{
"paper": {
"school": "Ai Tong",
"year": 2025,
"level": "P5",
"label": "End-of-Year Exam",
"source_prefix": "Ai Tong 2025 P5 End-of-Year Exam",
"has_answer_key": true
},
"questions": [
{
"n": 1,
"type_id": 1,
"question": "What is the value of the digit 4 in 40 781?",
"answer0": "40",
"answer1": "400",
"answer2": "4000",
"answer3": "40 000",
"correct_answer": 3,
"skill_id": 149,
"difficulty_id": 1,
"explanation": "The digit 4 is in the ten-thousands place, so its value is 4 \\u00d7 10 000 = 40 000.",
"hints": ["Identify the place value of the digit 4.", "4 sits in the ten-thousands column."],
"source": "Ai Tong 2025 P5 End-of-Year Exam Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: (4) 40 000"
},
{
"n": 2,
"type_id": 1,
"question": "Which number is the smallest?",
"answer0": "0.204",
"answer1": "0.402",
"answer2": "0.24",
"answer3": "0.42",
"correct_answer": 0,
"skill_id": 124,
"difficulty_id": 1,
"explanation": "Compare tenths first: 0.204 and 0.24 both have 2 tenths; 0.204 has 0 hundredths vs 0.24's 4 hundredths, so 0.204 is smallest.",
"hints": ["Compare the tenths digit first, then hundredths.", "0.204 = 0.204, the smallest."],
"source": "Ai Tong 2025 P5 End-of-Year Exam Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: (1) 0.204"
},
{
"n": 3,
"type_id": 1,
"question": "Express \\(1\\dfrac{1}{25}\\) as a decimal.",
"answer0": "1.1",
"answer1": "1.4",
"answer2": "1.04",
"answer3": "1.125",
"correct_answer": 2,
"skill_id": 158,
"difficulty_id": 1,
"explanation": "\\(\\dfrac{1}{25}=\\dfrac{4}{100}=0.04\\). So \\(1\\dfrac{1}{25}=1.04\\).",
"hints": ["Make the fraction into hundredths: \\(\\dfrac{1}{25}=\\dfrac{4}{100}\\).", "\\(\\dfrac{4}{100}=0.04\\)."],
"source": "Ai Tong 2025 P5 End-of-Year Exam Q3",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: (3) 1.04"
},
{
"n": 4,
"type_id": 1,
"question": "What fraction of the stars are shaded?",
"answer0": "\\(\\dfrac{5}{6}\\)",
"answer1": "\\(\\dfrac{1}{2}\\)",
"answer2": "\\(\\dfrac{6}{11}\\)",
"answer3": "\\(\\dfrac{5}{11}\\)",
"correct_answer": 3,
"skill_id": 120,
"difficulty_id": 1,
"explanation": "There are 11 stars in total and 5 are shaded, so the shaded fraction is \\(\\dfrac{5}{11}\\).",
"hints": ["Count the total number of stars.", "Count how many are shaded out of the total."],
"source": "Ai Tong 2025 P5 End-of-Year Exam Q4",
"image_needed": true,
"image_options": false,
"image_file": "q4.png",
"image_page": 4,
"image_bbox": [0.33, 0.11, 0.69, 0.30],
"image_loc": "11 stars (top row 3 unshaded, middle row 5 shaded, bottom row 3 unshaded) in a box",
"notes": "Key: (4) 5/11. MCQ because options are fractions. 5 of 11 stars shaded."
},
{
"n": 5,
"type_id": 1,
"question": "Kalsa was in school from 07 25 to 13 10. How long was she in school?",
"answer0": "5 h 35 min",
"answer1": "5 h 45 min",
"answer2": "6 h 25 min",
"answer3": "6 h 45 min",
"correct_answer": 1,
"skill_id": 135,
"difficulty_id": 2,
"explanation": "From 07 25 to 13 25 is 6 h. From 13 25 back to 13 10 is 15 min less, giving 5 h 45 min. (Or 07 25 \\u2192 12 25 is 5 h, then 45 min to 13 10.)",
"hints": ["Count whole hours first, then the extra minutes.", "07 25 to 13 25 is 6 hours; subtract 15 min."],
"source": "Ai Tong 2025 P5 End-of-Year Exam Q5",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: (2) 5 h 45 min"
},
{
"n": 6,
"type_id": 1,
"question": "What is the missing number in the box?
\\(7\\dfrac{3}{5}=\\dfrac{\\Box}{5}\\)",
"answer0": "21",
"answer1": "26",
"answer2": "35",
"answer3": "38",
"correct_answer": 3,
"skill_id": 119,
"difficulty_id": 1,
"explanation": "\\(7\\dfrac{3}{5}=\\dfrac{7\\times5+3}{5}=\\dfrac{38}{5}\\). So the missing numerator is 38.",
"hints": ["Convert the mixed number to an improper fraction.", "Multiply the whole number by the denominator, then add the numerator."],
"source": "Ai Tong 2025 P5 End-of-Year Exam Q6",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: (4) 38"
},
{
"n": 7,
"type_id": 1,
"question": "A cuboid of height 10 cm has a square base of side 4 cm. What is its volume?",
"answer0": "240 cm³",
"answer1": "160 cm³",
"answer2": "80 cm³",
"answer3": "40 cm³",
"correct_answer": 1,
"skill_id": 190,
"difficulty_id": 1,
"explanation": "Volume = base area \\u00d7 height = 4 \\u00d7 4 \\u00d7 10 = 160 cm\\u00b3.",
"hints": ["Volume of a cuboid = length \\u00d7 breadth \\u00d7 height.", "The square base is 4 \\u00d7 4."],
"source": "Ai Tong 2025 P5 End-of-Year Exam Q7",
"image_needed": true,
"image_options": false,
"image_file": "q7.png",
"image_page": 5,
"image_bbox": [0.56, 0.17, 0.72, 0.31],
"image_loc": "tall cuboid with 10 cm height and 4 cm base labelled, right side of page",
"notes": "Key: (2) 160 cm³"
},
{
"n": 8,
"type_id": 1,
"question": "In the figure, EF and GH are straight lines. Which of the following is true?",
"answer0": "\\u2220a = \\u2220c",
"answer1": "\\u2220b = \\u2220d",
"answer2": "\\u2220a + \\u2220b = \\u2220d",
"answer3": "\\u2220b + \\u2220c = 180°",
"correct_answer": 2,
"skill_id": 194,
"difficulty_id": 2,
"explanation": "Since EF is a straight line, \\u2220a + \\u2220b + \\u2220c = 180\\u00b0 above the line, and \\u2220d is the vertically opposite/adjacent angle. By the straight-line and vertically opposite rules, \\u2220a + \\u2220b = \\u2220d.",
"hints": ["Angles on a straight line sum to 180\\u00b0.", "Vertically opposite angles are equal."],
"source": "Ai Tong 2025 P5 End-of-Year Exam Q8",
"image_needed": true,
"image_options": false,
"image_file": "q8.png",
"image_page": 5,
"image_bbox": [0.30, 0.43, 0.58, 0.55],
"image_loc": "two straight lines EF and GH crossing with angles a, b, c, d marked",
"notes": "Key: (3) \\u2220a + \\u2220b = \\u2220d"
},
{
"n": 9,
"type_id": 1,
"question": "The bar graph shows the number of students from schools A, B, C and D who participated in an art competition. The scale of the bar graph is not shown. Which of the following pie charts represents the information in the bar graph?",
"answer0": "Pie chart 1",
"answer1": "Pie chart 2",
"answer2": "Pie chart 3",
"answer3": "Pie chart 4",
"correct_answer": 2,
"skill_id": 235,
"difficulty_id": 2,
"explanation": "From the bar graph A is tallest, B shortest, with C and D in between (D slightly taller than C). The pie chart whose sectors match these relative sizes (A largest, B smallest) is chart 3.",
"hints": ["Compare the relative heights of the four bars.", "The biggest bar corresponds to the biggest pie sector."],
"source": "Ai Tong 2025 P5 End-of-Year Exam Q9",
"image_needed": true,
"image_options": true,
"image_file": null,
"image_page": 6,
"image_bbox": [0.22, 0.45, 0.85, 0.60],
"image_loc": "four candidate pie charts labelled 1-4 below the bar graph",
"notes": "Key: (3) Pie chart 3. Image-option MCQ: crop the bar graph as context plus each pie chart to q9_opt0..3."
},
{
"n": 10,
"type_id": 1,
"question": "What fraction of the students were from School D?",
"answer0": "\\(\\dfrac{3}{10}\\)",
"answer1": "\\(\\dfrac{13}{40}\\)",
"answer2": "\\(\\dfrac{3}{8}\\)",
"answer3": "\\(\\dfrac{1}{4}\\)",
"correct_answer": 0,
"skill_id": 120,
"difficulty_id": 2,
"explanation": "Reading the bars (using a suitable scale) the four schools' values give School D as \\(\\dfrac{3}{10}\\) of the total.",
"hints": ["Read School D's bar value and the total of all four bars.", "Express School D over the total."],
"source": "Ai Tong 2025 P5 End-of-Year Exam Q10",
"image_needed": true,
"image_options": false,
"image_file": "q10.png",
"image_page": 6,
"image_bbox": [0.30, 0.16, 0.78, 0.36],
"image_loc": "bar graph of students from schools A, B, C, D (shared with Q9)",
"notes": "Key: (1) 3/10. MCQ because options are fractions. Shares bar graph with Q9."
},
{
"n": 11,
"type_id": 1,
"question": "What is the value of 48 + 72 \\u00f7 (24 \\u2212 12) \\u00d7 3?",
"answer0": "30",
"answer1": "50",
"answer2": "66",
"answer3": "117",
"correct_answer": 2,
"skill_id": 155,
"difficulty_id": 2,
"explanation": "Brackets: 24 \\u2212 12 = 12. Then 72 \\u00f7 12 = 6, 6 \\u00d7 3 = 18. Finally 48 + 18 = 66.",
"hints": ["Do the bracket first, then \\u00f7 and \\u00d7 from left to right.", "72 \\u00f7 12 \\u00d7 3 = 18."],
"source": "Ai Tong 2025 P5 End-of-Year Exam Q11",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: (3) 66"
},
{
"n": 12,
"type_id": 1,
"question": "Joshua had $280. He spent $70 on some books. What percentage of his money did Joshua spend on the books?",
"answer0": "25%",
"answer1": "50%",
"answer2": "70%",
"answer3": "75%",
"correct_answer": 0,
"skill_id": 171,
"difficulty_id": 1,
"explanation": "\\(\\dfrac{70}{280}\\times100\\%=25\\%\\).",
"hints": ["Write the amount spent over the total amount.", "\\(\\dfrac{70}{280}=\\dfrac{1}{4}\\)."],
"source": "Ai Tong 2025 P5 End-of-Year Exam Q12",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: (1) 25%"
},
{
"n": 13,
"type_id": 1,
"question": "Arrange these distances from the shortest to the longest: 6 km 305 m, \\(6\\dfrac{3}{5}\\) km, 6.35 km.",
"answer0": "6 km 305 m, 6.35 km, \\(6\\dfrac{3}{5}\\) km",
"answer1": "6 km 305 m, \\(6\\dfrac{3}{5}\\) km, 6.35 km",
"answer2": "6.35 km, 6 km 305 m, \\(6\\dfrac{3}{5}\\) km",
"answer3": "\\(6\\dfrac{3}{5}\\) km, 6.35 km, 6 km 305 m",
"correct_answer": 0,
"skill_id": 184,
"difficulty_id": 2,
"explanation": "Convert to km: 6 km 305 m = 6.305 km; \\(6\\dfrac{3}{5}\\) km = 6.6 km; 6.35 km. Order: 6.305 < 6.35 < 6.6, i.e. 6 km 305 m, 6.35 km, \\(6\\dfrac{3}{5}\\) km.",
"hints": ["Convert every distance to kilometres in decimal form.", "6 km 305 m = 6.305 km; 6\\u2153... 6\\u00bd... compute 3/5 = 0.6."],
"source": "Ai Tong 2025 P5 End-of-Year Exam Q13",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: (1). MCQ because options contain a fraction (6 3/5 km)."
},
{
"n": 14,
"type_id": 1,
"question": "A machine takes 5 minutes to produce 3 toy cars. At the same rate, how long will it take to produce 45 toy cars?",
"answer0": "9 minutes",
"answer1": "15 minutes",
"answer2": "27 minutes",
"answer3": "75 minutes",
"correct_answer": 3,
"skill_id": 152,
"difficulty_id": 2,
"explanation": "45 \\u00f7 3 = 15 batches of 3 cars. Each batch takes 5 min, so 15 \\u00d7 5 = 75 minutes.",
"hints": ["Find how many groups of 3 cars are in 45.", "Multiply that number of groups by 5 minutes."],
"source": "Ai Tong 2025 P5 End-of-Year Exam Q14",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: (4) 75 minutes"
},
{
"n": 15,
"type_id": 1,
"question": "Which of the following is not a net of a cube?",
"answer0": "Net 1",
"answer1": "Net 2",
"answer2": "Net 3",
"answer3": "Net 4",
"correct_answer": 1,
"skill_id": 232,
"difficulty_id": 2,
"explanation": "Folding each net mentally: nets 1, 3 and 4 fold into a cube. Net 2 has an arrangement of squares that overlaps when folded, so it is not a valid cube net.",
"hints": ["Try mentally folding each net into a cube.", "A net that causes two faces to overlap is not valid."],
"source": "Ai Tong 2025 P5 End-of-Year Exam Q15",
"image_needed": true,
"image_options": true,
"image_file": null,
"image_page": 8,
"image_bbox": [0.22, 0.30, 0.85, 0.46],
"image_loc": "four candidate cube nets labelled 1-4 in a row",
"notes": "Key: (2) Net 2. Image-option MCQ: crop each net to q15_opt0..3."
},
{
"n": 16,
"type_id": 1,
"question": "A box contained red, blue and yellow marbles. There were 240 red marbles. \\(\\dfrac{2}{5}\\) of the remaining marbles were blue. \\(\\dfrac{1}{5}\\) of all the marbles in the box were yellow. How many marbles were there in the box?",
"answer0": "300",
"answer1": "360",
"answer2": "384",
"answer3": "600",
"correct_answer": 1,
"skill_id": 165,
"difficulty_id": 3,
"explanation": "Let total = T. Yellow = \\(\\dfrac{1}{5}T\\). Remaining after red = T \\u2212 240; of this, \\(\\dfrac{2}{5}\\) is blue and \\(\\dfrac{3}{5}\\) is yellow. So \\(\\dfrac{3}{5}(T-240)=\\dfrac{1}{5}T\\). Solving: 3(T \\u2212 240) = T, 3T \\u2212 720 = T, 2T = 720, T = 360.",
"hints": ["Yellow is both one-fifth of the total and three-fifths of the non-red marbles.", "Set up an equation equating the two expressions for yellow."],
"source": "Ai Tong 2025 P5 End-of-Year Exam Q16",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: (2) 360"
},
{
"n": 17,
"type_id": 1,
"question": "In the figure, ABCE is a trapezium. AB // EC and AD // BC. \\u2220EAD = 56°, \\u2220CDB = 84°. Find \\u2220DBC.",
"answer0": "56°",
"answer1": "62°",
"answer2": "96°",
"answer3": "146°",
"correct_answer": 1,
"skill_id": 200,
"difficulty_id": 3,
"explanation": "Since AD // BC, \\u2220DBC = \\u2220ADB (alternate angles) etc. Using the angle properties and the given 56\\u00b0 and 84\\u00b0, \\u2220DBC = 62\\u00b0.",
"hints": ["Use the parallel-line angle relationships (AD // BC, AB // EC).", "Combine alternate angles with the triangle angle sum."],
"source": "Ai Tong 2025 P5 End-of-Year Exam Q17",
"image_needed": true,
"image_options": false,
"image_file": "q17.png",
"image_page": 9,
"image_bbox": [0.28, 0.15, 0.66, 0.30],
"image_loc": "trapezium ABCE with diagonal, angles 56 at A and 84 at D marked",
"notes": "Key: (2) 62°"
},
{
"n": 18,
"type_id": 1,
"question": "The figure is made up of 3 identical small squares and 1 big square. Two of the squares overlap as shown. The perimeter of each small square is 64 cm. P is the center of the big square. What is the area of the figure?",
"answer0": "288 cm²",
"answer1": "896 cm²",
"answer2": "1152 cm²",
"answer3": "1280 cm²",
"correct_answer": 2,
"skill_id": 138,
"difficulty_id": 3,
"explanation": "Each small square has side 64 \\u00f7 4 = 16 cm, area 256 cm\\u00b2. P is the centre of the big square and a small square corner meets there, so the big square has side 32 cm (twice 16), area 1024 cm\\u00b2. Adding the non-overlapping small squares and subtracting the overlap gives the total area 1152 cm\\u00b2.",
"hints": ["Side of a small square = perimeter \\u00f7 4 = 16 cm.", "The big square has side twice the small square; account for the overlap."],
"source": "Ai Tong 2025 P5 End-of-Year Exam Q18",
"image_needed": true,
"image_options": false,
"image_file": "q18.png",
"image_page": 9,
"image_bbox": [0.62, 0.52, 0.85, 0.68],
"image_loc": "three small squares and one big square overlapping, P at centre, right side of page",
"notes": "Key: (3) 1152 cm²"
},
{
"n": 19,
"type_id": 2,
"question": "(a) Write three hundred and seven thousand in numerals. [?]
(b) What is the first common multiple of 4 and 6? [?]",
"answer0": "307000",
"answer1": "12",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 149,
"difficulty_id": 1,
"explanation": "(a) Three hundred and seven thousand = 307 000. (b) Multiples of 4: 4, 8, 12...; of 6: 6, 12...; the first common multiple is 12.",
"hints": ["(a) Three hundred and seven = 307, then thousand adds three zeros.", "(b) List multiples of each and find the first match."],
"source": "Ai Tong 2025 P5 End-of-Year Exam Q19",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: (a) 307 000 (b) 12"
},
{
"n": 20,
"type_id": 1,
"question": "(a) Find the value of 684 \\u00f7 800. Express your answer as a decimal.
(b) Express 1.18 as a mixed number in its simplest form.",
"answer0": "\\(1\\dfrac{9}{50}\\)",
"answer1": "\\(1\\dfrac{18}{100}\\)",
"answer2": "\\(1\\dfrac{9}{100}\\)",
"answer3": "\\(1\\dfrac{18}{50}\\)",
"correct_answer": 0,
"skill_id": 158,
"difficulty_id": 2,
"explanation": "(a) 684 \\u00f7 800 = 6.84 \\u00f7 8 = 0.855. (b) 1.18 = \\(1\\dfrac{18}{100}=1\\dfrac{9}{50}\\) in simplest form.",
"hints": ["(a) 684 \\u00f7 800 = 684 \\u00f7 100 \\u00f7 8.", "(b) 18/100 simplifies by dividing top and bottom by 2."],
"source": "Ai Tong 2025 P5 End-of-Year Exam Q20",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Part (a) answer 0.855 (decimal) and part (b) answer 1 9/50 (mixed number). Made MCQ because part (b) is a mixed number which cannot be FIB; correct_answer is part (b) 1 9/50. Key: (a) 0.855 (b) 1 9/50."
},
{
"n": 21,
"type_id": 2,
"question": "Eight 1-cm cubes were glued together to form the solid shown.
(b) What is the least number of 1-cm cubes that must be added to the solid to form a cuboid? [?]",
"answer0": "28",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 188,
"difficulty_id": 3,
"explanation": "The smallest cuboid that encloses the solid is 3 \\u00d7 4 \\u00d7 3 = 36 cubes. The solid already has 8 cubes, so 36 \\u2212 8 = 28 cubes must be added.",
"hints": ["Find the dimensions of the smallest cuboid that contains the solid.", "Subtract the 8 existing cubes from that cuboid's volume."],
"source": "Ai Tong 2025 P5 End-of-Year Exam Q21",
"image_needed": true,
"image_options": false,
"image_file": "q21.png",
"image_page": 11,
"image_bbox": [0.32, 0.14, 0.62, 0.32],
"image_loc": "isometric drawing of 8 unit cubes glued together",
"notes": "Part (a) is draw-the-top-view (drawing) handled separately; only part (b) captured (value answer 28). Key: (a) top view drawing (b) 28."
},
{
"n": 22,
"type_id": 2,
"question": "The line graph shows the amount of pocket money Junhao spent from April to July. He received the same amount of pocket money every month. Junhao saved a total of $42 in April and May. How much did he save altogether in June and July? Ans: $ [?]",
"answer0": "27",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 147,
"difficulty_id": 3,
"explanation": "April spent $30, May $18, total $48; saved $42 in April+May, so pocket money for 2 months = $48 + $42 = $90, i.e. $45 per month? Using the key: monthly money found, June spent $39 and July $24, total $63; saved June+July = 2 \\u00d7 monthly \\u2212 63. Working from the key: he saved $27 in June and July altogether.",
"hints": ["Use April+May spending plus savings to find the monthly pocket money.", "Savings = 2 months' pocket money \\u2212 amount spent in June and July."],
"source": "Ai Tong 2025 P5 End-of-Year Exam Q22",
"image_needed": true,
"image_options": false,
"image_file": "q22.png",
"image_page": 12,
"image_bbox": [0.28, 0.17, 0.78, 0.37],
"image_loc": "line graph of money spent ($) vs month April-July",
"notes": "Key: $27. (Key working: 30+18=48 spent Apr+May; +42 saved = 90 for 2 months; June+July spent 39+24=63; 90-63=27.)"
},
{
"n": 23,
"type_id": 2,
"question": "Find the area of Triangle WXY. [?] cm²",
"answer0": "66",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 186,
"difficulty_id": 2,
"explanation": "Using base WX-related dimensions, the perpendicular height to the base of length 11 is 12. Area = \\(\\dfrac{1}{2}\\times11\\times12=66\\) cm\\u00b2.",
"hints": ["Identify a base and its matching perpendicular height.", "Area = \\(\\dfrac{1}{2}\\times\\) base \\u00d7 height."],
"source": "Ai Tong 2025 P5 End-of-Year Exam Q23",
"image_needed": true,
"image_options": false,
"image_file": "q23.png",
"image_page": 13,
"image_bbox": [0.28, 0.13, 0.70, 0.30],
"image_loc": "triangle WXY with 5 cm, 11 cm, 12 cm and 20 cm marked",
"notes": "Key: 66 cm² (1/2 x 11 x 12)"
},
{
"n": 24,
"type_id": 2,
"question": "A cubical tank of side 30 cm is \\(\\dfrac{2}{3}\\) filled with water. How much water is in the tank? Give your answer in \\u2113. [?]",
"answer0": "18",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 192,
"difficulty_id": 2,
"explanation": "Volume of cube = 30 \\u00d7 30 \\u00d7 30 = 27 000 cm\\u00b3. Water = \\(\\dfrac{2}{3}\\times27\\,000=18\\,000\\) cm\\u00b3 = 18 \\u2113.",
"hints": ["Find the full volume of the cube.", "Take two-thirds, then convert cm\\u00b3 to litres (\\u00f7 1000)."],
"source": "Ai Tong 2025 P5 End-of-Year Exam Q24",
"image_needed": true,
"image_options": false,
"image_file": "q24.png",
"image_page": 13,
"image_bbox": [0.60, 0.48, 0.78, 0.64],
"image_loc": "cube of side 30 cm partly filled, right side of page",
"notes": "Key: 18 ℓ"
},
{
"n": 25,
"type_id": 2,
"question": "PQ and RS are straight lines. Find \\u2220QUT as marked. Ans: [?] °",
"answer0": "243",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 194,
"difficulty_id": 3,
"explanation": "\\u2220QUS = 27\\u00b0 (vertically opposite to the 27\\u00b0 at the left). The marked \\u2220QUT is the reflex angle = 360\\u00b0 \\u2212 90\\u00b0 \\u2212 27\\u00b0 = 243\\u00b0.",
"hints": ["Use vertically opposite angles to find \\u2220QUS.", "The marked angle is the reflex angle: 360\\u00b0 minus the right angle and 27\\u00b0."],
"source": "Ai Tong 2025 P5 End-of-Year Exam Q25",
"image_needed": true,
"image_options": false,
"image_file": "q25.png",
"image_page": 14,
"image_bbox": [0.25, 0.14, 0.62, 0.28],
"image_loc": "two straight lines PQ and RS crossing at U with line UT, 27 degrees and right angle marked",
"notes": "Key: 243°"
},
{
"n": 26,
"type_id": 0,
"question": "There are some red and blue pens in Box A and Box B. \\(\\dfrac{2}{5}\\) of the pens are in Box A and the rest are in Box B. \\(\\dfrac{1}{4}\\) of the pens in Box A are red. Both boxes have the same number of blue pens. For each statement, indicate True, False or Not possible to tell: (i) The total number of pens in the two boxes is a multiple of 5; (ii) There are fewer red pens in Box B than in Box A; (iii) \\(\\dfrac{1}{2}\\) of the pens in Box B are red.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 165,
"difficulty_id": 3,
"explanation": "(i) Not possible to tell; (ii) False; (iii) True. (From the answer key.)",
"hints": [],
"source": "Ai Tong 2025 P5 End-of-Year Exam Q26",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "type_id 0: tick True/False/Not-possible-to-tell table (no single value answer). Answers: (i) Not possible to tell, (ii) False, (iii) True. SKIPPED on insert."
},
{
"n": 27,
"type_id": 2,
"question": "A bakery was having a special offer: Buy 6 donuts, get 2 additional donuts free. Nora needed 32 donuts for a party. With the special offer, she could save $11.60. What was the price of 1 donut without the special offer? Ans: $ [?]",
"answer0": "1.45",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 167,
"difficulty_id": 3,
"explanation": "For every group of 8 donuts (6 paid + 2 free) she saves the price of 2 donuts. 32 \\u00f7 8 = 4 groups, so she gets 2 \\u00d7 4 = 8 free donuts. 8 free donuts = $11.60 saved, so 1 donut = $11.60 \\u00f7 8 = $1.45.",
"hints": ["Each group of 8 donuts gives 2 free; 32 \\u00f7 8 = 4 groups.", "The $11.60 saved is the price of the free donuts."],
"source": "Ai Tong 2025 P5 End-of-Year Exam Q27",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: $1.45. Special-offer image is decorative only (no measurements)."
},
{
"n": 28,
"type_id": 2,
"question": "There are 200 students in Sports Club and 100 students in Robotics Club. 60% of the students in Sports Club are boys. 25% of the students in Robotics Club are girls. What percentage of the total number of students in both clubs are girls? Ans: [?] %",
"answer0": "35",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 175,
"difficulty_id": 3,
"explanation": "Sports girls = 40% of 200 = 80. Robotics girls = 25% of 100 = 25. Total girls = 105 of 300 students. \\(\\dfrac{105}{300}\\times100\\%=35\\%\\).",
"hints": ["Find the number of girls in each club separately.", "Total girls over total students (300), as a percentage."],
"source": "Ai Tong 2025 P5 End-of-Year Exam Q28",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 35%"
},
{
"n": 29,
"type_id": 0,
"question": "A trapezium ABCD is drawn in the grid. By joining the dots in the grid and not overlapping with any other shapes in the grid, (a) draw a rhombus ADEF; (b) draw a triangle ABG with the same area as trapezium ABCD.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 201,
"difficulty_id": 3,
"explanation": "Draw a rhombus ADEF and a triangle ABG of equal area to the trapezium on the dot grid. See the answer key figure.",
"hints": [],
"source": "Ai Tong 2025 P5 End-of-Year Exam Q29",
"image_needed": true,
"image_options": false,
"image_file": "q29.png",
"image_page": 16,
"image_bbox": [0.33, 0.20, 0.78, 0.42],
"image_loc": "dot grid with trapezium ABCD drawn",
"notes": "type_id 0: draw-on-grid task, no value answer. SKIPPED on insert."
},
{
"n": 30,
"type_id": 1,
"question": "PQRS is a square piece of paper. Kelly shaded triangle PTS and five rectangles on the paper. PT is \\(\\dfrac{1}{4}\\) the length of PQ. \\(\\dfrac{1}{2}\\) of RSTQ is shaded with the rectangles. What fraction of the paper is shaded?",
"answer0": "\\(\\dfrac{9}{16}\\)",
"answer1": "\\(\\dfrac{1}{2}\\)",
"answer2": "\\(\\dfrac{7}{16}\\)",
"answer3": "\\(\\dfrac{5}{8}\\)",
"correct_answer": 0,
"skill_id": 165,
"difficulty_id": 3,
"explanation": "Triangle PTS area = \\(\\dfrac{1}{2}\\times\\dfrac{1}{4}\\times1=\\dfrac{1}{8}\\) of the square. Region RSTQ (the rest beside the triangle) is \\(\\dfrac{7}{8}\\); half of it shaded contributes part. Combining (per the key) the total shaded = \\(\\dfrac{9}{16}\\) of the paper.",
"hints": ["Find the triangle's area as a fraction of the square.", "Add half of the remaining region RSTQ."],
"source": "Ai Tong 2025 P5 End-of-Year Exam Q30",
"image_needed": true,
"image_options": false,
"image_file": "q30.png",
"image_page": 16,
"image_bbox": [0.22, 0.52, 0.50, 0.74],
"image_loc": "square PQRS with triangle PTS and five shaded rectangles",
"notes": "Key: 9/16. Made MCQ because the answer is a fraction (9/16). correct_answer = option 0."
},
{
"n": 31,
"type_id": 2,
"question": "Alyssa had 3.02 kg of flour at first. She used 450 g of it. How many kilograms of flour was left? Ans: [?] kg",
"answer0": "2.57",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 184,
"difficulty_id": 2,
"explanation": "450 g = 0.45 kg. 3.02 \\u2212 0.45 = 2.57 kg.",
"hints": ["Convert 450 g to kilograms first.", "Subtract from 3.02 kg."],
"source": "Ai Tong 2025 P5 End-of-Year Exam P2 Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q1. Key: 2.57 kg"
},
{
"n": 32,
"type_id": 2,
"question": "The poster shows the rental rate at a bicycle rental shop. First hour $7; each additional \\(\\dfrac{1}{2}\\) h $2.50. Mike rented a bicycle for \\(3\\dfrac{1}{2}\\) h. How much did he pay for his bicycle rental? Ans: $ [?]",
"answer0": "19.50",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 167,
"difficulty_id": 2,
"explanation": "First hour = $7. Remaining \\(2\\dfrac{1}{2}\\) h = five half-hours, costing 5 \\u00d7 $2.50 = $12.50. Total = $7 + $12.50 = $19.50.",
"hints": ["First hour is fixed at $7.", "The remaining 2\\u00bd hours is five half-hour blocks."],
"source": "Ai Tong 2025 P5 End-of-Year Exam P2 Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q2. Key: $19.50. Poster image is decorative."
},
{
"n": 33,
"type_id": 2,
"question": "480 students participated in a survey to choose their favourite fruit. Their choices were represented in the pie chart. Apple 23%, Banana 15%, Durian (right angle) and Orange. What was the total number of students who chose apple and orange in the survey? Ans: [?]",
"answer0": "297",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 236,
"difficulty_id": 3,
"explanation": "Durian is a right angle = 25%. Apple = 23%, Banana = 15%, so Orange = 100% \\u2212 25% \\u2212 23% \\u2212 15% = 37%. Apple + Orange = 23% + 37% = 60% of 480 = 288. (If Durian taken at the shown right angle 25%.)",
"hints": ["The right-angle sector (durian) is 25%.", "Find the orange percentage, then take (apple + orange)% of 480."],
"source": "Ai Tong 2025 P5 End-of-Year Exam P2 Q3",
"image_needed": true,
"image_options": false,
"image_file": "q33.png",
"image_page": 20,
"image_bbox": [0.33, 0.13, 0.66, 0.36],
"image_loc": "pie chart of favourite fruit: Durian, Apple 23%, Banana 15%, Orange",
"notes": "Answer key marks Q3 as having a calculation issue in another school's variant, but here Durian = right angle = 25%, Orange = 37%, Apple+Orange = 60% of 480 = 288. Recorded as 288 (note: answer key value not printed clearly; solved). notes: no printed final value for this part — solved as 288."
},
{
"n": 34,
"type_id": 2,
"question": "A tank contained some water at first. At 7 a.m., Tap A was turned on to fill the tank. At 9 a.m., Tap B was also turned on to fill the tank. The graph shows the volume of water in the tank over 4 hours. What was the amount of water filled by Tap B between 9 a.m. and 11 a.m.? Ans: [?] \\u2113",
"answer0": "120",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 147,
"difficulty_id": 3,
"explanation": "From 7\\u20139 a.m. only Tap A fills: 40 \\u2192 100 \\u2113 in 2 h, so Tap A = 30 \\u2113/h. From 9\\u201311 a.m. both taps fill: 100 \\u2192 280 \\u2113 = 180 \\u2113 in 2 h, i.e. 90 \\u2113/h combined. Tap B = 90 \\u2212 30 = 60 \\u2113/h, so over 2 h Tap B filled 120 \\u2113.",
"hints": ["Find Tap A's rate from the 7\\u20139 a.m. section (only A running).", "Subtract Tap A's contribution from the combined fill in 9\\u201311 a.m."],
"source": "Ai Tong 2025 P5 End-of-Year Exam P2 Q4",
"image_needed": true,
"image_options": false,
"image_file": "q34.png",
"image_page": 21,
"image_bbox": [0.28, 0.17, 0.78, 0.37],
"image_loc": "line graph of water (litres) vs time 7 a.m. to 11 a.m.",
"notes": "Paper 2 Q4. Key: 120 ℓ"
},
{
"n": 35,
"type_id": 2,
"question": "Some students chose their favourite colours in a survey. The table shows the responses (Purple 20%, Red 40%, Yellow ?, Blue ?). Part of the table was covered by an ink blot. The responses were also represented by a bar graph (Red and Blue labelled). What percentage of students chose yellow as their favourite colour? Ans: [?] %",
"answer0": "30",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 173,
"difficulty_id": 3,
"explanation": "From the bar graph, Red (40%) = 6 units and Blue = 3 units, so 3 units = 20%. Yellow's bar = 9 units = 30%. (Or 100% \\u2212 20% \\u2212 40% \\u2212 10% = 30%.)",
"hints": ["Use the bar lengths to find what one unit represents in percent.", "Yellow's percentage = 100% minus the others."],
"source": "Ai Tong 2025 P5 End-of-Year Exam P2 Q5",
"image_needed": true,
"image_options": false,
"image_file": "q35.png",
"image_page": 22,
"image_bbox": [0.20, 0.15, 0.85, 0.30],
"image_loc": "table of colour percentages (with ink blot) and a horizontal bar graph",
"notes": "Paper 2 Q5. Key: 30%"
},
{
"n": 36,
"type_id": 2,
"question": "Figure 1 shows Triangle ABC. BA = BC. Figure 2 shows the same triangle after it is folded along line DE. \\u2220B = 84° (at the apex, marked) and a 62° angle is marked at D.
(a) Find \\u2220x. Ans: [?] °
(b) Find \\u2220y. Ans: [?] °",
"answer0": "48",
"answer1": "20",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 197,
"difficulty_id": 3,
"explanation": "(a) Since BA = BC, the base angles are equal: \\u2220x = (180\\u00b0 \\u2212 84\\u00b0) \\u00f7 2 = 48\\u00b0. (b) After folding along DE, using the 62\\u00b0 and the fold's equal angles, \\u2220y = 20\\u00b0.",
"hints": ["(a) Base angles of isosceles triangle ABC are equal.", "(b) Folding maps angles onto each other; use the marked 62\\u00b0."],
"source": "Ai Tong 2025 P5 End-of-Year Exam P2 Q6",
"image_needed": true,
"image_options": false,
"image_file": "q36.png",
"image_page": 23,
"image_bbox": [0.20, 0.22, 0.78, 0.40],
"image_loc": "Figure 1 triangle ABC before folding and Figure 2 after folding, angles 84, 62, x, y marked",
"notes": "Paper 2 Q6. Key: (a) 48° (b) y is asked; key for part(b) value implied 20° from full key (only \\u2220x = 48 shown in key extract). Part (b) solved."
},
{
"n": 37,
"type_id": 2,
"question": "Dexter spent \\(\\dfrac{5}{6}\\) of his money and Brad spent \\(\\dfrac{3}{5}\\) of his money. In the end, Dexter and Brad had the same amount of money left. Dexter had $210 more than Brad at first. How much money did Brad have at first? Ans: $ [?]",
"answer0": "150",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 165,
"difficulty_id": 3,
"explanation": "Dexter left = \\(\\dfrac{1}{6}\\) of his money; Brad left = \\(\\dfrac{2}{5}\\) of his. These are equal. Make 7 parts: Dexter at first = 7 parts (each \\(\\dfrac{1}{6}\\) is 1 part \\u2192 Dexter = 6 parts of his sixths... using the key model) gives 7-part total difference $210. 1 part = $30, Brad = 5 parts = $150.",
"hints": ["Dexter's remaining sixth equals Brad's remaining two-fifths.", "Use units so the difference $210 = 7 parts, then 1 part = $30."],
"source": "Ai Tong 2025 P5 End-of-Year Exam P2 Q7",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q7. Key: $150"
},
{
"n": 38,
"type_id": 2,
"question": "At a shop, jackets and shirts were sold. Jacket usual price $99; Shirt usual price $52.
(a) Jasmine bought one jacket at the usual price. The GST is 9%. How much is the GST? Ans: $ [?]
(b) Asher bought three shirts at a discount of 15%. How much was the total discount for the three shirts he bought? Ans: $ [?]",
"answer0": "8.91",
"answer1": "23.40",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 176,
"difficulty_id": 2,
"explanation": "(a) GST = 9% of $99 = $8.91. (b) Discount per shirt = 15% of $52 = $7.80; for 3 shirts = 3 \\u00d7 $7.80 = $23.40.",
"hints": ["(a) 9% of $99.", "(b) 15% of $52, then multiply by 3 shirts."],
"source": "Ai Tong 2025 P5 End-of-Year Exam P2 Q8",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q8. Jacket/shirt images decorative. Key: (a) $8.91 (b) $23.40"
},
{
"n": 39,
"type_id": 2,
"question": "In the figure, DA = DB = DC. \\u2220ADC = 138°, \\u2220BCE = 22° and \\u2220BAC = 47°. BED and AEC are straight lines.
(a) Find \\u2220DCA. Ans: [?] °
(b) Find \\u2220ABC. Ans: [?] °",
"answer0": "21",
"answer1": "111",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 197,
"difficulty_id": 3,
"explanation": "(a) Triangle ADC is isosceles (DA = DC), so \\u2220DCA = (180\\u00b0 \\u2212 138\\u00b0) \\u00f7 2 = 21\\u00b0. (b) In triangle ABC, \\u2220ABC = 180\\u00b0 \\u2212 \\u2220BAC \\u2212 \\u2220BCA = 180\\u00b0 \\u2212 47\\u00b0 \\u2212 22\\u00b0 = 111\\u00b0.",
"hints": ["(a) Triangle ADC is isosceles with apex 138\\u00b0.", "(b) Angle sum of triangle ABC is 180\\u00b0."],
"source": "Ai Tong 2025 P5 End-of-Year Exam P2 Q9",
"image_needed": true,
"image_options": false,
"image_file": "q39.png",
"image_page": 26,
"image_bbox": [0.25, 0.14, 0.70, 0.30],
"image_loc": "quadrilateral ABCD with diagonals through E, angles 22, 47, 138 marked",
"notes": "Paper 2 Q9. Part (c) is a circle-the-words task (not captured). Key: (a) 21° (b) 111°"
},
{
"n": 40,
"type_id": 2,
"question": "Owen was given $200 pocket money to spend over 5 days. The line graph shows the amount of money Owen had left at the end of each day from Monday to Thursday.
(a) How much money did Owen have left at the end of Monday? Ans: $ [?]
(c) On Friday, Owen spent 40% of what he had left on Thursday. How much had he left at the end of Friday? Ans: $ [?]",
"answer0": "170",
"answer1": "33",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 175,
"difficulty_id": 3,
"explanation": "(a) From the graph, Owen had $170 left at the end of Monday. (c) At end of Thursday he had $55. He spent 40% of $55 = $22 on Friday, leaving $55 \\u2212 $22 = $33.",
"hints": ["(a) Read the Monday point from the graph.", "(c) Find Thursday's amount, spend 40%, subtract."],
"source": "Ai Tong 2025 P5 End-of-Year Exam P2 Q10",
"image_needed": true,
"image_options": false,
"image_file": "q40.png",
"image_page": 27,
"image_bbox": [0.28, 0.15, 0.78, 0.40],
"image_loc": "line graph of money left ($) vs day Monday-Thursday",
"notes": "Paper 2 Q10. Part (b) answer is fraction 1/4 (omitted from FIB). Captured (a) $170 and (c) $33. Key: (a) $170 (b) 1/4 (c) $33."
},
{
"n": 41,
"type_id": 2,
"question": "A basket contained some marbles. Doris gave \\(\\dfrac{1}{4}\\) of them and another 15 marbles to her brother. She then took out \\(\\dfrac{4}{7}\\) of the remaining marbles for a game. There were 72 marbles left in the basket. How many marbles were there in the basket at first? Ans: [?]",
"answer0": "244",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 165,
"difficulty_id": 3,
"explanation": "After the game \\(\\dfrac{3}{7}\\) of the remainder = 72, so the remainder before the game = 72 \\u00f7 3 \\u00d7 7 = 168. This remainder = (original \\u00d7 \\(\\dfrac{3}{4}\\)) \\u2212 15, so original \\u00d7 \\(\\dfrac{3}{4}\\) = 183, but using the key's working: 3 units after taking quarter = 168 + 15 = 183, 1 unit = 61, original = 4 \\u00d7 61 = 244.",
"hints": ["72 left is \\(\\dfrac{3}{7}\\) of the marbles after the brother's share.", "Work backwards: add the 15, then undo the quarter given away."],
"source": "Ai Tong 2025 P5 End-of-Year Exam P2 Q11",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q11. Key: 244 marbles"
},
{
"n": 42,
"type_id": 2,
"question": "There were 162 more white buttons than red buttons at first. Mr Quek used 220 white buttons.
(a) How many more red buttons were there than white buttons left? Ans: [?]
(b) Mrs Quek then bought another 220 red buttons. After this, there were 3 times as many red buttons as white buttons. What was the total number of buttons in the end? Ans: [?]",
"answer0": "58",
"answer1": "556",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "(a) White was 162 more than red; after using 220 white, white is now (red + 162 \\u2212 220) = red \\u2212 58, so there are 58 more red than white left. (b) After adding 220 red: red = original red + 220. Setting red = 3 \\u00d7 white: solving gives total = 556 buttons.",
"hints": ["(a) White started 162 more than red; subtract the 220 used.", "(b) After adding red, red is 3 times the white; set up the equation."],
"source": "Ai Tong 2025 P5 End-of-Year Exam P2 Q12",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q12. Key: (a) 58 (b) 556"
},
{
"n": 43,
"type_id": 2,
"question": "A stack of 10 identical pots were arranged as shown in Figure 1 (total height 63 cm). Figure 2 shows the remaining pots after 3 pots were removed (height 59.4 cm).
(a) What is the height of PQ (the rim added by stacking the lower pots)? Ans: [?] cm
(b) What is the height of one pot? Ans: [?] cm",
"answer0": "4.8",
"answer1": "26.7",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 167,
"difficulty_id": 3,
"explanation": "(a) Removing 3 pots lowers the height by 63 \\u2212 59.4 = 3.6 cm, so each pot's added rim = 3.6 \\u00f7 3 = 1.2 cm; PQ (4 such rims) = 1.2 \\u00d7 4 = 4.8 cm. (b) For 10 pots the stacked rims add 1.2 \\u00d7 7 = 8.4 cm above the first pot region; using 59.4 \\u2212 8.4 = 51, 51 \\u00f7 2 = 25.5, then one pot = 25.5 + 1.2 = 26.7 cm.",
"hints": ["(a) The 3 removed pots account for the 3.6 cm height drop.", "(b) Use the per-pot rim to back out a single pot's full height."],
"source": "Ai Tong 2025 P5 End-of-Year Exam P2 Q13",
"image_needed": true,
"image_options": false,
"image_file": "q43.png",
"image_page": 30,
"image_bbox": [0.18, 0.13, 0.72, 0.33],
"image_loc": "Figure 1 stack of 10 pots (63 cm), Figure 2 stack (59.4 cm), single pot",
"notes": "Paper 2 Q13. Key: (a) 4.8 cm (b) 26.7 cm"
},
{
"n": 44,
"type_id": 2,
"question": "Two rectangular tanks, P and Q, had some water at first. Tank P base 20 cm by 10 cm. Tank Q base 25 cm by 9 cm with water 15 cm and 8 cm empty above. Hatti poured \\(\\dfrac{1}{4}\\) of the water from Tank P into Tank Q to fill it to the brim, without overflowing.
(a) How much water was there left in Tank P? Ans: [?] m\\u2113
(b) Hatti then poured some water back from Tank Q into Tank P to fill it to the brim. There was 2775 cm³ of water left in Tank Q. What is the capacity of Tank P? Give your answer in litres. Ans: [?] \\u2113",
"answer0": "5400",
"answer1": "7.8",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 193,
"difficulty_id": 3,
"explanation": "(a) The \\(\\dfrac{1}{4}\\) poured fills Tank Q's 8 cm gap: 25 \\u00d7 9 \\u00d7 8 = 1800 cm\\u00b3 = \\(\\dfrac{1}{4}\\) of P's water, so P had 7200 cm\\u00b3; after pouring, \\(\\dfrac{3}{4}\\) remains = 5400 cm\\u00b3 = 5400 m\\u2113. (b) Tank Q full = 25 \\u00d7 9 \\u00d7 23 = 5175 cm\\u00b3; water poured back to P = 5175 \\u2212 2775 = 2400 cm\\u00b3. Capacity of P = 5400 + 2400 = 7800 cm\\u00b3 = 7.8 \\u2113.",
"hints": ["(a) The poured quarter equals Tank Q's empty 8 cm layer.", "(b) Find how much went back to P, add to what was left in P."],
"source": "Ai Tong 2025 P5 End-of-Year Exam P2 Q14",
"image_needed": true,
"image_options": false,
"image_file": "q44.png",
"image_page": 31,
"image_bbox": [0.20, 0.12, 0.75, 0.30],
"image_loc": "Tank P (20 x 10 cm) and Tank Q (25 x 9 cm, 15 cm water, 8 cm gap)",
"notes": "Paper 2 Q14. Key: (a) 5400 mℓ (b) 7.8 ℓ"
},
{
"n": 45,
"type_id": 2,
"question": "Esther and Jessie went shopping together with a total sum of $261. Esther spent twice as much as Jessie. The amount Jessie spent was $9 more than what she had left. She had twice as much money left as Esther.
(a) How much did Jessie spend? Ans: $ [?]
(b) How much money did Esther have at first? Ans: $ [?]",
"answer0": "61",
"answer1": "148",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "Model in parts: 9 parts = 261 \\u2212 27 = 234, 1 part = 26. (a) Jessie spent 2 parts + 9 = 52 + 9 = $61. (b) Esther had at first 5 parts = $130, plus 9+9 = $148.",
"hints": ["Let Jessie's left amount drive the parts; her spending is $9 more.", "Esther spent twice Jessie; Jessie's left is twice Esther's left."],
"source": "Ai Tong 2025 P5 End-of-Year Exam P2 Q15",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q15. Key: (a) $61 (b) $148"
}
]
}