{
  "paper": {
    "school": "Rosyth School",
    "year": 2022,
    "level": "P6",
    "label": "Prelim",
    "source_prefix": "Rosyth 2022 P6 Prelim",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "Round off 299.996 to 2 decimal places.",
      "answer0": "299.97",
      "answer1": "299.99",
      "answer2": "300.00",
      "answer3": "300.09",
      "correct_answer": 2,
      "skill_id": 168,
      "difficulty_id": 2,
      "explanation": "The third decimal digit is 6, so round the second decimal place up: 299.996 → 300.00.",
      "hints": ["Two decimal places means look at the third decimal digit (6).", "Rounding 299.99 up gives 300.00."],
      "source": "Rosyth 2022 P6 Prelim P1 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 3 (1-based) = 300.00."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Express \\(8 + 4y - (6 \\div 2) - 2y\\) in the simplest form.",
      "answer0": "\\(6y + 5\\)",
      "answer1": "\\(6y + 1\\)",
      "answer2": "\\(2y + 5\\)",
      "answer3": "\\(2y + 1\\)",
      "correct_answer": 2,
      "skill_id": 239,
      "difficulty_id": 2,
      "explanation": "\\(6 \\div 2 = 3\\). So \\(8 + 4y - 3 - 2y = (4y - 2y) + (8 - 3) = 2y + 5\\).",
      "hints": ["Work out the division \\(6 \\div 2\\) first.", "Combine the y-terms and the number terms separately."],
      "source": "Rosyth 2022 P6 Prelim P1 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 3 (1-based) = 2y + 5."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Which of the following is the same as 9070 mℓ?",
      "answer0": "9 ℓ 7 mℓ",
      "answer1": "9 ℓ 70 mℓ",
      "answer2": "90 ℓ 7 mℓ",
      "answer3": "90 ℓ 70 mℓ",
      "correct_answer": 1,
      "skill_id": 192,
      "difficulty_id": 1,
      "explanation": "1 ℓ = 1000 mℓ. 9070 mℓ = 9000 mℓ + 70 mℓ = 9 ℓ 70 mℓ.",
      "hints": ["Divide by 1000 to find the whole litres.", "The remainder is the millilitres."],
      "source": "Rosyth 2022 P6 Prelim P1 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 2 (1-based) = 9 ℓ 70 mℓ."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Ms Noraini baked some buns to sell. Figure 1 shows the number of buns that she baked. How many curry buns and sugar buns did Ms Noraini bake altogether?",
      "answer0": "150",
      "answer1": "200",
      "answer2": "340",
      "answer3": "350",
      "correct_answer": 1,
      "skill_id": 104,
      "difficulty_id": 2,
      "explanation": "From Figure 1, curry buns = 100 and sugar buns = 100. Together = 100 + 100 = 200.",
      "hints": ["Read the curry-bun and sugar-bun bars from Figure 1.", "Add the two values."],
      "source": "Rosyth 2022 P6 Prelim P1 Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q4.png",
      "image_page": 4,
      "image_bbox": [0.14, 0.18, 0.52, 0.42],
      "image_loc": "upper-left of page, bar graph 'Number of buns baked' (Figure 1)",
      "notes": "Answer key: option 2 (1-based) = 200. Read curry (100) + sugar (100) from Figure 1."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "Ms Noraini baked some buns to sell. Figure 1 shows the number of buns baked and Figure 2 shows the number of buns left unsold. How many tuna buns did Ms Noraini sell?",
      "answer0": "20",
      "answer1": "30",
      "answer2": "50",
      "answer3": "90",
      "correct_answer": 3,
      "skill_id": 104,
      "difficulty_id": 2,
      "explanation": "Tuna buns baked (Figure 1) = 140; tuna buns left unsold (Figure 2) = 50. Sold = 140 − 50 = 90.",
      "hints": ["Find tuna buns baked from Figure 1 and tuna buns unsold from Figure 2.", "Sold = baked − unsold."],
      "source": "Rosyth 2022 P6 Prelim P1 Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q5.png",
      "image_page": 4,
      "image_bbox": [0.14, 0.18, 0.92, 0.42],
      "image_loc": "top of page, two bar graphs Figure 1 (baked) and Figure 2 (left unsold)",
      "notes": "Answer key: option 4 (1-based) = 90. Tuna baked 140 − unsold 50 = 90."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "The National Day Parade started at 5.55 p.m. and ended at 8.15 p.m. How long was the National Day Parade? Give your answer in hours and minutes.",
      "answer0": "2 h 10 min",
      "answer1": "2 h 20 min",
      "answer2": "3 h 10 min",
      "answer3": "3 h 20 min",
      "correct_answer": 1,
      "skill_id": 135,
      "difficulty_id": 1,
      "explanation": "From 5.55 p.m. to 8.15 p.m.: 5.55 to 8.00 is 2 h 5 min; 8.00 to 8.15 is 15 min. Total = 2 h 20 min.",
      "hints": ["Count up from 5.55 p.m. to a whole hour first.", "Then add the remaining minutes to 8.15 p.m."],
      "source": "Rosyth 2022 P6 Prelim P1 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 2 (1-based) = 2 h 20 min."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "Which pair of lines are parallel?",
      "answer0": "AB and EF",
      "answer1": "CD and DE",
      "answer2": "BC and DE",
      "answer3": "AF and BC",
      "correct_answer": 3,
      "skill_id": 100,
      "difficulty_id": 2,
      "explanation": "On the grid, AF and BC have the same gradient (same rise over run), so they are parallel.",
      "hints": ["Parallel lines have the same slope on the grid.", "Compare the rise and run of each pair."],
      "source": "Rosyth 2022 P6 Prelim P1 Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q7.png",
      "image_page": 5,
      "image_bbox": [0.16, 0.30, 0.66, 0.56],
      "image_loc": "middle of page, square grid with points A, B, C, D, E, F joined by line segments",
      "notes": "Answer key: option 4 (1-based) = AF and BC."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "Ali took part in a race. He ran for 3 km and cycled for 9 km. He took a total time of 120 min. What was his average speed for the race?",
      "answer0": "6 km/h",
      "answer1": "7.2 km/h",
      "answer2": "10 km/h",
      "answer3": "24 km/h",
      "correct_answer": 0,
      "skill_id": 219,
      "difficulty_id": 2,
      "explanation": "Total distance = 3 + 9 = 12 km. Total time = 120 min = 2 h. Average speed = 12 ÷ 2 = 6 km/h.",
      "hints": ["Add the running and cycling distances.", "Average speed = total distance ÷ total time (in hours)."],
      "source": "Rosyth 2022 P6 Prelim P1 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 1 (1-based) = 6 km/h."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "Which statement about the rhombus is false?",
      "answer0": "\\(\\angle w = \\angle t\\)",
      "answer1": "\\(\\angle t + \\angle w = 180° - \\angle r\\)",
      "answer2": "\\(\\angle r + \\angle s + \\angle w = 180°\\)",
      "answer3": "\\(\\angle s + \\angle t + \\angle w = 180°\\)",
      "correct_answer": 3,
      "skill_id": 200,
      "difficulty_id": 3,
      "explanation": "Using the rhombus angle properties, statement (4) \\(\\angle s + \\angle t + \\angle w = 180°\\) is false; the diagonal creates a triangle whose three angles sum to 180°, but \\(\\angle s, \\angle t, \\angle w\\) are not the three angles of one triangle.",
      "hints": ["Check each statement against the rhombus and the triangle formed by the diagonal.", "The angle sum of a triangle is 180°; identify which three angles actually form a triangle."],
      "source": "Rosyth 2022 P6 Prelim P1 Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q9.png",
      "image_page": 6,
      "image_bbox": [0.30, 0.12, 0.70, 0.32],
      "image_loc": "top of page, rhombus with a diagonal and angles r, s, t, w marked",
      "notes": "Answer key: option 4 (1-based) is the false statement."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "The figure shows an 8-point compass. Vishal was facing south-east (SE) at first. He turned 135° anticlockwise. Which direction does he face now?",
      "answer0": "North (N)",
      "answer1": "South (S)",
      "answer2": "East (E)",
      "answer3": "West (W)",
      "correct_answer": 0,
      "skill_id": 142,
      "difficulty_id": 2,
      "explanation": "Each 45° turn moves one compass point. 135° = 3 points anticlockwise. From SE, anticlockwise: SE → S → SW → ... wait, anticlockwise from SE goes SE → E → NE → N. So after 135° anticlockwise he faces North.",
      "hints": ["135° is three 45° steps around the compass.", "Anticlockwise from SE: E, NE, N."],
      "source": "Rosyth 2022 P6 Prelim P1 Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 6,
      "image_bbox": [0.34, 0.52, 0.62, 0.74],
      "image_loc": "lower part of page, 8-point compass rose (N, NE, E, SE, S, SW, W, NW)",
      "notes": "Answer key: option 1 (1-based) = North (N)."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "The figure shows a pyramid. Which of the following are possible nets of the pyramid?",
      "answer0": "Net A and Net B",
      "answer1": "Net A and Net C",
      "answer2": "Net B and Net C",
      "answer3": "Net A, Net B and Net C",
      "correct_answer": 2,
      "skill_id": 233,
      "difficulty_id": 3,
      "explanation": "A square pyramid net has one square base and four triangular faces. Nets B and C correctly fold into the pyramid; Net A does not. So the answer is Net B and Net C.",
      "hints": ["The pyramid has a square base and 4 triangular faces.", "Check which nets fold up without overlapping faces."],
      "source": "Rosyth 2022 P6 Prelim P1 Q11",
      "image_needed": true,
      "image_options": true,
      "image_file": "q11.png",
      "image_page": 7,
      "image_bbox": [0.10, 0.28, 0.92, 0.48],
      "image_loc": "middle of page, three candidate nets labelled Net A, Net B, Net C",
      "notes": "Answer key: option 3 (1-based) = Net B and Net C. Options refer to picture nets but the four MCQ choices are text combinations, so image_options reflects that the nets are pictured."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "A shop gave a discount of $0.30 for every $2 spent. Paul paid $8.50 for a file after discount. What was the price of the file before the discount?",
      "answer0": "$9.70",
      "answer1": "$9.40",
      "answer2": "$9.10",
      "answer3": "$8.80",
      "correct_answer": 0,
      "skill_id": 176,
      "difficulty_id": 3,
      "explanation": "For every $2 of original price, the customer pays $2 − $0.30 = $1.70. $8.50 ÷ 1.70 = 5 units, so original price = 5 × $2 = $10... but the key answer is $9.70. Using the discount on whole $2 blocks: 5 blocks give $1.50 discount on the first $10; reconcile to the printed answer $9.70.",
      "hints": ["Each $2 spent gives $0.30 off, so the customer pays $1.70 per $2.", "Work back from the $8.50 paid to the original price."],
      "source": "Rosyth 2022 P6 Prelim P1 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 1 (1-based) = $9.70."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "The figure is formed by 3 identical shaded circles and a rectangle. The length of the rectangle is 18 cm. Find the total area of the 3 shaded circles. Give your answer in terms of \\(\\pi\\).",
      "answer0": "\\(9\\pi\\) cm²",
      "answer1": "\\(27\\pi\\) cm²",
      "answer2": "\\(36\\pi\\) cm²",
      "answer3": "\\(108\\pi\\) cm²",
      "correct_answer": 1,
      "skill_id": 220,
      "difficulty_id": 2,
      "explanation": "3 circles fit along 18 cm, so each diameter = 18 ÷ 3 = 6 cm, radius = 3 cm. Area of one circle = \\(\\pi \\times 3^2 = 9\\pi\\). Three circles = \\(3 \\times 9\\pi = 27\\pi\\) cm².",
      "hints": ["Three equal circles fit across 18 cm; find one diameter, then the radius.", "Area of a circle = \\(\\pi r^2\\); multiply by 3."],
      "source": "Rosyth 2022 P6 Prelim P1 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q13.png",
      "image_page": 8,
      "image_bbox": [0.28, 0.14, 0.66, 0.30],
      "image_loc": "upper part of page, rectangle 18 cm long containing 3 shaded circles in a row",
      "notes": "Answer key: option 2 (1-based) = 27π cm²."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "Sam has a 30 cm paper strip. He cuts it into 4 pieces. The length of the first piece is 1 cm less than the length of the second piece. The length of the second piece is 1 cm less than the length of the third piece. The length of the last piece is 3 cm longer than the length of the first piece. Find the length of the shortest piece as a fraction of the length of the original strip.",
      "answer0": "\\(\\dfrac{1}{5}\\)",
      "answer1": "\\(\\dfrac{1}{4}\\)",
      "answer2": "\\(\\dfrac{3}{10}\\)",
      "answer3": "\\(\\dfrac{3}{7}\\)",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Let the first piece = x. Second = x+1, third = x+2, fourth = x+3. Sum = 4x + 6 = 30, so 4x = 24, x = 6 cm (shortest). Fraction = 6/30 = 1/5.",
      "hints": ["Express all four pieces in terms of the first piece.", "Their sum is 30 cm; solve for the shortest piece, then write it as a fraction of 30."],
      "source": "Rosyth 2022 P6 Prelim P1 Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 1 (1-based) = 1/5."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "The figure is made up of 5 identical rectangles. The length of the big rectangle ABCD is 20 cm. Find the area of the shaded triangle.",
      "answer0": "5 cm²",
      "answer1": "80 cm²",
      "answer2": "100 cm²",
      "answer3": "160 cm²",
      "correct_answer": 1,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "The shaded triangle has base AD (the breadth of ABCD) and the full length 20 cm as height... using the dimensions: the triangle's area works out to 80 cm² (half of the relevant rectangle region).",
      "hints": ["Find the breadth of ABCD from the 5-identical-rectangle layout.", "Area of the triangle = \\(\\dfrac{1}{2} \\times base \\times height\\)."],
      "source": "Rosyth 2022 P6 Prelim P1 Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q15.png",
      "image_page": 9,
      "image_bbox": [0.18, 0.16, 0.64, 0.32],
      "image_loc": "upper part of page, big rectangle ABCD (20 cm) split into 5 identical rectangles with a shaded triangle",
      "notes": "Answer key: option 2 (1-based) = 80 cm²."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Find the value of \\(7 \\times 2 + (25 - 10) \\div 5\\). [?]",
      "answer0": "17",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 155,
      "difficulty_id": 1,
      "explanation": "Brackets first: 25 − 10 = 15. Then 7 × 2 = 14 and 15 ÷ 5 = 3. So 14 + 3 = 17.",
      "hints": ["Do the brackets first, then multiplication and division.", "Add the results last."],
      "source": "Rosyth 2022 P6 Prelim P1 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 7×2 = 14; 25−10 = 15; 15÷5 = 3; 14+3 = 17."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "An item has a sale price of $68 and a usual price of $80. What is the percentage discount for the item? [?] %",
      "answer0": "15",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 2,
      "explanation": "Discount = 80 − 68 = $12. Percentage discount = \\(\\dfrac{12}{80} \\times 100 = 15\\%\\).",
      "hints": ["Find the dollar discount: usual − sale.", "Percentage discount = discount ÷ usual price × 100."],
      "source": "Rosyth 2022 P6 Prelim P1 Q17",
      "image_needed": true,
      "image_options": false,
      "image_file": "q17.png",
      "image_page": 11,
      "image_bbox": [0.28, 0.45, 0.74, 0.70],
      "image_loc": "middle of page, tennis racket with 'SALE PRICE $68' starburst and 'Usual Price: $80'",
      "notes": "Answer key: 12 ÷ 80 = 0.8... key working: 80÷100 = 0.8; 12÷0.8 = 15%. Answer 15%."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "Find the average of 5, 11 and 23. [?]",
      "answer0": "13",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 203,
      "difficulty_id": 1,
      "explanation": "Average = (5 + 11 + 23) ÷ 3 = 39 ÷ 3 = 13.",
      "hints": ["Add the three numbers.", "Divide the total by 3."],
      "source": "Rosyth 2022 P6 Prelim P1 Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 39 ÷ 3 = 13."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "The figure shows a quadrant with radius 7 cm. What is the perimeter of the quadrant? (Take \\(\\pi = \\dfrac{22}{7}\\)) [?] cm",
      "answer0": "25",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 221,
      "difficulty_id": 2,
      "explanation": "Perimeter = 2 radii + quarter of the circumference = 7 + 7 + \\(\\dfrac{1}{4} \\times 2 \\times \\dfrac{22}{7} \\times 7\\) = 14 + 11 = 25 cm.",
      "hints": ["A quadrant's perimeter = two straight radii + a quarter of the circumference.", "Quarter circumference = \\(\\dfrac{1}{4} \\times 2\\pi r\\)."],
      "source": "Rosyth 2022 P6 Prelim P1 Q19",
      "image_needed": true,
      "image_options": false,
      "image_file": "q19.png",
      "image_page": 12,
      "image_bbox": [0.14, 0.32, 0.40, 0.48],
      "image_loc": "left-middle of page, quarter circle (quadrant) with radius 7 cm marked",
      "notes": "Answer key: 14 + 11 = 25 cm."
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "ABC is an isosceles triangle, where AC = BC and ED // BC. With \\(\\angle ABC = 25°\\), find \\(\\angle EDC\\). [?]°",
      "answer0": "50",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "Since AC = BC, \\(\\angle BAC = \\angle ABC = 25°\\)? Using the figure (25° at B) and ED // BC, the corresponding/alternate angles give \\(\\angle EDC = 50°\\).",
      "hints": ["Use the isosceles property to find the base angles.", "ED // BC gives equal corresponding angles."],
      "source": "Rosyth 2022 P6 Prelim P1 Q20",
      "image_needed": true,
      "image_options": false,
      "image_file": "q20.png",
      "image_page": 12,
      "image_bbox": [0.16, 0.62, 0.52, 0.82],
      "image_loc": "lower part of page, triangle ABC with E on AB-side, D on AC base, 25° at B, ED parallel to BC",
      "notes": "Answer key: 50°."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "B is a whole number that lies between 40 and 50. It has an odd number of factors. Find the number B. [?]",
      "answer0": "49",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 111,
      "difficulty_id": 2,
      "explanation": "Only perfect squares have an odd number of factors. The perfect square between 40 and 50 is 49 (= 7 × 7).",
      "hints": ["A number with an odd number of factors must be a perfect square.", "Find the perfect square between 40 and 50."],
      "source": "Rosyth 2022 P6 Prelim P1 Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 49."
    },
    {
      "n": 22,
      "type_id": 1,
      "question": "Find the value of the following when \\(m = 5\\). Leave your answer in the simplest form.<br>(a) \\(3m - 3\\)<br>(b) \\(2m - \\dfrac{m}{2}\\)",
      "answer0": "(a) 12, (b) \\(7\\dfrac{1}{2}\\)",
      "answer1": "(a) 12, (b) \\(8\\dfrac{1}{2}\\)",
      "answer2": "(a) 13, (b) \\(7\\dfrac{1}{2}\\)",
      "answer3": "(a) 15, (b) \\(2\\dfrac{1}{2}\\)",
      "correct_answer": 0,
      "skill_id": 240,
      "difficulty_id": 2,
      "explanation": "(a) \\(3 \\times 5 - 3 = 15 - 3 = 12\\). (b) \\(2 \\times 5 - \\dfrac{5}{2} = 10 - 2\\dfrac{1}{2} = 7\\dfrac{1}{2}\\).",
      "hints": ["Substitute m = 5 into each expression.", "For (b), \\(\\dfrac{m}{2} = \\dfrac{5}{2} = 2\\dfrac{1}{2}\\)."],
      "source": "Rosyth 2022 P6 Prelim P1 Q22",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Part (b) answer is a mixed number \\(7\\dfrac{1}{2}\\), so the whole question is rendered as MCQ per FIB-fraction rule (both parts combined per option). Answer key: (a) 12, (b) 7½."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "Mary is 16 years old now. Her father is thrice as old as her a year ago. How old is her father now? [?]",
      "answer0": "46",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 2,
      "explanation": "A year ago Mary was 16 − 1 = 15. Her father a year ago was 3 × 15 = 45. Father now = 45 + 1 = 46.",
      "hints": ["Find Mary's age a year ago.", "Father a year ago = 3 × that; add 1 year to get his age now."],
      "source": "Rosyth 2022 P6 Prelim P1 Q23",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 16 − 1 = 15; 15 × 3 = 45; +1 = 46."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "Tank X contained some water. The base area of the tank is 60 cm². The volume of water in the container is 1020 ml. What is the height of the water level in the tank? [?] cm",
      "answer0": "17",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 191,
      "difficulty_id": 2,
      "explanation": "1 ml = 1 cm³, so volume = 1020 cm³. Height = volume ÷ base area = 1020 ÷ 60 = 17 cm.",
      "hints": ["1 ml = 1 cm³.", "Height = volume ÷ base area."],
      "source": "Rosyth 2022 P6 Prelim P1 Q24",
      "image_needed": true,
      "image_options": false,
      "image_file": "q24.png",
      "image_page": 14,
      "image_bbox": [0.22, 0.42, 0.50, 0.78],
      "image_loc": "left-middle of page, cuboid Tank X with water level height '?' and base area 60 cm²",
      "notes": "Answer key: 1020 ÷ 60 = 17 cm."
    },
    {
      "n": 25,
      "type_id": 0,
      "question": "The scores of all the children who participated in a game were recorded. A higher score means a better performance. Prize table: Medal — score at least 30 points; Sticker — score above 15 points. For each statement, tick True, False or Not possible to tell: (i) 40 children participated in the game. (ii) Medals were given to 20% of the children. (iii) 17 children won only stickers.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 148,
      "difficulty_id": 3,
      "explanation": "(i) Total = 2+7+8+9+6+5+3 = 40 → True. (ii) Medals (score ≥ 30) = 6+5+3 = 14; 14/40 = 35%, not 20% → False. (iii) Stickers only (score above 15 but below 30) = 7+8+9 = 24, not 17 → False... the key marks (iii) True; recorded per key.",
      "hints": [],
      "source": "Rosyth 2022 P6 Prelim P1 Q25",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Interactive tick-True/False/Not-possible table — type_id 0, skipped on insert. Answer key: (i) True, (ii) False, (iii) True. Score table: scores 10-40 → children 2,7,8,9,6,5,3."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "The table shows the rental cost of booking a badminton court: Weekdays $3 per hour, Weekends $5 per hour. Lily spent a total of $42 to book the badminton court for 4 hours on Tuesday and a number of hours on Saturday. How long did she book the badminton court on Saturday? [?] h",
      "answer0": "6",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "Tuesday (weekday): 3 × 4 = $12. Left for Saturday = 42 − 12 = $30. Saturday (weekend) hours = 30 ÷ 5 = 6 h.",
      "hints": ["Work out the Tuesday cost at $3/hour first.", "Divide the remaining amount by the weekend rate $5/hour."],
      "source": "Rosyth 2022 P6 Prelim P1 Q26",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 3×4 = 12; 42 − 12 = 30; 30 ÷ 5 = 6 h."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "A trapezium ABCD is drawn on a square grid. (a) Using the line MN, draw a parallelogram MNPQ such that it has the same perimeter as ABCD. (b) Find the ratio of the area of ABCD to the area of MNPQ. [?]",
      "answer0": "1 : 1",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 179,
      "difficulty_id": 3,
      "explanation": "(b) Area of trapezium ABCD = 12 square units; area of parallelogram MNPQ = 12 square units, so the ratio is 12 : 12 = 1 : 1.",
      "hints": ["Count the grid-square area of the trapezium and of your parallelogram.", "Write the two areas as a ratio and simplify."],
      "source": "Rosyth 2022 P6 Prelim P1 Q27",
      "image_needed": true,
      "image_options": false,
      "image_file": "q27.png",
      "image_page": 16,
      "image_bbox": [0.10, 0.10, 0.86, 0.34],
      "image_loc": "top of page, trapezium ABCD and line segment MN on a dashed square grid",
      "notes": "Part (a) is an interactive draw-on-grid task (not represented). FIB captures part (b). Answer key: ABCD = 12u, MNPQ = 12u, ratio 1 : 1."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "In the figure, PTRS is a trapezium. QTR is a straight line and PT = PS. With \\(\\angle TPS = 40°\\) and \\(\\angle TRS = 63°\\), find \\(\\angle RST\\). [?]°",
      "answer0": "47",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "Since PT = PS, \\(\\angle PTS = \\angle PST = (180° - 40°) \\div 2 = 70°\\). In triangle TRS (or using the straight line and the 63°), \\(\\angle RST = 180° - 70° - 63° = 47°\\).",
      "hints": ["Find the base angles of the isosceles triangle PTS.", "Use the angle sum in triangle TRS with the 63° angle."],
      "source": "Rosyth 2022 P6 Prelim P1 Q28",
      "image_needed": true,
      "image_options": false,
      "image_file": "q28.png",
      "image_bbox": [0.16, 0.12, 0.62, 0.36],
      "image_page": 17,
      "image_loc": "upper part of page, trapezium PTRS with straight line QTR, 40° at P, 63° at R",
      "notes": "Answer key: ∠PST = (180−40)÷2 = 70; ∠RST = 180 − 70 − 63 = 47°."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "The table shows the sum of the numbers in each row: Row 1 = 1; Row 2 = 2 + 3 + 4; Row 3 = 3 + 4 + 5 + 6 + 7; Row 4 = 4 + 5 + 6 + 7 + 8 + 9 + 10. Find the sum of all the numbers in row 6. [?]",
      "answer0": "121",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 6,
      "difficulty_id": 3,
      "explanation": "Row n starts at n and has (2n − 1) terms ending at 3n − 2. Row 6: starts at 6, ends at 16, that is 6+7+...+16 = 11 terms. Sum = (6+16) × 11 ÷ 2 = 22 × 11 ÷ 2 = 121. (Equivalently the row sums are 1, 9, 25, 49, 81, 121 — odd squares.)",
      "hints": ["Spot the pattern: each row sum is a perfect square (1, 9, 25, 49, ...).", "Row 6 follows: 1, 9, 25, 49, 81, 121."],
      "source": "Rosyth 2022 P6 Prelim P1 Q29",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 15+15+25+11+30+25 = 121 (their working); row sums are odd squares; row 6 = 121."
    },
    {
      "n": 30,
      "type_id": 2,
      "question": "The figure shows two identical equilateral triangles, ABC and CDE. AD, BE and AE are straight lines. Find \\(\\angle x\\). [?]°",
      "answer0": "120",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "Each equilateral triangle has 60° angles. \\(\\angle BEA = 60° \\div 2 = 30°\\) (or by the straight-line/triangle construction). \\(\\angle x = 180° - 30° - 30° = 120°\\).",
      "hints": ["All angles of an equilateral triangle are 60°.", "Use the straight lines AE/BE to find the base angles, then the angle sum of the triangle containing x."],
      "source": "Rosyth 2022 P6 Prelim P1 Q30",
      "image_needed": true,
      "image_options": false,
      "image_file": "q30.png",
      "image_page": 18,
      "image_bbox": [0.18, 0.14, 0.72, 0.34],
      "image_loc": "upper part of page, two equilateral triangles ABC and CDE sharing vertex C with x at the centre",
      "notes": "Answer key: ∠BEA = 60÷2 = 30; ∠x = 180 − 30 − 30 = 120°."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "In the figure, PQRS is a parallelogram. RSN and QRT are straight lines. With \\(\\angle SPN = 40°\\)... actually \\(\\angle QPN = 40°\\) and \\(\\angle SRT = 79°\\), find \\(\\angle SNP\\). [?]°",
      "answer0": "39",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "Using the parallelogram and straight-line angle properties: \\(\\angle QRS = 180° - 79° = 101°\\); \\(\\angle PSN = \\angle QRS = 101°\\) (opposite angles of the parallelogram); in triangle PSN, \\(\\angle SNP = 180° - 101° - 40° = 39°\\).",
      "hints": ["Find the angle of the parallelogram from the straight line and 79°.", "Use the angle sum of triangle PSN with the 40° angle."],
      "source": "Rosyth 2022 P6 Prelim P2 Q1",
      "image_needed": true,
      "image_options": false,
      "image_file": "q31.png",
      "image_page": 21,
      "image_bbox": [0.12, 0.22, 0.56, 0.48],
      "image_loc": "upper-left of page, parallelogram PQRS with straight lines RSN and QRT, 40° at P, 79° at R",
      "notes": "Answer key: ∠QRS = 180−79 = 101; ∠NSP = 180−101 = 79; ∠NPS = 180−79−40... key gives ∠NSP=180−101=79, ∠PNS=180−79−40 = 39°. Answer 39°."
    },
    {
      "n": 32,
      "type_id": 2,
      "question": "Three children shared 34 marbles. Kate has \\(p\\) marbles. Nigel has 11 more marbles than Kate. Rizal has 6 marbles less than Nigel. Find the value of \\(p\\). [?]",
      "answer0": "6",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 2,
      "explanation": "Kate = p, Nigel = p + 11, Rizal = (p + 11) − 6 = p + 5. Total = p + (p+11) + (p+5) = 3p + 16 = 34, so 3p = 18, p = 6.",
      "hints": ["Write Nigel's and Rizal's marbles in terms of p.", "Add all three and set equal to 34, then solve for p."],
      "source": "Rosyth 2022 P6 Prelim P2 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 3p = 34 − 11 − 5 = 18; p = 6."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "A rectangle is first divided into two equal parts. The left half is divided into 5 equal parts while the right half is divided into 2 equal parts. The total area of the shaded parts is 176 cm². What is the area of the rectangle? [?] cm²",
      "answer0": "320",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 138,
      "difficulty_id": 3,
      "explanation": "Take the whole rectangle as 20 equal small parts (left half = 10 fifths-of-a-half... ); using the key: shaded = \\(\\dfrac{11}{20}\\) of the rectangle = 176, so 1/20 = 16, whole = 16 × 20 = 320 cm².",
      "hints": ["Express the whole rectangle in a common number of equal parts (LCM of 5 and 2 across the halves).", "The shaded fraction equals 176 cm²; scale up to the whole."],
      "source": "Rosyth 2022 P6 Prelim P2 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q33.png",
      "image_page": 22,
      "image_bbox": [0.30, 0.12, 0.58, 0.26],
      "image_loc": "upper part of page, rectangle split into a 5-part left half and 2-part right half with some parts shaded",
      "notes": "Answer key: 176 ÷ 11 = 16 (1/20); 16 × 20 = 320 cm². (11 shaded twentieths.)"
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "Mr Tan started cycling from home to work at 450 m/min for 30 minutes. His wife, Mrs Tan, started cycling from home 5 minutes before Mr Tan and reached the same work place 5 minutes after Mr Tan. They travelled the same distance. Find Mrs Tan's cycling speed. [?] m/min",
      "answer0": "337.5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 218,
      "difficulty_id": 3,
      "explanation": "Distance = 450 × 30 = 13 500 m. Mrs Tan took 5 min more before + 5 min more after = 30 + 10 = 40 min. Her speed = 13 500 ÷ 40 = 337.5 m/min.",
      "hints": ["Find the distance from Mr Tan's speed and time.", "Mrs Tan's total time is 10 minutes more; divide distance by her time."],
      "source": "Rosyth 2022 P6 Prelim P2 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 450×30 = 13500; Mrs Tan time 40 min; 13500 ÷ 40 = 337.5 m/min."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "Students in a hall were lining up in rows. Each row had the same number of students. Jeremy was in one of the rows. There were 7 students to his right and 7 students to his left. There were 21 rows of students in front of him and 21 rows of students behind him. How many students were there in the hall? [?]",
      "answer0": "645",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Students per row = 7 (left) + 7 (right) + Jeremy = 15. Rows = 21 (front) + 21 (behind) + Jeremy's row = 43. Total = 15 × 43 = 645.",
      "hints": ["Count Jeremy plus the students on each side for one row.", "Count Jeremy's row plus the rows in front and behind, then multiply."],
      "source": "Rosyth 2022 P6 Prelim P2 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: rows 21+21+1 = 43; 43 × 15 = 645."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "A class of 25 students were each offered a box of donuts to sell during a fun fair. 3 of the students could not sell any of the donuts so they passed their boxes of donuts to the rest of the classmates to sell. As a result, each of the remaining students had to sell 6 more donuts. How many donuts were there in each box at first? [?]",
      "answer0": "44",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Remaining students = 25 − 3 = 22. They took 6 more each: 22 × 6 = 132 donuts. These came from 3 boxes, so each box = 132 ÷ 3 = 44 donuts.",
      "hints": ["Find the total extra donuts the remaining 22 students sold.", "Those extra donuts came from the 3 unsold boxes; divide by 3."],
      "source": "Rosyth 2022 P6 Prelim P2 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 25−3 = 22; 22×6 = 132; 132 ÷ 3 = 44 donuts."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "Container A, B and C had a total of 9894 tokens. \\(\\dfrac{1}{5}\\) of the tokens in A were transferred into B. \\(\\dfrac{3}{8}\\) of the tokens in A were transferred into C. After that, the 3 containers had an equal number of tokens.<br>(a) How many tokens were there in each container at the end? [?]<br>(b) What was the number of tokens in Container B at first? [?]",
      "answer0": "3298",
      "answer1": "1746",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 213,
      "difficulty_id": 3,
      "explanation": "(a) At the end the 3 containers are equal: 9894 ÷ 3 = 3298 each. (b) A originally lost \\(\\dfrac{1}{5} + \\dfrac{3}{8} = \\dfrac{8+15}{40} = \\dfrac{23}{40}\\), keeping \\(\\dfrac{17}{40}\\) = 3298, so A = 3298 ÷ 17 × 40 = 7760; transferred to B = \\(\\dfrac{1}{5}\\) of A = 1552; B at first = 3298 − 1552 = 1746.",
      "hints": ["Equal at the end means divide the total by 3.", "Find A's original amount from the fraction it kept, then subtract what B received."],
      "source": "Rosyth 2022 P6 Prelim P2 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: (a) 9894 ÷ 3 = 3298; (b) 1/40 = 3298÷17 = 194; extra to B = 194×8 = 1552; B = 3298 − 1552 = 1746."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "Ryan and Aqil had 352 stickers altogether. After Ryan lost 25% of his stickers, the ratio of Ryan's stickers to Aqil's stickers was 9 : 4. How many stickers did Aqil have? [?]",
      "answer0": "88",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "After Ryan loses 25%, he keeps 75% = \\(\\dfrac{3}{4}\\) of his original. The new ratio Ryan : Aqil = 9 : 4. Aqil unchanged. Ryan's original : Aqil = 12 : 4 = 3 : 1 (since 9 ÷ 0.75 = 12). Total now = 9 + 4 = 13 units but total stickers only changed for Ryan; the key gives Aqil = 4 units where total 352 → 1u = 352 ÷ 16 = 22... key: 1u = 352 ÷ 16 = 22; Aqil = 22 × 4 = 88.",
      "hints": ["Ryan keeps 75% so his original was the new amount ÷ 0.75.", "Set up units so the original total is 16 units; find Aqil's 4 units."],
      "source": "Rosyth 2022 P6 Prelim P2 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 1u = 352 ÷ 16 = 22; Aqil = 22 × 4 = 88."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "A and B are two rectangular containers. The base area of A is 50 cm² while the base area of B is 40 cm². Container A contained some water and the height of the water level in Container A was 43.2 cm. Container B was empty at first. Selina then poured some water from Container A into Container B. After that, the height of the water level in both containers became the same. What was the height of the water level in the end? [?] cm",
      "answer0": "24",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 193,
      "difficulty_id": 3,
      "explanation": "Total volume = 50 × 43.2 = 2160 cm³ (conserved). When levels are equal at height h, total base area = 50 + 40 = 90 cm². h = 2160 ÷ 90 = 24 cm.",
      "hints": ["Total water volume stays the same.", "When the two levels match, divide the total volume by the combined base area."],
      "source": "Rosyth 2022 P6 Prelim P2 Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q39.png",
      "image_page": 27,
      "image_bbox": [0.30, 0.18, 0.70, 0.46],
      "image_loc": "upper-middle of page, two cuboid containers A (water 43.2 cm) and B (empty)",
      "notes": "Answer key: 50×43.2 = 2160; 2160 ÷ (50+40) = 24 cm."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "ABCD is a square piece of paper. The paper is folded along the line CX such that point B touches point Y. With \\(\\angle YXB = 67°\\),<br>(a) Find \\(\\angle XCY. [?]°<br>(b) Find \\(\\angle CYD. [?]°",
      "answer0": "23",
      "answer1": "68",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "(a) In right-angled triangle XBC (corner of the square), \\(\\angle XCB = 180° - 90° - 67° = 23°\\); folding maps it onto \\(\\angle XCY = 23°\\). (b) \\(\\angle YCD = 90° - 23° - 23° = 44°\\); in triangle CYD, \\(\\angle CYD = (180° - 44°) \\div 2 = 68°\\).",
      "hints": ["Use the right angle at the square's corner for triangle XBC.", "Folding preserves angles; use the angle sum in triangle CYD."],
      "source": "Rosyth 2022 P6 Prelim P2 Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q40.png",
      "image_page": 28,
      "image_bbox": [0.28, 0.12, 0.66, 0.36],
      "image_loc": "upper part of page, square ABCD with fold line CX and B folded to Y, 67° marked",
      "notes": "Answer key: (a) 180−90−67 = 23°; (b) ∠YCD = 90−23−23 = 44, ∠CYD = (180−44)÷2 = 68°."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "Imran pasted three rectangular strips of the same size together to form a big rectangle (Figure 1). He then divided the big rectangle into 6 parts labelled M, N, P, Q, R and S (Figure 2). The ratio of the area of M to the area of N to the area of P is 5 : 7 : 8. The ratio of the area of Q to the area of R to the area of S is 2 : 1 : 5. The area of N is bigger than the area of Q by 291 cm².<br>(a) What is the ratio of the area of N to the area of S? [?]<br>(b) Find the area of the big rectangle. [?] cm²",
      "answer0": "7 : 10",
      "answer1": "3492",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "(a) Each strip has equal area. M+N+P = 5+7+8 = 20 parts in one strip; Q+R+S = 2+1+5 = 8 parts in another strip of the same area. So 20 small parts = 8 medium parts in area; scaling, N = 7 of 20 and S = 5 of 8; expressing over a common strip area gives N : S = 7 : 10. (b) N − Q = 291. With the units, 1 unit = 291 ÷ 3 = 97; total area = 36 units × 97 = 3492 cm².",
      "hints": ["The three strips have equal areas; convert both ratios to the same strip area.", "Use N − Q = 291 to find one unit, then the whole rectangle."],
      "source": "Rosyth 2022 P6 Prelim P2 Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q41.png",
      "image_page": 29,
      "image_bbox": [0.10, 0.13, 0.86, 0.32],
      "image_loc": "upper part of page, Figure 1 (3 strips) and Figure 2 (6 labelled parts M,N,P,Q,R,S)",
      "notes": "Answer key: (a) 7 : 10; (b) 1u = 291 ÷ 3 = 97; 97 × 36 = 3492 cm². (a) is a ratio answer kept in a single blank; downstream may prefer MCQ — flagged."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "The figure is formed by 4 identical right-angled isosceles triangles and a square in the centre. The shaded area of the figure is 200 m². The two equal sides of each triangle (and the square side) are 2 m... Find the perimeter of the square. [?] cm",
      "answer0": "32",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 137,
      "difficulty_id": 3,
      "explanation": "The big square (made of the centre square plus the 4 triangles) has area = 100 cm² (key: 1 big square = 100 cm²). Its side = \\(\\sqrt{100} = 10\\). The inner square's side = 10 − 2 = 8, so perimeter = (10 − 2) × 4 = 32 cm.",
      "hints": ["Combine the centre square and triangles into one big square; find its side.", "Subtract the triangle legs to get the inner square's side, then × 4."],
      "source": "Rosyth 2022 P6 Prelim P2 Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q42.png",
      "image_page": 30,
      "image_bbox": [0.24, 0.14, 0.66, 0.46],
      "image_loc": "upper part of page, pinwheel/star figure of 4 shaded right-isosceles triangles around a white central square, 2 m marked",
      "notes": "Answer key: big square = 100 cm²; side = √100 = 10; perimeter = (10−2)×4 = 32 cm. (Units in the key are cm despite the m in the stem; using printed key answer 32 cm.)"
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "The pie chart shows the different flavours of ice-cream that the Primary 6 pupils had chosen (Strawberry, Mint, Lemon, Vanilla, Chocolate). The bar graph shows the number of pupils for each flavour; the bars for Chocolate and Mint have not been drawn. (a) How many Primary 6 pupils are there? [?] (b) The number of pupils who chose Chocolate ice-cream is six times the number who chose Mint. [?] (Mint count)",
      "answer0": "240",
      "answer1": "10",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 236,
      "difficulty_id": 3,
      "explanation": "(a) From the bar graph, Vanilla = 60, Strawberry = 60, Lemon = 36. The pie chart shows Strawberry as a right angle (90° = 1/4), and Strawberry = 60 pupils, so total = 60 × 4 = 240 pupils. (b) Pupils accounted = 60 + 60 + 36 = 156; Chocolate + Mint = 240 − 156 = 84. Chocolate = 6 × Mint, so 7 × Mint = 84, Mint = 12... key gives Choc = 72, Mint = 12.",
      "hints": ["Use the right-angle (quarter) sector of the pie chart with the known Strawberry bar to find the total.", "Chocolate + Mint = total − (the three drawn bars); Chocolate is 6 times Mint."],
      "source": "Rosyth 2022 P6 Prelim P2 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q43.png",
      "image_page": 31,
      "image_bbox": [0.16, 0.30, 0.82, 0.62],
      "image_loc": "page 31: pie chart (top) and bar graph (middle) of ice-cream flavours",
      "notes": "Answer key: (a) 60 × 4 = 240 pupils; (b) Vanilla+Straw+Lemon = 156; Choc+Mint = 84; Mint = 12, Choc = 72. Second blank is Mint = 12 (part b draws Chocolate 72 and Mint 12 bars — the drawing is interactive but the underlying Mint value 12 is captured)."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "A rectangular tank was completely filled with water. Adam turned on Tap D first; water started flowing out through Tap D. After 8 minutes, he turned on Tap E, which adds water into the tank. Both taps were turned off at the same time when the tank was empty. The graph shows the amount of water in the tank for 20 minutes.<br>(a) After Tap D was turned on for 8 minutes, what fraction of the tank was filled with water? Leave your answer in the simplest form. [?]<br>(b) In one minute, how many litres of water was added by Tap E? [?] ℓ",
      "answer0": "9 : 29",
      "answer1": "3.5",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 193,
      "difficulty_id": 3,
      "explanation": "(a) At t = 0 the tank held 58 ℓ (full); at t = 8 min it held 18 ℓ. Fraction filled = 18/58 = 9/29. (b) From 8 to 20 min (12 min) the level dropped from 18 to 0 with Tap E adding water. Tap D's outflow rate (first 8 min) = (58 − 18)/8 = 5 ℓ/min. In the last 12 min the net drop = 18 ℓ, so net rate = 1.5 ℓ/min out; Tap E adds = 5 − 1.5 = 3.5 ℓ/min.",
      "hints": ["Read the volumes at t = 0 and t = 8 min for part (a).", "Find Tap D's outflow rate, then use the net rate after Tap E opens for part (b)."],
      "source": "Rosyth 2022 P6 Prelim P2 Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q44.png",
      "image_page": 33,
      "image_bbox": [0.14, 0.18, 0.74, 0.42],
      "image_loc": "upper part of page, line graph of volume of water in tank vs time (0-20 min)",
      "notes": "Answer key: (a) 18/58 = 9/29; (b) 18÷12 = 1.5; E → 5 − 1.5 = 3.5 ℓ/min. Part (a) answer is a fraction kept here as a single blank (ratio-style); downstream may prefer MCQ — flagged."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "In the figure, PQST is a rhombus and QRS is a triangle. TSR is a straight line and TS = SR. With \\(\\angle QST = 70°\\)... actually the angle at S inside is 70°.<br>(a) Find \\(\\angle QRS. [?]°<br>(b) Find \\(\\angle PTQ. [?]°",
      "answer0": "55",
      "answer1": "35",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "(a) \\(\\angle QSR = 180° - 70° = 110°\\) (angles on the straight line TSR). With TS = SR... using triangle QSR isosceles, \\(\\angle QRS = (180° - 70°) \\div 2 = 55°\\). (b) In the rhombus, \\(\\angle PTQ = 70° \\div 2 = 35°\\) (diagonal bisects the angle).",
      "hints": ["Use the straight line TSR and the isosceles triangle QSR for part (a).", "A rhombus diagonal bisects the vertex angle for part (b)."],
      "source": "Rosyth 2022 P6 Prelim P2 Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q45.png",
      "image_page": 34,
      "image_bbox": [0.20, 0.14, 0.66, 0.34],
      "image_loc": "upper part of page, rhombus PQST with triangle QRS, straight line TSR, 70° at S",
      "notes": "Answer key: (a) ∠QRS = (180−70)÷2 = 55°; (b) ∠PTQ = 70÷2 = 35°."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "At a shop, pens were only sold in boxes. A box of 6 ballpoint pens cost $1.80 and a box of 4 gel pens cost $6.40.<br>(a) Sam spent $10 to buy both types of pens. Find the least total number of ballpoint pens and gel pens bought by Sam. [?]<br>(b) Tom bought 22 more gel pens than ballpoint pens. The total number of pens he bought was more than 40 but fewer than 60. How many pens did Tom buy altogether? [?]",
      "answer0": "16",
      "answer1": "58",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "(a) Ballpoint box = $1.80 (6 pens), gel box = $6.40 (4 pens). To spend exactly $10 on both with the least total pens, buy 2 ballpoint boxes ($3.60, 12 pens)... key: 1 gel box ($6.40, 4 pens) + ballpoint boxes for the rest. The least total works out to 16 pens. (b) Gel pens come in 4s and ballpoint in 6s; 22 more gel than ballpoint, total between 40 and 60. The valid solution: 40 gel pens (10 boxes) and 18 ballpoint pens (3 boxes), total = 58.",
      "hints": ["For (a), use whole boxes of each type summing to exactly $10, minimising pens.", "For (b), gel = ballpoint + 22; both must be whole boxes (4s and 6s) with total 40-60."],
      "source": "Rosyth 2022 P6 Prelim P2 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: (a) 4 gel + 6+6+... = 16 pens; (b) 10 gel boxes = 40 gel pens, ballpoint = 40−22 = 18, total = 58."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "In January, a kindergarten was given a total sum of $2400. It spent 80% of the sum of money on books and the rest on stationery. In February, the sum given to the kindergarten was increased. It increased its spending on books by $240. It spent the remaining 20% of the sum given in February on stationery.<br>(a) How much did the kindergarten spend on stationery in January? [?]<br>(b) What was the percentage increase in the sum of money spent on stationery in February? [?] %",
      "answer0": "480",
      "answer1": "12.5",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 175,
      "difficulty_id": 3,
      "explanation": "(a) January stationery = 20% of $2400 = $480. (b) January books = 80% = $1920. February books = 1920 + 240 = $2160, which is 80% of February's sum, so February sum = 2160 ÷ 0.8 = $2700; February stationery = 20% = $540. Percentage increase in stationery = (540 − 480)/480 × 100 = 60/480 × 100 = 12.5%.",
      "hints": ["January stationery is 20% of $2400.", "Find February's total from the increased book spending (still 80%), then its 20% stationery, and the percentage increase."],
      "source": "Rosyth 2022 P6 Prelim P2 Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: (a) 10% = 240, stationery 20% = $480; (b) Feb books 1920+240 = 2160; 2160 ÷ 4 = 540 (stationery); %increase = 60/480 × 100 = 12.5%."
    }
  ]
}