{
 "paper": {
  "school": "Nan Hua",
  "year": 2023,
  "level": "P4",
  "label": "End of Year Exam",
  "source_prefix": "Nan Hua 2023 P4 End of Year Exam",
  "has_answer_key": true
 },
 "questions": [
  {
   "n": 1,
   "type_id": 1,
   "question": "The value of the digit 5 in 75 412 is [?].",
   "answer0": "50",
   "answer1": "500",
   "answer2": "5000",
   "answer3": "50 000",
   "correct_answer": 2,
   "skill_id": 105,
   "difficulty_id": 1,
   "explanation": "In 75 412, 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: value = 5 × 1000."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q1",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 3 (1-based) = 5000."
  },
  {
   "n": 2,
   "type_id": 1,
   "question": "32 769 rounded to the nearest hundred is [?].",
   "answer0": "32 700",
   "answer1": "32 770",
   "answer2": "32 800",
   "answer3": "33 000",
   "correct_answer": 2,
   "skill_id": 109,
   "difficulty_id": 1,
   "explanation": "Look at the tens digit (6). Since 6 ≥ 5, round the hundreds up: 32 769 → 32 800.",
   "hints": [
    "The hundreds digit is 7; check the tens digit to decide.",
    "Tens digit 6 rounds the hundreds up to 8."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q2",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 3 = 32 800."
  },
  {
   "n": 3,
   "type_id": 1,
   "question": "$$7\\frac{4}{5}$$ = $$\\frac{[?]}{5}$$ <br> What is the missing number in the box?",
   "answer0": "28",
   "answer1": "31",
   "answer2": "35",
   "answer3": "39",
   "correct_answer": 3,
   "skill_id": 119,
   "difficulty_id": 1,
   "explanation": "Convert the mixed number to an improper fraction: 7 × 5 + 4 = 39, so $$7\\frac{4}{5}=\\frac{39}{5}$$. Missing number = 39.",
   "hints": [
    "Multiply the whole number by the denominator, then add the numerator.",
    "7 × 5 + 4 = 39."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q3",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 4 = 39. Numerator box rendered as a blank."
  },
  {
   "n": 4,
   "type_id": 1,
   "question": "Express 0.08 as a fraction in its simplest form.",
   "answer0": "$$\\frac{2}{25}$$",
   "answer1": "$$\\frac{4}{5}$$",
   "answer2": "$$\\frac{1}{10}$$",
   "answer3": "$$\\frac{1}{8}$$",
   "correct_answer": 0,
   "skill_id": 126,
   "difficulty_id": 2,
   "explanation": "0.08 = $$\\frac{8}{100}$$. Divide numerator and denominator by 4: $$\\frac{8}{100}=\\frac{2}{25}$$.",
   "hints": [
    "0.08 means 8 hundredths.",
    "Simplify $$\\frac{8}{100}$$ by dividing both by 4."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q4",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 1 = 2/25."
  },
  {
   "n": 5,
   "type_id": 1,
   "question": "Write $$6\\frac{7}{20}$$ as a decimal.",
   "answer0": "6.72",
   "answer1": "6.7",
   "answer2": "6.35",
   "answer3": "6.072",
   "correct_answer": 2,
   "skill_id": 127,
   "difficulty_id": 2,
   "explanation": "$$\\frac{7}{20}=\\frac{35}{100}=0.35$$. So $$6\\frac{7}{20}=6.35$$.",
   "hints": [
    "Make the denominator 100: $$\\frac{7}{20}=\\frac{35}{100}$$.",
    "$$\\frac{35}{100}=0.35$$, add the whole number 6."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q5",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 3 = 6.35."
  },
  {
   "n": 6,
   "type_id": 1,
   "question": "ABCD is a square. Find ∠x.",
   "answer0": "75°",
   "answer1": "70°",
   "answer2": "55°",
   "answer3": "35°",
   "correct_answer": 2,
   "skill_id": 140,
   "difficulty_id": 3,
   "explanation": "At vertex A the square's corner angle DAB = 90°. The 20° angle and 15° angle are taken off the corner: ∠x = 90° − 20° − 15° = 55°.",
   "hints": [
    "The angle at corner A of a square is 90°.",
    "Subtract the two marked angles (20° and 15°) from 90°."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q6",
   "image_needed": true,
   "image_options": false,
   "image_file": "q6.png",
   "image_page": 4,
   "image_bbox": [
    0.46,
    0.58,
    0.83,
    0.84
   ],
   "image_loc": "right side of page, square ABCD with angles 20° and 15° marked at corner A",
   "notes": "Key: option 3 = 55°."
  },
  {
   "n": 7,
   "type_id": 1,
   "question": "The mass of the box of biscuit is [?].",
   "answer0": "30 g",
   "answer1": "300 g",
   "answer2": "1 kg 30 g",
   "answer3": "1 kg 300 g",
   "correct_answer": 3,
   "skill_id": 449,
   "difficulty_id": 2,
   "explanation": "The scale reads up to 4 kg. The needle points to 1.3 kg, which is 1 kg 300 g.",
   "hints": [
    "Read the position of the needle on the kitchen scale.",
    "1.3 kg = 1 kg 300 g."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q7",
   "image_needed": true,
   "image_options": false,
   "image_file": "q7.png",
   "image_page": 5,
   "image_bbox": [
    0.58,
    0.1,
    0.83,
    0.32
   ],
   "image_loc": "top-right of page, kitchen scale with biscuit box, dial reads 0-4 kg",
   "notes": "Key: option 4 = 1 kg 300 g. Note 'the box of biscuit is' kept verbatim per paper."
  },
  {
   "n": 8,
   "type_id": 1,
   "question": "Which two lines are perpendicular?",
   "answer0": "AB and BC",
   "answer1": "AB and AD",
   "answer2": "AB and DC",
   "answer3": "AD and BC",
   "correct_answer": 1,
   "skill_id": 143,
   "difficulty_id": 2,
   "explanation": "Reading the grid, lines AB and AD meet at a right angle (one runs along grid lines, the other perpendicular to it), so AB ⊥ AD.",
   "hints": [
    "Use the grid squares to spot which two lines form a right angle.",
    "Lines that turn a square corner (90°) are perpendicular."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q8",
   "image_needed": true,
   "image_options": false,
   "image_file": "q8.png",
   "image_page": 5,
   "image_bbox": [
    0.43,
    0.34,
    0.8,
    0.58
   ],
   "image_loc": "middle-right of page, quadrilateral ABCD drawn on a square grid",
   "notes": "Key: option 2 = AB and AD."
  },
  {
   "n": 9,
   "type_id": 1,
   "question": "Which of the following figure has a line of symmetry?",
   "answer0": "Figure 1",
   "answer1": "Figure 2",
   "answer2": "Figure 3",
   "answer3": "Figure 4",
   "correct_answer": 1,
   "skill_id": 145,
   "difficulty_id": 2,
   "explanation": "Figure 2 can be folded along a line so the two halves match exactly, so it has a line of symmetry.",
   "hints": [
    "Try to fold each pattern so both halves overlap.",
    "Only one shaded grid pattern matches when folded."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q9",
   "image_needed": true,
   "image_options": true,
   "image_file": null,
   "image_page": 5,
   "image_bbox": [
    0.1,
    0.62,
    0.9,
    0.82
   ],
   "image_loc": "bottom of page, four shaded grid patterns labelled (1)-(4)",
   "notes": "Key: option 2 = Figure 2. Options ARE pictures; crop each to q9_opt0..3.png."
  },
  {
   "n": 10,
   "type_id": 1,
   "question": "Which of the following figures are symmetrical?",
   "answer0": "A and B",
   "answer1": "A and C",
   "answer2": "B and C",
   "answer3": "B and D",
   "correct_answer": 1,
   "skill_id": 144,
   "difficulty_id": 2,
   "explanation": "The no-entry sign (A) and the sun (C) each have a line of symmetry; the musical note (B) and the dollar sign (D) do not. So A and C are symmetrical.",
   "hints": [
    "A symmetric figure folds onto itself along a line.",
    "The circle/sign and the sun are symmetric; the note and $ are not."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q10",
   "image_needed": true,
   "image_options": false,
   "image_file": "q10.png",
   "image_page": 6,
   "image_bbox": [
    0.1,
    0.12,
    0.9,
    0.32
   ],
   "image_loc": "top of page, four labelled icons A (no-entry), B (music note), C (sun), D (dollar sign)",
   "notes": "Key: option 2 = A and C. Figures labelled A-D; text options reference them."
  },
  {
   "n": 11,
   "type_id": 1,
   "question": "Arrange the following fractions from the greatest to the smallest. <br> $$1\\frac{1}{9}$$ , $$\\frac{11}{7}$$ , $$\\frac{8}{7}$$",
   "answer0": "$$1\\frac{1}{9}$$ , $$\\frac{8}{7}$$ , $$\\frac{11}{7}$$",
   "answer1": "$$\\frac{11}{7}$$ , $$1\\frac{1}{9}$$ , $$\\frac{8}{7}$$",
   "answer2": "$$\\frac{8}{7}$$ , $$1\\frac{1}{9}$$ , $$\\frac{11}{7}$$",
   "answer3": "$$\\frac{11}{7}$$ , $$\\frac{8}{7}$$ , $$1\\frac{1}{9}$$",
   "correct_answer": 3,
   "skill_id": 107,
   "difficulty_id": 2,
   "explanation": "As decimals: $$\\frac{11}{7}\\approx1.57$$, $$\\frac{8}{7}\\approx1.14$$, $$1\\frac{1}{9}\\approx1.11$$. Greatest to smallest: $$\\frac{11}{7}$$, $$\\frac{8}{7}$$, $$1\\frac{1}{9}$$.",
   "hints": [
    "Convert each fraction to a decimal to compare.",
    "1.57 > 1.14 > 1.11."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q11",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 4."
  },
  {
   "n": 12,
   "type_id": 1,
   "question": "Alice is standing at point A facing the stadium. She makes a 225° anticlockwise turn. Where is she facing now?",
   "answer0": "Cinema",
   "answer1": "Food Court",
   "answer2": "School",
   "answer3": "Shopping centre",
   "correct_answer": 0,
   "skill_id": 451,
   "difficulty_id": 3,
   "explanation": "The 8-point compass has 45° between adjacent directions. Starting facing Stadium (S) and turning 225° anticlockwise = 5 steps of 45° anticlockwise, landing on the Cinema (NW direction).",
   "hints": [
    "Each gap between two labels is 45°; 225° = 5 gaps.",
    "Turn 5 positions anticlockwise from Stadium."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q12",
   "image_needed": true,
   "image_options": false,
   "image_file": "q12.png",
   "image_page": 7,
   "image_bbox": [
    0.28,
    0.13,
    0.72,
    0.3
   ],
   "image_loc": "upper-middle of page, 8-point compass diagram with Park/Cinema/Food Court/Market/Library/School/Shopping centre/Stadium labels around point A",
   "notes": "Key: option 1 = Cinema."
  },
  {
   "n": 13,
   "type_id": 1,
   "question": "On Monday, 100 children visited the zoo. The number of children at a zoo decreased by 30 from Monday to Tuesday and increased by 50 from Tuesday to Wednesday. Which graph shows the number of children from Monday to Wednesday?",
   "answer0": "Graph 1",
   "answer1": "Graph 2",
   "answer2": "Graph 3",
   "answer3": "Graph 4",
   "correct_answer": 0,
   "skill_id": 147,
   "difficulty_id": 2,
   "explanation": "Mon=100, Tue=100−30=70 (a dip), Wed=70+50=120 (rises above Monday). Only Graph 1 shows down then up to a higher point.",
   "hints": [
    "Work out the value for each day: 100, 70, 120.",
    "The line should dip on Tuesday then rise past Monday's level."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q13",
   "image_needed": true,
   "image_options": true,
   "image_file": null,
   "image_page": 7,
   "image_bbox": [
    0.1,
    0.45,
    0.9,
    0.78
   ],
   "image_loc": "lower half of page, four line graphs labelled (1)-(4) over Mon/Tue/Wed",
   "notes": "Key: option 1 = Graph 1. Options ARE picture graphs; crop each to q13_opt0..3.png."
  },
  {
   "n": 14,
   "type_id": 1,
   "question": "Abby reached the bus stop at 12.20 p.m. She waited 15 minutes for the bus and the bus journey was 40 minutes. What time did she reach her destination?",
   "answer0": "01 15",
   "answer1": "13 05",
   "answer2": "13 15",
   "answer3": "13 25",
   "correct_answer": 2,
   "skill_id": 135,
   "difficulty_id": 2,
   "explanation": "12.20 p.m. = 1220. Add 15 min wait → 1235. Add 40 min journey → 1315 (in 24-hour time).",
   "hints": [
    "12.20 p.m. is 1220 in 24-hour time.",
    "Add 15 + 40 = 55 minutes to 1220."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q14",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 3 = 13 15."
  },
  {
   "n": 15,
   "type_id": 1,
   "question": "The difference between two numbers is 50. The smaller number is 300. What is the sum of the two numbers?",
   "answer0": "250",
   "answer1": "350",
   "answer2": "550",
   "answer3": "650",
   "correct_answer": 3,
   "skill_id": 118,
   "difficulty_id": 1,
   "explanation": "Larger number = 300 + 50 = 350. Sum = 300 + 350 = 650.",
   "hints": [
    "Find the larger number first: 300 + 50.",
    "Then add both numbers together."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q15",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 4 = 650."
  },
  {
   "n": 16,
   "type_id": 1,
   "question": "A flask contained 2 $$l$$ of hot water. Ms Tan used $$\\frac{3}{4}$$ $$l$$ of the hot water to make chocolate drinks and $$\\frac{7}{8}$$ $$l$$ of the hot water to make coffee. How much water was left in the flask?",
   "answer0": "$$\\frac{3}{8}$$ $$l$$",
   "answer1": "$$1\\frac{1}{4}$$ $$l$$",
   "answer2": "$$1\\frac{5}{8}$$ $$l$$",
   "answer3": "$$3\\frac{5}{8}$$ $$l$$",
   "correct_answer": 0,
   "skill_id": 122,
   "difficulty_id": 2,
   "explanation": "Used = $$\\frac{3}{4}+\\frac{7}{8}=\\frac{6}{8}+\\frac{7}{8}=\\frac{13}{8}=1\\frac{5}{8}$$ l. Left = $$2-1\\frac{5}{8}=\\frac{3}{8}$$ l.",
   "hints": [
    "Add the two amounts used: $$\\frac{3}{4}+\\frac{7}{8}$$.",
    "Subtract the total used from 2 litres."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q16",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 1 = 3/8 l."
  },
  {
   "n": 17,
   "type_id": 1,
   "question": "Find the perimeter of the figure shown. All the lines meet at right angles.",
   "answer0": "68 cm",
   "answer1": "120 cm",
   "answer2": "136 cm",
   "answer3": "864 cm",
   "correct_answer": 2,
   "skill_id": 138,
   "difficulty_id": 3,
   "explanation": "For an L/staircase shape with all right angles, the horizontal sides total twice the overall width and the vertical sides total twice the overall height: perimeter = 2 × 24 + 2 × 36 + the two 8 cm step edges that add to the outline. Adding all boundary segments gives 136 cm.",
   "hints": [
    "With all right angles, opposite horizontal runs sum to the full width and verticals to the full height.",
    "Total the outline: includes the 24 cm top, 36 cm side and the 8 cm notch edges."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q17",
   "image_needed": true,
   "image_options": false,
   "image_file": "q17.png",
   "image_page": 9,
   "image_bbox": [
    0.45,
    0.1,
    0.85,
    0.36
   ],
   "image_loc": "right side of page, right-angled figure with 24 cm width, 36 cm height and two 8 cm notch labels",
   "notes": "Key: option 3 = 136 cm."
  },
  {
   "n": 18,
   "type_id": 1,
   "question": "The figure shows a photo frame that measures 30 cm by 22 cm. A picture is mounted on the frame leaving a border of 1 cm around it. Find the area of the picture.",
   "answer0": "100 cm²",
   "answer1": "560 cm²",
   "answer2": "609 cm²",
   "answer3": "660 cm²",
   "correct_answer": 1,
   "skill_id": 138,
   "difficulty_id": 2,
   "explanation": "Border of 1 cm all round removes 2 cm from each dimension: picture = (30 − 2) × (22 − 2) = 28 × 20 = 560 cm².",
   "hints": [
    "A 1 cm border on each side reduces each dimension by 2 cm.",
    "Picture = 28 × 20."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q18",
   "image_needed": true,
   "image_options": false,
   "image_file": "q18.png",
   "image_page": 9,
   "image_bbox": [
    0.48,
    0.5,
    0.85,
    0.74
   ],
   "image_loc": "lower-right of page, photo frame 30 cm by 22 cm with 1 cm borders and mounted picture",
   "notes": "Key: option 2 = 560 cm²."
  },
  {
   "n": 19,
   "type_id": 1,
   "question": "There are three electric stars on a Christmas tree. The three electric stars will light up every 3 minutes, 4 minutes, and 6 minutes respectively. The three electric stars are switched on and light up together for the 1st time at 10 00. What time will the electric stars light up together for the 3rd time?",
   "answer0": "10 12",
   "answer1": "10 13",
   "answer2": "10 24",
   "answer3": "10 26",
   "correct_answer": 2,
   "skill_id": 115,
   "difficulty_id": 3,
   "explanation": "LCM of 3, 4 and 6 = 12, so they light together every 12 min. 1st at 1000, 2nd at 1012, 3rd at 1024.",
   "hints": [
    "Find the LCM of 3, 4 and 6.",
    "They re-light every 12 min; the 3rd time is 2 × 12 = 24 min after 1000."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q19",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 3 = 10 24. Christmas-tree picture is decorative only, not needed to solve."
  },
  {
   "n": 20,
   "type_id": 1,
   "question": "The table shows the number of books read by 4A and 4B students in a week. <br> Which of the following statement(s) is true? <br> X: The total number of students in 4A is 35. <br> Y: The total number of books read by students in 4B is 37. <br> Z: The total number of books read by students in 4A is 69.",
   "answer0": "X only",
   "answer1": "X and Y",
   "answer2": "X and Z",
   "answer3": "Y and Z",
   "correct_answer": 2,
   "skill_id": 148,
   "difficulty_id": 3,
   "explanation": "Students in 4A = 8 + 20 + 7 = 35 (X true). Books in 4A = 1×8 + 2×20 + 3×7 = 8 + 40 + 21 = 69 (Z true). Books in 4B = 1×10 + 2×18 + 3×9 = 10 + 36 + 27 = 73, not 37 (Y false). So X and Z.",
   "hints": [
    "Number of students = sum of the column. Books = storybooks × students.",
    "Check each statement: X and Z are correct, Y is not."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q20",
   "image_needed": true,
   "image_options": false,
   "image_file": "q20.png",
   "image_page": 10,
   "image_bbox": [
    0.22,
    0.44,
    0.74,
    0.58
   ],
   "image_loc": "middle of page, 3-row table: Number of storybooks (1,2,3), students in 4A (8,20,7), students in 4B (10,18,9)",
   "notes": "Key: option 3 = X and Z. Table content also stated in stem."
  },
  {
   "n": 21,
   "type_id": 2,
   "question": "Some factors of 12 are 1, 2, 3 and 12. What are the other two factors of 12? <br> Ans : [?] and [?]",
   "answer0": "6",
   "answer1": "4",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 111,
   "difficulty_id": 1,
   "explanation": "Factors of 12 are 1, 2, 3, 4, 6, 12. The two not yet listed are 4 and 6.",
   "hints": [
    "List all numbers that divide 12 exactly.",
    "1, 2, 3, 4, 6, 12 — which two are missing?"
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q21",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 6 and 4 (order interchangeable)."
  },
  {
   "n": 22,
   "type_id": 2,
   "question": "4304 ÷ 8 = [?]",
   "answer0": "538",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 117,
   "difficulty_id": 2,
   "explanation": "4304 ÷ 8 = 538 (8 × 538 = 4304).",
   "hints": [
    "Use long division by 8.",
    "Check: 8 × 538 = 4304."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q22",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 538."
  },
  {
   "n": 23,
   "type_id": 2,
   "question": "Write the missing number in the number pattern. <br> 32 400 , 32 000 , 31 600 , 31 200 , [?] , 30 400",
   "answer0": "30800",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 108,
   "difficulty_id": 1,
   "explanation": "The pattern decreases by 400 each step. 31 200 − 400 = 30 800.",
   "hints": [
    "Find the difference between consecutive terms.",
    "Each term is 400 less than the one before."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q23",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 30 800. FIB answer stored without space."
  },
  {
   "n": 24,
   "type_id": 2,
   "question": "What fraction of the buttons shown are grey in colour?",
   "answer0": "1/3",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 120,
   "difficulty_id": 2,
   "explanation": "There are 12 buttons in total and 4 of them are grey, so the fraction = $$\\frac{4}{12}=\\frac{1}{3}$$.",
   "hints": [
    "Count the grey buttons and the total buttons.",
    "Simplify $$\\frac{4}{12}$$."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q24",
   "image_needed": true,
   "image_options": false,
   "image_file": "q24.png",
   "image_page": 11,
   "image_bbox": [
    0.18,
    0.71,
    0.45,
    0.86
   ],
   "image_loc": "lower-left of page, box containing 12 numbered buttons, 4 shaded grey",
   "notes": "Key: 1/3. 4 grey out of 12; crop must show all 12 buttons. FIB fraction answer kept plain."
  },
  {
   "n": 25,
   "type_id": 2,
   "question": "Which two of the fractions are in the simplest form? <br> $$\\frac{2}{5}$$ , $$\\frac{3}{6}$$ , $$\\frac{4}{10}$$ , $$\\frac{5}{12}$$ <br> Ans : [?] and [?]",
   "answer0": "2/5",
   "answer1": "5/12",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 119,
   "difficulty_id": 2,
   "explanation": "A fraction is in simplest form when numerator and denominator share no common factor. $$\\frac{3}{6}=\\frac{1}{2}$$ and $$\\frac{4}{10}=\\frac{2}{5}$$ can be simplified; $$\\frac{2}{5}$$ and $$\\frac{5}{12}$$ cannot.",
   "hints": [
    "Check whether each fraction can be reduced.",
    "3/6 and 4/10 reduce; the other two do not."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q25",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Answer key OCR shows '% and 5/12'; correct simplest-form pair is 2/5 and 5/12 (3/6 and 4/10 are reducible). FIB fraction answers kept plain. Order interchangeable."
  },
  {
   "n": 26,
   "type_id": 2,
   "question": "What is the value of $$\\frac{5}{9}+\\frac{2}{3}$$? Express your answer as a mixed number.",
   "answer0": "1 2/9",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 121,
   "difficulty_id": 2,
   "explanation": "$$\\frac{2}{3}=\\frac{6}{9}$$, so $$\\frac{5}{9}+\\frac{6}{9}=\\frac{11}{9}=1\\frac{2}{9}$$.",
   "hints": [
    "Make the denominators the same (ninths).",
    "$$\\frac{5}{9}+\\frac{6}{9}=\\frac{11}{9}$$, then convert to a mixed number."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q26",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 1 2/9. Mixed-number FIB answer kept plain ('1 2/9')."
  },
  {
   "n": 27,
   "type_id": 2,
   "question": "6.4 − 0.73 = [?]",
   "answer0": "5.67",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 129,
   "difficulty_id": 1,
   "explanation": "Align decimals: 6.40 − 0.73 = 5.67.",
   "hints": [
    "Write 6.4 as 6.40 before subtracting.",
    "6.40 − 0.73 = 5.67."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q27",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 5.67."
  },
  {
   "n": 28,
   "type_id": 2,
   "question": "Find the value of 4.72 × 6.",
   "answer0": "28.32",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 130,
   "difficulty_id": 1,
   "explanation": "4.72 × 6 = 28.32.",
   "hints": [
    "Multiply 472 × 6 then place the decimal point.",
    "472 × 6 = 2832 → 28.32."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q28",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 28.32."
  },
  {
   "n": 29,
   "type_id": 2,
   "question": "Write the decimal represented by A.",
   "answer0": "0.57",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 123,
   "difficulty_id": 2,
   "explanation": "The number line from 0.5 to 0.6 is divided into 10 equal parts of 0.01 each. A is at the 7th mark from 0.5, so A = 0.57.",
   "hints": [
    "Each small interval between 0.5 and 0.6 is 0.01.",
    "Count the marks from 0.5 to A."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q29",
   "image_needed": true,
   "image_options": false,
   "image_file": "q29.png",
   "image_page": 13,
   "image_bbox": [
    0.25,
    0.12,
    0.72,
    0.24
   ],
   "image_loc": "top of page, number line marked 0.5 to 0.6 with arrow A at the 7th tick",
   "notes": "Key: 0.57."
  },
  {
   "n": 30,
   "type_id": 0,
   "question": "Use a protractor and draw ∠ABC = 100° using the given line. Mark and label the point C.",
   "answer0": null,
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 140,
   "difficulty_id": 2,
   "explanation": "Place the protractor centre on B, baseline along BA, mark 100°, draw ray BC. (Construction/drawing task.)",
   "hints": [
    "Centre the protractor at B with 0° along BA.",
    "Mark 100° and draw the ray to point C."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q30",
   "image_needed": true,
   "image_options": false,
   "image_file": "q30.png",
   "image_page": 13,
   "image_bbox": [
    0.28,
    0.5,
    0.62,
    0.58
   ],
   "image_loc": "middle of page, given horizontal line segment labelled A (left) and B (right)",
   "notes": "Interactive draw/construct task — no value answer. type_id 0, skipped on insert. Key shows angle ABC = 100° drawn."
  },
  {
   "n": 31,
   "type_id": 2,
   "question": "The table shows the times taken by four girls to complete a 100 m race. <br> Amy: 16.1 , Bess: 17.0 , Cleo: 15.8 , Dawn: 15.9 (time in seconds) <br> Write down the names of the girls from the 1st to the 4th position. <br> Ans : [?] (1st) , [?] , [?] , [?] (4th)",
   "answer0": "Cleo",
   "answer1": "Dawn",
   "answer2": "Amy",
   "answer3": "Bess",
   "correct_answer": null,
   "skill_id": 124,
   "difficulty_id": 2,
   "explanation": "The fastest runner (smallest time) is 1st. Times: Cleo 15.8 < Dawn 15.9 < Amy 16.1 < Bess 17.0. So 1st Cleo, 2nd Dawn, 3rd Amy, 4th Bess.",
   "hints": [
    "The shortest time wins the race (1st position).",
    "Order the times from smallest to largest."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q31",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: Cleo, Dawn, Amy, Bess. Ordering converted to 4-blank FIB."
  },
  {
   "n": 32,
   "type_id": 2,
   "question": "In a factory, sweets are equally packed into boxes. Bill bought two boxes of sweets. He received 1044 sweets altogether. How many sweets would Bill receive in total, if he buys five more boxes of sweets?",
   "answer0": "3654",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 118,
   "difficulty_id": 2,
   "explanation": "2 boxes = 1044, so 1 box = 1044 ÷ 2 = 522. Total boxes = 2 + 5 = 7. Total sweets = 7 × 522 = 3654.",
   "hints": [
    "Find the number of sweets in one box first.",
    "He has 2 + 5 = 7 boxes in total."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q32",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 3654 (1 box = 522; 7 boxes × 522)."
  },
  {
   "n": 33,
   "type_id": 0,
   "question": "In the grid, draw and label the square ABCD. Lines AB and BC have been drawn for you.",
   "answer0": null,
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 143,
   "difficulty_id": 2,
   "explanation": "Complete the square by drawing CD parallel and equal to AB and DA parallel and equal to BC, so ABCD is a square with all sides equal and right angles. (Drawing task.)",
   "hints": [
    "AB and BC are two sides of the square — equal length, meeting at 90°.",
    "Draw the remaining two sides to close the square and label D."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q33",
   "image_needed": true,
   "image_options": false,
   "image_file": "q33.png",
   "image_page": 14,
   "image_bbox": [
    0.22,
    0.5,
    0.68,
    0.84
   ],
   "image_loc": "lower-middle of page, square grid with points A, B (line AB-BC drawn) and C marked",
   "notes": "Interactive draw task — no value answer. type_id 0, skipped on insert."
  },
  {
   "n": 34,
   "type_id": 2,
   "question": "What was the total number of chocolates sold between 11 00 to 13 00?",
   "answer0": "152",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 147,
   "difficulty_id": 2,
   "explanation": "From the line graph, chocolates sold at 1200 = 62 and at 1300 = 90. Total between 11 00 and 13 00 = 62 + 90 = 152.",
   "hints": [
    "Read the graph values for the hours after 11 00.",
    "62 + 90 = 152."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q34",
   "image_needed": true,
   "image_options": false,
   "image_file": "q34.png",
   "image_page": 15,
   "image_bbox": [
    0.22,
    0.18,
    0.78,
    0.45
   ],
   "image_loc": "upper-middle of page, line graph of number of chocolates sold from 10 00 to 15 00 (shared with Q35)",
   "notes": "Key: 62 + 90 = 152. Graph shared between Q34 and Q35."
  },
  {
   "n": 35,
   "type_id": 2,
   "question": "In which one-hour interval was the increase in the number of chocolates sold the greatest? <br> Ans : [?] to [?]",
   "answer0": "1100",
   "answer1": "1200",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 147,
   "difficulty_id": 2,
   "explanation": "Hourly values: 1000=0, 1100=18, 1200=62, 1300=90. Increases: 18, 44, 28. The greatest rise (44) is from 11 00 to 12 00.",
   "hints": [
    "Find the increase for each one-hour step.",
    "The steepest upward segment is 11 00 to 12 00."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q35",
   "image_needed": true,
   "image_options": false,
   "image_file": "q34.png",
   "image_page": 15,
   "image_bbox": [
    0.22,
    0.18,
    0.78,
    0.45
   ],
   "image_loc": "upper-middle of page, same line graph as Q34",
   "notes": "Key: 1100 to 1200. Two-blank FIB (start time, end time). Shares Q34 graph image."
  },
  {
   "n": 36,
   "type_id": 0,
   "question": "The table shows the total value of the coins in the piggy bank. The graph shows the number of coins in the piggy bank. Label the bar graph by writing T for twenty-cent coins, F for fifty-cent coins and O for one-dollar coins in the boxes.",
   "answer0": null,
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 148,
   "difficulty_id": 3,
   "explanation": "Number of coins = total value ÷ coin value. 20-cent: $2 ÷ $0.20 = 10 coins. 50-cent: $2 ÷ $0.50 = 4 coins. $1: $4 ÷ $1 = 4 coins. The tallest bar (10) = T (twenty-cent), and the two equal shorter bars are F and O. Per key, the bars label as D/F/T order shown — from left: $1 (O), 50-cent (F), 20-cent (T).",
   "hints": [
    "Coins = total value ÷ value of one coin.",
    "20-cent gives the most coins (10), so its bar is the tallest = T."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q36",
   "image_needed": true,
   "image_options": false,
   "image_file": "q36.png",
   "image_page": 16,
   "image_bbox": [
    0.5,
    0.24,
    0.8,
    0.42
   ],
   "image_loc": "upper-right of page, bar graph 'Number of coins' with three bars and label boxes beneath",
   "notes": "Interactive label-the-bars task — no single value answer. type_id 0, skipped on insert. Key: bars labelled O, F, T (left to right) i.e. tallest 20-cent = T."
  },
  {
   "n": 37,
   "type_id": 2,
   "question": "James took a flight from Singapore to Taiwan. The plane left Singapore 20 min before midnight and he arrived in Taiwan at 04 50. What is the duration of the flight? <br> Ans : [?] h [?] min",
   "answer0": "5",
   "answer1": "10",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 135,
   "difficulty_id": 2,
   "explanation": "20 min before midnight = 2340. From 2340 to 2400 is 20 min; from 0000 to 0450 is 4 h 50 min. Total = 4 h 50 min + 20 min = 5 h 10 min.",
   "hints": [
    "20 min before midnight is 2340 (23 50? — 23 40).",
    "Count to midnight, then add the time to 04 50."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q37",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 5 h 10 min. Two-blank FIB (hours, minutes)."
  },
  {
   "n": 38,
   "type_id": 2,
   "question": "A number is between 30 and 40. When it is divided by 3, the answer is a whole number. When it is divided by 4, the remainder is 3. What is the number?",
   "answer0": "39",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 114,
   "difficulty_id": 2,
   "explanation": "Multiples of 3 between 30 and 40: 30, 33, 36, 39. Check remainder 3 when divided by 4: 39 ÷ 4 = 9 R3. So the number is 39.",
   "hints": [
    "List multiples of 3 in the range 30-40.",
    "Test which one leaves remainder 3 when divided by 4."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q38",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 39 (39 ÷ 4 = 9 R3)."
  },
  {
   "n": 39,
   "type_id": 1,
   "question": "At the school bookshop: Stapler $5, Scissors $8, Ruler $3. Bess spent a total of $31 at the school book shop. She bought 3 identical [?] and 2 identical [?].",
   "answer0": "scissors",
   "answer1": "staplers",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 118,
   "difficulty_id": 3,
   "explanation": "Try combinations totalling $31: 3 × scissors ($8) = $24, plus 2 × staplers ($5) = $10... that is $34. Re-check key: 3 scissors ($24) + ... The marked key circles 'staplers' in the first blank and 'scissors' in the second: 3 staplers ($15) + 2 scissors ($16) = $31. So she bought 3 staplers and 2 scissors.",
   "hints": [
    "Set up 3 × (one item) + 2 × (another item) = $31.",
    "3 × $5 + 2 × $8 = 15 + 16 = $31."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q39",
   "image_needed": true,
   "image_options": false,
   "image_file": "q39.png",
   "image_page": 17,
   "image_bbox": [
    0.12,
    0.13,
    0.83,
    0.27
   ],
   "image_loc": "top of page, three labelled items: Stapler $5, Scissors $8, Ruler $3",
   "notes": "Original is circle-the-correct-word (interactive). Converted to 2-blank choose-the-item FIB. Key circles 3 staplers and 2 scissors: 3×$5 + 2×$8 = $31. answer0=staplers (3 identical), answer1=scissors (2 identical)."
  },
  {
   "n": 40,
   "type_id": 2,
   "question": "28 flags were placed around a square field at equal distance apart. The number of flags on each side of the field is the same. There is a flag at every corner of the field. How many flags are there on each side of the field?",
   "answer0": "8",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 118,
   "difficulty_id": 3,
   "explanation": "The 4 corner flags are shared between sides. 28 ÷ 4 = 7 gaps... using corner sharing: 28 ÷ 4 = 7 flags per side excluding one corner; adding the shared corner gives 7 + 1 = 8 flags on each side.",
   "hints": [
    "The 4 corners are counted once but belong to two sides each.",
    "28 ÷ 4 = 7, then add 1 for the shared corner: 8 per side."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q40",
   "image_needed": true,
   "image_options": false,
   "image_file": "q40.png",
   "image_page": 17,
   "image_bbox": [
    0.14,
    0.58,
    0.5,
    0.84
   ],
   "image_loc": "lower-left of page, square 'Field' with two flags at a corner and '? flags' marking one side",
   "notes": "Key: 28 ÷ 4 = 7, 7 + 1 = 8 flags per side."
  },
  {
   "n": 41,
   "type_id": 2,
   "question": "Bill is 4 times as heavy as Charlotte. He is 98.4 kg. What is the total mass of Bill and Charlotte?",
   "answer0": "123",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 131,
   "difficulty_id": 2,
   "explanation": "Bill = 4 units = 98.4 kg, so 1 unit (Charlotte) = 98.4 ÷ 4 = 24.6 kg. Total = 5 units = 5 × 24.6 = 123 kg.",
   "hints": [
    "Let Charlotte = 1 unit, Bill = 4 units = 98.4 kg.",
    "Total = 5 units; find 1 unit first."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q41",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 123 (kg). 5 units × 24.6."
  },
  {
   "n": 42,
   "type_id": 2,
   "question": "Ben had a piece of string. He cut it into three pieces, String A, String B and String C. String B is 0.15 m longer than String A and 2.7 m longer than String C. String A is 4.36 m long. What is the length of String C?",
   "answer0": "1.81",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 131,
   "difficulty_id": 3,
   "explanation": "String B = String A + 0.15 = 4.36 + 0.15 = 4.51 m. String C = String B − 2.7 = 4.51 − 2.7 = 1.81 m.",
   "hints": [
    "Find String B from String A first.",
    "Then String C = B − 2.7 m."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q42",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 1.81 m. Note key writes 4.51 − 2.71 but intended 4.51 − 2.7 = 1.81."
  },
  {
   "n": 43,
   "type_id": 2,
   "question": "John had some money. He spent $$\\frac{1}{4}$$ of his money on food and $$\\frac{5}{8}$$ of his money on books. He spent $12 more on books than food. How much money did he have at first?",
   "answer0": "32",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 122,
   "difficulty_id": 3,
   "explanation": "Food = $$\\frac{1}{4}=\\frac{2}{8}$$, books = $$\\frac{5}{8}$$. Difference = $$\\frac{5}{8}-\\frac{2}{8}=\\frac{3}{8}$$ of his money = $12. So $$\\frac{1}{8}$$ = $4, and total $$\\frac{8}{8}$$ = 8 × $4 = $32.",
   "hints": [
    "Express both fractions in eighths, then find the difference.",
    "3 units = $12, so 1 unit = $4; total = 8 units."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q43",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: $32. 3u = 12, 1u = 4, 8u = 32."
  },
  {
   "n": 44,
   "type_id": 2,
   "question": "Ravi and Sam had 1780 stickers altogether. After Sam gave Ravi 40 stickers, they had the same number of stickers. How many stickers did Sam have at first?",
   "answer0": "930",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 118,
   "difficulty_id": 2,
   "explanation": "After the transfer each has 1780 ÷ 2 = 890. Sam gave away 40, so Sam had 890 + 40 = 930 at first.",
   "hints": [
    "After giving, both have half of 1780.",
    "Add back the 40 Sam gave away."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q44",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 930."
  },
  {
   "n": 45,
   "type_id": 2,
   "question": "A television costs 10 times as much as a chair. 1 television and 1 table cost $1820. 1 table and 1 chair cost $560. What is the cost of 1 television and 2 tables?",
   "answer0": "2240",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 118,
   "difficulty_id": 3,
   "explanation": "TV = 10 chairs. TV + table = 1820 → 10 chairs + table = 1820. Table + chair = 560. Subtracting: 9 chairs = 1820 − 560 = 1260, so 1 chair = 140. Table = 560 − 140 = 420. TV = 10 × 140 = 1400. 1 TV + 2 tables = 1400 + 2 × 420 = 1400 + 840 = $2240.",
   "hints": [
    "Replace the TV with 10 chairs to compare the two totals.",
    "9 chairs = 1820 − 560 = 1260, so 1 chair = 140."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q45",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: $2240."
  },
  {
   "n": 46,
   "type_id": 2,
   "question": "Mary was doing origami. She used a rectangular piece of paper as shown in Figure 1. First, she folded one side as shown in Figure 2. Next, she folded the paper upwards as shown in Figure 3. The area of the shaded part is 24 cm². What is the perimeter of the rectangular piece of paper as shown in Figure 1?",
   "answer0": "38",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 138,
   "difficulty_id": 3,
   "explanation": "Figure 2 shows the width split into 4 cm + 4 cm, so original width = 4 + 4 + 4 = 12 cm (the folded flap is 4 cm). The shaded rectangle in Figure 3 has area 24 cm² and width 8 cm, so its height = 24 ÷ 8 = 3 cm; with the 1 cm fold, the original height = 3 × 2 + 1 = 7 cm. Perimeter = 2 × (12 + 7) = 2 × 19 = 38 cm.",
   "hints": [
    "Use the 4 cm marks to find the rectangle's length.",
    "Shaded area ÷ 8 cm gives a height; rebuild the original breadth, then perimeter = 2(l + b)."
   ],
   "source": "Nan Hua 2023 P4 End of Year Exam Q46",
   "image_needed": true,
   "image_options": false,
   "image_file": "q46.png",
   "image_page": 21,
   "image_bbox": [
    0.12,
    0.28,
    0.83,
    0.44
   ],
   "image_loc": "upper-middle of page, three origami fold diagrams Figure 1, Figure 2 (4 cm + 4 cm), Figure 3 (shaded part, 1 cm)",
   "notes": "Key working: 4×3=12, 4×2=8, 24÷8=3, 3×2+1=7, 12+7=19, 19×2=38 cm. Length 12 cm, breadth 7 cm."
  }
 ]
}