{
  "paper": {
    "school": "Rosyth",
    "year": 2024,
    "level": "P6",
    "label": "Prelim",
    "source_prefix": "Rosyth 2024 P6 Prelim",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "Which of the following is four hundred and two thousand and thirty-one?",
      "answer0": "42 031",
      "answer1": "402 031",
      "answer2": "4 020 031",
      "answer3": "4 002 031",
      "correct_answer": 1,
      "skill_id": 2,
      "difficulty_id": 1,
      "explanation": "Four hundred and two thousand = 402 000. Add thirty-one: 402 000 + 31 = 402 031.",
      "hints": ["Break it into thousands and ones.", "Four hundred and two thousand is 402 000."],
      "source": "Rosyth 2024 P6 Prelim P1 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 2 (1-indexed)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Which of the following is the same as 9070 m?",
      "answer0": "9 km 7 m",
      "answer1": "9 km 70 m",
      "answer2": "90 km 7 m",
      "answer3": "90 km 70 m",
      "correct_answer": 1,
      "skill_id": 184,
      "difficulty_id": 1,
      "explanation": "9070 m = 9000 m + 70 m = 9 km 70 m (since 1 km = 1000 m).",
      "hints": ["1 km = 1000 m.", "9000 m = 9 km, leaving 70 m."],
      "source": "Rosyth 2024 P6 Prelim P1 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 2 (1-indexed)."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "The opening hours of a shop are shown.<br>Kovan Phone Repair Shop, Open Daily, 10.15 a.m. to 5 p.m.<br>How long is the shop open each day?",
      "answer0": "6 h 15 min",
      "answer1": "6 h 45 min",
      "answer2": "7 h 15 min",
      "answer3": "7 h 45 min",
      "correct_answer": 1,
      "skill_id": 184,
      "difficulty_id": 1,
      "explanation": "From 10.15 a.m. to 5.00 p.m. From 10.15 a.m. to 4.15 p.m. is 6 h; from 4.15 p.m. to 5.00 p.m. is 45 min. Total = 6 h 45 min.",
      "hints": ["Count from 10.15 a.m. to 5.00 p.m.", "5.00 p.m. is 17.00."],
      "source": "Rosyth 2024 P6 Prelim P1 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Sign figure is just the text 10.15 a.m. to 5 p.m.; reproduced in stem. Key: option 2 (1-indexed)."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "A tank was filled with 50 litres of water at 08 00. Water flowed out of the tank from 08 00 to 12 00. The graph shows the amount of water in the tank from 08 00 to 12 00.<br>Which one-hour period was the decrease in water the greatest?",
      "answer0": "Between 08 00 and 09 00",
      "answer1": "Between 09 00 and 10 00",
      "answer2": "Between 10 00 and 11 00",
      "answer3": "Between 11 00 and 12 00",
      "correct_answer": 0,
      "skill_id": 1,
      "difficulty_id": 1,
      "explanation": "Read the graph: 08 00->09 00 drops from 50 to 20 (decrease 30 L), the steepest segment. All later hours drop by less. Greatest decrease is between 08 00 and 09 00.",
      "hints": ["Find the steepest part of the line.", "Compare the drop in volume each hour."],
      "source": "Rosyth 2024 P6 Prelim P1 Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q4.png",
      "image_page": 3,
      "image_bbox": [0.20, 0.17, 0.92, 0.50],
      "image_loc": "line graph of volume of water vs time, upper-middle of page",
      "notes": "Key: option 1 (1-indexed)."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "The table shows the number of participants in an art class on Saturday and Sunday.<br>Saturday: Children 16, Adults 24. Sunday: Children 20, Adults 24.<br>What is the percentage increase in the number of participants from Saturday to Sunday?",
      "answer0": "10%",
      "answer1": "20%",
      "answer2": "25%",
      "answer3": "4%",
      "correct_answer": 0,
      "skill_id": 208,
      "difficulty_id": 2,
      "explanation": "Saturday total = 16 + 24 = 40. Sunday total = 20 + 24 = 44. Increase = 4. Percentage increase = 4/40 x 100% = 10%.",
      "hints": ["Find each day's total first.", "Percentage increase = increase / original x 100%."],
      "source": "Rosyth 2024 P6 Prelim P1 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Table values embedded in stem. Key: option 1 (1-indexed)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "What is the value of \\(\\dfrac{31w}{10} - w + 3\\) when \\(w = 2\\)?",
      "answer0": "1.2",
      "answer1": "3.6",
      "answer2": "7.2",
      "answer3": "9.2",
      "correct_answer": 2,
      "skill_id": 240,
      "difficulty_id": 2,
      "explanation": "Substitute w = 2: 31(2)/10 - 2 + 3 = 62/10 + 1 = 6.2 + 1 = 7.2.",
      "hints": ["Substitute w = 2 into each term.", "31 x 2 / 10 = 6.2."],
      "source": "Rosyth 2024 P6 Prelim P1 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 3 (1-indexed)."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "The figure is made up of squares. What is the least number of square(s) to be shaded so that the figure has one vertical line of symmetry?",
      "answer0": "1",
      "answer1": "2",
      "answer2": "3",
      "answer3": "4",
      "correct_answer": 2,
      "skill_id": 6,
      "difficulty_id": 2,
      "explanation": "For a vertical line of symmetry, each shaded square must have a mirror image across the centre line. Checking the existing shaded squares, 3 more squares need to be shaded to complete the symmetry.",
      "hints": ["Fold the grid along the vertical centre line.", "Each shaded square needs a matching shaded square on the other side."],
      "source": "Rosyth 2024 P6 Prelim P1 Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q7.png",
      "image_page": 4,
      "image_bbox": [0.18, 0.61, 0.38, 0.78],
      "image_loc": "small grid of squares with some shaded and a vertical dashed line, left side below the question",
      "notes": "Key: option 3 (1-indexed). Symmetry figure required."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "PQR is a straight line. AP = AQ = QR. \\(\\angle APQ = 70^\\circ\\). Find \\(\\angle RAQ\\).",
      "answer0": "35°",
      "answer1": "40°",
      "answer2": "55°",
      "answer3": "70°",
      "correct_answer": 0,
      "skill_id": 197,
      "difficulty_id": 2,
      "explanation": "Triangle APQ is isosceles (AP = AQ), so angle AQP = 70 deg, hence angle AQR (exterior) = 180 - 70 = 110 deg. Triangle AQR is isosceles (AQ = QR), so angle RAQ = angle ARQ = (180 - 110) / 2 = 35 deg.",
      "hints": ["Triangle APQ is isosceles, so angle AQP = angle APQ.", "angle AQR = 180 - angle AQP; then use isosceles triangle AQR."],
      "source": "Rosyth 2024 P6 Prelim P1 Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 5,
      "image_bbox": [0.20, 0.17, 0.55, 0.32],
      "image_loc": "triangle APQR with 70 degrees at P, upper-left below the question",
      "notes": "Key: option 1 (1-indexed)."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "A, B and C are three points on the grid. Point B is south of Point A and \\(\\angle ABC\\) is 225°. In what direction is Point C from Point B?",
      "answer0": "North-East",
      "answer1": "North-West",
      "answer2": "South-East",
      "answer3": "South-West",
      "correct_answer": 3,
      "skill_id": 6,
      "difficulty_id": 2,
      "explanation": "BA points north. Measuring 225 deg clockwise from BA (north) gives a bearing of 225 deg, which points South-West. So C is South-West of B.",
      "hints": ["BA points due north.", "Turn 225 deg from north to reach BC."],
      "source": "Rosyth 2024 P6 Prelim P1 Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q9.png",
      "image_page": 5,
      "image_bbox": [0.18, 0.59, 0.55, 0.78],
      "image_loc": "grid showing points A, B, C with 225 degree angle, lower-left below the question",
      "notes": "Key: option 4 (1-indexed). Direction question - kept as MCQ."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "Miss Lim travelled 3.2 km in a taxi from home to the mall. Her taxi fare was based on the charges shown.<br>First km: $4.80. Every additional 400 m or less: $0.20.<br>How much was her taxi fare?",
      "answer0": "$5.40",
      "answer1": "$5.80",
      "answer2": "$6.00",
      "answer3": "$6.40",
      "correct_answer": 2,
      "skill_id": 167,
      "difficulty_id": 2,
      "explanation": "First 1 km = $4.80. Remaining distance = 3.2 - 1 = 2.2 km = 2200 m. Number of 400 m blocks = 2200 / 400 = 5.5, round up to 6 blocks. Extra charge = 6 x $0.20 = $1.20. Total = $4.80 + $1.20 = $6.00.",
      "hints": ["First km is fixed at $4.80.", "Divide the remaining 2200 m into 400 m blocks, rounding up."],
      "source": "Rosyth 2024 P6 Prelim P1 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Charge table embedded in stem. Key: option 3 (1-indexed)."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "Sam spent $42 of his money on a gift and \\(\\dfrac{2}{5}\\) of the remaining money on a book. In the end, he had \\(\\dfrac{1}{4}\\) of his money left. How much money did Sam have at first?",
      "answer0": "$42",
      "answer1": "$70",
      "answer2": "$72",
      "answer3": "$180",
      "correct_answer": 2,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "After the gift he had R left. He spent 2/5 of R on a book, leaving 3/5 of R = 1/4 of total. So R = 5/12 of total spent? Work backwards: left = 1/4 total = 3/5 of remaining, so remaining after gift = (1/4) / (3/5) = 5/12 of total. Gift = total - 5/12 total = 7/12 total = $42, so total = 42 x 12/7 = $72.",
      "hints": ["Let the remaining money after the gift be the unit.", "The final 1/4 equals 3/5 of the money left after the gift."],
      "source": "Rosyth 2024 P6 Prelim P1 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 3 (1-indexed)."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "Limin, Ming and Raju each had some money at first. Limin gave Ming $2.50. Ming then gave Raju $1.80. Raju then spent $3 on a pen. In the end, they each had $5. What was the difference between the amount Limin and Raju had at first?",
      "answer0": "$0.50",
      "answer1": "$1.20",
      "answer2": "$1.30",
      "answer3": "$3.00",
      "correct_answer": 2,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "Work backwards from $5 each. Limin: gave away $2.50, so at first = 5 + 2.50 = $7.50. Raju: received $1.80 then spent $3, so at first = 5 + 3 - 1.80 = $6.20. Difference = 7.50 - 6.20 = $1.30.",
      "hints": ["Work backwards from the final $5 each.", "Reverse each transaction for Limin and Raju."],
      "source": "Rosyth 2024 P6 Prelim P1 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 3 (1-indexed)."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "ABCD is a trapezium with AB parallel to DC. \\(\\angle ADC = 100^\\circ\\), \\(\\angle AEC = 91^\\circ\\) and \\(\\angle ABE = 52^\\circ\\). Find \\(\\angle DAE\\).",
      "answer0": "39°",
      "answer1": "41°",
      "answer2": "80°",
      "answer3": "89°",
      "correct_answer": 1,
      "skill_id": 200,
      "difficulty_id": 3,
      "explanation": "AB parallel to DC, so angle DAB = 180 - 100 = 80 deg (co-interior with angle ADC). In triangle ABE, angle AEB = 180 - 91 = 89 deg (angles on straight line at E), so angle BAE = 180 - 89 - 52 = 39 deg. Then angle DAE = angle DAB - angle BAE = 80 - 39 = 41 deg.",
      "hints": ["Use co-interior angles to find angle DAB = 80 deg.", "Find angle BAE in triangle ABE, then subtract from angle DAB."],
      "source": "Rosyth 2024 P6 Prelim P1 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q13.png",
      "image_page": 7,
      "image_bbox": [0.30, 0.13, 0.66, 0.30],
      "image_loc": "trapezium ABCD with diagonal point E, upper-middle below the question",
      "notes": "Key: option 2 (1-indexed)."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "Mary glued some identical square papers in a straight line to form a length of 5.98 m. She glued the papers by overlapping one paper on the other paper. Each overlapping part was 3 cm long. Each square paper is 10 cm. What was the number of square papers she used?",
      "answer0": "59",
      "answer1": "60",
      "answer2": "84",
      "answer3": "85",
      "correct_answer": 3,
      "skill_id": 6,
      "difficulty_id": 3,
      "explanation": "Total length 5.98 m = 598 cm. With n papers of 10 cm each there are (n-1) overlaps of 3 cm: 10n - 3(n-1) = 598. So 7n + 3 = 598, 7n = 595, n = 85.",
      "hints": ["n papers give (n-1) overlaps.", "10n - 3(n-1) = 598."],
      "source": "Rosyth 2024 P6 Prelim P1 Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q14.png",
      "image_page": 7,
      "image_bbox": [0.22, 0.60, 0.86, 0.74],
      "image_loc": "row of overlapping square papers with 5.98 m, 10 cm and 3 cm labels, middle below the question",
      "notes": "Key: option 4 (1-indexed). Each square is 10 cm (from figure)."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "Bala used some wire to form the figure shown. In the figure, ABCD is a rectangle and the 4 identical triangles are equilateral triangles. The area of ABCD is 162 cm².<br>What is the perimeter of the figure?",
      "answer0": "72 cm",
      "answer1": "90 cm",
      "answer2": "99 cm",
      "answer3": "126 cm",
      "correct_answer": 1,
      "skill_id": 223,
      "difficulty_id": 3,
      "explanation": "ABCD is 9 by 18 (area 162). The 4 equilateral triangles sit on the sides. With side 9 on the rectangle, each triangle contributes 2 sides of 9 to the perimeter. The outer boundary consists of the triangle edges; total perimeter = 90 cm (per answer key).",
      "hints": ["Find the rectangle's dimensions from area 162.", "Each equilateral triangle's two outer sides equal the side it sits on."],
      "source": "Rosyth 2024 P6 Prelim P1 Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q15.png",
      "image_page": 8,
      "image_bbox": [0.24, 0.16, 0.66, 0.46],
      "image_loc": "rectangle ABCD with 4 equilateral triangles on its sides, upper-middle below the question",
      "notes": "Key: option 2 (1-indexed) = 90 cm."
    },
    {
      "n": 16,
      "type_id": 1,
      "question": "In the number line, P represents \\(\\dfrac{1}{8}\\) and R represents \\(\\dfrac{1}{2}\\). PQ = QR. What fraction is represented by Q?",
      "answer0": "\\(\\dfrac{5}{16}\\)",
      "answer1": "\\(\\dfrac{3}{16}\\)",
      "answer2": "\\(\\dfrac{1}{4}\\)",
      "answer3": "\\(\\dfrac{3}{8}\\)",
      "correct_answer": 0,
      "skill_id": 159,
      "difficulty_id": 2,
      "explanation": "Q is the midpoint of P and R. Distance PR = 1/2 - 1/8 = 3/8. Half of it = 3/16. Q = 1/8 + 3/16 = 2/16 + 3/16 = 5/16.",
      "hints": ["Q is halfway between P and R.", "Find PR, halve it, then add to P."],
      "source": "Rosyth 2024 P6 Prelim P1 Q16",
      "image_needed": true,
      "image_options": false,
      "image_file": "q16.png",
      "image_page": 10,
      "image_bbox": [0.22, 0.24, 0.74, 0.36],
      "image_loc": "number line with P, Q, R marked, upper-middle below the question",
      "notes": "Fraction answer (5/16) so converted to MCQ. Answer key: 1/2 - 1/8 = 3/8; 3/8 / 2 = 3/16; 3/16 + 1/8 = 5/16."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "The total mass of 9 durians is 16.2 kg. What is the average mass of the durians? [?] kg",
      "answer0": "1.8",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 203,
      "difficulty_id": 1,
      "explanation": "Average = total / number = 16.2 / 9 = 1.8 kg.",
      "hints": ["Average = total mass / number of durians.", "16.2 / 9 = 1.8."],
      "source": "Rosyth 2024 P6 Prelim P1 Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "FIB decimal answer 1.8."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "The volume of a cube is 64 cm³. Find the length of the cube. [?] cm",
      "answer0": "4",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 225,
      "difficulty_id": 1,
      "explanation": "Length = cube root of volume = \\(\\sqrt[3]{64}\\) = 4 cm (since 4 x 4 x 4 = 64).",
      "hints": ["Length = cube root of the volume.", "Find the number that cubed gives 64."],
      "source": "Rosyth 2024 P6 Prelim P1 Q18",
      "image_needed": true,
      "image_options": false,
      "image_file": "q18.png",
      "image_page": 10,
      "image_bbox": [0.27, 0.66, 0.40, 0.79],
      "image_loc": "small cube with '? cm' label, left side below the question",
      "notes": "FIB whole-number answer 4."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "The pie chart shows the number of pupils who chose their favourite sport in a survey. Half of the pupils chose badminton and swimming. Floorball 15, Jogging 10, Swimming 18. How many pupils chose badminton? [?]",
      "answer0": "32",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 1,
      "difficulty_id": 2,
      "explanation": "Floorball + Jogging = 15 + 10 = 25 pupils make up 1/4 of total (the quadrant), so 1/4 = 25, total = 100? Per key: 1/4 pupils = 15 + 10 = 25; so half the pupils (badminton + swimming) = 25 x 2 = 50. Badminton = 50 - 18 = 32.",
      "hints": ["Floorball and Jogging form a right-angle quarter of the chart.", "Badminton + Swimming = half the total; subtract Swimming."],
      "source": "Rosyth 2024 P6 Prelim P1 Q19",
      "image_needed": true,
      "image_options": false,
      "image_file": "q19.png",
      "image_page": 11,
      "image_bbox": [0.22, 0.13, 0.62, 0.40],
      "image_loc": "pie chart of favourite sports with right-angle mark, upper-middle below the question",
      "notes": "FIB whole-number answer 32. Floorball+Jogging form the quarter (right angle); badminton+swimming = half."
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "AD is a straight line, AG is parallel to CF and CD is parallel to FE. \\(\\angle ABG = 52^\\circ\\) and AB = GB. Find \\(\\angle DCF\\). [?]",
      "answer0": "64",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 2,
      "explanation": "Triangle ABG is isosceles (AB = GB) with angle ABG = 52 deg, so angle GAB = (180 - 52) / 2 = 64 deg. AG is parallel to CF, so angle DCF = angle GAB = 64 deg (corresponding angles).",
      "hints": ["Triangle ABG is isosceles; find angle GAB.", "AG parallel to CF gives equal corresponding angles."],
      "source": "Rosyth 2024 P6 Prelim P1 Q20",
      "image_needed": true,
      "image_options": false,
      "image_file": "q20.png",
      "image_page": 11,
      "image_bbox": [0.22, 0.56, 0.72, 0.74],
      "image_loc": "two triangles on straight line AD with parallel marks, lower-middle below the question",
      "notes": "FIB degree answer 64."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "Alice saves $2 every day. Her mother gives her $1 for every 10 days that she saves. What is the total amount of money she will have after 43 days? Ans: $[?]",
      "answer0": "90",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 2,
      "explanation": "In 43 days there are 4 complete sets of 10 days, so mother gives 4 x $1 = $4. Wait: per key, 2 x 10 = 20; 20 + 1 = 21 per 10 days; 21 x 4 = 84 (for 40 days). Remaining 3 days: 3 x $2 = $6. Total = 84 + 6 = $90.",
      "hints": ["Every 10 days she saves $20 and gets $1, total $21.", "43 days = 4 sets of 10 days plus 3 extra days."],
      "source": "Rosyth 2024 P6 Prelim P1 Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "FIB money answer 90 ($90)."
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "A solid is made up of 7 cubes (an L/T arrangement: a top cube on a base layer). Tyler painted the whole solid including the base. Then he took it apart into 7 cubes. What is the total number of faces that are painted? [?]",
      "answer0": "28",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 224,
      "difficulty_id": 3,
      "explanation": "Each of the 7 cubes has 6 faces = 42 total faces. Hidden (touching) faces between cubes are not painted. Per key the painted (exposed) faces total 4 + 6 + 4 + 4 + 4 + 6 = 28.",
      "hints": ["Count only the exposed (outer) faces of each cube.", "Faces where two cubes touch are not painted."],
      "source": "Rosyth 2024 P6 Prelim P1 Q22",
      "image_needed": true,
      "image_options": false,
      "image_file": "q22.png",
      "image_page": 13,
      "image_bbox": [0.34, 0.18, 0.66, 0.36],
      "image_loc": "isometric solid of 7 cubes with Top/Front/Side view arrows, upper-middle below the question",
      "notes": "Only part (b) is a value answer (28). Part (a) draw-the-top-view is interactive and omitted (not served). FIB answer 28."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "Judy and her brother had some stickers. After Judy gave him 30 stickers, she had 14 stickers more than him. How many more stickers did Judy have than her brother at first? [?]",
      "answer0": "74",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "Giving away 30 widens to Judy still being 14 more. Before giving, the gap was larger by 2 x 30 = 60. So at first Judy had 14 + 60 = 74 more. Per key: 30 x 2 + 14 = 74.",
      "hints": ["Giving 30 to her brother changes the difference by 2 x 30.", "Add back twice the 30 to the final 14."],
      "source": "Rosyth 2024 P6 Prelim P1 Q23",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "FIB whole-number answer 74."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "A group of students took part in a Math competition. \\(\\dfrac{3}{8}\\) of the boys and \\(\\dfrac{1}{6}\\) of the girls went on to the final round of the competition. There were 60 students who went on to the final round and \\(\\dfrac{3}{4}\\) of them were boys. What was the total number of students who took part in this competition? [?]",
      "answer0": "210",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Boys in final = 3/4 x 60 = 45, which is 3/8 of all boys, so total boys = 45 x 8/3 = 120. Girls in final = 60 - 45 = 15, which is 1/6 of all girls, so total girls = 15 x 6 = 90. Total students = 120 + 90 = 210.",
      "hints": ["Find boys and girls in the final round first.", "Reverse the fractions 3/8 and 1/6 to get the totals."],
      "source": "Rosyth 2024 P6 Prelim P1 Q24",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "FIB whole-number answer 210."
    },
    {
      "n": 25,
      "type_id": 1,
      "question": "Rectangle PQRS is made up of a rectangle and 2 squares, A and B. Square B has side y cm and SR includes a 12 cm part. Find the perimeter of rectangle PQRS in terms of y.",
      "answer0": "\\((6y + 48)\\) cm",
      "answer1": "\\((6y + 24)\\) cm",
      "answer2": "\\((3y + 48)\\) cm",
      "answer3": "\\((4y + 24)\\) cm",
      "correct_answer": 0,
      "skill_id": 238,
      "difficulty_id": 3,
      "explanation": "From the figure, length PQ = 12 + y and height = (12 + y) + y? Per key: perimeter = 2(y + 12 + 2y + 12) = 2(3y + 24) = (6y + 48) cm.",
      "hints": ["Express the length and breadth of PQRS in terms of y.", "Perimeter = 2 x (length + breadth)."],
      "source": "Rosyth 2024 P6 Prelim P1 Q25",
      "image_needed": true,
      "image_options": false,
      "image_file": "q25.png",
      "image_page": 15,
      "image_bbox": [0.36, 0.14, 0.66, 0.32],
      "image_loc": "rectangle PQRS containing square A and square B, with y cm and 12 cm labels, upper-middle below the question",
      "notes": "Algebraic expression answer so MCQ. Key working: 2(y + 12 + 2y + 12) = (6y + 48) cm. Distractors plausible."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "Allyn and Baxter started jogging from the same place in opposite directions along a straight path. They jogged for 45 min. At the end of the jog, they were 15 km apart. Allyn's average speed was 8 km/h. What was Baxter's average speed? [?] km/h",
      "answer0": "12",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 219,
      "difficulty_id": 3,
      "explanation": "45 min = 3/4 h. Allyn's distance = 8 x 3/4 = 6 km. Baxter's distance = 15 - 6 = 9 km. Baxter's speed = 9 / (3/4) = 9 x 4/3 = 12 km/h.",
      "hints": ["Convert 45 min to 3/4 hour.", "Find Allyn's distance, subtract from 15 km, then divide by time."],
      "source": "Rosyth 2024 P6 Prelim P1 Q26",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "FIB whole-number answer 12."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "The bar graph shows the number of cups of milk, juice, coffee and tea sold at a shop on a Friday. 84 cups of milk were sold. Find the total number of cups of drinks sold on Friday. [?]",
      "answer0": "448",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 1,
      "difficulty_id": 3,
      "explanation": "From the bar graph the units are: Milk 3 units = 84, so 1 unit = 28. Total of all bars = 16 units. Total = 16 x 28 = 448 cups. (Key: 3u = 84, u = 28, 16u = 448.)",
      "hints": ["Find the value of one unit using Milk = 84.", "Add up all the bar units and multiply by one unit."],
      "source": "Rosyth 2024 P6 Prelim P1 Q27",
      "image_needed": true,
      "image_options": false,
      "image_file": "q27.png",
      "image_page": 16,
      "image_bbox": [0.30, 0.14, 0.80, 0.36],
      "image_loc": "horizontal bar graph of cups sold for Milk/Juice/Coffee/Tea, upper-middle below the question",
      "notes": "Only part (b) is a value answer (448). Part (a) label-the-pie-chart is interactive and omitted (not served). FIB answer 448."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "Rectangle EFGH has an area of 2250 cm² and triangle MNH has an area of 750 cm². Find the area of the shaded triangle NFG. [?] cm²",
      "answer0": "375",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Triangle MNH and triangle NFG share related base-height. Per key: half the rectangle = 2250 / 2 = 1125 cm²; area NFG = 1125 - 750 = 375 cm².",
      "hints": ["Half the rectangle's area is 1125 cm².", "Subtract triangle MNH's area from 1125."],
      "source": "Rosyth 2024 P6 Prelim P1 Q28",
      "image_needed": true,
      "image_options": false,
      "image_file": "q28.png",
      "image_page": 17,
      "image_bbox": [0.24, 0.13, 0.80, 0.32],
      "image_loc": "rectangle EFGH with diagonals/triangles and shaded triangle NFG, upper-middle below the question",
      "notes": "FIB whole-number answer 375."
    },
    {
      "n": 29,
      "type_id": 0,
      "question": "The figure shows a triangle PQR. On the grid, draw a parallelogram RQXY with the same area as triangle PQR without overlapping it.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Draw a parallelogram RQXY on the grid below triangle PQR. A parallelogram with the same base RQ and half the height of the triangle has the same area; the key shows one valid construction.",
      "hints": ["A parallelogram has double the area of a triangle with the same base and height.", "Use half the triangle's height for the parallelogram."],
      "source": "Rosyth 2024 P6 Prelim P1 Q29",
      "image_needed": true,
      "image_options": false,
      "image_file": "q29.png",
      "image_page": 17,
      "image_bbox": [0.18, 0.50, 0.80, 0.92],
      "image_loc": "dot grid with triangle PQR drawn, lower half of page",
      "notes": "Draw-on-grid construction task - type_id 0, not served. Answer: construct parallelogram RQXY of equal area."
    },
    {
      "n": 30,
      "type_id": 0,
      "question": "Match the net of each solid in the table by writing the letter A, B, C or D on the blank. (a) Prism (b) Cube",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 224,
      "difficulty_id": 2,
      "explanation": "(a) Prism matches net C; (b) Cube matches net B.",
      "hints": ["Visualise folding each net into a solid.", "A triangular prism net has rectangles plus 2 triangles; a cube net has 6 squares."],
      "source": "Rosyth 2024 P6 Prelim P1 Q30",
      "image_needed": true,
      "image_options": false,
      "image_file": "q30.png",
      "image_page": 18,
      "image_bbox": [0.12, 0.14, 0.80, 0.48],
      "image_loc": "four nets labelled A, B, C, D, upper portion of page",
      "notes": "Matching/writing-letter task - type_id 0, not served. Answers: (a) Prism = C, (b) Cube = B."
    },
    {
      "n": 101,
      "type_id": 2,
      "question": "The figure shows a triangle EFG. It has a perimeter of 84 cm. Side EF = \\((8p - 9)\\) cm, side FG = \\((3p + 21)\\) cm and side EG = 39 cm. Find the value of p. [?]",
      "answer0": "3",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 2,
      "explanation": "Perimeter: (8p - 9) + (3p + 21) + 39 = 84, so 11p + 51 = 84, 11p = 33, p = 3.",
      "hints": ["Add the three sides and set equal to 84.", "Collect the p terms: 11p + 51 = 84."],
      "source": "Rosyth 2024 P6 Prelim P2 Q1",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q1.png",
      "image_page": 20,
      "image_bbox": [0.20, 0.27, 0.72, 0.42],
      "image_loc": "triangle EFG with side expressions and 39 cm base, upper-middle below the question",
      "notes": "Paper 2 Q1. FIB whole-number answer 3."
    },
    {
      "n": 102,
      "type_id": 2,
      "question": "Mdm Rosnah needs some pieces of ribbons, each of length 36 cm, to tie gift bags for a party. She bought 3 rolls of ribbon. Each roll is 15 m long. What is the greatest number of such ribbons that Mdm Rosnah can cut from the 3 rolls of ribbon? [?]",
      "answer0": "123",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 2,
      "explanation": "Each roll = 15 m = 1500 cm. 1500 / 36 = 41 remainder 24, so 41 ribbons per roll. 3 rolls = 41 x 3 = 123 ribbons.",
      "hints": ["Find how many 36 cm pieces fit in one 1500 cm roll.", "Multiply the whole-number result by 3 rolls (cut each roll separately)."],
      "source": "Rosyth 2024 P6 Prelim P2 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q2. FIB whole-number answer 123. Cut per roll (41 each), not combined length."
    },
    {
      "n": 103,
      "type_id": 2,
      "question": "Chairs are arranged in straight rows in a hall. There are 42 chairs in each row. Each chair has a length of 0.5 m. Every row is 1.5 m apart from the next row of chairs. There are 1470 chairs altogether. What is the distance between the first row of chairs and the last row of chairs in metres? [?] m",
      "answer0": "68.5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "Number of rows = 1470 / 42 = 35. Each row depth = 0.5 m x ... Per key: 35 rows of chairs (0.5 m each) = 35 x 0.5 = 17.5 m; gaps between rows = 34 x 1.5 = 51 m. Total distance = 17.5 + 51 = 68.5 m.",
      "hints": ["Find the number of rows: 1470 / 42.", "35 rows give 34 gaps; add chair depths and gaps."],
      "source": "Rosyth 2024 P6 Prelim P2 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q3.png",
      "image_page": 21,
      "image_bbox": [0.30, 0.20, 0.68, 0.42],
      "image_loc": "diagram of chair rows with 0.5 m, 1.5 m and 42 chairs labels, upper-middle below the question",
      "notes": "Paper 2 Q3. FIB decimal answer 68.5."
    },
    {
      "n": 104,
      "type_id": 2,
      "question": "ADE is an equilateral triangle and ABCD is a square. EH, EC and BH are straight lines. Find \\(\\angle AFC\\). [?]",
      "answer0": "105",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 200,
      "difficulty_id": 3,
      "explanation": "angle EDC = 90 (square) + 60 (equilateral) = 150 deg. Triangle EDC is isosceles (ED = DC), so angle FED = (180 - 150) / 2 = 15 deg. Then angle AFC = 180 - 60 - 15 = 105 deg.",
      "hints": ["angle EDC = angle EDA + angle ADC = 60 + 90.", "Triangle EDC is isosceles; use the angle sum."],
      "source": "Rosyth 2024 P6 Prelim P2 Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q4.png",
      "image_page": 22,
      "image_bbox": [0.18, 0.14, 0.58, 0.34],
      "image_loc": "square ABCD with equilateral triangle ADE and lines to F/H, upper-left below the question",
      "notes": "Paper 2 Q4. FIB degree answer 105."
    },
    {
      "n": 105,
      "type_id": 1,
      "question": "Dylan and Greg set off from their school at the same time and jogged towards the stadium using the same route. They jogged at a constant speed throughout the whole journey. When Greg covered \\(\\dfrac{1}{4}\\) of the distance, Dylan was 300 m behind him. Dylan reached the stadium at 9 a.m., jogging at a speed of 100 m/min. What time did Greg reach the stadium?",
      "answer0": "8.48 a.m.",
      "answer1": "8.45 a.m.",
      "answer2": "8.50 a.m.",
      "answer3": "8.52 a.m.",
      "correct_answer": 0,
      "skill_id": 219,
      "difficulty_id": 3,
      "explanation": "When Greg covered 1/4 of distance, Dylan was 300 m behind, so over a full journey Dylan is 4 x 300 = 1200 m behind in distance, i.e. Greg finishes earlier. Time difference = 1200 / 100 = 12 min. Greg reached 12 min before 9 a.m. = 8.48 a.m.",
      "hints": ["Scale the 300 m gap up to the full distance.", "Convert the distance gap to a time gap using 100 m/min."],
      "source": "Rosyth 2024 P6 Prelim P2 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q5. Time answer so MCQ. Key: 4(100x+300)=400x+1200; 1200/100=12 min; 12 min before 9am = 8.48 a.m."
    },
    {
      "n": 106,
      "type_id": 2,
      "question": "Mr Tan had a total of 1370 oranges and pears at first. He sold \\(\\dfrac{4}{7}\\) of the oranges and 265 pears. The number of oranges left was \\(\\dfrac{1}{2}\\) the number of pears left. How many more pears than oranges were there at first? [?]",
      "answer0": "180",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Let oranges = 7u. Sold 4/7, so 3u left. Pears left = 6u (since oranges left = 1/2 pears left). Pears at first = 6u + 265. Total: 7u + 6u + 265 = 1370, so 13u = 1105, u = 85. Oranges at first = 7u = 595; pears at first = 6u + 265 = 510 + 265 = 775. More pears = 775 - 595 = 180. (Key: 13u + 265 = 1370; u = 85; 265 - 85 = 180.)",
      "hints": ["Let oranges be 7 units; oranges left = 3 units.", "Pears left = 6 units; form an equation for the total 1370."],
      "source": "Rosyth 2024 P6 Prelim P2 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q6. FIB whole-number answer 180."
    },
    {
      "n": 107,
      "type_id": 2,
      "question": "A savings coupon gives: get the first refrigerator at 10% discount, get the second one at 20% discount. Mr Raj paid $3893 for two identical refrigerators using the savings coupon. How much more money did Mr Raj have to pay for the 2 refrigerators if he did not use the savings coupon? Ans: $[?]",
      "answer0": "687",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 3,
      "explanation": "Let usual price = 100u each. With coupon: 90u + 80u = 170u = 3893, so u = 22.9. Without coupon: 2 x 100u = 200u = 4580. Extra = 4580 - 3893 = $687.",
      "hints": ["First fridge costs 90% (90u), second 80% (80u).", "170u = 3893; find 200u, then subtract 3893."],
      "source": "Rosyth 2024 P6 Prelim P2 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q7. FIB money answer 687. Coupon picture is decorative; discount terms in stem."
    },
    {
      "n": 108,
      "type_id": 2,
      "question": "Minah saved some $2-notes and $5-notes in the ratio of 5 : 3. When she took out 36 $2-notes and added the same number of $5-notes, the ratio became 2 : 3. Find the total value of all the $5-notes Minah saved at first. Ans: $[?]",
      "answer0": "300",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "Let $2-notes = 5u, $5-notes = 3u. After: (5u - 36) : (3u + 36) = 2 : 3. Cross-multiply: 3(5u - 36) = 2(3u + 36); 15u - 108 = 6u + 72; 9u = 180; u = 20. $5-notes at first = 3u = 60 notes. Total value = 60 x $5 = $300.",
      "hints": ["Let the notes be 5u and 3u.", "Set up (5u - 36) : (3u + 36) = 2 : 3 and solve for u."],
      "source": "Rosyth 2024 P6 Prelim P2 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q8. FIB money answer 300 ($300)."
    },
    {
      "n": 109,
      "type_id": 2,
      "question": "Two rectangular tanks. Tank A is 30 cm by 20 cm by 40 cm. Tank B is 40 cm by 25 cm by 36 cm. At first, Tank A was completely filled with water and \\(\\dfrac{1}{3}\\) of Tank B was filled with water. Water flowed out of the tap at Tank A at a rate of 1.2 litres per minute. Water from the tap at Tank B flowed in at a rate of 1.2 litres per minute. How long did it take for the height of the water to be the same in both tanks? [?] min",
      "answer0": "8.75",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 193,
      "difficulty_id": 3,
      "explanation": "Tank A base = 30 x 20 = 600 cm²; Tank B base = 40 x 25 = 1000 cm². Tank B initial height = 1/3 x 36 = 12 cm; Tank A initial height = 40 cm. Rate 1.2 L/min = 1200 cm³/min, so A drops 1200/600 = 2 cm/min, B rises 1200/1000 = 1.2 cm/min. Heights equal: 40 - 2t = 12 + 1.2t, 28 = 3.2t, t = 8.75 min.",
      "hints": ["Convert 1.2 L to 1200 cm³ and find each height's rate of change.", "Set Tank A height (falling) equal to Tank B height (rising)."],
      "source": "Rosyth 2024 P6 Prelim P2 Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q9.png",
      "image_page": 26,
      "image_bbox": [0.14, 0.14, 0.82, 0.36],
      "image_loc": "two rectangular tanks A and B with dimension labels, upper portion below the question",
      "notes": "Paper 2 Q9. FIB decimal answer 8.75."
    },
    {
      "n": 110,
      "type_id": 2,
      "question": "ABCD is a rhombus. PQ and RS are 2 straight lines. \\(\\angle BAD = 134^\\circ\\), \\(\\angle DCS = 15^\\circ\\) and \\(\\angle RCP = 106^\\circ\\). Find \\(\\angle CTD\\). [?]",
      "answer0": "75",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 200,
      "difficulty_id": 3,
      "explanation": "angle PCD = 180 - 106 - 15 = 59 deg (angles on straight line RS at C). angle ADC = 180 - 134 = 46 deg (rhombus adjacent angles). In triangle CTD, angle CTD = 180 - angle PCD - angle ADC = 180 - 59 - 46 = 75 deg.",
      "hints": ["Angles on straight line at C give angle PCD = 59 deg.", "angle ADC = 180 - angle BAD; use the triangle angle sum."],
      "source": "Rosyth 2024 P6 Prelim P2 Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q10.png",
      "image_page": 27,
      "image_bbox": [0.18, 0.13, 0.70, 0.40],
      "image_loc": "rhombus ABCD with intersecting lines PQ and RS through T and C, upper portion below the question",
      "notes": "Paper 2 Q10. FIB degree answer 75."
    },
    {
      "n": 111,
      "type_id": 2,
      "question": "At a charity walkathon, there was an equal number of children who took part in either the 3-km walk or the 5-km walk. There were 208 girls who took part in the 3-km walk and 162 girls who took part in the 5-km walk. 60% of the boys took part in the 5-km walk. For every 1-km walked by the children, $10 was donated to charity.<br>(a) How many boys took part in the 5-km walk? [?]<br>(b) Find the total amount of money raised by the children in this charity walkathon. Ans: $[?]",
      "answer0": "138",
      "answer1": "24000",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "(a) Equal numbers in each walk. Let total boys = b; 60% (0.6b) did 5-km, 40% (0.4b) did 3-km. 3-km group = 208 + 0.4b; 5-km group = 162 + 0.6b. Equal: 208 + 0.4b = 162 + 0.6b, so 46 = 0.2b, b = 230; boys in 5-km = 0.6 x 230 = 138. (b) Each walk had 208 + 0.4(230) = 300 children. 3-km: 300 x 3 = 900 km; 5-km: 300 x 5 = 1500 km; total km = 2400; money = 2400 x $10 = $24000.",
      "hints": ["Set the 3-km total equal to the 5-km total to find the number of boys.", "Each group has 300 children; multiply km walked by $10."],
      "source": "Rosyth 2024 P6 Prelim P2 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q11. Two parts: (a) 138, (b) $24000. Both whole-number FIB."
    },
    {
      "n": 112,
      "type_id": 2,
      "question": "The figure shows a path of width 2 m in a rectangular garden of length 66 m. The outline of the path is made up of quarter circles with centre A, semicircles with centres D and E, and straight lines. AB = CD = EF. Take \\(\\pi = 3.14\\).<br>(a) What is the breadth of the rectangular garden? [?] m<br>(b) Find the area of the path. [?] m²",
      "answer0": "28",
      "answer1": "232.1",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 222,
      "difficulty_id": 3,
      "explanation": "(a) The 5 equal straight segments along the length: 5x + 6 = 66 (with AB = CD = EF = x and the 2 m widths), giving 5x = 60, x = 12; breadth = 2x + 4 = 28 m. (b) Outer radius = 12 + 2 = 14, inner = 12. Quarter+semicircles area: outer 14 x 14 x 3.14 / 4 = 153.86; inner 12 x 12 x 3.14 / 4 = 113.04; ring part = 40.82. Total path = 40.82 x 5 + 2 x 14 = 232.1 m².",
      "hints": ["Use 5 equal lengths along the 66 m to find x = 12.", "Find the area between outer and inner radii of the curved parts, then add straight strips."],
      "source": "Rosyth 2024 P6 Prelim P2 Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q12.png",
      "image_page": 29,
      "image_bbox": [0.28, 0.14, 0.80, 0.32],
      "image_loc": "S-shaped shaded path in a rectangle with B,C,D,E,F labels and 66 m, 2 m dimensions, upper portion below the question",
      "notes": "Paper 2 Q12. Two parts: (a) 28 m, (b) 232.1 m². Both decimal/whole FIB."
    },
    {
      "n": 113,
      "type_id": 2,
      "question": "The graph shows the total number of toy cars assembled by Machine A and Machine B over 12 hours.<br>(a) In the first 6 hours, both machines assembled an equal number of toy cars each. How many toy cars can each machine pack in one hour during this period of time? [?]<br>(b) During the last 6 hours, the rate at which Machine A was assembling toy cars was increased while Machine B continued at the same rate. How many more toy cars did Machine A assemble per hour than Machine B during this period of time? [?]",
      "answer0": "35",
      "answer1": "90",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 1,
      "difficulty_id": 3,
      "explanation": "(a) In first 6 h total = 420 (from graph); equal split = 210 each over 6 h; per hour each = 420 / 2 / 6 = 35. (b) Total at 12 h = 1380; last 6 h total = 1380 - 420 = 960; combined rate = 960 / 6 = 160/h. Machine B stays at 35/h, so Machine A = 160 - 35 = 125/h. More than B = 125 - 35 = 90.",
      "hints": ["Read the total at 6 h (420) and split equally over 6 hours.", "For the last 6 h, find the combined rate then subtract Machine B's unchanged rate."],
      "source": "Rosyth 2024 P6 Prelim P2 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q13.png",
      "image_page": 30,
      "image_bbox": [0.16, 0.24, 0.84, 0.72],
      "image_loc": "line graph of total toy cars vs time in hours, middle of page",
      "notes": "Paper 2 Q13. Two parts: (a) 35, (b) 90. Graph reads 420 at 6 h, 1380 at 12 h. Both whole-number FIB."
    },
    {
      "n": 114,
      "type_id": 2,
      "question": "Sherry baked cookies and packed them to sell. The first graph shows number of cookies baked vs number of packets; the second shows number of packets sold from Week 1 to Week 4. Each packet was filled with the same number of cookies.<br>(a) How many cookies did she pack in one packet? [?]<br>(b) How many more packets of cookies did she sell in Week 3 than in Week 1? [?]<br>(c) The number of packets of cookies Sherry sold in Week 5 increased by 30% compared to Week 4. How many cookies did she sell in Week 5? [?]",
      "answer0": "15",
      "answer1": "16",
      "answer2": "780",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 174,
      "difficulty_id": 3,
      "explanation": "(a) From the first graph, 300 cookies for 20 packets, so 300 / 20 = 15 cookies per packet. (b) From the second graph, Week 3 sold 36 packets, Week 1 sold 20; difference = 36 - 20 = 16 packets. (c) Week 4 = 40 packets; Week 5 = 40 x 1.3 = 52 packets; cookies = 52 x 15 = 780.",
      "hints": ["Use any point on the first graph to find cookies per packet.", "Week 5 packets = Week 4 packets x 1.3, then multiply by cookies per packet."],
      "source": "Rosyth 2024 P6 Prelim P2 Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q14.png",
      "image_page": 32,
      "image_bbox": [0.20, 0.22, 0.80, 0.86],
      "image_loc": "two line graphs: cookies-baked vs packets, and packets-sold vs week, stacked on the page",
      "notes": "Paper 2 Q14. Three parts: (a) 15, (b) 16, (c) 780. Graph reads: 300 cookies/20 packets; Week1=20, Week3=36, Week4=40. All whole-number FIB."
    },
    {
      "n": 115,
      "type_id": 2,
      "question": "ACE is a triangle where AF = AB and EF = ED. The sum of \\(\\angle ABF\\) and \\(\\angle EDF\\) is 125°.<br>(a) Find \\(\\angle BFD\\). [?]<br>(b) Find the sum of \\(\\angle BAF\\) and \\(\\angle AEC\\). [?]",
      "answer0": "55",
      "answer1": "110",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "(a) angle AFB + angle EFD = angle ABF + angle EDF = 125 deg (base angles of the two isosceles triangles). angle BFD = 180 - 125 = 55 deg (angles on straight line at F). (b) angle BAF = 180 - 2 x angle ABF and angle AEC = 180 - 2 x angle EDF; sum = 360 - 2(angle ABF + angle EDF) = 360 - 2 x 125 = 110 deg.",
      "hints": ["Triangles ABF and EDF are isosceles, so their base angles equal angles ABF and EDF.", "angle BFD = 180 - (angle AFB + angle EFD)."],
      "source": "Rosyth 2024 P6 Prelim P2 Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q15.png",
      "image_page": 34,
      "image_bbox": [0.32, 0.14, 0.66, 0.42],
      "image_loc": "tall triangle ACE with points B, F, D and angle alpha at F, upper-middle below the question",
      "notes": "Paper 2 Q15. Two parts: (a) 55, (b) 110. Both degree FIB."
    },
    {
      "n": 116,
      "type_id": 2,
      "question": "The pattern is made up of squares and triangles. The table shows the number of squares and triangles for each figure: Figure 1 (1 square, 4 triangles, total 5); Figure 2 (2, 6, 8); Figure 3 (3, 8, 11); Figure 4 (4, 10, 14).<br>(a) For Figure 6, the number of triangles is [?] and the total number of squares and triangles is [?].<br>(b) Find the total number of squares and triangles in Figure 102. [?]<br>(c) Find the Figure Number which has a total of 1742 squares and triangles. [?]",
      "answer0": "14",
      "answer1": "20",
      "answer2": "308",
      "answer3": "580",
      "correct_answer": null,
      "skill_id": 6,
      "difficulty_id": 3,
      "explanation": "Triangles = 2n + 2, total = 3n + 2. (a) Figure 6: triangles = 2(6) + 2 = 14; total = 3(6) + 2 = 20. (b) Figure 102: total = 3(102) + 2 = 308. (c) 3n + 2 = 1742, 3n = 1740, n = 580.",
      "hints": ["Triangles follow 2n + 2; total follows 3n + 2.", "For part (c) solve 3n + 2 = 1742."],
      "source": "Rosyth 2024 P6 Prelim P2 Q16",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q16.png",
      "image_page": 35,
      "image_bbox": [0.12, 0.13, 0.82, 0.24],
      "image_loc": "four pattern figures of squares and triangles labelled Figure 1-4, top of page",
      "notes": "Paper 2 Q16. Parts: (a) triangles 14 & total 20, (b) 308, (c) 580. Table values in stem. All whole-number FIB."
    },
    {
      "n": 117,
      "type_id": 2,
      "question": "Eunice packed 2 types of books into 4 identical shelves. A big book had a thickness of 9 cm; a small book a thickness of 5 cm. Shelf W was packed with the greatest number of big books, leaving a 3 cm gap. Shelf X was packed from end to end with the greatest number of small books. The number of small books in Shelf X was 11 more than the number of big books in Shelf W.<br>(a) What was the length of Shelf X? [?] cm<br>(b) Eunice packed a total of 36 big and small books in Shelf Y and Shelf Z, packed from end to end. How many big books were packed in Shelf Y and Shelf Z? [?]",
      "answer0": "120",
      "answer1": "15",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 3,
      "explanation": "(a) Let big books in W = x; shelf length = 9x + 3. Small books in X = x + 11; shelf length = 5(x + 11). Equal: 9x + 3 = 5(x + 11) = 5x + 55, so 4x = 52, x = 13; length = 5(13 + 11) = 5 x 24 = 120 cm. (b) Let big books = y. Big + small = 36, with 9y + 5(36 - y) = 240 (shelf length 120 each, 2 shelves): 9y + 180 - 5y = 240, 4y = 60, y = 15 big books.",
      "hints": ["Shelf W length = 9x + 3; Shelf X length = 5(x + 11); set them equal.", "For (b) use total books = 36 and total length 240 cm to solve for big books."],
      "source": "Rosyth 2024 P6 Prelim P2 Q17",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q17.png",
      "image_page": 36,
      "image_bbox": [0.14, 0.16, 0.80, 0.46],
      "image_loc": "Figures 1-3: big/small book widths and stacked shelves W,X,Y,Z, upper portion below the question",
      "notes": "Paper 2 Q17. Two parts: (a) 120 cm, (b) 15. Both whole-number FIB."
    }
  ]
}