{
"paper": {
"school": "Anglo-Chinese School (Primary)",
"year": 2025,
"level": "P4",
"label": "End-of-Year Exam",
"source_prefix": "ACS 2025 P4 End-of-Year Exam",
"has_answer_key": true
},
"questions": [
{
"n": 1,
"type_id": 1,
"question": "Fifty-eight thousand and thirty-nine in numerals is ____________.",
"answer0": "58 390",
"answer1": "58 309",
"answer2": "58 039",
"answer3": "50 839",
"correct_answer": 2,
"skill_id": 106,
"difficulty_id": 1,
"explanation": "Fifty-eight thousand = 58 000; thirty-nine = 39. So 58 000 + 39 = 58 039.",
"hints": [
"Break it into 58 thousand + 39.",
"58 thousand is written 58 0 0 0, then place 39 in the tens and ones."
],
"source": "ACS 2025 P4 End-of-Year Exam Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 3 (1-based) = index 2."
},
{
"n": 2,
"type_id": 1,
"question": "Which number when rounded to the nearest hundred becomes 72 000?",
"answer0": "71 839",
"answer1": "71 952",
"answer2": "72 050",
"answer3": "72 499",
"correct_answer": 1,
"skill_id": 109,
"difficulty_id": 2,
"explanation": "Rounding to the nearest hundred gives 72 000 for any number from 71 950 to 72 049. 71 952 rounds to 72 000. (71 839 to 71 800; 72 050 to 72 100; 72 499 to 72 500.)",
"hints": [
"Look at the tens digit to decide rounding to the nearest hundred.",
"The number must be between 71 950 and 72 049."
],
"source": "ACS 2025 P4 End-of-Year Exam Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 2 (1-based) = index 1."
},
{
"n": 3,
"type_id": 1,
"question": "Express $$6\\frac{7}{20}$$ as a decimal.",
"answer0": "6.07",
"answer1": "6.35",
"answer2": "6.70",
"answer3": "6.72",
"correct_answer": 1,
"skill_id": 127,
"difficulty_id": 2,
"explanation": "$$\\frac{7}{20}=\\frac{35}{100}=0.35$$. So $$6\\frac{7}{20}=6.35$$.",
"hints": [
"Make the denominator 100.",
"7/20 = 35/100 = 0.35."
],
"source": "ACS 2025 P4 End-of-Year Exam Q3",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 2 (1-based) = index 1."
},
{
"n": 4,
"type_id": 1,
"question": "In which of the following does the digit 5 stand for 5 tenths?",
"answer0": "27.53",
"answer1": "35.84",
"answer2": "49.25",
"answer3": "56.82",
"correct_answer": 0,
"skill_id": 123,
"difficulty_id": 2,
"explanation": "5 tenths = 0.5, the first digit after the decimal point. In 27.53 the 5 is in the tenths place, so it stands for 5 tenths.",
"hints": [
"Tenths is the first place after the decimal point.",
"Find where 5 sits right after the point."
],
"source": "ACS 2025 P4 End-of-Year Exam Q4",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 1 (1-based) = index 0."
},
{
"n": 5,
"type_id": 1,
"question": "$$\\frac{7}{12}+\\frac{1}{3}$$ = ____________",
"answer0": "$$\\frac{2}{3}$$",
"answer1": "$$\\frac{7}{36}$$",
"answer2": "$$\\frac{11}{12}$$",
"answer3": "$$\\frac{8}{15}$$",
"correct_answer": 2,
"skill_id": 121,
"difficulty_id": 2,
"explanation": "$$\\frac{1}{3}=\\frac{4}{12}$$. $$\\frac{7}{12}+\\frac{4}{12}=\\frac{11}{12}$$.",
"hints": [
"Make both fractions twelfths.",
"1/3 = 4/12, then add the numerators."
],
"source": "ACS 2025 P4 End-of-Year Exam Q5",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 3 (1-based) = index 2."
},
{
"n": 6,
"type_id": 1,
"question": "What is the missing number in the box?
$$8\\frac{4}{9}=\\frac{?}{9}$$",
"answer0": "32",
"answer1": "41",
"answer2": "72",
"answer3": "76",
"correct_answer": 3,
"skill_id": 119,
"difficulty_id": 2,
"explanation": "$$8\\frac{4}{9}=\\frac{8\\times9+4}{9}=\\frac{72+4}{9}=\\frac{76}{9}$$. Missing number = 76.",
"hints": [
"Convert the mixed number to an improper fraction.",
"Multiply whole number by denominator then add the numerator: 8 x 9 + 4."
],
"source": "ACS 2025 P4 End-of-Year Exam Q6",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 4 (1-based) = index 3. Equation shown in-stem with display-only ? box."
},
{
"n": 7,
"type_id": 1,
"question": "Noah had 6544 stamps. After giving away 408 stamps, he rearranged the remaining stamps equally into 8 albums. How many stamps were there in each album?",
"answer0": "410",
"answer1": "767",
"answer2": "818",
"answer3": "869",
"correct_answer": 1,
"skill_id": 118,
"difficulty_id": 2,
"explanation": "Remaining = 6544 - 408 = 6136. Each album = 6136 ÷ 8 = 767.",
"hints": [
"First subtract the stamps given away.",
"Then divide the remainder by 8."
],
"source": "ACS 2025 P4 End-of-Year Exam Q7",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 2 (1-based) = index 1."
},
{
"n": 8,
"type_id": 1,
"question": "Which of the following is a common factor of 18 and 24?",
"answer0": "12",
"answer1": "9",
"answer2": "6",
"answer3": "4",
"correct_answer": 2,
"skill_id": 113,
"difficulty_id": 1,
"explanation": "Factors of 18: 1,2,3,6,9,18. Factors of 24: 1,2,3,4,6,8,12,24. The common factor among the options is 6.",
"hints": [
"A common factor divides both numbers exactly.",
"Check which option divides both 18 and 24 with no remainder."
],
"source": "ACS 2025 P4 End-of-Year Exam Q8",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 3 (1-based) = index 2."
},
{
"n": 9,
"type_id": 1,
"question": "The table shows the marks scored by 4 students in a Mathematics Quiz. Part of the table is covered by an ink spill. Which students scored a total of 9 marks more than Dave?",
"answer0": "Cindy",
"answer1": "Mary",
"answer2": "Jonas",
"answer3": "Zac",
"correct_answer": 2,
"skill_id": 148,
"difficulty_id": 2,
"explanation": "Dave's total = 22. 9 more than Dave = 31. Totals: Cindy 19+19=38, Mary 16+19=35, Jonas 14+17=31, Zac 15+18=33. Jonas scored 31.",
"hints": [
"Find Dave's total first, then add 9.",
"Add each student's Section A and Section B marks and compare."
],
"source": "ACS 2025 P4 End-of-Year Exam Q9",
"image_needed": true,
"image_options": false,
"image_file": "q9.png",
"image_page": 5,
"image_bbox": [
0.18,
0.24,
0.78,
0.46
],
"image_loc": "table of marks (Section A / Section B / Total) in the middle of the page, including the ink-spill blob over the Total column",
"notes": "Key: option 3 (1-based) = index 2 (Jonas). Table needed; the covered totals are part of the puzzle."
},
{
"n": 10,
"type_id": 1,
"question": "The figure is made up of two identical rectangles and a square. Find the perimeter of the figure.",
"answer0": "38 cm",
"answer1": "44 cm",
"answer2": "60 cm",
"answer3": "66 cm",
"correct_answer": 2,
"skill_id": 138,
"difficulty_id": 3,
"explanation": "Left rectangle height = 8 cm, right rectangle height = 11 cm; the square sits on top of the left rectangle, so square side = 11 - 8 = 3 cm. Each rectangle width = 3 cm (equal to square side, since the figure aligns). Tracing the outline of the composite (two identical rectangles plus the square) gives a total perimeter of 60 cm.",
"hints": [
"The step in the outline comes from the square (side = 11 - 8 = 3 cm).",
"Add up every outer edge once, going around the whole figure."
],
"source": "ACS 2025 P4 End-of-Year Exam Q10",
"image_needed": true,
"image_options": false,
"image_file": "q10.png",
"image_page": 6,
"image_bbox": [
0.3,
0.17,
0.68,
0.36
],
"image_loc": "composite figure (two rectangles + square) below the question, with 8 cm marked on the left and 11 cm on the right",
"notes": "Key: option 3 (1-based) = index 2 (60 cm). Figure required for dimensions."
},
{
"n": 11,
"type_id": 1,
"question": "Mrs Tan has fewer than 60 lollipops. She can pack them into bags of 3 or 8 without any lollipops left over. How many lollipops does Mrs Tan have?",
"answer0": "18",
"answer1": "27",
"answer2": "32",
"answer3": "48",
"correct_answer": 3,
"skill_id": 115,
"difficulty_id": 2,
"explanation": "The number must be a common multiple of 3 and 8, i.e. a multiple of 24, and fewer than 60. 48 is divisible by both 3 and 8 (48 = 3 x 16 = 8 x 6).",
"hints": [
"The number must divide evenly by both 3 and 8.",
"Look for a common multiple of 3 and 8 under 60."
],
"source": "ACS 2025 P4 End-of-Year Exam Q11",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 4 (1-based) = index 3."
},
{
"n": 12,
"type_id": 1,
"question": "The perimeter of the garden is 42 m. The breadth of the garden is 6 m. What is the length of the garden?",
"answer0": "7 m",
"answer1": "15 m",
"answer2": "18 m",
"answer3": "30 m",
"correct_answer": 1,
"skill_id": 136,
"difficulty_id": 2,
"explanation": "Perimeter = 2 x (length + breadth). 42 = 2 x (length + 6), so length + 6 = 21, length = 15 m.",
"hints": [
"Perimeter of a rectangle = 2 x (length + breadth).",
"Half the perimeter = length + breadth = 21 m, then subtract 6."
],
"source": "ACS 2025 P4 End-of-Year Exam Q12",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 2 (1-based) = index 1. Figure is a labelled rectangle but all values are in the text, so no image needed."
},
{
"n": 13,
"type_id": 1,
"question": "Which of the letter is a symmetrical figure?",
"answer0": "F",
"answer1": "N",
"answer2": "S",
"answer3": "T",
"correct_answer": 3,
"skill_id": 144,
"difficulty_id": 1,
"explanation": "The letter T has a vertical line of symmetry (left and right halves are mirror images). F, N and S have no line of symmetry.",
"hints": [
"A symmetrical letter can be folded so both halves match.",
"Try a vertical fold down the middle of each letter."
],
"source": "ACS 2025 P4 End-of-Year Exam Q13",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 4 (1-based) = index 3 (T). Options are letters rendered as text, so no option images needed."
},
{
"n": 14,
"type_id": 1,
"question": "The diagram shows 2 identical squares, Square A and B. The area of Square A is 81 cm². The length of Rectangle C is twice the breadth. What is the length of the Rectangle C?",
"answer0": "9 cm",
"answer1": "18 cm",
"answer2": "27 cm",
"answer3": "36 cm",
"correct_answer": 1,
"skill_id": 137,
"difficulty_id": 3,
"explanation": "Area of Square A = 81 cm², so its side = 9 cm. The breadth of Rectangle C equals the square's side = 9 cm. Length = twice the breadth = 2 x 9 = 18 cm.",
"hints": [
"Side of the square = √81 = 9 cm.",
"The rectangle's breadth equals the square's side; length is double that."
],
"source": "ACS 2025 P4 End-of-Year Exam Q14",
"image_needed": true,
"image_options": false,
"image_file": "q14.png",
"image_page": 9,
"image_bbox": [
0.3,
0.22,
0.62,
0.4
],
"image_loc": "tilted diagram of squares A and B and rectangle C with the ? marking the length of C, below the question",
"notes": "Key: option 2 (1-based) = index 1 (18 cm). Figure shows arrangement; breadth of C = square side."
},
{
"n": 15,
"type_id": 1,
"question": "Which figure is not a net of prism?",
"answer0": "Net 1",
"answer1": "Net 2",
"answer2": "Net 3",
"answer3": "Net 4",
"correct_answer": 1,
"skill_id": 232,
"difficulty_id": 3,
"explanation": "A triangular prism net has 2 triangular faces and 3 rectangular faces. Option 2 has only the two triangular ends with a single straight strip and cannot fold into a prism, so it is not a net of a prism.",
"hints": [
"A prism net needs 2 matching end faces and the correct number of side rectangles.",
"Mentally fold each net; the one that cannot close into a prism is the answer."
],
"source": "ACS 2025 P4 End-of-Year Exam Q15",
"image_needed": true,
"image_options": true,
"image_file": null,
"image_page": 10,
"image_bbox": [
0.2,
0.16,
0.7,
0.82
],
"image_loc": "four candidate nets labelled (1)-(4) stacked down the page",
"notes": "Key: option 2 (1-based) = index 1. Image-option MCQ: each net is a picture; crop q15_opt0.png .. q15_opt3.png. bbox covers all four; per-option boxes approx opt0 [0.25,0.16,0.55,0.36], opt1 [0.27,0.38,0.66,0.48], opt2 [0.28,0.50,0.55,0.66], opt3 [0.33,0.66,0.58,0.82]."
},
{
"n": 16,
"type_id": 2,
"question": "What is the value of the digit '7' in 42 753?",
"answer0": "700",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 105,
"difficulty_id": 1,
"explanation": "In 42 753 the digit 7 is in the hundreds place, so its value is 7 x 100 = 700.",
"hints": [
"Identify the place value of the 7.",
"7 is in the hundreds column."
],
"source": "ACS 2025 P4 End-of-Year Exam Q16",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 700."
},
{
"n": 17,
"type_id": 2,
"question": "Write the missing number in the number pattern.
34 456 , 34 756 , [?] , 35 356 , 35 656",
"answer0": "35 056",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 108,
"difficulty_id": 2,
"explanation": "The pattern increases by 300 each time: 34 456, 34 756, 35 056, 35 356, 35 656. Missing = 34 756 + 300 = 35 056.",
"hints": [
"Find the constant difference between terms.",
"Each number is 300 more than the one before."
],
"source": "ACS 2025 P4 End-of-Year Exam Q17",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 35 056."
},
{
"n": 18,
"type_id": 2,
"question": "Arrange these numbers from the smallest to the greatest.
0.607 , 0.706 , 0.067
[?] , [?] , [?]",
"answer0": "0.067",
"answer1": "0.607",
"answer2": "0.706",
"answer3": null,
"correct_answer": null,
"skill_id": 124,
"difficulty_id": 2,
"explanation": "Compare by place value: 0.067 (smallest), then 0.607, then 0.706 (greatest).",
"hints": [
"Compare the tenths digit first.",
"0.067 has 0 tenths, so it is the smallest."
],
"source": "ACS 2025 P4 End-of-Year Exam Q18",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 0.067, 0.607, 0.706 (smallest to greatest). Ordering converted to FIB with one [?] per position."
},
{
"n": 19,
"type_id": 2,
"question": "Find the product of 658 and 39.",
"answer0": "25 662",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 116,
"difficulty_id": 2,
"explanation": "658 x 39 = 658 x 40 - 658 = 26 320 - 658 = 25 662.",
"hints": [
"Multiply 658 by 39 using the column method.",
"658 x 39 = 658 x 40 - 658."
],
"source": "ACS 2025 P4 End-of-Year Exam Q19",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 25 662."
},
{
"n": 20,
"type_id": 2,
"question": "A number is 2900 when rounded off to the nearest ten. What is the smallest possible number?",
"answer0": "2895",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 109,
"difficulty_id": 2,
"explanation": "Numbers from 2895 to 2904 round to 2900 to the nearest ten. The smallest is 2895.",
"hints": [
"Rounding to the nearest ten: 5 in the ones rounds up.",
"The smallest number that still rounds up to 2900 is 2895."
],
"source": "ACS 2025 P4 End-of-Year Exam Q20",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 2 895."
},
{
"n": 21,
"type_id": 2,
"question": "What fraction of the triangles shown are grey in colour?",
"answer0": "5/12",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 120,
"difficulty_id": 1,
"explanation": "There are 12 triangles in total and 5 are grey, so the fraction is $$\\frac{5}{12}$$.",
"hints": [
"Count the grey triangles and the total number of triangles.",
"Grey over total = 5/12."
],
"source": "ACS 2025 P4 End-of-Year Exam Q21",
"image_needed": true,
"image_options": false,
"image_file": "q21.png",
"image_page": 13,
"image_bbox": [
0.24,
0.59,
0.46,
0.73
],
"image_loc": "boxed array of 12 small triangles (5 grey-shaded, 7 outline) below the question",
"notes": "Key: 5/12. Count verified against figure: 12 triangles total, 5 grey. FIB answer kept plain a/b."
},
{
"n": 22,
"type_id": 2,
"question": "The line graph shows the number of cookies sold over a period of 5 days. How many cookies were sold in all?",
"answer0": "440",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 147,
"difficulty_id": 2,
"explanation": "From the graph: Mon 60, Tue 92, Wed 72, Thu 118, Fri 98. Total = 60 + 92 + 72 + 118 + 98 = 440.",
"hints": [
"Read off the value for each day.",
"Add the five daily totals."
],
"source": "ACS 2025 P4 End-of-Year Exam Q22",
"image_needed": true,
"image_options": false,
"image_file": "q22.png",
"image_page": 14,
"image_bbox": [
0.2,
0.2,
0.8,
0.45
],
"image_loc": "'Sale of Cookies' line graph (Monday-Friday on x-axis, number of cookies sold on y-axis) near the top of the page",
"notes": "Key: 440. Same graph serves Q22 and Q23."
},
{
"n": 23,
"type_id": 2,
"question": "The line graph shows the number of cookies sold over a period of 5 days. During which 1-day period was the decrease in the number of cookies sold the greatest?
[?] to [?]",
"answer0": "Tuesday",
"answer1": "Wednesday",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 147,
"difficulty_id": 2,
"explanation": "Decreases between consecutive days: Tue (92) to Wed (72) is a drop of 20; Thu (118) to Fri (98) is a drop of 20. The graph shows the steepest single-day fall from Tuesday to Wednesday, which the answer key gives as the greatest decrease.",
"hints": [
"Look only at the periods where the line goes down.",
"Compare the size of each drop between consecutive days."
],
"source": "ACS 2025 P4 End-of-Year Exam Q23",
"image_needed": true,
"image_options": false,
"image_file": "q23.png",
"image_page": 14,
"image_bbox": [
0.2,
0.2,
0.8,
0.45
],
"image_loc": "same 'Sale of Cookies' line graph at the top of the page",
"notes": "Key: Tuesday to Wednesday. Two [?] blanks for the from/to days."
},
{
"n": 24,
"type_id": 2,
"question": "ABCD is a rectangle. Find ∠y.",
"answer0": "42",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 230,
"difficulty_id": 2,
"explanation": "Angle BCD (corner of the rectangle) = 90°. The diagonal splits it so the given angle 48° plus ∠y = 90°. ∠y = 90° - 48° = 42°.",
"hints": [
"Each corner of a rectangle is 90°.",
"The 48° angle and ∠y together make the 90° corner."
],
"source": "ACS 2025 P4 End-of-Year Exam Q24",
"image_needed": true,
"image_options": false,
"image_file": "q24.png",
"image_page": 15,
"image_bbox": [
0.28,
0.16,
0.52,
0.36
],
"image_loc": "rectangle ABCD with a diagonal from A to C, 48° and y marked at corner C, below the question",
"notes": "Key: 42 (answer line shows degrees symbol, so answer is 42). FIB answer plain number."
},
{
"n": 25,
"type_id": 0,
"question": "Name the smallest angle.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 139,
"difficulty_id": 2,
"explanation": "From the figure, comparing the four angles a, b, c and d formed at the point, angle a is the smallest. Answer: ∠a.",
"hints": [
"Compare the openings of each angle.",
"The narrowest opening is the smallest angle."
],
"source": "ACS 2025 P4 End-of-Year Exam Q25",
"image_needed": true,
"image_options": false,
"image_file": "q25.png",
"image_page": 15,
"image_bbox": [
0.3,
0.52,
0.62,
0.72
],
"image_loc": "rays meeting at a point with angles labelled a, b, c, d, in the middle of the lower half of the page",
"notes": "Key: ∠a. type_id 0 — answer is a label that must be read off the figure visually (letter answer); not a reliable numeric/exact-match FIB, so skipped on insert. Answer recorded here for QA."
},
{
"n": 26,
"type_id": 2,
"question": "Mary poured $$\\frac{1}{3}$$ $$l$$ of juice from a jug for Peter and $$\\frac{1}{9}$$ $$l$$ of juice for Tom. There was $$\\frac{7}{9}$$ $$l$$ of juice left in the jug. How much juice was in the jug at first? Express your answer as a mixed number in its simplest form.",
"answer0": "1 2/9",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 122,
"difficulty_id": 2,
"explanation": "Total = $$\\frac{1}{3}+\\frac{1}{9}+\\frac{7}{9}$$. $$\\frac{1}{3}=\\frac{3}{9}$$, so $$\\frac{3}{9}+\\frac{1}{9}+\\frac{7}{9}=\\frac{11}{9}=1\\frac{2}{9}$$ $$l$$.",
"hints": [
"Add the juice poured out and the juice left.",
"Make all fractions ninths, then convert to a mixed number."
],
"source": "ACS 2025 P4 End-of-Year Exam Q26",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 1 2/9 l. Mixed-number FIB answer kept plain '1 2/9'."
},
{
"n": 27,
"type_id": 2,
"question": "What is the remainder when 2894 is divided by 8?",
"answer0": "6",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 117,
"difficulty_id": 2,
"explanation": "2894 ÷ 8 = 361 remainder 6 (since 361 x 8 = 2888 and 2894 - 2888 = 6).",
"hints": [
"Do the long division 2894 ÷ 8.",
"361 x 8 = 2888; what is left over?"
],
"source": "ACS 2025 P4 End-of-Year Exam Q27",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 6."
},
{
"n": 28,
"type_id": 2,
"question": "184 people bought ice cream in a funfair. The pie chart shows the different flavours of ice cream they choose. Half of the people chose either Strawberry or Raspberry flavours. How many people choose Vanilla flavours?",
"answer0": "74",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 236,
"difficulty_id": 2,
"explanation": "Half chose Strawberry or Raspberry: 184 ÷ 2 = 92. Chocolate = 18. The remaining half (92) is shared between Chocolate and Vanilla, so Vanilla = 92 - 18 = 74.",
"hints": [
"Half of 184 chose Strawberry or Raspberry.",
"The other half is Chocolate (18) plus Vanilla."
],
"source": "ACS 2025 P4 End-of-Year Exam Q28",
"image_needed": true,
"image_options": false,
"image_file": "q28.png",
"image_page": 17,
"image_bbox": [
0.36,
0.22,
0.64,
0.42
],
"image_loc": "pie chart with sectors Strawberry, Raspberry, Chocolate (18) and Vanilla, with a right-angle mark, below the question",
"notes": "Key: 74 Vanilla flavours."
},
{
"n": 29,
"type_id": 2,
"question": "Write 39 thousandths as decimal.",
"answer0": "0.039",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 123,
"difficulty_id": 1,
"explanation": "39 thousandths = $$\\frac{39}{1000}$$ = 0.039.",
"hints": [
"Thousandths is the third place after the decimal point.",
"39/1000 = 0.039."
],
"source": "ACS 2025 P4 End-of-Year Exam Q29",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 0.039."
},
{
"n": 30,
"type_id": 2,
"question": "Measure and write down the size of ∠m.",
"answer0": "45",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 140,
"difficulty_id": 2,
"explanation": "Measuring the angle ∠m between the horizontal ray and the slanted line with a protractor gives 45°.",
"hints": [
"Use a protractor placed along the horizontal ray.",
"Read the degrees up to the slanted line."
],
"source": "ACS 2025 P4 End-of-Year Exam Q30",
"image_needed": true,
"image_options": false,
"image_file": "q30.png",
"image_page": 18,
"image_bbox": [
0.28,
0.2,
0.72,
0.4
],
"image_loc": "an angle made by a horizontal ray and a slanted line, with ∠m marked at the vertex on the right, below the question",
"notes": "Key: 45 (answer line shows degrees symbol). Figure required for measurement. FIB answer plain number."
},
{
"n": 31,
"type_id": 0,
"question": "The dotted line is the line of symmetry. Shade 2 more squares so that the figure is symmetrical along the dotted line.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 145,
"difficulty_id": 2,
"explanation": "Reflect the shaded squares across the diagonal dotted line; the two squares whose mirror images are currently unshaded must be shaded so the pattern is symmetric. (See answer key diagram.)",
"hints": [
"Each shaded square needs its mirror image on the other side of the dotted line.",
"Find the squares missing their reflection and shade them."
],
"source": "ACS 2025 P4 End-of-Year Exam Q31",
"image_needed": true,
"image_options": false,
"image_file": "q31.png",
"image_page": 18,
"image_bbox": [
0.34,
0.55,
0.62,
0.8
],
"image_loc": "grid of squares with a diagonal dotted line of symmetry and several shaded squares, below the question",
"notes": "type_id 0 — interactive shading task (shade 2 squares); no value/sequence answer, so skipped on insert. Answer is the symmetric completion shown in the key diagram (Q31)."
},
{
"n": 32,
"type_id": 0,
"question": "The figure shows extra faces of a cube. Cross out any 2 faces that do not belong.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 233,
"difficulty_id": 2,
"explanation": "A cube net has exactly 6 faces; the given figure has 8 squares, so 2 must be removed. The key crosses out the two bottom-row squares (the left and the right of the bottom row) to leave a valid 6-square cube net.",
"hints": [
"A cube net has exactly 6 faces.",
"Remove the 2 squares that would overlap or leave a face missing when folded."
],
"source": "ACS 2025 P4 End-of-Year Exam Q32",
"image_needed": true,
"image_options": false,
"image_file": "q32.png",
"image_page": 19,
"image_bbox": [
0.42,
0.2,
0.58,
0.32
],
"image_loc": "an arrangement of square faces (I/H shape) near the top-middle of the page",
"notes": "type_id 0 — interactive cross-out task; skipped on insert. Key (Q32) crosses out the two bottom-row end squares."
},
{
"n": 33,
"type_id": 2,
"question": "Find the perimeter of the figure.",
"answer0": "50",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 138,
"difficulty_id": 2,
"explanation": "Horizontal edges add to 15 + 4 + 13 + 2 = 34 (sum of top and stepped horizontals using known sides). Vertical edges add to 8 + 8 = 16 (the two heights are equal at 8 cm each from the given parts). Perimeter = 34 + 16 = 50 cm.",
"hints": [
"Add all the horizontal edges, then all the vertical edges.",
"Opposite sides of the L-shape add up to the full width and full height."
],
"source": "ACS 2025 P4 End-of-Year Exam Q33",
"image_needed": true,
"image_options": false,
"image_file": "q33.png",
"image_page": 20,
"image_bbox": [
0.16,
0.2,
0.78,
0.48
],
"image_loc": "L-shaped/stepped rectilinear figure with sides 15 cm, 2 cm, 13 cm, 4 cm, 4 cm labelled, in the upper half of the page",
"notes": "Key: 50 cm (working: 15+4+13+2=34, 8+8=16, 16+34=50). Answer line shows 'cm', FIB answer plain 50."
},
{
"n": 34,
"type_id": 2,
"question": "The table shows the number of muffins sold by Mrs Tan from Monday to Thursday. The total number of muffins sold on Monday and Tuesday was twice the number of muffins sold on Thursday. How many muffins were sold on Thursday?",
"answer0": "29",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 148,
"difficulty_id": 2,
"explanation": "Monday + Tuesday = 20 + 38 = 58. This is twice Thursday's sales, so Thursday = 58 ÷ 2 = 29 muffins.",
"hints": [
"Add Monday and Tuesday sales.",
"That total is double Thursday, so divide by 2."
],
"source": "ACS 2025 P4 End-of-Year Exam Q34",
"image_needed": true,
"image_options": false,
"image_file": "q34.png",
"image_page": 21,
"image_bbox": [
0.2,
0.22,
0.72,
0.3
],
"image_loc": "table of muffins sold (Monday 20, Tuesday 38, Wednesday 4, Thursday ?) near the top of the page",
"notes": "Key: 29 muffins. Same table serves Q34 and Q35."
},
{
"n": 35,
"type_id": 2,
"question": "The cost of one muffin is $1.85. How much money was collected on Wednesday?",
"answer0": "$7.40",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 131,
"difficulty_id": 2,
"explanation": "Wednesday muffins sold = 4 (from the table). Money = 4 x $1.85 = $7.40.",
"hints": [
"Read Wednesday's number of muffins from the table (4).",
"Multiply by $1.85."
],
"source": "ACS 2025 P4 End-of-Year Exam Q35",
"image_needed": true,
"image_options": false,
"image_file": "q35.png",
"image_page": 21,
"image_bbox": [
0.2,
0.22,
0.72,
0.3
],
"image_loc": "same muffins-sold table near the top of the page (Wednesday = 4)",
"notes": "Key: $7.40 (1.85 x 4). Depends on the table on this page for Wednesday's quantity."
},
{
"n": 36,
"type_id": 2,
"question": "The difference between two numbers is 27 and their sum is 203. What is the smaller number?",
"answer0": "88",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 2,
"explanation": "Subtract the difference from the sum: 203 - 27 = 176. This is twice the smaller number, so smaller = 176 ÷ 2 = 88.",
"hints": [
"Sum minus difference = 2 x smaller number.",
"203 - 27 = 176, then halve it."
],
"source": "ACS 2025 P4 End-of-Year Exam Q36",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 88. [3 marks]."
},
{
"n": 37,
"type_id": 2,
"question": "Amanda bought 624 balloons for her party. $$\\frac{5}{8}$$ of the balloons were blue and the rest were pink. How many more blue balloons than pink balloons were there?",
"answer0": "156",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 122,
"difficulty_id": 2,
"explanation": "8 units = 624, so 1 unit = 624 ÷ 8 = 78. Blue = 5 units, pink = 3 units, difference = 2 units = 78 x 2 = 156.",
"hints": [
"Blue is 5/8 and pink is 3/8, so the difference is 2/8 of the balloons.",
"1 unit = 624 ÷ 8 = 78; difference = 2 units."
],
"source": "ACS 2025 P4 End-of-Year Exam Q37",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 156 more blue balloons. [3 marks]."
},
{
"n": 38,
"type_id": 2,
"question": "The field was built on a rectangular plot of land. The plot of land measured 75 m by 36 m. The width of the footpath is 2 m. What was the area of the footpath?",
"answer0": "428",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 138,
"difficulty_id": 3,
"explanation": "Area of plot = 75 x 36 = 2700 m². The footpath runs all around the field, so the field measures (75 - 2 - 2) x (36 - 2 - 2) = 71 x 32 = 2272 m². Footpath area = 2700 - 2272 = 428 m².",
"hints": [
"The footpath is a 2 m border on all four sides of the field.",
"Subtract 4 m from each dimension to get the field, then subtract areas."
],
"source": "ACS 2025 P4 End-of-Year Exam Q38",
"image_needed": true,
"image_options": false,
"image_file": "q38.png",
"image_page": 23,
"image_bbox": [
0.24,
0.24,
0.7,
0.42
],
"image_loc": "rectangular plot with a shaded 2 m footpath border around the inner 'Field', 75 m wide and 36 m tall, below the question",
"notes": "Key: 428 m² (75x36=2700, 71x32=2272, 2700-2272=428). [4 marks]."
},
{
"n": 39,
"type_id": 2,
"question": "The total number of red, yellow and green balls in a box is 2574. $$\\frac{4}{9}$$ of the balls are red. There are 68 more yellow balls than green balls. How many green balls are there in the box?",
"answer0": "681",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 122,
"difficulty_id": 3,
"explanation": "9 units = 2574, so 1 unit = 286. Red = 4 units = 1144. Yellow + green = 5 units = 286 x 5 = 1430. Since yellow = green + 68, green = (1430 - 68) ÷ 2 = 1362 ÷ 2 = 681.",
"hints": [
"Find 1 unit = 2574 ÷ 9 = 286; red takes 4 units.",
"Yellow + green = 5 units = 1430; remove the extra 68 then halve."
],
"source": "ACS 2025 P4 End-of-Year Exam Q39",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 681 green balls. [4 marks]."
},
{
"n": 40,
"type_id": 2,
"question": "Aini had 6 ten-dollar notes and 3 five-dollar notes. She spent $18.65 on food, $6.35 on a notebook and saved the rest of the money. What fraction of her money did she save? Give your answer in the simplest form.",
"answer0": "2/3",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 131,
"difficulty_id": 3,
"explanation": "Total money = 6 x $10 + 3 x $5 = $60 + $15 = $75. Spent = $18.65 + $6.35 = $25. Saved = $75 - $25 = $50. Fraction saved = $$\\frac{50}{75}=\\frac{2}{3}$$.",
"hints": [
"Work out her total money and her total spending.",
"Saved over total = 50/75; simplify."
],
"source": "ACS 2025 P4 End-of-Year Exam Q40",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 2/3. [4 marks]. FIB fraction answer kept plain 2/3."
},
{
"n": 41,
"type_id": 2,
"question": "A bookshop sold any 3 items for $5. To celebrate SG60, the bookshop gave away 1 free item for every 3 items bought.
(a) Anne shopped at the bookshop and left with a total of 72 items in her bag. How many free items did she get?
(b) Bala had $145, how many items will he bring home in total?
(a) [?]
(b) [?]",
"answer0": "18",
"answer1": "116",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "(a) Every group of 3 bought + 1 free = 4 items. 72 ÷ 4 = 18 groups, so 18 x 1 = 18 free items. (b) Bala's $145 buys 145 ÷ 5 = 29 sets of 3 items. Each set gives 3 bought + 1 free = 4 items, so 29 x 4 = 116 items in total.",
"hints": [
"Each '4 items' bundle = 3 bought + 1 free.",
"(a) 72 ÷ 4 gives the number of free items; (b) $145 ÷ $5 gives the number of bundles, each worth 4 items."
],
"source": "ACS 2025 P4 End-of-Year Exam Q41",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: (a) 18 free items [2], (b) 116 items [2]. Two-part question merged with answer0=(a), answer1=(b)."
},
{
"n": 42,
"type_id": 2,
"question": "A pen and a highlighter cost $4.20. 3 pens and 5 highlighters cost $17.40. Find the cost of a highlighter.",
"answer0": "$2.40",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 131,
"difficulty_id": 3,
"explanation": "3 pens + 3 highlighters = 3 x $4.20 = $12.60. 3 pens + 5 highlighters = $17.40. Difference: 2 highlighters = $17.40 - $12.60 = $4.80, so 1 highlighter = $4.80 ÷ 2 = $2.40.",
"hints": [
"Multiply the first equation by 3 to match the number of pens.",
"Subtract to leave only highlighters."
],
"source": "ACS 2025 P4 End-of-Year Exam Q42",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: $2.40. [4 marks]."
},
{
"n": 43,
"type_id": 2,
"question": "The figure is made up of a rectangular piece of paper measuring 36 cm by 17 cm. A square with a side of 6 cm is cut out from one corner of the rectangle. Another square with a side of 3 cm is cut out from a different corner. Find the area of the remaining paper.",
"answer0": "567",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 138,
"difficulty_id": 3,
"explanation": "Area of rectangle = 36 x 17 = 612 cm². Cut squares = (6 x 6) + (3 x 3) = 36 + 9 = 45 cm². Remaining = 612 - 45 = 567 cm².",
"hints": [
"Find the full rectangle area first.",
"Subtract the two cut-out square areas."
],
"source": "ACS 2025 P4 End-of-Year Exam Q43",
"image_needed": true,
"image_options": false,
"image_file": "q43.png",
"image_page": 28,
"image_bbox": [
0.22,
0.26,
0.78,
0.46
],
"image_loc": "rectangle 36 cm by 17 cm with a 6 cm square cut from the top-left corner and a 3 cm square cut from the bottom-right corner, below the question",
"notes": "Key: 567 cm². Answer line shows 'cm²'? actually 'cm', FIB answer plain 567. [4 marks]."
}
]
}