{
  "paper": {
    "school": "Rosyth",
    "year": 2023,
    "level": "P5",
    "label": "End-of-Year Exam",
    "source_prefix": "Rosyth 2023 P5 End-of-Year Exam",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "What is the value of \\(33 - (6 + 12) \\div 3\\)?",
      "answer0": "5",
      "answer1": "13",
      "answer2": "27",
      "answer3": "31",
      "correct_answer": 2,
      "skill_id": 155,
      "difficulty_id": 1,
      "explanation": "Work brackets first, then division, then subtraction. \\((6+12)=18\\); \\(18\\div3=6\\); \\(33-6=27\\).",
      "hints": ["Do the brackets first.", "Then divide before you subtract."],
      "source": "Rosyth 2023 P5 End-of-Year Exam Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Order of operations. Key: option 3 (27)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "What is the value of the digit 2 in 10 245?",
      "answer0": "20",
      "answer1": "200",
      "answer2": "2000",
      "answer3": "20 000",
      "correct_answer": 1,
      "skill_id": 149,
      "difficulty_id": 1,
      "explanation": "In 10 245 the digit 2 is in the hundreds place, so its value is \\(2 \\times 100 = 200\\).",
      "hints": ["Which place is the 2 in?", "It is the hundreds digit."],
      "source": "Rosyth 2023 P5 End-of-Year Exam Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Place value. Key: option 2 (200)."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "In the scale, what is the value of M?",
      "answer0": "5.3",
      "answer1": "5.6",
      "answer2": "5.03",
      "answer3": "5.06",
      "correct_answer": 3,
      "skill_id": 158,
      "difficulty_id": 2,
      "explanation": "Between 5.0 and the next mark each interval is 0.02 (the major marks 4.8, 4.9, 5.0 are split into 5 small parts of 0.02). M is 3 small marks past 5.0, so \\(5.0 + 3 \\times 0.02 = 5.06\\).",
      "hints": ["Find the size of one small interval.", "Count the small marks from 5.0 to M."],
      "source": "Rosyth 2023 P5 End-of-Year Exam Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q3.png",
      "image_page": 2,
      "image_bbox": [0.08, 0.62, 0.95, 0.73],
      "image_loc": "number-line scale across the page below the question, marks at 4.8, 4.9, 5.0 with arrow at M",
      "notes": "Key: option 4 (5.06)."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "The ratio of the shaded area of the circle to the unshaded area of the circle is 1 : 4. Which of the figures represents the given ratio?",
      "answer0": "A",
      "answer1": "B",
      "answer2": "C",
      "answer3": "D",
      "correct_answer": 3,
      "skill_id": 177,
      "difficulty_id": 2,
      "explanation": "Ratio shaded : unshaded = 1 : 4 means 1 of every 5 equal parts is shaded. Figure D is divided into 5 equal parts with 1 shaded, so shaded : unshaded = 1 : 4.",
      "hints": ["1 : 4 means 1 out of 5 parts is shaded.", "Find the circle split into 5 equal parts with 1 shaded."],
      "source": "Rosyth 2023 P5 End-of-Year Exam Q4",
      "image_needed": true,
      "image_options": true,
      "image_file": null,
      "image_page": 3,
      "image_bbox": [0.05, 0.15, 0.95, 0.32],
      "image_loc": "four circles A, B, C, D in a row near top of page; each is a labelled option image",
      "notes": "Image-option MCQ; crop each circle to q4_opt0..q4_opt3. Key: option 4 (D)."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "AB and CD are straight lines. Which two angles are equal?",
      "answer0": "\\(\\angle x\\) and \\(\\angle y\\)",
      "answer1": "\\(\\angle x\\) and \\(\\angle z\\)",
      "answer2": "\\(\\angle w\\) and \\(\\angle y\\)",
      "answer3": "\\(\\angle w\\) and \\(\\angle z\\)",
      "correct_answer": 3,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "Where two straight lines cross, vertically opposite angles are equal. \\(\\angle w\\) and \\(\\angle z\\) are vertically opposite, so they are equal.",
      "hints": ["Look for vertically opposite angles.", "They sit directly across the crossing point."],
      "source": "Rosyth 2023 P5 End-of-Year Exam Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q5.png",
      "image_page": 3,
      "image_bbox": [0.22, 0.45, 0.85, 0.58],
      "image_loc": "two crossing lines AB and CD with angles w, x, y, z marked at the intersection",
      "notes": "Vertically opposite angles. Key: option 4 (w and z)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "PQR is an equilateral triangle. Find \\(\\angle a\\).",
      "answer0": "100°",
      "answer1": "140°",
      "answer2": "260°",
      "answer3": "320°",
      "correct_answer": 2,
      "skill_id": 197,
      "difficulty_id": 2,
      "explanation": "Each angle of an equilateral triangle is 60°, so \\(\\angle QRP = 60°\\). At point R the angles around it total 360°. \\(\\angle a = 360° - 60° - 40° = 260°\\).",
      "hints": ["An equilateral triangle has all angles 60°.", "Angles at a point add up to 360°."],
      "source": "Rosyth 2023 P5 End-of-Year Exam Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q6.png",
      "image_page": 4,
      "image_bbox": [0.28, 0.14, 0.66, 0.36],
      "image_loc": "equilateral triangle PQR with a 40° angle and reflex angle a marked at R",
      "notes": "Angles at a point. Key: option 3 (260°)."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "The figure shows a right-angle triangle. Find the area of the triangle.",
      "answer0": "120 cm²",
      "answer1": "130 cm²",
      "answer2": "240 cm²",
      "answer3": "312 cm²",
      "correct_answer": 0,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "The two perpendicular sides are 24 cm and 10 cm (the 26 cm is the hypotenuse). Area \\(= \\dfrac{1}{2} \\times 24 \\times 10 = 120\\) cm².",
      "hints": ["Use the two sides that meet at the right angle.", "Area \\(= \\dfrac{1}{2} \\times \\text{base} \\times \\text{height}\\)."],
      "source": "Rosyth 2023 P5 End-of-Year Exam Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q7.png",
      "image_page": 4,
      "image_bbox": [0.28, 0.56, 0.66, 0.68],
      "image_loc": "right-angled triangle with sides 24 cm, 10 cm and base 26 cm",
      "notes": "Area of triangle; 26 cm is the hypotenuse, not a leg. Key: option 1 (120 cm²)."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "What fraction of the stars are shaded?",
      "answer0": "\\(\\dfrac{4}{9}\\)",
      "answer1": "\\(\\dfrac{5}{9}\\)",
      "answer2": "\\(\\dfrac{1}{2}\\)",
      "answer3": "\\(\\dfrac{4}{5}\\)",
      "correct_answer": 1,
      "skill_id": 157,
      "difficulty_id": 1,
      "explanation": "There are 9 stars in all, of which 5 are shaded. So the fraction shaded is \\(\\dfrac{5}{9}\\).",
      "hints": ["Count all the stars.", "Count how many are shaded, then write shaded over total."],
      "source": "Rosyth 2023 P5 End-of-Year Exam Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 5,
      "image_bbox": [0.55, 0.13, 0.95, 0.22],
      "image_loc": "row of 9 stars (5 shaded, 4 unshaded) in a box to the right of the question",
      "notes": "Count to verify: 9 stars total, 5 shaded. Key: option 2 (5/9)."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "Jon had 200 stickers. He gave 90 stickers to his friend. What percentage of his stickers did Jon give to his friend?",
      "answer0": "10%",
      "answer1": "45%",
      "answer2": "55%",
      "answer3": "90%",
      "correct_answer": 1,
      "skill_id": 171,
      "difficulty_id": 1,
      "explanation": "Fraction given \\(= \\dfrac{90}{200}\\). As a percentage \\(= \\dfrac{90}{200} \\times 100\\% = 45\\%\\).",
      "hints": ["Write what he gave as a fraction of the total.", "Multiply by 100 to get a percentage."],
      "source": "Rosyth 2023 P5 End-of-Year Exam Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Percentage of a whole. Key: option 2 (45%)."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "The total marks obtained by 4 students is 60. What is the average number of marks obtained by the 4 students?",
      "answer0": "15",
      "answer1": "56",
      "answer2": "64",
      "answer3": "240",
      "correct_answer": 0,
      "skill_id": 203,
      "difficulty_id": 1,
      "explanation": "Average \\(= \\dfrac{\\text{total}}{\\text{number of items}} = \\dfrac{60}{4} = 15\\).",
      "hints": ["Average = total ÷ number of items.", "Divide 60 by 4."],
      "source": "Rosyth 2023 P5 End-of-Year Exam Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Average. Key: option 1 (15)."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "Each box had a mass of 10 kg 8 g. Find the total mass of the 7 boxes.",
      "answer0": "756 kg",
      "answer1": "75.6 kg",
      "answer2": "70.56 kg",
      "answer3": "70.056 kg",
      "correct_answer": 3,
      "skill_id": 184,
      "difficulty_id": 2,
      "explanation": "10 kg 8 g \\(= 10.008\\) kg. Total \\(= 10.008 \\times 7 = 70.056\\) kg.",
      "hints": ["Convert 10 kg 8 g to kilograms: 8 g = 0.008 kg.", "Multiply by 7."],
      "source": "Rosyth 2023 P5 End-of-Year Exam Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q11.png",
      "image_page": 6,
      "image_bbox": [0.30, 0.13, 0.62, 0.24],
      "image_loc": "diagram of 7 stacked boxes near top of page",
      "notes": "Mass unit conversion; figure is decorative (7 boxes). 8 g = 0.008 kg. Key: option 4 (70.056 kg)."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "Ken saved \\(\\dfrac{1}{4}\\) of his allowance and spent \\(\\dfrac{3}{5}\\) of the remaining allowance on food. He had $72 left. How much was his allowance?",
      "answer0": "$120",
      "answer1": "$180",
      "answer2": "$240",
      "answer3": "$480",
      "correct_answer": 2,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Remaining after saving \\(= \\dfrac{3}{4}\\). He spent \\(\\dfrac{3}{5}\\) of that on food, leaving \\(\\dfrac{2}{5}\\) of the remainder. So $72 \\(= \\dfrac{2}{5} \\times \\dfrac{3}{4}\\) of allowance \\(= \\dfrac{6}{20} = \\dfrac{3}{10}\\) of allowance. Allowance \\(= 72 \\div \\dfrac{3}{10} = 72 \\times \\dfrac{10}{3} = \\$240\\).",
      "hints": ["After saving 1/4, three-quarters is left.", "Two-fifths of the remainder = $72."],
      "source": "Rosyth 2023 P5 End-of-Year Exam Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Fraction word problem. Key: option 3 ($240)."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "The figure shows 3 identical squares and a triangle. The area of each square is 36 cm². Find the area of the figure.",
      "answer0": "324 cm²",
      "answer1": "378 cm²",
      "answer2": "468 cm²",
      "answer3": "558 cm²",
      "correct_answer": 0,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Each square has area 36 cm², so side \\(= 6\\) cm and 3 stacked squares give a height of 18 cm. The triangle has base 30 cm and height 18 cm. Total area \\(= 3 \\times 36 + \\dfrac{1}{2} \\times 30 \\times 18 = 108 + 270 = 378\\) cm². The printed key gives option 1 (324 cm²); flagged.",
      "hints": ["Side of each square \\(= \\sqrt{36} = 6\\) cm.", "Triangle area \\(= \\dfrac{1}{2} \\times \\text{base} \\times \\text{height}\\)."],
      "source": "Rosyth 2023 P5 End-of-Year Exam Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q13.png",
      "image_page": 7,
      "image_bbox": [0.34, 0.18, 0.68, 0.36],
      "image_loc": "three stacked squares on the left with a right triangle (hypotenuse 30 cm, base 30 cm) to the right",
      "notes": "Printed key marks option 1 (324 cm²). Worked area is 378 cm² (option 2) using base 30 / height 18. Left as keyed (correct_answer 0) per the official answer; geometry ambiguity flagged — diagram not to scale, dimensions may differ from worked interpretation."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "Matthew had $25 more than Amy. When Amy gave Matthew $20, Matthew had 6 times as much money as Amy. How much money did Amy have at first?",
      "answer0": "$29",
      "answer1": "$33",
      "answer2": "$78",
      "answer3": "$108",
      "correct_answer": 1,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Let Amy have $a, so Matthew has $(a+25). After Amy gives $20: Matthew has $(a+45), Amy has $(a-20). Then \\(a+45 = 6(a-20)\\), so \\(a+45 = 6a-120\\), \\(165 = 5a\\), \\(a = 33\\). Amy had $33.",
      "hints": ["Write Matthew's amount as Amy's + $25.", "After the $20 move, Matthew = 6 × Amy."],
      "source": "Rosyth 2023 P5 End-of-Year Exam Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Before-after word problem. Key: option 2 ($33)."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "Ben shared a sum of money equally with Carla. To buy a present for their mother, Ben spent \\(\\dfrac{1}{6}\\) of his money and Carla spent $45 of her money. In the end, \\(\\dfrac{3}{4}\\) of the original sum of money was left. What was the original sum of money shared by Ben and Carla?",
      "answer0": "$135",
      "answer1": "$180",
      "answer2": "$270",
      "answer3": "$540",
      "correct_answer": 2,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Each had half the total, T/2. Together they spent \\(\\dfrac{1}{4}\\) of T (since \\(\\dfrac{3}{4}\\) is left), so total spent \\(= \\dfrac{T}{4}\\). Ben spent \\(\\dfrac{1}{6} \\times \\dfrac{T}{2} = \\dfrac{T}{12}\\); Carla spent $45. So \\(\\dfrac{T}{12} + 45 = \\dfrac{T}{4}\\). Then \\(45 = \\dfrac{T}{4} - \\dfrac{T}{12} = \\dfrac{2T}{12} = \\dfrac{T}{6}\\), giving \\(T = 270\\). Original sum was $270.",
      "hints": ["Each person started with half the total.", "Together they spent the quarter that is not left."],
      "source": "Rosyth 2023 P5 End-of-Year Exam Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Fraction word problem. Key: option 3 ($270)."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Express \\(3\\dfrac{7}{25}\\) as a decimal. [?]",
      "answer0": "3.28",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 158,
      "difficulty_id": 1,
      "explanation": "\\(\\dfrac{7}{25} = \\dfrac{28}{100} = 0.28\\), so \\(3\\dfrac{7}{25} = 3.28\\).",
      "hints": ["Make the denominator 100.", "\\(\\dfrac{7}{25} = \\dfrac{28}{100}\\)."],
      "source": "Rosyth 2023 P5 End-of-Year Exam Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer is a decimal (3.28) so FIB. Key: 3.28."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "Find the value of \\(24 \\times 400\\). [?]",
      "answer0": "9600",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 151,
      "difficulty_id": 1,
      "explanation": "\\(24 \\times 4 = 96\\), then \\(\\times 100 = 9600\\).",
      "hints": ["Multiply 24 by 4 first.", "Then multiply by 100."],
      "source": "Rosyth 2023 P5 End-of-Year Exam Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Multiplication by hundreds. Key: 9600."
    },
    {
      "n": 18,
      "type_id": 1,
      "question": "Find the value of \\(\\dfrac{1}{2} \\times \\dfrac{5}{8}\\).",
      "answer0": "\\(\\dfrac{5}{16}\\)",
      "answer1": "\\(\\dfrac{5}{10}\\)",
      "answer2": "\\(\\dfrac{6}{16}\\)",
      "answer3": "\\(\\dfrac{1}{4}\\)",
      "correct_answer": 0,
      "skill_id": 161,
      "difficulty_id": 1,
      "explanation": "Multiply numerators and denominators: \\(\\dfrac{1}{2} \\times \\dfrac{5}{8} = \\dfrac{1 \\times 5}{2 \\times 8} = \\dfrac{5}{16}\\).",
      "hints": ["Multiply the top numbers together.", "Multiply the bottom numbers together."],
      "source": "Rosyth 2023 P5 End-of-Year Exam Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer is a fraction (5/16) so MCQ per spec. Key: 5/16 = option 1; distractors plausible."
    },
    {
      "n": 19,
      "type_id": 1,
      "question": "Which line in the square grid is parallel to AF?",
      "answer0": "AB",
      "answer1": "BC",
      "answer2": "CD",
      "answer3": "BE",
      "correct_answer": 2,
      "skill_id": 199,
      "difficulty_id": 2,
      "explanation": "AF rises 1 unit for every 2 across. CD has the same slope (1 unit down for every 2 across, same gradient), so CD is parallel to AF.",
      "hints": ["Compare the slope (steepness) of each line to AF.", "Parallel lines have the same gradient on the grid."],
      "source": "Rosyth 2023 P5 End-of-Year Exam Q19",
      "image_needed": true,
      "image_options": false,
      "image_file": "q19.png",
      "image_page": 11,
      "image_bbox": [0.14, 0.07, 0.62, 0.27],
      "image_loc": "square grid with points A, B, C, D, E, F joined by line segments",
      "notes": "Answer is a line label (CD) — made MCQ. Key: CD."
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "PQRS is a rectangle. Find \\(\\angle a\\). [?]",
      "answer0": "40",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 200,
      "difficulty_id": 2,
      "explanation": "PQ is parallel to SR. The lines from S make angles 12° and 38° at Q with QR. \\(\\angle a\\) is the angle at Q between PQ and the line, equal to 90° − 38° − 12° = 40° (since the right angle PQR is split). \\(\\angle a = 40°\\).",
      "hints": ["Angle PQR in a rectangle is 90°.", "Subtract the two marked angles 38° and 12°."],
      "source": "Rosyth 2023 P5 End-of-Year Exam Q20",
      "image_needed": true,
      "image_options": false,
      "image_file": "q20.png",
      "image_page": 11,
      "image_bbox": [0.28, 0.40, 0.62, 0.62],
      "image_loc": "rectangle PQRS with two lines from S to corner Q marking 38° and 12°, angle a at top",
      "notes": "Answer is a plain number of degrees (unit ° is in the stem) so FIB. Key: 40°."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "Two cups and a jug contain 2.33 litres of water. The volume of water in each cup is the same. The volume of water in one cup is 1.61 litres less than the volume of water in the jug. Find the volume of water in each cup. [?]",
      "answer0": "0.24",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 2,
      "explanation": "Let each cup hold c litres. Jug \\(= c + 1.61\\). Total: \\(c + c + (c + 1.61) = 2.33\\), so \\(3c = 0.72\\), \\(c = 0.24\\). Each cup holds 0.24 litres.",
      "hints": ["Write the jug's volume as a cup plus 1.61 L.", "Add the three volumes to make 2.33 L."],
      "source": "Rosyth 2023 P5 End-of-Year Exam Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer in litres (decimal) so FIB; unit 'litres' stated in stem. Key: 0.24 ℓ."
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "Jill had $400. She spent 20% of her money on books. How much money did Jill spend on books? [?]",
      "answer0": "80",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 174,
      "difficulty_id": 1,
      "explanation": "20% of $400 \\(= \\dfrac{20}{100} \\times 400 = \\$80\\).",
      "hints": ["20% means 20 out of 100.", "Find 20% of $400."],
      "source": "Rosyth 2023 P5 End-of-Year Exam Q22",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Money answer (decimal/whole) so FIB; $ sign printed before blank. Key: $80."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "The table shows the number of blue pens and red pens in 4 boxes. Box A: 17 red, 12 blue. Box B: 10 red, 18 blue. Box C: 13 red, 12 blue. Box D: 11 red, 15 blue.<br>(a) Which coloured pen has a greater number? [?]<br>(b) All the pens are repacked such that each box contained the same number of pens. How many pens are there in each box now? [?]",
      "answer0": "Blue",
      "answer1": "27",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 203,
      "difficulty_id": 2,
      "explanation": "(a) Total red \\(= 17+10+13+11 = 51\\); total blue \\(= 12+18+12+15 = 57\\). Blue has more. (b) Total pens \\(= 51 + 57 = 108\\); shared into 4 boxes \\(= 108 \\div 4 = 27\\) per box.",
      "hints": ["Add up all the red, then all the blue.", "Total pens ÷ 4 boxes for part (b)."],
      "source": "Rosyth 2023 P5 End-of-Year Exam Q23",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Part (a) is a colour word — but it is a definite two-choice value transcribed into the table text; kept as FIB with answer 'Blue'. Part (b) numeric. Key: (a) Blue, (b) 27. Table data inlined into stem (no figure crop needed)."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "A box of toys was shared equally among 10 children. 3 of them gave all of their toys to the rest of the children. As a result, the rest of the children received 6 more toys each. How many toys were there in the box? [?]",
      "answer0": "140",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "The 3 children's toys were shared among the remaining 7, giving them 6 more each: \\(3 \\times s = 7 \\times 6 = 42\\), where s is each child's original share. So \\(s = 14\\). Total toys \\(= 10 \\times 14 = 140\\).",
      "hints": ["The 3 children's toys went to the other 7.", "7 children × 6 extra = the toys given up."],
      "source": "Rosyth 2023 P5 End-of-Year Exam Q24",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Word problem. Key: 140."
    },
    {
      "n": 25,
      "type_id": 0,
      "question": "The figure shows a line AB drawn on a grid. ABX is an isosceles triangle. ∠ABX is 90° and AB = BX. Draw and label triangle ABX on the grid.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 201,
      "difficulty_id": 2,
      "explanation": "From B, draw BX perpendicular to AB (∠ABX = 90°) and equal in length to AB, then join A to X. The key shows X placed below B so that triangle ABX is a right isosceles triangle.",
      "hints": [],
      "source": "Rosyth 2023 P5 End-of-Year Exam Q25",
      "image_needed": true,
      "image_options": false,
      "image_file": "q25.png",
      "image_page": 14,
      "image_bbox": [0.22, 0.36, 0.62, 0.52],
      "image_loc": "dot grid with line AB drawn (A lower-left, B upper-right of the segment)",
      "notes": "Draw-on-grid construction task — no app question type, type_id 0 (skipped on insert). Key answer: drawn triangle with X below, right angle at B, AB = BX."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "There are 248 marbles in a box. The ratio of the number of red marbles to the number of blue marbles is 3 : 1. The rest of the 60 marbles are green. How many blue marbles are there in the box? [?]",
      "answer0": "47",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 2,
      "explanation": "Non-green marbles \\(= 248 - 60 = 188\\). These split red : blue \\(= 3 : 1\\), i.e. 4 units \\(= 188\\), so 1 unit \\(= 47\\). Blue \\(= 1\\) unit \\(= 47\\).",
      "hints": ["Take away the 60 green marbles first.", "The rest is 4 equal units (3 red + 1 blue)."],
      "source": "Rosyth 2023 P5 End-of-Year Exam Q26",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Ratio word problem. Key: 47."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "PQRS is a parallelogram and NRS is an equilateral triangle. ST is a straight line. Find \\(\\angle PST\\). [?]",
      "answer0": "15",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 200,
      "difficulty_id": 3,
      "explanation": "In parallelogram PQRS, \\(\\angle PSR = 180° - 105° = 75°\\) (co-interior with \\(\\angle SPQ\\)... ). NRS is equilateral so \\(\\angle NSR = 60°\\). \\(\\angle PST = \\angle PSR - \\angle NSR = 75° - 60° = 15°\\).",
      "hints": ["Find ∠PSR using the parallelogram angle.", "Subtract the 60° angle of the equilateral triangle."],
      "source": "Rosyth 2023 P5 End-of-Year Exam Q27",
      "image_needed": true,
      "image_options": false,
      "image_file": "q27.png",
      "image_page": 15,
      "image_bbox": [0.12, 0.42, 0.42, 0.66],
      "image_loc": "parallelogram PQRS with equilateral triangle NRS inside, T on PQ, 105° marked at P",
      "notes": "Answer is plain degrees (° in stem) so FIB. Key: 15°."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "The diagram shows triangles P, Q and R on a grid.<br>Arrange the triangles from the smallest area to the biggest area. [?] , [?] , [?]",
      "answer0": "P",
      "answer1": "R",
      "answer2": "Q",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "Counting grid squares: triangle P (long thin) has the smallest area, R next, and Q the largest. Order smallest to biggest: P, R, Q.",
      "hints": ["Use base × height ÷ 2 by counting grid units.", "Compare the three areas and order them."],
      "source": "Rosyth 2023 P5 End-of-Year Exam Q28",
      "image_needed": true,
      "image_options": false,
      "image_file": "q28.png",
      "image_page": 16,
      "image_bbox": [0.10, 0.06, 0.66, 0.26],
      "image_loc": "grid showing three triangles labelled P (top), Q (right), R (lower-left)",
      "notes": "Ordering task → FIB with one [?] per position. Key order: P, R, Q."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "The figure is made up of squares. The area of the smallest square is 4 cm². The area of the biggest square is 81 cm². Find the area of the figure. [?]",
      "answer0": "134",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Smallest square side \\(= \\sqrt{4} = 2\\) cm; biggest square side \\(= \\sqrt{81} = 9\\) cm. The figure is built from squares whose total area sums to 134 cm² (per the printed key). Ans: 134 cm².",
      "hints": ["Side of smallest square \\(= \\sqrt{4}\\); biggest \\(= \\sqrt{81}\\).", "Add the areas of the squares making the figure."],
      "source": "Rosyth 2023 P5 End-of-Year Exam Q29",
      "image_needed": true,
      "image_options": false,
      "image_file": "q29.png",
      "image_page": 16,
      "image_bbox": [0.26, 0.55, 0.50, 0.68],
      "image_loc": "stepped figure made up of differently sized squares (small square at top-right, larger ones at left)",
      "notes": "Answer cm² whole number so FIB; unit cm² printed after blank. Key: 134 cm²."
    },
    {
      "n": 30,
      "type_id": 2,
      "question": "Ron cut a piece of paper into the shape of an isosceles right-angled triangle ABC, where AB = BC. He folded the triangle along the dotted lines DE & DH. Find \\(\\angle x\\). [?]",
      "answer0": "70",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "ABC is isosceles right-angled with the right angle at B, so \\(\\angle A = \\angle C = 45°\\). After folding, the angles at D about the line BC, together with the folded angles 40° (at E side) and the 120° marked, give \\(\\angle x = 70°\\) (the angle between the two folded flaps at D).",
      "hints": ["Base angles of the isosceles right triangle are 45° each.", "Angles on the straight line BC at D add to 180°."],
      "source": "Rosyth 2023 P5 End-of-Year Exam Q30",
      "image_needed": true,
      "image_options": false,
      "image_file": "q30.png",
      "image_page": 17,
      "image_bbox": [0.08, 0.13, 0.92, 0.34],
      "image_loc": "two diagrams: original right triangle ABC with fold lines DE & DH, and the folded result showing 40°, 120° and angle x at D",
      "notes": "Answer plain degrees (° in stem) so FIB. Key: 70°."
    }
  ]
}