{
"paper": {"school":"Tao Nan School","year":2023,"level":"P5","label":"End-of-Year Exam","source_prefix":"Tao Nan 2023 P5 End-of-Year Exam","has_answer_key":true},
"questions": [
{
"n": 1,
"type_id": 1,
"question": "In 9.358, which digit is in the hundredths place?",
"answer0": "9", "answer1": "8", "answer2": "3", "answer3": "5",
"correct_answer": 3,
"skill_id": 123,
"difficulty_id": 1,
"explanation": "In 9.358: 3 is tenths, 5 is hundredths, 8 is thousandths. The digit in the hundredths place is 5.",
"hints": ["The first digit after the decimal point is tenths.", "Hundredths is the second decimal place."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Q1",
"image_needed": false, "image_options": false, "image_file": null,
"notes": "Answer key Q1 = option 4 (=5)."
},
{
"n": 2,
"type_id": 1,
"question": "Dan participated in a school activity from 9 a.m. to 2 p.m. How many hours did the school activity last?",
"answer0": "5", "answer1": "6", "answer2": "7", "answer3": "9",
"correct_answer": 0,
"skill_id": 152,
"difficulty_id": 1,
"explanation": "From 9 a.m. to 2 p.m. is 9 to 12 (3 hours) plus 12 to 2 (2 hours) = 5 hours.",
"hints": ["Count the hours from 9 a.m. to 12 noon.", "Then add the hours from 12 noon to 2 p.m."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Q2",
"image_needed": false, "image_options": false, "image_file": null,
"notes": "Answer key Q2 = option 1 (=5)."
},
{
"n": 3,
"type_id": 1,
"question": "Round 71 809 to the nearest thousand.",
"answer0": "71 000", "answer1": "71 800", "answer2": "71 810", "answer3": "72 000",
"correct_answer": 3,
"skill_id": 150,
"difficulty_id": 1,
"explanation": "The hundreds digit of 71 809 is 8, which is 5 or more, so round up: 71 809 rounds to 72 000.",
"hints": ["Look at the hundreds digit to decide rounding.", "8 hundreds rounds the thousands up."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Q3",
"image_needed": false, "image_options": false, "image_file": null,
"notes": "Answer key Q3 = option 4 (=72 000)."
},
{
"n": 4,
"type_id": 1,
"question": "AB and CD are straight lines. Which of the following is true?",
"answer0": "\\(\\angle w = \\angle y\\)", "answer1": "\\(\\angle x = \\angle z\\)", "answer2": "\\(\\angle w + \\angle y = 180^\\circ\\)", "answer3": "\\(\\angle x + \\angle y + \\angle z = 180^\\circ\\)",
"correct_answer": 1,
"skill_id": 194,
"difficulty_id": 2,
"explanation": "Angles x and z are vertically opposite angles formed by the two straight lines AB and CD, so \\(\\angle x = \\angle z\\).",
"hints": ["Vertically opposite angles are equal.", "Identify which pair of marked angles are vertically opposite."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Q4",
"image_needed": true, "image_page": 3, "image_bbox": [0.55,0.14,0.92,0.27], "image_loc": "two crossing straight lines (AB, CD) with angles w, x, y, z labelled, right of the options",
"image_options": false, "image_file": "q4.png",
"notes": "Answer key Q4 = option 2."
},
{
"n": 5,
"type_id": 1,
"question": "Which of the following is equal to \\(4\\dfrac{5}{6}\\)?",
"answer0": "\\(\\dfrac{29}{6}\\)", "answer1": "\\(\\dfrac{26}{6}\\)", "answer2": "\\(\\dfrac{25}{6}\\)", "answer3": "\\(\\dfrac{20}{6}\\)",
"correct_answer": 0,
"skill_id": 119,
"difficulty_id": 1,
"explanation": "Convert the mixed number: \\(4\\dfrac{5}{6} = \\dfrac{4\\times6+5}{6} = \\dfrac{29}{6}\\).",
"hints": ["Multiply the whole number by the denominator and add the numerator.", "Keep the same denominator."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Q5",
"image_needed": false, "image_options": false, "image_file": null,
"notes": "Fraction options so MCQ. Answer key Q5 = option 1 (=29/6)."
},
{
"n": 6,
"type_id": 1,
"question": "What percentage of the shapes are squares \\(\\square\\)?",
"answer0": "35%", "answer1": "30%", "answer2": "25%", "answer3": "20%",
"correct_answer": 0,
"skill_id": 171,
"difficulty_id": 2,
"explanation": "There are 20 shapes in total and 7 of them are squares. \\(\\dfrac{7}{20} = \\dfrac{35}{100} = 35\\%\\).",
"hints": ["Count the total number of shapes and the number of squares.", "Write the fraction of squares out of 20 and convert to a percentage."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Q6",
"image_needed": true, "image_page": 3, "image_bbox": [0.28,0.58,0.78,0.72], "image_loc": "grid of 20 small shapes (circles, triangles, squares, hexagons) below the question",
"image_options": false, "image_file": "q6.png",
"notes": "20 shapes, 7 squares -> 35%. Answer key Q6 = option 1 (=35%). Count to verify against figure."
},
{
"n": 7,
"type_id": 1,
"question": "Which of the following is the related height of base AC?",
"answer0": "AB", "answer1": "BC", "answer2": "CE", "answer3": "DB",
"correct_answer": 1,
"skill_id": 186,
"difficulty_id": 2,
"explanation": "The height of a triangle is the perpendicular line from the opposite vertex to the base. For base AC, the corresponding height is BC.",
"hints": ["The height is perpendicular to the chosen base.", "Find the segment that meets AC at a right angle from the opposite vertex."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Q7",
"image_needed": true, "image_page": 4, "image_bbox": [0.30,0.10,0.82,0.34], "image_loc": "triangle with vertices A, C, B and points D, E, to the right of the options",
"image_options": false, "image_file": "q7.png",
"notes": "Answer key Q7 = option 2 (=BC)."
},
{
"n": 8,
"type_id": 1,
"question": "Bala has $1200. He saves $800 and spends the remainder. What fraction of his savings is his spending?",
"answer0": "\\(\\dfrac{1}{3}\\)", "answer1": "\\(\\dfrac{2}{5}\\)", "answer2": "\\(\\dfrac{1}{2}\\)", "answer3": "\\(\\dfrac{2}{3}\\)",
"correct_answer": 2,
"skill_id": 157,
"difficulty_id": 2,
"explanation": "Spending = $1200 - $800 = $400. Fraction of savings spent = \\(\\dfrac{400}{800} = \\dfrac{1}{2}\\).",
"hints": ["First find how much he spends.", "Write spending over savings and simplify."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Q8",
"image_needed": false, "image_options": false, "image_file": null,
"notes": "Fraction options so MCQ. Answer key Q8 = option 3 (=1/2)."
},
{
"n": 9,
"type_id": 1,
"question": "At a bookshop, the number of books sold in July is equal to the total number of books sold from April to June. Which of the following bar graphs represents the information correctly?",
"answer0": "Graph 1", "answer1": "Graph 2", "answer2": "Graph 3", "answer3": "Graph 4",
"correct_answer": 1,
"skill_id": 147,
"difficulty_id": 2,
"explanation": "The July bar must equal the sum of the April, May and June bars. Only graph 2 has the July bar length equal to the combined lengths of April, May and June.",
"hints": ["Add the lengths of the April, May and June bars.", "The July bar should match that total."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Q9",
"image_needed": true, "image_page": 5, "image_bbox": [0.18,0.13,0.85,0.95], "image_loc": "four labelled bar-graph options (1)-(4) stacked down the page",
"image_options": true, "image_file": "q9.png",
"notes": "Image-option MCQ: the four options are bar graphs. Answer key Q9 = option 2."
},
{
"n": 10,
"type_id": 1,
"question": "Carl gave away \\(\\dfrac{1}{4}\\) of his stamps and sold 60% of the remainder. What percentage of his stamps was left?",
"answer0": "15%", "answer1": "30%", "answer2": "40%", "answer3": "45%",
"correct_answer": 1,
"skill_id": 175,
"difficulty_id": 2,
"explanation": "After giving away 1/4, 3/4 (75%) remains. He sold 60% of that remainder, so 40% of the remainder is left: 40% of 75% = 0.4 x 75% = 30%.",
"hints": ["Find the percentage left after giving away 1/4.", "Then take 40% (the unsold part) of that remainder."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Q10",
"image_needed": false, "image_options": false, "image_file": null,
"notes": "Answer key Q10 = option 2 (=30%)."
},
{
"n": 11,
"type_id": 1,
"question": "What is the value of \\((2 + 2 \\times 2) + 2 + 2 \\times 2\\)?",
"answer0": "7", "answer1": "8", "answer2": "10", "answer3": "12",
"correct_answer": 0,
"skill_id": 155,
"difficulty_id": 2,
"explanation": "Inside the brackets: 2 + 2x2 = 2 + 4 = 6. Then 6 + 2 + 2x2 = 6 + 2 + 4 = 12. Note: the printed key marks option 1 (=7); using order of operations the value is 12, flagged.",
"hints": ["Do multiplication before addition.", "Work out the bracket first."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Q11",
"image_needed": false, "image_options": false, "image_file": null,
"notes": "Answer key Q11 = option 1 (=7). Honoured the printed key as required (correct_answer index 0). Mathematically (2+2x2)+2+2x2 = 12; possible key/typo or different bracket reading, flagged."
},
{
"n": 12,
"type_id": 1,
"question": "Arrange the following from the lightest to the heaviest:
7.45 kg, \\(7\\dfrac{4}{5}\\) kg, 7 kg 405 g",
"answer0": "7 kg 405 g, 7.45 kg, \\(7\\dfrac{4}{5}\\) kg", "answer1": "7 kg 405 g, \\(7\\dfrac{4}{5}\\) kg, 7.45 kg", "answer2": "\\(7\\dfrac{4}{5}\\) kg, 7.45 kg, 7 kg 405 g", "answer3": "7.45 kg, \\(7\\dfrac{4}{5}\\) kg, 7 kg 405 g",
"correct_answer": 0,
"skill_id": 184,
"difficulty_id": 2,
"explanation": "Convert all to kg: 7 kg 405 g = 7.405 kg; 7.45 kg = 7.45 kg; 7 4/5 kg = 7.8 kg. From lightest to heaviest: 7 kg 405 g, 7.45 kg, 7 4/5 kg.",
"hints": ["Convert every measurement to kilograms in decimal form.", "Order the decimals from smallest to largest."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Q12",
"image_needed": false, "image_options": false, "image_file": null,
"notes": "Options contain fractions so MCQ. Answer key Q12 = option 1."
},
{
"n": 13,
"type_id": 1,
"question": "At a shop, the ratio of the number of erasers to the number of pens to the number of rulers is 5 : 3 : 2. There is a total of 280 erasers and rulers. How many pens are there?",
"answer0": "168", "answer1": "120", "answer2": "105", "answer3": "84",
"correct_answer": 1,
"skill_id": 183,
"difficulty_id": 2,
"explanation": "Erasers + rulers = 5 + 2 = 7 units = 280, so 1 unit = 40. Pens = 3 units = 3 x 40 = 120.",
"hints": ["Add the eraser and ruler units to match 280.", "Find one unit, then multiply by the pen units."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Q13",
"image_needed": false, "image_options": false, "image_file": null,
"notes": "Answer key Q13 = option 2 (=120)."
},
{
"n": 14,
"type_id": 1,
"question": "A rectangular tile is printed with square patterns. The perimeter of the tile is 32 cm. What is the area of each square pattern?",
"answer0": "60 cm²", "answer1": "2 cm²", "answer2": "8 cm²", "answer3": "4 cm²",
"correct_answer": 3,
"skill_id": 138,
"difficulty_id": 3,
"explanation": "The tile is 5 squares wide and 3 squares tall, so its perimeter in side-lengths is 2(5+3) = 16 square-sides = 32 cm, giving each square side = 2 cm. Area of each square = 2 x 2 = 4 cm².",
"hints": ["Count the squares along the length and the width.", "Use the perimeter to find one square's side, then square it."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Q14",
"image_needed": true, "image_page": 7, "image_bbox": [0.30,0.30,0.55,0.40], "image_loc": "rectangle made of a 5-by-3 grid of small squares below the question",
"image_options": false, "image_file": "q14.png",
"notes": "5x3 grid of squares. Answer key Q14 = option 4 (=4 cm2)."
},
{
"n": 15,
"type_id": 1,
"question": "A piece of paper in the shape of an equilateral triangle is folded along the dotted line. Find \\(\\angle y\\).",
"answer0": "18°", "answer1": "20°", "answer2": "24°", "answer3": "42°",
"correct_answer": 2,
"skill_id": 197,
"difficulty_id": 3,
"explanation": "Each angle of the equilateral triangle is 60deg. The fold makes the apex angle 60deg split; after folding, the marked 18deg and y together with the folded portion give y = 60 - 18 - 18 = 24deg.",
"hints": ["An equilateral triangle has all angles 60deg.", "Folding reflects an angle, so equal angles are created at the apex."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Q15",
"image_needed": true, "image_page": 7, "image_bbox": [0.10,0.60,0.92,0.83], "image_loc": "equilateral triangle before folding and after folding (with 18deg and y marked) joined by an arrow",
"image_options": false, "image_file": "q15.png",
"notes": "Answer key Q15 = option 3 (=24deg)."
},
{
"n": 16,
"type_id": 2,
"question": "Express 205 minutes in hours and minutes.
Ans: [?] h [?] min",
"answer0": "3", "answer1": "25", "answer2": null, "answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 1,
"explanation": "205 min = 180 min + 25 min = 3 h 25 min.",
"hints": ["60 minutes make 1 hour.", "Divide 205 by 60 to get the hours and the remaining minutes."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Q16",
"image_needed": false, "image_options": false, "image_file": null,
"notes": "Answer key Q16 = 3h 25min."
},
{
"n": 17,
"type_id": 2,
"question": "Find the value of 902 ÷ 5. Express your answer as a decimal. [?]",
"answer0": "180.4", "answer1": null, "answer2": null, "answer3": null,
"correct_answer": null,
"skill_id": 125,
"difficulty_id": 1,
"explanation": "902 ÷ 5 = 180.4.",
"hints": ["Divide 902 by 5.", "5 goes into 902 a hundred eighty times with remainder 2; 2 ÷ 5 = 0.4."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Q17",
"image_needed": false, "image_options": false, "image_file": null,
"notes": "Answer key Q17 = 180.4."
},
{
"n": 18,
"type_id": 2,
"question": "Express \\(1\\dfrac{3}{20}\\) as a decimal. [?]",
"answer0": "1.15", "answer1": null, "answer2": null, "answer3": null,
"correct_answer": null,
"skill_id": 158,
"difficulty_id": 1,
"explanation": "\\(\\dfrac{3}{20} = \\dfrac{15}{100} = 0.15\\), so \\(1\\dfrac{3}{20} = 1.15\\).",
"hints": ["Convert 3/20 to hundredths.", "Add the whole number 1."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Q18",
"image_needed": false, "image_options": false, "image_file": null,
"notes": "Answer key Q18 = 1.15. Decimal answer so FIB."
},
{
"n": 19,
"type_id": 2,
"question": "What is 8% GST of the school bag? Ans: $[?]",
"answer0": "3.20", "answer1": null, "answer2": null, "answer3": null,
"correct_answer": null,
"skill_id": 176,
"difficulty_id": 1,
"explanation": "Price before GST = $40. 8% of $40 = 0.08 x 40 = $3.20.",
"hints": ["GST is a percentage of the price before GST.", "Work out 8% of $40."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Q19",
"image_needed": true, "image_page": 11, "image_bbox": [0.28,0.10,0.46,0.24], "image_loc": "picture of a school bag labelled $40 (Price before GST)",
"image_options": false, "image_file": "q19.png",
"notes": "Answer key Q19 = $3.20. Price $40 shown only in the figure."
},
{
"n": 20,
"type_id": 2,
"question": "The line graph shows the amount of rice left in a container at the start of each day from Day 1 to Day 4. What is the amount of rice left in the container at the start of Day 2? Ans: [?] kg",
"answer0": "10", "answer1": null, "answer2": null, "answer3": null,
"correct_answer": null,
"skill_id": 147,
"difficulty_id": 1,
"explanation": "Reading the line graph at Day 2, the amount of rice left is 10 kg.",
"hints": ["Find Day 2 on the horizontal axis.", "Read across to the vertical (Amount of rice left) axis."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Q20",
"image_needed": true, "image_page": 11, "image_bbox": [0.18,0.42,0.85,0.70], "image_loc": "line graph of amount of rice left (kg) versus Day 1 to Day 4",
"image_options": false, "image_file": "q20.png",
"notes": "Answer key Q20 = 10 kg. Value must be read from the graph."
},
{
"n": 21,
"type_id": 2,
"question": "Find the value of A in the ratio.
\\(63 : 56 : A = 81 : 72 : 27\\) [?]",
"answer0": "21", "answer1": null, "answer2": null, "answer3": null,
"correct_answer": null,
"skill_id": 181,
"difficulty_id": 2,
"explanation": "63 : 81 = 7 : 9, so the first ratio is the second multiplied by 7/9. A = 27 x 7/9 = 21. (Check: 56 = 72 x 7/9.)",
"hints": ["Find the relationship between 63 and 81.", "Apply the same scaling to 27 to find A."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Q21",
"image_needed": false, "image_options": false, "image_file": null,
"notes": "Answer key Q21 = 21."
},
{
"n": 22,
"type_id": 1,
"question": "The table shows the time taken by 6 runners to complete a race. Who was last in the race?",
"answer0": "B", "answer1": "C", "answer2": "E", "answer3": "F",
"correct_answer": 2,
"skill_id": 124,
"difficulty_id": 2,
"explanation": "The runner who was last took the longest time. Times: A 28.4, B 29.5, C 27.7, D 28.9, E 29.8, F 27.6. The largest time is 29.8 s, which is runner E.",
"hints": ["The last runner has the greatest time.", "Compare the decimals and pick the largest."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Q22",
"image_needed": true, "image_page": 12, "image_bbox": [0.10,0.40,0.40,0.55], "image_loc": "table of Runner (A-F) and Time (s)",
"image_options": false, "image_file": "q22.png",
"notes": "Letter answer (E) so MCQ rather than FIB. Answer key Q22 = E. Table provides the times."
},
{
"n": 23,
"type_id": 2,
"question": "How much does 3.5 kg of durians cost? Ans: $[?]",
"answer0": "70", "answer1": null, "answer2": null, "answer3": null,
"correct_answer": null,
"skill_id": 167,
"difficulty_id": 2,
"explanation": "Durians cost $20/kg. 3.5 kg x $20 = $70.",
"hints": ["The price is $20 for each kilogram.", "Multiply 3.5 by 20."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Q23",
"image_needed": true, "image_page": 12, "image_bbox": [0.10,0.70,0.40,0.90], "image_loc": "SPECIAL OFFER sign with a durian and $20/kg",
"image_options": false, "image_file": "q23.png",
"notes": "Answer key Q23 = $70. Unit price $20/kg shown in the figure."
},
{
"n": 24,
"type_id": 1,
"question": "The figure shows five roads drawn on a map in a square grid.
(a) Name two roads that are parallel to each other.
(b) Name two roads that are perpendicular to each other.",
"answer0": "(a) T and Q; (b) T and S", "answer1": "(a) T and S; (b) T and Q", "answer2": "(a) P and R; (b) T and Q", "answer3": "(a) T and Q; (b) P and R",
"correct_answer": 0,
"skill_id": 194,
"difficulty_id": 2,
"explanation": "Roads T and Q run in the same direction (parallel). Roads T and S meet at right angles (perpendicular).",
"hints": ["Parallel roads never meet and run the same way.", "Perpendicular roads meet at a right angle."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Q24",
"image_needed": true, "image_page": 13, "image_bbox": [0.18,0.10,0.70,0.34], "image_loc": "square grid map showing Roads P, Q, R, S, T",
"image_options": false, "image_file": "q24.png",
"notes": "Two-part road-letter answers so MCQ. Answer key Q24a = T and Q (parallel), Q24b = T and S (perpendicular)."
},
{
"n": 25,
"type_id": 0,
"question": "From the square marked 'A', a chess piece is moved 2 squares south-west and 1 square east. Mark the new position of the chess piece with an 'X'.",
"answer0": null, "answer1": null, "answer2": null, "answer3": null,
"correct_answer": null,
"skill_id": 142,
"difficulty_id": 2,
"explanation": "Move from A down-left (south-west) 2 squares, then 1 square right (east); mark that square with X. See answer key diagram showing the X position.",
"hints": ["South-west means down and to the left.", "Then move one square to the right."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Q25",
"image_needed": true, "image_page": 13, "image_bbox": [0.32,0.55,0.68,0.93], "image_loc": "8x8 chessboard with a square marked A and a north arrow",
"image_options": false, "image_file": "q25.png",
"notes": "Interactive 'mark with X' task - no value answer, so type_id 0 (skipped on insert). Answer key shows X two squares SW and one E of A."
},
{
"n": 26,
"type_id": 1,
"question": "Which box represents the top view of Solid Z?",
"answer0": "Box 1", "answer1": "Box 2", "answer2": "Box 3", "answer3": null,
"correct_answer": 0,
"skill_id": 231,
"difficulty_id": 2,
"explanation": "Looking down on Solid Z from the top gives the L-shaped outline shown in Box 1.",
"hints": ["Imagine looking straight down on the solid.", "Match the footprint of the cubes to one of the grid pictures."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Q26",
"image_needed": true, "image_page": 14, "image_bbox": [0.08,0.10,0.92,0.50], "image_loc": "isometric drawing of Solid Z (top) and three grid boxes (top-view options)",
"image_options": true, "image_file": "q26.png",
"notes": "Image-option MCQ: the three options are top-view grids. Answer key Q26 = Box 1. Solid Z drawing must be shown together with options."
},
{
"n": 27,
"type_id": 2,
"question": "In the scale, round the value marked X to 1 decimal place. Ans: [?]",
"answer0": "10.3", "answer1": null, "answer2": null, "answer3": null,
"correct_answer": null,
"skill_id": 128,
"difficulty_id": 2,
"explanation": "The scale runs from 9 to 11 with 10 small divisions, so each marking is 0.2. X points to about 10.3, which to 1 decimal place is 10.3.",
"hints": ["Work out the value of each small division between 9 and 11.", "Read X then round to 1 decimal place."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Q27",
"image_needed": true, "image_page": 14, "image_bbox": [0.10,0.55,0.55,0.72], "image_loc": "number-line scale from 9 to 11 with an arrow X above it",
"image_options": false, "image_file": "q27.png",
"notes": "Answer key Q27 = 10.3. Scale must be read from the figure."
},
{
"n": 28,
"type_id": 2,
"question": "A repeated pattern is formed using the numbers 0, 1 and 2. The first 13 numbers are: 0, 1, 2, 0, 2, 1, 0, 1, 2, 0, 2, 1, 0. What is the average value of the first 30 numbers? [?]",
"answer0": "1", "answer1": null, "answer2": null, "answer3": null,
"correct_answer": null,
"skill_id": 203,
"difficulty_id": 3,
"explanation": "The pattern repeats every 6 numbers: 0,1,2,0,2,1 with sum 6. In 30 numbers there are 5 complete groups, total = 5 x 6 = 30. Average = 30 ÷ 30 = 1.",
"hints": ["Find the length of the repeating block and its sum.", "Average = total of 30 numbers ÷ 30."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Q28",
"image_needed": false, "image_options": false, "image_file": null,
"notes": "Answer key Q28 = 1. Sequence transcribed verbatim from the strip."
},
{
"n": 29,
"type_id": 2,
"question": "6 jugs of water can fill \\(\\dfrac{5}{8}\\) of a pail. Another 3 jugs and 6 cups of water are needed to fill the pail completely. How many cups of water can the pail hold? [?]",
"answer0": "96",
"answer1": null, "answer2": null, "answer3": null,
"correct_answer": null,
"skill_id": 165,
"difficulty_id": 3,
"explanation": "6 jugs = 5/8 of the pail, so 1 jug = 5/48 of the pail. 3 jugs = 15/48 = 5/16 of the pail. The remaining 1 - 5/8 = 3/8 of the pail is filled by 3 jugs + 6 cups, so 6 cups = 3/8 - 5/16 = 1/16 of the pail. Thus 1/16 pail = 6 cups, so the whole pail = 16 x 6 = 96 cups.",
"hints": ["Find what fraction of the pail one jug fills.", "Work out the fraction the 6 cups fill, then scale up to the whole pail."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Q29",
"image_needed": false, "image_options": false, "image_file": null,
"notes": "Answer key Q29 = 96."
},
{
"n": 30,
"type_id": 2,
"question": "Ali had $36 of 20-cent and 50-cent coins in his piggy bank. There were twice as many 20-cent as 50-cent coins. Find the number of 50-cent coins in the piggy bank. [?]",
"answer0": "40",
"answer1": null, "answer2": null, "answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "Let the number of 50-cent coins be 1 unit; then 20-cent coins = 2 units. Value = 1u x 50c + 2u x 20c = 50c + 40c = 90c per unit. $36 = 3600c, so 3600 ÷ 90 = 40 units. Number of 50-cent coins = 40.",
"hints": ["Group one 50-cent coin with two 20-cent coins.", "Find the value of each group, then divide $36 by it."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Q30",
"image_needed": false, "image_options": false, "image_file": null,
"notes": "Answer key Q30 = 40."
},
{
"n": 31,
"type_id": 2,
"question": "The figure is made up of a rectangle and an equilateral triangle. Find \\(\\angle a\\). Ans: [?]°",
"answer0": "120",
"answer1": null, "answer2": null, "answer3": null,
"correct_answer": null,
"skill_id": 197,
"difficulty_id": 2,
"explanation": "The equilateral triangle has each angle 60deg. \\(\\angle a\\) is on a straight line with the 60deg angle: \\(\\angle a = 180^\\circ - 60^\\circ = 120^\\circ\\).",
"hints": ["Every angle of an equilateral triangle is 60deg.", "Angles on a straight line add to 180deg."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Paper2 Q1",
"image_needed": true, "image_page": 18, "image_bbox": [0.30,0.18,0.75,0.40], "image_loc": "rectangle overlapping an equilateral triangle with angle a marked at the inner corner",
"image_options": false, "image_file": "q31.png",
"notes": "Paper 2 Q1. Answer key: angle a = 180 - 60 = 120 degrees."
},
{
"n": 32,
"type_id": 2,
"question": "Peter was given a sum of money. He gave \\(\\dfrac{4}{5}\\) of the money to his parents and shared the rest of the money equally with his 2 sisters. His parents received $240. How much did Peter receive in the end? Ans: $[?]",
"answer0": "20",
"answer1": null, "answer2": null, "answer3": null,
"correct_answer": null,
"skill_id": 165,
"difficulty_id": 2,
"explanation": "Total = 5 units; parents got 4 units = $240, so 1 unit = $60. The remaining 1 unit ($60) is shared equally among Peter and his 2 sisters (3 people): $60 ÷ 3 = $20.",
"hints": ["Parents received 4/5, so find the value of 1/5.", "Share the last 1/5 among 3 people."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Paper2 Q2",
"image_needed": false, "image_options": false, "image_file": null,
"notes": "Paper 2 Q2. Answer key: 4u=$240, 1u=$60, $60 ÷ 3 = $20."
},
{
"n": 33,
"type_id": 2,
"question": "Ms Lim bought 25 boxes of doughnuts for a party. Each large box contained 12 doughnuts and each small box contained 8 doughnuts. There were 252 doughnuts in all. How many large boxes of doughnuts did she buy? [?]",
"answer0": "13",
"answer1": null, "answer2": null, "answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 2,
"explanation": "Assume all 25 boxes are small: 25 x 8 = 200 doughnuts. Extra needed = 252 - 200 = 52. Each large box has 12 - 8 = 4 more doughnuts. Large boxes = 52 ÷ 4 = 13.",
"hints": ["Assume all boxes are small and find the shortfall.", "Each large box adds 4 doughnuts; divide the shortfall by 4."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Paper2 Q3",
"image_needed": false, "image_options": false, "image_file": null,
"notes": "Paper 2 Q3. Answer key: 13 large boxes."
},
{
"n": 34,
"type_id": 2,
"question": "A tank contains 12.8 ℓ of water. Mr Lee pours 3 pails of water, each containing 0.65 ℓ of water, into the tank without spilling. Find the volume of water in the tank in the end. Ans: [?] ℓ",
"answer0": "14.75",
"answer1": null, "answer2": null, "answer3": null,
"correct_answer": null,
"skill_id": 167,
"difficulty_id": 1,
"explanation": "3 pails = 3 x 0.65 = 1.95 ℓ. Total = 12.8 + 1.95 = 14.75 ℓ.",
"hints": ["Find the total volume poured from 3 pails.", "Add it to the 12.8 ℓ already in the tank."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Paper2 Q4",
"image_needed": false, "image_options": false, "image_file": null,
"notes": "Paper 2 Q4. Answer key: 12.8 + (0.65 x 3) = 14.75 L."
},
{
"n": 35,
"type_id": 1,
"question": "A florist takes 25 minutes to make a bouquet of flowers. How much time is needed to make 9 such bouquets of flowers? Give your answer in hours.",
"answer0": "\\(3\\dfrac{3}{4}\\) h", "answer1": "\\(3\\dfrac{1}{2}\\) h", "answer2": "\\(4\\dfrac{1}{4}\\) h", "answer3": "\\(2\\dfrac{3}{4}\\) h",
"correct_answer": 0,
"skill_id": 152,
"difficulty_id": 2,
"explanation": "25 min x 9 = 225 min. 225 min = 180 min + 45 min = 3 h 45 min = \\(3\\dfrac{3}{4}\\) h.",
"hints": ["Multiply 25 minutes by 9.", "Convert the total minutes into hours."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Paper2 Q5",
"image_needed": false, "image_options": false, "image_file": null,
"notes": "Paper 2 Q5. Answer key: 225 min = 3 3/4 h. Mixed-number answer so MCQ, not FIB."
},
{
"n": 36,
"type_id": 2,
"question": "Mr Tan bought some sweets for his students. When he gave each student 3 sweets, he would have 4 sweets left over. When he gave each student 4 sweets, he would need another 2 sweets. How many sweets did Mr Tan buy? [?]",
"answer0": "22",
"answer1": null, "answer2": null, "answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "Going from 3 to 4 sweets each uses 1 more sweet per student. The 4 left over plus the 2 short = 6 extra sweets needed, so there are 6 students. Sweets = 3 x 6 + 4 = 22 (check: 4 x 6 = 24 = 22 + 2 short).",
"hints": ["The difference between 'left over' and 'short' tells you the number of students.", "Use either case to find the number of sweets."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Paper2 Q6",
"image_needed": false, "image_options": false, "image_file": null,
"notes": "Paper 2 Q6. Answer key (guess and check): 22 sweets."
},
{
"n": 37,
"type_id": 2,
"question": "Bala had 3 m of wire. He cut some of the wire to bend into the shape shown. All the sides are equal in length. He then had 0.4 m of wire left. Find the length of 1 side of the shape. Give your answer in metres, correct to 2 decimal places. Ans: [?] m",
"answer0": "0.22",
"answer1": null, "answer2": null, "answer3": null,
"correct_answer": null,
"skill_id": 132,
"difficulty_id": 2,
"explanation": "Wire used = 3 - 0.4 = 2.6 m. The six-pointed star is made of 12 equal sides, so 1 side = 2.6 ÷ 12 = 0.2166... ≈ 0.22 m.",
"hints": ["First find how much wire was used.", "The star has 12 equal edges; divide and round to 2 decimal places."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Paper2 Q7",
"image_needed": true, "image_page": 20, "image_bbox": [0.36,0.55,0.62,0.72], "image_loc": "six-pointed star (Star of David) outline",
"image_options": false, "image_file": "q37.png",
"notes": "Paper 2 Q7. Answer key: 2.6 ÷ 12 = 0.22 m (12 equal sides of the star)."
},
{
"n": 38,
"type_id": 2,
"question": "Ali needs 1 full tank of spring water for a gardening job. Given that 1 ℓ of spring water costs $0.65, how much money does Ali need for a tank measuring 100 cm by 80 cm by 50 cm? Ans: $[?]",
"answer0": "260",
"answer1": null, "answer2": null, "answer3": null,
"correct_answer": null,
"skill_id": 193,
"difficulty_id": 3,
"explanation": "Volume = 100 x 80 x 50 = 400 000 cm³ = 400 ℓ. Cost = 400 x $0.65 = $260.",
"hints": ["Find the volume in cubic cm, then convert to litres (1000 cm³ = 1 ℓ).", "Multiply the number of litres by $0.65."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Paper2 Q8",
"image_needed": true, "image_page": 21, "image_bbox": [0.30,0.10,0.62,0.25], "image_loc": "cuboid tank with dimensions 100 cm, 80 cm, 50 cm",
"image_options": false, "image_file": "q38.png",
"notes": "Paper 2 Q8. Answer key: 400 L x $0.65 = $260. Dimensions shown in the figure."
},
{
"n": 39,
"type_id": 2,
"question": "Mr Shelby took a bank loan of $90 000 to buy a car. The bank charged him an interest rate of 5% per year. He paid the loan in equal monthly payments over 2 years. What was the amount he had to pay each month? Ans: $[?]",
"answer0": "4125",
"answer1": null, "answer2": null, "answer3": null,
"correct_answer": null,
"skill_id": 176,
"difficulty_id": 3,
"explanation": "Total interest over 2 years = 0.05 x $90 000 x 2 = $9000. Total to repay = $90 000 + $9000 = $99 000. Monthly payment = $99 000 ÷ 24 = $4125.",
"hints": ["Find the interest for 2 years.", "Add it to the loan and divide by 24 months."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Paper2 Q9",
"image_needed": false, "image_options": false, "image_file": null,
"notes": "Paper 2 Q9. Answer key: $99 000 ÷ 24 = $4125."
},
{
"n": 40,
"type_id": 2,
"question": "The figure is not drawn to scale and all lines meet at right angles. Find the perimeter of the figure. Ans: [?] cm",
"answer0": "78",
"answer1": null, "answer2": null, "answer3": null,
"correct_answer": null,
"skill_id": 138,
"difficulty_id": 3,
"explanation": "Using the labelled lengths (4 cm, 3 cm, 5 cm, 5 cm, 15 cm), 15 - 4 = 11 cm. Perimeter = (15 x 2) + (11 x 2) + (5 x 2) + (3 x 2) + (5 x 2) = 30 + 22 + 10 + 6 + 10 = 78 cm.",
"hints": ["Use the given lengths to find the unknown sides.", "Add up all the outer edges."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Paper2 Q10",
"image_needed": true, "image_page": 22, "image_bbox": [0.30,0.10,0.62,0.40], "image_loc": "rectilinear (H-like) figure with right angles, labelled 4 cm, 3 cm, 5 cm, 5 cm, 15 cm",
"image_options": false, "image_file": "q40.png",
"notes": "Paper 2 Q10. Answer key: perimeter = 78 cm. Lengths shown in the figure."
},
{
"n": 41,
"type_id": 1,
"question": "One afternoon, Ahmad, Benny and Charlie took turns to play games on 2 computers from 2 p.m. to 4.30 p.m. At any time, 2 of them played on the computers while the other one watched. Benny and Charlie had the same amount of playing time while Ahmad had 30 minutes more playing time than Benny. Find the ratio of the amount of time Ahmad played to the amount of time Benny played to the amount of time Charlie played. Give your answer in the simplest form.",
"answer0": "4 : 3 : 3", "answer1": "5 : 4 : 4", "answer2": "3 : 2 : 2", "answer3": "12 : 9 : 9",
"correct_answer": 0,
"skill_id": 180,
"difficulty_id": 3,
"explanation": "Total playing time on 2 computers from 2 p.m. to 4.30 p.m. (2.5 h) = 2 x 150 = 300 min. Ahmad = Benny + 30. So Benny + 30 + Benny + Benny = 300, 3 Benny = 270, Benny = 90 min. Charlie = 90, Ahmad = 120. Ratio 120 : 90 : 90 = 4 : 3 : 3.",
"hints": ["Total play time = 2 computers x the duration.", "Let Benny = Charlie and Ahmad = Benny + 30; solve, then simplify the ratio."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Paper2 Q11",
"image_needed": false, "image_options": false, "image_file": null,
"notes": "Paper 2 Q11. Answer key: 120 : 90 : 90 = 4 : 3 : 3. Ratio answer so MCQ."
},
{
"n": 42,
"type_id": 2,
"question": "The heights of 4 children were shown in the table: Aini 1.42 m, Ben 1.43 m, Caleb 1.37 m, Devi 1.26 m.
(a) Find the average height of the 4 children. Give your answer in metres. [?]
(b) The average height of the children became 1.34 m when another child, Eric, joined the group. Find Eric's height. [?]",
"answer0": "1.37", "answer1": "1.22",
"answer2": null, "answer3": null,
"correct_answer": null,
"skill_id": 203,
"difficulty_id": 2,
"explanation": "(a) Average = (1.42 + 1.43 + 1.37 + 1.26) ÷ 4 = 5.48 ÷ 4 = 1.37 m. (b) Total of 5 children = 1.34 x 5 = 6.7 m. Eric = 6.7 - 5.48 = 1.22 m.",
"hints": ["Average = total of heights ÷ number of children.", "For (b), find the new total of 5 children and subtract the first four."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Paper2 Q12",
"image_needed": false, "image_options": false, "image_file": null,
"notes": "Paper 2 Q12 (a)&(b). Answer key: (a) 1.37 m, (b) 1.22 m. Heights given in text so no figure needed."
},
{
"n": 43,
"type_id": 2,
"question": "Mr Lee started making shirts at 9 a.m. He took 1 h 40 min to make each shirt. After making each shirt, he took a 15-min break. He finished making all the shirts at 6.20 p.m. How many shirts did he make? [?]",
"answer0": "5",
"answer1": null, "answer2": null, "answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "Each shirt + break = 1 h 40 min + 15 min = 1 h 55 min = 115 min. Total time 9 a.m. to 6.20 p.m. = 9 h 20 min = 560 min. 560 ÷ 115 = 4 remainder 100 min. The leftover 100 min (= 1 h 40 min) is enough to make 1 more shirt with no break after, giving 5 shirts.",
"hints": ["Each cycle is making time plus a 15-min break.", "After the last shirt there is no break; check if the leftover time fits one more shirt."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Paper2 Q13",
"image_needed": false, "image_options": false, "image_file": null,
"notes": "Paper 2 Q13. Answer key: 5 shirts."
},
{
"n": 44,
"type_id": 2,
"question": "A rectangular tank measures 30 cm by 12 cm by 18 cm.
(a) Given \\(\\dfrac{1}{3}\\) of the tank was filled with water, find the volume of water in the tank. Give your answer in litres. Ans: [?] ℓ
(b) Find the volume of water needed to fill the tank to half its height. Ans: [?] ℓ",
"answer0": "2.16", "answer1": "1.08",
"answer2": null, "answer3": null,
"correct_answer": null,
"skill_id": 191,
"difficulty_id": 3,
"explanation": "Volume of tank = 30 x 12 x 18 = 6480 cm³ = 6480 ml. (a) 1/3 filled = 6480 ÷ 3 = 2160 ml = 2.16 ℓ. (b) Half tank = 6480 ÷ 2 = 3240 ml; water needed = 3240 - 2160 = 1080 ml = 1.08 ℓ (1 ℓ 80 ml).",
"hints": ["Volume = length x breadth x height, then convert to litres.", "For (b) find half the tank volume and subtract the water already in it."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Paper2 Q14",
"image_needed": true, "image_page": 25, "image_bbox": [0.32,0.06,0.66,0.20], "image_loc": "cuboid tank partly filled, dimensions 30 cm, 12 cm, 18 cm",
"image_options": false, "image_file": "q44.png",
"notes": "Paper 2 Q14 (a)&(b). Answer key: (a) 2160 ml = 2.16 L (key writes 2 4/25 L); (b) 1080 ml = 1.08 L (1 L 80 ml). Decimal litres used for FIB."
},
{
"n": 45,
"type_id": 2,
"question": "Four identical triangles are used to form the figure. The triangles have legs 1 cm and 3 cm. Find the unshaded area of the figure. Ans: [?] cm²",
"answer0": "10",
"answer1": null, "answer2": null, "answer3": null,
"correct_answer": null,
"skill_id": 186,
"difficulty_id": 3,
"explanation": "The big square has side 1 + 3 = 4 cm, so its area = 4 x 4 = 16 cm². Each shaded right-angled triangle has area 1/2 x 1 x 3 = 1.5 cm²; the shaded part shown = 2 x (1 x 3) = 6 cm². Unshaded area = 16 - 6 = 10 cm².",
"hints": ["Work out the side of the large square from 1 cm + 3 cm.", "Subtract the shaded triangles' area from the square."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Paper2 Q15",
"image_needed": true, "image_page": 26, "image_bbox": [0.36,0.10,0.66,0.32], "image_loc": "tilted square with four identical shaded triangles at the corners, marked 1 cm and 3 cm",
"image_options": false, "image_file": "q45.png",
"notes": "Paper 2 Q15. Answer key: 16 - 6 = 10 cm2."
},
{
"n": 46,
"type_id": 2,
"question": "The first four figures of a bead pattern are shown. The table gives, for each figure, the number of grey beads, white beads and total beads: Fig 1 (1, 0, 1); Fig 2 (1, 2, 3); Fig 3 (4, 2, 6); Fig 4 (4, 6, 10); Fig 5 ([?] grey, 6 white, [?] total). Find the number of grey beads and the total number of beads for Figure 5.",
"answer0": "9", "answer1": "15",
"answer2": null, "answer3": null,
"correct_answer": null,
"skill_id": 108,
"difficulty_id": 2,
"explanation": "Grey beads follow odd squares: 1, 1, 4, 4, 9 (Fig 5 grey = 9). With 6 white beads, total for Figure 5 = 9 + 6 = 15.",
"hints": ["Look at how the grey-bead count grows across the figures.", "Total = grey beads + white beads."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Paper2 Q16a",
"image_needed": true, "image_page": 27, "image_bbox": [0.10,0.10,0.85,0.20], "image_loc": "row of Figure 1 to Figure 4 bead patterns (grey/white dots)",
"image_options": false, "image_file": "q46.png",
"notes": "Paper 2 Q16(a) (fill table for Figure 5). Answer key: grey = 9, total = 15."
},
{
"n": 47,
"type_id": 2,
"question": "In the bead pattern, the number of white beads in each figure follows the sequence 0, 2, 2, 6, 6, ... where the white beads added grow by even numbers. Find the number of white beads for Figure 21. [?]",
"answer0": "110",
"answer1": null, "answer2": null, "answer3": null,
"correct_answer": null,
"skill_id": 108,
"difficulty_id": 3,
"explanation": "The total white beads for Figure 21 = 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 = 110.",
"hints": ["The white beads added each step form 2, 4, 6, 8, ...", "Sum the added white beads up to Figure 21."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Paper2 Q16b",
"image_needed": false, "image_options": false, "image_file": null,
"notes": "Paper 2 Q16(b). Answer key: 2+4+6+...+20 = 110."
},
{
"n": 48,
"type_id": 1,
"question": "Using the bead pattern, decide each statement. (i) The number of white beads in each figure is always even. (ii) In Figure 32, the ratio of the number of grey beads to the number of white beads is 16 : 17. For each statement, is it True, False or Not possible to tell?",
"answer0": "(i) True, (ii) True", "answer1": "(i) True, (ii) False", "answer2": "(i) False, (ii) True", "answer3": "(i) Not possible to tell, (ii) True",
"correct_answer": 0,
"skill_id": 108,
"difficulty_id": 3,
"explanation": "(i) Every figure's white-bead count is even (0, 2, 2, 6, 6, ...), so True. (ii) For Figure 32 the grey-to-white ratio works out to 16 : 17, so True.",
"hints": ["Check whether each white-bead count is even.", "Compute the grey and white counts for Figure 32 and compare."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Paper2 Q16c",
"image_needed": false, "image_options": false, "image_file": null,
"notes": "Paper 2 Q16(c). Answer key: True, True. Converted true/false statements to a single MCQ."
},
{
"n": 49,
"type_id": 2,
"question": "Caili and Deepa had different amounts of money. After Caili spent 25% of her money and Deepa spent \\(\\dfrac{2}{3}\\) of her money, both of them had the same amount of money left. The total amount of money left was $480. Find the total amount of money they had at first. Ans: $[?]",
"answer0": "1040",
"answer1": null, "answer2": null, "answer3": null,
"correct_answer": null,
"skill_id": 209,
"difficulty_id": 3,
"explanation": "Each had $480 ÷ 2 = $240 left. Caili kept 75% (3/4), so Caili at first = $240 ÷ 3/4 = $320. Deepa kept 1/3, so Deepa at first = $240 ÷ 1/3 = $720. Total at first = $320 + $720 = $1040. (Key working with units: 6u = $480, 1u = $80, 13u = $1040.)",
"hints": ["Each person has the same amount left, so split $480 in two.", "Work each starting amount back from the fraction kept, then add."],
"source": "Tao Nan 2023 P5 End-of-Year Exam Paper2 Q17",
"image_needed": false, "image_options": false, "image_file": null,
"notes": "Paper 2 Q17. Answer key: 13u = $1040."
}
]
}