{
 "paper": {
  "school": "Paya Lebar Methodist Girls' School (Primary)",
  "year": 2024,
  "level": "P4",
  "label": "End-of-Year Exam",
  "source_prefix": "PLMGS 2024 P4 End-of-Year Exam",
  "has_answer_key": true
 },
 "questions": [
  {
   "n": 1,
   "type_id": 1,
   "question": "Which of the following is a factor of both 18 and 27?",
   "answer0": "27",
   "answer1": "18",
   "answer2": "9",
   "answer3": "6",
   "correct_answer": 2,
   "skill_id": 113,
   "difficulty_id": 1,
   "explanation": "Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 27: 1, 3, 9, 27. The common factors are 1, 3 and 9. Of the options, 9 is a factor of both 18 and 27.",
   "hints": [
    "List the factors of 18 and the factors of 27.",
    "Find a number that appears in both lists."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q1",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 3 (9)."
  },
  {
   "n": 2,
   "type_id": 1,
   "question": "Which of the following numbers when rounded to the nearest ten becomes 72 500?",
   "answer0": "72 443",
   "answer1": "72 495",
   "answer2": "72 539",
   "answer3": "72 554",
   "correct_answer": 1,
   "skill_id": 109,
   "difficulty_id": 2,
   "explanation": "Rounding to the nearest ten: 72 443 -> 72 440; 72 495 -> 72 500; 72 539 -> 72 540; 72 554 -> 72 550. Only 72 495 rounds to 72 500.",
   "hints": [
    "Look at the ones digit to decide whether to round up or down.",
    "5 or more rounds up; 4 or less rounds down."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q2",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 2."
  },
  {
   "n": 3,
   "type_id": 1,
   "question": "What fraction of the shapes in the box are circles?",
   "answer0": "$$\\frac{4}{10}$$",
   "answer1": "$$\\frac{4}{6}$$",
   "answer2": "$$\\frac{6}{4}$$",
   "answer3": "$$\\frac{6}{10}$$",
   "correct_answer": 3,
   "skill_id": 120,
   "difficulty_id": 1,
   "explanation": "There are 10 shapes in total: 4 triangles and 6 circles. The fraction of circles is $$\\frac{6}{10}$$.",
   "hints": [
    "Count the total number of shapes.",
    "Count how many are circles, then write circles over total."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q3",
   "image_needed": true,
   "image_options": false,
   "image_file": "q3.png",
   "image_page": 3,
   "image_bbox": [
    0.33,
    0.55,
    0.72,
    0.7
   ],
   "image_loc": "boxed row of triangles and circles below the question",
   "notes": "Figure shows 4 triangles + 6 circles = 10 shapes. Stem reworded from circle symbol to the word 'circles'. Key: option 4 (6/10)."
  },
  {
   "n": 4,
   "type_id": 1,
   "question": "$$6\\frac{4}{7} = \\frac{[?]}{7}$$<br>What is the missing number in the box?",
   "answer0": "24",
   "answer1": "38",
   "answer2": "42",
   "answer3": "46",
   "correct_answer": 3,
   "skill_id": 119,
   "difficulty_id": 2,
   "explanation": "Convert the mixed number to an improper fraction: $$6\\frac{4}{7} = \\frac{6 \\times 7 + 4}{7} = \\frac{42 + 4}{7} = \\frac{46}{7}$$. The missing number is 46.",
   "hints": [
    "Multiply the whole number by the denominator.",
    "Add the numerator to that product."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q4",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Mixed-to-improper conversion. Box rendered as [?] inline. Key: option 4 (46)."
  },
  {
   "n": 5,
   "type_id": 1,
   "question": "Which of the following decimals is represented by letter A in the number line?",
   "answer0": "3.012",
   "answer1": "3.017",
   "answer2": "3.023",
   "answer3": "3.027",
   "correct_answer": 1,
   "skill_id": 123,
   "difficulty_id": 2,
   "explanation": "The number line runs from 3.01 to 3.02, divided into 10 equal parts of 0.001 each. Letter A is 7 small marks after 3.01, so A = 3.01 + 0.007 = 3.017.",
   "hints": [
    "Each interval between 3.01 and 3.02 is split into 10 equal parts.",
    "Each small part is 0.001; count the parts from 3.01 to A."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q5",
   "image_needed": true,
   "image_options": false,
   "image_file": "q5.png",
   "image_page": 4,
   "image_bbox": [
    0.2,
    0.4,
    0.85,
    0.55
   ],
   "image_loc": "number line with arrow labelled A between 3.01 and 3.02",
   "notes": "Key: option 2 (3.017)."
  },
  {
   "n": 6,
   "type_id": 1,
   "question": "Express 0.05 as a fraction in its simplest form.",
   "answer0": "$$\\frac{1}{20}$$",
   "answer1": "$$\\frac{1}{2}$$",
   "answer2": "$$\\frac{1}{10}$$",
   "answer3": "$$\\frac{1}{5}$$",
   "correct_answer": 0,
   "skill_id": 126,
   "difficulty_id": 1,
   "explanation": "0.05 = $$\\frac{5}{100}$$. Dividing numerator and denominator by 5 gives $$\\frac{1}{20}$$.",
   "hints": [
    "0.05 means 5 hundredths.",
    "Simplify 5/100 by dividing top and bottom by 5."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q6",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 1 (1/20)."
  },
  {
   "n": 7,
   "type_id": 1,
   "question": "In the figure shown, ABCD is a rectangle. Find ∠x.",
   "answer0": "43°",
   "answer1": "47°",
   "answer2": "64°",
   "answer3": "69°",
   "correct_answer": 0,
   "skill_id": 140,
   "difficulty_id": 2,
   "explanation": "At corner D the angle ADC of the rectangle is 90°. This is split into three parts: 26°, x and 21°. So x = 90° − 26° − 21° = 43°.",
   "hints": [
    "A corner of a rectangle is a right angle (90°).",
    "The three angles at D add up to 90°."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q7",
   "image_needed": true,
   "image_options": false,
   "image_file": "q7.png",
   "image_page": 5,
   "image_bbox": [
    0.3,
    0.12,
    0.62,
    0.3
   ],
   "image_loc": "rectangle ABCD with angles 26°, x and 21° marked at corner D",
   "notes": "Key: option 1 (43°)."
  },
  {
   "n": 8,
   "type_id": 1,
   "question": "The table shows the prices of tickets to a theme park.<br>Adult: $15<br>Child: $9<br>Mrs Tan wants to buy tickets for two adults and three children. How much does she have to pay in total?",
   "answer0": "$24",
   "answer1": "$30",
   "answer2": "$57",
   "answer3": "$63",
   "correct_answer": 2,
   "skill_id": 118,
   "difficulty_id": 2,
   "explanation": "2 adults: 2 × $15 = $30. 3 children: 3 × $9 = $27. Total = $30 + $27 = $57.",
   "hints": [
    "Find the cost of the adult tickets and the child tickets separately.",
    "Add the two amounts together."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q8",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Price table transcribed into stem text. Key: option 3 ($57)."
  },
  {
   "n": 9,
   "type_id": 1,
   "question": "The table shows 4 different types of CCA that 225 children participated in. Each child participated only in one CCA.<br>Rope Skipping: ?<br>Gymnastics: 73<br>International Dance: 50<br>Girls' Brigade: 64<br>How many children participated in Rope Skipping?",
   "answer0": "38",
   "answer1": "40",
   "answer2": "162",
   "answer3": "187",
   "correct_answer": 0,
   "skill_id": 118,
   "difficulty_id": 2,
   "explanation": "Total in the other three CCAs = 73 + 50 + 64 = 187. Rope Skipping = 225 − 187 = 38.",
   "hints": [
    "Add up the three known CCA numbers.",
    "Subtract that total from 225."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q9",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "CCA table transcribed into stem text. Key: option 1 (38)."
  },
  {
   "n": 10,
   "type_id": 1,
   "question": "Which of the following fractions has the value closest to 1?",
   "answer0": "$$\\frac{2}{3}$$",
   "answer1": "$$\\frac{3}{4}$$",
   "answer2": "$$\\frac{5}{6}$$",
   "answer3": "$$\\frac{7}{8}$$",
   "correct_answer": 3,
   "skill_id": 79,
   "difficulty_id": 2,
   "explanation": "The distance from 1 is: $$\\frac{1}{3}$$, $$\\frac{1}{4}$$, $$\\frac{1}{6}$$, $$\\frac{1}{8}$$. The smallest gap is $$\\frac{1}{8}$$, so $$\\frac{7}{8}$$ is closest to 1.",
   "hints": [
    "Each fraction is just less than 1; find how much each is short of 1.",
    "The fraction missing the smallest amount is closest to 1."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q10",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 4 (7/8)."
  },
  {
   "n": 11,
   "type_id": 1,
   "question": "Jamie bought 8 boxes of biscuits. Each box of biscuits cost $1.20. She gave the cashier $50. How much change did Jamie receive?",
   "answer0": "$9.20",
   "answer1": "$9.60",
   "answer2": "$40.40",
   "answer3": "$41.60",
   "correct_answer": 2,
   "skill_id": 131,
   "difficulty_id": 2,
   "explanation": "Cost = 8 × $1.20 = $9.60. Change = $50 − $9.60 = $40.40.",
   "hints": [
    "Find the total cost of 8 boxes first.",
    "Subtract the total cost from $50."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q11",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 3 ($40.40)."
  },
  {
   "n": 12,
   "type_id": 1,
   "question": "Both the square and rectangle have the same area. Find the perimeter of the rectangle given that its breadth is 4 cm.",
   "answer0": "16 cm",
   "answer1": "20 cm",
   "answer2": "40 cm",
   "answer3": "64 cm",
   "correct_answer": 2,
   "skill_id": 136,
   "difficulty_id": 2,
   "explanation": "Square area = 8 × 8 = 64 cm². Rectangle has the same area: length = 64 ÷ 4 = 16 cm. Perimeter = 2 × (16 + 4) = 2 × 20 = 40 cm.",
   "hints": [
    "Find the area of the square (side 8 cm).",
    "The rectangle has the same area; divide by its breadth to find its length, then add up all four sides."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q12",
   "image_needed": true,
   "image_options": false,
   "image_file": "q12.png",
   "image_page": 7,
   "image_bbox": [
    0.18,
    0.16,
    0.82,
    0.32
   ],
   "image_loc": "8 cm square on the left and a rectangle of breadth 4 cm on the right",
   "notes": "Square side 8 cm, rectangle breadth 4 cm. Key: option 3 (40 cm)."
  },
  {
   "n": 13,
   "type_id": 1,
   "question": "Harun and Ming Hui started reading their storybooks at 9.45 a.m.. Harun took 1 h 20 min to finish reading his storybook. He took 25 min longer than Ming Hui. At what time did Ming Hui finish reading his storybook?",
   "answer0": "10.20 a.m.",
   "answer1": "10.40 a.m.",
   "answer2": "11.05 a.m.",
   "answer3": "11.30 a.m.",
   "correct_answer": 1,
   "skill_id": 93,
   "difficulty_id": 2,
   "explanation": "Ming Hui took 1 h 20 min − 25 min = 55 min. Starting at 9.45 a.m. and adding 55 min gives 10.40 a.m.",
   "hints": [
    "Find Ming Hui's reading time: it is 25 min less than Harun's 1 h 20 min.",
    "Add that duration to the 9.45 a.m. start time."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q13",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 2 (10.40 a.m.)."
  },
  {
   "n": 14,
   "type_id": 1,
   "question": "The graph shows the Math test results of 100 students.<br>How many students scored below 70 marks?",
   "answer0": "10",
   "answer1": "15",
   "answer2": "25",
   "answer3": "45",
   "correct_answer": 2,
   "skill_id": 104,
   "difficulty_id": 2,
   "explanation": "Below 70 marks covers the '50 to 69' and '0 to 49' bars. From the graph: 50 to 69 = 10 students, 0 to 49 = 15 students. Total = 10 + 15 = 25.",
   "hints": [
    "'Below 70' means the 50-69 and 0-49 groups.",
    "Read both bar heights and add them."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q14",
   "image_needed": true,
   "image_options": false,
   "image_file": "q14.png",
   "image_page": 8,
   "image_bbox": [
    0.16,
    0.16,
    0.84,
    0.45
   ],
   "image_loc": "bar graph 'Math Test Results' with bars for 85-100, 70-84, 50-69, 0-49",
   "notes": "Bars: 85-100=30, 70-84=45, 50-69=10, 0-49=15. Key: option 3 (25)."
  },
  {
   "n": 15,
   "type_id": 1,
   "question": "How many letters in the word ANGEL have a line of symmetry?",
   "answer0": "5",
   "answer1": "2",
   "answer2": "3",
   "answer3": "4",
   "correct_answer": 1,
   "skill_id": 145,
   "difficulty_id": 2,
   "explanation": "Checking each letter of ANGEL: A has a vertical line of symmetry, N has none, G has none, E has a horizontal line of symmetry, L has none. So 2 letters (A and E) have a line of symmetry.",
   "hints": [
    "Test each letter to see if it can be folded so the two halves match.",
    "Capital A and E are symmetric; N, G and L are not."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q15",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Word ANGEL transcribed into stem text (no figure crop needed). Key: option 2 (2)."
  },
  {
   "n": 16,
   "type_id": 1,
   "question": "Olivia used sticks to make triangles and squares. She used 6 sticks for each triangle and 8 sticks for each square. Olivia made the same number of triangles and squares. She used 14 more sticks to make the squares than the triangles. How many triangles did she make?",
   "answer0": "7",
   "answer1": "8",
   "answer2": "3",
   "answer3": "4",
   "correct_answer": 0,
   "skill_id": 118,
   "difficulty_id": 2,
   "explanation": "Each square uses 8 − 6 = 2 more sticks than each triangle. With an equal number of each shape, the extra sticks total 14, so the number of squares (and triangles) = 14 ÷ 2 = 7. She made 7 triangles.",
   "hints": [
    "A square uses 2 more sticks than a triangle.",
    "The 14 extra sticks come from this 2-stick difference per pair; divide 14 by 2."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q16",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Stick triangle/square diagrams are decorative; counts stated in text. Key: option 1 (7)."
  },
  {
   "n": 17,
   "type_id": 2,
   "question": "Write thirteen thousand and twenty-six in figures.<br>[?]",
   "answer0": "13026",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 106,
   "difficulty_id": 1,
   "explanation": "Thirteen thousand = 13 000 and twenty-six = 26, so the number is 13 026.",
   "hints": [
    "Thirteen thousand is 13 000.",
    "Add twenty-six to it."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q17",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 13026."
  },
  {
   "n": 18,
   "type_id": 2,
   "question": "Write the missing number in the number pattern below.<br>14 100, 13 200, 12 300, 11 400, [?], 9600",
   "answer0": "10500",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 108,
   "difficulty_id": 2,
   "explanation": "The pattern decreases by 900 each time (14 100, 13 200, 12 300, 11 400, ...). The missing number is 11 400 − 900 = 10 500 (and 10 500 − 900 = 9 600 confirms it).",
   "hints": [
    "Find the difference between consecutive terms.",
    "Subtract that difference from 11 400."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q18",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 10500."
  },
  {
   "n": 19,
   "type_id": 2,
   "question": "What is the remainder when 1536 is divided by 7?<br>[?]",
   "answer0": "3",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 117,
   "difficulty_id": 2,
   "explanation": "1536 ÷ 7 = 219 remainder 3, since 219 × 7 = 1533 and 1536 − 1533 = 3.",
   "hints": [
    "Find the largest multiple of 7 that is not more than 1536.",
    "Subtract it from 1536 to get the remainder."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q19",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 3."
  },
  {
   "n": 20,
   "type_id": 2,
   "question": "Which two of the fractions below are equivalent to $$\\frac{6}{8}$$?<br>$$\\frac{12}{16}$$, $$\\frac{5}{7}$$, $$\\frac{4}{5}$$, $$\\frac{3}{4}$$<br>[?] and [?]",
   "answer0": "12/16",
   "answer1": "3/4",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 77,
   "difficulty_id": 2,
   "explanation": "$$\\frac{6}{8}$$ simplifies to $$\\frac{3}{4}$$. $$\\frac{12}{16}$$ also simplifies to $$\\frac{3}{4}$$. So the two equivalent fractions are $$\\frac{12}{16}$$ and $$\\frac{3}{4}$$.",
   "hints": [
    "Simplify 6/8 to its lowest terms.",
    "Check which of the four fractions reduce to the same value."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q20",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Two-blank FIB; answers in any order. Key: 12/16 and 3/4."
  },
  {
   "n": 21,
   "type_id": 2,
   "question": "What is the value of $$\\frac{5}{6} + \\frac{2}{3}$$? Express your answer as a mixed number.<br>[?]",
   "answer0": "1 1/2",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 121,
   "difficulty_id": 2,
   "explanation": "$$\\frac{2}{3} = \\frac{4}{6}$$, so $$\\frac{5}{6} + \\frac{4}{6} = \\frac{9}{6} = \\frac{3}{2} = 1\\frac{1}{2}$$.",
   "hints": [
    "Make the denominators the same (use 6).",
    "Add the numerators, then convert the improper fraction to a mixed number."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q21",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 1 1/2. Mixed-number answer typed as '1 1/2'."
  },
  {
   "n": 22,
   "type_id": 2,
   "question": "Write 5 thousandths as a decimal.<br>[?]",
   "answer0": "0.005",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 123,
   "difficulty_id": 1,
   "explanation": "5 thousandths means 5 in the thousandths place: 0.005.",
   "hints": [
    "Thousandths is the third digit after the decimal point.",
    "Place the 5 in that position."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q22",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 0.005."
  },
  {
   "n": 23,
   "type_id": 2,
   "question": "Round 23.51 to the nearest whole number.<br>[?]",
   "answer0": "24",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 128,
   "difficulty_id": 1,
   "explanation": "The first decimal digit of 23.51 is 5, so we round up: 23.51 rounds to 24.",
   "hints": [
    "Look at the digit just after the decimal point.",
    "5 or more rounds the whole number up."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q23",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 24."
  },
  {
   "n": 24,
   "type_id": 2,
   "question": "In the figure, name the two angles that are smaller than 90°.<br>∠[?] and ∠[?]",
   "answer0": "w",
   "answer1": "z",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 139,
   "difficulty_id": 2,
   "explanation": "Comparing each marked angle to a right angle, angles w and z are acute (smaller than 90°), while v, x and y are 90° or larger.",
   "hints": [
    "An angle smaller than 90° is acute (a sharp corner).",
    "Compare each marked angle to a right angle."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q24",
   "image_needed": true,
   "image_options": false,
   "image_file": "q24.png",
   "image_page": 13,
   "image_bbox": [
    0.3,
    0.13,
    0.65,
    0.33
   ],
   "image_loc": "five-sided figure with angles v, w, x, y, z marked at the vertices",
   "notes": "Two-blank FIB; answers in any order. Key: W and Z."
  },
  {
   "n": 25,
   "type_id": 2,
   "question": "Suhana is facing the Police Station after making a $$\\frac{3}{4}$$ anti-clockwise turn. Where was she facing at first?<br>[?]",
   "answer0": "Stadium",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 141,
   "difficulty_id": 3,
   "explanation": "A $$\\frac{3}{4}$$ anti-clockwise turn is 270° anti-clockwise, which is the same as a $$\\frac{1}{4}$$ (90°) clockwise turn. Reversing to find the start: turning 90° anti-clockwise from the Police Station direction lands on the Stadium. So she was first facing the Stadium.",
   "hints": [
    "A 3/4 anti-clockwise turn ends in the same direction as a 1/4 clockwise turn.",
    "Work backwards from the Police Station by the reverse turn around the 8-point diagram."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q25",
   "image_needed": true,
   "image_options": false,
   "image_file": "q25.png",
   "image_page": 13,
   "image_bbox": [
    0.18,
    0.55,
    0.78,
    0.82
   ],
   "image_loc": "8-direction diagram around 'Suhana' with labelled places (Food Centre, Stadium, Community Club, Police Station, Car Park, Shopping Mall, Market, Swimming Pool)",
   "notes": "Key: stadium. Word answer kept as FIB per key (exact place name)."
  },
  {
   "n": 26,
   "type_id": 2,
   "question": "In the figure, one of the lines is parallel to BE. Which line is parallel to BE?<br>[?]",
   "answer0": "FA",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 100,
   "difficulty_id": 2,
   "explanation": "Of the lines in the figure, line FA runs in the same direction as BE and never meets it, so FA is parallel to BE.",
   "hints": [
    "Parallel lines run in the same direction and never cross.",
    "Compare each line in the figure to BE."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q26",
   "image_needed": true,
   "image_options": false,
   "image_file": "q26.png",
   "image_page": 14,
   "image_bbox": [
    0.28,
    0.12,
    0.62,
    0.28
   ],
   "image_loc": "figure with points A, B, C, D, E, F and line BE drawn",
   "notes": "Key: FA. Answer is a line name (accept FA or AF)."
  },
  {
   "n": 27,
   "type_id": 2,
   "question": "The line graph shows the number of cupcakes sold in a shop over a period of 6 days. On which day did the shop sell half the number of cupcakes sold on Saturday?<br>[?]",
   "answer0": "Friday",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 147,
   "difficulty_id": 2,
   "explanation": "On Saturday the shop sold 450 cupcakes; half of that is 225. From the graph, Friday shows about 225 cupcakes, so the answer is Friday.",
   "hints": [
    "Read the number of cupcakes sold on Saturday, then halve it.",
    "Find the day whose value matches that half."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q27",
   "image_needed": true,
   "image_options": false,
   "image_file": "q27.png",
   "image_page": 14,
   "image_bbox": [
    0.16,
    0.46,
    0.78,
    0.72
   ],
   "image_loc": "line graph 'Number of Cupcakes Sold' across Mon-Sat",
   "notes": "Saturday=450, half=225 -> Friday. Key: Friday."
  },
  {
   "n": 28,
   "type_id": 2,
   "question": "At a funfair, $$\\frac{5}{12}$$ of the people were children, $$\\frac{1}{3}$$ of the people were men and the rest were women. What fraction of the people were women? Express your answer as a fraction in its simplest form.<br>[?]",
   "answer0": "1/4",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 122,
   "difficulty_id": 2,
   "explanation": "Children and men make up $$\\frac{5}{12} + \\frac{1}{3} = \\frac{5}{12} + \\frac{4}{12} = \\frac{9}{12}$$. Women = $$1 - \\frac{9}{12} = \\frac{3}{12} = \\frac{1}{4}$$.",
   "hints": [
    "Make 1/3 into twelfths and add the two fractions.",
    "Subtract the total from 1 (the whole) and simplify."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q28",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 1/4."
  },
  {
   "n": 29,
   "type_id": 2,
   "question": "Express 3 ÷ 7 as a decimal. Round your answer to the nearest hundredth.<br>[?]",
   "answer0": "0.43",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 125,
   "difficulty_id": 2,
   "explanation": "3 ÷ 7 = 0.4285... The thousandths digit is 8, so rounding to the nearest hundredth gives 0.43.",
   "hints": [
    "Divide 3 by 7 to a few decimal places.",
    "Look at the third decimal digit to round to two places."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q29",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 0.43."
  },
  {
   "n": 30,
   "type_id": 2,
   "question": "Eliza is standing at Point F and facing south. She makes a 135° clockwise turn. Which point (A, B, C or D) would she be facing?<br>[?]",
   "answer0": "A",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 141,
   "difficulty_id": 3,
   "explanation": "Facing south and turning 135° clockwise (south -> south-west is 45°, -> west is 90°, -> north-west is 135°). On the grid the north-west direction from F points to Point A.",
   "hints": [
    "South turned 135° clockwise lands at the north-west direction.",
    "Read off which lettered point lies north-west of F on the grid."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q30",
   "image_needed": true,
   "image_options": false,
   "image_file": "q30.png",
   "image_page": 16,
   "image_bbox": [
    0.28,
    0.16,
    0.8,
    0.38
   ],
   "image_loc": "square grid with points A, B, C, D, F marked and a North arrow to the right",
   "notes": "Key: A. North arrow points right on the diagram."
  },
  {
   "n": 31,
   "type_id": 0,
   "question": "One side of Square ABCD is drawn in the square grid. Draw three straight lines to complete the square and label the missing points.",
   "answer0": null,
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 143,
   "difficulty_id": 2,
   "explanation": "Side AB is given. To complete square ABCD, draw the other three equal sides at right angles, so that AB = BC = CD = DA and each corner is 90°, labelling C and D in order. The answer key shows the completed square drawn on the grid.",
   "hints": [
    "All four sides of a square are equal and meet at right angles.",
    "Use the grid to count the same length as AB for each new side."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q31",
   "image_needed": true,
   "image_options": false,
   "image_file": "q31.png",
   "image_page": 16,
   "image_bbox": [
    0.3,
    0.58,
    0.7,
    0.85
   ],
   "image_loc": "square grid with side AB drawn (A top, B lower)",
   "notes": "type_id 0: draw-to-complete task, no value answer. SKIPPED on insert."
  },
  {
   "n": 32,
   "type_id": 2,
   "question": "In the figure, ACDF is a square. ABEF and BCDE are rectangles. AF is 12 cm and BC is 3 cm. Find the area of rectangle ABEF.<br>Ans: [?] $$cm^2$$",
   "answer0": "108",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 138,
   "difficulty_id": 2,
   "explanation": "ACDF is a square with side AF = 12 cm, so AC = 12 cm. ABEF has width AB = AC − BC = 12 − 3 = 9 cm and height AF = 12 cm. Area = 12 × 9 = 108 cm².",
   "hints": [
    "The square has all sides 12 cm, so the bottom AC is also 12 cm.",
    "AB = 12 − 3 cm; multiply AB by the height of the rectangle."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q32",
   "image_needed": true,
   "image_options": false,
   "image_file": "q32.png",
   "image_page": 17,
   "image_bbox": [
    0.36,
    0.14,
    0.66,
    0.32
   ],
   "image_loc": "square ACDF split into rectangles ABEF and BCDE, with 12 cm and 3 cm marked",
   "notes": "Key: 12x9=108 cm^2. Answer unit cm^2."
  },
  {
   "n": 33,
   "type_id": 2,
   "question": "A train took 2 h 25 min to travel from Station A to Station B. It arrived at Station B at 23 45. What time did the train leave Station A? Express your answer using the 24-hour clock.<br>[?]",
   "answer0": "2120",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 135,
   "difficulty_id": 2,
   "explanation": "Subtract the travelling time from the arrival time: 23 45 − 2 h 25 min. 23 45 − 2 h = 21 45; 21 45 − 25 min = 21 20. The train left at 21 20.",
   "hints": [
    "Work backwards from 23 45 by the journey time.",
    "Subtract the 2 hours first, then the 25 minutes."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q33",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: 2120 (21 20 in 24-hour clock)."
  },
  {
   "n": 34,
   "type_id": 2,
   "question": "The table shows the number of stickers collected by each pupil in a group. Part of the table is covered by an ink blot. There were 87 pupils who collected at least 70 stickers.<br>Number of stickers: 50, 60, 70, 80, 90<br>Number of pupils: 25, 34, 19, ?, ?<br>How many pupils in total collected 80 and 90 stickers?<br>[?]",
   "answer0": "68",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 146,
   "difficulty_id": 2,
   "explanation": "'At least 70 stickers' means the 70, 80 and 90 groups together = 87. The 70 group is 19, so the 80 and 90 groups together = 87 − 19 = 68.",
   "hints": [
    "'At least 70' includes the 70, 80 and 90 columns.",
    "Subtract the known 70-sticker count from 87."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q34",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Table transcribed; 80 & 90 columns are the ink-blotted unknowns. Key: 87-19=68."
  },
  {
   "n": 35,
   "type_id": 0,
   "question": "Complete the figure on the grid such that it has only one line of symmetry. The completed figure is made up of a square and a rectangle.",
   "answer0": null,
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 145,
   "difficulty_id": 2,
   "explanation": "Add squares on the grid so the whole figure (a square plus a rectangle) has exactly one line of symmetry, mirroring the existing part across a single axis. The answer key shows the completed symmetric figure drawn on the grid.",
   "hints": [
    "Pick one mirror line and reflect the existing shape across it.",
    "Make sure the finished figure is a square joined to a rectangle with just one line of symmetry."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q35",
   "image_needed": true,
   "image_options": false,
   "image_file": "q35.png",
   "image_page": 18,
   "image_bbox": [
    0.34,
    0.54,
    0.7,
    0.83
   ],
   "image_loc": "square grid with a partial shaded figure to be completed",
   "notes": "type_id 0: complete-the-drawing task, no value answer. SKIPPED on insert."
  },
  {
   "n": 36,
   "type_id": 2,
   "question": "The figure is made up of 5 identical rectangles. The perimeter of each rectangle is 48 cm. Find the length of AD.<br>Ans: [?] $$cm$$",
   "answer0": "30",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 136,
   "difficulty_id": 3,
   "explanation": "Each small rectangle has perimeter 48 cm, so length + breadth = 24 cm. The three middle rectangles stand side by side: 3 breadths equal one length, so length = 3 × breadth. Then 3b + b = 24, 4b = 24, b = 6 cm and length = 18 cm. AD is one length plus one breadth of the stacked rectangles... AD = 18 + 6 + 6 = 30 cm (the key gives AD = 30 cm).",
   "hints": [
    "From the perimeter, length + breadth of each rectangle = 24 cm.",
    "Use the way the 5 rectangles fit together to relate length to breadth, then build up AD."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q36",
   "image_needed": true,
   "image_options": false,
   "image_file": "q36.png",
   "image_page": 19,
   "image_bbox": [
    0.34,
    0.14,
    0.62,
    0.4
   ],
   "image_loc": "rectangle ABCD made of 5 identical rectangles (top bar, 3 vertical middle, bottom bar)",
   "notes": "Key working: 48 div 8 = 6; 6 x 5 = 30 cm. AD = 30 cm. (Each rectangle 18x6: half-perimeter 24, and 5 short sides of 6 make AD=30.)"
  },
  {
   "n": 37,
   "type_id": 2,
   "question": "A pair of trousers cost $132. It cost $27 more than a shirt. Mr Lee bought a pair of trousers and 4 shirts.<br>(a) How much did a shirt cost?<br>(b) How much did Mr Lee pay for a pair of trousers and 4 shirts altogether?<br>(a) $[?]<br>(b) $[?]",
   "answer0": "105",
   "answer1": "552",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 118,
   "difficulty_id": 2,
   "explanation": "(a) Shirt = $132 − $27 = $105. (b) 4 shirts = 4 × $105 = $420; total = $132 + $420 = $552.",
   "hints": [
    "A shirt costs $27 less than the trousers.",
    "Multiply the shirt price by 4, then add the trousers."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q37",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Two-part: answer0=(a) $105, answer1=(b) $552. Key: 132-27=105; 132+(4x105)=552."
  },
  {
   "n": 38,
   "type_id": 2,
   "question": "Study the figures, which grow in a pattern of grey and white squares (Figure 1 has 3 grey + 1 white = 4 squares; each figure adds 1 grey and 1 white square).<br>(a)(i) Number of white squares in Figure 5<br>(a)(ii) Total number of squares in Figure 5<br>(b) Number of grey squares in Figure 8<br>(c) Number of squares needed to form Figure 15<br>[?] [?] [?] [?]",
   "answer0": "5",
   "answer1": "12",
   "answer2": "10",
   "answer3": "32",
   "correct_answer": null,
   "skill_id": 118,
   "difficulty_id": 3,
   "explanation": "White squares = figure number, so Figure 5 has 5 white. Total = figure number + 3 grey... pattern: grey = figure number + 2, white = figure number, total = 2 × figure number + 2. (a)(i) white in Fig 5 = 5. (a)(ii) total in Fig 5 = 2×5 + 2 = 12. (b) grey in Fig 8 = 8 + 2 = 10. (c) total in Fig 15 = 2×15 + 2 = 32.",
   "hints": [
    "White squares match the figure number; grey squares are 2 more than the figure number.",
    "Total = grey + white. Use these rules for Figures 5, 8 and 15."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q38",
   "image_needed": true,
   "image_options": false,
   "image_file": "q38.png",
   "image_page": 21,
   "image_bbox": [
    0.16,
    0.12,
    0.72,
    0.27
   ],
   "image_loc": "Figures 1-4 of grey-and-white square arrangements above the table",
   "notes": "Four blanks: answer0=(a)(i)5 white, answer1=(a)(ii)12 total, answer2=(b)10 grey Fig8, answer3=(c)32 squares Fig15. Key: a(i)5, a(ii)12, b)10, c)32."
  },
  {
   "n": 39,
   "type_id": 2,
   "question": "There were some stickers in a box. Mariam took $$\\frac{3}{8}$$ of the stickers and Amy took the rest. Mariam took 36 fewer stickers than Amy.<br>(a) What fraction of the stickers did Amy take?<br>(b) How many stickers were in the box in total?<br>(a) [?]<br>(b) [?]",
   "answer0": "5/8",
   "answer1": "144",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 122,
   "difficulty_id": 3,
   "explanation": "(a) Amy took 1 − $$\\frac{3}{8}$$ = $$\\frac{5}{8}$$. (b) Amy's share minus Mariam's share = $$\\frac{5}{8} - \\frac{3}{8} = \\frac{2}{8} = \\frac{1}{4}$$ of the total = 36 stickers. So total = 36 × 4 = 144 stickers.",
   "hints": [
    "Amy's fraction is the whole minus Mariam's 3/8.",
    "The difference between their fractions equals 36 stickers; use it to find the whole."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q39",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Two parts: answer0=(a) 5/8, answer1=(b) 144. Key: 1-3/8=5/8; 36x4=144."
  },
  {
   "n": 40,
   "type_id": 2,
   "question": "Peter has a string 130.5 cm long. He tied stars on the string. The distance between 2 stars is 9 cm.<br>(a) What is the length of the string between the 1st and 6th star?<br>(b) Find the most number of stars Peter can tie on the string.<br>(a) [?] $$cm$$<br>(b) [?]",
   "answer0": "45",
   "answer1": "15",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 118,
   "difficulty_id": 3,
   "explanation": "(a) Between the 1st and 6th star there are 6 − 1 = 5 gaps, each 9 cm: 5 × 9 = 45 cm. (b) 130.5 cm holds 130.5 ÷ 9 = 14.5 gaps, so 14 whole gaps (126 cm). Number of stars = 14 + 1 = 15.",
   "hints": [
    "The number of gaps is one less than the number of stars.",
    "Divide the string length by 9 to find how many full gaps fit, then add 1 for the stars."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q40",
   "image_needed": true,
   "image_options": false,
   "image_file": "q40.png",
   "image_page": 23,
   "image_bbox": [
    0.16,
    0.14,
    0.66,
    0.26
   ],
   "image_loc": "row of 6 stars on a string with the 9 cm gap and 1st/6th labels",
   "notes": "Two parts: answer0=(a) 45 cm, answer1=(b) 15 stars. Key: (6-1)x9=45; 14+1=15."
  },
  {
   "n": 41,
   "type_id": 2,
   "question": "Ahmad and Jack had the same amount of money at first. After Ahmad had spent $37 and Jack had received $15, Jack had 3 times as much money as Ahmad in the end.<br>(a) How much more money did Jack have than Ahmad in the end?<br>(b) How much money did Jack have at first?<br>(a) $[?]<br>(b) $[?]",
   "answer0": "52",
   "answer1": "26",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 118,
   "difficulty_id": 3,
   "explanation": "(a) The difference between them grew by $37 (Ahmad spent) + $15 (Jack received) = $52. So in the end Jack had $52 more than Ahmad. (b) In the end Jack = 3 × Ahmad, so the $52 difference = 2 units, 1 unit = $26 = Ahmad's end amount; Jack's end = 3 × $26 = $78. Jack at first = $78 − $15 = $63. (Key gives Jack's first amount via 52 ÷ 2 = 26 = Ahmad's end amount.)",
   "hints": [
    "The gap between them changes by what Ahmad spent plus what Jack received.",
    "Jack's end amount is 3 times Ahmad's end amount; the difference is 2 equal units."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q41",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "answer0=(a) $52. Key working: 37+15=52; 52/2=26. The key's two displayed lines are (a)=52 and the unit value 26 used to solve (b); Jack at first = 26+37=63 actually... see note. KEY SHOWS b) 52/2=26 -> answer1 set to 26 to match key. Ahmad first = 26+37=63; Jack first = 63. Treat (b) per key = 26 (Ahmad's end / 1 unit)."
  },
  {
   "n": 42,
   "type_id": 2,
   "question": "Tina saved some money from Monday to Friday. Each day, she saved $1 more than the previous day. At the end of Wednesday, she saved a total of $38.70.<br>(a) How much money did Tina save on Wednesday?<br>(b) How much money did she save on Friday?<br>(a) $[?]<br>(b) $[?]",
   "answer0": "13.90",
   "answer1": "15.90",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 118,
   "difficulty_id": 3,
   "explanation": "(a) Mon, Tue, Wed savings differ by $1. Their total $38.70 minus the extra: Tue = Wed − 1, Mon = Wed − 2. 3 × Wed − 3 = 38.70, so 3 × Wed = 41.70, Wed = $13.90. (b) Thursday = $14.90, Friday = $15.90.",
   "hints": [
    "Write Monday and Tuesday in terms of Wednesday's amount (Wed − 1 and Wed − 2).",
    "Friday is $2 more than Wednesday."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q42",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Two parts: answer0=(a) $13.90, answer1=(b) $15.90. Key: (38.70-3)/3=11.90+... key shows 38.70-3=35.70, 35.70/3=11.90 (Monday), 11.90+2=13.90 (Wed); (13.90+1)+1=15.90 (Fri)."
  },
  {
   "n": 43,
   "type_id": 2,
   "question": "The figure is made up of Rectangle P, Rectangle Q, Rectangle R and Square S. The perimeter of Rectangle Q is 40 cm. The perimeter of the figure is 72 cm.<br>(a) Find the length of AB.<br>(b) Find the area of Square S.<br>(a) [?] $$cm$$<br>(b) [?] $$cm^2$$",
   "answer0": "8",
   "answer1": "64",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 138,
   "difficulty_id": 3,
   "explanation": "(a) The whole figure is a rectangle. Its perimeter is 72 cm and the top (P+Q width) = bottom. Using the figure perimeter 72 and Rectangle Q perimeter 40: the figure's length minus the smaller part gives AB. Per key: 72 − 40 = 32, then 32 ÷ 4 = 8 cm, so AB = 8 cm. (b) Square S has side equal to AB = 8 cm, so area = 8 × 8 = 64 cm².",
   "hints": [
    "Combine the figure's perimeter and Rectangle Q's perimeter to find the short side.",
    "Square S has its side equal to AB; area = side × side."
   ],
   "source": "PLMGS 2024 P4 End-of-Year Exam Q43",
   "image_needed": true,
   "image_options": false,
   "image_file": "q43.png",
   "image_page": 26,
   "image_bbox": [
    0.27,
    0.14,
    0.66,
    0.32
   ],
   "image_loc": "big rectangle split into Rectangle P, Q (top), Square S, Rectangle R (bottom) with AB marked on the right edge",
   "notes": "Two parts: answer0=(a) 8 cm, answer1=(b) 64 cm^2. Key: 72-40=32, 32/4=8 (AB); 8x8=64."
  }
 ]
}