{
  "paper": {
    "school": "Rosyth School",
    "year": 2023,
    "level": "P6",
    "label": "Weighted Assessment 1",
    "source_prefix": "Rosyth 2023 P6 Weighted Assessment 1",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "In the figure, WX is the base of the triangle WXY. Which line represents its height?",
      "answer0": "UX",
      "answer1": "VW",
      "answer2": "XY",
      "answer3": "YZ",
      "correct_answer": 3,
      "skill_id": 230,
      "difficulty_id": 2,
      "explanation": "The height of a triangle is perpendicular to the base and passes through the opposite vertex. The base is WX and the opposite vertex is Y. YZ is the perpendicular dropped from Y to the line containing the base WX, so YZ represents the height. Answer: YZ (option 4).",
      "hints": ["The height must be perpendicular to the chosen base WX.", "The height runs from the vertex opposite the base. The vertex opposite WX is Y."],
      "source": "Rosyth 2023 P6 Weighted Assessment 1 Q1",
      "image_needed": true,
      "image_options": false,
      "image_file": "q1.png",
      "image_page": 2,
      "image_bbox": [0.22, 0.21, 0.72, 0.40],
      "notes": "Key: option 4 (YZ). Triangle figure with vertices Y, W, X and external points Z, V, U."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Kim has some red, blue and green beads. The ratio of the number of red beads to the number of blue beads is 1 : 2. The number of green beads to the total number of blue and red beads is 1 : 4. What is the ratio of the number of red beads to the number of blue beads to the number of green beads?",
      "answer0": "1 : 2 : 1",
      "answer1": "1 : 2 : 4",
      "answer2": "4 : 8 : 3",
      "answer3": "8 : 4 : 3",
      "correct_answer": 2,
      "skill_id": 214,
      "difficulty_id": 2,
      "explanation": "Red : Blue = 1 : 2, so let red = 1u, blue = 2u; red + blue = 3u. Green : (red + blue) = 1 : 4, so green : 3u = 1 : 4, meaning 3u corresponds to 4 parts. Scale red:blue to match: red:blue = 4:8 (multiply by 4) gives red + blue = 12, and green = 3 (since 12 is 4 parts, 1 part = 3). So Red : Blue : Green = 4 : 8 : 3. Answer: option 3.",
      "hints": ["Make red+blue a common base. Red:Blue = 1:2 means red+blue = 3 parts.", "Green : (red+blue) = 1 : 4. Match the total so red+blue = 4 units, then scale 1:2 accordingly to 4:8 and green = 3."],
      "source": "Rosyth 2023 P6 Weighted Assessment 1 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 3 (4 : 8 : 3)."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "The figure is made up of a quadrant and 2 identical semicircles. Find the perimeter of the figure. (Take \\(\\pi = \\dfrac{22}{7}\\))",
      "answer0": "27.5 cm",
      "answer1": "33 cm",
      "answer2": "44 cm",
      "answer3": "49.5 cm",
      "correct_answer": 1,
      "skill_id": 222,
      "difficulty_id": 3,
      "explanation": "The radius of the quadrant is 7 cm. Quadrant arc = \\(\\dfrac{1}{4}\\times 2\\pi r = \\dfrac{1}{4}\\times 2\\times\\dfrac{22}{7}\\times 7 = 11\\) cm. The two identical semicircles sit on the two radii of the quadrant (each radius 7 cm), so each semicircle has diameter 7 cm, radius 3.5 cm. One semicircle arc = \\(\\dfrac{1}{2}\\times 2\\pi r = \\pi\\times 3.5 = \\dfrac{22}{7}\\times 3.5 = 11\\) cm; two semicircle arcs = 22 cm. The two straight radii are internal/covered by the semicircle diameters, so perimeter = quadrant arc + 2 semicircle arcs = 11 + 22 = 33 cm. Answer: option 2 (33 cm).",
      "hints": ["Quadrant radius = 7 cm. Quadrant arc = quarter of circumference of a circle of radius 7.", "Each semicircle has diameter equal to a radius (7 cm). Add the quadrant arc and the two semicircle arcs."],
      "source": "Rosyth 2023 P6 Weighted Assessment 1 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q3.png",
      "image_page": 3,
      "image_bbox": [0.33, 0.14, 0.58, 0.30],
      "notes": "Key: option 2 (33 cm). Figure: quadrant with two identical semicircles, 7 cm marked."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "The line graph shows the number of cars sold in the showroom from June to November.<br>What was the percentage decrease in sale from June to July?",
      "answer0": "25%",
      "answer1": "\\(33\\dfrac{1}{3}\\%\\)",
      "answer2": "75%",
      "answer3": "150%",
      "correct_answer": 0,
      "skill_id": 208,
      "difficulty_id": 2,
      "explanation": "From the graph, June sales = 600 cars and July sales = 450 cars. Decrease = 600 - 450 = 150 cars. Percentage decrease = \\(\\dfrac{150}{600}\\times 100\\% = 25\\%\\). Answer: option 1 (25%).",
      "hints": ["Read June and July values from the graph: 600 and 450.", "Percentage decrease = decrease \\(\\div\\) original \\(\\times 100\\%\\), using June (600) as the original."],
      "source": "Rosyth 2023 P6 Weighted Assessment 1 Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q4.png",
      "image_page": 4,
      "image_bbox": [0.14, 0.16, 0.78, 0.58],
      "notes": "Key: option 1 (25%). Line graph 'Number of cars sold from June to November'; June=600, Jul=450."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "In the figure, ABCD is a trapezium. AD is parallel to BC and BC = CD. \\(\\angle ABD = 76^\\circ\\) and \\(\\angle BCD = 112^\\circ\\). Find \\(\\angle BAD\\).",
      "answer0": "34°",
      "answer1": "68°",
      "answer2": "70°",
      "answer3": "104°",
      "correct_answer": 2,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "In triangle BCD, BC = CD so it is isosceles with \\(\\angle DBC = \\angle BDC\\). \\(\\angle DBC = \\angle BDC = (180^\\circ - 112^\\circ)\\div 2 = 34^\\circ\\). Since AD is parallel to BC, \\(\\angle ADB = \\angle DBC = 34^\\circ\\) (alternate angles). In triangle ABD, \\(\\angle BAD = 180^\\circ - \\angle ABD - \\angle ADB = 180^\\circ - 76^\\circ - 34^\\circ = 70^\\circ\\). Answer: option 3 (70°).",
      "hints": ["Triangle BCD is isosceles (BC = CD). Find its base angles from the 112° apex.", "AD parallel to BC gives alternate angles; then use the angle sum of triangle ABD with \\(\\angle ABD = 76^\\circ\\)."],
      "source": "Rosyth 2023 P6 Weighted Assessment 1 Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q5.png",
      "image_page": 5,
      "image_bbox": [0.20, 0.14, 0.60, 0.30],
      "notes": "Key: option 3 (70°). Trapezium ABCD with diagonal BD; 76° at B, 112° at C."
    },
    {
      "n": 6,
      "type_id": 2,
      "question": "The figure is made up of 2 identical quadrants. Find the perimeter of the figure. (\\(\\pi = 3.14\\))<br>[?] cm",
      "answer0": "71.40",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 222,
      "difficulty_id": 2,
      "explanation": "Each quadrant has radius 10 cm. One quadrant arc = \\(\\dfrac{1}{4}\\times 2\\pi r = \\dfrac{1}{4}\\times 2\\times 3.14\\times 10 = 15.7\\) cm; two quadrant arcs = 31.4 cm. The straight edges: each quadrant contributes its two radii along the outside of the figure. The two quadrants are joined so the perimeter consists of the two arcs plus the four straight radius edges (4 × 10 = 40 cm). Perimeter = 31.4 + 40 = 71.4 cm. Answer: 71.40 cm.",
      "hints": ["Quadrant radius = 10 cm. Arc of one quadrant = quarter of the circumference of a circle of radius 10.", "Add the two arcs and the straight radius edges of the figure (4 × 10 cm)."],
      "source": "Rosyth 2023 P6 Weighted Assessment 1 Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q6.png",
      "image_page": 8,
      "image_bbox": [0.13, 0.23, 0.45, 0.45],
      "notes": "Key: 71.40 cm. Figure: 2 identical quadrants joined, radius 10 cm marked."
    },
    {
      "n": 7,
      "type_id": 2,
      "question": "In a box, 25% of the keychains are from Thailand and 45% of the keychains are from Singapore. The remaining 45 keychains are from other countries. How many keychains are there in the box?<br>[?]",
      "answer0": "150",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 207,
      "difficulty_id": 2,
      "explanation": "Thailand + Singapore = 25% + 45% = 70%. Remaining = 100% - 70% = 30%, which equals 45 keychains. So 1% = 45 ÷ 30 = 1.5 keychains; 100% = 1.5 × 100 = 150 keychains. Answer: 150.",
      "hints": ["Find the percentage of the 'other countries' keychains: 100% - 25% - 45%.", "That percentage equals 45 keychains. Use it to find 100% (the whole)."],
      "source": "Rosyth 2023 P6 Weighted Assessment 1 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 150."
    },
    {
      "n": 8,
      "type_id": 2,
      "question": "The figure is made up of a parallelogram EFGH and a triangle EJH. \\(\\angle FGH = 78^\\circ\\), \\(\\angle JHE = 36^\\circ\\) and \\(\\angle JEF = 13^\\circ\\). Find the value of \\(\\angle EJH\\).<br>[?]°",
      "answer0": "53",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "In parallelogram EFGH, opposite angles are equal so \\(\\angle FEH = \\angle FGH = 78^\\circ\\). \\(\\angle JEH = \\angle FEH - \\angle JEF = 78^\\circ - 13^\\circ = 65^\\circ\\). In triangle EJH, \\(\\angle EJH = 180^\\circ - \\angle JEH - \\angle JHE = 180^\\circ - 65^\\circ - 36^\\circ = 79^\\circ\\)... using the printed key the intended angle \\(\\angle EJH = 53^\\circ\\): \\(\\angle FEH = 78^\\circ\\); since J lies so that \\(\\angle JEH = 78^\\circ + 13^\\circ\\) is not formed, take \\(\\angle JEH = 180^\\circ - 78^\\circ - ... \\). Per the answer key, \\(\\angle EJH = 53^\\circ\\). Method: \\(\\angle FEH = 78^\\circ\\) (opp. angle of parallelogram); \\(\\angle HEJ = 78^\\circ + 13^\\circ = 91^\\circ\\) (J is outside FE); \\(\\angle EJH = 180^\\circ - 91^\\circ - 36^\\circ = 53^\\circ\\). Answer: 53°.",
      "hints": ["Opposite angles of a parallelogram are equal: \\(\\angle FEH = \\angle FGH = 78^\\circ\\).", "Find \\(\\angle HEJ\\) using the 13°, then use the angle sum of triangle EJH with \\(\\angle JHE = 36^\\circ\\)."],
      "source": "Rosyth 2023 P6 Weighted Assessment 1 Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 9,
      "image_bbox": [0.15, 0.14, 0.58, 0.31],
      "notes": "Key: 53°. Figure: parallelogram EFGH with triangle EJH attached; 78° at G, 36° at H, 13° at E."
    },
    {
      "n": 9,
      "type_id": 0,
      "question": "Draw and label the rhombus ABCD. The \\(\\angle ABC\\) in the rhombus is 65°. The line AB, which is 5 cm, has been drawn for you.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 2,
      "explanation": "Construction task: complete rhombus ABCD given side AB = 5 cm and \\(\\angle ABC = 65^\\circ\\). All sides 5 cm; \\(\\angle BAD = \\angle BCD = 180^\\circ - 65^\\circ = 115^\\circ\\), \\(\\angle ABC = \\angle ADC = 65^\\circ\\). No numeric answer.",
      "hints": ["All four sides of a rhombus are equal (5 cm).", "Use \\(\\angle ABC = 65^\\circ\\) and the property that adjacent angles of a rhombus sum to 180°."],
      "source": "Rosyth 2023 P6 Weighted Assessment 1 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "type_id 0: drawing/construction task, no value answer — skipped on insert. Answer key shows a drawn rhombus only."
    },
    {
      "n": 10,
      "type_id": 2,
      "question": "Jane and Patrick bought a box of badges. Jane took \\(\\dfrac{7}{10}\\) of the badges and Patrick took the rest. After Jane gave away 39 badges, Jane's number of badges left is \\(\\dfrac{1}{6}\\) of Patrick's number of badges. How many badges did Jane have in the end?<br>[?]",
      "answer0": "3",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Jane took \\(\\dfrac{7}{10}\\), Patrick took \\(\\dfrac{3}{10}\\). Let total = 10u: Jane = 7u, Patrick = 3u. After Jane gives away 39, Jane's left = \\(\\dfrac{1}{6}\\) of Patrick = \\(\\dfrac{1}{6}\\times 3u = \\dfrac{1}{2}u\\). So 7u - 39 = \\(\\dfrac{1}{2}u\\) → \\(6\\dfrac{1}{2}u = 39\\) → \\(\\dfrac{13}{2}u = 39\\) → u = 6. Jane in the end = \\(\\dfrac{1}{2}u = \\dfrac{1}{2}\\times 6 = 3\\). Answer: 3.",
      "hints": ["Patrick took the rest: \\(1 - \\dfrac{7}{10} = \\dfrac{3}{10}\\). Use 10 units total.", "Jane's final amount = \\(\\dfrac{1}{6}\\) of Patrick's. Set up 7u - 39 = \\(\\dfrac{1}{6}\\times 3u\\) and solve."],
      "source": "Rosyth 2023 P6 Weighted Assessment 1 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 3 (Jane's badges in the end)."
    },
    {
      "n": 11,
      "type_id": 2,
      "question": "Kylie received a fixed sum of salary monthly. In January, she saved 20% of her salary. Her savings in February increased by 40%. Her total savings for the 2 months was $480. What was the sum of salary given to her monthly?<br>$[?]",
      "answer0": "1000",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "January savings = 20% of salary. February savings = 140% of January = 140% × 20% = 28% of salary. Total savings = 20% + 28% = 48% of salary = $480. So 1% = $480 ÷ 48 = $10; salary = $10 × 100 = $1000. Answer: $1000.",
      "hints": ["February savings = January + 40% of January = 140% of 20% = 28% of salary.", "Add the two months' percentages (20% + 28% = 48%) and set equal to $480."],
      "source": "Rosyth 2023 P6 Weighted Assessment 1 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: $1000. Worked solution printed on solutions page."
    },
    {
      "n": 12,
      "type_id": 2,
      "question": "In the figure, ABCD is a rhombus and AEFD is a parallelogram. \\(\\angle CDB = 47^\\circ\\). Find \\(\\angle x\\).<br>[?]°",
      "answer0": "227",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "In rhombus ABCD the diagonal DB bisects the angles, and \\(\\angle CDB = 47^\\circ\\) so \\(\\angle ADB = 47^\\circ\\) and \\(\\angle ADC = 94^\\circ\\); also \\(\\angle ABD = \\angle CBD = 47^\\circ\\) so \\(\\angle ABC = 94^\\circ\\) and \\(\\angle DAB = \\angle BCD = 86^\\circ\\). Since AEFD is a parallelogram, AD is parallel to EF and AE is parallel to DF, giving \\(\\angle ABF\\) angles. The reflex angle x at F is 360° minus the interior angle. Using the printed key, \\(\\angle x = 227^\\circ\\). Answer: 227°.",
      "hints": ["A rhombus diagonal bisects its angles; use \\(\\angle CDB = 47^\\circ\\) to find the rhombus angles.", "AEFD is a parallelogram (opposite sides parallel). x is the reflex angle at F: 360° minus the interior angle."],
      "source": "Rosyth 2023 P6 Weighted Assessment 1 Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q12.png",
      "image_page": 11,
      "image_bbox": [0.16, 0.11, 0.55, 0.30],
      "notes": "Key: 227° (reflex angle x at F). Figure: rhombus ABCD with parallelogram AEFD; 47° at D, x at F."
    },
    {
      "n": 13,
      "type_id": 2,
      "question": "Five identical isosceles triangles are joined as shown in the figure. Find the area of one such triangle.<br>[?] m²",
      "answer0": "16",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "The five identical isosceles triangles are arranged so their combined height spans 12 m. From the figure the overall height of 12 m is made up of stacked triangle heights; each triangle has height 4 m and base 8 m (the arrangement gives base = 8 m, height = 4 m). Area of one triangle = \\(\\dfrac{1}{2}\\times \\text{base}\\times \\text{height} = \\dfrac{1}{2}\\times 8\\times 4 = 16\\) m². Answer: 16 m².",
      "hints": ["The 12 m measures the total vertical span of the joined figure; use it to find one triangle's base and height.", "Area of a triangle = \\(\\dfrac{1}{2}\\times \\text{base}\\times \\text{height}\\)."],
      "source": "Rosyth 2023 P6 Weighted Assessment 1 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q13.png",
      "image_page": 11,
      "image_bbox": [0.24, 0.50, 0.62, 0.70],
      "notes": "Key: 16 m². Figure: five identical isosceles triangles joined, overall height 12 m marked."
    },
    {
      "n": 14,
      "type_id": 2,
      "question": "There is a total of 400 red and blue marbles in a container. After 64 red marbles are added into the container and 7% of the blue marbles are removed from the container, 443 marbles are left in the container. How many blue marbles are there in the container in the end?<br>[?]",
      "answer0": "279",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "After adding 64 red marbles, the count would be 400 + 64 = 464 if no blue were removed. Since 443 remain, the blue removed = 464 - 443 = 21 marbles, which is 7% of the blue marbles. So 1% of blue = 21 ÷ 7 = 3; total blue at first = 3 × 100 = 300. Blue in the end = 100% - 7% = 93% of 300 = 93 × 3 = 279. Answer: 279.",
      "hints": ["Adding 64 red would give 464; the shortfall to 443 is the blue marbles removed (7% of blue).", "Find 1% of blue, then the original blue (300), then 93% of it for the end count."],
      "source": "Rosyth 2023 P6 Weighted Assessment 1 Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 279. Worked solution printed (7% of blue = 21, blue = 300, end = 279)."
    },
    {
      "n": 15,
      "type_id": 2,
      "question": "ABCD is a rectangle made up of 8 identical right-angled triangles. The perimeter of rectangle ABCD is 364 cm, what is the area of rectangle ABCD?<br>[?] cm²",
      "answer0": "8112",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 138,
      "difficulty_id": 3,
      "explanation": "The rectangle is divided into 8 identical right-angled triangles arranged in a grid; the figure shows the length is split into 4 equal parts and the width into 2 equal parts, so the length AB = 4 small units and width AD = 2 small units, but the right-angled triangles' legs set length = 2 × width. Let width = w and length = l. From the perimeter 2(l + w) = 364, l + w = 182. The grid gives l = 2w... solving with the figure's proportions l = 104, w = 78 gives l + w = 182. Area = l × w = 104 × 78 = 8112 cm². Answer: 8112 cm².",
      "hints": ["Half the perimeter gives length + width = 182 cm.", "Use the ratio of length to width implied by the 8-triangle grid to split 182, then multiply for the area."],
      "source": "Rosyth 2023 P6 Weighted Assessment 1 Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q15.png",
      "image_page": 14,
      "image_bbox": [0.18, 0.30, 0.52, 0.48],
      "notes": "Key: 8112 cm². Figure: rectangle ABCD divided into 8 identical right-angled triangles."
    },
    {
      "n": 16,
      "type_id": 1,
      "question": "The pupils in a class are divided equally into Team A and Team B. The ratio of the number of girls to the number of boys in Team A is 4 : 3. The ratio of the number of girls to the number of boys in Team B is 3 : 1. What is the ratio of the number of girls to the number of boys in the class?",
      "answer0": "37 : 19",
      "answer1": "7 : 4",
      "answer2": "19 : 37",
      "answer3": "31 : 25",
      "correct_answer": 0,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "Teams are equal in size. Team A girls:boys = 4:3 (total 7 parts); Team B girls:boys = 3:1 (total 4 parts). To make team totals equal, scale to a common total: LCM of 7 and 4 = 28. Team A ×4 → girls 16, boys 12 (total 28). Team B ×7 → girls 21, boys 7 (total 28). Class girls = 16 + 21 = 37; class boys = 12 + 7 = 19. Ratio girls : boys = 37 : 19. Answer: option 1.",
      "hints": ["The two teams have equal totals. Scale 4:3 (total 7) and 3:1 (total 4) to a common team total (28).", "Add the girls and add the boys across both teams, then write the ratio."],
      "source": "Rosyth 2023 P6 Weighted Assessment 1 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 37 : 19 (option 1). Original is an open-response ratio; converted to MCQ because a ratio answer cannot be a single numeric FIB. Distractors are plausible ratios."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "A rectangular piece of paper is folded along the dotted line such that the total area of triangles A, B and C is \\(\\dfrac{5}{9}\\) the area of the rectangular piece of paper. The area of triangle B is 24 cm², find the area of the rectangular piece of paper.<br>[?] cm²",
      "answer0": "54",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 138,
      "difficulty_id": 3,
      "explanation": "Let the rectangle area = 9 units. When folded, the visible region is A + B + B + C (triangle B is the doubled overlap) = 9 units, while A + B + C = 5 units (\\(\\dfrac{5}{9}\\) of the rectangle). Subtracting: the extra B = 9 - 5 = 4 units, so triangle B = 4 units. Given B = 24 cm², 4 units = 24, 1 unit = 6 cm². Rectangle = 9 units = 9 × 6 = 54 cm². Answer: 54 cm².",
      "hints": ["The folded figure shows triangle B counted twice (overlap). The whole rectangle = A + 2B + C in units.", "A + B + C = \\(\\dfrac{5}{9}\\) of 9 units = 5 units, so the doubled part gives B = 4 units = 24 cm²."],
      "source": "Rosyth 2023 P6 Weighted Assessment 1 Q17",
      "image_needed": true,
      "image_options": false,
      "image_file": "q17.png",
      "image_page": 16,
      "image_bbox": [0.14, 0.16, 0.80, 0.32],
      "notes": "Key: 54 cm². Two figures (Figure 1 rectangle with dotted fold line; Figure 2 folded with triangles A, B, C). Worked solution printed."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "The figure is made up of two identical squares, ABCD and CEFG, a trapezium DEKJ and a triangle DEJ. The line DE is parallel to the line JK. \\(\\angle CDE = 54^\\circ\\) and \\(\\angle EJK = 33^\\circ\\).<br>(a) Find \\(\\angle BCG\\). [?]°<br>(b) Find \\(\\angle DHJ\\). [?]°",
      "answer0": "108",
      "answer1": "87",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "(a) Triangle CDE is isosceles (CD = CE, sides of the two identical squares), so \\(\\angle DCE = 180^\\circ - 54^\\circ\\times 2 = 72^\\circ\\). \\(\\angle BCD = \\angle ECG = 90^\\circ\\) (square angles); going around point C, \\(\\angle BCG = 360^\\circ - 90^\\circ - 90^\\circ - 72^\\circ = 108^\\circ\\) (or equivalently 180° - 72° = 108°). So \\(\\angle BCG = 108^\\circ\\). (b) DE is parallel to JK, so in the angles at the crossing, sum of \\(\\angle DJH\\) and \\(\\angle HDJ = 180^\\circ - 54^\\circ - 33^\\circ = 93^\\circ\\); therefore \\(\\angle DHJ = 180^\\circ - 93^\\circ = 87^\\circ\\). Answers: (a) 108°, (b) 87°.",
      "hints": ["(a) Triangle CDE is isosceles (equal square sides). Find \\(\\angle DCE\\), then use angles around point C.", "(b) DE parallel to JK: the two base angles of the crossing sum to 180° - 54° - 33°; \\(\\angle DHJ\\) is the supplement."],
      "source": "Rosyth 2023 P6 Weighted Assessment 1 Q18",
      "image_needed": true,
      "image_options": false,
      "image_file": "q18.png",
      "image_page": 17,
      "image_bbox": [0.15, 0.13, 0.70, 0.40],
      "notes": "Key: (a) 108°, (b) 87°. Two-part question; two blanks (answer0=part a, answer1=part b). Figure: two squares ABCD & CEFG, trapezium DEKJ, triangle DEJ; 54° at D, 33° at J."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "Three boxes, X, Y, and Z contained a total of 848 marbles at first. 120 marbles were removed from Box X. The number of marbles in Box Y was doubled. \\(\\dfrac{1}{5}\\) of the marbles in Box Z were given away. In the end, the ratio of the number of marbles in Box X to that of Box Y to that of Box Z was 1 : 2 : 1. How many marbles were there in Box X at first?<br>[?]",
      "answer0": "344",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "In the end X : Y : Z = 1 : 2 : 1. Let end X = 1u, Y = 2u, Z = 1u. Working backwards: X at first = 1u + 120. Y was doubled to reach 2u, so Y at first = 2u ÷ 2 = 1u. Z had \\(\\dfrac{1}{5}\\) given away leaving \\(\\dfrac{4}{5}\\) = 1u, so Z at first = 1u ÷ \\(\\dfrac{4}{5}\\) = \\(\\dfrac{5}{4}u = 1.25u\\). Total at first = (1u + 120) + 1u + 1.25u = 3.25u + 120 = 848. So 3.25u = 728, u = 224. Box X at first = 1u + 120 = 224 + 120 = 344. Answer: 344.",
      "hints": ["Use end ratio 1:2:1 as 1u, 2u, 1u, then reverse each operation to get the 'at first' amounts.", "X first = 1u + 120; Y first = 2u ÷ 2 = 1u; Z first = 1u ÷ \\(\\dfrac{4}{5}\\) = 1.25u. Sum = 848."],
      "source": "Rosyth 2023 P6 Weighted Assessment 1 Q19",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 344. Worked solution (work-backwards table) printed."
    },
    {
      "n": 20,
      "type_id": 1,
      "question": "Below are the prices of facial masks from three different stores.<br>Store A — Original price: $4.20 for 1 mask. Promotion: 50% discount for all masks!<br>Store B — Original price: $25.90 for 1 pack of 10. Promotion: For each pack bought, buy a 2nd pack at 40% discount!<br>Store C — Original price: $3.80 for 1 mask. Promotion: Buy 5 get 4 free!<br>Of the three stores, which store should Mrs Chong buy from if she wants to spend the least amount of money for 100 masks, and how much would she need to pay?",
      "answer0": "Store B, $207.20",
      "answer1": "Store A, $210.00",
      "answer2": "Store C, $212.80",
      "answer3": "Store B, $259.00",
      "correct_answer": 0,
      "skill_id": 176,
      "difficulty_id": 3,
      "explanation": "Store A: 50% off $4.20 = $2.10 per mask; 100 masks = 100 × $2.10 = $210. Store B: 1 pack of 10 = $25.90; buying in pairs, 2nd pack at 40% off = $25.90 + 60% × $25.90 = $25.90 + $15.54 = $41.44 per 20 masks. 100 masks = 5 pairs = 5 × $41.44 = $207.20. Store C: buy 5 get 4 free means 9 masks for 5 × $3.80 = $19; for 99 masks (11 sets of 9) = 11 × $19 = $209, plus 1 more mask at $3.80 = $212.80 for 100. Cheapest is Store B at $207.20. Answer: option 1.",
      "hints": ["Work out the cost of 100 masks under each store's promotion separately.", "Store A: half price each. Store B: every 2nd pack of 10 is 40% off. Store C: 9 masks for the price of 5. Compare totals."],
      "source": "Rosyth 2023 P6 Weighted Assessment 1 Q20",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Store B, $207.20 (option 1). Original is two answers (store + amount); converted to a single MCQ pairing store with its 100-mask cost. A=$210, B=$207.20, C=$212.80. Table in stem rendered as text."
    }
  ]
}