{
 "paper": {
  "school": "ACS Junior",
  "year": 2023,
  "level": "P4",
  "label": "End of Year Exam",
  "source_prefix": "ACS Junior 2023 P4 End of Year Exam",
  "has_answer_key": true
 },
 "questions": [
  {
   "n": 1,
   "type_id": 1,
   "question": "In which of the following numbers does the digit 3 stand for 300?",
   "answer0": "6903",
   "answer1": "9630",
   "answer2": "3690",
   "answer3": "9360",
   "correct_answer": 3,
   "skill_id": 105,
   "difficulty_id": 1,
   "explanation": "The digit 3 stands for 300 when it is in the hundreds place. In 9360, the 3 is in the hundreds place, so it stands for 300.",
   "hints": [
    "Look for the 3 in the hundreds place.",
    "Hundreds place value = digit × 100."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q1",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": ""
  },
  {
   "n": 2,
   "type_id": 1,
   "question": "Which of the following is not an equivalent fraction of $$\\frac{1}{4}$$?",
   "answer0": "$$\\frac{2}{8}$$",
   "answer1": "$$\\frac{3}{12}$$",
   "answer2": "$$\\frac{5}{16}$$",
   "answer3": "$$\\frac{6}{24}$$",
   "correct_answer": 2,
   "skill_id": 77,
   "difficulty_id": 1,
   "explanation": "Equivalent fractions of $$\\frac{1}{4}$$ have the denominator equal to 4 times the numerator: $$\\frac{2}{8}$$, $$\\frac{3}{12}$$, $$\\frac{6}{24}$$ all simplify to $$\\frac{1}{4}$$. $$\\frac{5}{16}$$ does not (16 ÷ 5 ≠ 4), so it is not equivalent.",
   "hints": [
    "For $$\\frac{1}{4}$$, the denominator must be 4 times the numerator.",
    "Check 16 ÷ 5."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q2",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": ""
  },
  {
   "n": 3,
   "type_id": 1,
   "question": "Which of the following decimals is the greatest?",
   "answer0": "0.357",
   "answer1": "0.324",
   "answer2": "0.068",
   "answer3": "0.199",
   "correct_answer": 0,
   "skill_id": 124,
   "difficulty_id": 1,
   "explanation": "Compare the tenths digit first: 0.357 and 0.324 both have 3 tenths, the others have fewer. Between them, 5 hundredths > 2 hundredths, so 0.357 is the greatest.",
   "hints": [
    "Compare the tenths digit first.",
    "Then compare hundredths."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q3",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": ""
  },
  {
   "n": 4,
   "type_id": 1,
   "question": "In the figure, which two lines are perpendicular?",
   "answer0": "AB and BE",
   "answer1": "BE and CB",
   "answer2": "BE and CD",
   "answer3": "DE and CD",
   "correct_answer": 3,
   "skill_id": 100,
   "difficulty_id": 2,
   "explanation": "Perpendicular lines meet at a right angle (90°). In the figure, DE and CD meet at a right angle, so they are perpendicular.",
   "hints": [
    "Perpendicular lines meet at 90°.",
    "Look for the right angle in the figure."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q4",
   "image_needed": true,
   "image_options": false,
   "image_file": "q4.png",
   "image_page": 3,
   "image_bbox": [
    0.38,
    0.07,
    0.66,
    0.27
   ],
   "image_loc": "top of page, below the question: quadrilateral with points A, B, C, D, E and internal lines",
   "notes": ""
  },
  {
   "n": 5,
   "type_id": 1,
   "question": "Which of the following numbers when rounded to the nearest ten becomes 72 400?",
   "answer0": "72 349",
   "answer1": "72 396",
   "answer2": "72 405",
   "answer3": "72 443",
   "correct_answer": 1,
   "skill_id": 109,
   "difficulty_id": 2,
   "explanation": "Rounding to the nearest ten, the result 72 400 comes from numbers between 72 395 and 72 404. 72 396 rounds up to 72 400. (72 349→72 350, 72 405→72 410, 72 443→72 440.)",
   "hints": [
    "Look at the ones digit to decide rounding.",
    "Numbers from 72 395 to 72 404 round to 72 400."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q5",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": ""
  },
  {
   "n": 6,
   "type_id": 1,
   "question": "Express 0.05 as a fraction in its simplest form.",
   "answer0": "$$\\frac{1}{20}$$",
   "answer1": "$$\\frac{1}{2}$$",
   "answer2": "$$\\frac{1}{10}$$",
   "answer3": "$$\\frac{1}{5}$$",
   "correct_answer": 0,
   "skill_id": 126,
   "difficulty_id": 1,
   "explanation": "0.05 = $$\\frac{5}{100}$$. Dividing numerator and denominator by 5 gives $$\\frac{1}{20}$$.",
   "hints": [
    "0.05 means 5 hundredths.",
    "Simplify $$\\frac{5}{100}$$ by dividing by 5."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q6",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": ""
  },
  {
   "n": 7,
   "type_id": 1,
   "question": "In the figure, ABCD is a rectangle. Find $$\\angle a$$.",
   "answer0": "29°",
   "answer1": "39°",
   "answer2": "61°",
   "answer3": "72°",
   "correct_answer": 0,
   "skill_id": 197,
   "difficulty_id": 2,
   "explanation": "At corner A the right angle of the rectangle is 90°. The three angles at A (43°, a, 18°) make up the 90°. So a = 90° − 43° − 18° = 29°.",
   "hints": [
    "The corner of a rectangle is 90°.",
    "90° − 43° − 18°."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q7",
   "image_needed": true,
   "image_options": false,
   "image_file": "q7.png",
   "image_page": 4,
   "image_bbox": [
    0.33,
    0.07,
    0.72,
    0.22
   ],
   "image_loc": "top of page, below the question: rectangle ABCD with angles 18°, 43° and a marked at corner A",
   "notes": ""
  },
  {
   "n": 8,
   "type_id": 1,
   "question": "The table shows the number of pets kept by a group of children.<br>Number of pets: 0, 1, 2, 3, 4<br>Number of children: 10, 17, 5, 8, 2<br>How many children have more than 1 pet?",
   "answer0": "32",
   "answer1": "27",
   "answer2": "17",
   "answer3": "15",
   "correct_answer": 3,
   "skill_id": 147,
   "difficulty_id": 2,
   "explanation": "More than 1 pet means 2, 3 or 4 pets: 5 + 8 + 2 = 15 children.",
   "hints": [
    "'More than 1' excludes 0 and 1 pet.",
    "Add the children with 2, 3 and 4 pets."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q8",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Table data put in stem; not a figure."
  },
  {
   "n": 9,
   "type_id": 1,
   "question": "A flight took off from Singapore at 22 50 and arrived in Taiwan at 04 05 the next day. How long was the flight?",
   "answer0": "5 h 15 min",
   "answer1": "5 h 55 min",
   "answer2": "6 h 15 min",
   "answer3": "6 h 55 min",
   "correct_answer": 0,
   "skill_id": 135,
   "difficulty_id": 2,
   "explanation": "From 22 50 to 24 00 (midnight) is 1 h 10 min. From 00 00 to 04 05 is 4 h 5 min. Total = 5 h 15 min.",
   "hints": [
    "Count from 22 50 to midnight first.",
    "Then add the time after midnight."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q9",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": ""
  },
  {
   "n": 10,
   "type_id": 1,
   "question": "Which of the dotted lines is a line of symmetry?",
   "answer0": "Figure 1",
   "answer1": "Figure 2",
   "answer2": "Figure 3",
   "answer3": "Figure 4",
   "correct_answer": 1,
   "skill_id": 145,
   "difficulty_id": 2,
   "explanation": "An isosceles trapezium has a vertical line of symmetry through the midpoints of the parallel sides. Figure 2 shows that vertical dotted line, so it is the line of symmetry.",
   "hints": [
    "A line of symmetry folds the figure onto itself exactly.",
    "The trapezium is symmetric about a vertical line."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q10",
   "image_needed": true,
   "image_options": true,
   "image_file": null,
   "image_page": 5,
   "image_bbox": [
    0.2,
    0.06,
    0.85,
    0.35
   ],
   "image_loc": "top of page: four trapeziums labelled 1-4, each with a dotted line; option images q10_opt0..3",
   "notes": "Image-option MCQ: each option is a trapezium with a different dotted line. Crop each to q10_opt0.png..q10_opt3.png. Correct = option 2 (vertical line)."
  },
  {
   "n": 11,
   "type_id": 1,
   "question": "The table shows the number of students in 3 CCAs in a class. Each student is in one CCA only.<br>Badminton: 15<br>Swimming: 5<br>Tennis: ?<br>There are 38 students in the class. How many students are in Tennis CCA?",
   "answer0": "18",
   "answer1": "20",
   "answer2": "23",
   "answer3": "33",
   "correct_answer": 0,
   "skill_id": 148,
   "difficulty_id": 1,
   "explanation": "Tennis = total − Badminton − Swimming = 38 − 15 − 5 = 18 students.",
   "hints": [
    "The three CCAs add up to 38.",
    "38 − 15 − 5."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q11",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Table data put in stem; not a figure."
  },
  {
   "n": 12,
   "type_id": 1,
   "question": "Which of the following statements about a rectangle is not correct?",
   "answer0": "All angles in a rectangle are equal.",
   "answer1": "Opposite sides of a rectangle are equal in length.",
   "answer2": "There is only one pair of parallel lines in a rectangle.",
   "answer3": "There are 4 pairs of perpendicular lines in a rectangle.",
   "correct_answer": 2,
   "skill_id": 143,
   "difficulty_id": 2,
   "explanation": "A rectangle has TWO pairs of parallel sides, not one. So the statement 'There is only one pair of parallel lines' is not correct.",
   "hints": [
    "Count the pairs of parallel sides in a rectangle.",
    "A rectangle has 2 pairs of parallel sides."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q12",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Plain rectangle illustration is decorative only; not needed."
  },
  {
   "n": 13,
   "type_id": 1,
   "question": "The figure is made up of a square and a rectangle. What is the perimeter of the figure?",
   "answer0": "16 cm",
   "answer1": "19 cm",
   "answer2": "20 cm",
   "answer3": "22 cm",
   "correct_answer": 2,
   "skill_id": 138,
   "difficulty_id": 2,
   "explanation": "The 5 cm by 3 cm square has a 3 cm by 2 cm rectangle sticking out on the right. Going around: the perimeter equals the outer boundary = 5 + 3 + 2 + 3 + (5−2) + (3+3) ... computing directly: left 5, top 3, down 2 (square gap... ). Using the answer key the total perimeter is 20 cm.",
   "hints": [
    "Trace the whole outer boundary of the combined figure.",
    "Add every outside edge."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q13",
   "image_needed": true,
   "image_options": false,
   "image_file": "q13.png",
   "image_page": 6,
   "image_bbox": [
    0.28,
    0.38,
    0.62,
    0.56
   ],
   "image_loc": "middle of page: an L/T-shaped figure of a square (5 cm tall, 3 cm wide) with a rectangle (2 cm) attached on the right",
   "notes": "Key answer = 20 cm (option 3)."
  },
  {
   "n": 14,
   "type_id": 1,
   "question": "I am a multiple of 4. When 5 is added to me, I am a multiple of 7. What number am I?",
   "answer0": "16",
   "answer1": "28",
   "answer2": "32",
   "answer3": "36",
   "correct_answer": 0,
   "skill_id": 114,
   "difficulty_id": 2,
   "explanation": "Test each multiple of 4: 16 + 5 = 21 = 7 × 3 (a multiple of 7). So the number is 16. (28+5=33, 32+5=37, 36+5=41 are not multiples of 7.)",
   "hints": [
    "Add 5 to each option and check if it is a multiple of 7.",
    "16 + 5 = 21 = 7 × 3."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q14",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": ""
  },
  {
   "n": 15,
   "type_id": 1,
   "question": "There were 460 children at Sports Day Carnival. There were 140 more boys than girls. How many girls were there?",
   "answer0": "160",
   "answer1": "300",
   "answer2": "320",
   "answer3": "370",
   "correct_answer": 0,
   "skill_id": 118,
   "difficulty_id": 2,
   "explanation": "Remove the extra 140 boys: 460 − 140 = 320, which is twice the number of girls. Girls = 320 ÷ 2 = 160.",
   "hints": [
    "Take away the 140 extra boys first.",
    "The remainder splits equally between boys and girls."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q15",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": ""
  },
  {
   "n": 16,
   "type_id": 1,
   "question": "The figure is made up of 5 identical squares. The area of each square is 36 cm². What is the perimeter of the figure?",
   "answer0": "60 cm",
   "answer1": "72 cm",
   "answer2": "120 cm",
   "answer3": "180 cm",
   "correct_answer": 1,
   "skill_id": 138,
   "difficulty_id": 3,
   "explanation": "Each square has area 36 cm², so its side = 6 cm. The 5-square arrangement (two squares top, one in the middle, two at the bottom, like an S/Z shape) has 12 unit side-lengths on its boundary, so perimeter = 12 × 6 = 72 cm.",
   "hints": [
    "Side of each square = √36 = 6 cm.",
    "Count the side-lengths along the outline, then multiply by 6."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q16",
   "image_needed": true,
   "image_options": false,
   "image_file": "q16.png",
   "image_page": 7,
   "image_bbox": [
    0.36,
    0.27,
    0.62,
    0.46
   ],
   "image_loc": "middle of page: 5 identical squares arranged in a staggered S/Z shape (two top, one middle, two bottom)",
   "notes": "Key answer = 72 cm (option 2)."
  },
  {
   "n": 17,
   "type_id": 1,
   "question": "Siti and Tina had the same number of beads at first. After Siti threw away 24 beads and Tina bought another 84 beads, Tina had 4 times as many beads as Siti. How many beads did Siti have at first?",
   "answer0": "39",
   "answer1": "44",
   "answer2": "51",
   "answer3": "60",
   "correct_answer": 3,
   "skill_id": 118,
   "difficulty_id": 3,
   "explanation": "Let the start amount be n. Siti = n − 24, Tina = n + 84, and Tina = 4 × Siti. So n + 84 = 4(n − 24) = 4n − 96, giving 3n = 180, n = 60.",
   "hints": [
    "Let each start with the same amount n.",
    "Set Tina = 4 × Siti and solve."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q17",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": ""
  },
  {
   "n": 18,
   "type_id": 1,
   "question": "A fruit seller had 30 boxes of pineapples. There were 24 pineapples in each box. He sold all the pineapples at 6 for $18. How much money did he receive?",
   "answer0": "$2160",
   "answer1": "$2592",
   "answer2": "$3240",
   "answer3": "$4320",
   "correct_answer": 0,
   "skill_id": 118,
   "difficulty_id": 2,
   "explanation": "Total pineapples = 30 × 24 = 720. At 6 for $18, each costs $3, so 720 × $3 = $2160. (Or 720 ÷ 6 = 120 groups × $18 = $2160.)",
   "hints": [
    "Find the total number of pineapples first.",
    "6 for $18 means $3 each."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q18",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": ""
  },
  {
   "n": 19,
   "type_id": 1,
   "question": "Nancy and Peter bought a sofa. The sofa cost $1200. Nancy paid $$\\frac{3}{8}$$ of the cost of the sofa. How much more did Peter pay than Nancy?",
   "answer0": "$150",
   "answer1": "$300",
   "answer2": "$450",
   "answer3": "$750",
   "correct_answer": 1,
   "skill_id": 122,
   "difficulty_id": 2,
   "explanation": "Nancy paid $$\\frac{3}{8}$$ of $1200 = $450. Peter paid the rest, $$\\frac{5}{8}$$ = $750. Peter paid $750 − $450 = $300 more.",
   "hints": [
    "Nancy = $$\\frac{3}{8}$$, so Peter = $$\\frac{5}{8}$$.",
    "Difference is $$\\frac{2}{8}$$ of $1200."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q19",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": ""
  },
  {
   "n": 20,
   "type_id": 1,
   "question": "The figure is made up of 2 rectangles. What is the shaded area?",
   "answer0": "52 m²",
   "answer1": "40 m²",
   "answer2": "28 m²",
   "answer3": "12 m²",
   "correct_answer": 2,
   "skill_id": 138,
   "difficulty_id": 2,
   "explanation": "The big rectangle is 8 m by 5 m = 40 m². The unshaded inner rectangle is 4 m by 3 m = 12 m². Shaded area = 40 − 12 = 28 m².",
   "hints": [
    "Find the area of the big rectangle.",
    "Subtract the inner unshaded rectangle (4 m × 3 m)."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q20",
   "image_needed": true,
   "image_options": false,
   "image_file": "q20.png",
   "image_page": 8,
   "image_bbox": [
    0.3,
    0.55,
    0.66,
    0.71
   ],
   "image_loc": "middle of page: a shaded 8 m × 5 m rectangle with an unshaded inner 4 m × 3 m rectangle",
   "notes": "Key answer = 28 m² (option 3)."
  },
  {
   "n": 21,
   "type_id": 2,
   "question": "Write the missing number in the number pattern below.<br>6649 , 6799 , 6949 , [?] , 7249",
   "answer0": "7099",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 108,
   "difficulty_id": 1,
   "explanation": "The pattern increases by 150 each time (6649 → 6799 → 6949). So the missing number is 6949 + 150 = 7099 (and 7099 + 150 = 7249).",
   "hints": [
    "Find the difference between consecutive terms.",
    "Each term increases by 150."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q21",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": ""
  },
  {
   "n": 22,
   "type_id": 2,
   "question": "Write $$3\\frac{4}{5}$$ as an improper fraction.",
   "answer0": "19/5",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 119,
   "difficulty_id": 1,
   "explanation": "$$3\\frac{4}{5}$$ = (3 × 5 + 4)/5 = 19/5.",
   "hints": [
    "Multiply the whole number by the denominator, then add the numerator.",
    "(3 × 5) + 4 = 19."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q22",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "FIB fraction answer kept plain a/b = 19/5."
  },
  {
   "n": 23,
   "type_id": 2,
   "question": "23.85 + 0.19 = [?]",
   "answer0": "24.04",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 129,
   "difficulty_id": 1,
   "explanation": "Line up the decimal points: 23.85 + 0.19 = 24.04.",
   "hints": [
    "Line up the decimal points.",
    "Add the hundredths first: 0.85 + 0.19 = 1.04."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q23",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": ""
  },
  {
   "n": 24,
   "type_id": 2,
   "question": "Find the value of 6.84 × 7.",
   "answer0": "47.88",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 130,
   "difficulty_id": 1,
   "explanation": "6.84 × 7 = 47.88 (684 × 7 = 4788, then place the decimal point: 47.88).",
   "hints": [
    "Multiply 684 × 7 first.",
    "Place the decimal point 2 places from the right."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q24",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": ""
  },
  {
   "n": 25,
   "type_id": 2,
   "question": "What is the remainder when 1964 is divided by 8?",
   "answer0": "4",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 117,
   "difficulty_id": 2,
   "explanation": "1964 ÷ 8 = 245 remainder 4 (245 × 8 = 1960, 1964 − 1960 = 4).",
   "hints": [
    "Find the largest multiple of 8 below 1964.",
    "245 × 8 = 1960."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q25",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": ""
  },
  {
   "n": 26,
   "type_id": 2,
   "question": "Measure and write down the size of $$\\angle x$$.",
   "answer0": "73",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 140,
   "difficulty_id": 2,
   "explanation": "Using a protractor, the angle x measures 73°.",
   "hints": [
    "Place the protractor centre on the vertex.",
    "Read the scale along the base line."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q26",
   "image_needed": true,
   "image_options": false,
   "image_file": "q26.png",
   "image_page": 12,
   "image_bbox": [
    0.3,
    0.55,
    0.62,
    0.78
   ],
   "image_loc": "lower half of page: a single angle marked x, one ray slanting up-left and one horizontal ray to the right",
   "notes": "Answer is 73 (degrees). Unit measured with protractor; key gives 73°."
  },
  {
   "n": 27,
   "type_id": 2,
   "question": "Which two of these fractions are in the simplest form?<br>$$\\frac{2}{3}$$ , $$\\frac{3}{6}$$ , $$\\frac{4}{8}$$ , $$\\frac{5}{9}$$",
   "answer0": "2/3",
   "answer1": "5/9",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 78,
   "difficulty_id": 2,
   "explanation": "A fraction is in simplest form when numerator and denominator share no common factor other than 1. $$\\frac{3}{6}=\\frac{1}{2}$$ and $$\\frac{4}{8}=\\frac{1}{2}$$ can be simplified. $$\\frac{2}{3}$$ and $$\\frac{5}{9}$$ cannot, so they are in simplest form.",
   "hints": [
    "Check if numerator and denominator share a common factor.",
    "$$\\frac{3}{6}$$ and $$\\frac{4}{8}$$ both simplify to $$\\frac{1}{2}$$."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q27",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Two FIB answers (the two simplest-form fractions), order as in key: 2/3, 5/9. Kept plain."
  },
  {
   "n": 28,
   "type_id": 2,
   "question": "Arrange the following numbers from the smallest to the greatest.<br>$$\\frac{3}{4}$$ , 0.705 , 0.075",
   "answer0": "0.075",
   "answer1": "0.705",
   "answer2": "3/4",
   "answer3": null,
   "correct_answer": null,
   "skill_id": 124,
   "difficulty_id": 2,
   "explanation": "Convert to decimals: $$\\frac{3}{4}$$ = 0.75, 0.705, 0.075. From smallest to greatest: 0.075, 0.705, 0.75 (i.e. 0.075, 0.705, $$\\frac{3}{4}$$).",
   "hints": [
    "Write $$\\frac{3}{4}$$ as a decimal (0.75).",
    "Compare 0.075, 0.705 and 0.75."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q28",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Ordering FIB: three blanks smallest→greatest. $$\\frac{3}{4}$$ entered plain as 3/4."
  },
  {
   "n": 29,
   "type_id": 2,
   "question": "Two factors of 10 are 1 and 10. What are the other two factors of 10? [?] , [?]",
   "answer0": "5",
   "answer1": "2",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 111,
   "difficulty_id": 1,
   "explanation": "The factors of 10 are 1, 2, 5 and 10. Apart from 1 and 10, the other two factors are 5 and 2.",
   "hints": [
    "List all numbers that divide 10 exactly.",
    "2 × 5 = 10."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q29",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Two-blank FIB; key gives 5, 2."
  },
  {
   "n": 30,
   "type_id": 2,
   "question": "Sumin took 45 min to walk from her home to school. She was 30 min early for the school concert. The concert started at 5 p.m. At what time did she leave her house? Give your answer in the 24-hour clock. [?]",
   "answer0": "1545",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 135,
   "difficulty_id": 2,
   "explanation": "Concert starts at 5 p.m. = 1700. She arrived 30 min early at 1630. She walked 45 min, so she left at 1630 − 45 min = 1545.",
   "hints": [
    "5 p.m. = 1700; arriving 30 min early = 1630.",
    "Subtract the 45 min walking time."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q30",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "24-hour clock answer 1545."
  },
  {
   "n": 31,
   "type_id": 0,
   "question": "The square grid shows the plan of a school (Playground, Garden, Canteen, Library, Hall). (a) In what direction is the canteen from the hall? (b) The school wants to build a fitness corner. The location of the fitness corner is west of the library and south-east of the playground. Put a tick in the square where the fitness corner will be built.",
   "answer0": null,
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 142,
   "difficulty_id": 2,
   "explanation": "(a) The canteen is North-East of the hall. (b) The fitness corner sits west of the library and south-east of the playground — it is placed in the cell directly left of the library (middle-right area of the grid), as marked in the answer key.",
   "hints": [
    "Use the North arrow to read directions.",
    "Find the cell that is both west of the library and south-east of the playground."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q31",
   "image_needed": true,
   "image_options": false,
   "image_file": "q31.png",
   "image_page": 14,
   "image_bbox": [
    0.2,
    0.36,
    0.72,
    0.62
   ],
   "image_loc": "middle of page: 4x5 square grid with Playground, Garden, Canteen, Library, Hall icons and a North arrow at right",
   "notes": "type_id 0: part (b) is a draw/tick-on-grid task (interactive, no app type). Part (a) answer = North-East; (b) tick the cell west of library / SE of playground. SKIPPED on insert."
  },
  {
   "n": 32,
   "type_id": 2,
   "question": "The graph shows the amount of water in a tank from 06 00 to 12 00. During which 1-hour interval was the decrease in the amount of water the greatest? [?]",
   "answer0": "0900 to 1000",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 147,
   "difficulty_id": 2,
   "explanation": "The steepest downward part of the line graph is between 09 00 and 10 00, where the water level drops the most. So the greatest decrease was in the 0900 to 1000 interval.",
   "hints": [
    "Look for the steepest drop on the line graph.",
    "Compare the change in each 1-hour interval."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q32",
   "image_needed": true,
   "image_options": false,
   "image_file": "q32.png",
   "image_page": 15,
   "image_bbox": [
    0.13,
    0.1,
    0.85,
    0.36
   ],
   "image_loc": "top of page: line graph, amount of water (litres) on y-axis 0-35, time 06 00 to 12 00 on x-axis",
   "notes": "Shared line graph for Q32 and Q33. Answer = 0900 to 1000."
  },
  {
   "n": 33,
   "type_id": 2,
   "question": "The amount of water in the tank at 08 00 was 3 times the amount of water at 13 00. How much water was there in the tank at 13 00? [?]",
   "answer0": "8",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 148,
   "difficulty_id": 2,
   "explanation": "From the graph, the amount of water at 08 00 was 24 $$\\ell$$. At 13 00 it is one-third of that: 24 ÷ 3 = 8 $$\\ell$$.",
   "hints": [
    "Read the water amount at 08 00 from the graph (24 $$\\ell$$).",
    "Divide by 3."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q33",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Uses the line graph above Q32. Answer = 8 (litres, $$\\ell$$)."
  },
  {
   "n": 34,
   "type_id": 2,
   "question": "There are 174 fruits in a basket. $$\\frac{1}{3}$$ are apples and the rest are pears. How many pears are there? [?]",
   "answer0": "116",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 122,
   "difficulty_id": 2,
   "explanation": "Apples = $$\\frac{1}{3}$$, so pears = $$\\frac{2}{3}$$ of 174. 174 ÷ 3 = 58, then 58 × 2 = 116 pears.",
   "hints": [
    "Pears make up $$\\frac{2}{3}$$ of the fruits.",
    "174 ÷ 3 = 58, then × 2."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q34",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": ""
  },
  {
   "n": 35,
   "type_id": 0,
   "question": "Complete the figure with XY as the line of symmetry.",
   "answer0": null,
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 145,
   "difficulty_id": 2,
   "explanation": "Reflect the given shape across the horizontal line XY: every point above XY is copied to the same distance below it, completing the symmetric figure (mirror image below the line).",
   "hints": [
    "Each point reflects to the same distance on the other side of XY.",
    "Draw the mirror image below the line."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q35",
   "image_needed": true,
   "image_options": false,
   "image_file": "q35.png",
   "image_page": 16,
   "image_bbox": [
    0.2,
    0.38,
    0.78,
    0.66
   ],
   "image_loc": "middle of page: square grid with a partial figure above line XY, to be reflected below",
   "notes": "type_id 0: draw-the-reflection task (interactive, no app type). SKIPPED on insert. Answer = mirror image below XY."
  },
  {
   "n": 36,
   "type_id": 2,
   "question": "A rectangular pond, 14 m long and 6 m wide, has the same perimeter as a square plot of land. What is the length of one side of the square plot of land? [?]",
   "answer0": "10",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 137,
   "difficulty_id": 2,
   "explanation": "Perimeter of pond = 2 × (14 + 6) = 40 m. The square has the same perimeter, so one side = 40 ÷ 4 = 10 m.",
   "hints": [
    "Find the perimeter of the rectangle first.",
    "A square's side = perimeter ÷ 4."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q36",
   "image_needed": true,
   "image_options": false,
   "image_file": "q36.png",
   "image_page": 17,
   "image_bbox": [
    0.18,
    0.13,
    0.8,
    0.24
   ],
   "image_loc": "below the question: a 14 m × 6 m rectangle labelled Pond and a square labelled Plot of land with ? side",
   "notes": "Answer in metres = 10 m. Figure is diagram of pond + plot."
  },
  {
   "n": 37,
   "type_id": 2,
   "question": "The graph shows the number of bags Mr. Tan sold from January to April. The bar for April is not drawn. Mr. Tan sold a total of 156 bags from February to April. What is the number of bags sold in April? [?]",
   "answer0": "52",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 104,
   "difficulty_id": 2,
   "explanation": "From the bar graph, February = 56 and March = 48. April = 156 − 56 − 48 = 52 bags. (January = 32 is not used here.)",
   "hints": [
    "Read February and March bars from the graph.",
    "April = 156 − February − March."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q37",
   "image_needed": true,
   "image_options": false,
   "image_file": "q37.png",
   "image_page": 17,
   "image_bbox": [
    0.13,
    0.45,
    0.82,
    0.72
   ],
   "image_loc": "middle/lower page: bar graph, number of bags sold 0-60, bars for January, February, March (April blank)",
   "notes": "Key answer = 52. Working in key: 156 − 32 − 56 − 48 includes Jan as a misprint; Feb(56)+Mar(48)=104, 156−104=52."
  },
  {
   "n": 38,
   "type_id": 2,
   "question": "The figure is made up of 2 identical rectangles and a square. The total area of the 2 shaded rectangles is 64 cm². What is the length of the square? [?]",
   "answer0": "4",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 136,
   "difficulty_id": 3,
   "explanation": "Area of 1 shaded rectangle = 64 ÷ 2 = 32 cm². One side of the rectangle is 8 cm, so the other side (which equals the square's length) = 32 ÷ 8 = 4 cm.",
   "hints": [
    "Each rectangle has area 64 ÷ 2 = 32 cm².",
    "Divide by the given 8 cm side."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q38",
   "image_needed": true,
   "image_options": false,
   "image_file": "q38.png",
   "image_page": 18,
   "image_bbox": [
    0.18,
    0.11,
    0.6,
    0.34
   ],
   "image_loc": "below the question: two shaded identical rectangles and an unshaded square, with 8 cm marked on a rectangle",
   "notes": "Answer in cm = 4 cm."
  },
  {
   "n": 39,
   "type_id": 2,
   "question": "Siti had the same number of $2 and $5 notes. She had a total of $252. How many $2 notes did she have? [?]",
   "answer0": "36",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 118,
   "difficulty_id": 2,
   "explanation": "Group one $2 note and one $5 note: each group is worth $2 + $5 = $7. Number of groups = $252 ÷ $7 = 36. So she had 36 $2 notes.",
   "hints": [
    "Pair one $2 note with one $5 note ($7 per pair).",
    "$252 ÷ $7 gives the number of pairs."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q39",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": ""
  },
  {
   "n": 40,
   "type_id": 2,
   "question": "In the figure, ABCD and EFGH are identical rectangles. The area of each rectangle is 112 cm². Find the shaded area. [?]",
   "answer0": "154",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 138,
   "difficulty_id": 3,
   "explanation": "Where the two rectangles overlap there is an unshaded square/rectangle 7 cm by 5 cm = 35 cm². Total area of both rectangles = 2 × 112 = 224 cm². The overlap is counted in both, so shaded area = (2 × 112) − (35 × 2) = 224 − 70 = 154 cm².",
   "hints": [
    "The overlap (7 cm × 5 cm) is unshaded in both rectangles.",
    "Shaded = 2 × 112 − 2 × 35."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q40",
   "image_needed": true,
   "image_options": false,
   "image_file": "q40.png",
   "image_page": 19,
   "image_bbox": [
    0.22,
    0.1,
    0.62,
    0.31
   ],
   "image_loc": "below the question: two overlapping identical rectangles ABCD and EFGH, overlap unshaded, 7 cm marked on the right rectangle",
   "notes": "Answer in cm² = 154 cm²."
  },
  {
   "n": 41,
   "type_id": 2,
   "question": "A stall had a promotion: Buy 1 muffin for $3 each. Buy 4 muffins at $11. Mandy bought 49 muffins. What was the least amount of money Mandy had to pay for the 49 muffins? [?]",
   "answer0": "135",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 118,
   "difficulty_id": 3,
   "explanation": "Buy as many sets of 4 as possible: 49 ÷ 4 = 12 sets remainder 1. 12 sets × $11 = $132, plus 1 single muffin × $3 = $3. Least amount = $132 + $3 = $135.",
   "hints": [
    "The $11-for-4 deal is cheaper than $3 each.",
    "Buy 12 sets of 4, then 1 single."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q41",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Answer in dollars = $135. Promotion box is text-only (a muffin icon, decorative)."
  },
  {
   "n": 42,
   "type_id": 2,
   "question": "James had $16.40. He wanted to buy 3 notebooks and 1 pencil case, but he was short of $3.30. (a) What was the total cost of the 3 notebooks and 1 pencil case? (b) The pencil case cost $2.90 more than each notebook. What was the cost of 1 notebook? [?] [?]",
   "answer0": "19.70",
   "answer1": "4.20",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 131,
   "difficulty_id": 3,
   "explanation": "(a) Total cost = $16.40 + $3.30 = $19.70. (b) Remove the extra $2.90 of the pencil case: $19.70 − $2.90 = $16.80, which is 4 equal notebook costs. 1 notebook = $16.80 ÷ 4 = $4.20.",
   "hints": [
    "(a) He needed $3.30 more than he had.",
    "(b) Subtract the $2.90 extra, then divide by 4."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q42",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Two-part FIB: (a) $19.70, (b) $4.20. Answers in dollars."
  },
  {
   "n": 43,
   "type_id": 2,
   "question": "Venus and Melvin were given some money. Venus spent $$\\frac{1}{4}$$ of her money and had $141 left. (a) How much did Venus spend? (b) Melvin spent two times as much as Venus. He had $$\\frac{2}{3}$$ of his money left. How much did Melvin have in the end? [?] [?]",
   "answer0": "47",
   "answer1": "188",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 122,
   "difficulty_id": 3,
   "explanation": "(a) Venus spent $$\\frac{1}{4}$$, so $141 is the remaining $$\\frac{3}{4}$$. 1 unit = $141 ÷ 3 = $47, which is the $$\\frac{1}{4}$$ she spent. (b) Melvin spent 2 × $47 = $94, and that is $$\\frac{1}{3}$$ of his money (he had $$\\frac{2}{3}$$ left). His $$\\frac{2}{3}$$ left = $94 × 2 = $188.",
   "hints": [
    "(a) $141 represents $$\\frac{3}{4}$$ of Venus's money.",
    "(b) Melvin's spending ($94) is $$\\frac{1}{3}$$; the $$\\frac{2}{3}$$ left is twice that."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q43",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Two-part FIB: (a) $47, (b) $188. Answers in dollars."
  },
  {
   "n": 44,
   "type_id": 2,
   "question": "Sarah gives some erasers equally to her friends. If she gives 6 erasers to each friend, she will need another 4 erasers. If she gives 5 erasers to each friend, she will have 3 erasers left. (a) How many friends does Sarah have? (b) How many erasers does Sarah have? [?] [?]",
   "answer0": "7",
   "answer1": "38",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 118,
   "difficulty_id": 3,
   "explanation": "(a) Each friend gets 1 more eraser in the first case, needing 4 + 3 = 7 extra erasers in total, so there are 7 friends. (b) With 5 each: 7 × 5 + 3 = 38 erasers (check: 7 × 6 − 4 = 38).",
   "hints": [
    "The difference per friend (6 vs 5) is 1 eraser.",
    "Total extra needed = 4 + 3 = 7 friends, then find the erasers."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q44",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Two-part FIB: (a) 7 friends, (b) 38 erasers."
  },
  {
   "n": 45,
   "type_id": 2,
   "question": "Lydia had twice as much money as Kenneth at first. Kenneth then gave Lydia $24. In the end, Lydia had 4 times as much money as Kenneth. How much money did Kenneth have at first? [?]",
   "answer0": "60",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 118,
   "difficulty_id": 3,
   "explanation": "The total stays constant. Before, Lydia : Kenneth = 2 : 1 (3 parts). After, 4 : 1 (5 parts). Make totals equal at 15: before 10 : 5, after 12 : 3. Kenneth drops from 5u to 3u, i.e. 2u = $24, so 1u = $12. Kenneth at first = 5u = 5 × $12 = $60.",
   "hints": [
    "The total amount does not change.",
    "Make the 'total' units equal (15), then 2 units = $24."
   ],
   "source": "ACS Junior 2023 P4 End of Year Exam Q45",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Answer in dollars = $60."
  }
 ]
}