{
"paper": {
"school": "Nanyang Primary School",
"year": 2025,
"level": "P4",
"label": "End-of-Year Exam",
"source_prefix": "Nanyang 2025 P4 End-of-Year Exam",
"has_answer_key": true
},
"questions": [
{
"n": 1,
"type_id": 1,
"question": "The value of the digit 5 in 25 980 is ____________.",
"answer0": "50 000",
"answer1": "5000",
"answer2": "500",
"answer3": "50",
"correct_answer": 1,
"skill_id": 105,
"difficulty_id": 1,
"explanation": "In 25 980, the digit 5 is in the thousands place, so its value is 5 × 1000 = 5000.",
"hints": [
"Identify which place the digit 5 sits in.",
"5 is in the thousands column: 5 × 1000."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 2 = 5000."
},
{
"n": 2,
"type_id": 1,
"question": "In which of the following are the numbers arranged from the smallest to the greatest?",
"answer0": "4891, 4819, 4189",
"answer1": "4189, 4891, 4819",
"answer2": "4891, 4189, 4819",
"answer3": "4189, 4819, 4891",
"correct_answer": 3,
"skill_id": 107,
"difficulty_id": 1,
"explanation": "Compare the numbers: 4189 < 4819 < 4891. Option 4 lists them smallest to greatest.",
"hints": [
"Compare thousands first (all 4), then hundreds.",
"Smallest hundreds digit is 1 (4189), then 8 with tens 1 (4819), then 8 with tens 9 (4891)."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 4."
},
{
"n": 3,
"type_id": 1,
"question": "Which of the following is not a factor of 63?",
"answer0": "6",
"answer1": "7",
"answer2": "3",
"answer3": "9",
"correct_answer": 0,
"skill_id": 112,
"difficulty_id": 1,
"explanation": "63 = 7 × 9 = 3 × 21. Factors of 63 are 1, 3, 7, 9, 21, 63. 63 ÷ 6 = 10 r 3, so 6 is not a factor.",
"hints": [
"Test each option by dividing 63 by it.",
"63 ÷ 6 leaves a remainder, so 6 is not a factor."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q3",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 1 = 6."
},
{
"n": 4,
"type_id": 1,
"question": "The figure is made up of identical triangles. What fraction of the figure is shaded?",
"answer0": "$$\\frac{7}{9}$$",
"answer1": "$$\\frac{7}{15}$$",
"answer2": "$$\\frac{7}{16}$$",
"answer3": "$$\\frac{9}{16}$$",
"correct_answer": 2,
"skill_id": 120,
"difficulty_id": 2,
"explanation": "The rectangle is split into 8 small squares, each made of 2 identical triangles, giving 16 triangles in total. 7 of the 16 triangles are shaded, so the shaded fraction is $$\\frac{7}{16}$$.",
"hints": [
"Count the total number of identical triangles in the whole figure.",
"Count the shaded triangles, then write shaded over total."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q4",
"image_needed": true,
"image_options": false,
"image_file": "q4.png",
"image_page": 4,
"image_bbox": [
0.4,
0.18,
0.66,
0.31
],
"image_loc": "centre-top of page, grid of shaded/unshaded triangles below the question",
"notes": "Key: option 3 = 7/16. 16 triangles total, 7 shaded."
},
{
"n": 5,
"type_id": 1,
"question": "Express $$\\frac{52}{100}$$ as a decimal.",
"answer0": "0.52",
"answer1": "5.20",
"answer2": "0.052",
"answer3": "0.502",
"correct_answer": 0,
"skill_id": 127,
"difficulty_id": 1,
"explanation": "$$\\frac{52}{100}$$ means 52 hundredths = 0.52.",
"hints": [
"A denominator of 100 means hundredths.",
"52 hundredths is written as 0.52."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q5",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 1 = 0.52."
},
{
"n": 6,
"type_id": 1,
"question": "Which angle is greater than a right angle?",
"answer0": "∠a",
"answer1": "∠b",
"answer2": "∠c",
"answer3": "∠d",
"correct_answer": 2,
"skill_id": 99,
"difficulty_id": 2,
"explanation": "A right angle is 90°. In the quadrilateral, ∠c is the obtuse angle, larger than 90°, so it is greater than a right angle.",
"hints": [
"A right angle looks like the corner of a square (90°).",
"Find the angle that opens wider than 90°."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q6",
"image_needed": true,
"image_options": false,
"image_file": "q6.png",
"image_page": 5,
"image_bbox": [
0.37,
0.15,
0.62,
0.3
],
"image_loc": "upper-centre of page, four-sided figure with marked angles a, b, c, d",
"notes": "Key: option 3 = ∠c."
},
{
"n": 7,
"type_id": 1,
"question": "How many pairs of perpendicular lines are there in the figure?",
"answer0": "1",
"answer1": "2",
"answer2": "3",
"answer3": "4",
"correct_answer": 1,
"skill_id": 100,
"difficulty_id": 2,
"explanation": "A rectangle has 4 right-angle corners, but each pair of perpendicular lines is counted once. The two long sides each meet two short sides; there are 4 corners but only the distinct pairs of perpendicular sides — the key gives 2.",
"hints": [
"Perpendicular lines meet at a right angle.",
"Look at where the sides of the rectangle meet at 90°; the key counts 2 pairs."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q7",
"image_needed": true,
"image_options": false,
"image_file": "q7.png",
"image_page": 5,
"image_bbox": [
0.34,
0.55,
0.62,
0.66
],
"image_loc": "middle of page, a plain rectangle below the question",
"notes": "Key: option 2 = 2."
},
{
"n": 8,
"type_id": 1,
"question": "Which figure is a net of a cuboid?",
"answer0": "Net 1",
"answer1": "Net 2",
"answer2": "Net 3",
"answer3": "Net 4",
"correct_answer": 2,
"skill_id": 232,
"difficulty_id": 2,
"explanation": "A net of a cuboid folds into a closed box with 6 rectangular faces. Net 3 is the arrangement of 6 rectangles that folds correctly into a cuboid.",
"hints": [
"A cuboid net has 6 rectangular faces.",
"Mentally fold each net; only one closes into a box without overlapping."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q8",
"image_needed": true,
"image_options": true,
"image_file": null,
"image_page": 6,
"image_bbox": [
0.26,
0.16,
0.55,
0.87
],
"image_loc": "four candidate nets stacked vertically, labelled (1)-(4)",
"notes": "Key: option 3 = Net 3. Image-option MCQ: crop each option q8_opt0.png..q8_opt3.png. opt0 page6 bbox approx [0.26,0.16,0.42,0.27]; opt1 [0.26,0.31,0.45,0.49]; opt2 [0.36,0.50,0.55,0.68]; opt3 [0.26,0.69,0.52,0.87]."
},
{
"n": 9,
"type_id": 1,
"question": "The perimeter of a square is 64 m. Find the length of the square.",
"answer0": "8 m",
"answer1": "16 m",
"answer2": "32 m",
"answer3": "60 m",
"correct_answer": 1,
"skill_id": 137,
"difficulty_id": 1,
"explanation": "A square has 4 equal sides. Length = perimeter ÷ 4 = 64 ÷ 4 = 16 m.",
"hints": [
"Perimeter of a square = 4 × side length.",
"Divide 64 by 4 to get one side."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q9",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 2 = 16 m. Figure is a plain square labelled 'Perimeter = 64 m' — no figure-only data needed; treated as text question."
},
{
"n": 10,
"type_id": 1,
"question": "The figure is made up of Square A with side 10 cm and Rectangle B with breadth 8 cm. Find the area of Rectangle B.",
"answer0": "176 cm$$^2$$",
"answer1": "100 cm$$^2$$",
"answer2": "96 cm$$^2$$",
"answer3": "60 cm$$^2$$",
"correct_answer": 0,
"skill_id": 138,
"difficulty_id": 2,
"explanation": "Square A has side 10 cm. Rectangle B is taller by 12 cm above A, so its length = 10 + 12 = 22 cm. Breadth = 8 cm. Area of B = 22 × 8 = 176 cm$$^2$$.",
"hints": [
"Find the full length of Rectangle B: it rises 12 cm above the 10 cm square.",
"Length of B = 12 + 10 = 22 cm; area = length × breadth = 22 × 8."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q10",
"image_needed": true,
"image_options": false,
"image_file": "q10.png",
"image_page": 7,
"image_bbox": [
0.38,
0.48,
0.66,
0.69
],
"image_loc": "centre of page, square A beside taller rectangle B with dimensions 12 cm, 10 cm, 8 cm",
"notes": "Key: option 1 = 176 cm^2."
},
{
"n": 11,
"type_id": 1,
"question": "The table shows the amount of money earned by 5 shops last week.
Shop A: $900, Shop B: $650, Shop C: $1000, Shop D: $800, Shop E: $650.
Which of the following bar graphs best represents the data shown in the table?",
"answer0": "Bar graph 1",
"answer1": "Bar graph 2",
"answer2": "Bar graph 3",
"answer3": "Bar graph 4",
"correct_answer": 1,
"skill_id": 102,
"difficulty_id": 2,
"explanation": "The data: A=900, B=650, C=1000 (tallest), D=800, E=650 (B and E equal). Bar graph 2 shows C tallest, A next, D shorter, with B and E equal and shortest, matching the table.",
"hints": [
"C must be the tallest bar and B = E.",
"Check which graph has the correct relative heights for all five shops."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q11",
"image_needed": true,
"image_options": true,
"image_file": null,
"image_page": 8,
"image_bbox": [
0.2,
0.28,
0.8,
0.85
],
"image_loc": "four candidate bar graphs in a 2x2 grid, labelled (1)-(4)",
"notes": "Key: option 2 = Bar graph 2. Image-option MCQ: crop q11_opt0..3. opt0 page8 approx [0.20,0.28,0.50,0.55]; opt1 [0.55,0.28,0.85,0.55]; opt2 [0.20,0.56,0.50,0.83]; opt3 [0.55,0.56,0.85,0.83]."
},
{
"n": 12,
"type_id": 1,
"question": "How much did Shop A, Shop B and Shop E earn in all?",
"answer0": "$2200",
"answer1": "$2550",
"answer2": "$3350",
"answer3": "$4000",
"correct_answer": 0,
"skill_id": 102,
"difficulty_id": 1,
"explanation": "From the table: A = $900, B = $650, E = $650. Total = 900 + 650 + 650 = $2200.",
"hints": [
"Read the amounts for A, B and E from the table in Q11.",
"Add 900 + 650 + 650."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q12",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 1 = $2200. Uses the same table as Q11."
},
{
"n": 13,
"type_id": 1,
"question": "The figure is made of 6 identical squares. The area of each square is 49 cm$$^2$$. What is the perimeter of the figure?",
"answer0": "42 cm",
"answer1": "84 cm",
"answer2": "96 cm",
"answer3": "98 cm",
"correct_answer": 3,
"skill_id": 138,
"difficulty_id": 3,
"explanation": "Each square has area 49 cm$$^2$$, so side = 7 cm. The figure (two end squares each above/sharing with a middle row) has 14 unit side-lengths along its outline. Perimeter = 14 × 7 = 98 cm.",
"hints": [
"Area 49 = side × side, so each side = 7 cm.",
"Count the exposed unit edges around the whole figure, then multiply by 7."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q13",
"image_needed": true,
"image_options": false,
"image_file": "q13.png",
"image_page": 9,
"image_bbox": [
0.4,
0.39,
0.64,
0.5
],
"image_loc": "centre of page, arrangement of 6 identical squares",
"notes": "Key: option 4 = 98 cm."
},
{
"n": 14,
"type_id": 1,
"question": "A number, when divided by 8, gives a quotient of 123 and a remainder of 5. What is the number?",
"answer0": "615",
"answer1": "979",
"answer2": "984",
"answer3": "989",
"correct_answer": 3,
"skill_id": 117,
"difficulty_id": 2,
"explanation": "Number = divisor × quotient + remainder = 8 × 123 + 5 = 984 + 5 = 989.",
"hints": [
"Number = divisor × quotient + remainder.",
"Compute 8 × 123 = 984, then add the remainder 5."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q14",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 4 = 989."
},
{
"n": 15,
"type_id": 1,
"question": "The table shows the prices of highlighters and pens sold in a shop in June and July.
Highlighter: June $3.50, July $2.80. Pen: June $2.60, July $1.70.
Meiling bought 6 highlighters and 4 pens in June. Nancy bought 6 highlighters and 4 pens in July. How much more money did Meiling spend than Nancy?",
"answer0": "$7.00",
"answer1": "$7.80",
"answer2": "$8.20",
"answer3": "$9.00",
"correct_answer": 1,
"skill_id": 131,
"difficulty_id": 2,
"explanation": "Highlighters are $3.50 − $2.80 = $0.70 cheaper each in July; pens are $2.60 − $1.70 = $0.90 cheaper each. Meiling (June) spends more by 6 × $0.70 + 4 × $0.90 = $4.20 + $3.60 = $7.80.",
"hints": [
"Find the price drop per item from June to July.",
"Multiply each drop by the quantity (6 highlighters, 4 pens) and add."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q15",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 2 = $7.80."
},
{
"n": 16,
"type_id": 2,
"question": "Subtract 386 from 954.
[?]",
"answer0": "568",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 70,
"difficulty_id": 1,
"explanation": "954 − 386 = 568.",
"hints": [
"'Subtract 386 from 954' means 954 − 386.",
"Use column subtraction with regrouping."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q16",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Worked solution shows 568."
},
{
"n": 17,
"type_id": 2,
"question": "Write $$3\\frac{4}{5}$$ as an improper fraction.
[?]",
"answer0": "19/5",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 119,
"difficulty_id": 1,
"explanation": "$$3\\frac{4}{5} = \\frac{3 \\times 5 + 4}{5} = \\frac{19}{5}$$.",
"hints": [
"Multiply the whole number by the denominator, then add the numerator.",
"3 × 5 + 4 = 19, keep denominator 5."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q17",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "FIB fraction answer kept plain: 19/5."
},
{
"n": 18,
"type_id": 2,
"question": "What is the value of $$\\frac{5}{8} + \\frac{3}{4}$$? Express your answer as a mixed number.
[?]",
"answer0": "1 3/8",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 121,
"difficulty_id": 2,
"explanation": "$$\\frac{5}{8} + \\frac{3}{4} = \\frac{5}{8} + \\frac{6}{8} = \\frac{11}{8} = 1\\frac{3}{8}$$.",
"hints": [
"Make the denominators the same: $$\\frac{3}{4} = \\frac{6}{8}$$.",
"Add to get $$\\frac{11}{8}$$, then write as a mixed number."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q18",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "FIB mixed-number answer kept plain: 1 3/8."
},
{
"n": 19,
"type_id": 2,
"question": "How many one-sixths are there in 1 whole?
[?]",
"answer0": "6",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 119,
"difficulty_id": 1,
"explanation": "1 whole = $$\\frac{6}{6}$$, which is 6 sixths. So there are 6 one-sixths in 1 whole.",
"hints": [
"Write 1 whole as a fraction with denominator 6.",
"$$1 = \\frac{6}{6}$$, so there are 6 sixths."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q19",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Worked solution shows 6."
},
{
"n": 20,
"type_id": 2,
"question": "Arrange these numbers from the greatest to the smallest.
0.078 , 0.807 , 0.708
[?] , [?] , [?]",
"answer0": "0.807",
"answer1": "0.708",
"answer2": "0.078",
"answer3": null,
"correct_answer": null,
"skill_id": 124,
"difficulty_id": 2,
"explanation": "Compare tenths first: 0.807 (8 tenths) > 0.708 (7 tenths) > 0.078 (0 tenths). Greatest to smallest: 0.807, 0.708, 0.078.",
"hints": [
"Compare the tenths digit first.",
"8 tenths > 7 tenths > 0 tenths."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q20",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Ordering FIB, greatest first. Key: 0.807, 0.708, 0.078."
},
{
"n": 21,
"type_id": 2,
"question": "$$0.4 = \\frac{4}{[?]}$$
What is the missing number in the box?",
"answer0": "10",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 126,
"difficulty_id": 1,
"explanation": "0.4 means 4 tenths = $$\\frac{4}{10}$$. The missing denominator is 10.",
"hints": [
"0.4 is read as four tenths.",
"Four tenths is written as $$\\frac{4}{10}$$."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q21",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Worked solution shows 10."
},
{
"n": 22,
"type_id": 2,
"question": "Round 16.77 to the nearest whole number.
[?]",
"answer0": "17",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 128,
"difficulty_id": 1,
"explanation": "The tenths digit of 16.77 is 7, which is 5 or more, so round up: 16.77 ≈ 17.",
"hints": [
"Look at the digit after the decimal point (tenths).",
"7 is 5 or more, so round the whole number up."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q22",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Worked solution shows 17 (round up)."
},
{
"n": 23,
"type_id": 2,
"question": "8.87 − 6.54 = [?]",
"answer0": "2.33",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 129,
"difficulty_id": 1,
"explanation": "8.87 − 6.54 = 2.33 (subtract aligning the decimal points).",
"hints": [
"Line up the decimal points.",
"Subtract hundredths, tenths, then ones."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q23",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Worked solution shows 2.33."
},
{
"n": 24,
"type_id": 2,
"question": "Measure and write down the size of ∠x.
[?]",
"answer0": "87",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 140,
"difficulty_id": 2,
"explanation": "Measuring ∠x with a protractor gives 87°.",
"hints": [
"Place the protractor centre on the vertex of ∠x.",
"Read the scale starting from 0° along the base line."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q24",
"image_needed": true,
"image_options": false,
"image_file": "q24.png",
"image_page": 15,
"image_bbox": [
0.36,
0.45,
0.62,
0.72
],
"image_loc": "centre of page, angle marked x between a vertical-ish ray and a horizontal base line",
"notes": "Answer is in degrees; key shows 87. Worked solution gives 87."
},
{
"n": 25,
"type_id": 2,
"question": "WXYZ is a rectangle. Find ∠OXW.
[?]",
"answer0": "53",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 230,
"difficulty_id": 2,
"explanation": "∠WXY is a corner of the rectangle = 90°. The 37° angle is between XO and the side XY, so ∠OXW = 90° − 37° = 53°.",
"hints": [
"A rectangle's corner ∠WXY is 90°.",
"Subtract the given 37° from 90°."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q25",
"image_needed": true,
"image_options": false,
"image_file": "q25.png",
"image_page": 16,
"image_bbox": [
0.3,
0.14,
0.6,
0.28
],
"image_loc": "upper area of page, rectangle WXYZ with point O on side ZY and a 37° angle marked at X",
"notes": "Answer in degrees; key/solution = 53."
},
{
"n": 26,
"type_id": 2,
"question": "The table shows the number of boys and girls in the school field and school hall during a recess. Complete the table.
Boys: School Field 127, School Hall (a), Total 315.
Girls: School Field 208, School Hall 50, Total (b).
(a) [?]
(b) [?]",
"answer0": "188",
"answer1": "258",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 146,
"difficulty_id": 2,
"explanation": "(a) Boys in hall = total boys − boys in field = 315 − 127 = 188. (b) Total girls = 208 + 50 = 258.",
"hints": [
"For (a), subtract the boys in the field from the boys' total.",
"For (b), add the girls in the field and the girls in the hall."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q26",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Two blanks (a) and (b). Key: a=188, b=258. Table data given in stem so no image needed."
},
{
"n": 27,
"type_id": 2,
"question": "When a number is rounded to the nearest hundred, the answer is 1200.
(a) What is the smallest possible whole number?
(b) What is the greatest possible whole number?
(a) [?]
(b) [?]",
"answer0": "1150",
"answer1": "1249",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 109,
"difficulty_id": 2,
"explanation": "Numbers rounding to 1200 to the nearest hundred lie from 1150 up to 1249. (a) Smallest = 1150. (b) Greatest = 1249.",
"hints": [
"The number must round to 1200, so it lies between 1150 and 1249.",
"Smallest rounds up from 1150; greatest is just below 1250, i.e. 1249."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q27",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Two parts. Key: a=1150, b=1249."
},
{
"n": 28,
"type_id": 2,
"question": "Linus wanted to pack 1504 apples. Each box could contain 5 apples. What was the least number of boxes Linus needed to pack all the apples?
[?]",
"answer0": "301",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 117,
"difficulty_id": 2,
"explanation": "1504 ÷ 5 = 300 remainder 4. The 4 leftover apples still need 1 more box, so 300 + 1 = 301 boxes.",
"hints": [
"Divide 1504 by 5 to find full boxes.",
"Any leftover apples need one extra box, so round up."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q28",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Worked solution: 300 r4 → 301 boxes."
},
{
"n": 29,
"type_id": 2,
"question": "Harif spent $17.60 on a shirt. He spent $4.85 more on the shirt than on a pair of shorts. How much did Harif spend altogether?
[?]",
"answer0": "30.35",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 131,
"difficulty_id": 2,
"explanation": "Shorts = $17.60 − $4.85 = $12.75. Altogether = $17.60 + $12.75 = $30.35.",
"hints": [
"Find the cost of the shorts first by subtracting $4.85 from the shirt's price.",
"Add the shirt and shorts prices for the total."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q29",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answer is money; key/solution = $30.35. Enter as 30.35."
},
{
"n": 30,
"type_id": 2,
"question": "The figure is made up of 2 identical squares and 4 identical rectangles. The length of a square is 4 times as long as the breadth of a rectangle. Find the total area of the 4 identical rectangles.
[?]",
"answer0": "240",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 138,
"difficulty_id": 3,
"explanation": "The height 24 cm stacks 1 square (top) over the 4 rectangles is the left column: square side + 4 breadths along the left side equals... taking square side = 8 units of breadth: the left height 24 cm is 1 square side; square side = 4 breadths, so breadth = 24 ÷ (4+ ... ). Using the key: square side = 24 ÷ ... ; given working: 8 units → 24 cm so 1 unit = 3 cm, square side = 4 units = 12 cm... rectangle breadth = 3 cm. Width 32 cm = square length 12 + rectangle length, so rectangle length = 32 − 12 = 20 cm. Area of 1 rectangle = 20 × 3 = 60 cm$$^2$$; 4 rectangles = 60 × 4 = 240 cm$$^2$$.",
"hints": [
"Use the 24 cm height to find the breadth of one rectangle.",
"Find one rectangle's length from the 32 cm width, then area × 4."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q30",
"image_needed": true,
"image_options": false,
"image_file": "q30.png",
"image_page": 18,
"image_bbox": [
0.3,
0.18,
0.66,
0.35
],
"image_loc": "upper-centre of page, composite figure of two squares and four stacked rectangles, marked 24 cm (height) and 32 cm (width)",
"notes": "Answer in cm^2; key/solution = 240. Enter as 240."
},
{
"n": 31,
"type_id": 0,
"question": "Using a protractor and a ruler, draw ∠DEF = 118°. Mark and label the angle. The line DE has been drawn for you.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 140,
"difficulty_id": 2,
"explanation": "Place the protractor centre at E, measure 118° from line ED, mark point F and draw EF. Label the angle ∠DEF = 118°.",
"hints": [],
"source": "Nanyang 2025 P4 End-of-Year Exam Q31",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Construction/drawing task (draw an angle with protractor). No value answer — type_id 0, skipped on insert. Answer: draw ∠DEF = 118° at vertex E."
},
{
"n": 32,
"type_id": 0,
"question": "Draw and label square ABCD on the square grid. One side of the square has been drawn for you.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 143,
"difficulty_id": 2,
"explanation": "Side AB is drawn diagonally across the grid. Complete the square by drawing the other three equal sides at right angles to form square ABCD (each side the same length as AB), labelling C and D.",
"hints": [],
"source": "Nanyang 2025 P4 End-of-Year Exam Q32",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Drawing task on a square grid — type_id 0, skipped on insert. Answer: complete square ABCD using the given diagonal side AB."
},
{
"n": 33,
"type_id": 0,
"question": "The dotted line MN is the line of symmetry. Complete the figure on the square grid to make it symmetrical.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 145,
"difficulty_id": 2,
"explanation": "Reflect the existing shape across the line MN, plotting each point the same number of squares on the opposite side of MN to complete the symmetrical figure.",
"hints": [],
"source": "Nanyang 2025 P4 End-of-Year Exam Q33",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Symmetry-completion drawing task — type_id 0, skipped on insert. Answer: mirror the half-figure across MN."
},
{
"n": 34,
"type_id": 2,
"question": "The pie chart represents a group of children's favourite ice cream flavour. Half of the children like chocolate flavour and vanilla flavour. There is an equal number of children who like strawberry flavour and vanilla flavour.
How many children like mango flavour?
[?]",
"answer0": "33",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 235,
"difficulty_id": 3,
"explanation": "Chocolate (108) + Vanilla (42) = 150, which is half the children, so the total = 300 and the other half (Chocolate Chip + Strawberry + Mango) = 150. Chocolate Chip is a right angle = quarter = 75. Strawberry = Vanilla = 42. Mango = 150 − 75 − 42 = 33.",
"hints": [
"Chocolate + Vanilla make up half, so find the other half's total.",
"Chocolate Chip is a quarter (right angle); Strawberry equals Vanilla. Subtract to get Mango."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q34",
"image_needed": true,
"image_options": false,
"image_file": "q34.png",
"image_page": 20,
"image_bbox": [
0.33,
0.18,
0.66,
0.4
],
"image_loc": "upper-centre of page, pie chart with sectors Strawberry, Mango, Chocolate 108, Vanilla 42, Chocolate Chip (right-angle sector marked)",
"notes": "Key/solution = 33 children."
},
{
"n": 35,
"type_id": 2,
"question": "Jamilah drew a total of 30 squares and triangles. She drew a total of 108 sides. How many triangles did Jamilah draw?
[?]",
"answer0": "12",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "Suppose all 30 are squares: 30 × 4 = 120 sides. Actual sides = 108, a shortfall of 120 − 108 = 12. Each triangle has 1 fewer side than a square (4 − 3 = 1), so number of triangles = 12 ÷ 1 = 12.",
"hints": [
"Assume all 30 figures are squares and count the sides.",
"Each triangle removes 1 side; divide the difference by 1."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q35",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Supposition method. Key/solution = 12 triangles."
},
{
"n": 36,
"type_id": 2,
"question": "The line graph shows the number of buns sold. The data for years 2021 and 2022 was covered by some ink. The increase in number of buns sold from 2020 to 2021 is 4 times as many as the increase in the number of buns sold from 2019 to 2020. Find the number of buns sold in 2021.
[?]",
"answer0": "3250",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 147,
"difficulty_id": 3,
"explanation": "From the graph: 2019 = 750, 2020 = 1250. Increase 2019→2020 = 1250 − 750 = 500. Increase 2020→2021 = 4 × 500 = 2000. Buns in 2021 = 1250 + 2000 = 3250.",
"hints": [
"Read 2019 and 2020 values from the graph, then find their increase.",
"Multiply that increase by 4 and add to the 2020 value."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q36",
"image_needed": true,
"image_options": false,
"image_file": "q36.png",
"image_page": 22,
"image_bbox": [
0.3,
0.27,
0.72,
0.5
],
"image_loc": "centre of page, line graph 'Number of Buns Sold' vs Year (2019-2022) with 2021/2022 hidden by an ink splat; 2019≈750, 2020≈1250",
"notes": "Key/solution = 3250."
},
{
"n": 37,
"type_id": 2,
"question": "The total mass of 5 chickens and 2 ducks is 12.6 kg. The mass of a duck is 2 times as much as the mass of a chicken.
(a) Find the mass of 1 chicken.
(b) Find the total mass of 1 chicken and 1 duck.
(a) [?]
(b) [?]",
"answer0": "1.4",
"answer1": "4.2",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 131,
"difficulty_id": 3,
"explanation": "Each duck = 2 chickens, so 2 ducks = 4 chickens. Total = 5 + 4 = 9 chicken-units = 12.6 kg, so 1 chicken = 12.6 ÷ 9 = 1.4 kg. (b) 1 duck = 1.4 × 2 = 2.8 kg; 1 chicken + 1 duck = 1.4 + 2.8 = 4.2 kg.",
"hints": [
"Express the ducks in terms of chickens to get total units.",
"Divide 12.6 kg by 9 units for one chicken, then build up."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q37",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answers in kg. Key/solution: (a) 1.4 kg, (b) 4.2 kg. Enter as 1.4 and 4.2."
},
{
"n": 38,
"type_id": 2,
"question": "At a library, there were 7 times as many fiction books as non-fiction books. There were 3528 fiction books.
(a) How many more fiction books than non-fiction books were there at the library?
(b) How many books were there altogether in the library?
(a) [?]
(b) [?]",
"answer0": "3024",
"answer1": "4032",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 2,
"explanation": "Fiction = 7 units = 3528, so 1 unit (non-fiction) = 3528 ÷ 7 = 504. (a) More fiction than non-fiction = 6 units = 504 × 6 = 3024. (b) Altogether = 8 units = 504 × 8 = 4032.",
"hints": [
"Fiction is 7 units = 3528; find 1 unit (non-fiction).",
"Difference = 6 units; total = 8 units."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q38",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key/solution: (a) 3024, (b) 4032."
},
{
"n": 39,
"type_id": 2,
"question": "A field was built on a rectangular plot of land. The plot of land measured 24 m by 13 m. A 3-metre wide footpath was built around the field.
(a) Find the area of the footpath.
(b) Find the perimeter of the field.
(a) [?]
(b) [?]",
"answer0": "186",
"answer1": "50",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 138,
"difficulty_id": 3,
"explanation": "Plot area = 24 × 13 = 312 m$$^2$$. The footpath is 3 m wide all around, so the field = (24 − 3 − 3) × (13 − 3 − 3) = 18 × 7 = 126 m$$^2$$. (a) Footpath area = 312 − 126 = 186 m$$^2$$. (b) Perimeter of field = 18 + 7 + 18 + 7 = 50 m.",
"hints": [
"Find the plot's area, then the inner field's dimensions by subtracting 3 m from each side (twice).",
"Footpath area = plot area − field area; field perimeter = 2 × (length + breadth)."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q39",
"image_needed": true,
"image_options": false,
"image_file": "q39.png",
"image_page": 25,
"image_bbox": [
0.3,
0.16,
0.72,
0.36
],
"image_loc": "upper area of page, rectangular plot 24 m by 13 m with a shaded inner field and 3 m footpath border marked",
"notes": "Answers: (a) in m^2 = 186, (b) in m = 50. Enter as 186 and 50."
},
{
"n": 40,
"type_id": 2,
"question": "The figure is made up of two identical rectangles, ABIJ and EFGH, and a square CDHI. JIHG is a straight line. AB = CD = EF.
(a) Find the area of the figure.
(b) Find the perimeter of the figure.
(a) [?]
(b) [?]",
"answer0": "473",
"answer1": "108",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 138,
"difficulty_id": 3,
"explanation": "Total width JG = 33 cm split into 3 equal parts (AB = CD = EF), so each = 33 ÷ 3 = 11 cm. The small square CDHI has side 11 cm minus the 5 cm gap... using the working: area of square CDHI = 11 × 5 = 55. Whole bounding rectangle = 33 × 16 = 528. Figure area = 528 − 55 = 473 cm$$^2$$. (b) Perimeter = 33 + 16 + 33 + 16 + 5 + 5 = 108 cm.",
"hints": [
"Split the 33 cm width into 3 equal widths of 11 cm.",
"Area = full outer rectangle minus the cut-out; trace the outline for the perimeter."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q40",
"image_needed": true,
"image_options": false,
"image_file": "q40.png",
"image_page": 26,
"image_bbox": [
0.3,
0.16,
0.66,
0.34
],
"image_loc": "upper area of page, figure of two rectangles ABIJ and EFGH with square CDHI between them, marked 5 cm, 16 cm and 33 cm",
"notes": "Answers: (a) cm^2 = 473, (b) cm = 108. Enter as 473 and 108."
},
{
"n": 41,
"type_id": 2,
"question": "There were 3 bottles of oil. All 3 bottles had the same amount of oil at first. $$\\frac{1}{8}$$ $$l$$ of oil was poured from bottle A to bottle B. $$\\frac{1}{2}$$ $$l$$ was then poured from bottle B to bottle C. There was $$\\frac{5}{8}$$ $$l$$ of oil in bottle B in the end.
(a) What was the total amount of oil in bottles A, B and C at first?
(b) Each litre of oil cost $7.80. Find the cost of the total amount of oil in bottles A, B and C.
(a) [?]
(b) [?]",
"answer0": "3",
"answer1": "23.40",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 122,
"difficulty_id": 3,
"explanation": "Bottle B at first = X. After receiving $$\\frac{1}{8}$$ and giving away $$\\frac{1}{2}$$: X + $$\\frac{1}{8}$$ − $$\\frac{1}{2}$$ = $$\\frac{5}{8}$$. $$\\frac{1}{8} - \\frac{1}{2} = \\frac{1}{8} - \\frac{4}{8} = -\\frac{3}{8}$$, so X − $$\\frac{3}{8}$$ = $$\\frac{5}{8}$$, giving X = 1 $$l$$. Each bottle started with 1 $$l$$, so total = 1 × 3 = 3 $$l$$. (b) Cost = 3 × $7.80 = $23.40.",
"hints": [
"Set the starting amount in B and track the pour in and pour out.",
"Once one bottle's start is found, multiply by 3, then by $7.80."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q41",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Answers: (a) litres = 3, (b) money = $23.40. Enter as 3 and 23.40."
},
{
"n": 42,
"type_id": 2,
"question": "There were 540 more girls than boys in a school hall. After $$\\frac{3}{4}$$ of the girls and $$\\frac{1}{2}$$ of the boys exited the hall, there was an equal number of boys and girls who remained behind in the hall.
(a) Find the total number of boys and girls who exited the hall.
(b) Find the total number of boys and girls who were in the hall at first.
(a) [?]
(b) [?]",
"answer0": "1080",
"answer1": "1620",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 122,
"difficulty_id": 3,
"explanation": "Let boys = 2 units (so half remain = 1 unit) and girls = 4 units (so a quarter remain = 1 unit) to make the remainders equal. Girls − boys = 4u − 2u = 2u = 540, so 1 unit = 270. Boys = 540, girls = 1080. (a) Exited = half the boys + three-quarters of girls = 270 + 810 = 1080; equivalently 4 units = 270 × 4 = 1080. (b) Total at first = 6 units = 270 × 6 = 1620.",
"hints": [
"Choose units so that the remaining boys and girls are equal (boys 2u, girls 4u).",
"Use the 540 difference to find 1 unit, then total exited and total at first."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q42",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key/solution: (a) 1080, (b) 1620."
},
{
"n": 43,
"type_id": 2,
"question": "Lily baked 2425 more muffins than Jasmine at first. After Jasmine sold 1125 muffins, Lily had 6 times as many muffins as Jasmine in the end.
(a) How many muffins did Jasmine have in the end?
(b) How many muffins did Lily bake at first?
(a) [?]
(b) [?]",
"answer0": "710",
"answer1": "4260",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "Lily is unchanged. In the end Lily = 6 units and Jasmine = 1 unit. Lily − Jasmine (end) = 5 units. The gap grew by the 1125 Jasmine sold: 2425 + 1125 = 3550 = 5 units, so 1 unit = 710. (a) Jasmine in the end = 1 unit = 710. (b) Lily = 6 units = 710 × 6 = 4260.",
"hints": [
"After selling, Lily = 6 units and Jasmine = 1 unit; the difference is 5 units.",
"The original 2425 gap plus the 1125 sold equals 5 units."
],
"source": "Nanyang 2025 P4 End-of-Year Exam Q43",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key/solution: (a) 710, (b) 4260."
}
]
}