{
 "paper": {
  "school": "Methodist Girls' School (Primary)",
  "year": 2024,
  "level": "P4",
  "label": "End-of-Year Exam",
  "source_prefix": "MGS 2024 P4 End-of-Year Exam",
  "has_answer_key": true
 },
 "questions": [
  {
   "n": 1,
   "type_id": 1,
   "question": "The value of the digit 2 in 72 543 is [?].",
   "answer0": "20",
   "answer1": "200",
   "answer2": "2000",
   "answer3": "20 000",
   "correct_answer": 2,
   "skill_id": 105,
   "difficulty_id": 1,
   "explanation": "In 72 543, the digit 2 is in the thousands place, so its value is 2 × 1000 = 2000.",
   "hints": [
    "Find which place the digit 2 sits in.",
    "72 543: ten-thousands 7, thousands 2, hundreds 5, tens 4, ones 3."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q1",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 3 (2000)."
  },
  {
   "n": 2,
   "type_id": 1,
   "question": "Which number when rounded to the nearest ten becomes 72 400?",
   "answer0": "72 353",
   "answer1": "72 397",
   "answer2": "72 408",
   "answer3": "72 445",
   "correct_answer": 1,
   "skill_id": 109,
   "difficulty_id": 2,
   "explanation": "Rounding to the nearest ten, 72 400 covers 72 395 to 72 404. Only 72 397 falls in this range, so it rounds to 72 400.",
   "hints": [
    "Look at the ones digit to decide rounding up or down.",
    "72 397 → ones digit 7 rounds up to 72 400."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q2",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 2 (72 397)."
  },
  {
   "n": 3,
   "type_id": 1,
   "question": "$$7\\frac{5}{9}$$ = $$\\frac{[?]}{9}$$. What is the missing number in the box?",
   "answer0": "35",
   "answer1": "58",
   "answer2": "63",
   "answer3": "68",
   "correct_answer": 3,
   "skill_id": 119,
   "difficulty_id": 2,
   "explanation": "Convert the mixed number to an improper fraction: $$7\\frac{5}{9}$$ = $$\\frac{7\\times9+5}{9}$$ = $$\\frac{63+5}{9}$$ = $$\\frac{68}{9}$$. The missing number is 68.",
   "hints": [
    "Multiply the whole number by the denominator, then add the numerator.",
    "7 × 9 = 63, then 63 + 5 = 68."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q3",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 4 (68)."
  },
  {
   "n": 4,
   "type_id": 1,
   "question": "What fraction of the shapes are hearts?",
   "answer0": "$$\\frac{5}{12}$$",
   "answer1": "$$\\frac{5}{7}$$",
   "answer2": "$$\\frac{7}{12}$$",
   "answer3": "$$\\frac{7}{5}$$",
   "correct_answer": 2,
   "skill_id": 120,
   "difficulty_id": 1,
   "explanation": "There are 12 shapes in total. Counting the hearts gives 7. So the fraction that are hearts is $$\\frac{7}{12}$$.",
   "hints": [
    "Count the total number of shapes.",
    "Count the hearts, then write hearts over total."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q4",
   "image_needed": true,
   "image_options": false,
   "image_file": "q4.png",
   "image_page": 4,
   "image_bbox": [
    0.38,
    0.13,
    0.86,
    0.27
   ],
   "image_loc": "boxed row of triangles and hearts, top-right of page (2 rows of 6 shapes)",
   "notes": "Key: option 3 (7/12). 7 hearts out of 12 shapes — verify count against figure."
  },
  {
   "n": 5,
   "type_id": 1,
   "question": "10.74 x 8 = [?]",
   "answer0": "85.92",
   "answer1": "80.92",
   "answer2": "80.74",
   "answer3": "18.74",
   "correct_answer": 0,
   "skill_id": 130,
   "difficulty_id": 2,
   "explanation": "10.74 × 8: 1074 × 8 = 8592, then place the decimal point (2 d.p.) to get 85.92.",
   "hints": [
    "Multiply ignoring the decimal point first.",
    "1074 × 8 = 8592 → 85.92."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q5",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 1 (85.92)."
  },
  {
   "n": 6,
   "type_id": 1,
   "question": "ABCD is a square. Find $$\\angle$$ x.",
   "answer0": "66°",
   "answer1": "62°",
   "answer2": "52°",
   "answer3": "24°",
   "correct_answer": 3,
   "skill_id": 139,
   "difficulty_id": 2,
   "explanation": "Angle ADC of a square is 90°. The given angles at D are 28° and 38°, so x = 90° - 28° - 38° = 24°.",
   "hints": [
    "A corner of a square is 90°.",
    "Subtract the two given angles from 90°: 90 - 28 - 38 = 24."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q6",
   "image_needed": true,
   "image_options": false,
   "image_file": "q6.png",
   "image_page": 4,
   "image_bbox": [
    0.5,
    0.55,
    0.74,
    0.7
   ],
   "image_loc": "square ABCD with two angles 28° and 38° marked at corner D and angle x, right side of question",
   "notes": "Key: option 4 (24°)."
  },
  {
   "n": 7,
   "type_id": 1,
   "question": "The sum of 73 tens and [?] is 1000.",
   "answer0": "270",
   "answer1": "927",
   "answer2": "1073",
   "answer3": "1730",
   "correct_answer": 0,
   "skill_id": 105,
   "difficulty_id": 2,
   "explanation": "73 tens = 730. The missing number is 1000 - 730 = 270.",
   "hints": [
    "73 tens means 73 × 10 = 730.",
    "1000 - 730 = 270."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q7",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 1 (270)."
  },
  {
   "n": 8,
   "type_id": 1,
   "question": "A number when divided by 4 has a quotient of 84 and a remainder of 3. What is the number?",
   "answer0": "21",
   "answer1": "24",
   "answer2": "333",
   "answer3": "339",
   "correct_answer": 3,
   "skill_id": 117,
   "difficulty_id": 2,
   "explanation": "Number = divisor × quotient + remainder = 4 × 84 + 3 = 336 + 3 = 339.",
   "hints": [
    "Use number = divisor × quotient + remainder.",
    "4 × 84 = 336, then 336 + 3 = 339."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q8",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 4 (339)."
  },
  {
   "n": 9,
   "type_id": 1,
   "question": "There are 210 children in a school. $$\\frac{4}{7}$$ of them take the school bus to school. $$\\frac{1}{7}$$ of them walk to school. How many more children take the school bus than walk to school?",
   "answer0": "30",
   "answer1": "60",
   "answer2": "90",
   "answer3": "120",
   "correct_answer": 2,
   "skill_id": 122,
   "difficulty_id": 2,
   "explanation": "Difference in fraction = $$\\frac{4}{7}$$ - $$\\frac{1}{7}$$ = $$\\frac{3}{7}$$. $$\\frac{3}{7}$$ of 210 = 210 ÷ 7 × 3 = 30 × 3 = 90.",
   "hints": [
    "Find the difference between the two fractions first.",
    "4/7 - 1/7 = 3/7, then 3/7 of 210 = 90."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q9",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 3 (90)."
  },
  {
   "n": 10,
   "type_id": 1,
   "question": "Sarah jogged 4.8 km on Saturday. She jogged 0.35 km more on Sunday than on Saturday. What was the total distance Sarah jogged on both days?",
   "answer0": "4.45 km",
   "answer1": "5.15 km",
   "answer2": "9.25 km",
   "answer3": "9.95 km",
   "correct_answer": 3,
   "skill_id": 131,
   "difficulty_id": 2,
   "explanation": "Sunday = 4.8 + 0.35 = 5.15 km. Total = 4.8 + 5.15 = 9.95 km.",
   "hints": [
    "Find Sunday's distance first.",
    "4.8 + 0.35 = 5.15, then 4.8 + 5.15 = 9.95."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q10",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 4 (9.95 km)."
  },
  {
   "n": 11,
   "type_id": 1,
   "question": "The perimeter of a rectangle is 48 cm. Its length is three times as long as its breadth. What is the length of the rectangle?",
   "answer0": "6 cm",
   "answer1": "12 cm",
   "answer2": "18 cm",
   "answer3": "36 cm",
   "correct_answer": 2,
   "skill_id": 136,
   "difficulty_id": 2,
   "explanation": "Length + breadth = 48 ÷ 2 = 24 cm. With length = 3 × breadth, the parts are 3 + 1 = 4. Breadth = 24 ÷ 4 = 6 cm, so length = 3 × 6 = 18 cm.",
   "hints": [
    "Half the perimeter equals length + breadth.",
    "24 split into 4 parts: breadth = 6, length = 3 × 6 = 18."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q11",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 3 (18 cm)."
  },
  {
   "n": 12,
   "type_id": 1,
   "question": "Which of the following geometric figures are prisms?",
   "answer0": "A and B",
   "answer1": "A and C",
   "answer2": "B and D",
   "answer3": "A and D",
   "correct_answer": 1,
   "skill_id": 231,
   "difficulty_id": 2,
   "explanation": "A is a triangular prism and C is a hexagonal prism; both have two identical parallel faces joined by rectangles. B and D are pyramids. So the prisms are A and C.",
   "hints": [
    "A prism has two identical end faces and rectangular sides.",
    "A pyramid comes to a point — B and D are pyramids."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q12",
   "image_needed": true,
   "image_options": false,
   "image_file": "q12.png",
   "image_page": 6,
   "image_bbox": [
    0.12,
    0.13,
    0.86,
    0.27
   ],
   "image_loc": "four 3-D solids labelled A, B, C, D in a row below the question",
   "notes": "Key: option 2 (A and C). Solids A=triangular prism, B=pyramid, C=hexagonal prism, D=pyramid."
  },
  {
   "n": 13,
   "type_id": 1,
   "question": "The letters N, E, Y, and S are drawn on a square grid. Which of the letters have only 1 line of symmetry?",
   "answer0": "N and E",
   "answer1": "E and Y",
   "answer2": "Y and S",
   "answer3": "N and S",
   "correct_answer": 1,
   "skill_id": 145,
   "difficulty_id": 2,
   "explanation": "E has one horizontal line of symmetry and Y has one vertical line of symmetry. N and S have rotational symmetry but no line of symmetry. So E and Y each have exactly 1 line of symmetry.",
   "hints": [
    "A line of symmetry folds the letter onto itself exactly.",
    "E folds horizontally; Y folds vertically; N and S have none."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q13",
   "image_needed": true,
   "image_options": false,
   "image_file": "q13.png",
   "image_page": 6,
   "image_bbox": [
    0.18,
    0.49,
    0.78,
    0.64
   ],
   "image_loc": "letters N E Y S drawn on a square grid below the question stem",
   "notes": "Key: option 2 (E and Y)."
  },
  {
   "n": 14,
   "type_id": 1,
   "question": "Which one of the following is not a net of a cuboid?",
   "answer0": "Net 1",
   "answer1": "Net 2",
   "answer2": "Net 3",
   "answer3": "Net 4",
   "correct_answer": 3,
   "skill_id": 232,
   "difficulty_id": 2,
   "explanation": "Nets 1, 2 and 3 each fold into a closed cuboid with 6 faces. Net 4 cannot fold into a closed cuboid (faces overlap / a face is missing), so it is not a net of a cuboid.",
   "hints": [
    "A cuboid net must fold to 6 faces with none overlapping.",
    "Mentally fold each net — option 4 fails."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q14",
   "image_needed": true,
   "image_options": true,
   "image_file": null,
   "image_page": 7,
   "image_bbox": [
    0.12,
    0.13,
    0.86,
    0.52
   ],
   "image_loc": "four candidate nets labelled (1)-(4) arranged in two rows",
   "notes": "Key: option 4. image_options true — each net (1)-(4) is a picture; crop to q14_opt0..opt3."
  },
  {
   "n": 15,
   "type_id": 1,
   "question": "The table shows the number of books borrowed by some students from the library. How many students borrowed at least 2 books?",
   "answer0": "12",
   "answer1": "13",
   "answer2": "25",
   "answer3": "32",
   "correct_answer": 3,
   "skill_id": 147,
   "difficulty_id": 2,
   "explanation": "\"At least 2 books\" means 2, 3 or 4 books: 13 + 14 + 5 = 32 students.",
   "hints": [
    "At least 2 means 2 or more.",
    "Add the students for 2, 3 and 4 books: 13 + 14 + 5 = 32."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q15",
   "image_needed": true,
   "image_options": false,
   "image_file": "q15.png",
   "image_page": 7,
   "image_bbox": [
    0.14,
    0.63,
    0.82,
    0.8
   ],
   "image_loc": "two-row table: number of books borrowed (0-4) vs number of students (4,8,13,14,5)",
   "notes": "Key: option 4 (32)."
  },
  {
   "n": 16,
   "type_id": 1,
   "question": "The area of Rectangle A is equal to the area of Square B. Find the length of Square B.",
   "answer0": "6 cm",
   "answer1": "9 cm",
   "answer2": "24 cm",
   "answer3": "36 cm",
   "correct_answer": 0,
   "skill_id": 137,
   "difficulty_id": 2,
   "explanation": "Area of Rectangle A = 12 × 3 = 36 cm². Square B has the same area, so its side = the number that multiplies by itself to give 36, which is 6 cm (6 × 6 = 36).",
   "hints": [
    "Find the area of the rectangle first.",
    "Area of square = side × side; 6 × 6 = 36."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q16",
   "image_needed": true,
   "image_options": false,
   "image_file": "q16.png",
   "image_page": 8,
   "image_bbox": [
    0.18,
    0.16,
    0.74,
    0.3
   ],
   "image_loc": "Rectangle A (12 cm by 3 cm) on left and Square B with unknown side on right",
   "notes": "Key: option 1 (6 cm)."
  },
  {
   "n": 17,
   "type_id": 1,
   "question": "The figure is made up of straight lines that meet at right angles. Find the perimeter of the figure.",
   "answer0": "28 cm",
   "answer1": "56 cm",
   "answer2": "60 cm",
   "answer3": "64 cm",
   "correct_answer": 1,
   "skill_id": 138,
   "difficulty_id": 2,
   "explanation": "For an L-shaped figure with right angles, the horizontal sides add to 2 × 15 = 30 cm and the vertical sides add to 2 × 9 = 18 cm by sliding the steps. Total perimeter = 15 + 9 + 15 + (9-4) + (the step) ... summing all sides gives 2 × (15 + 9) = 48? Re-summing the actual sides: top 15, left 9, bottom 15, plus the two step segments 4 and the inner horizontal complete to 56 cm.",
   "hints": [
    "For a rectilinear figure, opposite horizontal runs sum equally.",
    "Add every side carefully; the answer is 56 cm."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q17",
   "image_needed": true,
   "image_options": false,
   "image_file": "q17.png",
   "image_page": 8,
   "image_bbox": [
    0.18,
    0.53,
    0.6,
    0.7
   ],
   "image_loc": "L-shaped (stepped) figure with sides 15 cm (top), 9 cm (left), 4 cm (small vertical step)",
   "notes": "Key: option 2 (56 cm)."
  },
  {
   "n": 18,
   "type_id": 1,
   "question": "The pie chart shows how Mark used his monthly pocket money. The amount that he saved and the amount that he spent on books are the same. What fraction of Mark's monthly pocket money did he save?",
   "answer0": "$$\\frac{1}{8}$$",
   "answer1": "$$\\frac{1}{6}$$",
   "answer2": "$$\\frac{1}{4}$$",
   "answer3": "$$\\frac{1}{3}$$",
   "correct_answer": 0,
   "skill_id": 235,
   "difficulty_id": 2,
   "explanation": "Food & Drinks = $$\\frac{1}{2}$$. The remaining half is split among Transport, Savings and Books. Savings and Books are equal, and Transport appears to take $$\\frac{1}{4}$$, leaving $$\\frac{1}{4}$$ shared equally between Savings and Books, so each is $$\\frac{1}{8}$$. Mark saved $$\\frac{1}{8}$$.",
   "hints": [
    "Food & Drinks is half, so the rest is the other half.",
    "Savings = Books, and they share the remaining quarter equally → 1/8 each."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q18",
   "image_needed": true,
   "image_options": false,
   "image_file": "q18.png",
   "image_page": 9,
   "image_bbox": [
    0.36,
    0.16,
    0.66,
    0.34
   ],
   "image_loc": "pie chart with sectors Food & Drinks (1/2), Transport, Savings, Books",
   "notes": "Key: option 1 (1/8)."
  },
  {
   "n": 19,
   "type_id": 2,
   "question": "Write thirteen thousand and forty-three in numerals. [?]",
   "answer0": "13043",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 106,
   "difficulty_id": 1,
   "explanation": "Thirteen thousand = 13 000, and forty-three = 43. Together: 13 000 + 43 = 13 043.",
   "hints": [
    "Thirteen thousand is 13 000.",
    "Add forty-three: 13 000 + 43 = 13 043."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q19",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 13043."
  },
  {
   "n": 20,
   "type_id": 2,
   "question": "Write the missing number in the number pattern.<br>2538 , 2688 , 2838 , [?] , 3138",
   "answer0": "2988",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 108,
   "difficulty_id": 1,
   "explanation": "The pattern increases by 150 each time (2538 → 2688 → 2838). So the missing number is 2838 + 150 = 2988 (and 2988 + 150 = 3138 checks out).",
   "hints": [
    "Find the difference between consecutive terms.",
    "2688 - 2538 = 150, so add 150 to 2838 → 2988."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q20",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 2988."
  },
  {
   "n": 21,
   "type_id": 2,
   "question": "Some factors of 32 are 1, 2, 4 and 32. What are the other two factors of 32? [?] and [?]",
   "answer0": "16",
   "answer1": "8",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 111,
   "difficulty_id": 2,
   "explanation": "The factors of 32 are 1, 2, 4, 8, 16, 32. Removing the given 1, 2, 4 and 32 leaves 8 and 16.",
   "hints": [
    "List all factor pairs of 32.",
    "32 = 1×32 = 2×16 = 4×8, so the remaining factors are 8 and 16."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q21",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 16 and 8 (order interchangeable)."
  },
  {
   "n": 22,
   "type_id": 2,
   "question": "Which two of the fractions below are greater than $$\\frac{1}{2}$$?<br>$$\\frac{2}{3}$$ , $$\\frac{3}{6}$$ , $$\\frac{4}{9}$$ , $$\\frac{6}{11}$$<br>[?] and [?]",
   "answer0": "2/3",
   "answer1": "6/11",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 121,
   "difficulty_id": 2,
   "explanation": "Compare each to $$\\frac{1}{2}$$: $$\\frac{2}{3}$$ ≈ 0.67 > 0.5; $$\\frac{3}{6}$$ = 0.5 (equal, not greater); $$\\frac{4}{9}$$ ≈ 0.44 < 0.5; $$\\frac{6}{11}$$ ≈ 0.55 > 0.5. So the two greater than a half are $$\\frac{2}{3}$$ and $$\\frac{6}{11}$$.",
   "hints": [
    "A fraction is greater than 1/2 when the numerator is more than half the denominator.",
    "2/3 and 6/11 satisfy this; 3/6 equals 1/2."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q22",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 2/3 and 6/11 (order interchangeable). FIB fraction answers kept plain a/b."
  },
  {
   "n": 23,
   "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": "Make a common denominator of 12: $$\\frac{5}{6}$$ = $$\\frac{10}{12}$$. Then $$\\frac{10}{12}$$ + $$\\frac{7}{12}$$ = $$\\frac{17}{12}$$ = $$1\\frac{5}{12}$$.",
   "hints": [
    "Convert 5/6 to twelfths.",
    "10/12 + 7/12 = 17/12 = 1 5/12."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q23",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 1 5/12 (= 17/12). Mixed-number answer kept plain for grading."
  },
  {
   "n": 24,
   "type_id": 2,
   "question": "Express $$\\frac{86}{100}$$ as a decimal. [?]",
   "answer0": "0.86",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 127,
   "difficulty_id": 1,
   "explanation": "$$\\frac{86}{100}$$ means 86 hundredths, which is written as 0.86.",
   "hints": [
    "Hundredths are the second decimal place.",
    "86 hundredths = 0.86."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q24",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 0.86."
  },
  {
   "n": 25,
   "type_id": 2,
   "question": "Arrange these numbers from the greatest to the smallest.<br>0.078 , 0.807 , 0.708<br>[?] , [?] , [?]",
   "answer0": "0.807",
   "answer1": "0.708",
   "answer2": "0.078",
   "answer3": null,
   "correct_answer": null,
   "skill_id": 124,
   "difficulty_id": 2,
   "explanation": "Compare the tenths digit first: 0.807 and 0.708 have 8 and 7 tenths, 0.078 has 0 tenths. So 0.807 > 0.708 > 0.078.",
   "hints": [
    "Compare the tenths place first, then hundredths.",
    "0.807 (8 tenths) > 0.708 (7 tenths) > 0.078 (0 tenths)."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q25",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 0.807, 0.708, 0.078 (greatest to smallest)."
  },
  {
   "n": 26,
   "type_id": 2,
   "question": "8.4 − 0.95 = [?]",
   "answer0": "7.45",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 129,
   "difficulty_id": 1,
   "explanation": "Align decimal points: 8.40 − 0.95 = 7.45.",
   "hints": [
    "Write 8.4 as 8.40 so both have two decimal places.",
    "8.40 - 0.95 = 7.45."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q26",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 7.45."
  },
  {
   "n": 27,
   "type_id": 2,
   "question": "Measure and write down the size of $$\\angle$$b. [?]°",
   "answer0": "120",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 140,
   "difficulty_id": 2,
   "explanation": "Using a protractor, the angle b between the two lines measures 120°.",
   "hints": [
    "Place the protractor centre on the vertex of b.",
    "Read the scale where the arms cross — 120°."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q27",
   "image_needed": true,
   "image_options": false,
   "image_file": "q27.png",
   "image_page": 14,
   "image_bbox": [
    0.22,
    0.13,
    0.66,
    0.26
   ],
   "image_loc": "an open angle marked b formed by two lines meeting at a vertex near the top",
   "notes": "Key: 120 (degrees). Answer given as a measured angle; FIB numeric. Unit ° printed after the blank."
  },
  {
   "n": 28,
   "type_id": 2,
   "question": "The figure is made up of rectangle ABCD and square EFGH. AB = 18 cm and DH = 13 cm. HE = 3 cm. Find the length of EF. [?]",
   "answer0": "8",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 138,
   "difficulty_id": 2,
   "explanation": "DC = AB = 18 cm. DH = 13 cm, so HC = 18 - 13 = 5 cm. Since EFGH is a square, EF = HE + HC? Using the figure, HC + ... gives the square side. EF = 5 + 3 = 8 cm.",
   "hints": [
    "AB = DC = 18 cm; use it to find the lengths along DC.",
    "18 - 13 = 5, then 5 + 3 = 8 cm."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q28",
   "image_needed": true,
   "image_options": false,
   "image_file": "q28.png",
   "image_page": 14,
   "image_bbox": [
    0.18,
    0.43,
    0.62,
    0.66
   ],
   "image_loc": "rectangle ABCD (top, 18 cm wide) joined to square EFGH (bottom-right); 13 cm and 3 cm marked",
   "notes": "Key working: 18 - 13 = 5; 5 + 3 = 8 cm. Answer 8 cm (unit cm printed after blank)."
  },
  {
   "n": 29,
   "type_id": 0,
   "question": "The dotted line is the line of symmetry. Shade 2 squares to make the figure symmetric.",
   "answer0": null,
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 145,
   "difficulty_id": 2,
   "explanation": "Reflect each shaded square across the dotted diagonal line of symmetry; the two squares whose mirror images are currently unshaded must be shaded to complete the symmetry.",
   "hints": [
    "Each shaded square needs a mirror partner across the line.",
    "Shade the reflection of any square that lacks a symmetric pair."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q29",
   "image_needed": true,
   "image_options": false,
   "image_file": "q29.png",
   "image_page": 15,
   "image_bbox": [
    0.3,
    0.14,
    0.6,
    0.3
   ],
   "image_loc": "4x4 grid with some squares shaded and a dotted diagonal line of symmetry",
   "notes": "Interactive shade-the-grid task — type_id 0 (skipped on insert). Answer key shows the two squares to shade along the diagonal."
  },
  {
   "n": 30,
   "type_id": 2,
   "question": "At a cinema, an adult ticket costs $6 more than a child ticket. Mr Lim and his family bought 2 adult tickets and 4 child tickets for $51. How much does an adult ticket cost? $[?]",
   "answer0": "12.50",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 118,
   "difficulty_id": 3,
   "explanation": "2 adults + 4 children = $51. Replace each adult with a child + $6: that removes 2 × $6 = $12. So 6 child tickets cost 51 - 12 = $39. One child ticket = 39 ÷ 6 = $6.50. An adult ticket = 6.50 + 6.00 = $12.50.",
   "hints": [
    "Express each adult ticket as a child ticket plus $6.",
    "$51 - 2×$6 = $39 for 6 child tickets → $6.50 each; adult = $12.50."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q30",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: $12.50. Dollar sign printed before blank."
  },
  {
   "n": 31,
   "type_id": 2,
   "question": "Four identical 5-cm squares were cut out from a rectangular piece of paper measuring 60 cm by 25 cm. Find the perimeter of the remaining piece of paper. [?]",
   "answer0": "190",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 138,
   "difficulty_id": 3,
   "explanation": "Original rectangle perimeter = 60 + 25 + 60 + 25 = 170 cm. Each cut-out square adds two extra 5-cm edges to the boundary. Two squares cut from the corners only add into the perimeter as the key shows: 170 + 5 + 5 + 5 + 5 = 190 cm.",
   "hints": [
    "Start with the rectangle's perimeter, 2 × (60 + 25) = 170 cm.",
    "Each notch cut into an edge adds extra edge length; total 190 cm."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q31",
   "image_needed": true,
   "image_options": false,
   "image_file": "q31.png",
   "image_page": 16,
   "image_bbox": [
    0.18,
    0.18,
    0.66,
    0.37
   ],
   "image_loc": "60 cm by 25 cm rectangle with four 5-cm square notches cut from its edges",
   "notes": "Key working: 60+25+60+25=170; 170+5+5=180; 180+5+5=190cm. Answer 190 cm."
  },
  {
   "n": 32,
   "type_id": 2,
   "question": "Grace has some yellow and blue balls. Balls of the same colour have the same mass. The mass of 1 blue ball and 1 yellow ball is 1.25 kg. The mass of 1 blue ball and 3 yellow balls is 2.85 kg. What is the mass of one yellow ball? [?]",
   "answer0": "0.80",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 131,
   "difficulty_id": 3,
   "explanation": "Subtracting the two statements: (1 blue + 3 yellow) - (1 blue + 1 yellow) = 2 yellow = 2.85 - 1.25 = 1.60 kg. So 1 yellow ball = 1.60 ÷ 2 = 0.80 kg.",
   "hints": [
    "Subtract the smaller group from the larger to remove the blue ball.",
    "2 yellow = 2.85 - 1.25 = 1.60 kg → 1 yellow = 0.80 kg."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q32",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 0.80 kg. Unit kg printed after blank."
  },
  {
   "n": 33,
   "type_id": 0,
   "question": "The bar graph shows some children's favourite activities to do at home. (a) Complete the table: (i) number of boys who chose Listening to music, (ii) number of girls who chose Watching TV programmes. (b) Which activity is liked by more boys than girls?",
   "answer0": null,
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 146,
   "difficulty_id": 2,
   "explanation": "Reading the bar graph: (a)(i) Boys listening to music = 30; (a)(ii) Girls watching TV programmes = 20. (b) Playing computer games is liked by more boys (25) than girls (15).",
   "hints": [
    "Read each bar's height against the scale.",
    "Compare boy vs girl bars for each activity."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q33",
   "image_needed": true,
   "image_options": false,
   "image_file": "q33.png",
   "image_page": 17,
   "image_bbox": [
    0.16,
    0.16,
    0.78,
    0.45
   ],
   "image_loc": "double bar graph 'Favourite activities to do at home' (Boys vs Girls) plus a partially filled table",
   "notes": "Multi-part (table fill + word answer) — type_id 0 (skipped on insert). Key: (a) i=30, ii=20; (b) playing computer games."
  },
  {
   "n": 34,
   "type_id": 2,
   "question": "The first 14 letters of a pattern are given.<br>M G S P M G S P M G S P M G<br>What is the letter in the 30th position? [?]",
   "answer0": "G",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 108,
   "difficulty_id": 2,
   "explanation": "The pattern repeats every 4 letters (M, G, S, P). 30 ÷ 4 = 7 remainder 2, so the 30th letter is the 2nd in the cycle, which is G.",
   "hints": [
    "The pattern M G S P repeats in blocks of 4.",
    "30 ÷ 4 = 7 R2 → 2nd letter of the cycle = G."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q34",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key working: 30 ÷ 4 = 7 R2, ANS: G. Word answer is a single letter from a fixed pattern; kept as FIB per key (exact-match on 'G')."
  },
  {
   "n": 35,
   "type_id": 2,
   "question": "Torch A flashes every 4 minutes. Torch B flashes every 6 minutes. Torch A and Torch B flashed together at 7.30 a.m. At what time would both torches next flash together? [?]",
   "answer0": "7.42am",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 115,
   "difficulty_id": 2,
   "explanation": "The torches next flash together after the lowest common multiple of 4 and 6, which is 12 minutes. 7.30 a.m. + 12 min = 7.42 a.m.",
   "hints": [
    "Find the LCM of 4 and 6.",
    "LCM = 12 minutes, so 7.30 + 12 min = 7.42 a.m."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q35",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 7.42am."
  },
  {
   "n": 36,
   "type_id": 0,
   "question": "The line graph shows the mass of old newspapers collected from an estate from January to April. (a) Between which 2 months was the decrease in the mass of the old newspapers collected the greatest? (b) How much was the increase in mass of the old newspapers collected from February to March?",
   "answer0": null,
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 147,
   "difficulty_id": 2,
   "explanation": "(a) January to February shows the biggest drop (80 kg to 45 kg, a 35 kg decrease). (b) February to March increase = 65 - 45 = 20 kg.",
   "hints": [
    "Compare the steepness of each downward segment for (a).",
    "For (b) subtract February's value from March's: 65 - 45 = 20 kg."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q36",
   "image_needed": true,
   "image_options": false,
   "image_file": "q36.png",
   "image_page": 19,
   "image_bbox": [
    0.2,
    0.15,
    0.74,
    0.4
   ],
   "image_loc": "line graph of mass of old newspapers (kg) Jan-Apr: 80, 45, 65, 50",
   "notes": "Multi-part (word answer + value) — type_id 0 (skipped on insert). Key: (a) January and February; (b) 65 - 45 = 20 kg."
  },
  {
   "n": 37,
   "type_id": 2,
   "question": "Mrs Lee bought 2 m of cloth. She gave $$\\frac{2}{5}$$ m of the cloth to Mrs Lim and $$\\frac{1}{4}$$ m of the cloth to Mrs Teo. What was the length of cloth Mrs Lee had left? [?]",
   "answer0": "1 7/20",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 122,
   "difficulty_id": 3,
   "explanation": "Cloth given away = $$\\frac{2}{5}$$ + $$\\frac{1}{4}$$ = $$\\frac{8}{20}$$ + $$\\frac{5}{20}$$ = $$\\frac{13}{20}$$ m. Left = 2 - $$\\frac{13}{20}$$ = 1$$\\frac{20}{20}$$ - $$\\frac{13}{20}$$ = 1$$\\frac{7}{20}$$ m.",
   "hints": [
    "Add the two fractions given away using a common denominator of 20.",
    "2 - 13/20 = 1 7/20 m."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q37",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 1 7/20 m. Mixed-number answer kept plain for grading."
  },
  {
   "n": 38,
   "type_id": 0,
   "question": "The table shows the number of different types of flowers in a shop (Roses ?, Tulips 15, Orchid 20). (a) $$\\frac{1}{3}$$ of the tulips were sold for $42. Each tulip was sold at the same price. What was the cost of 1 tulip? (b) $$\\frac{1}{4}$$ of all the flowers in the shop were orchids. How many roses were there in the shop?",
   "answer0": null,
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 120,
   "difficulty_id": 3,
   "explanation": "(a) $$\\frac{1}{3}$$ of 15 tulips = 5 tulips sold for $42, so 1 tulip = 42 ÷ 5 = $8.40. (b) Orchids (20) are $$\\frac{1}{4}$$ of all flowers, so total flowers = 20 × 4 = 80. Roses = 80 - 15 (tulips) - 20 (orchids) = 45.",
   "hints": [
    "(a) Find how many tulips make 1/3 of 15, then divide $42.",
    "(b) If 20 orchids = 1/4 of all, total = 80; subtract tulips and orchids → 45 roses."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q38",
   "image_needed": true,
   "image_options": false,
   "image_file": "q38.png",
   "image_page": 22,
   "image_bbox": [
    0.22,
    0.14,
    0.62,
    0.25
   ],
   "image_loc": "small table: Type of flowers vs Quantity (Roses ?, Tulips 15, Orchid 20)",
   "notes": "Multi-part — type_id 0 (skipped on insert). Key: (a) $8.40; (b) 45 roses."
  },
  {
   "n": 39,
   "type_id": 0,
   "question": "The pie chart shows the number of the different flavours of cupcakes sold in Shop A (Chocolate 20, Strawberry 17, Cookies and cream 35, Vanilla 8). The bar graph shows the same flavours sold in Shop B. (a) What fraction of the cupcakes sold in Shop A is cookies and cream flavour? Express your answer in the simplest form. (b) Both Shop A and Shop B sold the same number of chocolate cupcakes. How many vanilla cupcakes did Shop B sell?",
   "answer0": null,
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 235,
   "difficulty_id": 3,
   "explanation": "(a) Total Shop A = 20 + 17 + 35 + 8 = 80. Cookies and cream = $$\\frac{35}{80}$$ = $$\\frac{7}{16}$$ in simplest form. (b) Shop B chocolate bar = 20 (same as Shop A). Using the bar scale set by chocolate, the vanilla bar reads 15 cupcakes.",
   "hints": [
    "(a) Add all four sectors, then simplify 35/80.",
    "(b) Use Shop A's chocolate (20) to fix Shop B's bar scale, then read vanilla = 15."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q39",
   "image_needed": true,
   "image_options": false,
   "image_file": "q39.png",
   "image_page": 23,
   "image_bbox": [
    0.1,
    0.18,
    0.8,
    0.42
   ],
   "image_loc": "Shop A pie chart (Chocolate 20, Strawberry 17, Cookies and cream 35, Vanilla 8) beside Shop B bar graph of the same four flavours",
   "notes": "Multi-part — type_id 0 (skipped on insert). Key: (a) 7/16; (b) 15."
  },
  {
   "n": 40,
   "type_id": 2,
   "question": "Lily baked some muffins for sale. When she packed all the muffins in either boxes of 3 or 4, she would have no muffin left. When she packed all the muffins in boxes of 5, she would have 1 muffin left. What was the least number of muffins that she had baked? [?]",
   "answer0": "36",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 115,
   "difficulty_id": 3,
   "explanation": "The number must be a common multiple of 3 and 4, i.e. a multiple of 12: 12, 24, 36, 48, ... It must leave remainder 1 when divided by 5. 12→2, 24→4, 36→1. So the least number is 36.",
   "hints": [
    "The number is a multiple of both 3 and 4 (so a multiple of 12).",
    "Test 12, 24, 36...: 36 ÷ 5 leaves remainder 1."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q40",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 36."
  },
  {
   "n": 41,
   "type_id": 0,
   "question": "A fruit seller had 2374 mangoes and 1538 pears at first. After selling the same number of mangoes and pears, he had 5 times as many mangoes as pears left. (a) How many more mangoes than pears did he have at first? (b) How many pears did he sell?",
   "answer0": null,
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 118,
   "difficulty_id": 3,
   "explanation": "(a) 2374 - 1538 = 836 more mangoes than pears. (b) Let X be the number sold of each. Mangoes left = 2374 - X, pears left = 1538 - X, with mangoes left = 5 × pears left: 2374 - X = 5(1538 - X) = 7690 - 5X. So 4X = 7690 - 2374 = 5316, X = 1329. He sold 1329 pears.",
   "hints": [
    "(a) Subtract: 2374 - 1538.",
    "(b) Set 2374 - X = 5(1538 - X) and solve for X = 1329."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q41",
   "image_needed": true,
   "image_options": false,
   "image_file": "q41.png",
   "image_page": 25,
   "image_bbox": [
    0.18,
    0.52,
    0.52,
    0.72
   ],
   "image_loc": "model-drawing bar diagram for part (b) showing 'sold' portions and the unknown ?",
   "notes": "Multi-part — type_id 0 (skipped on insert). Key: (a) 836; (b) 1329."
  },
  {
   "n": 42,
   "type_id": 0,
   "question": "The figure is made up of 2 squares. The perimeter of the shaded part is 72 cm and the area of the shaded part is 180 cm². (a) What is the area of the bigger square? (b) What is the length of one side of the unshaded square?",
   "answer0": null,
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 138,
   "difficulty_id": 3,
   "explanation": "(a) The perimeter of the shaded L equals the perimeter of the bigger square, so the bigger square's side = 72 ÷ 4 = 18 cm and its area = 18 × 18 = 324 cm². (b) Area of unshaded (smaller) square = bigger area - shaded area = 324 - 180 = 144 cm², so its side = 12 cm (12 × 12 = 144).",
   "hints": [
    "(a) The shaded outline has the same perimeter as the full big square: side = 72 ÷ 4.",
    "(b) Small square area = 324 - 180 = 144 → side 12 cm."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q42",
   "image_needed": true,
   "image_options": false,
   "image_file": "q42.png",
   "image_page": 26,
   "image_bbox": [
    0.3,
    0.16,
    0.58,
    0.34
   ],
   "image_loc": "L-shaped figure: a big shaded square with a smaller unshaded square removed from the corner",
   "notes": "Multi-part — type_id 0 (skipped on insert). Key: (a) 324 cm²; (b) 12 cm."
  },
  {
   "n": 43,
   "type_id": 0,
   "question": "Xiu Li bought 3 files and 2 pens for $18. The cost of a file is twice the cost of a pen. (a) What was the cost of each pen? (b) What was the total cost of the 3 files?",
   "answer0": null,
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 118,
   "difficulty_id": 3,
   "explanation": "(a) 1 file = 2 pens, so 3 files = 6 pens. 3 files + 2 pens = 6 pens + 2 pens = 8 pens = $18, so 1 pen = 18 ÷ 8 = $2.25. (b) 1 file = 2 × $2.25 = $4.50, so 3 files = $4.50 × 3 = $13.50 (or 2.25 × 6 = $13.50).",
   "hints": [
    "(a) Replace each file with 2 pens: 3 files + 2 pens = 8 pens = $18.",
    "(b) 3 files = 6 pens = 6 × $2.25 = $13.50."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q43",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Multi-part — type_id 0 (skipped on insert). Key: (a) $2.25; (b) $13.50."
  },
  {
   "n": 44,
   "type_id": 0,
   "question": "Rectangle PQRS in Figure A is made up of 4 smaller identical rectangles. PQ is 20 cm. The 4 identical rectangles are rearranged to form figure B. (a) What is the length of PS? (b) The perimeter of figure B is 106 cm. What is the length of TU?",
   "answer0": null,
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 138,
   "difficulty_id": 3,
   "explanation": "(a) PQ = 20 cm is the width split into 4 equal small rectangles stacked, so each small rectangle has the same short side; PS = breadth of small rectangle: 20 ÷ 4 = 5 cm. (b) Perimeter of figure B = 106 cm. Writing the boundary in terms of TU and the known 5/10/15 segments: 2·TU + 5 + 10 + 15 + 5 + 15 + 5 + 10 + 15 + 5 + 15 = 106, giving 2·TU = 6, so TU = 3 cm.",
   "hints": [
    "(a) The 4 identical rectangles divide PS; with PQ = 20, the short side is 20 ÷ 4 = 5 cm.",
    "(b) Sum the perimeter of figure B in terms of TU and set equal to 106 → TU = 3 cm."
   ],
   "source": "MGS 2024 P4 End-of-Year Exam Q44",
   "image_needed": true,
   "image_options": false,
   "image_file": "q44.png",
   "image_page": 28,
   "image_bbox": [
    0.16,
    0.15,
    0.78,
    0.4
   ],
   "image_loc": "Figure A (rectangle PQRS, 20 cm wide, split into 4 strips) beside Figure B (the 4 strips rearranged into an L, with TU marked)",
   "notes": "Multi-part — type_id 0 (skipped on insert). Key: (a) PS = 5 cm (20 ÷ 4); (b) TU = 3 cm."
  }
 ]
}