{
 "paper": {
  "school": "Anglo-Chinese School (Primary)",
  "year": 2024,
  "level": "P4",
  "label": "End-of-Year Exam",
  "source_prefix": "ACS 2024 P4 End-of-Year Exam",
  "has_answer_key": true
 },
 "questions": [
  {
   "n": 1,
   "type_id": 1,
   "question": "12 thousands and 7 tens is the same as [?].",
   "answer0": "127",
   "answer1": "1207",
   "answer2": "12 070",
   "answer3": "12 700",
   "correct_answer": 2,
   "skill_id": 105,
   "difficulty_id": 1,
   "explanation": "12 thousands = 12 000 and 7 tens = 70. 12 000 + 70 = 12 070.",
   "hints": [
    "1 thousand = 1000, 1 ten = 10.",
    "Add 12 000 and 70."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q1",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 3 (12 070)."
  },
  {
   "n": 2,
   "type_id": 1,
   "question": "Which number when rounded to the nearest ten becomes 36 500?",
   "answer0": "36 498",
   "answer1": "36 505",
   "answer2": "36 512",
   "answer3": "36 524",
   "correct_answer": 0,
   "skill_id": 109,
   "difficulty_id": 2,
   "explanation": "Rounding to the nearest ten, 36 498 rounds to 36 500 (ones digit 8 rounds up). 36 505 -> 36 510, 36 512 -> 36 510, 36 524 -> 36 520.",
   "hints": [
    "Look at the ones digit; 5 or more rounds up.",
    "36 498: tens is 9, ones is 8 -> 36 500."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q2",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 1 (36 498)."
  },
  {
   "n": 3,
   "type_id": 1,
   "question": "Express $$4\\frac{3}{25}$$ as a decimal.",
   "answer0": "4.012",
   "answer1": "4.325",
   "answer2": "4.12",
   "answer3": "4.65",
   "correct_answer": 2,
   "skill_id": 127,
   "difficulty_id": 2,
   "explanation": "$$\\frac{3}{25}=\\frac{12}{100}=0.12$$. So $$4\\frac{3}{25}=4.12$$.",
   "hints": [
    "Make the denominator 100.",
    "3/25 = 12/100 = 0.12."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q3",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 3 (4.12)."
  },
  {
   "n": 4,
   "type_id": 1,
   "question": "What is the length of the pencil in cm?",
   "answer0": "8.3 cm",
   "answer1": "8.7 cm",
   "answer2": "9.3 cm",
   "answer3": "9.7 cm",
   "correct_answer": 1,
   "skill_id": 123,
   "difficulty_id": 2,
   "explanation": "The pencil starts at 0 cm and the tip ends just before the 9 cm mark, at 8.7 cm.",
   "hints": [
    "Read where the pencil tip ends on the ruler.",
    "It is between 8 and 9 cm."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q4",
   "image_needed": true,
   "image_options": false,
   "image_file": "q4.png",
   "image_page": 4,
   "image_bbox": [
    0.16,
    0.18,
    0.82,
    0.3
   ],
   "image_loc": "below the question: a pencil drawn above a 0-12 cm ruler",
   "notes": "Key: option 2 (8.7 cm)."
  },
  {
   "n": 5,
   "type_id": 1,
   "question": "Which mixed number is represented by A in the number line?",
   "answer0": "$$1\\frac{1}{5}$$",
   "answer1": "$$1\\frac{3}{5}$$",
   "answer2": "$$2\\frac{1}{5}$$",
   "answer3": "$$2\\frac{3}{5}$$",
   "correct_answer": 1,
   "skill_id": 119,
   "difficulty_id": 2,
   "explanation": "Each interval between 0,1,2 is split into 5 parts (fifths). A is the 3rd mark after 1, i.e. 1 and 3/5.",
   "hints": [
    "Count the small divisions between 1 and 2.",
    "Each is one-fifth; A is 3 fifths past 1."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q5",
   "image_needed": true,
   "image_options": false,
   "image_file": "q5.png",
   "image_page": 4,
   "image_bbox": [
    0.2,
    0.5,
    0.56,
    0.63
   ],
   "image_loc": "number line 0 to 2 marked in fifths with arrow A pointing up",
   "notes": "Key: option 2 (1 3/5)."
  },
  {
   "n": 6,
   "type_id": 1,
   "question": "How many one-thirds are there in 5 wholes?",
   "answer0": "$$\\frac{3}{5}$$",
   "answer1": "$$\\frac{5}{3}$$",
   "answer2": "3",
   "answer3": "15",
   "correct_answer": 3,
   "skill_id": 119,
   "difficulty_id": 1,
   "explanation": "5 wholes ÷ (1/3) = 5 × 3 = 15. There are 15 thirds in 5 wholes.",
   "hints": [
    "Each whole has 3 thirds.",
    "5 × 3 = 15."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q6",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 4 (15)."
  },
  {
   "n": 7,
   "type_id": 1,
   "question": "Ahmad and Bala had 180 erasers altogether.<br>Bala had three times as many erasers as Ahmad.<br>How many more erasers did Bala have than Ahmad?",
   "answer0": "45",
   "answer1": "60",
   "answer2": "90",
   "answer3": "120",
   "correct_answer": 2,
   "skill_id": 118,
   "difficulty_id": 2,
   "explanation": "Total = 4 units = 180, so 1 unit = 45. Ahmad = 45, Bala = 135. Difference = 135 - 45 = 90 (or 2 units = 90).",
   "hints": [
    "Ahmad = 1 unit, Bala = 3 units, total 4 units.",
    "Difference = 2 units."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q7",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 3 (90)."
  },
  {
   "n": 8,
   "type_id": 1,
   "question": "The first two common multiples of 6 and 8 are [?].",
   "answer0": "1 and 2",
   "answer1": "2 and 4",
   "answer2": "12 and 24",
   "answer3": "24 and 48",
   "correct_answer": 3,
   "skill_id": 115,
   "difficulty_id": 2,
   "explanation": "Multiples of 6: 6,12,18,24,... Multiples of 8: 8,16,24,... LCM = 24, next common multiple = 48. So 24 and 48.",
   "hints": [
    "List multiples of 6 and 8.",
    "Find the smallest two numbers in both lists."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q8",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 4 (24 and 48)."
  },
  {
   "n": 9,
   "type_id": 1,
   "question": "The table shows the number of students who wear and do not wear spectacles in two Primary 4 classes.<br>How many students from both classes wear spectacles?",
   "answer0": "46",
   "answer1": "42",
   "answer2": "39",
   "answer3": "35",
   "correct_answer": 1,
   "skill_id": 147,
   "difficulty_id": 2,
   "explanation": "Wear spectacles: P4Q girls 9 + boys 11 = 20; P4R girls 12 + boys 10 = 22. Total = 20 + 22 = 42.",
   "hints": [
    "Add the 'Wear spectacles' columns only.",
    "9 + 11 + 12 + 10."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q9",
   "image_needed": true,
   "image_options": false,
   "image_file": "q9.png",
   "image_page": 6,
   "image_bbox": [
    0.11,
    0.2,
    0.82,
    0.4
   ],
   "image_loc": "table of girls/boys who wear and do not wear spectacles for P4Q and P4R",
   "notes": "Key: option 2 (42)."
  },
  {
   "n": 10,
   "type_id": 1,
   "question": "The figure is made up of a square A and a rectangle B.<br>Find the area of the figure.",
   "answer0": "22 cm²",
   "answer1": "26 cm²",
   "answer2": "28 cm²",
   "answer3": "40 cm²",
   "correct_answer": 0,
   "skill_id": 138,
   "difficulty_id": 2,
   "explanation": "Rectangle B = 3 cm × 6 cm = 18 cm². Square A = 2 cm × 2 cm = 4 cm². Total = 18 + 4 = 22 cm².",
   "hints": [
    "Find area of B (3 × 6) and A (2 × 2).",
    "Add the two areas."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q10",
   "image_needed": true,
   "image_options": false,
   "image_file": "q10.png",
   "image_page": 7,
   "image_bbox": [
    0.18,
    0.21,
    0.45,
    0.4
   ],
   "image_loc": "L-shaped figure: rectangle B (3 by 6 cm) with square A (2 by 2 cm) at lower right",
   "notes": "Key: option 1 (22 cm²)."
  },
  {
   "n": 11,
   "type_id": 1,
   "question": "The total mass of 4 similar tennis balls and 5 similar marbles is as shown in the diagram. Each tennis ball has a mass of 65 g.<br>What is the total mass of the 5 marbles?",
   "answer0": "14 g",
   "answer1": "70 g",
   "answer2": "260 g",
   "answer3": "330 g",
   "correct_answer": 1,
   "skill_id": 130,
   "difficulty_id": 2,
   "explanation": "Scale reads 330 g total. 4 tennis balls = 4 × 65 = 260 g. 5 marbles = 330 - 260 = 70 g.",
   "hints": [
    "Read the total mass from the scale (330 g).",
    "Subtract the mass of the 4 tennis balls."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q11",
   "image_needed": true,
   "image_options": false,
   "image_file": "q11.png",
   "image_page": 8,
   "image_bbox": [
    0.18,
    0.25,
    0.4,
    0.46
   ],
   "image_loc": "weighing scale holding tennis balls and marbles, pointer near 330 g",
   "notes": "Key: option 2 (70 g). Scale total = 330 g."
  },
  {
   "n": 12,
   "type_id": 1,
   "question": "In the figure, $$\\frac{3}{4}$$ of the square is shaded. The unshaded area is 25 cm².<br>Find the length of the square.",
   "answer0": "5 cm",
   "answer1": "10 cm",
   "answer2": "75 cm",
   "answer3": "100 cm",
   "correct_answer": 1,
   "skill_id": 137,
   "difficulty_id": 3,
   "explanation": "Unshaded = 1/4 of square = 25 cm², so whole square = 100 cm². Length = √100 = 10 cm.",
   "hints": [
    "If 3/4 is shaded, 1/4 is unshaded.",
    "1/4 = 25 cm² so area = 100 cm²; find the side."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q12",
   "image_needed": true,
   "image_options": false,
   "image_file": "q12.png",
   "image_page": 9,
   "image_bbox": [
    0.18,
    0.21,
    0.39,
    0.36
   ],
   "image_loc": "shaded square with unshaded arrow shape labelled 25 cm² and side marked ?",
   "notes": "Key: option 2 (10 cm)."
  },
  {
   "n": 13,
   "type_id": 1,
   "question": "Which of the following figures does not have a line of symmetry?",
   "answer0": "Figure 1",
   "answer1": "Figure 2",
   "answer2": "Figure 3",
   "answer3": "Figure 4",
   "correct_answer": 0,
   "skill_id": 145,
   "difficulty_id": 2,
   "explanation": "Figures 2, 3 and 4 each have at least one line of symmetry; Figure 1's shading pattern has none.",
   "hints": [
    "A line of symmetry folds the figure onto itself.",
    "Test each diagonal and centre line."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q13",
   "image_needed": true,
   "image_options": true,
   "image_file": null,
   "image_page": 10,
   "image_bbox": [
    0.18,
    0.18,
    0.75,
    0.55
   ],
   "image_loc": "four 3x3 shaded-square grids labelled (1)-(4)",
   "notes": "Key: option 1. Image-option MCQ: crop each grid to q13_opt0.png..q13_opt3.png. opt0 box ~[0.20,0.20,0.42,0.34], opt1 ~[0.52,0.20,0.74,0.34], opt2 ~[0.20,0.40,0.42,0.55], opt3 ~[0.52,0.40,0.74,0.55]."
  },
  {
   "n": 14,
   "type_id": 1,
   "question": "The diagram shows Rectangle X and Square Y. Rectangle X and Square Y have the same area. What is the perimeter of Square Y?",
   "answer0": "12 m",
   "answer1": "48 m",
   "answer2": "50 m",
   "answer3": "144 m",
   "correct_answer": 1,
   "skill_id": 137,
   "difficulty_id": 2,
   "explanation": "Area of X = 16 × 9 = 144 m². Square Y has area 144 m², so side = √144 = 12 m. Perimeter = 4 × 12 = 48 m.",
   "hints": [
    "Find the area of rectangle X.",
    "Square side = √area; perimeter = 4 × side."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q14",
   "image_needed": true,
   "image_options": false,
   "image_file": "q14.png",
   "image_page": 11,
   "image_bbox": [
    0.3,
    0.22,
    0.7,
    0.34
   ],
   "image_loc": "rectangle X (16 m by 9 m) beside square Y",
   "notes": "Key: option 2 (48 m)."
  },
  {
   "n": 15,
   "type_id": 1,
   "question": "This solid is a pyramid.<br>Which of the following is not a net of this pyramid?",
   "answer0": "Net 1",
   "answer1": "Net 2",
   "answer2": "Net 3",
   "answer3": "Net 4",
   "correct_answer": 0,
   "skill_id": 232,
   "difficulty_id": 3,
   "explanation": "A square-based pyramid net is one square with four triangles attached. Nets 2, 3 and 4 fold into the pyramid; net 1 does not.",
   "hints": [
    "The pyramid has 1 square base and 4 triangular faces.",
    "Check which arrangement cannot fold into the solid."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q15",
   "image_needed": true,
   "image_options": true,
   "image_file": null,
   "image_page": 12,
   "image_bbox": [
    0.18,
    0.16,
    0.78,
    0.72
   ],
   "image_loc": "pyramid solid at top; four candidate nets labelled (1)-(4) below",
   "notes": "Key: option 1. Image-option MCQ: crop the pyramid (q15_solid.png) plus each net q15_opt0.png..q15_opt3.png. opt0 ~[0.20,0.38,0.45,0.50], opt1 ~[0.52,0.36,0.80,0.50], opt2 ~[0.18,0.55,0.46,0.72], opt3 ~[0.55,0.55,0.78,0.72]."
  },
  {
   "n": 16,
   "type_id": 2,
   "question": "76 509 = 70 000 + 6000 + [?] + 9<br>What is the missing number?",
   "answer0": "500",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 105,
   "difficulty_id": 1,
   "explanation": "76 509 = 70 000 + 6000 + 500 + 9. The missing number is the hundreds value, 500.",
   "hints": [
    "Break 76 509 into place values.",
    "The hundreds digit is 5 -> 500."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q16",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 500."
  },
  {
   "n": 17,
   "type_id": 2,
   "question": "Write the missing number in the number pattern.<br>14 000 , 13 400 , 12 800 , 12 200 , [?] , 11 000",
   "answer0": "11600",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 108,
   "difficulty_id": 2,
   "explanation": "The pattern decreases by 600 each time: 12 200 - 600 = 11 600.",
   "hints": [
    "Find the difference between consecutive terms.",
    "Subtract 600 from 12 200."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q17",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 11 600."
  },
  {
   "n": 18,
   "type_id": 2,
   "question": "Arrange these numbers from the smallest to the greatest.<br>$$\\frac{4}{5}$$    0.405    0.045<br>[?] , [?] , [?]",
   "answer0": "0.045",
   "answer1": "0.405",
   "answer2": "4/5",
   "answer3": null,
   "correct_answer": null,
   "skill_id": 124,
   "difficulty_id": 2,
   "explanation": "4/5 = 0.8. Compare 0.045, 0.405, 0.8. Smallest to greatest: 0.045, 0.405, 4/5.",
   "hints": [
    "Convert 4/5 to a decimal (0.8).",
    "Line up decimal places to compare."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q18",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 0.045, 0.405, 4/5. Three blanks in order smallest->greatest."
  },
  {
   "n": 19,
   "type_id": 2,
   "question": "What is the remainder when 3079 is divided by 8?",
   "answer0": "7",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 117,
   "difficulty_id": 2,
   "explanation": "3079 ÷ 8 = 384 remainder 7 (384 × 8 = 3072; 3079 - 3072 = 7).",
   "hints": [
    "Find the largest multiple of 8 not exceeding 3079.",
    "384 × 8 = 3072."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q19",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 7 (3079 ÷ 8 = 384 R7)."
  },
  {
   "n": 20,
   "type_id": 2,
   "question": "Tony listed the factors of 81 below.<br>1, 3, 81<br>He missed out two factors. What are the two missing factors?<br>[?] and [?]",
   "answer0": "9",
   "answer1": "27",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 111,
   "difficulty_id": 2,
   "explanation": "Factors of 81: 1, 3, 9, 27, 81. The missing factors are 9 and 27.",
   "hints": [
    "List all numbers that divide 81 exactly.",
    "81 = 9 × 9 = 3 × 27."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q20",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 9 and 27. Two blanks (order interchangeable)."
  },
  {
   "n": 21,
   "type_id": 2,
   "question": "What is the value of $$\\frac{5}{8}+\\frac{3}{4}$$?<br>Express your answer as a mixed number.",
   "answer0": "1 3/8",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 121,
   "difficulty_id": 2,
   "explanation": "$$\\frac{3}{4}=\\frac{6}{8}$$. $$\\frac{5}{8}+\\frac{6}{8}=\\frac{11}{8}=1\\frac{3}{8}$$.",
   "hints": [
    "Make the denominators the same (eighths).",
    "5/8 + 6/8 = 11/8."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q21",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 1 3/8."
  },
  {
   "n": 22,
   "type_id": 2,
   "question": "How many vanilla muffins were sold on all four days?",
   "answer0": "256",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 148,
   "difficulty_id": 2,
   "explanation": "Vanilla: Thu 35 + Fri 51 + Sat 82 + Sun 88 = 256.",
   "hints": [
    "Add the Vanilla column for all four days.",
    "35 + 51 + 82 + 88."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q22",
   "image_needed": true,
   "image_options": false,
   "image_file": "q22.png",
   "image_page": 16,
   "image_bbox": [
    0.1,
    0.18,
    0.82,
    0.4
   ],
   "image_loc": "table of vanilla and chocolate muffins sold Thursday-Sunday (shared by Q22 and Q23)",
   "notes": "Key: 256. Table shared with Q23."
  },
  {
   "n": 23,
   "type_id": 2,
   "question": "What fraction of the muffins sold on Sunday was chocolate?<br>Give your answer in the simplest form.",
   "answer0": "15/26",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 120,
   "difficulty_id": 2,
   "explanation": "Sunday total = 88 + 120 = 208. Chocolate = 120. $$\\frac{120}{208}=\\frac{15}{26}$$ (÷8).",
   "hints": [
    "Find the total muffins sold on Sunday.",
    "Chocolate ÷ total, then simplify."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q23",
   "image_needed": true,
   "image_options": false,
   "image_file": "q22.png",
   "image_page": 16,
   "image_bbox": [
    0.1,
    0.18,
    0.82,
    0.4
   ],
   "image_loc": "same muffin sales table as Q22",
   "notes": "Key: 15/26."
  },
  {
   "n": 24,
   "type_id": 2,
   "question": "WXYZ is a rectangle. Find ∠VWY.",
   "answer0": "18",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 140,
   "difficulty_id": 3,
   "explanation": "∠ZWX = 90° (rectangle corner). Marked angles 26° + 46° = 72° from one side. ∠VWY = 90 - (26 + 46) = 18°.",
   "hints": [
    "The corner angle ZWX of a rectangle is 90°.",
    "Subtract the two marked angles from 90°."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q24",
   "image_needed": true,
   "image_options": false,
   "image_file": "q24.png",
   "image_page": 17,
   "image_bbox": [
    0.27,
    0.17,
    0.7,
    0.35
   ],
   "image_loc": "rectangle WXYZ with diagonals from W, angles 26° and 46° marked at W; V on ZY",
   "notes": "Key: 18 (degrees). Unit ° printed after the blank."
  },
  {
   "n": 25,
   "type_id": 1,
   "question": "One of the angles is a right angle. Name the angle.",
   "answer0": "∠b",
   "answer1": "∠c",
   "answer2": "∠d",
   "answer3": "∠e",
   "correct_answer": 1,
   "skill_id": 139,
   "difficulty_id": 2,
   "explanation": "Of the marked angles b, c, d, e, angle c is the right angle (90°).",
   "hints": [
    "A right angle is exactly 90°, a square corner.",
    "Compare each marked angle to a square corner."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q25",
   "image_needed": true,
   "image_options": false,
   "image_file": "q25.png",
   "image_page": 17,
   "image_bbox": [
    0.3,
    0.52,
    0.62,
    0.68
   ],
   "image_loc": "irregular quadrilateral with angles b, c, d, e marked",
   "notes": "Key: angle c. Originally a fill-in (Answer: ∠____); converted to MCQ over the four labelled angles to avoid fragile word grading. correct_answer index 1 (∠c)."
  },
  {
   "n": 26,
   "type_id": 2,
   "question": "What is the value of $$5-\\frac{7}{11}$$?<br>Express your answer as an improper fraction.",
   "answer0": "48/11",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 121,
   "difficulty_id": 2,
   "explanation": "$$5=\\frac{55}{11}$$. $$\\frac{55}{11}-\\frac{7}{11}=\\frac{48}{11}$$.",
   "hints": [
    "Write 5 as elevenths (55/11).",
    "Subtract the numerators."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q26",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 48/11."
  },
  {
   "n": 27,
   "type_id": 2,
   "question": "There were twice as many women as men at a carnival. After 180 women left the carnival, the number of men was twice the number of women who remained. How many men were there?",
   "answer0": "120",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 118,
   "difficulty_id": 3,
   "explanation": "Let men = M, women = 2M. After 180 left: women = 2M - 180. Men = twice remaining women: M = 2(2M - 180) = 4M - 360, so 3M = 360, M = 120. (Key: 180 ÷ 3 = 60, 60 × 2 = 120.)",
   "hints": [
    "Use units: men = 1 part, women = 2 parts at first.",
    "Set men = twice the remaining women and solve."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q27",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 120 men."
  },
  {
   "n": 28,
   "type_id": 2,
   "question": "The pie chart shows the favourite hobbies of students in ABC Primary School. 540 students play Sports. Find the number of students who play Music.",
   "answer0": "180",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 236,
   "difficulty_id": 3,
   "explanation": "Sports = 3/8 = 540, so 1/8 = 180 and total = 8 × 180 = 1440. Arts and Crafts equals Sports section (right angle marked) ... Music = 1/8 of total = 180. (Key: 540 ÷ 3 = 180.)",
   "hints": [
    "Sports is 3/8 and equals 540 students.",
    "Find 1/8 (= 540 ÷ 3); Music is one such part."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q28",
   "image_needed": true,
   "image_options": false,
   "image_file": "q28.png",
   "image_page": 19,
   "image_bbox": [
    0.33,
    0.2,
    0.62,
    0.4
   ],
   "image_loc": "pie chart with sectors Arts and Crafts, Sports (3/8), Music, Reading; right-angle mark between Arts/Sports",
   "notes": "Key: 180. 1 unit = 540 ÷ 3 = 180; Music = 180."
  },
  {
   "n": 29,
   "type_id": 2,
   "question": "Round 599.83 to the nearest whole number.",
   "answer0": "600",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 128,
   "difficulty_id": 1,
   "explanation": "The tenths digit is 8 (≥5), so round up: 599.83 -> 600.",
   "hints": [
    "Look at the first decimal place.",
    "8 rounds the whole part up from 599 to 600."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q29",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 600."
  },
  {
   "n": 30,
   "type_id": 2,
   "question": "Write down the size of ∠KLM.",
   "answer0": "131",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 140,
   "difficulty_id": 2,
   "explanation": "Reading the protractor, ray LK is at 164° and ray LM at 33° on the same scale: ∠KLM = 164 - 33 = 131°.",
   "hints": [
    "Read both arms on the same protractor scale.",
    "Subtract the smaller reading from the larger."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q30",
   "image_needed": true,
   "image_options": false,
   "image_file": "q30.png",
   "image_page": 20,
   "image_bbox": [
    0.26,
    0.15,
    0.72,
    0.34
   ],
   "image_loc": "protractor with rays to K and M from vertex L",
   "notes": "Key: 131 (degrees). Unit ° printed after the blank. Key working 164 - 33 = 131."
  },
  {
   "n": 31,
   "type_id": 0,
   "question": "The dotted line is the line of symmetry. Complete the figure to make it symmetric.",
   "answer0": null,
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 144,
   "difficulty_id": 2,
   "explanation": "Reflect the given V-shape across the horizontal dotted line to draw its mirror image above the line.",
   "hints": [],
   "source": "ACS 2024 P4 End-of-Year Exam Q31",
   "image_needed": true,
   "image_options": false,
   "image_file": "q31.png",
   "image_page": 20,
   "image_bbox": [
    0.28,
    0.55,
    0.74,
    0.8
   ],
   "image_loc": "grid with a V-shape below a horizontal dotted line of symmetry",
   "notes": "Drawing/reflection task — no value answer. type_id 0 (skipped on insert). Answer: reflect the V over the dotted line."
  },
  {
   "n": 32,
   "type_id": 2,
   "question": "The figure is made up of 4 identical rectangles. DC measures 72 cm.<br>What is the length of AD?",
   "answer0": "54",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 143,
   "difficulty_id": 3,
   "explanation": "DC = 72 cm is the long side of one rectangle plus its short side arrangement; one short side = 72 ÷ 4 = 18 cm. AD = 72 - 18 = 54 cm. (Key: 72 ÷ 4 = 18; 72 - 18 = 54.)",
   "hints": [
    "The width DC is split by the 4 identical rectangles.",
    "Find one short side (72 ÷ 4), then AD = 72 - short side."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q32",
   "image_needed": true,
   "image_options": false,
   "image_file": "q32.png",
   "image_page": 21,
   "image_bbox": [
    0.3,
    0.19,
    0.62,
    0.38
   ],
   "image_loc": "square ABCD split into 4 identical rectangles; DC = 72 cm, AD marked ?",
   "notes": "Key: 54 cm. Unit cm printed after blank. Key working 72÷4=18, 72-18=54."
  },
  {
   "n": 33,
   "type_id": 0,
   "question": "Shade 2 more squares to complete the nets of a cube.",
   "answer0": null,
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 232,
   "difficulty_id": 2,
   "explanation": "Add two more shaded squares so the six shaded squares form a valid net of a cube (e.g. extend the cross/T arrangement).",
   "hints": [],
   "source": "ACS 2024 P4 End-of-Year Exam Q33",
   "image_needed": true,
   "image_options": false,
   "image_file": "q33.png",
   "image_page": 21,
   "image_bbox": [
    0.18,
    0.62,
    0.45,
    0.86
   ],
   "image_loc": "grid with 4 shaded squares forming a partial cube net",
   "notes": "Shading/drawing task — no value answer. type_id 0 (skipped on insert). Key shows the completed shaded net."
  },
  {
   "n": 34,
   "type_id": 2,
   "question": "Which 1-month period had the least decrease in the number of magazines sold?<br>[?] to [?]",
   "answer0": "October",
   "answer1": "November",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 147,
   "difficulty_id": 2,
   "explanation": "Decreases: Jul->Aug 300-100=200; Sep->Oct 450-300=150; Oct->Nov 300-250=50. The smallest decrease (50) is October to November.",
   "hints": [
    "Look only at months where sales went down.",
    "Find the smallest drop between consecutive months."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q34",
   "image_needed": true,
   "image_options": false,
   "image_file": "q34.png",
   "image_page": 22,
   "image_bbox": [
    0.18,
    0.22,
    0.85,
    0.48
   ],
   "image_loc": "line graph of magazines sold July-December (shared by Q34 and Q35)",
   "notes": "Key: October to November (300-250=50). Two blanks. Graph shared with Q35."
  },
  {
   "n": 35,
   "type_id": 2,
   "question": "How many more magazines were sold in September than in August?",
   "answer0": "350",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 148,
   "difficulty_id": 2,
   "explanation": "September = 450, August = 100. 450 - 100 = 350.",
   "hints": [
    "Read the September and August values from the graph.",
    "Subtract August from September."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q35",
   "image_needed": true,
   "image_options": false,
   "image_file": "q34.png",
   "image_page": 22,
   "image_bbox": [
    0.18,
    0.22,
    0.85,
    0.48
   ],
   "image_loc": "same magazines line graph as Q34",
   "notes": "Key: 350."
  },
  {
   "n": 36,
   "type_id": 2,
   "question": "A crate weighs 36 kg when it is completely filled with sand.<br>It weighs 12 kg when it is $$\\frac{1}{4}$$ filled with sand.<br>What is the mass of the crate when it is empty?",
   "answer0": "4",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 122,
   "difficulty_id": 3,
   "explanation": "Full sand = 36 - crate. 1/4 sand = 12 - crate. Full sand is 4 times the quarter: 36 - c = 4(12 - c) => 36 - c = 48 - 4c => 3c = 12 => c = 4 kg. (Key: 8×4=32; 36-32=4.)",
   "hints": [
    "Difference between full and 1/4 full equals 3/4 of the sand.",
    "(36 - 12) is 3/4 of full sand; find full sand, then subtract from 36."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q36",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 4 kg. Unit kg."
  },
  {
   "n": 37,
   "type_id": 2,
   "question": "Muthu has fewer than 50 comic books.<br>If he gives all his comic books equally to 7 friends, there will be 3 comic books left.<br>If he gives all his comic books equally to 9 friends, he will have no comic books left.<br>How many comic books does Muthu have?",
   "answer0": "45",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 115,
   "difficulty_id": 3,
   "explanation": "Must be a multiple of 9 under 50: 9, 18, 27, 36, 45. It leaves remainder 3 when divided by 7. 45 ÷ 7 = 6 R3. So 45. (Key: 45 ÷ 9 = 5.)",
   "hints": [
    "The number is a multiple of 9 less than 50.",
    "Test which gives remainder 3 when divided by 7."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q37",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 45."
  },
  {
   "n": 38,
   "type_id": 2,
   "question": "The figure is made up of two squares ABCD and FGCE. The length of DE and BG measure 3 cm each. Given that the area of the FGCE is 64 cm², what is the perimeter of the shaded region?",
   "answer0": "44",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 137,
   "difficulty_id": 3,
   "explanation": "FGCE area 64 cm² so its side = 8 cm. Big square ABCD side = 8 + 3 = 11 cm. The shaded L-frame perimeter = outer (4 × 11) plus inner two sides... = 8 + 3 = 11; perimeter = 11 × 4 = 44 cm. (Key: 8+3=11; 11×4=44.)",
   "hints": [
    "Side of FGCE = √64 = 8 cm.",
    "Side of ABCD = 8 + 3; the shaded border perimeter equals 4 × that side."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q38",
   "image_needed": true,
   "image_options": false,
   "image_file": "q38.png",
   "image_page": 25,
   "image_bbox": [
    0.3,
    0.24,
    0.62,
    0.45
   ],
   "image_loc": "large square ABCD with smaller square FGCE inside; L-shaped shaded border, DE and BG = 3 cm",
   "notes": "Key: 44 cm."
  },
  {
   "n": 39,
   "type_id": 2,
   "question": "Mrs Lim bought some highlighters in different colours. $$\\frac{1}{5}$$ of the highlighters were blue and $$\\frac{3}{10}$$ were yellow. The rest of the highlighters were green.<br>(a) What fraction of the highlighters were green? Give your answer in its simplest form.<br>(b) Mrs Lim bought 48 yellow highlighters. How many highlighters did she buy altogether?",
   "answer0": "1/2",
   "answer1": "160",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 122,
   "difficulty_id": 3,
   "explanation": "(a) Blue = 1/5 = 2/10, Yellow = 3/10. Green = 1 - 2/10 - 3/10 = 5/10 = 1/2. (b) Yellow 3/10 = 48, so 1/10 = 16; total = 10 × 16 = 160.",
   "hints": [
    "(a) Convert 1/5 to tenths, then subtract both from a whole.",
    "(b) Yellow is 3/10 = 48; find 1/10 then the whole."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q39",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Two-part: (a) answer0 = 1/2; (b) answer1 = 160. Key: a) 1/2, b) 48÷3=16, 48-16=32, 32×5=160."
  },
  {
   "n": 40,
   "type_id": 2,
   "question": "Gordon had 9 bags of flour. Each bag contained 12.25 kg of flour.<br>(a) How much flour did Gordon have altogether?<br>(b) Gordon bought another 24.75 kg of flour. He then repacked all the flour equally into smaller packets. If each smaller packet contained 3 kg of flour, how many smaller packets of flour did Gordon pack?",
   "answer0": "110.25",
   "answer1": "45",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 131,
   "difficulty_id": 3,
   "explanation": "(a) 9 × 12.25 = 110.25 kg. (b) Total = 110.25 + 24.75 = 135 kg. 135 ÷ 3 = 45 packets.",
   "hints": [
    "(a) Multiply 12.25 by 9.",
    "(b) Add the new flour, then divide the total by 3."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q40",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Two-part: (a) answer0 = 110.25 (kg); (b) answer1 = 45 (packets). Key: 12.25×9=110.25; 110.25+24.75=135; 135÷3=45."
  },
  {
   "n": 41,
   "type_id": 2,
   "question": "Shirley had a total of twenty-six $5 notes and $10 notes. The total value of the notes was $180. How many more $5 notes than $10 notes did she have?",
   "answer0": "6",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 118,
   "difficulty_id": 3,
   "explanation": "If all 26 were $10: 26 × 10 = 260. Excess = 260 - 180 = 80. Each $5 note reduces value by 5: number of $5 notes = 80 ÷ 5 = 16, $10 notes = 26 - 16 = 10. More $5 than $10 = 16 - 10 = 6.",
   "hints": [
    "Assume all 26 are $10 notes and find the surplus.",
    "Each swap to a $5 note lowers the total by $5."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q41",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 6. Working 26×10=260, 260-180=80, 80÷5=16 ($5 notes), 26-16=10 ($10 notes), 16-10=6."
  },
  {
   "n": 42,
   "type_id": 2,
   "question": "Farah had three times as much sugar as Linda. Farah used 27.5 kg of sugar and Linda used 3.5 kg of sugar. Both had an equal amount of sugar left.<br>(a) How many kilograms of sugar did Linda have at first?<br>(b) How many kilograms of sugar did Farah have in the end?",
   "answer0": "12",
   "answer1": "8.5",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 131,
   "difficulty_id": 3,
   "explanation": "(a) Farah = 3 units, Linda = 1 unit. After use, equal: 3u - 27.5 = u - 3.5 => 2u = 24 => u = 12. Linda had 12 kg. (b) Linda's end = 12 - 3.5 = 8.5 kg; Farah's end equals it = 8.5 kg.",
   "hints": [
    "(a) Let Linda = 1 unit, Farah = 3 units; set the leftovers equal.",
    "(b) Both ended with the same amount: Linda's start minus 3.5."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q42",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Two-part: (a) answer0 = 12 (kg); (b) answer1 = 8.5 (kg). Key: 27.5-3.5=24, 24÷2=12; 12-3.5=8.5."
  },
  {
   "n": 43,
   "type_id": 2,
   "question": "The figure is made up of 2 identical small squares and 1 large square.<br>The perimeter of the figure is 120 cm. Find the area of the whole figure.",
   "answer0": "864",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 138,
   "difficulty_id": 3,
   "explanation": "Let the small square side = s; large square side = 2s. The outer perimeter = 10 small-side lengths = 120, so s = 12 cm. Large square = 24 × 24 = 576 cm²; two small squares = 2 × (12 × 12) = 288 cm². Total = 576 + 288 = 864 cm². (Key: 120÷10=12; 12×12... 144×6=864.)",
   "hints": [
    "Let the small square side be one unit; express the perimeter in those units.",
    "Large square side = 2 × small side; add all three areas."
   ],
   "source": "ACS 2024 P4 End-of-Year Exam Q43",
   "image_needed": true,
   "image_options": false,
   "image_file": "q43.png",
   "image_page": 30,
   "image_bbox": [
    0.3,
    0.18,
    0.58,
    0.34
   ],
   "image_loc": "rectangle split into one large square (right) and two stacked small squares (left)",
   "notes": "Key: 864 cm². Key working 120÷10=12, 12×12=144, 144×6=864."
  }
 ]
}