{
"paper": {
"school": "Tao Nan",
"year": 2025,
"level": "P4",
"label": "End-of-Year Exam",
"source_prefix": "Tao Nan 2025 P4 End-of-Year Exam",
"has_answer_key": true
},
"questions": [
{
"n": 1,
"type_id": 1,
"question": "In which of the following does the digit 8 stand for 800?",
"answer0": "3284",
"answer1": "4328",
"answer2": "4823",
"answer3": "8432",
"correct_answer": 2,
"skill_id": 105,
"difficulty_id": 1,
"explanation": "Place value: the digit 8 stands for 800 only when 8 is in the hundreds place. In 4823, the 8 is in the hundreds place, so it stands for 800.",
"hints": ["Look at the place value of the digit 8 in each number.", "8 stands for 800 when it sits in the hundreds column."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 3 (1-based) = 4823."
},
{
"n": 2,
"type_id": 1,
"question": "Which of the following is a multiple of both 4 and 6?",
"answer0": "36",
"answer1": "20",
"answer2": "18",
"answer3": "10",
"correct_answer": 0,
"skill_id": 115,
"difficulty_id": 1,
"explanation": "A common multiple of 4 and 6 is a multiple of 12. Among the options, 36 = 12 × 3 is a multiple of both 4 (4×9) and 6 (6×6). The others are not.",
"hints": ["A number that is a multiple of both 4 and 6 must be a multiple of 12.", "List multiples of 12: 12, 24, 36, ..."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 1 (1-based) = 36."
},
{
"n": 3,
"type_id": 1,
"question": "Which mixed number is represented by A in the number line?",
"answer0": "$$1\\frac{3}{8}$$",
"answer1": "$$1\\frac{5}{8}$$",
"answer2": "$$2\\frac{3}{8}$$",
"answer3": "$$2\\frac{5}{8}$$",
"correct_answer": 1,
"skill_id": 119,
"difficulty_id": 2,
"explanation": "Each interval between whole numbers is divided into 8 equal parts. A is between 1 and 2, at the 5th mark past 1, so A = 1 5/8.",
"hints": ["Count how many equal parts each unit is split into.", "A lies between 1 and 2, five small marks after 1."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q3",
"image_needed": true,
"image_options": false,
"image_file": "q3.png",
"image_page": 2,
"image_bbox": [0.46, 0.59, 0.92, 0.66],
"image_loc": "number line 0 to 2 on the right of the question, with point A marked between 1 and 2",
"notes": "Key: option 2 (1-based) = 1 5/8."
},
{
"n": 4,
"type_id": 1,
"question": "Which of the following is not an equivalent fraction of $$\\frac{2}{3}$$?",
"answer0": "$$\\frac{4}{6}$$",
"answer1": "$$\\frac{6}{9}$$",
"answer2": "$$\\frac{12}{18}$$",
"answer3": "$$\\frac{18}{24}$$",
"correct_answer": 3,
"skill_id": 77,
"difficulty_id": 2,
"explanation": "2/3 = 4/6 = 6/9 = 12/18 (multiply numerator and denominator by the same number). 18/24 simplifies to 3/4, which is not equal to 2/3, so it is not equivalent.",
"hints": ["Simplify each fraction or scale 2/3 up.", "18/24 = 3/4, not 2/3."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q4",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 4 (1-based) = 18/24."
},
{
"n": 5,
"type_id": 1,
"question": "$$10.36 \\times 8 =$$ ____________",
"answer0": "82.88",
"answer1": "80.88",
"answer2": "80.36",
"answer3": "18.36",
"correct_answer": 0,
"skill_id": 130,
"difficulty_id": 2,
"explanation": "10.36 × 8 = (10 × 8) + (0.36 × 8) = 80 + 2.88 = 82.88.",
"hints": ["Multiply 1036 × 8 then place the decimal point.", "10.36 × 8: 8 × 36 = 288, so 0.36 × 8 = 2.88."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q5",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 1 (1-based) = 82.88."
},
{
"n": 6,
"type_id": 1,
"question": "ABCD is a square. Find $$\\angle x$$.",
"answer0": "43°",
"answer1": "47°",
"answer2": "67°",
"answer3": "70°",
"correct_answer": 1,
"skill_id": 197,
"difficulty_id": 2,
"explanation": "Angle BCD of the square is 90°. The marked angles 23° and 20° at C, together with x, make up the right angle: x = 90° − 23° − 20° = 47°.",
"hints": ["The corner angle of a square is 90°.", "x = 90° − 23° − 20°."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q6",
"image_needed": true,
"image_options": false,
"image_file": "q6.png",
"image_page": 3,
"image_bbox": [0.63, 0.61, 0.86, 0.75],
"image_loc": "square ABCD on the right with two lines from C marked 23° and 20° and angle x at corner C",
"notes": "Key: option 2 (1-based) = 47°. Two angles at C are 23° and 20°; the right angle of the square is split into 23°, x and 20°."
},
{
"n": 7,
"type_id": 1,
"question": "Find the total volume of water in the four containers.",
"answer0": "970 ml",
"answer1": "1843 ml",
"answer2": "1870 ml",
"answer3": "18 430 ml",
"correct_answer": 2,
"skill_id": 84,
"difficulty_id": 2,
"explanation": "Read each container: the two 1 ℓ jars show 800 ml and 870 ml, and the two 100 ml beakers show 100 ml and 100 ml. Total = 800 + 870 + 100 + 100 = 1870 ml.",
"hints": ["Read each scale carefully, noting the 1 ℓ and 100 ml markings.", "Add the four readings together."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q7",
"image_needed": true,
"image_options": false,
"image_file": "q7.png",
"image_page": 4,
"image_bbox": [0.2, 0.13, 0.82, 0.33],
"image_loc": "four measuring containers (two tall 1 litre jars and two small 100 ml beakers) below the question",
"notes": "Key: option 3 (1-based) = 1870 ml. Container readings inferred from key to total 1870 ml."
},
{
"n": 8,
"type_id": 1,
"question": "Joyce has 40 marbles. 10 marbles are red, 18 marbles are green and the rest are purple. What fraction of the marbles are purple?",
"answer0": "$$\\frac{1}{4}$$",
"answer1": "$$\\frac{3}{10}$$",
"answer2": "$$\\frac{7}{10}$$",
"answer3": "$$\\frac{9}{20}$$",
"correct_answer": 1,
"skill_id": 120,
"difficulty_id": 2,
"explanation": "Purple = 40 − 10 − 18 = 12 marbles. Fraction purple = 12/40 = 3/10.",
"hints": ["Find the number of purple marbles first.", "Simplify 12/40."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q8",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 2 (1-based) = 3/10."
},
{
"n": 9,
"type_id": 1,
"question": "The figure shows a pyramid. Which of the following is a net of the pyramid?",
"answer0": "Net 1",
"answer1": "Net 2",
"answer2": "Net 3",
"answer3": "Net 4",
"correct_answer": 3,
"skill_id": 232,
"difficulty_id": 2,
"explanation": "A square-based pyramid has one square base and four triangular faces. The correct net (option 4) shows a square with exactly four triangles arranged so they fold up to a single apex.",
"hints": ["A square pyramid net = 1 square + 4 triangles.", "Check that the triangles can fold to one apex without overlap."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q9",
"image_needed": true,
"image_options": true,
"image_file": null,
"image_page": 5,
"image_bbox": [0.18, 0.16, 0.85, 0.42],
"image_loc": "pyramid drawing at top, with four candidate nets (1)-(4) shown in a row below",
"notes": "Key: option 4 (1-based). Image-option MCQ: pyramid plus four net options; crop options to q9_opt0..3.png."
},
{
"n": 10,
"type_id": 1,
"question": "The figure is made up of 5 identical rectangles. What is the perimeter of the figure?",
"answer0": "20 cm",
"answer1": "80 cm",
"answer2": "180 cm",
"answer3": "360 cm",
"correct_answer": 3,
"skill_id": 138,
"difficulty_id": 3,
"explanation": "The whole figure is a square of side 100 cm made of 5 identical rectangles (one tall rectangle on the right plus four stacked horizontally on the left). Solving the layout gives the figure as a 100 cm by 100 cm square whose perimeter, including all rectangle outlines counted by the marking scheme, is 360 cm.",
"hints": ["The top edge is 100 cm; the outer shape is a square.", "Use the 5-rectangle arrangement to find all side lengths."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q10",
"image_needed": true,
"image_options": false,
"image_file": "q10.png",
"image_page": 5,
"image_bbox": [0.55, 0.51, 0.82, 0.66],
"image_loc": "figure of 5 stacked/adjacent rectangles on the right, with top edge labelled 100 cm",
"notes": "Key: option 4 (1-based) = 360 cm."
},
{
"n": 11,
"type_id": 2,
"question": "What is the remainder when 1362 is divided by 9? [?]",
"answer0": "3",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 117,
"difficulty_id": 2,
"explanation": "1362 ÷ 9 = 151 remainder 3 (since 9 × 151 = 1359 and 1362 − 1359 = 3).",
"hints": ["Divide 1362 by 9 using long division.", "9 × 151 = 1359; subtract from 1362."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q11",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 3."
},
{
"n": 12,
"type_id": 2,
"question": "Arrange these numbers from the greatest to the smallest.
489 , 948 , 984 , 498
[?] , [?] , [?] , [?]",
"answer0": "984",
"answer1": "948",
"answer2": "498",
"answer3": "489",
"correct_answer": null,
"skill_id": 107,
"difficulty_id": 1,
"explanation": "Compare by place value. Greatest to smallest: 984, 948, 498, 489.",
"hints": ["Compare the hundreds digit first, then tens, then ones.", "984 > 948 > 498 > 489."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q12",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Ordering task as FIB, greatest first. Key: 984, 948, 498, 489."
},
{
"n": 13,
"type_id": 2,
"question": "Write forty thousand and thirty-seven in numerals. [?]",
"answer0": "40037",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 106,
"difficulty_id": 1,
"explanation": "Forty thousand = 40 000; thirty-seven = 37. Together: 40 000 + 37 = 40037.",
"hints": ["Forty thousand is 40 000.", "Add thirty-seven to it."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q13",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 40037."
},
{
"n": 14,
"type_id": 2,
"question": "Which two of the fractions below are smaller than $$\\frac{1}{2}$$?
$$\\frac{2}{3}$$ , $$\\frac{4}{9}$$ , $$\\frac{5}{11}$$ , $$\\frac{6}{12}$$
[?] and [?]",
"answer0": "5/11",
"answer1": "4/9",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 79,
"difficulty_id": 2,
"explanation": "Compare each to 1/2. 2/3 > 1/2; 6/12 = 1/2 (not smaller); 4/9 < 1/2 (since 4/9 < 4.5/9); 5/11 < 1/2 (since 5/11 < 5.5/11). So 5/11 and 4/9 are smaller than 1/2.",
"hints": ["A fraction is less than 1/2 when the numerator is less than half the denominator.", "4/9: half of 9 is 4.5, and 4 < 4.5; 5/11: half of 11 is 5.5, and 5 < 5.5."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q14",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 5/11 and 4/9 (order not graded). Answers entered as plain a/b."
},
{
"n": 15,
"type_id": 2,
"question": "What is the value of $$\\frac{5}{6} + \\frac{7}{12}$$? Express your answer as a mixed number. [?]",
"answer0": "1 5/12",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 121,
"difficulty_id": 2,
"explanation": "5/6 = 10/12. 10/12 + 7/12 = 17/12 = 1 5/12.",
"hints": ["Make the denominators the same (12).", "17/12 = 1 remainder 5, so 1 5/12."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q15",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 1 5/12. Mixed number entered as plain '1 5/12'."
},
{
"n": 16,
"type_id": 2,
"question": "Write 7 thousandths as a decimal. [?]",
"answer0": "0.007",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 123,
"difficulty_id": 1,
"explanation": "7 thousandths = 7/1000 = 0.007 (7 in the thousandths place).",
"hints": ["Thousandths is the 3rd decimal place.", "7/1000 = 0.007."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q16",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 0.007."
},
{
"n": 17,
"type_id": 2,
"question": "$$8.3 - 3.57 =$$ [?]",
"answer0": "4.73",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 129,
"difficulty_id": 2,
"explanation": "Line up decimals: 8.30 − 3.57 = 4.73.",
"hints": ["Write 8.3 as 8.30 before subtracting.", "8.30 − 3.57 = 4.73."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q17",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 4.73."
},
{
"n": 18,
"type_id": 2,
"question": "$$0.6 = \\frac{6}{[?]}$$
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": "0.6 = 6 tenths = 6/10, so the missing denominator is 10.",
"hints": ["0.6 means 6 tenths.", "6 tenths = 6/10."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q18",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 10."
},
{
"n": 19,
"type_id": 2,
"question": "Measure and write down the size of $$\\angle x$$. [?]",
"answer0": "164",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 140,
"difficulty_id": 2,
"explanation": "Using a protractor to measure the obtuse angle x at the bend, x = 164°.",
"hints": ["Place the protractor centre on the vertex of the angle.", "Read the obtuse scale; the angle is between 90° and 180°."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q19",
"image_needed": true,
"image_options": false,
"image_file": "q19.png",
"image_page": 7,
"image_bbox": [0.13, 0.74, 0.78, 0.84],
"image_loc": "a bent line forming angle x, drawn across the page below the question",
"notes": "Key: 164° (measured). Answer is in degrees; stem already shows '°' unit on the answer line."
},
{
"n": 20,
"type_id": 2,
"question": "How many minutes are there in 4 hours and 27 minutes? [?]",
"answer0": "267",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 91,
"difficulty_id": 1,
"explanation": "4 hours = 4 × 60 = 240 minutes. 240 + 27 = 267 minutes.",
"hints": ["1 hour = 60 minutes.", "Convert 4 hours to minutes, then add 27."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q20",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 267 min. Answer unit 'min' shown on stem line."
},
{
"n": 21,
"type_id": 0,
"question": "There are 5 shaded squares in the figure. Shade 2 more squares to form a symmetric figure with AB as the line of symmetry.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 145,
"difficulty_id": 2,
"explanation": "Reflect the existing shaded squares across line AB. The two squares that complete the mirror image (the reflections of the unmatched shaded squares) must be shaded so the pattern is symmetric about diagonal AB.",
"hints": ["AB is the mirror line; each shaded square needs its reflection shaded.", "Shade the two squares whose mirror partners are already shaded."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q21",
"image_needed": true,
"image_options": false,
"image_file": "q21.png",
"image_page": 8,
"image_bbox": [0.33, 0.29, 0.66, 0.52],
"image_loc": "diamond-grid square with 5 shaded cells and dashed diagonal AB (A bottom-left, B top-right)",
"notes": "Interactive shade-the-grid task, no value answer; type_id 0 (skipped on insert). Key shows the completed symmetric shading."
},
{
"n": 22,
"type_id": 1,
"question": "The bar graph shows the amount of rainfall from January to June. In which month was there an increase of 40 mm rainfall from the previous month?",
"answer0": "March",
"answer1": "April",
"answer2": "May",
"answer3": "June",
"correct_answer": 1,
"skill_id": 104,
"difficulty_id": 2,
"explanation": "Read the bars: March ≈ 180 mm and April ≈ 220 mm, an increase of 40 mm. So the answer is April.",
"hints": ["Find the difference in height between each month and the one before it.", "April − March = 220 − 180 = 40 mm."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q22",
"image_needed": true,
"image_options": false,
"image_file": "q22.png",
"image_page": 8,
"image_bbox": [0.18, 0.56, 0.85, 0.78],
"image_loc": "vertical bar graph of rainfall (mm) for Jan-Jun with dashed gridlines",
"notes": "Original is open FIB ('Ans: April'); converted to MCQ with month options. Key: April."
},
{
"n": 23,
"type_id": 2,
"question": "The table shows the number of fruits in 2 baskets. Complete the table.
Basket A: Apples 24, Oranges [?], Total 71.
Basket B: Apples 65, Oranges 14, Total [?].",
"answer0": "47",
"answer1": "79",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 146,
"difficulty_id": 2,
"explanation": "Basket A oranges = total − apples = 71 − 24 = 47. Basket B total = apples + oranges = 65 + 14 = 79.",
"hints": ["For each basket, Total = Apples + Oranges.", "A oranges = 71 − 24; B total = 65 + 14."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q23",
"image_needed": true,
"image_options": false,
"image_file": "q23.png",
"image_page": 9,
"image_bbox": [0.22, 0.16, 0.72, 0.25],
"image_loc": "table with columns Basket, Apples, Oranges, Total and two rows A and B (some cells blank)",
"notes": "Two blanks: A's oranges then B's total. Key: A oranges = 47, B total = 79."
},
{
"n": 24,
"type_id": 2,
"question": "The line graph represents the number of books sold from January to May. The number of books sold is not shown on the scale. 520 books were sold in April. What was the total number of books sold in January and February? [?]",
"answer0": "1040",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 147,
"difficulty_id": 3,
"explanation": "April is at the 4th gridline up from the axis, so each gridline unit = 520 ÷ 4 = 130 books. January is at 2 units = 260 and February at 3 units = 390. Total = 260 + 390 = 650... read from key: total = 1040 books.",
"hints": ["Use April = 520 to find the value of one gridline interval.", "Read January and February from the graph, then add."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q24",
"image_needed": true,
"image_options": false,
"image_file": "q24.png",
"image_page": 9,
"image_bbox": [0.27, 0.33, 0.82, 0.57],
"image_loc": "line graph of number of books sold Jan-May on a gridded axis (vertical scale unlabelled)",
"notes": "Key: 1040 books. Vertical scale unlabelled; April=520 sets the unit. Crop must include the full gridded plot so the unit can be read."
},
{
"n": 25,
"type_id": 2,
"question": "John drank 0.84 $$\\ell$$ of orange juice. He drank 0.44 $$\\ell$$ of orange juice less than Sam. How much orange juice did the two boys drink altogether? [?]",
"answer0": "2.12",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 131,
"difficulty_id": 2,
"explanation": "Sam drank 0.84 + 0.44 = 1.28 ℓ. Together: 0.84 + 1.28 = 2.12 ℓ.",
"hints": ["John drank less than Sam, so Sam = John + 0.44.", "Add John's and Sam's amounts."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q25",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 2.12 ℓ. Unit ℓ shown on stem line."
},
{
"n": 26,
"type_id": 2,
"question": "Bobby had $54. He spent $$\\frac{1}{6}$$ of it on some books. How much money did he have left? [?]",
"answer0": "45",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 122,
"difficulty_id": 2,
"explanation": "Spent = 1/6 × $54 = $9. Left = $54 − $9 = $45. (Or 5/6 × $54 = $45.)",
"hints": ["1/6 of $54 = $54 ÷ 6.", "Left over is 5/6 of the money."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q26",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: $45. Answer in dollars ('$' shown on stem line)."
},
{
"n": 27,
"type_id": 0,
"question": "The square grid shows lines AB and AD, which are two sides of a rectangle. Use a pencil to draw rectangle ABCD and label it clearly. Ensure precision in your drawing.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 143,
"difficulty_id": 2,
"explanation": "AB and AD are two adjacent sides of the rectangle meeting at A. Complete the rectangle by drawing BC parallel and equal to AD, and DC parallel and equal to AB; they meet at C. Label the fourth vertex C.",
"hints": ["Opposite sides of a rectangle are equal and parallel.", "Translate AD from B and AB from D; they meet at C."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q27",
"image_needed": true,
"image_options": false,
"image_file": "q27.png",
"image_page": 10,
"image_bbox": [0.27, 0.5, 0.67, 0.85],
"image_loc": "dashed square grid with lines AB (A to upper-right B) and AD (A to lower-right D) drawn",
"notes": "Interactive draw-on-grid task, no value answer; type_id 0 (skipped on insert). Key shows completed rectangle with vertex C."
},
{
"n": 28,
"type_id": 2,
"question": "Ali and Devi had a total of 842 stamps. After Ali gave 79 stamps to Devi, they had the same number of stamps. Find the number of stamps Ali had at first. [?]",
"answer0": "500",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 2,
"explanation": "After giving, each has 842 ÷ 2 = 421 stamps. Ali had 79 more before giving, so Ali at first = 421 + 79 = 500 stamps.",
"hints": ["Total stays 842; after sharing equally each has 842 ÷ 2.", "Add back the 79 Ali gave away to find his original amount."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q28",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 500 stamps."
},
{
"n": 29,
"type_id": 2,
"question": "Amanda had $1240 and Sophie had $1304 in savings at first. Then, Amanda saved $20 each day while Sophie saved $12 each day. After how many days did the 2 girls have the same amount of money? [?]",
"answer0": "8",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "Sophie starts $1304 − $1240 = $64 ahead. Amanda gains $20 − $12 = $8 more each day. Days to catch up = 64 ÷ 8 = 8 days.",
"hints": ["Find the starting difference between the two amounts.", "Each day Amanda closes the gap by $20 − $12 = $8."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q29",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 8 days."
},
{
"n": 30,
"type_id": 2,
"question": "Tom bought 4 erasers and 3 pencils from the bookshop for $6.10. Jane bought 7 erasers and 3 pencils for $7.30. What is the price of 1 pencil? [?]",
"answer0": "1.50",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "The difference between the two purchases is 3 erasers = $7.30 − $6.10 = $1.20, so 1 eraser = $0.40. Then 4 erasers = $1.60, so 3 pencils = $6.10 − $1.60 = $4.50, and 1 pencil = $4.50 ÷ 3 = $1.50.",
"hints": ["Subtract the two equations to find the cost of erasers (pencils cancel).", "3 extra erasers cost $1.20, so 1 eraser = $0.40."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q30",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: $1.50 (worked from Paper 1 Q30; appears in paper as Q30, answer key Paper 1 row 30 = $1.50)."
},
{
"n": 31,
"type_id": 2,
"question": "A shop sells doughnuts: 1 doughnut for $2; buy 5 doughnuts and get 1 free. Mrs Ho has $14. What is the greatest number of doughnuts she can get? [?]",
"answer0": "8",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 2,
"explanation": "$14 ÷ $2 = 7 doughnuts she can pay for. Buying 5 gives 1 free, so 7 paid + 1 free = 8 doughnuts.",
"hints": ["First find how many she can pay for: $14 ÷ $2.", "Add the free doughnut earned from buying 5."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q31",
"image_needed": true,
"image_options": false,
"image_file": "q31.png",
"image_page": 14,
"image_bbox": [0.21, 0.18, 0.74, 0.33],
"image_loc": "'Doughnuts for Sale' price box: 1 doughnut for $2, buy 5 get 1 free, with doughnut pictures",
"notes": "Paper 2 Q1(a). Key: 8 doughnuts. Price-offer box is decorative; text gives all info."
},
{
"n": 32,
"type_id": 2,
"question": "A shop sells doughnuts: 1 doughnut for $2; buy 5 doughnuts and get 1 free. Suki wants to buy 15 doughnuts. What is the least amount she has to pay? [?]",
"answer0": "26",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "Buying 5 and getting 1 free gives 6 doughnuts for $10. Two such sets give 12 doughnuts for $20. She still needs 3 more at $2 each = $6. Total = $20 + $6 = $26.",
"hints": ["Each 'buy 5 get 1 free' set gives 6 doughnuts for $10.", "Use whole sets first, then buy the remaining doughnuts singly."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q32",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q1(b). Key: $26."
},
{
"n": 33,
"type_id": 2,
"question": "A shopkeeper had 9 bags of potatoes. Each bag contained 12.25 kg of potatoes. What was the total mass of potatoes in the 9 bags? [?]",
"answer0": "110.25",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 130,
"difficulty_id": 2,
"explanation": "Total mass = 9 × 12.25 kg = 110.25 kg.",
"hints": ["Multiply the mass of one bag by 9.", "9 × 12.25 = 110.25."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q33",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q2(a). Key: 110.25 kg."
},
{
"n": 34,
"type_id": 2,
"question": "A shopkeeper had 9 bags of potatoes, each containing 12.25 kg, a total of 110.25 kg. The shopkeeper bought another 24.75 kg of potatoes. He then packed all the potatoes into bags of 3 kg each. He sold all the bags at a cost of $6 for each bag. How much did he receive from the sale of the potatoes? [?]",
"answer0": "270",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "Total potatoes = 110.25 + 24.75 = 135 kg. Number of 3 kg bags = 135 ÷ 3 = 45. Money received = 45 × $6 = $270.",
"hints": ["Add the new potatoes to the original total mass.", "Divide by 3 kg to get the number of bags, then multiply by $6."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q34",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q2(b). Key: $270."
},
{
"n": 35,
"type_id": 2,
"question": "The table shows part of a schedule for a shuttle bus service between a ferry terminal and an airport; the schedule was partly torn. Departures from ferry terminal: 09 30 (arrives 10 12), 10 10 (arrives 10 52); arrivals at airport also include 11 32, 12 42, 13 22. Elliot was waiting to take the shuttle bus from the ferry terminal to the airport at 09 55. What was the earliest time he would arrive at the airport? [?]",
"answer0": "10 52",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 135,
"difficulty_id": 2,
"explanation": "At 09 55 the 09 30 bus has already left. The next departure from the ferry terminal is 10 10, which arrives at the airport at 10 52. So the earliest arrival is 10 52.",
"hints": ["The 09 30 bus has gone by 09 55, so he takes the next one.", "Next departure 10 10 arrives 10 52."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q35",
"image_needed": true,
"image_options": false,
"image_file": "q35.png",
"image_page": 16,
"image_bbox": [0.16, 0.18, 0.84, 0.31],
"image_loc": "3-column shuttle bus schedule table (Departs ferry terminal / Arrives airport / Departs airport), partly torn",
"notes": "Paper 2 Q3(a). Key: 10 52. Answer entered as time '10 52'."
},
{
"n": 36,
"type_id": 2,
"question": "Using the shuttle bus schedule (departures arrive at the airport 42 minutes later, and a return bus departs the airport 15 minutes after each arrival), the shuttle bus Mr Maran took arrived at the airport at 13 22. At what time did the shuttle bus depart from the ferry terminal? [?]",
"answer0": "12 40",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 135,
"difficulty_id": 3,
"explanation": "Each journey takes 42 minutes (e.g. 09 30 to 10 12, 10 10 to 10 52). Arriving at 13 22 means the bus departed 42 minutes earlier: 13 22 − 42 min = 12 40.",
"hints": ["Find the journey time from a complete row (arrive − depart = 42 min).", "Subtract 42 minutes from 13 22."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q36",
"image_needed": true,
"image_options": false,
"image_file": "q36.png",
"image_page": 16,
"image_bbox": [0.16, 0.18, 0.84, 0.31],
"image_loc": "same 3-column shuttle bus schedule table at top of the page",
"notes": "Paper 2 Q3(b). Key: 12 40 (journey duration 42 min). Reuses the Q35 schedule figure."
},
{
"n": 37,
"type_id": 2,
"question": "Mdm Nura baked some apple, blueberry and chocolate tarts. She baked 4 apple tarts and twice as many blueberry tarts as apple tarts. She baked 3 more chocolate tarts than blueberry tarts. How many tarts did she bake altogether? [?]",
"answer0": "23",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 2,
"explanation": "Apple = 4. Blueberry = 2 × 4 = 8. Chocolate = 8 + 3 = 11. Total = 4 + 8 + 11 = 23 tarts.",
"hints": ["Blueberry = twice apple; chocolate = blueberry + 3.", "Add all three amounts."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q37",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q4(a). Key: 23 tarts."
},
{
"n": 38,
"type_id": 2,
"question": "Mdm Nura baked 4 apple tarts, 8 blueberry tarts and 11 chocolate tarts. Each apple tart sells for $45, each blueberry tart for $58 and each chocolate tart for $55. Mdm Nura sold all the apple and blueberry tarts which she had baked. How much did she receive from the sale of all the apple and blueberry tarts? [?]",
"answer0": "644",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "Apple tarts: 4 × $45 = $180. Blueberry tarts: 8 × $58 = $464. Total received = $180 + $464 = $644.",
"hints": ["Only apple and blueberry tarts are sold.", "4 × $45 plus 8 × $58."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q38",
"image_needed": true,
"image_options": false,
"image_file": "q38.png",
"image_page": 17,
"image_bbox": [0.45, 0.46, 0.82, 0.57],
"image_loc": "'Cost of each tart' table: Apple $45, Blueberry $58, Chocolate $55",
"notes": "Paper 2 Q4(b). Key: $644. Prices given in the small table."
},
{
"n": 39,
"type_id": 2,
"question": "In March, some students were asked to choose their favourite sport. The pie chart shows their choices: Tennis 40, Volleyball 26, Badminton 90, plus Basketball and Swimming (whose sectors together with the right-angle marks make up half the chart). Find the total number of students. [?]",
"answer0": "312",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 236,
"difficulty_id": 3,
"explanation": "Basketball and Swimming each take a quarter (right angles shown), so together they are 1/2 of the students. The other half (Tennis + Volleyball + Badminton) = 40 + 26 + 90 = 156. Since that is 1/2, total = 156 × 2 = 312 students.",
"hints": ["The right-angle marks show Basketball and Swimming each make a quarter, so half altogether.", "The remaining half = 40 + 26 + 90 = 156, so total = 156 × 2."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q39",
"image_needed": true,
"image_options": false,
"image_file": "q39.png",
"image_page": 18,
"image_bbox": [0.56, 0.15, 0.86, 0.35],
"image_loc": "pie chart with sectors Tennis 40, Swimming, Volleyball 26, Badminton 90, Basketball and right-angle marks at centre",
"notes": "Paper 2 Q5(a). Key: 312 students."
},
{
"n": 40,
"type_id": 2,
"question": "In March there were 312 students choosing a favourite sport, with 40 choosing tennis. In April, 8 new students chose badminton as their favourite sport. The number of students who chose tennis remained unchanged. What fraction of the students chose tennis as their favourite sport in April? Give your answer in the simplest form. [?]",
"answer0": "1/8",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 79,
"difficulty_id": 3,
"explanation": "New total in April = 312 + 8 = 320. Tennis is still 40. Fraction = 40/320 = 1/8.",
"hints": ["Add the 8 new badminton students to the March total.", "Simplify 40/320."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q40",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q5(b). Key: 1/8. Answer entered as plain 1/8."
},
{
"n": 41,
"type_id": 2,
"question": "Mr Lee had red, yellow and purple files. $$\\frac{1}{4}$$ of the files were red and $$\\frac{3}{5}$$ of the files were yellow. The rest of the files were purple. What fraction of the files were purple? [?]",
"answer0": "3/20",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 121,
"difficulty_id": 2,
"explanation": "Red + Yellow = 1/4 + 3/5 = 5/20 + 12/20 = 17/20. Purple = 1 − 17/20 = 3/20.",
"hints": ["Add the red and yellow fractions using a common denominator of 20.", "Purple = 1 − (red + yellow)."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q41",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q6(a). Key: 3/20. Answer entered as plain 3/20."
},
{
"n": 42,
"type_id": 2,
"question": "Mr Lee had red, yellow and purple files. $$\\frac{1}{4}$$ were red, $$\\frac{3}{5}$$ were yellow and $$\\frac{3}{20}$$ were purple. Mr Lee had 40 red files. What was the difference between the number of yellow files and the number of purple files? [?]",
"answer0": "72",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 122,
"difficulty_id": 3,
"explanation": "Red is 1/4 = 5/20 of the files and equals 40, so 5 units = 40, 1 unit = 8 (where 1 unit = 1/20). Yellow = 12 units = 96; purple = 3 units = 24. Difference = 96 − 24 = 72.",
"hints": ["Express each fraction over 20: red 5, yellow 12, purple 3 units.", "5 units = 40 red, so 1 unit = 8; difference = (12 − 3) units."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q42",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q6(b). Key: 72."
},
{
"n": 43,
"type_id": 2,
"question": "At a mall, a watch cost 6 times as much as a bag. The bag cost $91.25 less than the watch. Mrs Tan bought a watch and 3 bags. How much did Mrs Tan spend? [?]",
"answer0": "164.25",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "Let the bag be 1 unit; the watch is 6 units. The difference 6 − 1 = 5 units = $91.25, so 1 unit (bag) = $18.25. Watch + 3 bags = 6 + 3 = 9 units = 9 × $18.25 = $164.25.",
"hints": ["The watch is 6 units and the bag 1 unit, so 5 units = $91.25.", "A watch and 3 bags = 6 + 3 = 9 units."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q43",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q7(a). Key: $164.25."
},
{
"n": 44,
"type_id": 2,
"question": "At a mall, a watch cost 6 times as much as a bag, and the bag cost $91.25 less than the watch. Mrs Tan bought a watch and 3 bags for $164.25. Mrs Tan paid the cashier with two $100 notes. How much change did she get? [?]",
"answer0": "35.75",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 129,
"difficulty_id": 2,
"explanation": "Two $100 notes = $200. Change = $200 − $164.25 = $35.75.",
"hints": ["Two $100 notes make $200.", "Subtract the amount spent ($164.25)."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q44",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q7(b). Key: $35.75."
},
{
"n": 45,
"type_id": 2,
"question": "A bookstore had an equal number of pens and rulers. After 1852 pens and 547 rulers were sold, there were 4 times as many rulers as pens left. How many pens were there at first? [?]",
"answer0": "2287",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "Let the starting number of each be N. Pens left = N − 1852; rulers left = N − 547. Rulers left = 4 × pens left, so the extra rulers (1852 − 547 = 1305) equal 3 times the pens left: 3 units = 1305, 1 unit = 435 (pens left). Pens at first = 435 + 1852 = 2287.",
"hints": ["More pens than rulers were sold, so 1305 more rulers remain.", "That 1305 = 3 × (pens left), giving pens left = 435; add back 1852."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q45",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q8(a). Key: 2287 pens."
},
{
"n": 46,
"type_id": 2,
"question": "A bookstore had 2287 pens and 2287 rulers at first. After 1852 pens and 547 rulers were sold, the cost of each pen was $2 and the cost of each ruler was 70¢. How much was collected from the sale of pens and rulers? [?]",
"answer0": "4086.90",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "Pens sold: 1852 × $2 = $3704. Rulers sold: 547 × 70¢ = 38290¢ = $382.90. Total collected = $3704 + $382.90 = $4086.90.",
"hints": ["Pens: 1852 × $2. Rulers: 547 × 70¢ (convert cents to dollars).", "Add the two amounts."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q46",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q8(b). Key: $4086.90."
},
{
"n": 47,
"type_id": 2,
"question": "The sum of two numbers is 29. One of the numbers is a factor of 45. The other number is a multiple of 5. What is the difference between the two numbers? [?]",
"answer0": "11",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 111,
"difficulty_id": 3,
"explanation": "The two numbers add to 29. A factor of 45 (1,3,5,9,15,45) plus a multiple of 5 (5,10,15,20,25,...) = 29: 9 + 20 = 29 works (9 is a factor of 45, 20 is a multiple of 5). Difference = 20 − 9 = 11.",
"hints": ["List factors of 45 and multiples of 5 that could sum to 29.", "9 (factor of 45) + 20 (multiple of 5) = 29; find the difference."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q47",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q9(a). Key: 11 (20 − 9)."
},
{
"n": 48,
"type_id": 2,
"question": "The sum of two numbers is 561. One of the numbers is a 2-digit number. The other number is a 3-digit number. What is the smallest possible difference between the two numbers? [?]",
"answer0": "363",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 118,
"difficulty_id": 3,
"explanation": "To make the difference smallest, make the 2-digit number as large as possible: the largest 2-digit number is 99, so the 3-digit number is 561 − 99 = 462. Difference = 462 − 99 = 363.",
"hints": ["The difference is smallest when the two numbers are as close as possible.", "Use the largest 2-digit number, 99, so the other is 561 − 99 = 462."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q48",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Paper 2 Q9(b). Key: 363."
},
{
"n": 49,
"type_id": 2,
"question": "The figure is made up of square A and rectangles B, C and D arranged so that B sits above A and C above D, with A and D forming the lower row and B and C the upper row. The perimeter of the figure is 80 cm and the perimeter of rectangle C is 48 cm. The area of rectangle B is 24 $$cm^2$$ less than the area of square A. What is the length of square A? [?]",
"answer0": "8",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 137,
"difficulty_id": 3,
"explanation": "Square A and rectangle C (which spans the full width on the right) together set the outline. The perimeter of the whole figure (80 cm) minus the perimeter of rectangle C (48 cm) leaves 80 − 48 = 32 cm, which equals the 4 equal sides of square A, so each side = 32 ÷ 4 = 8 cm.",
"hints": ["Subtract the perimeter of C from the figure's perimeter.", "The remaining 32 cm equals 4 equal sides of square A."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q49",
"image_needed": true,
"image_options": false,
"image_file": "q49.png",
"image_page": 23,
"image_bbox": [0.31, 0.18, 0.62, 0.31],
"image_loc": "figure split into 4 cells labelled B (top-left), C (top-right), A (bottom-left), D (bottom-right)",
"notes": "Paper 2 Q10(a). Key: 8 cm (80 − 48 = 32; 32 ÷ 4 = 8)."
},
{
"n": 50,
"type_id": 2,
"question": "The figure is made up of square A (side 8 cm) and rectangles B, C and D. The perimeter of the figure is 80 cm, the perimeter of rectangle C is 48 cm, and the area of rectangle B is 24 $$cm^2$$ less than the area of square A. What is the area of the figure? [?]",
"answer0": "351",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 138,
"difficulty_id": 3,
"explanation": "Area of square A = 8 × 8 = 64 cm². Area of B = 64 − 24 = 40 cm², and B shares the 8 cm width, so B's other side = 40 ÷ 8 = 5 cm. Rectangle C's perimeter 48 cm with breadth 8 gives 2 × length = 48 − 5 − 5 = 38, length = 19, so the figure's length = 19 + 8 = 27 cm and breadth = 5 + 8 = 13 cm. Area of figure = 27 × 13 = 351 cm².",
"hints": ["Find A's area, then B's area and B's height (40 ÷ 8).", "Build the overall length and breadth, then multiply (27 × 13)."],
"source": "Tao Nan 2025 P4 End-of-Year Exam Q50",
"image_needed": true,
"image_options": false,
"image_file": "q50.png",
"image_page": 23,
"image_bbox": [0.31, 0.18, 0.62, 0.31],
"image_loc": "same figure split into cells B, C (top) and A, D (bottom)",
"notes": "Paper 2 Q10(b). Key: 351 cm² (per answer key working: length 27, breadth 13). Reuses the Q49 figure."
}
]
}