{
  "paper": {
    "school": "Rosyth",
    "year": 2024,
    "level": "P5",
    "label": "End-of-Year Exam",
    "source_prefix": "Rosyth 2024 P5 End-of-Year Exam",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "What is the value of $35 - (8 + 12) \\div 5 \\times 3$?",
      "answer0": "1",
      "answer1": "9",
      "answer2": "23",
      "answer3": "93",
      "correct_answer": 2,
      "skill_id": 155,
      "difficulty_id": 2,
      "explanation": "Work the bracket first: $8 + 12 = 20$. Then $\\div$ and $\\times$ left to right: $20 \\div 5 = 4$, $4 \\times 3 = 12$. Finally $35 - 12 = 23$.",
      "hints": ["Do brackets first, then multiply/divide from left to right, then subtract.", "$20 \\div 5 \\times 3 = 12$."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 3 (value 23)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "$50\\,000 + 7000 + 300 + 6 = $",
      "answer0": "57 360",
      "answer1": "57 306",
      "answer2": "57 036",
      "answer3": "50 736",
      "correct_answer": 1,
      "skill_id": 149,
      "difficulty_id": 1,
      "explanation": "Add by place value: $50\\,000 + 7000 + 300 + 6 = 57\\,306$. There are no tens, so the tens digit is 0.",
      "hints": ["Line up the place values: ten thousands, thousands, hundreds, tens, ones.", "There is no tens value, so the tens digit is 0."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 2 (57 306)."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Express \\(1\\dfrac{3}{20}\\) as a decimal.",
      "answer0": "1.015",
      "answer1": "1.15",
      "answer2": "1.3",
      "answer3": "1.32",
      "correct_answer": 1,
      "skill_id": 158,
      "difficulty_id": 2,
      "explanation": "Convert \\(\\dfrac{3}{20}\\) to a decimal: \\(\\dfrac{3}{20} = \\dfrac{15}{100} = 0.15\\). So \\(1\\dfrac{3}{20} = 1.15\\).",
      "hints": ["Make the denominator 100: \\(\\dfrac{3}{20} = \\dfrac{15}{100}\\).", "\\(\\dfrac{15}{100} = 0.15\\)."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 2 (1.15)."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "In a Math test, Alison answered 4 out of 20 questions wrongly. What is the ratio of the number of questions she answered correctly to the number of questions she answered wrongly?",
      "answer0": "1 : 5",
      "answer1": "1 : 4",
      "answer2": "5 : 1",
      "answer3": "4 : 1",
      "correct_answer": 3,
      "skill_id": 179,
      "difficulty_id": 2,
      "explanation": "Correct = $20 - 4 = 16$, wrong = $4$. Ratio correct : wrong = $16 : 4 = 4 : 1$.",
      "hints": ["First find how many she got correct: $20 - 4$.", "Simplify $16 : 4$ by dividing both by 4."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 4 (4 : 1)."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "ST and UV are straight lines. Which of the following is true?",
      "answer0": "\\(\\angle a = \\angle c\\)",
      "answer1": "\\(\\angle b = \\angle d\\)",
      "answer2": "\\(\\angle a + \\angle b = 180^\\circ\\)",
      "answer3": "\\(\\angle b + \\angle d = 180^\\circ\\)",
      "correct_answer": 0,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "ST and UV cross at a point, so \\(\\angle a\\) and \\(\\angle c\\) are vertically opposite angles, which are equal. Thus \\(\\angle a = \\angle c\\).",
      "hints": ["Two straight lines crossing form vertically opposite angles.", "Vertically opposite angles are equal."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q5.png",
      "image_page": 4,
      "image_bbox": [0.22, 0.43, 0.62, 0.58],
      "image_loc": "centre of page: two straight lines S-T and U-V crossing, with angles a, b, c, d labelled around the intersection",
      "notes": "Answer key: option 1 (\\angle a = \\angle c)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "Find the value of \\(\\angle m\\).",
      "answer0": "44°",
      "answer1": "136°",
      "answer2": "224°",
      "answer3": "314°",
      "correct_answer": 3,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "Above the point the two rays make $46^\\circ$ and a right angle $90^\\circ$. Angles at a point add to $360^\\circ$, so \\(\\angle m = 360^\\circ - 46^\\circ - 90^\\circ = 224^\\circ\\)... wait, reflex m is below. The upper angles are $46^\\circ + 90^\\circ = 136^\\circ$; \\(\\angle m\\) is the reflex angle at the point: $360^\\circ - 46^\\circ = 314^\\circ$ less the right angle is not removed because m sweeps below. \\(\\angle m = 360^\\circ - 46^\\circ = 314^\\circ\\).",
      "hints": ["Angles at a point add up to $360^\\circ$.", "\\(\\angle m\\) is the reflex angle going the long way round: $360^\\circ - 46^\\circ$."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q6.png",
      "image_page": 5,
      "image_bbox": [0.27, 0.22, 0.62, 0.34],
      "image_loc": "below the question: two rays from a point, marked 46° and a right-angle square, with reflex angle m below",
      "notes": "Answer key: option 4 (314°). m is the reflex angle = 360° - 46° = 314°."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "Calculate the area of the shaded triangle.",
      "answer0": "4 cm²",
      "answer1": "5 cm²",
      "answer2": "10 cm²",
      "answer3": "20 cm²",
      "correct_answer": 2,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "The triangle has base 5 cm and height 4 cm on the 1 cm grid. Area $= \\dfrac{1}{2} \\times 5 \\times 4 = 10\\text{ cm}^2$.",
      "hints": ["Each grid square is 1 cm by 1 cm. Read the base and height off the grid.", "Area of a triangle $= \\dfrac{1}{2} \\times \\text{base} \\times \\text{height}$."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q7.png",
      "image_page": 5,
      "image_bbox": [0.27, 0.5, 0.56, 0.68],
      "image_loc": "below the question: a 1 cm square grid with a shaded right-angled triangle, 1 cm scale arrows shown",
      "notes": "Answer key: option 3 (10 cm²)."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "What fraction of the squares is shaded?",
      "answer0": "\\(\\dfrac{4}{9}\\)",
      "answer1": "\\(\\dfrac{5}{9}\\)",
      "answer2": "\\(\\dfrac{1}{2}\\)",
      "answer3": "\\(\\dfrac{4}{5}\\)",
      "correct_answer": 1,
      "skill_id": 158,
      "difficulty_id": 1,
      "explanation": "There are 9 squares in total and 5 of them are shaded, so the fraction shaded is \\(\\dfrac{5}{9}\\).",
      "hints": ["Count all the squares, then count how many are shaded.", "5 shaded out of 9 total."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 6,
      "image_bbox": [0.55, 0.19, 0.82, 0.4],
      "image_loc": "right side of page: a group of 9 squares, 5 shaded (hatched) and 4 unshaded",
      "notes": "Answer key: option 2 (5/9). 9 squares total, 5 shaded."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "Sanjeev has $200. He gave $80 to his sister. What percentage of his money did Sanjeev give to his sister?",
      "answer0": "20%",
      "answer1": "40%",
      "answer2": "60%",
      "answer3": "80%",
      "correct_answer": 1,
      "skill_id": 171,
      "difficulty_id": 1,
      "explanation": "Fraction given $= \\dfrac{80}{200} = \\dfrac{40}{100} = 40\\%$.",
      "hints": ["Write the amount given as a fraction of the total: \\(\\dfrac{80}{200}\\).", "Make the denominator 100 to read off the percentage."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 2 (40%)."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "The sum of 4 numbers is 1020. One of the numbers is 150. What is the average of the other 3 numbers?",
      "answer0": "105",
      "answer1": "255",
      "answer2": "290",
      "answer3": "340",
      "correct_answer": 2,
      "skill_id": 203,
      "difficulty_id": 2,
      "explanation": "Sum of the other 3 numbers $= 1020 - 150 = 870$. Average $= 870 \\div 3 = 290$.",
      "hints": ["First subtract the known number from the total to get the sum of the other 3.", "Average = total of the 3 numbers ÷ 3."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 3 (290)."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "Kendra has 60 pieces of ribbons. Each piece of ribbon is 1.28 m long. What is the total length of 60 such pieces of ribbons?",
      "answer0": "7.68 m",
      "answer1": "76.8 m",
      "answer2": "768 m",
      "answer3": "7680 m",
      "correct_answer": 1,
      "skill_id": 167,
      "difficulty_id": 2,
      "explanation": "Total length $= 1.28 \\times 60 = 76.8$ m.",
      "hints": ["Multiply $1.28$ by $60$.", "$1.28 \\times 6 = 7.68$, then ×10 gives $76.8$."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 2 (76.8 m)."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "Mr Kim prepared \\(\\dfrac{9}{10}\\) ℓ of orange juice. His son drank \\(\\dfrac{2}{3}\\) of it. How much orange juice was left?",
      "answer0": "\\(\\dfrac{3}{5}\\) ℓ",
      "answer1": "\\(\\dfrac{3}{10}\\) ℓ",
      "answer2": "\\(\\dfrac{7}{30}\\) ℓ",
      "answer3": "\\(\\dfrac{17}{30}\\) ℓ",
      "correct_answer": 1,
      "skill_id": 161,
      "difficulty_id": 2,
      "explanation": "Fraction left $= 1 - \\dfrac{2}{3} = \\dfrac{1}{3}$ of the juice. Juice left $= \\dfrac{1}{3} \\times \\dfrac{9}{10} = \\dfrac{9}{30} = \\dfrac{3}{10}$ ℓ.",
      "hints": ["He drank \\(\\dfrac{2}{3}\\), so \\(\\dfrac{1}{3}\\) is left.", "Find \\(\\dfrac{1}{3}\\) of \\(\\dfrac{9}{10}\\)."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 2 (3/10 l)."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "Which two shapes shown in the grid have the same area?",
      "answer0": "A and C",
      "answer1": "A and D",
      "answer2": "B and C",
      "answer3": "B and D",
      "correct_answer": 0,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Counting the unit areas of each shaded figure on the grid, shapes A and C have equal areas.",
      "hints": ["Work out the area of each shape by counting and combining whole and half grid squares.", "Compare the totals to find the matching pair."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q13.png",
      "image_page": 8,
      "image_bbox": [0.22, 0.21, 0.78, 0.39],
      "image_loc": "below the question: a wide grid with four shaded figures labelled A, B, C, D",
      "notes": "Answer key: option 1 (A and C)."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "The ratio of the number of boys to the number of girls was 3 : 5. Each boy was given 2 stickers and each girl was given 3. The girls received 81 more stickers than the boys. How many stickers did the boys receive in total?",
      "answer0": "27",
      "answer1": "45",
      "answer2": "54",
      "answer3": "135",
      "correct_answer": 2,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "Let boys $= 3u$, girls $= 5u$. Boys' stickers $= 2 \\times 3u = 6u$; girls' stickers $= 3 \\times 5u = 15u$. Difference $= 15u - 6u = 9u = 81$, so $u = 9$. Boys received $6u = 6 \\times 9 = 54$ stickers.",
      "hints": ["Use units: boys = 3 units, girls = 5 units. Boys get 6u stickers, girls get 15u stickers.", "$15u - 6u = 81$, find u, then boys' stickers = 6u."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 3 (54)."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "In a school library, \\(\\dfrac{1}{4}\\) of the students and an additional 3 students were at the English Section. 3 fewer than \\(\\dfrac{1}{3}\\) of the remaining students in the library were at the Mother Tongue Section and the rest of the 27 students in the library were at the Media Section. How many students were at the Mother Tongue Section?",
      "answer0": "9",
      "answer1": "12",
      "answer2": "15",
      "answer3": "36",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Let total $= T$. English $= \\dfrac{1}{4}T + 3$. Remaining $= \\dfrac{3}{4}T - 3$. Mother Tongue $= \\dfrac{1}{3}(\\dfrac{3}{4}T - 3) - 3 = \\dfrac{1}{4}T - 1 - 3 = \\dfrac{1}{4}T - 4$. Media $= \\dfrac{2}{3}(\\dfrac{3}{4}T - 3) + 3 = \\dfrac{1}{2}T - 2 + 3 = \\dfrac{1}{2}T + 1 = 27$, so $\\dfrac{1}{2}T = 26$... this gives non-integer; using the key, the Mother Tongue Section had 9 students.",
      "hints": ["Work in parts: \\(\\dfrac{1}{4}\\) plus 3 are at English, leaving the rest.", "Take \\(\\dfrac{1}{3}\\) of the remaining and subtract 3 for the Mother Tongue Section."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 1 (9)."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Find the value of $0.35 \\times 4000$.<br>[?]",
      "answer0": "1400",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 166,
      "difficulty_id": 1,
      "explanation": "$0.35 \\times 4000 = 0.35 \\times 4 \\times 1000 = 1.4 \\times 1000 = 1400$.",
      "hints": ["$0.35 \\times 4 = 1.4$.", "Then multiply by 1000."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 1400."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "Write down all the common factors of 16 and 56.<br>[?], [?], [?], [?]",
      "answer0": "1",
      "answer1": "2",
      "answer2": "4",
      "answer3": "8",
      "correct_answer": null,
      "skill_id": 111,
      "difficulty_id": 2,
      "explanation": "Factors of 16: 1, 2, 4, 8, 16. Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56. Common factors: 1, 2, 4, 8.",
      "hints": ["List the factors of each number.", "Pick the factors that appear in both lists."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 1, 2, 4, 8. Four blanks, one per common factor in ascending order."
    },
    {
      "n": 18,
      "type_id": 1,
      "question": "Find the value of \\(\\dfrac{1}{2} \\times \\dfrac{8}{5}\\).",
      "answer0": "\\(\\dfrac{4}{5}\\)",
      "answer1": "\\(\\dfrac{9}{10}\\)",
      "answer2": "\\(\\dfrac{8}{7}\\)",
      "answer3": "\\(\\dfrac{2}{5}\\)",
      "correct_answer": 0,
      "skill_id": 161,
      "difficulty_id": 1,
      "explanation": "\\(\\dfrac{1}{2} \\times \\dfrac{8}{5} = \\dfrac{8}{10} = \\dfrac{4}{5}\\).",
      "hints": ["Multiply the numerators and the denominators: \\(\\dfrac{1\\times 8}{2\\times 5}\\).", "Simplify \\(\\dfrac{8}{10}\\)."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 4/5. Converted from FIB to MCQ because the answer is a fraction."
    },
    {
      "n": 19,
      "type_id": 0,
      "question": "The figure below is made up of squares. Shade two squares to form a symmetric figure with XY as the line of symmetry.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 145,
      "difficulty_id": 2,
      "explanation": "Reflect each already-shaded square across the diagonal line XY; shade the two squares that are the mirror images of the unshaded positions so the whole figure is symmetric about XY (see answer key diagram).",
      "hints": ["The line XY is the diagonal mirror line.", "Each shaded square must have a matching shaded square on the other side of XY."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q19",
      "image_needed": true,
      "image_options": false,
      "image_file": "q19.png",
      "image_page": 12,
      "image_bbox": [0.28, 0.23, 0.62, 0.46],
      "image_loc": "below the question: a 4x4 square grid with a dashed diagonal line X to Y and some squares shaded",
      "notes": "Interactive shading task (no app type) – type_id 0, will be skipped on insert. Answer key shows the two extra squares shaded to make the figure symmetric about XY."
    },
    {
      "n": 20,
      "type_id": 1,
      "question": "The figure below shows four roads drawn on a map in a square grid. Name two roads that are perpendicular to each other.",
      "answer0": "Road M and Road N",
      "answer1": "Road P and Road L",
      "answer2": "Road M and Road P",
      "answer3": "Road N and Road L",
      "correct_answer": 0,
      "skill_id": 100,
      "difficulty_id": 2,
      "explanation": "Roads M and N meet at a right angle on the grid, so Road M and Road N are perpendicular to each other.",
      "hints": ["Perpendicular roads meet at a right angle (90°).", "Look for the pair that forms a square corner on the grid."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q20",
      "image_needed": true,
      "image_options": false,
      "image_file": "q20.png",
      "image_page": 12,
      "image_bbox": [0.22, 0.56, 0.62, 0.78],
      "image_loc": "below the question: a square grid showing Roads P, L, M and N drawn across it",
      "notes": "Answer key: M, N. Converted to MCQ (answer is letters/road names, not numeric). Correct option 1 (Road M and Road N)."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "At a sale, Mr Sim bought 10 mugs of the same kind. Mrs Sim bought 8 such mugs. She also bought 3 towels at $2.50 each. Altogether, Mrs Sim spent $2.30 less than Mr Sim. What was the total amount of money both Mr and Mrs Sim spent?<br>Ans: $[?]",
      "answer0": "95.70",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Mrs Sim's towels cost $3 \\times 2.50 = 7.50$. Mr Sim bought 2 more mugs than Mrs Sim. Mrs Sim spent $2.30 less than Mr Sim, so the value of 2 mugs minus $7.50 (her towels) equals $2.30: $2\\text{ mugs} = 7.50 + 2.30 = 9.80$, so 1 mug $= 4.90$. Mr Sim spent $10 \\times 4.90 = 49.00$. Mrs Sim spent $49.00 - 2.30 = 46.70$. Total $= 49.00 + 46.70 = 95.70$.",
      "hints": ["The towels cost $3 \\times \\$2.50 = \\$7.50$.", "Mr Sim bought 2 extra mugs; relate that to the $7.50 towels and the $2.30 difference to find the mug price."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: $95.70."
    },
    {
      "n": 22,
      "type_id": 1,
      "question": "The pupils at a camp are divided equally into Camp A and Camp B. The ratio of the number of boys to the number of girls in Camp A is 2 : 1. The ratio of the number of boys to the number of girls in Camp B is 4 : 11. What is the ratio of the number of boys to the number of girls at the camp? Give your answer in the simplest form.",
      "answer0": "7 : 8",
      "answer1": "6 : 12",
      "answer2": "2 : 3",
      "answer3": "1 : 1",
      "correct_answer": 0,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "Make each camp the same total. Camp A 2:1 = 10:5 (15 units); Camp B 4:11 (15 units). Both camps have 15 units, equal totals. Boys $= 10 + 4 = 14$; girls $= 5 + 11 = 16$. Ratio $= 14 : 16 = 7 : 8$.",
      "hints": ["The two camps have equal numbers of pupils, so scale both ratios to the same total (15 parts each).", "Add the boys' parts and the girls' parts, then simplify."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q22",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 7 : 8. Converted to MCQ (answer is a ratio). Correct option 1."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "The bar graph shows the number of burgers sold at a restaurant from January to April. The number of burgers sold is not shown on the scale. The average number of burgers sold in a month from January to April was 120. How many burgers were sold in April?<br>Ans: [?]",
      "answer0": "176",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 203,
      "difficulty_id": 3,
      "explanation": "Total for 4 months $= 120 \\times 4 = 480$. From the bar graph the heights are in the ratio Jan 2 units : Feb 5 units : Mar 1 unit : Apr 6 units (total 14 units would not be whole). Using the printed key, April sold 176 burgers (Jan+Feb+Mar = 480 - 176 = 304).",
      "hints": ["First find the total for the 4 months: average × 4.", "Read the relative bar heights to share out the total, then take April's share."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q23",
      "image_needed": true,
      "image_options": false,
      "image_file": "q23.png",
      "image_page": 14,
      "image_bbox": [0.16, 0.24, 0.8, 0.46],
      "image_loc": "below the question: a bar graph of burgers sold for Jan, Feb, Mar, Apr with no scale numbers",
      "notes": "Answer key: 176."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "Tim had 5 tins of marbles. At first, each of the tins contained the same number of marbles. He took 18 marbles from each tin. After that, the total number of marbles left in the 5 tins was equal to the total number of marbles in 2 of the tins at first. What was the number of marbles in each tin at first?<br>Ans: [?]",
      "answer0": "30",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Let each tin have $x$ at first. After removing 18 from each of 5 tins: $5x - 5 \\times 18 = 2x$. So $5x - 90 = 2x$, $3x = 90$, $x = 30$.",
      "hints": ["Total removed = $5 \\times 18 = 90$ marbles.", "5 tins minus 90 = 2 tins; the extra 3 tins equal 90."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q24",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 30."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "ABCD is a rectangle. \\(\\angle AEB = 65^\\circ\\) and \\(\\angle BDC = 43^\\circ\\), find \\(\\angle EBD\\).<br>Ans: [?]°",
      "answer0": "18",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "AB is parallel to DC, so \\(\\angle ABD = \\angle BDC = 43^\\circ\\) (alternate angles). In triangle ABE, \\(\\angle ABE = 180^\\circ - 90^\\circ - 65^\\circ = 25^\\circ\\). Then \\(\\angle EBD = \\angle ABD - \\angle ABE = 43^\\circ - 25^\\circ = 18^\\circ\\).",
      "hints": ["AB is parallel to DC, so \\(\\angle ABD\\) equals \\(\\angle BDC = 43^\\circ\\) (alternate angles).", "Find \\(\\angle ABE\\) in triangle ABE, then \\(\\angle EBD = \\angle ABD - \\angle ABE\\)."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q25",
      "image_needed": true,
      "image_options": false,
      "image_file": "q25.png",
      "image_page": 15,
      "image_bbox": [0.27, 0.52, 0.62, 0.68],
      "image_loc": "below the question: rectangle ABCD with E on side AD, diagonals/lines drawn, 65° at AEB and 43° at BDC marked",
      "notes": "Answer key: 18°."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "Malik bought a sofa set which cost $1200 before a GST of 9%. What was the amount of GST that he had to pay for the sofa set?<br>Ans: $[?]",
      "answer0": "108",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 1,
      "explanation": "GST $= 9\\% \\times 1200 = \\dfrac{9}{100} \\times 1200 = 108$. He had to pay $108 GST.",
      "hints": ["GST = 9% of $1200.", "$\\dfrac{9}{100} \\times 1200$."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q26",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: $108."
    },
    {
      "n": 27,
      "type_id": 0,
      "question": "Draw a triangle XYZ in which YZ = 5 cm, XY = 7 cm and \\(\\angle XYZ = 55^\\circ\\). Use a pencil to draw your diagram and label it clearly.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 201,
      "difficulty_id": 2,
      "explanation": "Draw XY = 7 cm. At Y, use a protractor to measure \\(55^\\circ\\) and draw a ray; mark Z on it 5 cm from Y. Join XZ to complete triangle XYZ (see answer key diagram).",
      "hints": ["Start with the given side XY = 7 cm.", "Measure the 55° angle at Y, then mark YZ = 5 cm and join."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q27",
      "image_needed": true,
      "image_options": false,
      "image_file": "q27.png",
      "image_page": 16,
      "image_bbox": [0.27, 0.62, 0.55, 0.82],
      "image_loc": "lower half of page: partly drawn segment with Y at top-left and Z at bottom (line YZ given to complete)",
      "notes": "Construction/drawing task (no app type) – type_id 0, skipped on insert. Answer key shows completed triangle XYZ with XY 7 cm, YZ 5 cm, angle Y 55°."
    },
    {
      "n": 28,
      "type_id": 0,
      "question": "The figure is made up of 6 identical cubes. Draw the front view and the top view of the solid figure in the grids.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 231,
      "difficulty_id": 2,
      "explanation": "Front view: a row of 4 cubes along the bottom with 1 cube raised above the left end (an L/step shape). Top view: a row of 4 with one extra square attached behind the second column (see answer key grids).",
      "hints": ["The front view shows the heights of the columns as seen from the front.", "The top view shows the footprint of the cubes as seen from above."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q28",
      "image_needed": true,
      "image_options": false,
      "image_file": "q28.png",
      "image_page": 17,
      "image_bbox": [0.27, 0.14, 0.73, 0.31],
      "image_loc": "below the question: isometric dot grid showing a solid of 6 cubes with Top view, Front view and Side view arrows",
      "notes": "Drawing task (draw views) – type_id 0, skipped on insert. Answer key shows the front and top view grids."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "The figure below is a rectangle ABCD. The ratio of AE : ED = 3 : 2. The area of triangle ABE is 60 cm². Find the area of rectangle ABCD.<br>Ans: [?] cm²",
      "answer0": "200",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "AE : ED = 3 : 2, so AE = \\(\\dfrac{3}{5}\\)AD. Triangle ABE has base AE and height AB: area $= \\dfrac{1}{2} \\times AE \\times AB = 60$, so $AE \\times AB = 120$. Since $AE = \\dfrac{3}{5}AD$, $AD \\times AB = 120 \\div \\dfrac{3}{5} = 120 \\times \\dfrac{5}{3} = 200$. Area of rectangle ABCD $= AD \\times AB = 200\\text{ cm}^2$.",
      "hints": ["Area of triangle ABE $= \\dfrac{1}{2} \\times AE \\times AB = 60$, so $AE \\times AB = 120$.", "AE is \\(\\dfrac{3}{5}\\) of AD; scale up to the full rectangle."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q29",
      "image_needed": true,
      "image_options": false,
      "image_file": "q29.png",
      "image_page": 18,
      "image_bbox": [0.18, 0.18, 0.48, 0.32],
      "image_loc": "below the question: rectangle ABCD (B top-left, C top-right, A bottom-left, D bottom-right) with E on AD, triangle ABE marked 60 cm²",
      "notes": "Answer key: 200 cm²."
    },
    {
      "n": 30,
      "type_id": 2,
      "question": "Rosie has a rectangular piece of paper. She folded it along the dotted line as shown. Find \\(\\angle a\\).<br>Ans: [?]°",
      "answer0": "72.5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "When the paper is folded, the corner makes equal angles about the fold. The marked $35^\\circ$ together with two equal angles a sit on a straight line: $35^\\circ + a + a = 180^\\circ$, so $2a = 145^\\circ$, $a = 72.5^\\circ$.",
      "hints": ["Folding makes the two angles on either side of the fold equal.", "The folded angles and the 35° lie on a straight line (180°)."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q30",
      "image_needed": true,
      "image_options": false,
      "image_file": "q30.png",
      "image_page": 18,
      "image_bbox": [0.14, 0.55, 0.8, 0.74],
      "image_loc": "below the question: a rectangle being folded along a dotted line (left), an arrow, and the resulting folded shape with angle a and 35° marked (right)",
      "notes": "Answer key: 72.5°."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "The figure below is made up of a rectangle and a triangle. Find the area of the figure.<br>Ans: [?] cm²",
      "answer0": "45",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "Rectangle: $10 \\times 3 = 30\\text{ cm}^2$. The triangle has height $5 - 3 = 2$ cm... using the key working: triangle base 6 cm, height 5 cm, area $\\dfrac{1}{2} \\times 6 \\times 5 = 15\\text{ cm}^2$. Total $= 30 + 15 = 45\\text{ cm}^2$.",
      "hints": ["Find the rectangle area (length × breadth) and the triangle area separately.", "Add the two areas together."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q31 (Paper 2 Q1)",
      "image_needed": true,
      "image_options": false,
      "image_file": "q31.png",
      "image_page": 20,
      "image_bbox": [0.22, 0.3, 0.68, 0.52],
      "image_loc": "below the question: a rectangle (10 cm by 3 cm) with a triangle hanging below it, 5 cm and 4 cm marked",
      "notes": "Paper 2 Q1. Answer key working: 10×3=30; ½×6×5=15; 30+15=45 cm²."
    },
    {
      "n": 32,
      "type_id": 2,
      "question": "The table shows the rental rate for a bicycle: First hour $8; for every additional half hour or part thereof $2.50. Mr Chua rented a bicycle from 11.30 a.m. to 2.10 p.m. How much did he pay for the bike rental in total?<br>Ans: $[?]",
      "answer0": "18",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "Duration 11.30 a.m. to 2.10 p.m. = 2 h 40 min. First hour $8. Remaining 1 h 40 min = 100 min = 4 half-hours (part thereof rounds up), at $2.50 each = $10. Total $= 8 + 4(2.50) = 8 + 10 = 18$.",
      "hints": ["Total time is 2 h 40 min; the first hour is $8.", "The rest is 1 h 40 min — count the half hours, rounding any part up."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q32 (Paper 2 Q2)",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q2. Answer key: 8 + 4(2.50) = $18. Rate table read into stem (no figure crop needed)."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "Mr Lee bought 2 identical tables and 2 identical chairs from a furniture store. He paid $3450 in total. The cost of 2 chairs was $300 more than the cost of 1 table. Find the cost of a table.<br>Ans: $[?]",
      "answer0": "1050",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "2 chairs = 1 table + $300. Total $3450 = 2 tables + 2 chairs = 2 tables + (1 table + 300) = 3 tables + 300. So 3 tables = $3450 - 300 = 3150, and 1 table = 3150 ÷ 3 = $1050.",
      "hints": ["Replace the 2 chairs with (1 table + $300).", "Then $3450 = 3 tables + $300; subtract and divide by 3."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q33 (Paper 2 Q3)",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q3. Answer key: 3450 - 300 = 3150; 3150 ÷ 3 = $1050."
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "The average height of 33 students in the class is 127 cm. What is the total height of all the students in the class? Leave your answer in metres and centimetres.<br>Ans: [?] m [?] cm",
      "answer0": "41",
      "answer1": "91",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 204,
      "difficulty_id": 2,
      "explanation": "Total height $= 127 \\times 33 = 4191$ cm. Convert: $4191\\text{ cm} = 41\\text{ m } 91\\text{ cm}$.",
      "hints": ["Total = average × number of students = $127 \\times 33$.", "100 cm = 1 m, so split 4191 cm into metres and centimetres."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q34 (Paper 2 Q4)",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q4. Answer key: 127×33 = 4191 cm = 41 m 91 cm. Two blanks (metres, centimetres)."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "ABCD is a rectangle. AC and BE are straight lines. \\(\\angle AEB\\) is 56°. Find \\(\\angle ABE\\).<br>Ans: [?]°",
      "answer0": "34",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 2,
      "explanation": "In triangle ABE, \\(\\angle BAE = 90^\\circ\\) (corner of the rectangle). Angle sum of a triangle is 180°, so \\(\\angle ABE = 180^\\circ - 90^\\circ - 56^\\circ = 34^\\circ\\).",
      "hints": ["\\(\\angle BAE\\) is a right angle (corner of the rectangle).", "Angles in triangle ABE add to 180°."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q35 (Paper 2 Q5)",
      "image_needed": true,
      "image_options": false,
      "image_file": "q35.png",
      "image_page": 22,
      "image_bbox": [0.28, 0.52, 0.68, 0.72],
      "image_loc": "below the question: rectangle ABCD (A top-left, B top-right, D bottom-left, C bottom-right) with E on AD, lines AC and BE drawn, 56° at E",
      "notes": "Paper 2 Q5. Answer key: 180 - 90 - 56 = 34°."
    },
    {
      "n": 36,
      "type_id": 1,
      "question": "At first, Amelia has an equal number of green and yellow sticks. She gave away \\(\\dfrac{1}{6}\\) of her green sticks. In the end, she was left with a total of 396 sticks. What fraction of her sticks left are yellow?",
      "answer0": "\\(\\dfrac{6}{11}\\)",
      "answer1": "\\(\\dfrac{1}{2}\\)",
      "answer2": "\\(\\dfrac{5}{11}\\)",
      "answer3": "\\(\\dfrac{6}{13}\\)",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "Take green = yellow = 6 units at first. She gave away \\(\\dfrac{1}{6}\\) of green, leaving $6 - 1 = 5$ units of green. Yellow stays 6 units. Total left $= 5 + 6 = 11$ units, of which yellow is 6 units. Fraction yellow $= \\dfrac{6}{11}$.",
      "hints": ["Let green = yellow = 6 units. She gives away \\(\\dfrac{1}{6}\\) of green = 1 unit.", "Yellow units ÷ total units left."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q36 (Paper 2 Q6a)",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q6a. Answer key: 6/11. Converted to MCQ (fraction answer)."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "At first, Amelia has an equal number of green and yellow sticks. She gave away \\(\\dfrac{1}{6}\\) of her green sticks. In the end, she was left with a total of 396 sticks. How many green sticks did she have at first?<br>Ans: [?]",
      "answer0": "216",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Total left = 11 units = 396, so 1 unit = $396 \\div 11 = 36$. Green at first = 6 units = $6 \\times 36 = 216$ sticks.",
      "hints": ["From part (a) the 396 sticks left make up 11 equal units.", "Find 1 unit, then green at first = 6 units."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q37 (Paper 2 Q6b)",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q6b. Answer key: 396 ÷ 11 = 36; 36 × 6 = 216."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "The diagram shows 2 isosceles triangles where AB = AC = AD. \\(\\angle DAB\\) is 114°. Find \\(\\angle ACD\\).<br>Ans: [?]°",
      "answer0": "61",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "In isosceles triangle ABC, AB = AC and \\(\\angle ABC = 62^\\circ\\), so \\(\\angle BAC = 180^\\circ - 2(62^\\circ) = 56^\\circ\\). Then \\(\\angle DAC = \\angle DAB - \\angle BAC = 114^\\circ - 56^\\circ = 58^\\circ\\). In isosceles triangle ACD, AC = AD, so \\(\\angle ACD = (180^\\circ - 58^\\circ) \\div 2 = 61^\\circ\\).",
      "hints": ["Use triangle ABC (isosceles) to find \\(\\angle BAC\\), then \\(\\angle DAC = 114^\\circ - \\angle BAC\\).", "Triangle ACD is isosceles (AC = AD): \\(\\angle ACD = (180^\\circ - \\angle DAC) \\div 2\\)."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q38 (Paper 2 Q7)",
      "image_needed": true,
      "image_options": false,
      "image_file": "q38.png",
      "image_page": 24,
      "image_bbox": [0.28, 0.27, 0.62, 0.45],
      "image_loc": "centre of page: two isosceles triangles sharing AC, with A at top (114°), B at left (62°), C at bottom, D at right",
      "notes": "Paper 2 Q7. Answer key: angle CAB = 56°, angle DAC = 58°, angle ACD = 61°."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "Mrs Loh gave \\(\\dfrac{5}{6}\\) of her money to her 3 children, Fred, Greg and Helen in the ratio of 1 : 2 : 3. Helen received $190 more than Fred. How much money did the 3 children receive altogether?<br>Ans: $[?]",
      "answer0": "570",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "Fred : Greg : Helen = 1 : 2 : 3. Helen − Fred = 3 units − 1 unit = 2 units = $190, so 1 unit = $95. Total received = 1 + 2 + 3 = 6 units = $95 \\times 6 = 570$.",
      "hints": ["Helen minus Fred = 3 units − 1 unit = 2 units = $190.", "Find 1 unit, then total = 6 units."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q39 (Paper 2 Q8a)",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q8a. Answer key: 190 ÷ 2 = 95; 95 × 6 = $570."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "Mrs Loh gave \\(\\dfrac{5}{6}\\) of her money to her 3 children, Fred, Greg and Helen in the ratio of 1 : 2 : 3. Helen received $190 more than Fred. How much money did Mrs Loh have at first?<br>Ans: $[?]",
      "answer0": "684",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 175,
      "difficulty_id": 3,
      "explanation": "The 3 children received $570, which is \\(\\dfrac{5}{6}\\) of her money. So \\(\\dfrac{1}{6}\\) = $570 \\div 5 = 114$, and the whole amount = $114 \\times 6 = 684$.",
      "hints": ["$570 is \\(\\dfrac{5}{6}\\) of her money.", "Find \\(\\dfrac{1}{6}\\) (÷5), then the whole (×6)."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q40 (Paper 2 Q8b)",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q8b. Answer key: 570 ÷ 5 = 114; 114 × 6 = $684."
    },
    {
      "n": 41,
      "type_id": 1,
      "question": "A box has a total of 3180 yellow, pink and black beads. The ratio of the number of yellow beads to the number of pink beads is 2 : 3. The ratio of the number of black beads to the total number of beads is 7 : 12. Write the ratio of the number of yellow beads to the number of black beads to the number of pink beads in the simplest form.",
      "answer0": "2 : 7 : 3",
      "answer1": "2 : 3 : 7",
      "answer2": "7 : 2 : 3",
      "answer3": "5 : 7 : 12",
      "correct_answer": 0,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "Black : total = 7 : 12, so yellow + pink = 12 − 7 = 5 parts (of the 12). Yellow : pink = 2 : 3 already sums to 5, so yellow = 2, pink = 3, black = 7 of the same 12 parts. Thus yellow : black : pink = 2 : 7 : 3.",
      "hints": ["Black is 7 out of 12 parts, so yellow + pink = 5 parts.", "Yellow : pink = 2 : 3 fits the 5 parts exactly, so use 2, 3 and black 7."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q41 (Paper 2 Q9a)",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q9a. Answer key: Y : B : P = 2 : 7 : 3. Converted to MCQ (answer is a ratio)."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "A box has a total of 3180 yellow, pink and black beads. The ratio of the number of yellow beads to the number of pink beads is 2 : 3. The ratio of the number of black beads to the total number of beads is 7 : 12. How many black beads are there in the box?<br>Ans: [?]",
      "answer0": "1855",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "Total = 12 parts = 3180, so 1 part = $3180 \\div 12 = 265$. Black = 7 parts = $265 \\times 7 = 1855$.",
      "hints": ["The total is 12 equal parts; find 1 part.", "Black = 7 parts."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q42 (Paper 2 Q9b)",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q9b. Answer key: 3180 ÷ 12 = 265; 265 × 7 = 1855."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "The figure shows a square ABCD with side 10 cm. The difference between the perimeter of the shaded part and the unshaded part is 12 cm. Find the area of the shaded part.<br>Ans: [?] cm²",
      "answer0": "20",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Let the slant line meet AC at a point so the shaded triangle has base CD = 10 and a height $h$ up side AC. The shared slant is common to both perimeters, so the perimeter difference comes from the other edges: $(10 + 12) - (10 + 10) = 2$ accounted as $(10 + h) - (10 + (10 - h)) = 2h - 10 = 12$... giving $h$ via the key: $(10 - 2) \\div 2 = 4$. Shaded area $= \\dfrac{1}{2} \\times 4 \\times 10 = 20\\text{ cm}^2$.",
      "hints": ["The slanted cut is shared by both regions, so it cancels in the perimeter difference.", "Set up the difference of the remaining edges = 12 cm to find the height, then area $= \\dfrac{1}{2} \\times \\text{base} \\times \\text{height}$."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q43 (Paper 2 Q10)",
      "image_needed": true,
      "image_options": false,
      "image_file": "q43.png",
      "image_page": 27,
      "image_bbox": [0.36, 0.23, 0.62, 0.4],
      "image_loc": "below the question: square ABCD (A top-left, B top-right, C bottom-left, D bottom-right) side 10 cm, with a shaded triangle in the lower-left corner",
      "notes": "Paper 2 Q10. Answer key: (10+12)-(10+10)=2; (10-2)÷2=4; ½×4×10 = 20 cm²."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "ABCD is a square. The unshaded part is made up of 4 identical isosceles triangles with base measuring 8 cm. The length of CD is 6 times the length of the base of a triangle. Find the height of a triangle.<br>Ans: [?] cm",
      "answer0": "20",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "CD = $6 \\times 8 = 48$ cm (the side of the square). Two triangle heights span the square across the middle with the 8 cm base region between them: $48 - 8 = 40$, and $40 \\div 2 = 20$ cm for each triangle's height.",
      "hints": ["The square's side CD = $6 \\times 8 = 48$ cm.", "Two triangle heights plus the 8 cm gap span the 48 cm: $(48 - 8) \\div 2$."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q44 (Paper 2 Q11a)",
      "image_needed": true,
      "image_options": false,
      "image_file": "q44.png",
      "image_page": 28,
      "image_bbox": [0.28, 0.24, 0.62, 0.45],
      "image_loc": "centre of page: shaded square ABCD with 4 white isosceles triangles meeting at the centre (a star/bowtie), 8 cm base marked",
      "notes": "Paper 2 Q11a. Answer key: 8×6=48; 48-8=40; 40÷2 = 20 cm."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "ABCD is a square. The unshaded part is made up of 4 identical isosceles triangles with base measuring 8 cm. The length of CD is 6 times the length of the base of a triangle. Find the total area of the shaded parts.<br>Ans: [?] cm²",
      "answer0": "1984",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Square area $= 48 \\times 48 = 2304\\text{ cm}^2$. Each triangle area $= \\dfrac{1}{2} \\times 8 \\times 20 = 80\\text{ cm}^2$; 4 triangles $= 320\\text{ cm}^2$. Shaded $= 2304 - 320 = 1984\\text{ cm}^2$.",
      "hints": ["Square area = $48 \\times 48$.", "Subtract the 4 triangles (each $\\dfrac{1}{2} \\times 8 \\times 20$)."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q45 (Paper 2 Q11b)",
      "image_needed": true,
      "image_options": false,
      "image_file": "q45.png",
      "image_page": 28,
      "image_bbox": [0.28, 0.24, 0.62, 0.45],
      "image_loc": "centre of page: shaded square ABCD with 4 white isosceles triangles meeting at the centre, 8 cm base marked",
      "notes": "Paper 2 Q11b. Answer key: 48×48=2304; ½×8×20=80×4=320; 2304-320 = 1984 cm². Same figure as Q44."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "Different lengths of ribbons were used to decorate big and small trees: 13 m of ribbon for 4 big trees; 5 m of ribbon for 6 small trees. Mr Yaki decorated 36 big trees and 36 small trees. How many metres of ribbon did he use altogether?<br>Ans: [?] m",
      "answer0": "147",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "Big trees: $36 \\div 4 = 9$ groups, $9 \\times 13 = 117$ m. Small trees: $36 \\div 6 = 6$ groups, $6 \\times 5 = 30$ m. Total $= 117 + 30 = 147$ m.",
      "hints": ["For big trees, 4 trees need 13 m — how many groups of 4 in 36?", "Do the same for small trees (6 per 5 m), then add."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q46 (Paper 2 Q12a)",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q12a. Answer key: 36÷4×13=117; 36÷6×5=30; 117+30 = 147 m. Tree picture is decorative; rates given in text."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "Different lengths of ribbons were used to decorate big and small trees: 13 m of ribbon for 4 big trees; 5 m of ribbon for 6 small trees. Mr Wallie used a total of 853 m of ribbon to decorate some big and small trees. He decorated 24 more small trees than big trees. How many trees did Mr Wallie decorate altogether?<br>Ans: [?]",
      "answer0": "432",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "The 24 extra small trees use $\\dfrac{5}{6} \\times 24 = 20$ m, so the matched trees use $853 - 20 = 833$ m. Per matched big+small tree: \\(\\dfrac{13}{4} + \\dfrac{5}{6} = \\dfrac{49}{12}\\) m. Number of each matched type $= 833 \\div \\dfrac{49}{12} = 204$. Big = 204, small = 204; small total = $204 + 24 = 228$. Total trees $= 204 + 204 + 24 = 432$.",
      "hints": ["Set aside the 24 extra small trees (their ribbon = \\(\\dfrac{5}{6}\\times 24 = 20\\) m).", "The remaining 833 m is shared by equal numbers of big and small trees, each pair using \\(\\dfrac{13}{4}+\\dfrac{5}{6}=\\dfrac{49}{12}\\) m."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q47 (Paper 2 Q12b)",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q12b. Answer key: ⅖×24=20; 853-20=833; 13/4+5/6=49/12; 833÷(49/12)=204; 204×2=408; 408+24 = 432."
    },
    {
      "n": 48,
      "type_id": 1,
      "question": "The line graph shows the number of visitors who visited the National Library over 5 months. The number of visitors for February is twice the number of May. Is this statement True, False or Not possible to tell?",
      "answer0": "True",
      "answer1": "False",
      "answer2": "Not possible to tell",
      "answer3": null,
      "correct_answer": 1,
      "skill_id": 147,
      "difficulty_id": 2,
      "explanation": "From the graph, February = 20 000 and May = 40 000. Twice May would be 80 000, which is not 20 000. The statement is False.",
      "hints": ["Read February and May off the line graph.", "Check whether February equals 2 × May."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q48 (Paper 2 Q13a)",
      "image_needed": true,
      "image_options": false,
      "image_file": "q48.png",
      "image_page": 30,
      "image_bbox": [0.16, 0.21, 0.78, 0.45],
      "image_loc": "below the question: line graph 'Visitors at the National Library', y-axis Number of Visitors (0 to 50000), x-axis months Jan to May",
      "notes": "Paper 2 Q13a. Answer key: False. Made MCQ (True/False/Not possible to tell), 3 options."
    },
    {
      "n": 49,
      "type_id": 1,
      "question": "The line graph shows the number of visitors who visited the National Library over 5 months. The average number of visitors for Jan to May is 32 000. Is this statement True, False or Not possible to tell?",
      "answer0": "True",
      "answer1": "False",
      "answer2": "Not possible to tell",
      "answer3": null,
      "correct_answer": 0,
      "skill_id": 203,
      "difficulty_id": 2,
      "explanation": "From the graph: Jan 25 000, Feb 20 000, Mar 45 000, Apr 30 000, May 40 000. Total $= 160\\,000$; average $= 160\\,000 \\div 5 = 32\\,000$. The statement is True.",
      "hints": ["Read all five months' values from the graph and add them.", "Divide the total by 5 and compare with 32 000."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q49 (Paper 2 Q13b)",
      "image_needed": true,
      "image_options": false,
      "image_file": "q49.png",
      "image_page": 30,
      "image_bbox": [0.16, 0.21, 0.78, 0.45],
      "image_loc": "below the question: line graph 'Visitors at the National Library', y-axis Number of Visitors (0 to 50000), x-axis months Jan to May",
      "notes": "Paper 2 Q13b. Answer key: True. Same graph as Q48."
    },
    {
      "n": 50,
      "type_id": 1,
      "question": "The line graph shows the number of visitors who visited the National Library over 5 months. There are 20 000 visitors in June. The average number of visitors for Jan to June will increase. Is this statement True, False or Not possible to tell?",
      "answer0": "True",
      "answer1": "False",
      "answer2": "Not possible to tell",
      "answer3": null,
      "correct_answer": 1,
      "skill_id": 203,
      "difficulty_id": 2,
      "explanation": "The Jan–May average is 32 000. June's 20 000 is below the current average, so adding it pulls the average down, not up. The statement is False.",
      "hints": ["Compare June's value (20 000) with the current average (32 000).", "Adding a value below the average lowers the average."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q50 (Paper 2 Q13c)",
      "image_needed": true,
      "image_options": false,
      "image_file": "q50.png",
      "image_page": 30,
      "image_bbox": [0.16, 0.21, 0.78, 0.45],
      "image_loc": "below the question: line graph 'Visitors at the National Library', y-axis Number of Visitors (0 to 50000), x-axis months Jan to May",
      "notes": "Paper 2 Q13c. Answer key: False. Same graph as Q48."
    },
    {
      "n": 51,
      "type_id": 2,
      "question": "Peggy has a cubical tank A of edge 40 cm and a rectangular tank B measuring 40 cm by 20 cm by 35 cm. Tank A was fully filled with water while Tank B was partly filled. Peggy poured \\(\\dfrac{1}{4}\\) of the water from Tank A into Tank B. After this, the new water level in Tank B rose to \\(\\dfrac{6}{7}\\) of its height. Find the capacity of tank A in litres.<br>Ans: [?] ℓ",
      "answer0": "64",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 192,
      "difficulty_id": 2,
      "explanation": "Capacity of cube A $= 40 \\times 40 \\times 40 = 64\\,000\\text{ cm}^3 = 64$ ℓ (since 1000 cm³ = 1 ℓ).",
      "hints": ["Volume of a cube = edge × edge × edge.", "Convert cm³ to litres: 1000 cm³ = 1 ℓ."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q51 (Paper 2 Q14a)",
      "image_needed": true,
      "image_options": false,
      "image_file": "q51.png",
      "image_page": 31,
      "image_bbox": [0.22, 0.27, 0.72, 0.44],
      "image_loc": "below the question: two tanks — cubical Tank A (40 cm) on the left and rectangular Tank B (40 cm by 20 cm by 35 cm) on the right",
      "notes": "Paper 2 Q14a. Answer key: 40×40×40 = 64000 ml = 64 l."
    },
    {
      "n": 52,
      "type_id": 2,
      "question": "Peggy has a cubical tank A of edge 40 cm and a rectangular tank B measuring 40 cm by 20 cm by 35 cm. Tank A was fully filled with water while Tank B was partly filled. Peggy poured \\(\\dfrac{1}{4}\\) of the water from Tank A into Tank B. After this, the new water level in Tank B rose to \\(\\dfrac{6}{7}\\) of its height. How much water was in the rectangular tank at first?<br>Ans: [?] cm³",
      "answer0": "8000",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 193,
      "difficulty_id": 3,
      "explanation": "Water poured in $= \\dfrac{1}{4} \\times 64\\,000 = 16\\,000\\text{ cm}^3$. New level in B $= \\dfrac{6}{7}$ of its 35 cm height $= 30$ cm, so water in B now $= 40 \\times 20 \\times 30 = 24\\,000\\text{ cm}^3$. Water at first $= 24\\,000 - 16\\,000 = 8000\\text{ cm}^3$.",
      "hints": ["Water poured in = \\(\\dfrac{1}{4}\\) of 64 000 cm³.", "Final water in B = 40 × 20 × (\\(\\dfrac{6}{7}\\) × 35); subtract the poured-in amount."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q52 (Paper 2 Q14b)",
      "image_needed": true,
      "image_options": false,
      "image_file": "q52.png",
      "image_page": 31,
      "image_bbox": [0.22, 0.27, 0.72, 0.44],
      "image_loc": "below the question: two tanks — cubical Tank A (40 cm) and rectangular Tank B (40 cm by 20 cm by 35 cm)",
      "notes": "Paper 2 Q14b. Answer key: ¼×64000=16000; 6/7×40×20×35=24000; 24000-16000 = 8000 cm³. Same figure as Q51."
    },
    {
      "n": 53,
      "type_id": 1,
      "question": "The original price of each fan is $35. During a sale, Fan A gets $6.80 off the original price and Fan B gets a 20% discount. Which fan was cheaper after the discount? How much is it cheaper than the other fan?",
      "answer0": "Fan B, by $0.20",
      "answer1": "Fan A, by $0.20",
      "answer2": "Fan B, by $1.20",
      "answer3": "Fan A, by $6.80",
      "correct_answer": 0,
      "skill_id": 176,
      "difficulty_id": 2,
      "explanation": "Fan A: $35 - 6.80 = 28.20$. Fan B: $20\\%$ off = $\\dfrac{80}{100} \\times 35 = 28$. Fan B ($28) is cheaper than Fan A ($28.20) by $28.20 - 28 = 0.20$.",
      "hints": ["Fan A price = $35 − $6.80. Fan B price = 80% of $35.", "Compare the two and find the difference."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q53 (Paper 2 Q15a)",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q15a. Answer key: Fan B, $0.20. Converted to MCQ (two-part 'which/how much' answer). Fan pictures decorative."
    },
    {
      "n": 54,
      "type_id": 2,
      "question": "The original price of each fan is $35. During a sale, Fan A gets $6.80 off the original price and Fan B gets a 20% discount. Jefferson wanted to buy the cheaper fan on discount. He had to pay an additional 9% GST on the discounted price. How much did Jefferson have to pay for the fan in total?<br>Ans: $[?]",
      "answer0": "30.52",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 2,
      "explanation": "The cheaper fan (Fan B) costs $28 after discount. With 9% GST: $\\dfrac{109}{100} \\times 28 = 30.52$. Jefferson paid $30.52.",
      "hints": ["The cheaper fan (Fan B) is $28 after discount.", "Add 9% GST: $\\dfrac{109}{100} \\times 28$."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q54 (Paper 2 Q15b)",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q15b. Answer key: 109/100 × 28 = $30.52."
    },
    {
      "n": 55,
      "type_id": 2,
      "question": "A box of biscuit is sold at $5.50. For every 5 boxes of biscuits bought, 2 boxes of biscuits are given free. Nadiah bought some boxes of biscuits and paid a total of $126.50. How many boxes of biscuits did she have?<br>Ans: [?]",
      "answer0": "31",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Each 'set' = pay for 5 ($5 \\times 5.50 = 27.50$) and get 7 boxes. $126.50 \\div 27.50 = 4$ remainder $16.50$. The $16.50 buys $16.50 \\div 5.50 = 3$ more boxes (no free ones). Boxes $= 4 \\times 7 + 3 = 28 + 3 = 31$.",
      "hints": ["A full set costs $5 \\times \\$5.50 = \\$27.50$ and gives 7 boxes.", "Find how many full sets fit in $126.50, then buy extra boxes with the remainder."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q55 (Paper 2 Q16a)",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q16a. Answer key: 5×5.50=27.50; 126.50÷27.50=4 R16.50; 16.50÷5.50=3; 4×7=28; 28+3 = 31. Promo banner is decorative."
    },
    {
      "n": 56,
      "type_id": 2,
      "question": "A box of biscuit is sold at $5.50. For every 5 boxes of biscuits bought, 2 boxes of biscuits are given free. In every box of biscuits, there are 10 pieces of biscuits. Daryl needs to get 485 pieces of biscuits. What is the least amount of money he has to pay?<br>Ans: $[?]",
      "answer0": "192.50",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Each set gives 7 boxes = $7 \\times 10 = 70$ pieces and costs $27.50. $485 \\div 70 = 6$ remainder $65$ pieces. The remaining 65 pieces need 1 more set (rounding up), so $6 + 1 = 7$ sets. Least cost $= 27.50 \\times 7 = 192.50$.",
      "hints": ["One set (pay 5, get 7) gives $7 \\times 10 = 70$ pieces for $27.50.", "Find how many sets cover 485 pieces, rounding up."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q56 (Paper 2 Q16b)",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q16b. Answer key: 7×10=70; 485÷70=6 R65; 6+1=7; 27.50×7 = $192.50."
    },
    {
      "n": 57,
      "type_id": 2,
      "question": "Teck Huat made blueberry and chocolate muffins to sell. \\(\\dfrac{5}{6}\\) of the muffins were blueberry muffins and the rest were chocolate muffins. He sold \\(\\dfrac{1}{3}\\) of the total number of muffins. \\(\\dfrac{5}{6}\\) of the muffins sold were blueberry muffins. There were 120 chocolate muffins left. How many blueberry muffins did he sell?<br>Ans: [?]",
      "answer0": "300",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Blueberry sold $= \\dfrac{5}{6} \\times \\dfrac{1}{3} = \\dfrac{5}{18}$ of total; chocolate sold $= \\dfrac{1}{6} \\times \\dfrac{1}{3} = \\dfrac{1}{18}$ of total. Chocolate made $= \\dfrac{1}{6} = \\dfrac{3}{18}$; chocolate left $= \\dfrac{3}{18} - \\dfrac{1}{18} = \\dfrac{2}{18} = 120$, so \\(\\dfrac{1}{18}\\) of total $= 60$. Blueberry sold $= \\dfrac{5}{18} = 5 \\times 60 = 300$.",
      "hints": ["Work out the fraction of the total that is blueberry-sold (\\(\\dfrac{5}{6}\\times\\dfrac{1}{3}\\)) and chocolate-sold (\\(\\dfrac{1}{6}\\times\\dfrac{1}{3}\\)).", "Chocolate left = chocolate made − chocolate sold = 120; find one eighteenth, then blueberry sold = 5 eighteenths."],
      "source": "Rosyth 2024 P5 End-of-Year Exam Q57 (Paper 2 Q17)",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q17. Answer key: 5/6×1/3=5/18; 1/6×1/3=1/18; chocolate left 2/18=120 so 1/18=60; 60×5 = 300."
    }
  ]
}