{
  "paper": {
    "school": "Rosyth",
    "year": 2023,
    "level": "P6",
    "label": "Prelim",
    "source_prefix": "Rosyth 2023 P6 Prelim",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 2,
      "question": "Round 8.685 to 2 decimal places.<br>[?]",
      "answer0": "8.69",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 207,
      "difficulty_id": 1,
      "explanation": "The third decimal place is 5, so round the second decimal place up: 8.685 → 8.69.",
      "hints": ["Look at the third decimal digit (5).", "Since it is 5, round the second decimal place up."],
      "source": "Rosyth 2023 P6 Prelim Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key Q1=option 3 (8.69). Decimal answer, converted MCQ to FIB."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Simplify \\(8a + 21 - 7 - 4a\\).",
      "answer0": "\\(4a + 14\\)",
      "answer1": "\\(4a + 28\\)",
      "answer2": "\\(12a + 14\\)",
      "answer3": "\\(12a + 28\\)",
      "correct_answer": 0,
      "skill_id": 239,
      "difficulty_id": 1,
      "explanation": "Combine like terms: \\(8a - 4a = 4a\\); \\(21 - 7 = 14\\). So \\(8a + 21 - 7 - 4a = 4a + 14\\).",
      "hints": ["Group the terms with \\(a\\) together.", "Group the number terms together."],
      "source": "Rosyth 2023 P6 Prelim Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key Q2=option 1 (4a + 14). Algebraic answer kept as MCQ."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Which of the following is the same as 2050 cm?",
      "answer0": "2 m 5 cm",
      "answer1": "2 m 50 cm",
      "answer2": "20 m 5 cm",
      "answer3": "20 m 50 cm",
      "correct_answer": 3,
      "skill_id": 464,
      "difficulty_id": 1,
      "explanation": "1 m = 100 cm, so 2050 cm = 2000 cm + 50 cm = 20 m 50 cm.",
      "hints": ["Divide by 100 to get the metres.", "The remainder is the centimetres."],
      "source": "Rosyth 2023 P6 Prelim Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key Q3=option 4 (20 m 50 cm)."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Alynna conducted a survey of the favourite sport of the students in 4 classes. Which of the classes has the greatest number of students choosing Football?",
      "answer0": "Primary 6A",
      "answer1": "Primary 6B",
      "answer2": "Primary 6C",
      "answer3": "Primary 6D",
      "correct_answer": 2,
      "skill_id": 461,
      "difficulty_id": 1,
      "explanation": "Read the Football bar for each class: 6A = 13, 6B = 10, 6C = 20, 6D = 13. The greatest is Primary 6C with 20.",
      "hints": ["Read the Football bar in each of the 4 graphs.", "Compare the four Football values."],
      "source": "Rosyth 2023 P6 Prelim Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q4.png",
      "image_page": 3,
      "image_bbox": [0.15, 0.13, 0.78, 0.52],
      "image_loc": "Four bar graphs (Primary 6A-6D) below the survey statement on page 3.",
      "notes": "Key Q4=option 3 (Primary 6C). Shared figure with Q5."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "Alynna conducted a survey of the favourite sport of the students in 4 classes. In these 4 classes, how many more students choose Badminton as compared to Basketball?",
      "answer0": "15",
      "answer1": "25",
      "answer2": "34",
      "answer3": "49",
      "correct_answer": 0,
      "skill_id": 461,
      "difficulty_id": 2,
      "explanation": "Badminton: 6A=10, 6B=15, 6C=10, 6D=14, total = 49. Basketball: 6A=8, 6B=5, 6C=15, 6D=6, total = 34. Difference = 49 - 34 = 15.",
      "hints": ["Add the Badminton bars across all four classes.", "Add the Basketball bars, then subtract."],
      "source": "Rosyth 2023 P6 Prelim Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q5.png",
      "image_page": 3,
      "image_bbox": [0.15, 0.13, 0.78, 0.52],
      "image_loc": "Four bar graphs (Primary 6A-6D) on page 3 (same figure as Q4).",
      "notes": "Key Q5=option 1 (15). Shared figure with Q4."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "After travelling for 2 hours and 15 minutes, a train arrived in Kuala Lumpur from Singapore at 6.15 p.m. At what time did the train leave Singapore?",
      "answer0": "3.45 p.m.",
      "answer1": "4.00 p.m.",
      "answer2": "4.15 p.m.",
      "answer3": "8.30 p.m.",
      "correct_answer": 1,
      "skill_id": 464,
      "difficulty_id": 1,
      "explanation": "Subtract the journey time from the arrival time: 6.15 p.m. - 2 h 15 min = 4.00 p.m.",
      "hints": ["Work backwards from the arrival time.", "Take away 2 hours then 15 minutes."],
      "source": "Rosyth 2023 P6 Prelim Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key Q6=option 2 (4.00 p.m.)."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "The figure shows 12 identical squares. What is the least number of such squares that must be added to the figure so that the line AB becomes a line of symmetry?",
      "answer0": "1",
      "answer1": "2",
      "answer2": "3",
      "answer3": "4",
      "correct_answer": 1,
      "skill_id": 230,
      "difficulty_id": 2,
      "explanation": "For AB to be a line of symmetry, every square above AB must have a mirror image below it (and vice versa). Comparing the squares above and below line AB, 2 squares must be added to balance the figure.",
      "hints": ["AB must reflect the figure top to bottom.", "Count which squares lack a mirror partner across AB."],
      "source": "Rosyth 2023 P6 Prelim Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q7.png",
      "image_page": 4,
      "image_bbox": [0.27, 0.42, 0.65, 0.62],
      "image_loc": "Arrangement of 12 squares with line AB through the middle, on page 4.",
      "notes": "Key Q7=option 2 (2)."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "In the figure, AB and CD are straight lines. Find \\(\\angle p\\).",
      "answer0": "40°",
      "answer1": "45°",
      "answer2": "50°",
      "answer3": "70°",
      "correct_answer": 0,
      "skill_id": 230,
      "difficulty_id": 2,
      "explanation": "There is a right angle (90°) marked between the 110° ray and angle p. Angles on the straight line CD: 110° + 90° (the right angle covering p plus the 60°)... Using vertically opposite/straight-line reasoning, p + 60° + right angle relationships give p = 180° - 110° - ... ; the printed key gives p = 40°.",
      "hints": ["Use angles on a straight line sum to 180°.", "Note the right-angle mark next to p."],
      "source": "Rosyth 2023 P6 Prelim Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 5,
      "image_bbox": [0.27, 0.11, 0.55, 0.30],
      "image_loc": "Intersecting straight lines AB and CD with angles 110°, 60°, right-angle and p marked, on page 5.",
      "notes": "Key Q8=option 1 (40°)."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "Which of the following statements is TRUE of the diagram shown?",
      "answer0": "Point E is north-east of Point F",
      "answer1": "Point D is north-east of Point E",
      "answer2": "Point D is north-east of Point B",
      "answer3": "Point F is north-east of Point E",
      "correct_answer": 3,
      "skill_id": 464,
      "difficulty_id": 2,
      "explanation": "North is up. Reading the grid positions, Point F lies to the right of and above Point E, so F is north-east of E.",
      "hints": ["North is the up direction shown by the arrow.", "North-east means up and to the right."],
      "source": "Rosyth 2023 P6 Prelim Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q9.png",
      "image_page": 5,
      "image_bbox": [0.33, 0.49, 0.62, 0.69],
      "image_loc": "Square grid with points A-F and a North arrow, on page 5.",
      "notes": "Key Q9=option 4 (Point F is north-east of Point E)."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "The postage rate for sending letters to Japan is: First 20 g costs $0.80; per additional 10 g or part thereof costs $0.25. Mrs Tan sent a letter weighing 38 g to Japan. How much did she pay for the postage?",
      "answer0": "$1.00",
      "answer1": "$1.05",
      "answer2": "$1.30",
      "answer3": "$1.60",
      "correct_answer": 2,
      "skill_id": 464,
      "difficulty_id": 2,
      "explanation": "First 20 g = $0.80. Remaining 18 g = 2 lots of 10 g (or part thereof) = 2 × $0.25 = $0.50. Total = $0.80 + $0.50 = $1.30.",
      "hints": ["Charge $0.80 for the first 20 g.", "The remaining 18 g rounds up to 2 blocks of 10 g."],
      "source": "Rosyth 2023 P6 Prelim Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key Q10=option 3 ($1.30). Postage table transcribed into stem."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "Mr Tan has 200 g of sugar. He wants to pack the sugar into 1000 packets equally. What is the mass of each packet of the sugar?",
      "answer0": "0.02 g",
      "answer1": "0.2 g",
      "answer2": "50 g",
      "answer3": "5 g",
      "correct_answer": 1,
      "skill_id": 464,
      "difficulty_id": 1,
      "explanation": "200 g ÷ 1000 = 0.2 g per packet.",
      "hints": ["Divide the total mass by the number of packets.", "200 ÷ 1000 = 0.2."],
      "source": "Rosyth 2023 P6 Prelim Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key Q11=option 2 (0.2 g)."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "Eddie bought a card and a sunflower for $8.20. Jane bought a card and 2 sunflowers for $14. How much did a card cost?",
      "answer0": "$2.40",
      "answer1": "$5.80",
      "answer2": "$11.60",
      "answer3": "$22.20",
      "correct_answer": 0,
      "skill_id": 464,
      "difficulty_id": 2,
      "explanation": "The extra sunflower Jane bought costs $14 - $8.20 = $5.80, so 1 sunflower = $5.80. A card = $8.20 - $5.80 = $2.40.",
      "hints": ["The difference in cost is one extra sunflower.", "Subtract the sunflower price from $8.20."],
      "source": "Rosyth 2023 P6 Prelim Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key Q12=option 1 ($2.40)."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "Ansen and Beirul drank all the water in a bottle of water. Ansen drank 100 ml more than \\(\\dfrac{3}{8}\\) of the total amount of water in the bottle. Beirul drank 250 ml. How much water was there in the bottle of water at first?",
      "answer0": "150 ml",
      "answer1": "240 ml",
      "answer2": "350 ml",
      "answer3": "560 ml",
      "correct_answer": 3,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Ansen + Beirul = total. (\\(\\dfrac{3}{8}\\) of total + 100) + 250 = total. So 350 = total - \\(\\dfrac{3}{8}\\) total = \\(\\dfrac{5}{8}\\) total. Total = 350 ÷ 5 × 8 = 560 ml.",
      "hints": ["Ansen's share plus Beirul's 250 ml is the whole bottle.", "The non-fraction parts (100 + 250) equal \\(\\dfrac{5}{8}\\) of the total."],
      "source": "Rosyth 2023 P6 Prelim Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key Q13=option 4 (560 ml)."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "Three parts of a circle with a radius of 14 cm are shaded. These three parts add up to a quarter of the circle. What is the total perimeter of the three shaded parts? Take \\(\\pi = \\dfrac{22}{7}\\).",
      "answer0": "22 cm",
      "answer1": "50 cm",
      "answer2": "95 cm",
      "answer3": "106 cm",
      "correct_answer": 3,
      "skill_id": 222,
      "difficulty_id": 3,
      "explanation": "The three sectors total a quarter circle, so their arcs add up to a quarter of the circumference: \\(\\dfrac{1}{4} \\times 2 \\times \\dfrac{22}{7} \\times 14 = 22\\) cm. Each of the 3 sectors has 2 radii; total radii length = 6 × 14 = 84 cm. Total perimeter = 22 + 84 = 106 cm.",
      "hints": ["The arcs together make a quarter of the circumference.", "Each shaded sector also has two straight radii of 14 cm."],
      "source": "Rosyth 2023 P6 Prelim Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q14.png",
      "image_page": 8,
      "image_bbox": [0.36, 0.13, 0.60, 0.30],
      "image_loc": "Circle with three shaded sectors, on page 8.",
      "notes": "Key Q14=option 4 (106 cm)."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "ACE and BDF are equilateral triangles. AF = FE and BC = CD. Find \\(\\angle y\\) in the figure.",
      "answer0": "60°",
      "answer1": "90°",
      "answer2": "120°",
      "answer3": "240°",
      "correct_answer": 2,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "Each equilateral triangle has 60° angles. The two triangles overlap; angle y is the angle at the crossing point. Using the angle sum of the small triangle formed at the intersection, \\(\\angle y = 180° - 60° = 120°\\).",
      "hints": ["Every angle in an equilateral triangle is 60°.", "Use angle sum of the triangle around point y."],
      "source": "Rosyth 2023 P6 Prelim Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q15.png",
      "image_page": 8,
      "image_bbox": [0.22, 0.55, 0.45, 0.73],
      "image_loc": "Two overlapping equilateral triangles ACE and BDF with angle y marked, on page 8.",
      "notes": "Key Q15=option 3 (120°)."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Find the value of \\(10 \\times (24 + 36 \\div 6)\\).<br>[?]",
      "answer0": "300",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 464,
      "difficulty_id": 1,
      "explanation": "Order of operations: \\(36 \\div 6 = 6\\); \\(24 + 6 = 30\\); \\(10 \\times 30 = 300\\).",
      "hints": ["Do division before addition.", "Work inside the brackets first."],
      "source": "Rosyth 2023 P6 Prelim Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key Q16 = 300."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "The table shows the mark Chelsie scored for 3 tests: Test 1 = 37, Test 2 = 48, Test 3 = 44. What is the average mark she scored for these 3 tests?<br>[?]",
      "answer0": "43",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 203,
      "difficulty_id": 1,
      "explanation": "Total = 37 + 48 + 44 = 129. Average = 129 ÷ 3 = 43.",
      "hints": ["Add the three test marks.", "Divide the total by 3."],
      "source": "Rosyth 2023 P6 Prelim Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key Q17 = 43. Table values transcribed into the stem."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "Find the area of triangle ABC.<br>[?] cm²",
      "answer0": "9",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 464,
      "difficulty_id": 2,
      "explanation": "Base BC = 6 cm (from B to C), height AC drop = 3 cm. Area = \\(\\dfrac{1}{2} \\times 6 \\times 3 = 9\\) cm². (The 3 cm to the right of C is not part of the base.)",
      "hints": ["Area of a triangle = \\(\\dfrac{1}{2} \\times\\) base \\(\\times\\) height.", "Use base 6 cm and height 3 cm."],
      "source": "Rosyth 2023 P6 Prelim Q18",
      "image_needed": true,
      "image_options": false,
      "image_file": "q18.png",
      "image_page": 10,
      "image_bbox": [0.20, 0.62, 0.65, 0.80],
      "image_loc": "Triangle ABC with base 6 cm, extra 3 cm and height 3 cm, on page 10.",
      "notes": "Key Q18: 1/2 x 6 x 3 = 9 cm²."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "The pie chart shows Natalie's expenditure last month. Bills = 15%, Food = \\(\\dfrac{1}{2}\\), Transport is a right angle (25%), Books = $40. How much did she spend on food?<br>$[?]",
      "answer0": "200",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Transport (right angle) = 25%. Books percentage = 100% - 25% - 15% - 50% = 10%. Books = 10% = $40, so 1% = $4. Food = 50% = 50 × $4 = $200.",
      "hints": ["The right angle for Transport is 25% of the circle.", "Find the Books percentage first, then scale up to Food."],
      "source": "Rosyth 2023 P6 Prelim Q19",
      "image_needed": true,
      "image_options": false,
      "image_file": "q19.png",
      "image_page": 11,
      "image_bbox": [0.20, 0.14, 0.50, 0.36],
      "image_loc": "Pie chart of expenditure (Bills 15%, Food 1/2, Transport, Books $40), on page 11.",
      "notes": "Key Q19 = $200. Pie-chart labels transcribed into stem."
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "ABCD is a trapezium with AB parallel to DC. \\(\\angle ADC = 112°\\). Find \\(\\angle BAD\\).<br>[?]°",
      "answer0": "68",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 2,
      "explanation": "AB is parallel to DC, so \\(\\angle BAD\\) and \\(\\angle ADC\\) are interior angles on the same side (co-interior) and add to 180°. \\(\\angle BAD = 180° - 112° = 68°\\).",
      "hints": ["AB parallel to DC makes co-interior angles add to 180°.", "180° - 112° = 68°."],
      "source": "Rosyth 2023 P6 Prelim Q20",
      "image_needed": true,
      "image_options": false,
      "image_file": "q20.png",
      "image_page": 11,
      "image_bbox": [0.25, 0.52, 0.75, 0.74],
      "image_loc": "Trapezium ABCD with angle ADC = 112° marked at D, on page 11.",
      "notes": "Key Q20: 180° - 112° = 68°."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "Using all the digits 4, 9, 0, 5, form:<br>(a) the smallest 4-digit number that is a multiple of 5. [?]<br>(b) a 4-digit number closest to 5000. [?]",
      "answer0": "4095",
      "answer1": "5049",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 464,
      "difficulty_id": 2,
      "explanation": "(a) A multiple of 5 ends in 0 or 5. Smallest uses 4 in thousands, then arrange remaining to be smallest and end in 5: 4095. (b) Closest to 5000: 5049 (smallest number starting with 50). Key: (a) 4095, (b) 5049.",
      "hints": ["A multiple of 5 ends in 0 or 5.", "For closest to 5000, start with 50__."],
      "source": "Rosyth 2023 P6 Prelim Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key Q21: (a) 4095, (b) 5049. Two-part FIB."
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "Dave had more money than Jerry. After Dave gave Jerry $140, they have the same amount of money. How much more money did Dave have than Jerry at first?<br>$[?]",
      "answer0": "280",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 464,
      "difficulty_id": 2,
      "explanation": "Giving $140 closes the gap entirely, so the original difference was 2 × $140 = $280.",
      "hints": ["Transferring money closes the gap by twice the amount transferred.", "2 × $140 = $280."],
      "source": "Rosyth 2023 P6 Prelim Q22",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key Q22 = $280."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "Mr Fong bought a box of markers. \\(\\dfrac{1}{7}\\) of the markers were black. \\(\\dfrac{1}{3}\\) of the remaining markers were red and the rest were green. There were 400 green markers. How many markers did Mr Fong buy altogether?<br>[?]",
      "answer0": "700",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Black = \\(\\dfrac{1}{7}\\), remaining = \\(\\dfrac{6}{7}\\). Red = \\(\\dfrac{1}{3}\\) of remaining, so green = \\(\\dfrac{2}{3}\\) of remaining = \\(\\dfrac{2}{3} \\times \\dfrac{6}{7} = \\dfrac{4}{7}\\) of total. \\(\\dfrac{4}{7}\\) = 400, so \\(\\dfrac{1}{7}\\) = 100, total = 700.",
      "hints": ["Find what fraction of the whole the green markers are.", "Green = \\(\\dfrac{2}{3}\\) of the remaining \\(\\dfrac{6}{7}\\)."],
      "source": "Rosyth 2023 P6 Prelim Q23",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key Q23: 4u=400, 1u=100, 7u=700."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "Uncle John sold \\((p + 4)\\) muffins on Monday. He sold \\(2p\\) more muffins on Tuesday than on Monday. Altogether, he sold 240 muffins on the two days. Find the value of \\(p\\).<br>[?]",
      "answer0": "58",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 2,
      "explanation": "Monday = \\(p + 4\\); Tuesday = \\((p + 4) + 2p = 3p + 4\\). Total = \\(4p + 8 = 240\\). \\(4p = 232\\), \\(p = 58\\).",
      "hints": ["Write Tuesday's count in terms of p.", "Add the two days and set equal to 240."],
      "source": "Rosyth 2023 P6 Prelim Q24",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key Q24: 4P+8=240, P=58."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "The table shows the favourite subject of the students in Primary 6C and is used to draw the pie chart shown. Mathematics is the most favourite subject. English = 12, Chinese = 16, Science = 8 marked, Science sector = 28%. How many students chose Science as their favourite subject?<br>[?]",
      "answer0": "14",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Science is 28% of the total. From the table the known counts (12 + 16 + 8) make up the non-Science portion = 72% = 36 students, so 1% = 0.5 student. Science = 28% = 28 × 0.5 = 14 students.",
      "hints": ["Science is 28%, so the rest is 72%.", "The 72% equals the sum of the known table values."],
      "source": "Rosyth 2023 P6 Prelim Q25",
      "image_needed": true,
      "image_options": false,
      "image_file": "q25.png",
      "image_page": 14,
      "image_bbox": [0.30, 0.27, 0.65, 0.52],
      "image_loc": "Favourite Subject pie chart (Chinese, English, Science 28%, Math), on page 14.",
      "notes": "Key Q25: 100u-28u=72u; 72u=12+16+8=36; 1u=0.5; Science(28u)=14."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "Two squares of different sizes are drawn. An unshaded square is formed where the 2 squares overlap each other. The difference between the area of the shaded part A and the area of the shaded part B is 24 cm². The larger square has a side of 10 cm. Find the area of the unshaded part.<br>[?] cm²",
      "answer0": "4",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 464,
      "difficulty_id": 3,
      "explanation": "Let the overlap (unshaded) area = x. Area A = (large square 10×10=100) - x = 100 - x. Area B = (small square) - x. A - B = (large square) - (small square) = 24, so small square = 100 - 24 = 76... using the printed key the unshaded overlap area = 4 cm².",
      "hints": ["Shaded A = big square minus overlap; shaded B = small square minus overlap.", "The overlap cancels in the difference A - B."],
      "source": "Rosyth 2023 P6 Prelim Q26",
      "image_needed": true,
      "image_options": false,
      "image_file": "q26.png",
      "image_page": 15,
      "image_bbox": [0.22, 0.18, 0.48, 0.36],
      "image_loc": "Two overlapping squares (shaded A and B, white overlap), base 10 cm, on page 15.",
      "notes": "Key Q26 = 4 (cm²)."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "The solid is made up of nine 1-cm cubes. Find the greatest number of cubes that can be added to the solid without changing the top view and the side view.<br>[?]",
      "answer0": "4",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 229,
      "difficulty_id": 3,
      "explanation": "The maximum cubes that can be added while keeping the same top view and side view footprint is 4 (per the printed answer key).",
      "hints": ["Fill in empty positions that do not enlarge the top or side outline.", "Each added cube must hide behind the existing silhouette."],
      "source": "Rosyth 2023 P6 Prelim Q27",
      "image_needed": true,
      "image_options": false,
      "image_file": "q27.png",
      "image_page": 16,
      "image_bbox": [0.30, 0.13, 0.70, 0.32],
      "image_loc": "Isometric drawing of the 9-cube solid with Top/Front/Side view arrows, on page 16.",
      "notes": "Key Q27(b) = 4. Part (a) (draw top view) is a draw task, omitted; only the countable part (b) is captured here."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "Mrs Lee left Town P for Town Q, driving at an average speed of 60 km/h. 20 minutes later, Mr Kumar left Town Q for Town P, driving at an average speed of 80 km/h. Mrs Lee met Mr Kumar 50 minutes after she left Town P. What is the distance between Town P and Town Q?<br>[?] km",
      "answer0": "90",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 219,
      "difficulty_id": 3,
      "explanation": "Mrs Lee travels 50 min = \\(\\dfrac{5}{6}\\) h: distance = 60 × \\(\\dfrac{5}{6}\\) = 50 km. Mr Kumar starts 20 min later, so travels 30 min = \\(\\dfrac{1}{2}\\) h: distance = 80 × \\(\\dfrac{1}{2}\\) = 40 km. When they meet, total distance = 50 + 40 = 90 km.",
      "hints": ["Convert each travel time to hours, then distance = speed × time.", "Mr Kumar drives for 30 min, Mrs Lee for 50 min; add the two distances."],
      "source": "Rosyth 2023 P6 Prelim P2Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q5. Key: 50 km + 40 km = 90 km."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "13 pots of plants are arranged in a row of equal distance apart. The distance between the first pot of plant and the fifth pot of plant is \\(1\\dfrac{3}{4}\\) m. What is the distance between the 2nd pot of plant and the 12th pot of plant?<br>[?] m",
      "answer0": "4.375",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 464,
      "difficulty_id": 3,
      "explanation": "1st to 5th pot = 4 gaps = \\(1\\dfrac{3}{4}\\) m = 175 cm, so 1 gap = 43.75 cm. 2nd to 12th pot = 10 gaps = 10 × 43.75 = 437.5 cm = 4.375 m.",
      "hints": ["Count gaps, not pots: 1st to 5th is 4 gaps.", "Find one gap, then multiply by the number of gaps from 2nd to 12th."],
      "source": "Rosyth 2023 P6 Prelim P2Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q1. Key: 4 gaps=175cm, 10 gaps=437.5cm=4.375 m."
    },
    {
      "n": 30,
      "type_id": 1,
      "question": "A tray of cookies is arranged in 3 rows. Each row has \\(p\\) more cookies than the row in front of it. There are \\(5p\\) cookies in the last row. How many cookies are there in the front row? Give your answer in terms of \\(p\\) in the simplest form.",
      "answer0": "\\(3p\\)",
      "answer1": "\\(5p\\)",
      "answer2": "\\(7p\\)",
      "answer3": "\\(15p\\)",
      "correct_answer": 0,
      "skill_id": 239,
      "difficulty_id": 2,
      "explanation": "Last (3rd) row = \\(5p\\). 2nd row = \\(5p - p = 4p\\). Front (1st) row = \\(4p - p = 3p\\).",
      "hints": ["Each row back adds p; work backwards from the last row.", "5p - p - p = 3p."],
      "source": "Rosyth 2023 P6 Prelim P2Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q2. Key: 5P - 2P = 3P. Algebraic answer kept as MCQ."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "A strip of paper 60 cm long is folded to form the shape shown. The difference in area between the strip of paper and the folded strip is 18 cm². Find the area of the shaded folded strip.<br>[?] cm²",
      "answer0": "162",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 464,
      "difficulty_id": 3,
      "explanation": "Width of strip = \\(\\sqrt{9}\\) = 3 cm. Area of unfolded strip = 60 × 3 = 180 cm². Area of shaded folded strip = 180 - 18 = 162 cm².",
      "hints": ["Find the width of the strip first.", "Folded area = original area minus the 18 cm² difference."],
      "source": "Rosyth 2023 P6 Prelim P2Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q31.png",
      "image_page": 21,
      "image_bbox": [0.18, 0.13, 0.55, 0.34],
      "image_loc": "Strip XY before and after folding into a frame shape, on page 21.",
      "notes": "Paper 2 Q3. Key: width=3cm, 60x3=180, 180-18=162 cm²."
    },
    {
      "n": 32,
      "type_id": 1,
      "question": "The figure is made up of a trapezium and 2 parallel lines, with angles c, b, a, d, e and given angles 240°, 75°, 50° marked. Which 2 angles add up to 75°?",
      "answer0": "\\(\\angle a\\) and \\(\\angle c\\)",
      "answer1": "\\(\\angle b\\) and \\(\\angle e\\)",
      "answer2": "\\(\\angle c\\) and \\(\\angle d\\)",
      "answer3": "\\(\\angle d\\) and \\(\\angle e\\)",
      "correct_answer": 0,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "At the bottom-left vertex, angles a, the 75° and angle b lie on the parallel line; reflex/straight-line relationships give \\(\\angle a + \\angle c = 75°\\) (the printed key answers angles A and C).",
      "hints": ["Use angles on a straight line and the parallel lines.", "Look for the two angles flanking the 75° angle."],
      "source": "Rosyth 2023 P6 Prelim P2Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q32.png",
      "image_page": 22,
      "image_bbox": [0.20, 0.18, 0.55, 0.46],
      "image_loc": "Trapezium between two parallel lines with angles a,b,c,d,e and 240°,75°,50°, on page 22.",
      "notes": "Paper 2 Q4(a). Key answer: A and C. (Part b answer = B and E, asked separately as Q33.)"
    },
    {
      "n": 33,
      "type_id": 1,
      "question": "The figure is made up of a trapezium and 2 parallel lines, with angles c, b, a, d, e and given angles 240°, 75°, 50° marked. Which 2 angles add up to 165°?",
      "answer0": "\\(\\angle a\\) and \\(\\angle c\\)",
      "answer1": "\\(\\angle b\\) and \\(\\angle e\\)",
      "answer2": "\\(\\angle c\\) and \\(\\angle d\\)",
      "answer3": "\\(\\angle a\\) and \\(\\angle d\\)",
      "correct_answer": 1,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "\\(\\angle b + \\angle e = 360° - 120° - 75° = 165°\\) (the printed key answers angles B and E).",
      "hints": ["Use the 240° reflex angle and angle sums.", "The two angles inside the trapezium at the slanted sides."],
      "source": "Rosyth 2023 P6 Prelim P2Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q33.png",
      "image_page": 22,
      "image_bbox": [0.20, 0.18, 0.55, 0.46],
      "image_loc": "Trapezium between two parallel lines with angles a,b,c,d,e (same figure as Q32), on page 22.",
      "notes": "Paper 2 Q4(b). Key answer: B and E. Same figure as Q32."
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "A school is collecting money for a donation drive. \\(\\dfrac{1}{2}\\) of the students in the school donated $3. \\(\\dfrac{2}{5}\\) of them donated $4. The rest of the students donated $5. A total of $9000 in donation is collected from the school. How many students are there in the school?<br>[?]",
      "answer0": "2500",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Take 10 units of students. \\(\\dfrac{1}{2}\\) = 5u donate $3 → 15u of money; \\(\\dfrac{2}{5}\\) = 4u donate $4 → 16u; rest = 1u donate $5 → 5u. Total money = 15u + 16u + 5u = 36u = $9000. 1u = 250, students = 10u = 2500.",
      "hints": ["Split students into convenient units (use 10).", "Add the money from each group and equate to $9000."],
      "source": "Rosyth 2023 P6 Prelim P2Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q6. Key: 36u=9000, students=2500."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "At first, Jing Jing had a total of 4000 paper clips and magnets. After she gave away 50 paper clips and 10% of the magnets, she had a total of 1125 magnets left. How many paper clips did Jing Jing have at first?<br>[?]",
      "answer0": "2750",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "After giving 10% of magnets away, 90% remain = 1125. So 9u = 1125, 1u = 125, original magnets = 10u = 1250. Paper clips at first = 4000 - 1250 = 2750.",
      "hints": ["The 1125 left is 90% of the original magnets.", "Find the original magnets, then subtract from 4000."],
      "source": "Rosyth 2023 P6 Prelim P2Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q7. Key: 9u=1125, magnets=1250, paper clips=2750."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "There are 210 students in the level and they are divided into groups of three. It is found that: there are 23 groups with only 1 boy; there are 34 groups with two or more boys; the number of all-boy groups is twice the number of all-girl groups. How many girls are there in the level?<br>[?]",
      "answer0": "93",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 464,
      "difficulty_id": 3,
      "explanation": "Total groups = 210 ÷ 3 = 70. All-girl groups = 70 - (34 + 23) = 13. All-boy groups = 2 × 13 = 26; two-boys-one-girl = 34 - 26 = 8. Girls = (all-girl: 13 × 3) + (two-boys-one-girl: 1 × 8) + (one-boy-two-girls: 23 × 2) = 39 + 8 + 46 = 93.",
      "hints": ["Find the total number of groups first.", "Split the 34 into all-boy and two-boys-one-girl groups."],
      "source": "Rosyth 2023 P6 Prelim P2Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q8. Key: total girls = 39 + 8 + 46 = 93."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "There was 21.6 litres of water altogether in container A and container B. The water level in container A was the same as container B. The base area of container A was 700 cm² and the base of container B has dimensions 40 cm by 50 cm.<br>(a) What was the height of water in container B? [?] cm<br>(b) From which container should water be poured out so both containers would have the same amount of water, and how much water should be poured? Pour out [?] cm³ from Container B.",
      "answer0": "8",
      "answer1": "5200",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 229,
      "difficulty_id": 3,
      "explanation": "(a) Base of B = 40 × 50 = 2000 cm². Total water = 21.6 L = 21600 cm³. Equal water height h: h × (700 + 2000) = 21600, h = 21600 ÷ 2700 = 8 cm. (b) Volume in A = 8 × 700 = 5600 cm³; volume in B = 8 × 2000 = 16000 cm³. Equal share = 21600 ÷ 2 = 10800 cm³. Pour from Container B: 16000 - 10800 = 5200 cm³.",
      "hints": ["Same water height means combined base area shares the total volume.", "For (b), each container should end with half the total volume."],
      "source": "Rosyth 2023 P6 Prelim P2Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q37.png",
      "image_page": 26,
      "image_bbox": [0.20, 0.18, 0.78, 0.40],
      "image_loc": "Two cuboid containers A and B with B's base 40 cm by 50 cm, on page 26.",
      "notes": "Paper 2 Q9. Key: (a) 8 cm; (b) Container B, pour 5200 cm³. Part (b) container choice (B) recorded in notes; the numeric volume is the FIB answer."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "ABCD is a rhombus and CDEF is a parallelogram. \\(\\angle ABC = 46°\\) (at B) and \\(\\angle DEF\\)/\\(\\angle EFG = 128°\\) (at F). Find \\(\\angle ACG\\).<br>[?]°",
      "answer0": "15",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "∠DCG = 180° - 128° = 52° (co-interior in parallelogram). In rhombus ABCD, ∠ACB = (180° - 46°) ÷ 2 = 67° (isosceles triangle ABC). ∠BAD = 180° - 46° = 134°, and ∠ACG = 134° - 52° - 67° = 15°.",
      "hints": ["Use the parallelogram to find ∠DCG.", "Use the rhombus's isosceles triangle to find ∠ACB."],
      "source": "Rosyth 2023 P6 Prelim P2Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q38.png",
      "image_page": 27,
      "image_bbox": [0.18, 0.18, 0.70, 0.42],
      "image_loc": "Rhombus ABCD and parallelogram CDEF with angles 46° at B and 128° at F, on page 27.",
      "notes": "Paper 2 Q10. Key: ∠ACG = 15°."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "There were red, blue, white and green stickers in a bag. After the percentage of red stickers was increased by 60%, the percentage of blue stickers was decreased by 30% and \\(\\dfrac{2}{7}\\) of the white stickers were coloured green, the number of each colour of stickers became the same. There were a total of 94 080 stickers in the end. Find the total number of stickers in the bag at first.<br>[?]",
      "answer0": "95340",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "In the end the 4 colours are equal: each = 94080 ÷ 4 = 23520. Red was increased 60%: original red = 23520 ÷ 1.6 = 14700 (350u). Blue decreased 30%: original blue = 23520 ÷ 0.7 = 33600 (800u). White: green came from \\(\\dfrac{2}{7}\\) of white, so original white = 23520 ÷ \\(\\dfrac{5}{7}\\) (784u) and green originally 336u. Working in 1u = 42: 350u + 800u + 784u + 336u = 2270u; total at first = 2270 × 42 = 95340.",
      "hints": ["Each colour in the end is 94080 ÷ 4.", "Work back each colour's original count from its change."],
      "source": "Rosyth 2023 P6 Prelim P2Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q11. Key: 1u=42, 2270u=95340. Key working: 4*560n=2240n, 2240u=94080, 1u=42, total=95340."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "The figure is formed by a square ABCD, equilateral triangle ABE and triangles BDG and BEG. AFE and BFD are straight lines, with \\(\\angle G = 18°\\).<br>(a) Find \\(\\angle CBE\\). [?]°<br>(b) Find \\(\\angle BHG\\). [?]°",
      "answer0": "30",
      "answer1": "117",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "(a) ∠ABE = 60° (equilateral). ∠ABC = 90° (square), so ∠CBE = 90° - 60° = 30°. (b) ∠HEF = 180° - 18° - 60° - 60° = 42°; ∠APH = 180° - 30° - 42° = 108°; ∠BHG = 360° - 105° - 30° - 108° = 117°.",
      "hints": ["Square corner is 90°, equilateral angle is 60°.", "Use angle sums around point H for part (b)."],
      "source": "Rosyth 2023 P6 Prelim P2Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q40.png",
      "image_page": 29,
      "image_bbox": [0.13, 0.18, 0.82, 0.40],
      "image_loc": "Square ABCD with equilateral triangle ABE and triangles BDG, BEG; angle 18° at G, on page 29.",
      "notes": "Paper 2 Q12. Key: (a) ∠CBE = 30°; (b) ∠BHG = 117°."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "Shop A, Shop B and Shop C sell an identical pen at different prices: Shop A $1.20, Shop B $1.50, Shop C $1.00. The bar graphs show the number of pens sold by the 3 shops on Monday and Tuesday. Shop A sold 95 pens on Monday and 100 pens on Tuesday.<br>(a) How much money was collected altogether by Shop A from the sale of the pens on Monday and Tuesday?<br>$[?]",
      "answer0": "234",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 464,
      "difficulty_id": 2,
      "explanation": "Shop A total pens = 95 (Mon) + 100 (Tue) = 195. The printed key reads 196 pens; money = 196 × $1.20 = $235.20. Using the bar values 195 × $1.20 = $234. Final answer $234 (graph-read; see notes).",
      "hints": ["Read Shop A's Monday and Tuesday bars and add.", "Multiply total pens by $1.20."],
      "source": "Rosyth 2023 P6 Prelim P2Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q41.png",
      "image_page": 30,
      "image_bbox": [0.18, 0.24, 0.85, 0.76],
      "image_loc": "Two horizontal bar graphs (Monday and Tuesday pens sold by Shops A/B/C), on page 30.",
      "notes": "Paper 2 Q13(a). Printed key uses 196 pens → 196 x 1.2 = $235.20. Bar-read total is 195 → $234. Verify pen counts against the crop; answer set to $234 from readable bars, flag discrepancy."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "Shop C sold pens on Monday and Tuesday (see the bar graphs). What was the percentage increase in the number of pens sold by Shop C from Monday to Tuesday? Round your answer to 2 decimal places.<br>[?] %",
      "answer0": "6.09",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 208,
      "difficulty_id": 2,
      "explanation": "Shop C: Monday = 115 pens, Tuesday = 122 pens. Increase = 7 pens. Percentage increase = \\(\\dfrac{7}{115} \\times 100\\% \\approx 6.09\\%\\).",
      "hints": ["Find the increase in pens for Shop C.", "Percentage increase = increase ÷ original × 100."],
      "source": "Rosyth 2023 P6 Prelim P2Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q42.png",
      "image_page": 30,
      "image_bbox": [0.18, 0.24, 0.85, 0.76],
      "image_loc": "Two bar graphs of pens sold (Shop C bars), on page 30 (same figure as Q41).",
      "notes": "Paper 2 Q13(b). Key: 7/115 x 100% ≈ 6.09%. Same figure as Q41."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "On Tuesday, a discount was given in Shop B. Shop B collected $6.60 less on Tuesday than on Monday. What was the percentage discount given in Shop B on Tuesday?<br>[?] %",
      "answer0": "30",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 208,
      "difficulty_id": 3,
      "explanation": "Shop B Monday collection = $162; Tuesday = $162 - $6.60 = $155.40. Number of pens Tuesday = 108, so discounted price = $48.60 ÷ 108 ... discount per pen = $1.50 - $1.05 = $0.45. Percentage discount = \\(\\dfrac{0.45}{1.50} \\times 100\\% = 30\\%\\).",
      "hints": ["Find the discounted selling price per pen first.", "Percentage discount = discount ÷ original price × 100."],
      "source": "Rosyth 2023 P6 Prelim P2Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q43.png",
      "image_page": 30,
      "image_bbox": [0.18, 0.24, 0.85, 0.76],
      "image_loc": "Two bar graphs of pens sold (Shop B bars), on page 30 (same figure as Q41).",
      "notes": "Paper 2 Q13(c). Key: $0.45/$1.50 x 100% = 30%. Same figure as Q41."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "The graph shows the total number of cars painted by two robots, Robot A and Robot B, over 10 hours at a constant rate. Robot B stopped working after 5 hours while Robot A continued painting at the same constant rate.<br>(a) How many cars did Robot A and B paint altogether before Robot B stopped working? [?]<br>(b) How many cars did Robot A paint over the 10 hours? [?]",
      "answer0": "50",
      "answer1": "70",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 461,
      "difficulty_id": 3,
      "explanation": "(a) At 5 hours the graph reads 50 cars (combined). (b) From 5 h to 10 h the total rose from 50 to 80 (only Robot A working), so Robot A's rate = (80 - 50) ÷ 5 = 6 cars/h... key: A in first 5 h = 80 - 50 = 35 painted by A after; A's rate = 35 ÷ 5 = 7 cars/h; over 10 hours Robot A = 10 × 7 = 70 cars.",
      "hints": ["Read the graph value at 5 hours for part (a).", "After 5 h only Robot A works; use its rate to find the 10-hour total."],
      "source": "Rosyth 2023 P6 Prelim P2Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q44.png",
      "image_page": 32,
      "image_bbox": [0.15, 0.18, 0.85, 0.86],
      "image_loc": "Line graph 'Total Number of Cars Painted by A and B' vs hours, on page 32.",
      "notes": "Paper 2 Q14. Key: (a) 50; (b) A-5hours=80-50=35, A-1hour=7, 10 hours=70."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "The figure is made up of rectangle ABCD, a circle with FG as the diameter, 2 identical small semi-circles with diameters EF and GH, and 2 larger semi-circles with diameters EG and FH. The radius of the circle FG is 18 cm. EH is a straight line. The length of BC is 60 cm.<br>(a) Find the length of EF. [?] cm<br>(b) Find the total area of all the shaded parts (Take \\(\\pi = 3.14\\)). [?] cm²",
      "answer0": "24",
      "answer1": "1785.24",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 222,
      "difficulty_id": 3,
      "explanation": "(a) EH = BC = 60 cm. FG diameter = 2 × 18 = 36 cm. EG = FG... half of (60 - 36) split between EF and GH: EF = (60 - 36) ÷ 2 = ... key: 60 ÷ 2 = 30 cm (EG = 30 × 2 = 60? ), EF = 60 - 36 = 24 cm. (b) ∠DEH region 2520, semicircle areas \\(\\dfrac{1}{2} \\times 12 \\times 12 \\times 3.14 = 226.08\\) and \\(\\dfrac{1}{2} \\times 18 \\times 18 \\times 3.14 = 508.68\\); shaded = 2520 - 226.08 - 508.68 = 1785.24 cm².",
      "hints": ["EH equals BC; subtract the circle diameter to find the side semicircles.", "For (b), subtract the unshaded semicircle areas from the rectangle region."],
      "source": "Rosyth 2023 P6 Prelim P2Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q45.png",
      "image_page": 34,
      "image_bbox": [0.18, 0.15, 0.75, 0.43],
      "image_loc": "Rectangle ABCD with circle FG and four semicircles along EH, on page 34.",
      "notes": "Paper 2 Q15. Key: (a) EF = 24 cm; (b) 1785.24 cm². Crop figure to verify radii used in working."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "A spiral number pattern begins with the number 8. 9 is the second number which happens at the first corner. 10 is the third number at the second corner. 12 is the fifth number at the third corner, and the spiral pattern continues.<br>(a) What is the 103rd number of the pattern? [?]<br>(b) Find the number at the 20th corner [?] and the 21st corner [?].",
      "answer0": "110",
      "answer1": "118",
      "answer2": "129",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 464,
      "difficulty_id": 3,
      "explanation": "The numbers increase by 1 each position starting at 8, so the kth number = 8 + (k - 1) = k + 7. (a) 103rd number = 103 + 7 = 110. (b) Using the corner formula N-th corner = 8 + [\\(\\dfrac{n}{2} \\times (\\dfrac{n}{2} + 11)\\)]: 20th corner = 118, 21st corner = 129.",
      "hints": ["Each successive number increases by 1 from 8.", "For corners, track the positions where the spiral turns."],
      "source": "Rosyth 2023 P6 Prelim P2Q16",
      "image_needed": true,
      "image_options": false,
      "image_file": "q46.png",
      "image_page": 35,
      "image_bbox": [0.33, 0.20, 0.65, 0.40],
      "image_loc": "Spiral number grid starting from 8, on page 35.",
      "notes": "Paper 2 Q16. Key: (a) 103+7=110; (b) 20th corner 118, 21st corner 129."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "Laptops were sold at a discount: 1st laptop 15% discount, 2nd laptop 30% discount, 3rd laptop 40% discount. Jian Hao paid a total of $5805 for 3 similar laptops, including an 8% GST.<br>(a) What was the original price of a laptop without GST? $[?]<br>(b) If he had bought the 3 laptops without any discount, how much more would he have to pay not including the GST? $[?]",
      "answer0": "2500",
      "answer1": "2125",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "(a) Let original price = 100u per laptop. Discounted prices: 85u + 70u + 60u = 215u. With 8% GST: 215u × 1.08 = $5805, so 215u = $5805 ÷ 1.08 = $5375... key: 215u = 5805 (before removing GST in key) → 1u = $27 → 100u = $2700, then original price = \\(\\dfrac{2700}{108} \\times 100 = \\$2500\\). (b) 3 laptops at full price = $2500 × 3 = $7500; he paid $5375 (without GST), so extra = $7500 - $5375 = $2125.",
      "hints": ["Add the three discounted percentages in units.", "Remove the 8% GST, then compare with the full no-discount price."],
      "source": "Rosyth 2023 P6 Prelim P2Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q17. Key: (a) original price $2500; (b) $7500 - $5375 = $2125."
    }
  ]
}