "correct_answer": 0,
   "skill_id": 124,
   "difficulty_id": 1,
   "explanation": "Compare the tenths digit first: 0.369 and 0.346 have 3 tenths, the others have 1 tenth. Between 0.369 and 0.346, the hundredths digit 6 > 4, so 0.369 is greatest.",
   "hints": [
    "Compare the tenths digit first.",
    "If tied, compare the hundredths digit."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q6",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key Q6 = option 1 (0.369)."
  },
  {
   "n": 7,
   "type_id": 1,
   "question": "Which of the following is a factor of both 12 and 90?",
   "answer0": "8",
   "answer1": "6",
   "answer2": "5",
   "answer3": "4",
   "correct_answer": 1,
   "skill_id": 113,
   "difficulty_id": 2,
   "explanation": "Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90. The common factor among the options is 6.",
   "hints": [
    "A common factor divides both numbers exactly.",
    "Check which option divides both 12 and 90 with no remainder."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q7",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key Q7 = option 2 (6). 4 divides 12 but not 90; 5 divides 90 but not 12."
  },
  {
   "n": 8,
   "type_id": 1,
   "question": "Express $$1\\frac{3}{20}$$ as a decimal.",
   "answer0": "1.32",
   "answer1": "1.30",
   "answer2": "1.15",
   "answer3": "1.015",
   "correct_answer": 2,
   "skill_id": 127,
   "difficulty_id": 2,
   "explanation": "$$\\frac{3}{20}=\\frac{15}{100}=0.15$$, so $$1\\frac{3}{20}=1.15$$.",
   "hints": [
    "Make the denominator 100 by multiplying by 5.",
    "3/20 = 15/100 = 0.15."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q8",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key Q8 = option 3 (1.15)."
  },
  {
   "n": 9,
   "type_id": 1,
   "question": "What is the length of the pencil?",
   "answer0": "3.3 cm",
   "answer1": "5.6 cm",
   "answer2": "7.3 cm",
   "answer3": "10.6 cm",
   "correct_answer": 2,
   "skill_id": 85,
   "difficulty_id": 1,
   "explanation": "The pencil starts at the 3.3 cm mark and ends at about the 10.6 cm mark, so its length is 10.6 − 3.3 = 7.3 cm.",
   "hints": [
    "Read where the pencil starts and where it ends on the ruler.",
    "Length = end reading − start reading."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q9",
   "image_needed": true,
   "image_options": false,
   "image_file": "q9.png",
   "image_page": 5,
   "image_bbox": [
    0.13,
    0.55,
    0.88,
    0.68
   ],
   "image_loc": "pencil lying above a ruler, middle of page",
   "notes": "Key Q9 = option 3 (7.3 cm)."
  },
  {
   "n": 10,
   "type_id": 1,
   "question": "Mrs Lee had some stickers. After she gave 6 stickers to each of her 28 pupils, she had 12 stickers left. How many stickers did Mrs Lee have at first?",
   "answer0": "168",
   "answer1": "180",
   "answer2": "336",
   "answer3": "342",
   "correct_answer": 1,
   "skill_id": 118,
   "difficulty_id": 2,
   "explanation": "Stickers given out = 6 × 28 = 168. Add the 12 left over: 168 + 12 = 180.",
   "hints": [
    "First find how many stickers were given out altogether.",
    "Then add the leftover stickers."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q10",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key Q10 = option 2 (180)."
  },
  {
   "n": 11,
   "type_id": 1,
   "question": "The figure is made up of 3 identical rectangles. Find the area of the figure.",
   "answer0": "12 cm²",
   "answer1": "40 cm²",
   "answer2": "72 cm²",
   "answer3": "96 cm²",
   "correct_answer": 3,
   "skill_id": 138,
   "difficulty_id": 2,
   "explanation": "The 12 cm width spans two rectangle widths plus... each small rectangle is 6 cm wide. The right rectangle is upright (6 cm by length); two stacked rectangles on the left share the same length. Total width 12 cm = two rectangle long sides, so each rectangle is 6 cm by 8 cm = 48 cm² is not consistent; using the key the figure area is 96 cm² (3 identical rectangles each 4 cm by 8 cm = 32 cm², 3 × 32 = 96 cm²).",
   "hints": [
    "The whole figure is 3 identical rectangles.",
    "Use the 12 cm to work out each rectangle's dimensions, then multiply area by 3."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q11",
   "image_needed": true,
   "image_options": false,
   "image_file": "q11.png",
   "image_page": 6,
   "image_bbox": [
    0.24,
    0.36,
    0.54,
    0.55
   ],
   "image_loc": "figure of 3 rectangles with 12 cm width arrow beneath, upper-middle of page",
   "notes": "Key Q11 = option 4 (96 cm²). Figure needed for the layout; dimensions inferred to match key."
  },
  {
   "n": 12,
   "type_id": 1,
   "question": "Find the perimeter of the figure.",
   "answer0": "24 cm",
   "answer1": "42 cm",
   "answer2": "48 cm",
   "answer3": "54 cm",
   "correct_answer": 2,
   "skill_id": 96,
   "difficulty_id": 2,
   "explanation": "The outer rectangle is 14 cm by 7 cm. A square notch 3 cm wide is cut from the top. The perimeter = 14 + 7 + 14 + 7 + (two vertical sides of the notch) but the cut removes the 3 cm of top while adding the two depth sides and bottom of the notch. Total perimeter = 2 × (14 + 7) + 2 × (notch depth) = 42 + 6 = 48 cm.",
   "hints": [
    "Find the perimeter of the full rectangle first.",
    "A notch cut inward adds the extra edges of the cut."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q12",
   "image_needed": true,
   "image_options": false,
   "image_file": "q12.png",
   "image_page": 7,
   "image_bbox": [
    0.18,
    0.1,
    0.6,
    0.28
   ],
   "image_loc": "rectangle with a square notch on top edge, 3 cm/7 cm/14 cm labels, top of page",
   "notes": "Key Q12 = option 3 (48 cm)."
  },
  {
   "n": 13,
   "type_id": 1,
   "question": "ABCD is a square. Find $$\\angle z$$.",
   "answer0": "13°",
   "answer1": "41°",
   "answer2": "62°",
   "answer3": "77°",
   "correct_answer": 0,
   "skill_id": 197,
   "difficulty_id": 2,
   "explanation": "Angle ADC of the square is 90°. The two marked angles at D are 49° and 28°. So $$\\angle z = 90° - 49° - 28° = 13°$$.",
   "hints": [
    "The corner of a square is 90°.",
    "Subtract the two given angles from 90°."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q13",
   "image_needed": true,
   "image_options": false,
   "image_file": "q13.png",
   "image_page": 7,
   "image_bbox": [
    0.17,
    0.5,
    0.49,
    0.72
   ],
   "image_loc": "square ABCD with diagonals from D, angles 49°, 28° and z marked, lower-left of page",
   "notes": "Key Q13 = option 1 (13°)."
  },
  {
   "n": 14,
   "type_id": 1,
   "question": "The figure shows a cube. Which of the following is not the net of the cube?",
   "answer0": "Net 1",
   "answer1": "Net 2",
   "answer2": "Net 3",
   "answer3": "Net 4",
   "correct_answer": 3,
   "skill_id": 232,
   "difficulty_id": 2,
   "explanation": "Nets 1, 2 and 3 each fold into a cube. Net 4 has an arrangement of six squares that overlaps when folded, so it is not a valid net of the cube.",
   "hints": [
    "A valid cube net folds up with no overlapping or missing faces.",
    "Mentally fold each option."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q14",
   "image_needed": true,
   "image_options": true,
   "image_file": null,
   "image_page": 8,
   "image_bbox": [
    0.18,
    0.1,
    0.55,
    0.95
   ],
   "image_loc": "cube at top, then four candidate nets labelled (1)-(4) down the page",
   "notes": "Image-option MCQ: options are the four nets. Crop each net to q14_opt0..3.png. Key Q14 = option 4."
  },
  {
   "n": 15,
   "type_id": 1,
   "question": "What could be the mass of a Primary 4 Mathematics textbook?",
   "answer0": "33 g",
   "answer1": "330 g",
   "answer2": "33 kg",
   "answer3": "330 kg",
   "correct_answer": 1,
   "skill_id": 85,
   "difficulty_id": 1,
   "explanation": "A textbook has a mass of a few hundred grams. 33 g is far too light, 33 kg and 330 kg are far too heavy. 330 g is the sensible estimate.",
   "hints": [
    "Think about the mass of objects you can lift easily.",
    "1 kg is about the mass of 1 litre of water."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q15",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key Q15 = option 2 (330 g)."
  },
  {
   "n": 16,
   "type_id": 1,
   "question": "The table shows the height of five girls. What is the difference in height between Agnes and the tallest girl?",
   "answer0": "32 cm",
   "answer1": "28 cm",
   "answer2": "18 cm",
   "answer3": "14 cm",
   "correct_answer": 3,
   "skill_id": 147,
   "difficulty_id": 1,
   "explanation": "Agnes is 138 cm. The tallest girl is Devi at 152 cm. Difference = 152 − 138 = 14 cm.",
   "hints": [
    "Find the tallest girl in the table.",
    "Subtract Agnes's height from the tallest height."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q16",
   "image_needed": true,
   "image_options": false,
   "image_file": "q16.png",
   "image_page": 9,
   "image_bbox": [
    0.17,
    0.38,
    0.74,
    0.57
   ],
   "image_loc": "two-column table of names and heights, middle of page",
   "notes": "Key Q16 = option 4 (14 cm). Devi 152 is tallest."
  },
  {
   "n": 17,
   "type_id": 1,
   "question": "The line graph shows the number of visitors who visited an art gallery over a period of 7 months. The number of visitors decreased the most in the 1-month period between [?] and [?].",
   "answer0": "January and February",
   "answer1": "February and March",
   "answer2": "April and May",
   "answer3": "June and July",
   "correct_answer": 1,
   "skill_id": 147,
   "difficulty_id": 2,
   "explanation": "Reading the graph: Feb ≈ 2100 to Mar ≈ 800 is a drop of about 1300, the largest single-month decrease. (Apr 1800 to May 700 is about 1100.)",
   "hints": [
    "Look for the steepest downward segment.",
    "Compare the drop in visitors for each 1-month gap."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q17",
   "image_needed": true,
   "image_options": false,
   "image_file": "q17.png",
   "image_page": 10,
   "image_bbox": [
    0.18,
    0.17,
    0.85,
    0.52
   ],
   "image_loc": "line graph 'Visitors to Art Gallery', Jan-Jul on x-axis, middle of page",
   "notes": "Key Q17 = option 2 (February and March)."
  },
  {
   "n": 18,
   "type_id": 1,
   "question": "Which of the following shape does not have a line of symmetry?",
   "answer0": "Triangle",
   "answer1": "Pentagon",
   "answer2": "Three-quarter circle (pac-man)",
   "answer3": "Parallelogram",
   "correct_answer": 3,
   "skill_id": 145,
   "difficulty_id": 2,
   "explanation": "The triangle, pentagon and three-quarter circle each have at least one line of symmetry. A general parallelogram has no line of symmetry.",
   "hints": [
    "A line of symmetry folds the shape onto itself exactly.",
    "A slanted parallelogram cannot be folded to match."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q18",
   "image_needed": true,
   "image_options": true,
   "image_file": null,
   "image_page": 11,
   "image_bbox": [
    0.15,
    0.11,
    0.85,
    0.25
   ],
   "image_loc": "row of four shapes labelled (1)-(4) near top of page",
   "notes": "Image-option MCQ: crop each shape to q18_opt0..3.png. Key Q18 = option 4 (parallelogram)."
  },
  {
   "n": 19,
   "type_id": 1,
   "question": "Mei Ling started running a marathon at 6.35 a.m. and finished it at 11.10 a.m. How long did she take to complete the marathon?",
   "answer0": "4 h 25 min",
   "answer1": "4 h 35 min",
   "answer2": "5 h 25 min",
   "answer3": "5 h 35 min",
   "correct_answer": 1,
   "skill_id": 135,
   "difficulty_id": 2,
   "explanation": "From 6.35 a.m. to 11.35 a.m. is 5 h, but she finished at 11.10 a.m., which is 25 min earlier: 5 h − 25 min = 4 h 35 min. (From 6.35 to 11.10 = 4 h to 10.35, plus 35 min to 11.10 = 4 h 35 min.)",
   "hints": [
    "Count the whole hours first, then the extra minutes.",
    "6.35 to 10.35 is 4 h; 10.35 to 11.10 is 35 min."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q19",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key Q19 = option 2 (4 h 35 min)."
  },
  {
   "n": 20,
   "type_id": 1,
   "question": "Funfair tickets: Adult ticket $36, Child ticket $18. Special promotion: 2 adult tickets and 1 child ticket $80. 5 adults and 4 children went to the funfair. What would be the least possible amount of money they need to pay for the tickets?",
   "answer0": "$134",
   "answer1": "$214",
   "answer2": "$232",
   "answer3": "$252",
   "correct_answer": 2,
   "skill_id": 118,
   "difficulty_id": 3,
   "explanation": "Use the promotion as much as possible. Two promo bundles cover 4 adults + 2 children = 2 × $80 = $160. Remaining: 1 adult ($36) + 2 children (2 × $18 = $36) = $72. Total = $160 + $72 = $232.",
   "hints": [
    "The promotion bundle is cheaper per person, so use it as much as possible.",
    "After using bundles, price the leftover adults and children separately."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q20",
   "image_needed": true,
   "image_options": false,
   "image_file": "q20.png",
   "image_page": 11,
   "image_bbox": [
    0.35,
    0.5,
    0.75,
    0.69
   ],
   "image_loc": "boxed funfair ticket price poster, middle of page",
   "notes": "Key Q20 = option 3 ($232). Poster gives the prices used in the stem."
  },
  {
   "n": 21,
   "type_id": 2,
   "question": "Write thirteen thousand and ninety-four in numerals. [?]",
   "answer0": "13094",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 106,
   "difficulty_id": 1,
   "explanation": "Thirteen thousand = 13 000, plus ninety-four = 94, giving 13 094.",
   "hints": [
    "Thirteen thousand is 13 000.",
    "Add ninety-four to get the final numeral."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q21",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key Q21 = 13094."
  },
  {
   "n": 22,
   "type_id": 2,
   "question": "Write the missing number in the number pattern.<br>14 000, 13 200, 12 400, [?], 10 800, 10 000",
   "answer0": "11600",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 108,
   "difficulty_id": 1,
   "explanation": "The pattern decreases by 800 each time: 14 000, 13 200, 12 400, 11 600, 10 800, 10 000. The missing number is 11 600.",
   "hints": [
    "Find the difference between consecutive terms.",
    "Each term is 800 less than the one before."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q22",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key Q22 = 11600."
  },
  {
   "n": 23,
   "type_id": 2,
   "question": "Find the sum of 647 and 978. [?]",
   "answer0": "1625",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 70,
   "difficulty_id": 1,
   "explanation": "647 + 978 = 1625.",
   "hints": [
    "'Sum' means add.",
    "Add 647 and 978."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q23",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key Q23 = 1625."
  },
  {
   "n": 24,
   "type_id": 2,
   "question": "Write $$4\\frac{2}{3}$$ as an improper fraction. [?]",
   "answer0": "14/3",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 119,
   "difficulty_id": 1,
   "explanation": "$$4\\frac{2}{3}=\\frac{4\\times3+2}{3}=\\frac{14}{3}$$.",
   "hints": [
    "Multiply the whole number by the denominator.",
    "Add the numerator, keep the same denominator."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q24",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key Q24 = 14/3. FIB answer plain a/b."
  },
  {
   "n": 25,
   "type_id": 2,
   "question": "$$\\frac{2}{9}+\\frac{1}{3}=$$ [?]",
   "answer0": "5/9",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 121,
   "difficulty_id": 1,
   "explanation": "Make the denominators the same: $$\\frac{1}{3}=\\frac{3}{9}$$. Then $$\\frac{2}{9}+\\frac{3}{9}=\\frac{5}{9}$$.",
   "hints": [
    "Convert 1/3 to ninths.",
    "Add the numerators over the common denominator."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q25",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key Q25 = 5/9. FIB answer plain a/b."
  },
  {
   "n": 26,
   "type_id": 2,
   "question": "$$0.8=\\frac{8}{[?]}$$ What is the missing number in the box?",
   "answer0": "10",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 126,
   "difficulty_id": 1,
   "explanation": "0.8 means 8 tenths, so $$0.8=\\frac{8}{10}$$. The missing number is 10.",
   "hints": [
    "0.8 is read as 8 tenths.",
    "Tenths means a denominator of 10."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q26",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key Q26 = 10."
  },
  {
   "n": 27,
   "type_id": 2,
   "question": "Round 42.64 to the nearest whole number. [?]",
   "answer0": "43",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 128,
   "difficulty_id": 1,
   "explanation": "The tenths digit is 6, which is 5 or more, so round up: 42.64 ≈ 43.",
   "hints": [
    "Look at the first decimal digit (the tenths).",
    "If it is 5 or more, round the whole number up."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q27",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key Q27 = 43."
  },
  {
   "n": 28,
   "type_id": 0,
   "question": "Name the two angles that are greater than 90°.",
   "answer0": null,
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 139,
   "difficulty_id": 2,
   "explanation": "From the intersecting-lines diagram, the two obtuse angles greater than 90° are $$\\angle a$$ and $$\\angle d$$.",
   "hints": [
    "An angle greater than 90° is obtuse (wider than a right angle).",
    "Vertically opposite angles are equal."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q28",
   "image_needed": true,
   "image_options": false,
   "image_file": "q28.png",
   "image_page": 13,
   "image_bbox": [
    0.17,
    0.45,
    0.45,
    0.58
   ],
   "image_loc": "intersecting lines forming angles a, b, c, d, e, left side of page",
   "notes": "type_id 0: answer is naming angles a and d (letter answer, not numeric/MCQ-friendly). Key Q28 = angle a and angle d. SKIPPED on insert."
  },
  {
   "n": 29,
   "type_id": 2,
   "question": "Measure and write down the size of $$\\angle y$$. [?]°",
   "answer0": "124",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 140,
   "difficulty_id": 2,
   "explanation": "Measuring with a protractor, $$\\angle y = 124°$$.",
   "hints": [
    "Place the protractor centre at the vertex.",
    "Read the scale where the slanted line crosses."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q29",
   "image_needed": true,
   "image_options": false,
   "image_file": "q29.png",
   "image_page": 13,
   "image_bbox": [
    0.3,
    0.62,
    0.78,
    0.86
   ],
   "image_loc": "one slanted ray and one horizontal ray forming angle y, lower-middle of page",
   "notes": "Key Q29 = 124. Answer is the measured degree value (unit ° in stem)."
  },
  {
   "n": 30,
   "type_id": 2,
   "question": "Which two of the fractions below are smaller than $$\\frac{1}{2}$$?<br>$$\\frac{4}{11}$$, $$\\frac{3}{4}$$, $$\\frac{5}{10}$$, $$\\frac{2}{7}$$<br>[?] and [?]",
   "answer0": "4/11",
   "answer1": "2/7",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 79,
   "difficulty_id": 2,
   "explanation": "Compare each with $$\\frac{1}{2}$$: $$\\frac{4}{11}<\\frac{1}{2}$$ (since 4 < 5.5), $$\\frac{3}{4}>\\frac{1}{2}$$, $$\\frac{5}{10}=\\frac{1}{2}$$, $$\\frac{2}{7}<\\frac{1}{2}$$ (since 2 < 3.5). The two smaller than a half are $$\\frac{4}{11}$$ and $$\\frac{2}{7}$$.",
   "hints": [
    "A fraction is less than 1/2 if the numerator is less than half the denominator.",
    "Check each fraction against half its denominator."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q30",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key Q30 = 4/11 and 2/7. FIB answers plain a/b, in given order (4/11 listed before 2/7)."
  },
  {
   "n": 31,
   "type_id": 2,
   "question": "Mrs Tan took 20 min to travel from her home to the office. She spent 6 h 30 min in the office. She left her office at 18 15. What time did she leave her home in the morning? Give your answer in 24-hour clock. [?]",
   "answer0": "1125",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 135,
   "difficulty_id": 2,
   "explanation": "Left office at 18 15. Subtract 6 h 30 min in office: 18 15 − 6 h 30 min = 11 45 (arrived at office). Subtract 20 min travel: 11 45 − 20 min = 11 25. She left home at 11 25.",
   "hints": [
    "Work backwards from 18 15.",
    "Subtract the time in the office, then the travel time."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q31",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key Q31 = 1125 (i.e. 11 25)."
  },
  {
   "n": 32,
   "type_id": 2,
   "question": "PQRS is a square with perimeter 28 cm. Find its area. [?] cm²",
   "answer0": "49",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 137,
   "difficulty_id": 2,
   "explanation": "Side of square = 28 ÷ 4 = 7 cm. Area = 7 × 7 = 49 cm².",
   "hints": [
    "A square has 4 equal sides; divide the perimeter by 4.",
    "Area of a square = side × side."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q32",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key Q32 = 49 (28÷4=7, 7×7=49). Figure is just a labelled square, not needed."
  },
  {
   "n": 33,
   "type_id": 0,
   "question": "In the figure, shade 3 squares such that line QR is the line of symmetry.",
   "answer0": null,
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 145,
   "difficulty_id": 2,
   "explanation": "Reflect the already-shaded squares across the diagonal line QR; shade the 3 squares whose mirror images across QR are currently unshaded so the pattern becomes symmetric about QR.",
   "hints": [
    "The line QR is the diagonal mirror line.",
    "Each shaded square must have a matching shaded square on the other side of QR."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q33",
   "image_needed": true,
   "image_options": false,
   "image_file": "q33.png",
   "image_page": 15,
   "image_bbox": [
    0.33,
    0.15,
    0.6,
    0.45
   ],
   "image_loc": "8x8 grid with some shaded squares, diagonal QR from bottom-left to top-right, upper-middle of page",
   "notes": "type_id 0: interactive shade-the-grid task, no value answer. SKIPPED on insert."
  },
  {
   "n": 34,
   "type_id": 0,
   "question": "(a) Draw the geometric figure shown on the isometric grid on the right. (b) Name the geometric figure.",
   "answer0": null,
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 231,
   "difficulty_id": 2,
   "explanation": "(a) The solid is a triangular prism; redraw it on the blank isometric grid. (b) The figure is a (triangular) prism.",
   "hints": [
    "Look at the cross-section to identify the solid.",
    "A prism has the same shape running through its length."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q34",
   "image_needed": true,
   "image_options": false,
   "image_file": "q34.png",
   "image_page": 15,
   "image_bbox": [
    0.18,
    0.52,
    0.5,
    0.75
   ],
   "image_loc": "triangular prism drawn on left isometric dot grid, blank dot grid on right, middle of page",
   "notes": "type_id 0: part (a) is a draw-on-grid task. Part (b) answer = prism. Whole question SKIPPED on insert (interactive drawing)."
  },
  {
   "n": 35,
   "type_id": 2,
   "question": "The total cost of a handbag and purse is $242. The handbag costs $20 more than the purse. Find the cost of the handbag. [?]",
   "answer0": "131",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 118,
   "difficulty_id": 2,
   "explanation": "Remove the extra $20: 242 − 20 = 222, which is twice the purse. Purse = 222 ÷ 2 = 111. Handbag = 111 + 20 = 131.",
   "hints": [
    "Subtract the $20 difference, then halve to find the cheaper item.",
    "Add the $20 back to find the handbag's cost."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q35",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key Q35 = $131. Answer in dollars (stem prints Ans: $ ___)."
  },
  {
   "n": 36,
   "type_id": 2,
   "question": "The chairs in the hall are arranged in rows. Each row has the same number of chairs. When Ali sits at one of the chairs, there are 6 chairs to his right and 5 chairs to his left. There are 8 chairs in front of him and 4 chairs behind him. How many chairs are there in the hall? [?]",
   "answer0": "156",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 118,
   "difficulty_id": 3,
   "explanation": "Chairs in Ali's row = 6 + 5 + 1 = 12. Number of rows = 8 + 4 + 1 = 13. Total chairs = 12 × 13 = 156.",
   "hints": [
    "Count Ali plus the chairs on both sides for the row length.",
    "Count Ali's row plus rows in front and behind for the number of rows."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q36",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key Q36 = 156 (12 × 13)."
  },
  {
   "n": 37,
   "type_id": 2,
   "question": "The table shows the number of swimmers and non-swimmers in 3 schools. Some of the information are missing from the table. What is the total number of non-swimmers in School B and C? [?]",
   "answer0": "1113",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 146,
   "difficulty_id": 2,
   "explanation": "School B non-swimmers = 1460 − 890 = 570. School C non-swimmers = 2273 − 1730 = 543. Total = 570 + 543 = 1113.",
   "hints": [
    "Non-swimmers = total − swimmers for each school.",
    "Add the two non-swimmer counts."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q37",
   "image_needed": true,
   "image_options": false,
   "image_file": "q37.png",
   "image_page": 16,
   "image_bbox": [
    0.17,
    0.57,
    0.81,
    0.7
   ],
   "image_loc": "table of swimmers/non-swimmers/total for Schools A, B, C, middle of page",
   "notes": "Key Q37 = 1113."
  },
  {
   "n": 38,
   "type_id": 2,
   "question": "A piece of rectangular paper is folded as shown. Find $$\\angle x$$. [?]°",
   "answer0": "15",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 197,
   "difficulty_id": 3,
   "explanation": "The 60° angle and angle x with its folded equal angle sit on the straight bottom edge: the fold makes two equal angles, so the angle and its reflection plus 60° form a straight line. 180° − 60° = 120° is shared by two equal folded angles, but using the key: 90° − 60° = 30° is split into two equal parts by the fold, so x = 30° ÷ 2 = 15°.",
   "hints": [
    "A fold creates two equal angles.",
    "Use the right angle (corner of the paper) minus 60°, then halve."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q38",
   "image_needed": true,
   "image_options": false,
   "image_file": "q38.png",
   "image_page": 17,
   "image_bbox": [
    0.24,
    0.11,
    0.75,
    0.37
   ],
   "image_loc": "rectangular paper folded to form a triangle, 60° and x marked at bottom-right, top of page",
   "notes": "Key Q38 = 15° (90 − 60 = 30; 30 ÷ 2 = 15)."
  },
  {
   "n": 39,
   "type_id": 2,
   "question": "Mrs Wong baked between 70 to 90 cookies. She could pack all the cookies into boxes of 5 cookies or boxes of 8 cookies without any remainder. How many cookies did Mrs Wong bake? [?]",
   "answer0": "80",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 115,
   "difficulty_id": 3,
   "explanation": "The number must be a common multiple of 5 and 8, i.e. a multiple of 40. Between 70 and 90, the multiple of 40 is 80.",
   "hints": [
    "The number must divide exactly by both 5 and 8.",
    "Find the common multiples of 5 and 8 between 70 and 90."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q39",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key Q39 = 80."
  },
  {
   "n": 40,
   "type_id": 2,
   "question": "The figure is made up of four identical squares. Find the perimeter of the figure. [?] cm",
   "answer0": "90",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 96,
   "difficulty_id": 2,
   "explanation": "Each square has side 9 cm. Tracing the outline of the four-square figure gives 10 side-lengths around the perimeter: 10 × 9 = 90 cm. (Key working: 9+9+9+9+9+9+9+9 = 72 for the central column edges, plus 1+8+6+3 = 18 = 90 cm.)",
   "hints": [
    "Each square's side is 9 cm.",
    "Count the unit-side edges that lie on the outside of the figure."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q40",
   "image_needed": true,
   "image_options": false,
   "image_file": "q40.png",
   "image_page": 18,
   "image_bbox": [
    0.27,
    0.16,
    0.57,
    0.31
   ],
   "image_loc": "four squares in a pinwheel/cross arrangement, 9 cm width arrow under the centre square, upper part of page",
   "notes": "Key Q40 = 90 cm."
  },
  {
   "n": 41,
   "type_id": 2,
   "question": "$$\\frac{5}{12}$$ of the passengers on the MRT were female.<br>(a) What fraction of the passengers were male?<br>(b) There were 40 female passengers, how many passengers were there on the MRT?<br>(a) [?] (b) [?]",
   "answer0": "7/12",
   "answer1": "96",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 122,
   "difficulty_id": 2,
   "explanation": "(a) Male fraction = $$\\frac{12}{12}-\\frac{5}{12}=\\frac{7}{12}$$. (b) $$\\frac{5}{12}$$ corresponds to 40 female passengers, so 1 unit = 40 ÷ 5 = 8, and the total = 8 × 12 = 96 passengers.",
   "hints": [
    "The whole is 12/12; subtract the female fraction for male.",
    "If 5/12 = 40, find 1/12 then multiply by 12."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q41",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Two-part FIB. Key Q41a = 7/12 (plain), Q41b = 96."
  },
  {
   "n": 42,
   "type_id": 2,
   "question": "The total mass of an empty school bag and 5 similar books was 5.4 kg. The total mass of the same school bag and 2 similar books was 3 kg.<br>(a) What was the mass of 1 book?<br>(b) What was the mass of the empty school bag?<br>(a) [?] kg (b) [?] kg",
   "answer0": "0.8",
   "answer1": "1.4",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 131,
   "difficulty_id": 3,
   "explanation": "(a) The difference of 3 books = 5.4 − 3 = 2.4 kg, so 1 book = 2.4 ÷ 3 = 0.8 kg. (b) 2 books = 0.8 × 2 = 1.6 kg, so the bag = 3 − 1.6 = 1.4 kg.",
   "hints": [
    "The mass difference comes from the extra books.",
    "Subtract the books' mass from a total to get the bag."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q42",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Two-part FIB. Key Q42a = 0.8 kg, Q42b = 1.4 kg. Decimals plain."
  },
  {
   "n": 43,
   "type_id": 2,
   "question": "Ravi had $92 more than Peter. After Ravi gave $100 to Peter, Peter had 5 times as much as Ravi.<br>(a) How much money did Ravi have at first?<br>(b) How much money did Peter have in the end?<br>(a) [?] (b) [?]",
   "answer0": "127",
   "answer1": "135",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 118,
   "difficulty_id": 3,
   "explanation": "After the transfer the total is unchanged. Ravi gave away $100, so the difference shifts by $200: originally Ravi had $92 more, after giving $100 Peter has $108 more than Ravi. Peter = 5 × Ravi, so the difference = 4 units = $108? Using the key: Ravi's amount after = (total)÷6 of a 1:5 split. (100+8)÷4 = 27 → Ravi after = $27, Ravi at first = 27 + 100 = $127. (b) Peter at first = 127 − 92 = $35; Peter in the end = 35 + 100 = $135.",
   "hints": [
    "After the gift, Peter : Ravi = 5 : 1, so Ravi has 1 unit of the total.",
    "Add back the $100 to find Ravi's original amount; track Peter separately."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q43",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Two-part FIB. Key Q43a = $127, Q43b = $135. Key working: (100+8)÷4=27, 27+100=127; 4+1=5, 27×5=135."
  },
  {
   "n": 44,
   "type_id": 2,
   "question": "The bar graph shows the number of books donated by the Primary 4 pupils. The number of books is not shown on the scale.<br>(a) Which class donated twice as many books as 4B?<br>(b) Class 4C donated 20 more books than Class 4D. How many books were donated by Class 4E?<br>(c) The pie chart represents the number of books donated by the boys and girls in Class 4E. How many books were donated by the girls?<br>(a) [?] (b) [?] (c) [?]",
   "answer0": "4C",
   "answer1": "120",
   "answer2": "90",
   "answer3": null,
   "correct_answer": null,
   "skill_id": 148,
   "difficulty_id": 3,
   "explanation": "(a) 4C's bar is twice the height of 4B's bar, so 4C. (b) Reading the equal-interval scale, 4C = 10 units and 4D = 8 units; 2 units = 20 books, so 1 unit = 10 books, and 4E = 12 units = 120 books. (c) The pie chart shows Boys = a right angle = $$\\frac{1}{4}$$, so Girls = $$\\frac{3}{4}$$ of 120 = 90 books.",
   "hints": [
    "For (a), compare bar heights.",
    "For (b), use the 20-book gap to find the value of one grid interval.",
    "For (c), the boys' right angle is a quarter of the circle."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q44",
   "image_needed": true,
   "image_options": false,
   "image_file": "q44.png",
   "image_page": 22,
   "image_bbox": [
    0.22,
    0.13,
    0.85,
    0.35
   ],
   "image_loc": "bar graph of books donated by classes 4A-4E (top); a pie chart of Boys/Girls for 4E sits lower on the page near part (c)",
   "notes": "Three-part FIB. Key Q44a = 4C, Q44b = 120, Q44c = 90. Two figures on page 22 (bar graph for a/b, pie chart for c near bbox [0.22,0.68,0.50,0.88]). Primary crop is the bar graph."
  },
  {
   "n": 45,
   "type_id": 2,
   "question": "A photograph measuring 7 cm by 5 cm is placed on a cardboard leaving a 2-cm border around it.<br>(a) What is the area of the photograph?<br>(b) What is the area of the cardboard not covered by the photograph?<br>(a) [?] cm² (b) [?] cm²",
   "answer0": "35",
   "answer1": "64",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 138,
   "difficulty_id": 3,
   "explanation": "(a) Photograph area = 7 × 5 = 35 cm². (b) The cardboard is (7 + 2 + 2) by (5 + 2 + 2) = 11 cm by 9 cm = 99 cm². Area not covered = 99 − 35 = 64 cm².",
   "hints": [
    "Area of a rectangle = length × width.",
    "Add the 2-cm border to both sides of each dimension to get the cardboard size."
   ],
   "source": "Raffles 2024 P4 End-of-Year Exam Q45",
   "image_needed": true,
   "image_options": false,
   "image_file": "q45.png",
   "image_page": 23,
   "image_bbox": [
    0.23,
    0.12,
    0.66,
    0.37
   ],
   "image_loc": "cardboard rectangle with photograph inside and 2 cm border, 5 cm/7 cm labels, top of page",
   "notes": "Two-part FIB. Key Q45a = 35 cm², Q45b = 64 cm²."
  }
 ]
}