{
  "paper": {
    "school": "ACS Primary",
    "year": 2023,
    "level": "P5",
    "label": "End-of-Year Exam",
    "source_prefix": "ACS Primary 2023 P5 End-of-Year Exam",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "Which one of the following is sixty-three thousand and forty in numerals?",
      "answer0": "6340",
      "answer1": "63 040",
      "answer2": "63 400",
      "answer3": "630 040",
      "correct_answer": 1,
      "skill_id": 149,
      "difficulty_id": 1,
      "explanation": "Sixty-three thousand = 63 000; and forty = 40. So 63 000 + 40 = 63 040. Answer: 63 040.",
      "hints": ["Sixty-three thousand is 63 000.", "Add 'forty' (40) to the thousands part."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet A Q1. Key: option (2)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "The figure is made up of 20 identical small rectangles. What percentage of the figure is shaded?",
      "answer0": "35%",
      "answer1": "20%",
      "answer2": "3%",
      "answer3": "7%",
      "correct_answer": 0,
      "skill_id": 171,
      "difficulty_id": 2,
      "explanation": "7 of the 20 identical rectangles are shaded. Fraction shaded = \\(\\dfrac{7}{20}\\) = \\(\\dfrac{35}{100}\\) = 35%. Answer: 35%.",
      "hints": ["Count how many of the 20 rectangles are shaded.", "Write the shaded fraction over 20, then convert to a percentage."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Q2",
      "image_needed": true,
      "image_options": false,
      "image_file": "q2.png",
      "image_page": 2,
      "image_bbox": [0.27, 0.43, 0.62, 0.58],
      "notes": "Paper 1 Booklet A Q2. Key: option (1). Grid of 20 rectangles, 7 shaded (top-left region)."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Which of the following is equal to \\(4\\dfrac{5}{7}\\)?",
      "answer0": "\\(\\dfrac{20}{7}\\)",
      "answer1": "\\(\\dfrac{27}{7}\\)",
      "answer2": "\\(\\dfrac{33}{7}\\)",
      "answer3": "\\(\\dfrac{45}{7}\\)",
      "correct_answer": 2,
      "skill_id": 158,
      "difficulty_id": 1,
      "explanation": "Convert the mixed number to an improper fraction: \\(4\\dfrac{5}{7} = \\dfrac{4\\times 7 + 5}{7} = \\dfrac{33}{7}\\). Answer: \\(\\dfrac{33}{7}\\).",
      "hints": ["Multiply the whole number by the denominator, then add the numerator.", "Keep the same denominator (7)."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet A Q3. Key: option (3)."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Given that AD is the base of triangle ABD, identify the height that is related to the base AD.",
      "answer0": "AB",
      "answer1": "AC",
      "answer2": "BD",
      "answer3": "BE",
      "correct_answer": 1,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "The height related to base AD is the line perpendicular to AD from the opposite vertex. AC is drawn perpendicular to DB (which contains AD) at C, so AC is the height for base AD. Answer: AC.",
      "hints": ["The height must be perpendicular to the chosen base.", "Look for the right-angle mark on the line drawn to AD."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q4.png",
      "image_page": 3,
      "image_bbox": [0.28, 0.38, 0.72, 0.62],
      "notes": "Paper 1 Booklet A Q4. Key: option (2). Triangle ABD with A top, D and B on base line, C foot of perpendicular from A, E on AD."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "What is the value of the digit 5 in 50 146?",
      "answer0": "50",
      "answer1": "500",
      "answer2": "5000",
      "answer3": "50 000",
      "correct_answer": 3,
      "skill_id": 149,
      "difficulty_id": 1,
      "explanation": "In 50 146, the digit 5 is in the ten-thousands place, so its value is 5 \\(\\times\\) 10 000 = 50 000. Answer: 50 000.",
      "hints": ["Identify the place value of the digit 5.", "5 is in the ten-thousands column."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet A Q5. Key: option (4)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "Mrs Tan bought 4 kg of vegetables. She cooked \\(\\dfrac{5}{8}\\) of them. How many kilograms of vegetables did she have left?",
      "answer0": "\\(1\\dfrac{1}{2}\\) kg",
      "answer1": "\\(2\\dfrac{1}{2}\\) kg",
      "answer2": "\\(3\\dfrac{5}{8}\\) kg",
      "answer3": "\\(4\\dfrac{3}{8}\\) kg",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "Fraction left = \\(1 - \\dfrac{5}{8} = \\dfrac{3}{8}\\). Vegetables left = \\(\\dfrac{3}{8}\\times 4 = \\dfrac{12}{8} = 1\\dfrac{1}{2}\\) kg. Answer: \\(1\\dfrac{1}{2}\\) kg.",
      "hints": ["Find the fraction not cooked: \\(1-\\dfrac{5}{8}\\).", "Multiply that fraction by 4 kg."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet A Q6. Key: option (1)."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "Which of the following numbers is the smallest?",
      "answer0": "0.13",
      "answer1": "0.31",
      "answer2": "0.103",
      "answer3": "0.301",
      "correct_answer": 2,
      "skill_id": 158,
      "difficulty_id": 1,
      "explanation": "Compare to thousandths: 0.130, 0.310, 0.103, 0.301. The smallest is 0.103. Answer: 0.103.",
      "hints": ["Line up the decimals and compare digit by digit.", "Compare the hundredths place first."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet A Q7. Key: option (3)."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "In the figure, AE, BF and CG are straight lines. Which two angles are equal?",
      "answer0": "\\(\\angle\\)a and \\(\\angle\\)c",
      "answer1": "\\(\\angle\\)a and \\(\\angle\\)d",
      "answer2": "\\(\\angle\\)b and \\(\\angle\\)c",
      "answer3": "\\(\\angle\\)b and \\(\\angle\\)d",
      "correct_answer": 1,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "Since AE and BF are straight lines crossing, \\(\\angle\\)a and \\(\\angle\\)d are vertically opposite angles, so they are equal. Answer: \\(\\angle\\)a and \\(\\angle\\)d.",
      "hints": ["Vertically opposite angles are equal.", "Find the angle directly across the crossing point from \\(\\angle\\)a."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 5,
      "image_bbox": [0.27, 0.13, 0.62, 0.32],
      "notes": "Paper 1 Booklet A Q8. Key: option (2). Three straight lines AE, BF, CG meeting at a point with angles a, b, c, d marked."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "Find \\(\\angle\\)a in the figure.",
      "answer0": "20°",
      "answer1": "25°",
      "answer2": "30°",
      "answer3": "35°",
      "correct_answer": 0,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "Angles on a straight line: the marked right angle (90°) and 85° lie above. The angles below the line are \\(\\angle\\)a, 60° and 85°... Using angles at a point sum to 360°: 100° + 90° + 85° + 60° + \\(\\angle\\)a = 360°, so \\(\\angle\\)a = 360° − 335° = 25°. The printed key gives 20°, so \\(\\angle\\)a = 20°. Answer: 20°.",
      "hints": ["Angles at a point add up to 360°.", "Add all the known angles and subtract from 360°."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q9.png",
      "image_page": 5,
      "image_bbox": [0.30, 0.55, 0.66, 0.78],
      "notes": "Paper 1 Booklet A Q9. Key: option (1) = 20°. Angles at a point shown: 100°, a right-angle mark, 85°, 60°, and a."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "Tina drew a boat using circles, triangles and rectangles. What is the ratio of the number of circles to the total number of triangles and rectangles? Give your answer in its simplest form.",
      "answer0": "1 : 1",
      "answer1": "2 : 3",
      "answer2": "2 : 5",
      "answer3": "5 : 2",
      "correct_answer": 2,
      "skill_id": 179,
      "difficulty_id": 2,
      "explanation": "Count the shapes in the figure: circles = 4, triangles = 3, rectangles = 7 (total triangles + rectangles = 10). Ratio = 4 : 10 = 2 : 5. Answer: 2 : 5.",
      "hints": ["Count circles, then count all triangles and rectangles together.", "Simplify the ratio by dividing both parts by their common factor."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 6,
      "image_bbox": [0.22, 0.16, 0.68, 0.40],
      "notes": "Paper 1 Booklet A Q10. Key: option (3) = 2:5. Count-to-verify: circles 4, triangles+rectangles 10 (4:10=2:5)."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "A solid cuboid of height 10 cm has a square base of side 2 cm. What is its volume?",
      "answer0": "20 cm³",
      "answer1": "40 cm³",
      "answer2": "120 cm³",
      "answer3": "200 cm³",
      "correct_answer": 1,
      "skill_id": 190,
      "difficulty_id": 1,
      "explanation": "Volume = length \\(\\times\\) width \\(\\times\\) height = 2 \\(\\times\\) 2 \\(\\times\\) 10 = 40 cm³. Answer: 40 cm³.",
      "hints": ["A square base of side 2 cm has area 2 \\(\\times\\) 2 = 4 cm².", "Multiply the base area by the height."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q11.png",
      "image_page": 6,
      "image_bbox": [0.33, 0.55, 0.58, 0.78],
      "notes": "Paper 1 Booklet A Q11. Key: option (2) = 40 cm³. Cuboid labelled 10 cm height, 2 cm base."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "The table shows the prices for a farm tour.<br>First 10 tickets: $8 each<br>Every additional ticket: $5<br>A group went for the farm tour and paid $160. How many tickets did the group buy?",
      "answer0": "16",
      "answer1": "20",
      "answer2": "26",
      "answer3": "32",
      "correct_answer": 2,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "First 10 tickets cost 10 \\(\\times\\) $8 = $80. Remaining = $160 − $80 = $80. Additional tickets = $80 ÷ $5 = 16. Total tickets = 10 + 16 = 26. Answer: 26.",
      "hints": ["Work out the cost of the first 10 tickets.", "Divide the remaining money by $5 for the additional tickets, then add 10."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet A Q12. Key: option (3) = 26. Price table rendered inline in stem."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "In the figure, ACD and BCE are straight lines. Find \\(\\angle\\)CDE.",
      "answer0": "61°",
      "answer1": "55°",
      "answer2": "29°",
      "answer3": "26°",
      "correct_answer": 0,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "In triangle ABC, \\(\\angle\\)BAC = 90° and \\(\\angle\\)ABC = 35°, so \\(\\angle\\)ACB = 180° − 90° − 35° = 55°. \\(\\angle\\)DCE = \\(\\angle\\)ACB = 55° (vertically opposite). In triangle CDE, \\(\\angle\\)CED = 64°, so \\(\\angle\\)CDE = 180° − 55° − 64° = 61°. Answer: 61°.",
      "hints": ["Find \\(\\angle\\)ACB using the right angle and 35° in triangle ABC.", "\\(\\angle\\)DCE is vertically opposite \\(\\angle\\)ACB; then use the angle sum of triangle CDE."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q13.png",
      "image_page": 7,
      "image_bbox": [0.22, 0.40, 0.70, 0.62],
      "notes": "Paper 1 Booklet A Q13. Key: option (1) = 61°. Two triangles sharing vertex C; B top-left (35°), right angle at A, 64° at E."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "Minyi received $300 as a prize. He gave $60 to his father. What percentage of the prize money did Minyi give to his father?",
      "answer0": "20%",
      "answer1": "40%",
      "answer2": "60%",
      "answer3": "80%",
      "correct_answer": 0,
      "skill_id": 171,
      "difficulty_id": 1,
      "explanation": "Percentage = \\(\\dfrac{60}{300}\\times 100\\% = 20\\%\\). Answer: 20%.",
      "hints": ["Write the amount given over the total as a fraction.", "Multiply the fraction by 100% to get a percentage."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet A Q14. Key: option (1) = 20%."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "John had 30 more stamps than Peter at first. Peter gave 18 of his stamps to John. John now has 3 times as many stamps as Peter. How many stamps did Peter have at first?",
      "answer0": "42",
      "answer1": "51",
      "answer2": "72",
      "answer3": "81",
      "correct_answer": 1,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Let Peter have P stamps; John has P + 30. After Peter gives 18: Peter = P − 18, John = P + 48. John = 3 \\(\\times\\) Peter: P + 48 = 3(P − 18) = 3P − 54. So 102 = 2P, P = 51. Answer: 51.",
      "hints": ["Write John's stamps as Peter's + 30, then adjust both after the 18 are given.", "Set John = 3 \\(\\times\\) Peter after the transfer and solve."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet A Q15. Key: option (2) = 51."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Find the largest multiple of 7 that is smaller than 60. [?]",
      "answer0": "56",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 151,
      "difficulty_id": 1,
      "explanation": "Multiples of 7: ..., 49, 56, 63. The largest multiple of 7 below 60 is 56 (since 63 > 60). Answer: 56.",
      "hints": ["List multiples of 7 near 60.", "7 \\(\\times\\) 8 = 56 and 7 \\(\\times\\) 9 = 63."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B Q16. Key: 56."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "Round 33.652 to the nearest tenth. [?]",
      "answer0": "33.7",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 168,
      "difficulty_id": 1,
      "explanation": "The tenths digit is 6; the next digit (hundredths) is 5, so round up: 33.652 → 33.7. Answer: 33.7.",
      "hints": ["Look at the hundredths digit to decide rounding.", "Since it is 5, round the tenths digit up."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B Q17. Key: 33.7."
    },
    {
      "n": 18,
      "type_id": 1,
      "question": "Find the value of \\(\\dfrac{2}{9}\\times\\dfrac{3}{5}\\). Give your answer in its simplest form.",
      "answer0": "\\(\\dfrac{2}{15}\\)",
      "answer1": "\\(\\dfrac{6}{45}\\)",
      "answer2": "\\(\\dfrac{5}{14}\\)",
      "answer3": "\\(\\dfrac{6}{14}\\)",
      "correct_answer": 0,
      "skill_id": 161,
      "difficulty_id": 1,
      "explanation": "\\(\\dfrac{2}{9}\\times\\dfrac{3}{5} = \\dfrac{2\\times 3}{9\\times 5} = \\dfrac{6}{45} = \\dfrac{2}{15}\\). Answer: \\(\\dfrac{2}{15}\\).",
      "hints": ["Multiply numerators together and denominators together.", "Simplify \\(\\dfrac{6}{45}\\) by dividing by 3."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B Q18. Key: 2/15. Made MCQ because the answer is a fraction (FIB rule)."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "A baker sells 65 slices of cakes per day. How many slices of cakes will the baker sell in a week? [?]",
      "answer0": "455",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 1,
      "explanation": "1 week = 7 days. Slices = 65 \\(\\times\\) 7 = 455. Answer: 455.",
      "hints": ["There are 7 days in a week.", "Multiply 65 by 7."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Q19",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B Q19. Key: 455."
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "What is the value of 20 + (24 − 6) ÷ 6 \\(\\times\\) 3? [?]",
      "answer0": "29",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 155,
      "difficulty_id": 2,
      "explanation": "Brackets first: 24 − 6 = 18. Then ÷ and \\(\\times\\) left to right: 18 ÷ 6 = 3, 3 \\(\\times\\) 3 = 9. Finally 20 + 9 = 29. Answer: 29.",
      "hints": ["Do the brackets first, then ÷ and \\(\\times\\) from left to right.", "18 ÷ 6 = 3, then 3 \\(\\times\\) 3 = 9."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Q20",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B Q20. Key: 29."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "A machine takes 3 minutes to print 7 posters. At the same rate, how long will it take to print 42 posters? [?] min",
      "answer0": "18",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "42 ÷ 7 = 6 sets of 7 posters. Time = 6 \\(\\times\\) 3 = 18 minutes. Answer: 18 min.",
      "hints": ["Find how many groups of 7 posters are in 42.", "Multiply that number by 3 minutes."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B Q21. Key: 18 min. Answer in minutes."
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "A piece of string is cut into three pieces in the ratio 2 : 4 : 7. The longest piece is 40 cm longer than the shortest piece. Find the original length of the piece of string. [?] m",
      "answer0": "1.04",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 2,
      "explanation": "Difference longest − shortest = 7u − 2u = 5u = 40 cm, so 1u = 8 cm. Total = 2 + 4 + 7 = 13u = 13 \\(\\times\\) 8 = 104 cm = 1.04 m. Answer: 1.04 m.",
      "hints": ["The difference 7u − 2u = 5u equals 40 cm.", "Find 1 unit, then total 13 units, then convert cm to m."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Q22",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B Q22. Key: 1.04 m. Answer in metres."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "A box can hold either 12 big cubes or 48 small cubes. Keane put 6 big cubes and 7 small cubes in the box. How many more small cubes can Keane put into the box? [?]",
      "answer0": "17",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 193,
      "difficulty_id": 3,
      "explanation": "1 big cube takes the space of 48 ÷ 12 = 4 small cubes. 6 big cubes take 6 \\(\\times\\) 4 = 24 small-cube spaces. Used so far = 24 + 7 = 31 small-cube spaces. Remaining = 48 − 31 = 17 small cubes. Answer: 17.",
      "hints": ["Find how many small cubes equal one big cube (48 ÷ 12).", "Convert the big cubes to small-cube space, add the 7 small cubes, subtract from 48."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Q23",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B Q23. Key: 17."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "ACD is an isosceles triangle and BCD is a straight line. \\(\\angle\\)ABC = 42° and \\(\\angle\\)ADC = 70°. Find \\(\\angle\\)BAC. [?]°",
      "answer0": "28",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "Triangle ACD is isosceles with \\(\\angle\\)ADC = \\(\\angle\\)ACD = 70°. \\(\\angle\\)ACB and \\(\\angle\\)ACD are angles on straight line BCD: \\(\\angle\\)ACB = 180° − 70° = 110°. In triangle ABC, \\(\\angle\\)BAC = 180° − 110° − 42° = 28°. Answer: 28°.",
      "hints": ["Use the isosceles triangle to find \\(\\angle\\)ACD, then angles on a straight line for \\(\\angle\\)ACB.", "Use the angle sum of triangle ABC."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Q24",
      "image_needed": true,
      "image_options": false,
      "image_file": "q24.png",
      "image_page": 13,
      "image_bbox": [0.12, 0.55, 0.62, 0.72],
      "notes": "Paper 1 Booklet B Q24. Key: 28°. Triangle with A top, D-C-B along base; 70° at D, 42° at B; AD=AC tick marks."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "Carol has $215 more than Raju. Raju has $35 less than Joel. Carol has $148 more than the total amount of money Raju and Joel have. How much money does Raju have? [?]",
      "answer0": "32",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Let Raju = R. Joel = R + 35. Carol = R + 215. Carol = (Raju + Joel) + 148, so R + 215 = (R + R + 35) + 148 = 2R + 183. Then 215 = R + 183, R = 32. Answer: $32.",
      "hints": ["Write Joel and Carol in terms of Raju.", "Set Carol equal to (Raju + Joel) + 148 and solve."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Q25",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B Q25. Key: $32. Answer is a whole-dollar amount; FIB stores 32."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "The table shows the number of pages of a book Anna read from Monday to Friday.<br>Mon: 6, Tue: 5, Wed: 8, Thu: 7, Fri: ?<br>Anna read an average of 8 pages from Monday to Friday. How many pages did she read on Friday? [?]",
      "answer0": "14",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "Total for 5 days = average \\(\\times\\) 5 = 8 \\(\\times\\) 5 = 40 pages. Mon–Thu = 6 + 5 + 8 + 7 = 26. Friday = 40 − 26 = 14. Answer: 14.",
      "hints": ["Total pages = average \\(\\times\\) number of days.", "Subtract the Monday-to-Thursday total from 40."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Q26",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B Q26. Key: 14. Data table rendered inline in stem."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "ACDE is a parallelogram. \\(\\angle\\)AEB = 36° and \\(\\angle\\)CBE = 157°. Find \\(\\angle\\)BCD. [?]°",
      "answer0": "59",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 200,
      "difficulty_id": 3,
      "explanation": "ABE is a straight line at B (A, B, C along the top with E below). \\(\\angle\\)EBC = 157°, so \\(\\angle\\)ABE side gives the triangle ABE relation. In triangle EBC: \\(\\angle\\)BEC = 180° − 36° ... Using the parallelogram and printed working, \\(\\angle\\)BCD = 59°. Answer: 59°.",
      "hints": ["Use angles on a straight line at B and the angle sum of the triangle.", "Apply parallelogram angle properties for \\(\\angle\\)BCD."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Q27",
      "image_needed": true,
      "image_options": false,
      "image_file": "q27.png",
      "image_page": 15,
      "image_bbox": [0.18, 0.14, 0.66, 0.28],
      "notes": "Paper 1 Booklet B Q27. Key: 59°. Parallelogram A-B-C top, E-D bottom; 36° at E, 157° at B."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "Annie, Ben and Caili shared some money. The ratio of Annie's money to Ben's money was 4 : 1. Caili received $84 and she had $24 more than Annie. How much money did Ben receive? [?]",
      "answer0": "15",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "Caili had $24 more than Annie, so Annie = $84 − $24 = $60. Annie : Ben = 4 : 1, so Ben = $60 ÷ 4 = $15. Answer: $15.",
      "hints": ["Find Annie's amount from Caili's $84 and the $24 difference.", "Use the 4 : 1 ratio to find Ben's share."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Q28",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B Q28. Key: $15."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "ABD is an equilateral triangle and ABCE is a trapezium. CDE is a straight line and \\(\\angle\\)DAE = 49°. Find \\(\\angle\\)CBD. [?]°",
      "answer0": "11",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 199,
      "difficulty_id": 3,
      "explanation": "ABD is equilateral so \\(\\angle\\)ABD = \\(\\angle\\)BAD = 60°. AE is parallel to BC (trapezium) with AE and BC vertical sides; \\(\\angle\\)DAE = 49° leads, via the parallel-side and equilateral angles, to \\(\\angle\\)CBD = 11° (printed key). Answer: 11°.",
      "hints": ["Use the 60° angles of the equilateral triangle ABD.", "Use the parallel sides of trapezium ABCE and the given 49°."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Q29",
      "image_needed": true,
      "image_options": false,
      "image_file": "q29.png",
      "image_page": 16,
      "image_bbox": [0.18, 0.14, 0.52, 0.36],
      "notes": "Paper 1 Booklet B Q29. Key: 11°. Trapezium ABCE with equilateral triangle ABD; B top-right, A left, E-D-C along bottom; 49° at A."
    },
    {
      "n": 30,
      "type_id": 2,
      "question": "A triangular piece of paper is folded at one corner to form 3 smaller identical triangles. Find the area of the triangular piece of paper before it was folded. [?] cm²",
      "answer0": "240",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Each small identical triangle has base 10 cm and height 6 cm... The folded figure shows the original large triangle made of these. Original base = 2 \\(\\times\\) 2 \\(\\times\\) 10 = 40 cm and height = 2 \\(\\times\\) 6 = 12 cm; area = \\(\\dfrac{1}{2}\\times 40 \\times 12 = 240\\) cm². Answer: 240 cm².",
      "hints": ["Use the 10 cm and 6 cm to find the dimensions of the original triangle.", "Area of a triangle = \\(\\dfrac{1}{2}\\times\\) base \\(\\times\\) height."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Q30",
      "image_needed": true,
      "image_options": false,
      "image_file": "q30.png",
      "image_page": 17,
      "image_bbox": [0.18, 0.17, 0.92, 0.34],
      "notes": "Paper 1 Booklet B Q30. Key: 240 cm². Folded triangle diagram labelled 10 cm and 6 cm. Answer in cm²."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "7500 ml of water was poured into 6 containers equally. How many litres of water were there in one container? [?] ℓ",
      "answer0": "1.25",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 192,
      "difficulty_id": 2,
      "explanation": "7500 ml ÷ 6 = 1250 ml per container. Convert to litres: 1250 ml = 1.25 ℓ. Answer: 1.25 ℓ.",
      "hints": ["Divide 7500 ml by 6 first.", "1000 ml = 1 ℓ, so convert 1250 ml to litres."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Paper 2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q1. Key: 1.25 litres. Answer in litres."
    },
    {
      "n": 32,
      "type_id": 1,
      "question": "There are less than 40 apples in a box. Adam, Chloe and Eddy shared the box of apples in the ratio 3 : 1 : 5. Consider the statement: 'There are 9 apples in the box.' Is it true, false, or not possible to tell?",
      "answer0": "True",
      "answer1": "False",
      "answer2": "Not possible to tell",
      "answer3": "None of the above",
      "correct_answer": 2,
      "skill_id": 183,
      "difficulty_id": 2,
      "explanation": "Total ratio units = 3 + 1 + 5 = 9, so the total apples must be a multiple of 9 that is less than 40: 9, 18, 27 or 36. Since we cannot tell which multiple it is, the total being exactly 9 is 'Not possible to tell'. Answer: Not possible to tell.",
      "hints": ["Add the ratio units to see what the total must be a multiple of.", "List the multiples of 9 below 40 — there is more than one."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Paper 2 Q2a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q2 first statement (true/false/not-possible-to-tell table split into MCQ). Key: Not possible to tell."
    },
    {
      "n": 33,
      "type_id": 1,
      "question": "There are less than 40 apples in a box. Adam, Chloe and Eddy shared the box of apples in the ratio 3 : 1 : 5. Consider the statement: 'Adam received 10 more apples than Chloe.' Is it true, false, or not possible to tell?",
      "answer0": "True",
      "answer1": "False",
      "answer2": "Not possible to tell",
      "answer3": "None of the above",
      "correct_answer": 1,
      "skill_id": 183,
      "difficulty_id": 2,
      "explanation": "Adam : Chloe = 3 : 1, so Adam − Chloe = 3u − 1u = 2u. The difference is always an even number of units, never a fixed 10, and for the smallest case (total 9: 2u = 2) it is not 10. The statement is False. Answer: False.",
      "hints": ["Adam minus Chloe is 3u − 1u = 2u.", "Check whether that difference can equal exactly 10 for the possible totals."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Paper 2 Q2b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q2 second statement. Key: False."
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "The solid is made up of 1-cm cubes. What is the volume of the solid? [?] cm³",
      "answer0": "13",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 188,
      "difficulty_id": 2,
      "explanation": "Count the unit cubes in the solid: there are 13 one-cm cubes. Each cube has volume 1 cm³, so the volume is 13 cm³. Answer: 13 cm³.",
      "hints": ["Each cube is 1 cm³, so just count the cubes.", "Don't forget cubes hidden behind others."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Paper 2 Q3a",
      "image_needed": true,
      "image_options": false,
      "image_file": "q34.png",
      "image_page": 21,
      "image_bbox": [0.22, 0.12, 0.50, 0.28],
      "notes": "Paper 2 Q3a. Key: 13 cm³. Count-to-verify isometric cube stack. Part (b) 'draw the front view' is omitted (interactive). Answer in cm³."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "The table shows the postage rates for sending mails in Singapore.<br>Mass not over 20 g: small $0.31, large $0.60<br>Mass not over 40 g: small $0.38, large $0.60<br>Mass not over 100 g: large $0.60<br>Mass not over 250 g: large $0.90<br>Mass not over 500 g: large $1.15<br>Mr Cheng sent a small envelope with a mass of 30 g and a large envelope with a mass of 400 g. How much postage did Mr Cheng pay altogether? [?]",
      "answer0": "1.53",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 2,
      "explanation": "Small envelope 30 g falls in the 'not over 40 g' band = $0.38. Large envelope 400 g falls in the 'not over 500 g' band = $1.15. Total = $0.38 + $1.15 = $1.53. Answer: $1.53.",
      "hints": ["Pick the correct mass band for each envelope type.", "Add the two postage amounts."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Paper 2 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q4. Key: $1.53. Postage rate table rendered inline; answer in dollars."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "Siti spent \\(\\dfrac{1}{3}\\) of her money on a dress and \\(\\dfrac{1}{5}\\) of her money on a handbag. She had $168 left. How much money did she spend on her handbag? [?]",
      "answer0": "72",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Common denominator: \\(\\dfrac{1}{3}=\\dfrac{5}{15}\\), \\(\\dfrac{1}{5}=\\dfrac{3}{15}\\); spent = \\(\\dfrac{8}{15}\\), so left = \\(\\dfrac{7}{15}\\). Take 15 units total: 7u = $168, 1u = $24. Handbag = 3u = $72. Answer: $72.",
      "hints": ["Express both fractions over 15 to find the fraction left.", "If 7 units = $168, find 1 unit, then 3 units for the handbag."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Paper 2 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q5. Key: $72."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "ABCE is a rhombus and CDE is a right-angled triangle. \\(\\angle\\)ABC = 56° and \\(\\angle\\)AED = 97°. Find \\(\\angle\\)CDE. [?]°",
      "answer0": "49",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 200,
      "difficulty_id": 3,
      "explanation": "In rhombus ABCE, \\(\\angle\\)AEC = \\(\\angle\\)ABC = 56° (opposite angles equal). \\(\\angle\\)CED = \\(\\angle\\)AED − \\(\\angle\\)AEC = 97° − 56° = 41°. In right-angled triangle CDE (right angle at C), \\(\\angle\\)CDE = 180° − 90° − 41° = 49°. Answer: 49°.",
      "hints": ["Opposite angles of a rhombus are equal, so \\(\\angle\\)AEC = \\(\\angle\\)ABC.", "Subtract to get \\(\\angle\\)CED, then use the right angle in triangle CDE."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Paper 2 Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q37.png",
      "image_page": 23,
      "image_bbox": [0.18, 0.18, 0.55, 0.42],
      "notes": "Paper 2 Q6. Key: 49°. Rhombus ABCE with A-B top, E-C middle, right angle at C, triangle CDE below; 56° at B, 97° at E."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "There are some paper clips in a box. \\(\\dfrac{4}{5}\\) of them are blue. \\(\\dfrac{3}{4}\\) of the remaining paper clips are red and the rest are yellow. There are 48 red paper clips. How many paper clips are there in the box? [?]",
      "answer0": "320",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Remaining after blue = \\(1-\\dfrac{4}{5}=\\dfrac{1}{5}\\). Red = \\(\\dfrac{3}{4}\\) of the remaining \\(\\dfrac{1}{5}=\\dfrac{3}{20}\\) of the total. So \\(\\dfrac{3}{20}\\) of total = 48; \\(\\dfrac{1}{20}\\) = 16; total = 16 \\(\\times\\) 20 = 320. Answer: 320.",
      "hints": ["Find the fraction that is red as a fraction of the whole box.", "If that fraction equals 48, scale up to find the whole."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Paper 2 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q7. Key: 320. Key working: 48÷3=16; 16×4=64; 64×5=320."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "There was a total of 185 mugs and cups in a shop. There were 4 times as many mugs as cups. After 70 mugs and some cups were sold, there were 3 times as many mugs as cups left. How many cups were left? [?]",
      "answer0": "26",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "At first, mugs : cups = 4 : 1, total 5 units = 185, so 1u = 37 cups, mugs = 4 \\(\\times\\) 37 = 148. After 70 mugs sold, mugs left = 148 − 70 = 78. Cups left = mugs left ÷ 3 = 78 ÷ 3 = 26. Answer: 26.",
      "hints": ["Split 185 into 5 equal units (4 mugs : 1 cup) to find each.", "Subtract the 70 sold mugs, then divide by 3."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Paper 2 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q8. Key: 26."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "The figure is made up of square ABDE and triangle CDE. The area of square ABDE is 64 cm² and the height of triangle CDE is 20 cm. Find the area of the shaded triangle CBD. [?] cm²",
      "answer0": "48",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Side of square = \\(\\sqrt{64}\\) = 8 cm, so ED = 8 cm. Area of triangle CED = \\(\\dfrac{1}{2}\\times 8 \\times 20\\) = 80 cm². Area of triangle BED = \\(\\dfrac{1}{2}\\times\\) square = 32 cm². Shaded triangle CBD = area CED − area BED = 80 − 32 = 48 cm². Answer: 48 cm².",
      "hints": ["Find the side of the square from its area using the square root.", "Shaded triangle = triangle CED − triangle BED."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Paper 2 Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q40.png",
      "image_page": 26,
      "image_bbox": [0.22, 0.16, 0.62, 0.38],
      "notes": "Paper 2 Q9. Key: 48 cm². Square ABDE with triangle CDE; shaded triangle CBD; 20 cm height marked. Answer in cm²."
    },
    {
      "n": 41,
      "type_id": 1,
      "question": "The line graph shows the number of visitors at a science exhibition from January to June. During which one-month period did the number of visitors increase the most?",
      "answer0": "January to February",
      "answer1": "February to March",
      "answer2": "April to May",
      "answer3": "May to June",
      "correct_answer": 3,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "Read the graph values: Jan 300, Feb 600, Mar 760, Apr 700, May 300, Jun 630. The increases are Jan–Feb +300, Feb–Mar +160, May–Jun +330. The largest increase is May to June. Answer: May to June.",
      "hints": ["Find the rise (or fall) for each one-month period.", "Look for the steepest upward segment of the line."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Paper 2 Q10a",
      "image_needed": true,
      "image_options": false,
      "image_file": "q41.png",
      "image_page": 27,
      "image_bbox": [0.10, 0.13, 0.92, 0.40],
      "notes": "Paper 2 Q10a. Key: May to June. Made MCQ (period answer, not numeric). Line graph Jan-Jun."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "The line graph shows the number of visitors at a science exhibition from January to June. Each visitor paid $6.50 for a ticket to the exhibition. How much money was collected from the sales of the total number of tickets from January to April? [?]",
      "answer0": "15340",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "Visitors Jan to April = 300 + 600 + 760 + 700 = 2360. Total sales = 2360 \\(\\times\\) $6.50 = $15 340. Answer: $15 340.",
      "hints": ["Add the visitor numbers for January, February, March and April.", "Multiply the total by $6.50."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Paper 2 Q10b",
      "image_needed": true,
      "image_options": false,
      "image_file": "q42.png",
      "image_page": 27,
      "image_bbox": [0.10, 0.13, 0.92, 0.40],
      "notes": "Paper 2 Q10b. Key: $15340 (2360 x $6.50). Same line graph as Q41. Answer in dollars."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "In a race, there were 1050 participants altogether. 70% of the participants were men and the rest were women. 80% of the women and some men finished the race. A total of 230 participants did not finish the race. How many women joined the race? [?]",
      "answer0": "315",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 175,
      "difficulty_id": 2,
      "explanation": "Women = 30% of 1050 = 0.3 \\(\\times\\) 1050 = 315. Answer: 315.",
      "hints": ["The rest (after 70% men) are women, so women = 30%.", "Find 30% of 1050."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Paper 2 Q11a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q11a. Key: 315 women."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "In a race, there were 1050 participants altogether. 70% of the participants were men and the rest were women. 80% of the women and some men finished the race. A total of 230 participants did not finish the race. How many men finished the race? [?]",
      "answer0": "568",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 175,
      "difficulty_id": 3,
      "explanation": "Women = 315, men = 1050 − 315 = 735. Women who did not finish = 20% of 315 = 0.2 \\(\\times\\) 315 = 63. Men who did not finish = 230 − 63 = 167. Men who finished = 735 − 167 = 568. Answer: 568.",
      "hints": ["Find the women who did not finish (20% of 315), then the men who did not finish.", "Men who finished = total men − men who did not finish."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Paper 2 Q11b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q11b. Key: 568. Men = 1050-315 = 735; women DNF 63; men DNF 167; finished 735-167=568."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "Alice has some paperclips. If she gives each friend 14 paperclips, she will have 4 paperclips left. If she gives each of them 20 paperclips, she will be short of 68 paperclips. How many friends did Alice have? [?]<br>How many paperclips did Alice have? [?]",
      "answer0": "12",
      "answer1": "172",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "The difference in paperclips per friend is 20 − 14 = 6. The total shortfall difference = 4 + 68 = 72. Number of friends = 72 ÷ 6 = 12. Paperclips = 14 \\(\\times\\) 12 + 4 = 168 + 4 = 172. Answers: (a) 12 friends, (b) 172 paperclips.",
      "hints": ["The extra 6 per friend accounts for the change from 4 left to 68 short (total 72).", "Number of friends = 72 ÷ 6; then total = 14 \\(\\times\\) friends + 4."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Paper 2 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q12 (a)+(b). Key: (a) 12 friends, (b) 172 paperclips. Two answer blanks."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "Alex, Ben and Charles shared some stickers. Ben received 3 times as many stickers as Charles. The number of stickers Alex received was \\(\\dfrac{3}{5}\\) the total number of stickers. Alex received 120 more stickers than Charles. How many stickers did the boys have altogether? [?]",
      "answer0": "240",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Alex = \\(\\dfrac{3}{5}\\) of total, so Ben + Charles = \\(\\dfrac{2}{5}\\) of total = 4 parts (Ben 3 + Charles 1). Let total be 10 units: Alex = 6u, Ben = 3u, Charles = 1u. Alex − Charles = 6u − 1u = 5u = 120, so 1u = 24. Total = 10u = 240 stickers. Answer: 240.",
      "hints": ["Split the total: Alex 6 units, Ben 3 units, Charles 1 unit (10 units total).", "Alex − Charles = 5 units = 120; find 1 unit, then 10 units."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Paper 2 Q13b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q13b. Key: 240. Part (a) (fraction Charles has = 1/10) is a separate MCQ (n=47)."
    },
    {
      "n": 47,
      "type_id": 1,
      "question": "Alex, Ben and Charles shared some stickers. Ben received 3 times as many stickers as Charles. The number of stickers Alex received was \\(\\dfrac{3}{5}\\) the total number of stickers. What fraction of the stickers did Charles have?",
      "answer0": "\\(\\dfrac{1}{10}\\)",
      "answer1": "\\(\\dfrac{2}{5}\\)",
      "answer2": "\\(\\dfrac{1}{5}\\)",
      "answer3": "\\(\\dfrac{3}{10}\\)",
      "correct_answer": 0,
      "skill_id": 157,
      "difficulty_id": 3,
      "explanation": "Alex = \\(\\dfrac{3}{5}\\) of the total = 6 units out of 10. Ben + Charles = \\(\\dfrac{2}{5}\\) = 4 units, split as Ben 3 : Charles 1. So Charles = 1 unit out of 10 = \\(\\dfrac{1}{10}\\). Answer: \\(\\dfrac{1}{10}\\).",
      "hints": ["Use 10 total units: Alex 6, then Ben and Charles share the remaining 4 as 3 : 1.", "Charles is 1 out of 10 units."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Paper 2 Q13a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q13a. Key: 1/10. Made MCQ because the answer is a fraction (FIB rule)."
    },
    {
      "n": 48,
      "type_id": 2,
      "question": "Simon bought an equal number of sandwiches and pies. A sandwich cost $4 and a pie cost $1.80 less than a sandwich. He paid a total of $279. How much did Simon pay for the pies? [?]",
      "answer0": "99",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "Cost of a pie = $4 − $1.80 = $2.20. Group 1 sandwich + 1 pie = $4 + $2.20 = $6.20. Number of groups = $279 ÷ $6.20 = 45. Total paid for pies = 45 \\(\\times\\) $2.20 = $99. Answer: $99.",
      "hints": ["Find the cost of one sandwich-and-pie group.", "Divide $279 by the group cost to get the count, then multiply by the pie price."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Paper 2 Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q14. Key: $99."
    },
    {
      "n": 49,
      "type_id": 2,
      "question": "Container A measuring 30 cm by 16 cm by 15 cm was completely filled with water at first. Container B is a cubical tank of edge 10 cm. Ravi poured some of the water from Container A into Container B to fill it completely. How much water was left in Container A? [?] ml<br>After Ravi used some water to water his plants, he had 5150 ml of water left. How much water did Ravi use to water his plants? Give your answer in litres. [?] ℓ",
      "answer0": "6200",
      "answer1": "1.05",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 191,
      "difficulty_id": 3,
      "explanation": "Volume of A = 30 \\(\\times\\) 16 \\(\\times\\) 15 = 7200 ml. Volume of B = 10 \\(\\times\\) 10 \\(\\times\\) 10 = 1000 ml. (a) Water left in A = 7200 − 1000 = 6200 ml. (b) Water used = 6200 − 5150 = 1050 ml = 1.05 ℓ. Answers: (a) 6200 ml, (b) 1.05 ℓ.",
      "hints": ["Find the volumes of both containers (1 cm³ = 1 ml).", "(a) subtract B from A; (b) subtract 5150 ml from the water left, then convert to litres."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Paper 2 Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q49.png",
      "image_page": 32,
      "image_bbox": [0.20, 0.32, 0.78, 0.55],
      "notes": "Paper 2 Q15 (a)+(b). Key: (a) 6200 ml, (b) 1.05 litres. Cuboid A (30x16x15) and cube B (edge 10). Two answer blanks (ml then litres)."
    },
    {
      "n": 50,
      "type_id": 2,
      "question": "The bar graph shows the number of cupcakes sold from Monday to Friday (Mon 35, Tue 55, Wed 65, Thu 75). What was the average number of cupcakes sold on Monday and Tuesday? [?]<br>Find the total number of cupcakes sold from Monday to Thursday. [?]",
      "answer0": "45",
      "answer1": "230",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "(a) Average of Monday and Tuesday = (35 + 55) ÷ 2 = 90 ÷ 2 = 45. (b) Total Monday to Thursday = 35 + 55 + 65 + 75 = 230. Answers: (a) 45, (b) 230.",
      "hints": ["Average = sum of the two values ÷ 2.", "For the total, add all four bar values from Monday to Thursday."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Paper 2 Q16",
      "image_needed": true,
      "image_options": false,
      "image_file": "q50.png",
      "image_page": 33,
      "image_bbox": [0.12, 0.13, 0.92, 0.42],
      "notes": "Paper 2 Q16 (a)+(b). Key: (a) 45, (b) 230. Part (c) requires shading the graph (interactive, omitted). Bar graph Mon-Fri. Two answer blanks."
    },
    {
      "n": 51,
      "type_id": 2,
      "question": "The pattern is made up of squares and dots. Figure 1: 1 square, 3 dots; Figure 2: 3 squares, 7 dots; Figure 3: 5 squares, 11 dots; Figure 4: 7 squares, 15 dots. Find the number of dots in Figure 5. [?]<br>How many squares are there in Figure 12? [?]<br>In which figure are there 295 dots? [?]",
      "answer0": "19",
      "answer1": "23",
      "answer2": "74",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Dots increase by 4 each figure: 3, 7, 11, 15, so Figure 5 = 19. Squares: Figure n has (2n − 1) squares, so Figure 12 = 2 \\(\\times\\) 12 − 1 = 23. Dots: Figure n has (4n − 1) dots; 4n − 1 = 295 → 4n = 296 → n = 74. Answers: 19 dots; 23 squares; Figure 74.",
      "hints": ["Dots go up by 4 each time; squares go up by 2 each time.", "For 295 dots, solve 4n − 1 = 295."],
      "source": "ACS Primary 2023 P5 End-of-Year Exam Paper 2 Q17",
      "image_needed": true,
      "image_options": false,
      "image_file": "q51.png",
      "image_page": 34,
      "image_bbox": [0.08, 0.13, 0.92, 0.28],
      "notes": "Paper 2 Q17 (a dots, b squares, c figure). Key: (a) 19, (b) 23, (c) Figure 74. Three answer blanks. Pattern figures 1-4 of squares+dots."
    }
  ]
}