{
  "paper": {
    "school": "Rulang",
    "year": 2025,
    "level": "P5",
    "label": "End-of-Year Exam",
    "source_prefix": "Rulang 2025 P5 End-of-Year Exam",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "What is the value of the digit 5 in 50 983?",
      "answer0": "50", "answer1": "500", "answer2": "5000", "answer3": "50 000",
      "correct_answer": 3,
      "skill_id": 149,
      "difficulty_id": 1,
      "explanation": "In 50 983 the digit 5 is in the ten thousands place, so its value is 50 000.",
      "hints": ["Identify the place of the digit 5.", "5 is in the ten thousands column."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 1 Q1",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": ""
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "70 000 + 3000 + 600 + 2 = ____________",
      "answer0": "70 362", "answer1": "73 062", "answer2": "73 602", "answer3": "73 620",
      "correct_answer": 2,
      "skill_id": 149,
      "difficulty_id": 1,
      "explanation": "Add the place values: 70 000 + 3000 + 600 + 2 = 73 602.",
      "hints": ["Line up the digits by place value.", "There are no tens, so the tens digit is 0."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 1 Q2",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": ""
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "What fraction of the stars are shaded?",
      "answer0": "\\(\\dfrac{3}{7}\\)", "answer1": "\\(\\dfrac{4}{7}\\)", "answer2": "\\(\\dfrac{1}{2}\\)", "answer3": "\\(\\dfrac{3}{4}\\)",
      "correct_answer": 0,
      "skill_id": 157,
      "difficulty_id": 1,
      "explanation": "There are 7 stars in total and 3 are shaded, so the shaded fraction is 3/7.",
      "hints": ["Count the total number of stars.", "Count how many are shaded out of the total."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 1 Q3",
      "image_needed": true, "image_options": false, "image_file": "q3.png",
      "image_page": 2, "image_bbox": [0.40, 0.43, 0.68, 0.55],
      "image_loc": "row of stars, some shaded, in a box",
      "notes": "Printed key: option (1) 3/7."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Which of the following is equal to \\(4\\dfrac{7}{8}\\)?",
      "answer0": "\\(\\dfrac{28}{8}\\)", "answer1": "\\(\\dfrac{32}{8}\\)", "answer2": "\\(\\dfrac{39}{8}\\)", "answer3": "\\(\\dfrac{47}{8}\\)",
      "correct_answer": 2,
      "skill_id": 119,
      "difficulty_id": 1,
      "explanation": "4 7/8 = (4 × 8 + 7)/8 = (32 + 7)/8 = 39/8.",
      "hints": ["Multiply the whole number by the denominator and add the numerator.", "(4 × 8 + 7)/8."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 1 Q4",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Printed key: option (3) 39/8."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "\\(60 + \\dfrac{6}{10} + \\dfrac{6}{100}\\) = ____________",
      "answer0": "60.06", "answer1": "60.66", "answer2": "60.066", "answer3": "60.606",
      "correct_answer": 1,
      "skill_id": 123,
      "difficulty_id": 1,
      "explanation": "6/10 = 0.6 (tenths) and 6/100 = 0.06 (hundredths). So 60 + 0.6 + 0.06 = 60.66.",
      "hints": ["6/10 is 0.6 and 6/100 is 0.06.", "Add the whole number and the decimal parts."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 1 Q5",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Printed key: option (2) 60.66."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "Candice folds 3 stars in 5 minutes. At this rate, how many stars can Candice fold in 30 minutes?",
      "answer0": "15", "answer1": "18", "answer2": "90", "answer3": "150",
      "correct_answer": 1,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "30 ÷ 5 = 6 sets of 5 minutes. Each set folds 3 stars, so 6 × 3 = 18 stars.",
      "hints": ["How many 5-minute sets are in 30 minutes?", "Multiply that by 3 stars."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 1 Q6",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Printed key: option (2) 18."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "The figure is divided into 20 equal parts. What percentage of the figure is shaded?",
      "answer0": "15%", "answer1": "75%", "answer2": "3%", "answer3": "4%",
      "correct_answer": 1,
      "skill_id": 171,
      "difficulty_id": 2,
      "explanation": "15 of the 20 equal parts are shaded. 15/20 = 75/100 = 75%.",
      "hints": ["Count the shaded parts out of 20.", "15/20 as a percentage."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 1 Q7",
      "image_needed": true, "image_options": false, "image_file": "q7.png",
      "image_page": 3, "image_bbox": [0.46, 0.30, 0.66, 0.40],
      "image_loc": "grid of 20 equal parts with some shaded",
      "notes": "Printed key: option (2) 75% (15 of 20 shaded)."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "A solid cuboid of height 10 cm has a square base of side 5 cm. What is its volume?",
      "answer0": "50 cm³", "answer1": "100 cm³", "answer2": "250 cm³", "answer3": "500 cm³",
      "correct_answer": 2,
      "skill_id": 190,
      "difficulty_id": 1,
      "explanation": "Volume = base area × height = (5 × 5) × 10 = 25 × 10 = 250 cm³.",
      "hints": ["Base area = 5 × 5.", "Multiply the base area by the height 10 cm."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 1 Q8",
      "image_needed": true, "image_options": false, "image_file": "q8.png",
      "image_page": 3, "image_bbox": [0.48, 0.42, 0.66, 0.56],
      "image_loc": "cuboid with square base 5 cm and height 10 cm",
      "notes": "Printed key: option (3) 250 cm³."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "Which angle is a right angle?",
      "answer0": "∠a", "answer1": "∠b", "answer2": "∠c", "answer3": "∠d",
      "correct_answer": 0,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "Comparing the marked angles in the quadrilateral, ∠a is exactly 90° (a right angle).",
      "hints": ["A right angle is exactly 90° (a square corner).", "Compare each marked angle to a square corner."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 1 Q9",
      "image_needed": true, "image_options": false, "image_file": "q9.png",
      "image_page": 3, "image_bbox": [0.46, 0.58, 0.80, 0.74],
      "image_loc": "quadrilateral with angles a, b, c, d marked",
      "notes": "Printed key: option (1) ∠a."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "PQ and RS are straight lines. Which of the following is true?",
      "answer0": "∠a = ∠c", "answer1": "∠b = ∠d", "answer2": "∠a + ∠c = 180°", "answer3": "∠c + ∠d = 180°",
      "correct_answer": 1,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "Where two straight lines cross, vertically opposite angles are equal. ∠b and ∠d are vertically opposite, so ∠b = ∠d.",
      "hints": ["Look for vertically opposite angles at the crossing point.", "Vertically opposite angles are equal."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 1 Q10",
      "image_needed": true, "image_options": false, "image_file": "q10.png",
      "image_page": 3, "image_bbox": [0.46, 0.76, 0.82, 0.90],
      "image_loc": "two straight lines PQ and RS crossing with angles a, b, c, d marked",
      "notes": "Printed key: option (2) ∠b = ∠d."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "GHJ is a right-angled triangle (right angle at H). Find ∠y (at G). The angle at J is 30°.",
      "answer0": "20°", "answer1": "40°", "answer2": "60°", "answer3": "80°",
      "correct_answer": 2,
      "skill_id": 197,
      "difficulty_id": 2,
      "explanation": "Angle sum of a triangle is 180°. ∠H = 90°, ∠J = 30°, so ∠y = 180° − 90° − 30° = 60°.",
      "hints": ["The angles in a triangle add to 180°.", "Subtract the 90° and 30° angles."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 1 Q11",
      "image_needed": true, "image_options": false, "image_file": "q11.png",
      "image_page": 4, "image_bbox": [0.40, 0.13, 0.70, 0.26],
      "image_loc": "right-angled triangle GHJ with right angle at H and 30° at J",
      "notes": "Printed key: option (3) 60°."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "EFGH is a rhombus. Find ∠a (at E). The angle at F is 64°.",
      "answer0": "32°", "answer1": "58°", "answer2": "64°", "answer3": "116°",
      "correct_answer": 1,
      "skill_id": 200,
      "difficulty_id": 3,
      "explanation": "The diagonal of the rhombus from E forms an isosceles triangle. With the 64° angle at F and the rhombus's properties, ∠a = (180° − 64°) ÷ 2 = 58°.",
      "hints": ["A rhombus has all sides equal, forming isosceles triangles with a diagonal.", "Base angles of the isosceles triangle are equal."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 1 Q12",
      "image_needed": true, "image_options": false, "image_file": "q12.png",
      "image_page": 4, "image_bbox": [0.40, 0.28, 0.62, 0.42],
      "image_loc": "rhombus EFGH with diagonal, angles a and 64° marked",
      "notes": "Printed key: option (2) 58°."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "\\(\\dfrac{3}{4} \\times \\dfrac{6}{7}\\) = ____________",
      "answer0": "\\(\\dfrac{1}{14}\\)", "answer1": "\\(\\dfrac{2}{14}\\)", "answer2": "\\(\\dfrac{6}{14}\\)", "answer3": "\\(\\dfrac{9}{14}\\)",
      "correct_answer": 3,
      "skill_id": 161,
      "difficulty_id": 1,
      "explanation": "3/4 × 6/7 = 18/28 = 9/14.",
      "hints": ["Multiply across, then simplify.", "18/28 simplifies to 9/14."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 1 Q13",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Printed key: option (4) 9/14."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "Mr Tan has 20 bags of rice and 10 bags of salt. Each bag of rice has a mass of 4.25 kg. Each bag of salt has a mass of 1.7 kg. What is the total mass of all the bags of rice and salt?",
      "answer0": "85 kg", "answer1": "86.7 kg", "answer2": "102 kg", "answer3": "178.5 kg",
      "correct_answer": 2,
      "skill_id": 130,
      "difficulty_id": 2,
      "explanation": "Rice = 20 × 4.25 = 85 kg. Salt = 10 × 1.7 = 17 kg. Total = 85 + 17 = 102 kg.",
      "hints": ["Find the total mass of rice, then the total mass of salt.", "Add the two totals."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 1 Q14",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Printed key: option (3) 102 kg."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "Mrs Lee parked her car at a mall from 1:30 pm to 8:00 pm. The parking rates were: From 6:00 am to 6:00 pm: $1.50 per hour or part thereof. From 6:00 pm to 6:00 am: $2. How much did she pay for her parking charges?",
      "answer0": "$8", "answer1": "$9.50", "answer2": "$11.50", "answer3": "$12",
      "correct_answer": 1,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "From 1:30 pm to 6:00 pm = 4 h 30 min, charged at $1.50 per hour or part thereof = 5 hours × $1.50 = $7.50. From 6:00 pm to 8:00 pm = 2 hours at $2... using the daytime/evening split per the key, the total works out to $9.50.",
      "hints": ["Split the time into the daytime rate and the evening rate.", "Round up part-hours in the daytime portion."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 1 Q15",
      "image_needed": true, "image_options": false, "image_file": "q15.png",
      "image_page": 4, "image_bbox": [0.26, 0.66, 0.78, 0.76],
      "image_loc": "parking-rates table",
      "notes": "Printed key: option (2) $9.50."
    },
    {
      "n": 16,
      "type_id": 1,
      "question": "There are 500 pupils in the school hall. 40% of them are girls. How many girls are there?",
      "answer0": "8", "answer1": "20", "answer2": "200", "answer3": "300",
      "correct_answer": 2,
      "skill_id": 174,
      "difficulty_id": 1,
      "explanation": "40% of 500 = 40/100 × 500 = 200 girls.",
      "hints": ["Find 40% of 500.", "40/100 × 500 = 200."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 1 Q16",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Printed key: option (3) 200."
    },
    {
      "n": 17,
      "type_id": 1,
      "question": "The figure is made up of 2 squares, ABFG and CDEF. Find the area of triangle CDG. GF = 10 cm and FE = 6 cm.",
      "answer0": "18 cm²", "answer1": "30 cm²", "answer2": "36 cm²", "answer3": "60 cm²",
      "correct_answer": 0,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Square CDEF has side 6 cm, so CD = 6 cm. Triangle CDG has base CD = 6 cm and height equal to the 6 cm height of the small square: area = ½ × 6 × 6 = 18 cm².",
      "hints": ["The small square CDEF has side 6 cm.", "Use ½ × base × height for triangle CDG."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 1 Q17",
      "image_needed": true, "image_options": false, "image_file": "q17.png",
      "image_page": 5, "image_bbox": [0.46, 0.30, 0.74, 0.42],
      "image_loc": "two squares ABFG and CDEF with triangle CDG shaded, 10 cm and 6 cm marked",
      "notes": "Printed key: option (1) 18 cm²."
    },
    {
      "n": 18,
      "type_id": 1,
      "question": "A rectangular glass tank is partially filled with 1-cm cubes. How many more 1-cm cubes are needed to fill the tank completely?",
      "answer0": "206", "answer1": "207", "answer2": "208", "answer3": "209",
      "correct_answer": 2,
      "skill_id": 188,
      "difficulty_id": 3,
      "explanation": "The full tank holds (length × width × height) cubes; subtracting the cubes already placed (a single layer around the base) leaves 208 more cubes needed (the printed key answer).",
      "hints": ["Find the full capacity of the tank in 1-cm cubes.", "Subtract the cubes already inside."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 1 Q18",
      "image_needed": true, "image_options": false, "image_file": "q18.png",
      "image_page": 5, "image_bbox": [0.26, 0.46, 0.62, 0.64],
      "image_loc": "3D drawing of a tank partly filled with 1-cm cubes",
      "notes": "Printed key: option (3) 208."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "Find the value of (a) \\(280 \\times 27\\). [?]<br>(b) \\(5405 \\div 5\\). [?]",
      "answer0": "7560", "answer1": "1081",
      "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 151,
      "difficulty_id": 1,
      "explanation": "(a) 280 × 27 = 7560. (b) 5405 ÷ 5 = 1081.",
      "hints": ["(a) Multiply 280 by 27.", "(b) Divide 5405 by 5."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 1 Q19",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Printed key: (a) 7560, (b) 1081."
    },
    {
      "n": 20,
      "type_id": 1,
      "question": "Find the value of (a) \\(\\dfrac{2}{9} \\times 4\\) and (b) \\(\\dfrac{1}{3} \\times \\dfrac{4}{5}\\).",
      "answer0": "(a) \\(\\dfrac{8}{9}\\), (b) \\(\\dfrac{4}{15}\\)",
      "answer1": "(a) \\(\\dfrac{8}{36}\\), (b) \\(\\dfrac{4}{15}\\)",
      "answer2": "(a) \\(\\dfrac{8}{9}\\), (b) \\(\\dfrac{5}{8}\\)",
      "answer3": "(a) \\(\\dfrac{6}{9}\\), (b) \\(\\dfrac{4}{8}\\)",
      "correct_answer": 0,
      "skill_id": 161,
      "difficulty_id": 2,
      "explanation": "(a) 2/9 × 4 = 8/9. (b) 1/3 × 4/5 = 4/15.",
      "hints": ["(a) Multiply the numerator by 4.", "(b) Multiply across the fractions."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 1 Q20",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Both parts give fraction answers, so rendered as MCQ. Printed key: (a) 8/9, (b) 4/15."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "Jenny had 2.05 kg of flour at first. She used 450 g of it. How many kilograms of flour was left? [?] kg",
      "answer0": "1.6",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 184,
      "difficulty_id": 2,
      "explanation": "450 g = 450 ÷ 1000 = 0.45 kg. Flour left = 2.05 − 0.45 = 1.6 kg.",
      "hints": ["Convert 450 g to kilograms.", "Subtract 0.45 kg from 2.05 kg."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 1 Q21",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Printed key: 1.6 kg."
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "Find the value of (a) \\(0.45 \\times 70\\). [?]<br>(b) \\(4.5 \\div 300\\). [?]",
      "answer0": "31.5", "answer1": "0.015",
      "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 130,
      "difficulty_id": 2,
      "explanation": "(a) 0.45 × 70 = 31.5. (b) 4.5 ÷ 300 = 0.015.",
      "hints": ["(a) 0.45 × 7 × 10.", "(b) 4.5 ÷ 3 ÷ 100."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 1 Q22",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Printed key: (a) 31.5, (b) 0.015."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "Name the two angles that are greater than 90°. (Answer with the two angle letters, e.g. a and c.) [?]",
      "answer0": "a and c",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 99,
      "difficulty_id": 2,
      "explanation": "Comparing the marked angles around the point, ∠a and ∠c are each greater than 90° (obtuse).",
      "hints": ["An angle greater than 90° is wider than a square corner.", "Compare each marked angle to a right angle."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 1 Q23",
      "image_needed": true, "image_options": false, "image_file": "q23.png",
      "image_page": 8, "image_bbox": [0.30, 0.44, 0.60, 0.60],
      "image_loc": "rays from a point with angles a, b, c, d, e marked",
      "notes": "Printed key: ∠a and ∠c. answer0 is a label answer."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "Express \\(\\dfrac{3}{8}\\) as a percentage. [?] %",
      "answer0": "37.5",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 173,
      "difficulty_id": 2,
      "explanation": "3/8 × 100% = 300/8 % = 37.5%.",
      "hints": ["Multiply the fraction by 100%.", "3/8 × 100 = 37.5."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 1 Q24",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Printed key: 37.5%."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "The pie chart shows the favourite sports of the children in a class. Football = \\(\\dfrac{1}{5}\\). A right angle is marked between the volleyball and basketball sectors. What percentage of the children chose basketball as their favourite sport? [?] %",
      "answer0": "55",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 235,
      "difficulty_id": 3,
      "explanation": "Volleyball is a right angle = 1/4 = 25%. Football = 1/5 = 20%. Basketball = 100% − 25% − 20% = 55%.",
      "hints": ["The right angle marks volleyball as 25%; football is 1/5 = 20%.", "Basketball = 100% − volleyball − football."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 1 Q25",
      "image_needed": true, "image_options": false, "image_file": "q25.png",
      "image_page": 9, "image_bbox": [0.20, 0.14, 0.50, 0.36],
      "image_loc": "pie chart (volleyball, football 1/5, basketball) with right angle marked",
      "notes": "Printed key: 55%."
    },
    {
      "n": 26,
      "type_id": 1,
      "question": "Joy had 8 m of ribbon. She cut it equally into 10 pieces. What was the length of each piece of ribbon? Express your answer as a fraction in its simplest form.",
      "answer0": "\\(\\dfrac{4}{5}\\) m", "answer1": "\\(\\dfrac{8}{10}\\) m", "answer2": "\\(\\dfrac{1}{10}\\) m", "answer3": "\\(\\dfrac{5}{4}\\) m",
      "correct_answer": 0,
      "skill_id": 157,
      "difficulty_id": 2,
      "explanation": "8 ÷ 10 = 8/10 = 4/5 m.",
      "hints": ["Each piece = 8 ÷ 10.", "8/10 simplifies to 4/5."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 1 Q26",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Answer is a fraction (4/5 m) → rendered as MCQ. Printed key: 4/5 m."
    },
    {
      "n": 27,
      "type_id": 0,
      "question": "Draw the top view and front view of the given solid on the grid.",
      "answer0": null, "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 187,
      "difficulty_id": 2,
      "explanation": "Draw the top view and front view of the solid of unit cubes on the dotted grids (see paper for the model views).",
      "hints": ["The top view is what you see looking straight down.", "The front view is what you see looking along the front-view arrow."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 1 Q27",
      "image_needed": true, "image_options": false, "image_file": "q27.png",
      "image_page": 10, "image_bbox": [0.30, 0.18, 0.62, 0.34],
      "image_loc": "isometric drawing of the solid with Top view and Front view arrows",
      "notes": "Draw-the-views task → type_id 0, skipped on insert."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "The figure is made up of a rectangle and 2 shaded triangles. The rectangle is 24 cm wide and 11 cm tall. Find the total area of the shaded triangles. [?] cm²",
      "answer0": "132",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "The two shaded triangles together have the rectangle's width as base (24 cm) and the rectangle's height as the combined height (11 cm). Total shaded area = ½ × 24 × 11 = 132 cm².",
      "hints": ["The two triangles share the base 24 cm and the height 11 cm.", "Total = ½ × 24 × 11."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 1 Q28",
      "image_needed": true, "image_options": false, "image_file": "q28.png",
      "image_page": 10, "image_bbox": [0.22, 0.62, 0.52, 0.80],
      "image_loc": "rectangle 24 cm by 11 cm with two shaded triangles",
      "notes": "Printed key: ½ × 24 × 11 = 132 cm²."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "In the figure, FGH is a straight line. EF = EG. ∠FEG = 50°. Find ∠EGH. [?] °",
      "answer0": "115",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "Triangle EFG is isosceles (EF = EG), so ∠EGF = (180° − 50°) ÷ 2 = 65°. FGH is a straight line, so ∠EGH = 180° − 65° = 115°.",
      "hints": ["Use the isosceles triangle EF = EG to find ∠EGF.", "Angles on a straight line FGH add to 180°."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 1 Q29",
      "image_needed": true, "image_options": false, "image_file": "q29.png",
      "image_page": 11, "image_bbox": [0.18, 0.16, 0.46, 0.30],
      "image_loc": "isosceles triangle EFG on straight line FGH, 50° marked at E",
      "notes": "Printed key: ∠EGH = 115°."
    },
    {
      "n": 30,
      "type_id": 0,
      "question": "In the figure, AB, BC, CD and DA are straight lines. AB is parallel to DC. AD is parallel to BC. Each statement is either true, false or not possible to tell from the information given: ∠DAB = ∠DCB; ∠ABC + ∠ADC = 180°; ABCD is a trapezium. Put a tick in the correct column.",
      "answer0": null, "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 199,
      "difficulty_id": 3,
      "explanation": "AB // DC and AD // BC make ABCD a parallelogram. In a parallelogram opposite angles are equal, so ∠DAB = ∠DCB is True. Co-interior angles between parallel sides sum to 180°, so ∠ABC + ∠ADC... here both are opposite-side angles, so the statement is False. A parallelogram is not a trapezium under the exclusive definition, so 'ABCD is a trapezium' is False.",
      "hints": ["Two pairs of parallel sides make ABCD a parallelogram.", "Use the angle properties of a parallelogram for each statement."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 1 Q30",
      "image_needed": true, "image_options": false, "image_file": "q30.png",
      "image_page": 11, "image_bbox": [0.20, 0.42, 0.66, 0.56],
      "image_loc": "parallelogram ABCD",
      "notes": "Tick-the-box True/False/Not-possible task → type_id 0, skipped on insert. Printed key: ∠DAB=∠DCB True; ∠ABC+∠ADC=180° False; ABCD is a trapezium False."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "Mr Tan bought an oven for $1035. After a down payment of $90, he paid the remaining amount in monthly payments of $135 each. How many months did Mr Tan take to pay the remaining amount? [?]",
      "answer0": "7",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "Remaining amount = $1035 − $90 = $945. Months = $945 ÷ $135 = 7 months.",
      "hints": ["Subtract the down payment from the total cost.", "Divide the remaining amount by the monthly payment."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 2 Q1",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Printed key: 7 months."
    },
    {
      "n": 32,
      "type_id": 2,
      "question": "A sum of money was shared among Amy, Betty and Clara. Amy received $260 more than Betty. Clara received 4 times as much money as Amy. Betty received $227. How much more money did Clara receive than Amy? [?]",
      "answer0": "1461",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Amy = Betty + $260 = $227 + $260 = $487. Clara = 4 × Amy = 4 × $487 = $1948. Clara − Amy = $1948 − $487 = $1461 (which is 3 × Amy = 3 × $487 = $1461).",
      "hints": ["Find Amy's amount from Betty's $227 plus $260.", "Clara − Amy = 4 units − 1 unit = 3 units = 3 × Amy."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 2 Q2",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Printed key: $1461."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "Darren had 240 stamps. \\(\\dfrac{1}{8}\\) of them were from Malaysia, \\(\\dfrac{1}{6}\\) of them were from Japan and the rest of the stamps were from Singapore. How many stamps were from Singapore? [?]",
      "answer0": "170",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Using 24ths: 1/8 = 3/24 (Malaysia), 1/6 = 4/24 (Japan). Singapore = 24/24 − 3/24 − 4/24 = 17/24. 240 ÷ 24 = 10 per unit, so Singapore = 17 × 10 = 170 stamps.",
      "hints": ["Use a common denominator of 24 for the fractions.", "Singapore is the remaining fraction; apply it to 240."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 2 Q3",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Printed key: 170 Singapore stamps."
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "Sally spent a certain amount of money in 7 days. She spent $5 on the first day, and \\(\\dfrac{3}{8}\\) of the remainder on the second day. She spent a total of $10 over the remaining 5 days. How much money did she spend over the 7 days? [?]",
      "answer0": "21",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "After the first day, the remainder is split: 3/8 on day 2, leaving 5/8 for the last 5 days = $10. So 5 parts = $10, 1 part = $2, and the whole remainder (8 parts) = $16. Total over 7 days = $16 + $5 (first day) = $21.",
      "hints": ["The last 5 days' $10 is 5/8 of the remainder after day 1.", "Find the whole remainder, then add the first day's $5."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 2 Q4",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Printed key: $21."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "∠WOY and ∠XOZ are right angles. ∠WOX + ∠YOZ = ∠XOY. Find ∠XOY. [?] °",
      "answer0": "60",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 194,
      "difficulty_id": 3,
      "explanation": "∠WOY = ∠WOX + ∠XOY = 90° and ∠XOZ = ∠XOY + ∠YOZ = 90°. Adding: ∠WOX + ∠YOZ + 2∠XOY = 180°. Since ∠WOX + ∠YOZ = ∠XOY, this gives 3∠XOY = 180°... so ∠XOY = 90° − 30° = 60° (per the working: 90° ÷ 3 = 30°, ∠XOY = 90° − 30° = 60°).",
      "hints": ["Write ∠WOY and ∠XOZ each as a sum that equals 90°.", "Substitute ∠WOX + ∠YOZ = ∠XOY and solve for ∠XOY."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 2 Q5",
      "image_needed": true, "image_options": false, "image_file": "q35.png",
      "image_page": 14, "image_bbox": [0.20, 0.50, 0.56, 0.70],
      "image_loc": "rays W, X, Y, Z from point O",
      "notes": "Printed key: ∠XOY = 60°."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "The solid is made up of 1-cm cubes. How many more 1-cm cubes must be added to the solid such that the solid formed is the smallest possible cube? [?]",
      "answer0": "195",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 188,
      "difficulty_id": 3,
      "explanation": "The smallest cube that can contain the solid has edge 6 cm, so 6 × 6 × 6 = 216 cubes. The solid already has 21 cubes, so cubes to add = 216 − 21 = 195.",
      "hints": ["Find the edge of the smallest cube that fits the solid.", "Subtract the cubes already in the solid from the cube's total."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 2 Q6",
      "image_needed": true, "image_options": false, "image_file": "q36.png",
      "image_page": 15, "image_bbox": [0.34, 0.22, 0.62, 0.36],
      "image_loc": "isometric drawing of the solid made of 1-cm cubes",
      "notes": "Printed key: 6 × 6 × 6 − 21 = 195. The solid has 21 cubes."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "Apples were sold at 5 for $3.20 and pears were sold at 3 for $4.90. Mr Lee bought an equal number of apples and pears to sell at a carnival. He spent $551.30 more on the pears than on the apples. How many apples did he buy? [?]",
      "answer0": "555",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "For 15 fruits (LCM of 5 and 3): apples = $3.20 × 3 = $9.60, pears = $4.90 × 5 = $24.50. Difference per 15 = $24.50 − $9.60 = $14.90. Number of 15-fruit groups = $551.30 ÷ $14.90 = 37. Apples = 37 × 15 = 555.",
      "hints": ["Use 15 fruits at a time (LCM of 5 and 3) to compare costs.", "The cost difference per 15 fruits is $14.90; divide $551.30 by it."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 2 Q7",
      "image_needed": true, "image_options": false, "image_file": "q37.png",
      "image_page": 16, "image_bbox": [0.14, 0.20, 0.78, 0.34],
      "image_loc": "bags of apples (5 for $3.20) and pears (3 for $4.90)",
      "notes": "Printed key: 555 apples."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "Ellie and Freya had an equal number of beads at first. After Ellie gave Freya 24 beads, Freya had 5 times as many beads as Ellie. How many beads did they have altogether? [?]",
      "answer0": "72",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "After Ellie gives 24 beads, the difference between them is 2 × 24 = 48 beads. Freya = 5 units, Ellie = 1 unit, so 4 units = 48 and 1 unit = 12. The total is unchanged = 5 + 1 = 6 units = 6 × 12 = 72 beads.",
      "hints": ["Giving 24 beads makes the difference 2 × 24 = 48.", "Freya 5 units, Ellie 1 unit; total = 6 units."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 2 Q8",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Printed key: 72 beads."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "Gary and Henry had the same amount of sugar at first. After each of them used some sugar to bake a cake, Henry had 5.46 kg less sugar than Gary. Henry used 4 times as much sugar as Gary to bake the cake.<br>(a) How much sugar did Henry use? [?] kg<br>(b) Gary had 6.5 kg of sugar left. How much sugar did both boys have altogether at first? [?] kg",
      "answer0": "7.28", "answer1": "16.64",
      "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Henry used 4 units and Gary used 1 unit. Since they started equal, Henry's smaller amount left is 3 units less = 5.46 kg, so 3 units = 5.46 and 1 unit = 1.82 kg. (a) Henry used 4 units = 4 × 1.82 = 7.28 kg. (b) Gary had 6.5 kg left and used 1 unit = 1.82 kg, so each started with 6.5 + 1.82 = 8.32 kg; together = 8.32 × 2 = 16.64 kg.",
      "hints": ["Henry used 4 units, Gary 1 unit; the difference 3 units = 5.46 kg.", "(b) Gary's start = left + used; double it for both boys."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 2 Q9",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Printed key: (a) 7.28 kg, (b) 16.64 kg."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "A rectangular tank measuring 45 cm by 18 cm by 36 cm was \\(\\dfrac{2}{9}\\) filled with water. Mrs Tay had 12 identical bottles that were completely filled with water. She poured all the water from the bottles into the tank and it became \\(\\dfrac{1}{2}\\) filled with water.<br>(a) How much water was in the tank at first? [?] ml<br>(b) What was the capacity of each bottle? [?] ml",
      "answer0": "6480", "answer1": "675",
      "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 193,
      "difficulty_id": 3,
      "explanation": "Tank capacity = 45 × 18 × 36 = 29 160 cm³. (a) Water at first = 2/9 × 29 160 = 6480 cm³ = 6480 ml. (b) Volume of 1/2 tank = 1/2 × 29 160 = 14 580 cm³. The 12 bottles added 14 580 − 6480 = 8100 cm³, so each bottle = 8100 ÷ 12 = 675 ml.",
      "hints": ["(a) Water at first = 2/9 of the tank's volume.", "(b) The bottles fill the gap from 2/9 to 1/2; divide by 12."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 2 Q10",
      "image_needed": true, "image_options": false, "image_file": "q40.png",
      "image_page": 19, "image_bbox": [0.34, 0.20, 0.66, 0.36],
      "image_loc": "rectangular tank 45 cm by 18 cm by 36 cm partly filled",
      "notes": "Printed key: (a) 6480 ml, (b) 675 ml."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "At a Science exhibition, \\(\\dfrac{1}{2}\\) of the entrance tickets were sold at full price and \\(\\dfrac{3}{7}\\) of the tickets were sold at half price. The remaining 45 tickets were given away free of charge. The full price of each ticket was $38.<br>(a) How many tickets were there altogether? [?]<br>(b) What was the total amount of money collected from the sale of all the tickets? [?]",
      "answer0": "630", "answer1": "17100",
      "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Full + half + free = 1: 1/2 + 3/7 + free fraction = 1. Common denominator 14: 7/14 + 6/14 = 13/14, so free = 1/14 = 45 tickets, giving total = 14 × 45 = 630. (b) Full-price tickets = 1/2 × 630 = 315 at $38 = $11 970. Half-price = 3/7 × 630 = 270 at $19 = $5130. Total = $11 970 + $5130 = $17 100.",
      "hints": ["The free 45 tickets are the remaining fraction (1/14) of the total.", "(b) Full-price tickets at $38 plus half-price tickets at $19."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 2 Q11",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Printed key: (a) 630 tickets, (b) $17 100."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "Mrs Yeo had some oranges. She threw away \\(\\dfrac{2}{9}\\) of the oranges, which were rotten. She gave \\(\\dfrac{1}{3}\\) of the remainder to her neighbours. She then sold the rest of the oranges at 4 for $2.20. She received $231 from the sale of the oranges.<br>(a) What fraction of the oranges did she give to her neighbours? [?]<br>(b) How many oranges did she have altogether at first? [?]",
      "answer0": null, "answer1": "810",
      "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Threw away 2/9, so remainder = 7/9. Gave 1/3 of the remainder = 1/3 × 7/9 = 7/27 of the total. (a) Fraction given to neighbours = 7/27. (b) Oranges sold at 4 for $2.20: $231 ÷ $2.20 = 105 lots of 4 = 420 oranges sold. These 420 are 14/27 of the total (27/27 − 6/27 rotten... using the working 24 parts in the model: 14 parts = 420, 1 part = 30, so total = 27 parts = 810). Total = 810 oranges.",
      "hints": ["(a) Neighbours got 1/3 of the 7/9 remainder.", "(b) Use the $231 sale (4 for $2.20) to find the oranges sold, then scale to the total."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 2 Q12",
      "image_needed": false, "image_options": false, "image_file": null,
      "notes": "Part (a) answer is a fraction (7/27) → recorded null in answer0; part (b) = 810 (FIB). Printed key: (a) 7/27, (b) 810 oranges."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "Two identical watches are sold at discounted prices in Store A and Store B during a sale. Store A: usual price $350, 15% off. Store B: usual price $320, 10% off.<br>(a) What is the price of the watch in Store A after the discount is given? [?]<br>(b) Mr Neo wants to buy the watch from Store B. How much cheaper will the watch cost in Store B than in Store A during the sale? [?]",
      "answer0": "297.50", "answer1": "9.50",
      "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 3,
      "explanation": "(a) Store A discount = 15% of $350 = $52.50, so price = $350 − $52.50 = $297.50. (b) Store B discount = 10% of $320 = $32, so price = $320 − $32 = $288. Store B is cheaper by $297.50 − $288 = $9.50.",
      "hints": ["(a) Find 15% of $350 and subtract.", "(b) Find Store B's price (10% off $320), then the difference."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 2 Q13",
      "image_needed": true, "image_options": false, "image_file": "q43.png",
      "image_page": 22, "image_bbox": [0.18, 0.14, 0.82, 0.32],
      "image_loc": "two watches: Store A ($350, 15% off) and Store B ($320, 10% off)",
      "notes": "Printed key: (a) $297.50, (b) $9.50."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "In the figure, a rectangular piece of paper EFGH was folded along HJ. ∠EHK = 34°.<br>(a) Find ∠HKJ. [?] °<br>(b) Find ∠JHK. [?] °<br>(c) Find ∠KJF. [?] °",
      "answer0": "90", "answer1": "28", "answer2": "56",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 200,
      "difficulty_id": 3,
      "explanation": "(a) ∠HKJ = 90° (the folded right angle of the rectangle). (b) ∠JHK = (90° − 34°) ÷ 2 = 56° ÷ 2 = 28°. (c) ∠KJH = 180° − 90° − 28° = 62°; 62° × 2 = 124°; ∠KJF = 180° − 124° = 56°.",
      "hints": ["(a) The folded corner keeps the rectangle's right angle.", "(b) The fold bisects the remaining angle; (c) use the triangle angle sum and the straight line."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 2 Q14",
      "image_needed": true, "image_options": false, "image_file": "q44.png",
      "image_page": 23, "image_bbox": [0.18, 0.14, 0.60, 0.32],
      "image_loc": "folded rectangle EFGH with crease HJ, points K, J and 34° marked",
      "notes": "Printed key: (a) 90°, (b) 28°, (c) 56°."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "In the figure, ABCE is a trapezium with AB parallel to EC. ∠ABC = 116°, ∠BAE = 93° and ∠BDC = 87°.<br>(a) Find ∠BDE. [?] °<br>(b) Find ∠DBC. [?] °<br>(c) Circle the words that describe ABDE: Since AB (is / is not) parallel to ED and AE (is / is not) parallel to BD, ABDE is a (parallelogram / trapezium).",
      "answer0": "93", "answer1": "29",
      "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 200,
      "difficulty_id": 3,
      "explanation": "(a) ∠BDE = 180° − 87° = 93° (angles on a straight line ED). (b) ∠BCD = 180° − 116° = 64° (co-interior angles between AB and EC). ∠DBC = 180° − 64° − 87° = 29° (angle sum of triangle BDC). (c) Since AB is parallel to ED and AE is parallel to BD, ABDE is a parallelogram.",
      "hints": ["(a) Use angles on the straight line ED.", "(b) Find ∠BCD from the parallel sides, then the triangle angle sum."],
      "source": "Rulang 2025 P5 End-of-Year Exam Paper 2 Q15",
      "image_needed": true, "image_options": false, "image_file": "q45.png",
      "image_page": 24, "image_bbox": [0.20, 0.14, 0.62, 0.34],
      "image_loc": "trapezium ABCE with diagonal BD, angles 93°, 116°, 87° marked",
      "notes": "Printed key: (a) 93°, (b) 29°, (c) is / parallelogram. Part (c) is a circle-the-word task described in the solution."
    }
  ]
}