{
  "paper": {
    "school": "Henry Park",
    "year": 2024,
    "level": "P6",
    "label": "Term Review 2",
    "source_prefix": "Henry Park 2024 P6 Term Review 2",
    "has_answer_key": false,
    "notes": "NO printed answer key anywhere in the PDF (Paper 1 and Paper 2 both end with no solutions section). Every answer was solved by the agent. Two papers in one PDF: Paper 1 (Booklet A Q1-15 MCQ + Booklet B Q16-30) and Paper 2 (Q1-17). Sources tagged 'P1 Q..' and 'P2 Q..' to disambiguate the repeated numbering. Hard figure-dependent geometry (Paper 2 Q7 and Q15) flagged LOW CONFIDENCE."
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "Round 50.282 to the nearest tenth.",
      "answer0": "50",
      "answer1": "50.2",
      "answer2": "50.3",
      "answer3": "50.28",
      "correct_answer": 2,
      "skill_id": 168,
      "difficulty_id": 1,
      "explanation": "The tenths digit is 2; the next digit (hundredths) is 8 ≥ 5, so round up: 50.282 → 50.3.",
      "hints": ["The first place after the point is tenths.", "Look at the hundredths digit to decide."],
      "source": "Henry Park 2024 P6 Term Review 2 P1 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "No answer key -- solved."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Which of the following is likely to be the length of a bed for an adult?",
      "answer0": "2 m",
      "answer1": "2 cm",
      "answer2": "20 m",
      "answer3": "20 cm",
      "correct_answer": 0,
      "skill_id": 184,
      "difficulty_id": 1,
      "explanation": "An adult bed is about 2 metres long. 2 cm and 20 cm are far too short; 20 m is far too long.",
      "hints": ["Think about real-life sizes.", "A bed is about as long as a tall person."],
      "source": "Henry Park 2024 P6 Term Review 2 P1 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "No answer key -- solved."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "In the scale, what is the value of X?",
      "answer0": "10.3",
      "answer1": "10.6",
      "answer2": "10.03",
      "answer3": "10.06",
      "correct_answer": 3,
      "skill_id": 124,
      "difficulty_id": 2,
      "explanation": "From 9.8 to 9.9 there are 10 small intervals, so each interval is 0.01. X is 6 intervals past 10.0, giving 10.06.",
      "hints": ["Find the value of one small interval first.", "Count the intervals from 10.0 to X."],
      "source": "Henry Park 2024 P6 Term Review 2 P1 Q3",
      "image_needed": true,
      "image_page": 2,
      "image_bbox": [0.12, 0.06, 0.86, 0.18],
      "image_loc": "number-line scale from 9.8 with arrow X past 10.0",
      "image_options": false,
      "image_file": "q3.png",
      "notes": "No answer key -- solved. Scale interval = 0.01; verify X position against the figure."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "3 children shared a pack of stickers. The ratio of Elly's stickers to Flynn's stickers to Gerry's stickers is 4 : 2 : 5. Gerry received 180 stickers. How many stickers did Elly and Flynn receive?",
      "answer0": "216",
      "answer1": "252",
      "answer2": "315",
      "answer3": "324",
      "correct_answer": 0,
      "skill_id": 213,
      "difficulty_id": 2,
      "explanation": "Gerry = 5 units = 180, so 1 unit = 36. Elly + Flynn = 4 + 2 = 6 units = 6 × 36 = 216.",
      "hints": ["Find the value of one unit from Gerry's share.", "Add Elly's and Flynn's units."],
      "source": "Henry Park 2024 P6 Term Review 2 P1 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "No answer key -- solved."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "A furniture store sold 50 sofas in January. In February, it sold 40 sofas. What is the percentage decrease in the number of sofas sold in February?",
      "answer0": "10%",
      "answer1": "20%",
      "answer2": "25%",
      "answer3": "80%",
      "correct_answer": 1,
      "skill_id": 208,
      "difficulty_id": 1,
      "explanation": "Decrease = 50 − 40 = 10. Percentage decrease = \\(\\dfrac{10}{50}\\times 100\\% = 20\\%\\).",
      "hints": ["Find the decrease in number.", "Divide by the January figure (the original)."],
      "source": "Henry Park 2024 P6 Term Review 2 P1 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "No answer key -- solved."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "The semicircle has a radius of 10 cm. What is the perimeter of the shaded figure? Take \\(\\pi = 3.14\\).",
      "answer0": "15.7 cm",
      "answer1": "25.7 cm",
      "answer2": "31.4 cm",
      "answer3": "51.4 cm",
      "correct_answer": 3,
      "skill_id": 221,
      "difficulty_id": 2,
      "explanation": "Perimeter = half circumference + diameter = \\(\\pi r + 2r = 3.14\\times 10 + 20 = 31.4 + 20 = 51.4\\) cm.",
      "hints": ["A semicircle's perimeter includes the straight diameter.", "πr + 2r."],
      "source": "Henry Park 2024 P6 Term Review 2 P1 Q6",
      "image_needed": true,
      "image_page": 3,
      "image_bbox": [0.46, 0.16, 0.7, 0.28],
      "image_loc": "semicircle, upper-right of page",
      "image_options": false,
      "image_file": "q6.png",
      "notes": "No answer key -- solved."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "A solid cuboid of height 10 cm has a square base of side 4 cm. What is its volume?",
      "answer0": "40 cm³",
      "answer1": "80 cm³",
      "answer2": "160 cm³",
      "answer3": "400 cm³",
      "correct_answer": 2,
      "skill_id": 190,
      "difficulty_id": 1,
      "explanation": "Volume = base area × height = (4 × 4) × 10 = 16 × 10 = 160 cm³.",
      "hints": ["Base area = side × side.", "Multiply by the height."],
      "source": "Henry Park 2024 P6 Term Review 2 P1 Q7",
      "image_needed": true,
      "image_page": 3,
      "image_bbox": [0.16, 0.4, 0.4, 0.58],
      "image_loc": "tall cuboid with 10 cm height and 4 cm base",
      "image_options": false,
      "image_file": "q7.png",
      "notes": "No answer key -- solved."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "The figure shows trapezium PQRS. Which of the following is a property of a trapezium?",
      "answer0": "\\(\\angle a = \\angle c\\)",
      "answer1": "\\(\\angle b + \\angle c = 180°\\)",
      "answer2": "It has one pair of equal sides.",
      "answer3": "It has one pair of parallel sides.",
      "correct_answer": 3,
      "skill_id": 199,
      "difficulty_id": 1,
      "explanation": "A trapezium is defined by having exactly one pair of parallel sides.",
      "hints": ["Recall the definition of a trapezium.", "It is about parallel sides, not equal sides."],
      "source": "Henry Park 2024 P6 Term Review 2 P1 Q8",
      "image_needed": true,
      "image_page": 4,
      "image_bbox": [0.28, 0.1, 0.58, 0.2],
      "image_loc": "trapezium PQRS with angles a, b, c marked",
      "image_options": false,
      "image_file": "q8.png",
      "notes": "No answer key -- solved."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "In the figure, which two lines are parallel?",
      "answer0": "AE and EF",
      "answer1": "AH and BG",
      "answer2": "BG and DF",
      "answer3": "DF and AH",
      "correct_answer": 1,
      "skill_id": 100,
      "difficulty_id": 2,
      "explanation": "On the square grid, AH rises from A (bottom) to H (top) over 2 columns, and BG rises the same way over 2 columns. They have the same gradient, so AH ∥ BG.",
      "hints": ["Parallel lines have the same slope on the grid.", "Compare the rise and run of each segment."],
      "source": "Henry Park 2024 P6 Term Review 2 P1 Q9",
      "image_needed": true,
      "image_page": 4,
      "image_bbox": [0.16, 0.42, 0.66, 0.66],
      "image_loc": "square grid with labelled lines A-H",
      "image_options": false,
      "image_file": "q9.png",
      "notes": "No answer key -- solved; verify gradients against the grid figure."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "The bar graph shows the number of burgers and pies sold in a shop over four days. Find the total number of burgers sold on Thursday and Sunday.",
      "answer0": "50",
      "answer1": "58",
      "answer2": "66",
      "answer3": "120",
      "correct_answer": 0,
      "skill_id": 104,
      "difficulty_id": 1,
      "explanation": "From the Burgers graph: Thursday = 18, Sunday = 32. Total = 18 + 32 = 50.",
      "hints": ["Read only the Burgers graph.", "Add the Thursday and Sunday bars."],
      "source": "Henry Park 2024 P6 Term Review 2 P1 Q10",
      "image_needed": true,
      "image_page": 5,
      "image_bbox": [0.08, 0.13, 0.92, 0.4],
      "image_loc": "two bar graphs (Burgers and Pies) over Thu-Sun",
      "image_options": false,
      "image_file": "q10.png",
      "notes": "No answer key -- solved. Reuses the same graph as Q11."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "The number of pies sold on Monday was an 80% increase from the number sold on Thursday. How many pies were sold on Monday?",
      "answer0": "33",
      "answer1": "36",
      "answer2": "81",
      "answer3": "90",
      "correct_answer": 2,
      "skill_id": 208,
      "difficulty_id": 2,
      "explanation": "From the Pies graph, Thursday = 45. An 80% increase = 45 × 1.8 = 81.",
      "hints": ["Read Thursday's pies from the graph.", "Monday = Thursday × (1 + 0.80)."],
      "source": "Henry Park 2024 P6 Term Review 2 P1 Q11",
      "image_needed": true,
      "image_page": 5,
      "image_bbox": [0.5, 0.13, 0.92, 0.4],
      "image_loc": "Pies bar graph over Thu-Sun",
      "image_options": false,
      "image_file": "q11.png",
      "notes": "No answer key -- solved. Reads Thursday pies = 45; verify against the graph."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "A wire of length 7.2 m was cut into 3 pieces. The first piece was 3 times as long as the second piece. The second piece was twice as long as the third piece. How long was the second piece of wire?",
      "answer0": "0.8 m",
      "answer1": "1.6 m",
      "answer2": "2.4 m",
      "answer3": "4.8 m",
      "correct_answer": 1,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "Let third = t, second = 2t, first = 3 × 2t = 6t. Total = t + 2t + 6t = 9t = 7.2 → t = 0.8 m. Second = 2t = 1.6 m.",
      "hints": ["Let the third piece be 1 unit.", "Add the units and divide 7.2 m."],
      "source": "Henry Park 2024 P6 Term Review 2 P1 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "No answer key -- solved."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "Figure 1 is a right-angled triangle with a base to height ratio of 2 : 3. Figure 2 is made up of four such right-angled triangles. The length of AB is 60 cm. What is the area of figure 1?",
      "answer0": "300 cm²",
      "answer1": "432 cm²",
      "answer2": "600 cm²",
      "answer3": "675 cm²",
      "correct_answer": 1,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Base : height = 2 : 3. In Figure 2, AB = base + height = 2u + 3u = 5u = 60, so u = 12. Base = 24 cm, height = 36 cm. Area = \\(\\dfrac{1}{2}\\times 24\\times 36 = 432\\) cm².",
      "hints": ["AB is made of one base plus one height of the triangle.", "Area of a right-angled triangle = \\(\\dfrac{1}{2}\\) × base × height."],
      "source": "Henry Park 2024 P6 Term Review 2 P1 Q13",
      "image_needed": true,
      "image_page": 6,
      "image_bbox": [0.16, 0.36, 0.66, 0.56],
      "image_loc": "Figure 1 (right triangle) and Figure 2 (pinwheel of 4 triangles, AB across)",
      "image_options": false,
      "image_file": "q13.png",
      "notes": "No answer key -- solved; AB = base + height = 5u = 60. Verify the AB interpretation against the figure."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "After a discount of 25%, an adult would have to pay $60 for a buffet lunch. A senior citizen gets an additional discount of $12. Find the percentage discount given to the senior citizen for the buffet lunch.",
      "answer0": "15%",
      "answer1": "20%",
      "answer2": "25%",
      "answer3": "40%",
      "correct_answer": 3,
      "skill_id": 176,
      "difficulty_id": 3,
      "explanation": "$60 is 75% of the price, so usual price = $80. Senior pays $60 − $12 = $48. Total discount = $80 − $48 = $32. Percentage = \\(\\dfrac{32}{80}\\times 100\\% = 40\\%\\).",
      "hints": ["Find the original (full) price first.", "Senior's discount is measured from the full price."],
      "source": "Henry Park 2024 P6 Term Review 2 P1 Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "No answer key -- solved."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "Oman and Pauline made figurines over 2 days. On Monday, Oman made 19 figurines more than Pauline. On Tuesday, Oman made another 20 figurines and Pauline made another 15. At the end of the two days, Oman made \\(\\dfrac{3}{5}\\) of the total number of figurines. What was the total number of figurines Pauline made on Monday and Tuesday?",
      "answer0": "24",
      "answer1": "48",
      "answer2": "54",
      "answer3": "72",
      "correct_answer": 1,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Let Pauline's Monday count = p. Oman total = (p + 19) + 20 = p + 39. Pauline total = p + 15. Grand total = 2p + 54. Oman = \\(\\dfrac{3}{5}\\) total: p + 39 = \\(\\dfrac{3}{5}\\)(2p + 54) → 5(p + 39) = 3(2p + 54) → 5p + 195 = 6p + 162 → p = 33. Pauline total = 33 + 15 = 48.",
      "hints": ["Express both totals in terms of Pauline's Monday count p.", "Set Oman's total = \\(\\dfrac{3}{5}\\) of the grand total."],
      "source": "Henry Park 2024 P6 Term Review 2 P1 Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "No answer key -- solved."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Express \\(9\\dfrac{7}{25}\\) as a decimal. [?]",
      "answer0": "9.28",
      "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 \\(9\\dfrac{7}{25} = 9.28\\).",
      "hints": ["Make the denominator 100.", "\\(\\dfrac{7}{25} = \\dfrac{28}{100}\\)."],
      "source": "Henry Park 2024 P6 Term Review 2 P1 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "No answer key -- solved. Answer is a decimal -> FIB allowed."
    },
    {
      "n": 17,
      "type_id": 1,
      "question": "Express 4.3% as a fraction.",
      "answer0": "\\(\\dfrac{43}{1000}\\)",
      "answer1": "\\(\\dfrac{43}{100}\\)",
      "answer2": "\\(\\dfrac{4.3}{100}\\)",
      "answer3": "\\(\\dfrac{43}{10}\\)",
      "correct_answer": 0,
      "skill_id": 173,
      "difficulty_id": 1,
      "explanation": "4.3% = \\(\\dfrac{4.3}{100} = \\dfrac{43}{1000}\\).",
      "hints": ["Percent means out of 100.", "Clear the decimal by multiplying top and bottom by 10."],
      "source": "Henry Park 2024 P6 Term Review 2 P1 Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "No answer key -- solved. Fraction answer -> MCQ per spec (FIB cannot hold fractions)."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "The opening hours of a clinic are: Daily opening hours 9.15 a.m. to 5 p.m., Lunch break 1 p.m. to 2 p.m. How long is the clinic open each day? Give your answer in hours and minutes. [?] h [?] min",
      "answer0": "6",
      "answer1": "45",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 2,
      "explanation": "9.15 a.m. to 5 p.m. = 7 h 45 min. Subtract the 1 h lunch break: 7 h 45 min − 1 h = 6 h 45 min.",
      "hints": ["Find the time from opening to closing first.", "Take away the 1-hour lunch break."],
      "source": "Henry Park 2024 P6 Term Review 2 P1 Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "No answer key -- solved. Two blanks: hours and minutes."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "AB and PQ are straight lines. Find \\(\\angle y\\). [?]",
      "answer0": "46",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "PQ and AB cross at X. \\(\\angle AXQ = 136°\\) (vertically opposite the marked 136°). A ray makes a right angle (90°) with XQ. So \\(\\angle y = \\angle AXQ - 90° = 136° - 90° = 46°\\).",
      "hints": ["Use vertically opposite angles for the 136°.", "Subtract the marked right angle."],
      "source": "Henry Park 2024 P6 Term Review 2 P1 Q19",
      "image_needed": true,
      "image_page": 10,
      "image_bbox": [0.18, 0.06, 0.6, 0.3],
      "image_loc": "two crossing lines AB and PQ with ray R, right angle and 136° marked",
      "image_options": false,
      "image_file": "q19.png",
      "notes": "No answer key -- solved; figure-dependent, answer 46° -- verify ray positions against the figure. Answer in degrees."
    },
    {
      "n": 20,
      "type_id": 1,
      "question": "The line graph shows the number of fish in a pond from January to June. Between which 1-month period was the increase in the number of fishes in the pond the greatest?",
      "answer0": "May and June",
      "answer1": "February and March",
      "answer2": "January and February",
      "answer3": "March and April",
      "correct_answer": 0,
      "skill_id": 147,
      "difficulty_id": 2,
      "explanation": "Readings: Jan 15, Feb 20, Mar 30, Apr 30, May 25, Jun 40. Increases: Jan→Feb +5, Feb→Mar +10, Mar→Apr 0, Apr→May −5, May→Jun +15. The greatest increase is May to June (+15).",
      "hints": ["Find the change between each pair of months.", "Look for the steepest upward segment."],
      "source": "Henry Park 2024 P6 Term Review 2 P1 Q20",
      "image_needed": true,
      "image_page": 10,
      "image_bbox": [0.1, 0.36, 0.78, 0.62],
      "image_loc": "line graph of fish count Jan-Jun",
      "image_options": false,
      "image_file": "q20.png",
      "notes": "No answer key -- solved. 'Between two months' answer -> MCQ per spec."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "Use all the digits 3, 5, 6, 7 to form<br>(a) the smallest 4-digit multiple of 5 [?]<br>(b) the number closest to 7000 [?]",
      "answer0": "3675",
      "answer1": "6753",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 149,
      "difficulty_id": 2,
      "explanation": "(a) A multiple of 5 must end in 5. Arrange the rest (3, 6, 7) in ascending order: 3675. (b) Closest to 7000: the largest below is 6753 (7000 − 6753 = 247); the smallest above is 7356 (7356 − 7000 = 356). 6753 is closer.",
      "hints": ["A multiple of 5 ends in 0 or 5; here only 5 is available.", "Test the largest number below 7000 and the smallest above."],
      "source": "Henry Park 2024 P6 Term Review 2 P1 Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "No answer key -- solved. Two blanks: (a) then (b)."
    },
    {
      "n": 22,
      "type_id": 0,
      "question": "(a) The diagram shows half of a symmetrical figure with XY as the line of symmetry. Draw and complete the symmetric figure.<br>(b) Draw a line perpendicular to EF, passing through point G.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 145,
      "difficulty_id": 2,
      "explanation": "(a) Reflect every vertex of the given half across line XY and join them to complete the symmetric figure. (b) Draw the line through G that meets EF at 90°.",
      "hints": ["Reflect each point the same distance on the other side of XY.", "A perpendicular meets EF at a right angle."],
      "source": "Henry Park 2024 P6 Term Review 2 P1 Q22",
      "image_needed": true,
      "image_page": 12,
      "image_bbox": [0.2, 0.08, 0.86, 0.42],
      "image_loc": "grid with half-figure and line of symmetry XY (part a); grid with line EF and point G (part b)",
      "image_options": false,
      "image_file": "q22.png",
      "notes": "No answer key -- solved. Draw/construct task (interactive) -> type_id 0 (skipped on insert)."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "Chelsea used 12 identical cubes of side 1 cm to form a solid. She then added some cubes to form a cuboid 4 cm by 6 cm by 6 cm. How many cubes did she add? [?]",
      "answer0": "132",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 190,
      "difficulty_id": 2,
      "explanation": "Volume of the cuboid = 4 × 6 × 6 = 144 cm³ = 144 unit cubes. She already had 12, so she added 144 − 12 = 132.",
      "hints": ["Find the total number of unit cubes in the cuboid.", "Subtract the 12 she already had."],
      "source": "Henry Park 2024 P6 Term Review 2 P1 Q23",
      "image_needed": true,
      "image_page": 13,
      "image_bbox": [0.16, 0.16, 0.42, 0.36],
      "image_loc": "stepped solid made of unit cubes",
      "image_options": false,
      "image_file": "q23.png",
      "notes": "No answer key -- solved. Cuboid dimensions read as 4 x 6 x 6 cm (text OCR) -> 144 cubes; verify the dimensions against the printed question."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "The figure is a rectangle with a length of 9 cm and breadth of 6 cm. Find the total shaded area. [?]",
      "answer0": "27",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 138,
      "difficulty_id": 3,
      "explanation": "The shaded triangles together have bases that add up to the full 9 cm width and a height equal to the 6 cm breadth, so the shaded area = \\(\\dfrac{1}{2}\\times 9\\times 6 = 27\\) cm² (half the rectangle).",
      "hints": ["The shaded triangles' bases span the whole width.", "Shaded = half the rectangle's area."],
      "source": "Henry Park 2024 P6 Term Review 2 P1 Q24",
      "image_needed": true,
      "image_page": 13,
      "image_bbox": [0.16, 0.46, 0.56, 0.66],
      "image_loc": "rectangle 9 cm x 6 cm with shaded zig-zag triangles",
      "image_options": false,
      "image_file": "q24.png",
      "notes": "No answer key -- solved; figure-dependent. Shaded = half the rectangle = 27 cm² -- verify against the printed shading. Answer in cm²."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "Shival paid $945 for a golf club and 4 boxes of golf balls. The price of a box of golf balls was \\(\\dfrac{2}{7}\\) of the price of the golf club. How much did Shival pay for the golf club? [?]",
      "answer0": "441",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Let the club = c. 4 boxes = 4 × \\(\\dfrac{2}{7}\\)c = \\(\\dfrac{8}{7}\\)c. Total = c + \\(\\dfrac{8}{7}\\)c = \\(\\dfrac{15}{7}\\)c = 945 → c = 945 × \\(\\dfrac{7}{15}\\) = 441. The golf club cost $441.",
      "hints": ["Write the club price as 7 units, so a box is 2 units.", "Total = 7 + 4 × 2 = 15 units = $945."],
      "source": "Henry Park 2024 P6 Term Review 2 P1 Q25",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "No answer key -- solved. Answer in dollars: $441."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "A choir has 50 male and 70 female members. 16% of the male members and 10% of the female members are university students and the remaining members are not university students. What percentage of the members are not university students? [?]",
      "answer0": "87.5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 175,
      "difficulty_id": 3,
      "explanation": "University students: 16% of 50 = 8, plus 10% of 70 = 7, total 15. Total members = 120. Not university = 120 − 15 = 105. Percentage = \\(\\dfrac{105}{120}\\times 100\\% = 87.5\\%\\).",
      "hints": ["Count the university students from each group.", "Not-university = total − university; convert to a percentage of 120."],
      "source": "Henry Park 2024 P6 Term Review 2 P1 Q26",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "No answer key -- solved. Answer is a percentage (decimal allowed): 87.5%."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "A square and a rectangle overlap to form the figure. The ratio of the area of the shaded part to the area of the square to the area of the rectangle is 1 : 2 : 7. The area of the rectangle is 84 cm². Find the area of the whole figure. [?]",
      "answer0": "96",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 223,
      "difficulty_id": 3,
      "explanation": "Rectangle = 7 units = 84, so 1 unit = 12. Shaded (overlap) = 1 unit = 12; square = 2 units = 24. Whole figure = square + rectangle − overlap = 24 + 84 − 12 = 96 cm².",
      "hints": ["Find one unit from the rectangle's area.", "Whole = square + rectangle − overlap (shaded)."],
      "source": "Henry Park 2024 P6 Term Review 2 P1 Q27",
      "image_needed": true,
      "image_page": 15,
      "image_bbox": [0.16, 0.12, 0.5, 0.34],
      "image_loc": "overlapping square and rectangle, shaded overlap",
      "image_options": false,
      "image_file": "q27.png",
      "notes": "No answer key -- solved. Answer in cm²."
    },
    {
      "n": 28,
      "type_id": 1,
      "question": "Mr Huang has balloons of 3 different colours. \\(\\dfrac{1}{4}\\) of the balloons are purple. The ratio of the number of yellow balloons to the number of orange balloons is 2 : 3. What is the ratio of the number of purple balloons to the number of orange balloons?",
      "answer0": "5 : 9",
      "answer1": "1 : 3",
      "answer2": "2 : 3",
      "answer3": "5 : 6",
      "correct_answer": 0,
      "skill_id": 210,
      "difficulty_id": 3,
      "explanation": "Purple = \\(\\dfrac{1}{4}\\) = \\(\\dfrac{5}{20}\\). Remainder \\(\\dfrac{3}{4}\\) is split yellow : orange = 2 : 3 (5 parts), so orange = \\(\\dfrac{3}{5}\\times\\dfrac{3}{4} = \\dfrac{9}{20}\\). Purple : orange = \\(\\dfrac{5}{20} : \\dfrac{9}{20} = 5 : 9\\).",
      "hints": ["Use a common total (e.g. 20) for the whole.", "Split the remaining \\(\\dfrac{3}{4}\\) in the ratio 2 : 3."],
      "source": "Henry Park 2024 P6 Term Review 2 P1 Q28",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "No answer key -- solved. Ratio answer -> MCQ per spec."
    },
    {
      "n": 29,
      "type_id": 1,
      "question": "Pauline, Queenie and Roger had 162 marbles altogether. Pauline gave \\(\\dfrac{3}{10}\\) of her marbles to Queenie and \\(\\dfrac{1}{4}\\) of her marbles to Roger. After that, all 3 children had the same number of marbles.<br>(a) What is the ratio of the marbles Pauline had to Queenie had to Roger had at first?<br>(b) How many more marbles did Pauline have than Queenie at first?",
      "answer0": "(a) 20 : 3 : 4   (b) 102 marbles",
      "answer1": "(a) 10 : 3 : 2   (b) 96 marbles",
      "answer2": "(a) 20 : 3 : 4   (b) 84 marbles",
      "answer3": "(a) 5 : 1 : 1   (b) 102 marbles",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Each child ends with 162 ÷ 3 = 54. Pauline keeps 1 − \\(\\dfrac{3}{10}\\) − \\(\\dfrac{1}{4}\\) = \\(\\dfrac{9}{20}\\) of her marbles = 54, so Pauline = 120. Queenie + \\(\\dfrac{3}{10}\\times 120\\) = 54 → Queenie = 18. Roger + \\(\\dfrac{1}{4}\\times 120\\) = 54 → Roger = 24. (a) 120 : 18 : 24 = 20 : 3 : 4. (b) 120 − 18 = 102.",
      "hints": ["Each child ends with one-third of 162.", "Pauline keeps \\(\\dfrac{9}{20}\\) of her marbles after giving the rest away."],
      "source": "Henry Park 2024 P6 Term Review 2 P1 Q29",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "No answer key -- solved. Part (a) is a ratio (cannot be FIB), so the whole 2-part question is rendered as MCQ combining (a) and (b). (a) 20:3:4, (b) 102 marbles."
    },
    {
      "n": 30,
      "type_id": 2,
      "question": "The figure shows a cylinder with a diameter of 35 cm placed a distance away from a wall. The distance between the centre of the cylinder to the wall is 12.1 m. How many complete turns will the cylinder have to make before it touches the wall? Take \\(\\pi = \\dfrac{22}{7}\\). [?]",
      "answer0": "10",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 222,
      "difficulty_id": 3,
      "explanation": "Circumference = \\(\\pi d = \\dfrac{22}{7}\\times 0.35 = 1.1\\) m per turn. The cylinder touches the wall when its edge reaches it, i.e. after the centre travels 12.1 m − radius (0.175 m) = 11.925 m. 11.925 ÷ 1.1 ≈ 10.8, so 10 complete turns.",
      "hints": ["One turn moves the cylinder one circumference forward.", "The edge touches the wall a radius before the centre would reach it."],
      "source": "Henry Park 2024 P6 Term Review 2 P1 Q30",
      "image_needed": true,
      "image_page": 16,
      "image_bbox": [0.1, 0.4, 0.92, 0.62],
      "image_loc": "cylinder (35 cm diameter) on the ground, 12.1 m from a wall",
      "image_options": false,
      "image_file": "q30.png",
      "notes": "No answer key -- solved. If the radius is ignored (centre travels the full 12.1 m), the answer would be exactly 11 turns (12.1 ÷ 1.1); accounting for the 0.175 m radius gives 10 complete turns. UNCERTAIN -- verify the intended interpretation."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "Mrs Chan bought 150 pencils and 100 erasers for her students. She divided the pencils equally among them and had 17 pencils left. She also divided the erasers equally among the students and had 5 erasers left. How many students were there? [?]",
      "answer0": "19",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 113,
      "difficulty_id": 3,
      "explanation": "Pencils given out = 150 − 17 = 133; erasers given out = 100 − 5 = 95. The number of students divides both 133 (= 7 × 19) and 95 (= 5 × 19), so it is a common factor = 19. Since 17 pencils were left over, there must be more than 17 students, so the number of students = 19.",
      "hints": ["Work out how many pencils and erasers were actually shared.", "The number of students is a common factor greater than 17."],
      "source": "Henry Park 2024 P6 Term Review 2 P2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "No answer key -- solved."
    },
    {
      "n": 32,
      "type_id": 2,
      "question": "Five boys shared the cost of a present equally. When calculating the amount for each share, one of the boys made a mistake by dividing the cost of the present by 4 instead of 5. Each boy paid $3.75 more than his original share. What is the cost of the present? [?]",
      "answer0": "75",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "Let cost = C. Wrong share = \\(\\dfrac{C}{4}\\), correct share = \\(\\dfrac{C}{5}\\). \\(\\dfrac{C}{4} - \\dfrac{C}{5} = 3.75\\) → \\(\\dfrac{C}{20} = 3.75\\) → C = 75. The present cost $75.",
      "hints": ["The $3.75 is the difference between dividing by 4 and by 5.", "\\(\\dfrac{C}{4} - \\dfrac{C}{5} = \\dfrac{C}{20}\\)."],
      "source": "Henry Park 2024 P6 Term Review 2 P2 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "No answer key -- solved. Answer in dollars: $75."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "The figure is made up of three identical squares. Given that EH = 72 cm, CY = 16 cm and BX = YF, find the area of the shaded part. [?]",
      "answer0": "288",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 138,
      "difficulty_id": 3,
      "explanation": "Three identical squares make EH = 72 cm, so each square has side 24 cm. The diagonal AE drops 24 cm over 72 cm. At G (x = 24): XG = 24 − 8 = 16 cm; at F (x = 48): YF = 24 − 16 = 8 cm (and CY = 24 − 8 = 16 cm, matching the given). The shaded region is the trapezium XGFY with parallel sides 16 cm and 8 cm and width 24 cm: area = \\(\\dfrac{1}{2}(16 + 8)\\times 24 = 288\\) cm².",
      "hints": ["Each square's side = 72 ÷ 3.", "The shaded region is a trapezium under the diagonal in the middle square."],
      "source": "Henry Park 2024 P6 Term Review 2 P2 Q3",
      "image_needed": true,
      "image_page": 18,
      "image_bbox": [0.16, 0.1, 0.6, 0.28],
      "image_loc": "three identical squares with diagonal AE and points B,C,D,E,F,G,H,X,Y",
      "image_options": false,
      "image_file": "q33.png",
      "notes": "No answer key -- solved. Answer in cm²."
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "The average cost of 3 different backpacks is $12.70. The total cost of 2 of the backpacks is $16.80. What is the cost of the third backpack? [?]",
      "answer0": "21.30",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 204,
      "difficulty_id": 2,
      "explanation": "Total of 3 backpacks = 3 × $12.70 = $38.10. Third backpack = $38.10 − $16.80 = $21.30.",
      "hints": ["Total = average × number of items.", "Subtract the cost of the two known backpacks."],
      "source": "Henry Park 2024 P6 Term Review 2 P2 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "No answer key -- solved. Answer in dollars: $21.30."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "Malik had 140 postcards and Neil had 112 postcards. After Malik gave some of his postcards to Neil, the ratio of the number of postcards that Malik had to the number of postcards that Neil had was 1 : 2. How many postcards did Neil have in the end? [?]",
      "answer0": "168",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 213,
      "difficulty_id": 2,
      "explanation": "Total postcards stay 140 + 112 = 252. New ratio Malik : Neil = 1 : 2 means 3 units = 252, so 1 unit = 84. Neil = 2 units = 168.",
      "hints": ["The total number of postcards does not change.", "Split 252 in the ratio 1 : 2."],
      "source": "Henry Park 2024 P6 Term Review 2 P2 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "No answer key -- solved."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "ABC bookshop sells only 1 type of calculator. The bar graph shows the number of calculators sold from January to June; the bar for June has not been drawn.<br>(a) Given that the average number of calculators sold from January to June was 55, find the number of calculators sold in June. [?]<br>(b) The total amount collected from all the calculators sold in March was $1046.40 including 9% GST. Find the cost of 1 calculator excluding GST. [?]",
      "answer0": "105",
      "answer1": "32",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 3,
      "explanation": "(a) Total for 6 months = 55 × 6 = 330. Jan 35 + Feb 55 + Mar 30 + Apr 45 + May 60 = 225. June = 330 − 225 = 105. (b) Excluding GST, March total = $1046.40 ÷ 1.09 = $960. March sold 30 calculators, so 1 calculator = $960 ÷ 30 = $32.",
      "hints": ["Total = average × 6, then subtract the five known bars.", "Divide by 1.09 to remove the 9% GST, then by the number sold."],
      "source": "Henry Park 2024 P6 Term Review 2 P2 Q6",
      "image_needed": true,
      "image_page": 20,
      "image_bbox": [0.12, 0.18, 0.86, 0.48],
      "image_loc": "bar graph of calculators sold Jan-June (June bar missing)",
      "image_options": false,
      "image_file": "q36.png",
      "notes": "No answer key -- solved. Bar readings (Jan 35, Feb 55, Mar 30, Apr 45, May 60) -- verify against the graph. answer0=(a) June, answer1=(b) cost in dollars."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "ABPJ is a parallelogram and LDEG is a trapezium. AMPF is a straight line. LD is parallel to JP. \\(\\angle ABP = 65°\\), \\(\\angle MPH = 48°\\) and \\(\\angle LHJ = 54°\\).<br>(a) Find \\(\\angle JAP\\). [?]<br>(b) Find \\(\\angle GLD\\). [?]",
      "answer0": "67",
      "answer1": "78",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "Multi-step angle work using the parallelogram ABPJ (opposite angle \\(\\angle AJP = 65°\\), co-interior \\(\\angle JAB = 115°\\)), the straight line AMPF, the parallel pair LD ∥ JP, and the given 48° and 54°. Provisional values: \\(\\angle JAP \\approx 67°\\) and \\(\\angle GLD \\approx 78°\\).",
      "hints": ["Use opposite and co-interior angles of the parallelogram.", "Use the parallel lines LD ∥ JP with the straight line AMPF."],
      "source": "Henry Park 2024 P6 Term Review 2 P2 Q7",
      "image_needed": true,
      "image_page": 21,
      "image_bbox": [0.16, 0.12, 0.78, 0.42],
      "image_loc": "parallelogram ABPJ + trapezium LDEG with straight line AMPF, angles 65°, 48°, 54° marked",
      "image_options": false,
      "image_file": "q37.png",
      "notes": "No answer key -- solved, but LOW CONFIDENCE: this is figure-dependent multi-step geometry with no printed key. The provisional answers (a) 67° and (b) 78° MUST be verified by a human against the actual diagram before use. answer0=(a), answer1=(b)."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "Candice takes 30 days to knit 5 identical scarves while Shelley takes 20 days to knit 4 identical sweaters. Given that Candice and Shelley started knitting on the same day, how many sweaters would Shelley have knitted completely by the time Candice has knitted 24 scarves? [?]",
      "answer0": "28",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Candice: 5 scarves in 30 days = 6 days per scarf. 24 scarves take 24 × 6 = 144 days. Shelley: 4 sweaters in 20 days = 5 days per sweater. In 144 days she completes 144 ÷ 5 = 28.8, i.e. 28 complete sweaters.",
      "hints": ["Find days per scarf and days per sweater.", "Find the total time, then how many whole sweaters fit."],
      "source": "Henry Park 2024 P6 Term Review 2 P2 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "No answer key -- solved. 'Completely' -> take the whole number (28)."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "Pauline, Queenie and Roger had 162 marbles altogether. Pauline gave \\(\\dfrac{3}{10}\\) of her marbles to Queenie and \\(\\dfrac{1}{4}\\) of her marbles to Roger. After that, all 3 children had the same number of marbles. How many more marbles did Pauline have than Queenie at first? [?]",
      "answer0": "102",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Each child ends with 162 ÷ 3 = 54. Pauline keeps \\(1 - \\dfrac{3}{10} - \\dfrac{1}{4} = \\dfrac{9}{20}\\) of her marbles = 54 → Pauline = 120. Queenie + \\(\\dfrac{3}{10}\\times 120\\) = 54 → Queenie = 18. Pauline − Queenie = 120 − 18 = 102.",
      "hints": ["Each child ends with one-third of 162.", "Pauline keeps \\(\\dfrac{9}{20}\\) of her marbles."],
      "source": "Henry Park 2024 P6 Term Review 2 P2 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "No answer key -- solved. Part (a) of this Paper-2 question asks for the ratio 20:3:4 (a ratio, so not FIB) -- here only the numeric part (b) = 102 is captured as the FIB answer; the ratio is noted: P:Q:R = 20:3:4."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "Andrea baked some cookies. She gave \\(\\dfrac{1}{5}\\) of them to her relatives and 56 of them to her friends. She was left with \\(\\dfrac{2}{3}\\) of the cookies. She packed these cookies into 34 bags. Some bags contained 4 cookies while the rest contained 12 cookies.<br>(a) How many cookies were packed into the 34 bags? [?]<br>(b) How many bags contained 4 cookies each? [?]",
      "answer0": "280",
      "answer1": "16",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "(a) Cookies given away = \\(\\dfrac{1}{5}\\) + 56 = \\(\\dfrac{1}{3}\\) of the total (since \\(\\dfrac{2}{3}\\) is left). So \\(\\dfrac{1}{3} - \\dfrac{1}{5} = \\dfrac{2}{15}\\) of the total = 56 → total = 420. Cookies packed = \\(\\dfrac{2}{3}\\times 420 = 280\\). (b) Let x bags of 4 and (34 − x) bags of 12: 4x + 12(34 − x) = 280 → 408 − 8x = 280 → 8x = 128 → x = 16. So 16 bags held 4 cookies.",
      "hints": ["The 56 cookies plus \\(\\dfrac{1}{5}\\) make up \\(\\dfrac{1}{3}\\) of the total.", "Set up 4x + 12(34 − x) = packed total."],
      "source": "Henry Park 2024 P6 Term Review 2 P2 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "No answer key -- solved. answer0=(a) cookies packed, answer1=(b) number of 4-cookie bags."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "At a musical, a total of 1932 photocards were given out. Each adult received 5 photocards, each boy received 4 photocards and each girl received 3 photocards. \\(\\dfrac{1}{4}\\) of the people who attended the musical were adults, \\(\\dfrac{4}{9}\\) of the remainder were boys and the rest were girls. How many adults were there at the musical? [?]",
      "answer0": "126",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Let total people = 36u (a common multiple). Adults = \\(\\dfrac{1}{4}\\) = 9u. Remainder = 27u; boys = \\(\\dfrac{4}{9}\\times 27u = 12u\\); girls = 15u. Photocards = 5(9u) + 4(12u) + 3(15u) = 45u + 48u + 45u = 138u = 1932 → u = 14. Adults = 9u = 126. (Re-checking with the fractions gives adults = 9 × 14 = 126.)",
      "hints": ["Pick a total that makes \\(\\dfrac{1}{4}\\) and \\(\\dfrac{4}{9}\\) whole (e.g. 36u).", "Total photocards = 5 × adults + 4 × boys + 3 × girls = 1932."],
      "source": "Henry Park 2024 P6 Term Review 2 P2 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "No answer key -- solved. NOTE: working gives 138u = 1932 -> u = 14 -> adults = 9u = 126 (not 84); answer0 corrected to 126."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "A shop had 60 t-shirts and some blouses at first. After 10 t-shirts and 20% of the blouses were sold, the shop had a total of 118 t-shirts and blouses left. How many blouses did the shop have at first? [?]",
      "answer0": "85",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 175,
      "difficulty_id": 3,
      "explanation": "T-shirts left = 60 − 10 = 50. So blouses left = 118 − 50 = 68. These are 80% of the blouses (20% sold), so blouses at first = 68 ÷ 0.8 = 85.",
      "hints": ["Find how many t-shirts are left, then how many blouses are left.", "The 68 blouses left are 80% of the original blouses."],
      "source": "Henry Park 2024 P6 Term Review 2 P2 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "No answer key -- solved."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "The figure is made up of a big semicircle, two small semicircles and a square. The base of the big semicircle is 120 cm.<br>(a) Find the radius of the small semicircle. [?]<br>(b) Find the area of the unshaded parts of the figure. (Take \\(\\pi = 3.14\\)) [?]",
      "answer0": "30",
      "answer1": "4239",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 222,
      "difficulty_id": 3,
      "explanation": "(a) Big semicircle diameter = 120 cm, radius = 60 cm. The two small semicircles sit along the radius (60 cm) split into two diameters, so each small diameter = 60 cm and small radius = 30 cm. (b) Big semicircle area = \\(\\dfrac{1}{2}\\times 3.14\\times 60^2 = 5652\\) cm². The square has side 60 cm (= small diameter) and the shaded region (square + small-semicircle parts) totals about 1413 cm², leaving an unshaded area of approximately 4239 cm².",
      "hints": ["The small semicircles lie along the big semicircle's radius.", "Unshaded = big semicircle area − shaded square/semicircle parts."],
      "source": "Henry Park 2024 P6 Term Review 2 P2 Q13",
      "image_needed": true,
      "image_page": 27,
      "image_bbox": [0.3, 0.1, 0.66, 0.28],
      "image_loc": "big semicircle (120 cm base) containing two small semicircles and a square",
      "image_options": false,
      "image_file": "q43.png",
      "notes": "No answer key -- solved. Part (a) radius = 30 cm is confident; part (b) is figure-dependent (exact shaded/unshaded layout) and LOW CONFIDENCE -- the ~4239 cm² value must be verified against the actual figure. answer0=(a) cm, answer1=(b) cm²."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "Jason has several identical square-based wooden blocks. He glued 5 such blocks to form a cuboid as shown in Figure 1. He stacked 4 such cuboids to form a larger cuboid shown in Figure 2. Given that the length of the cuboid is 80 cm, find the volume of the cuboid shown in Figure 2. [?]",
      "answer0": "81920",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 190,
      "difficulty_id": 3,
      "explanation": "Five square-based blocks in a row make a cuboid of length 80 cm, so each block is 80 ÷ 5 = 16 cm, and its square base is 16 cm × 16 cm. One Figure-1 cuboid = 80 × 16 × 16 = 20 480 cm³. Figure 2 stacks 4 of them: 4 × 20 480 = 81 920 cm³.",
      "hints": ["Each block's side = 80 ÷ 5.", "Volume of Figure 2 = 4 × volume of one Figure-1 cuboid."],
      "source": "Henry Park 2024 P6 Term Review 2 P2 Q14",
      "image_needed": true,
      "image_page": 28,
      "image_bbox": [0.16, 0.16, 0.82, 0.42],
      "image_loc": "single block, Figure 1 (5 blocks in a row), Figure 2 (4 such cuboids stacked), 80 cm marked",
      "image_options": false,
      "image_file": "q44.png",
      "notes": "No answer key -- solved. NOTE: each block = 16 cm, one cuboid = 20 480 cm³, Figure 2 = 4 × 20 480 = 81 920 cm³; answer0 corrected to 81920. Answer in cm³. Verify how the 4 cuboids are stacked against the figure."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "ABXD and WXYZ are overlapping rectangles and XMNO is a square. \\(\\angle YXO = \\angle OXW\\) and \\(\\angle MXD = 20°\\).<br>(a) Find \\(\\angle t\\). [?]<br>(b) Find \\(\\angle p\\). [?]",
      "answer0": "25",
      "answer1": "20",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "WXYZ is a rectangle so \\(\\angle WXY = 90°\\); since \\(\\angle YXO = \\angle OXW\\), XO bisects it giving \\(\\angle OXW = \\angle OXY = 45°\\). XMNO is a square so \\(\\angle MXO = 90°\\). With \\(\\angle MXD = 20°\\) and the right angle of rectangle ABXD at X, the sub-angles p and t are found by subtracting the known angles at X. Provisional values: \\(\\angle t \\approx 25°\\), \\(\\angle p \\approx 20°\\).",
      "hints": ["A rectangle gives a 90° angle at X; XO bisects it.", "A square gives \\(\\angle MXO = 90°\\); combine with \\(\\angle MXD = 20°\\)."],
      "source": "Henry Park 2024 P6 Term Review 2 P2 Q15",
      "image_needed": true,
      "image_page": 29,
      "image_bbox": [0.16, 0.1, 0.7, 0.36],
      "image_loc": "two overlapping rectangles ABXD and WXYZ with square XMNO, angle 20° marked, angles p and t at X",
      "image_options": false,
      "image_file": "q45.png",
      "notes": "No answer key -- solved, but LOW CONFIDENCE: figure-dependent multi-step geometry with no printed key. Provisional (a) t ≈ 25°, (b) p ≈ 20° MUST be verified by a human against the diagram. answer0=(a) t, answer1=(b) p."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "Bessie stacked 8 identical cups: the stack of 8 cups is 82 cm tall and a stack of 4 cups is 44 cm tall. Find the height of the 6 stacked cups. [?]",
      "answer0": "63",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Each extra cup adds the same 'lip' height. From 4 cups (44 cm) to 8 cups (82 cm): 4 extra cups add 82 − 44 = 38 cm, so each extra cup = 9.5 cm. Height = first cup + (n − 1) × 9.5. From 4 cups: first cup + 3 × 9.5 = 44 → first cup = 15.5 cm. For 6 cups: 15.5 + 5 × 9.5 = 15.5 + 47.5 = 63 cm.",
      "hints": ["Find how much each extra cup adds (the lip).", "Use one stack to find the base cup height, then compute 6 cups."],
      "source": "Henry Park 2024 P6 Term Review 2 P2 Q16",
      "image_needed": true,
      "image_page": 30,
      "image_bbox": [0.14, 0.08, 0.92, 0.3],
      "image_loc": "Figure A (stack of 8 = 82 cm, 4 = 44 cm) and Figure B (stack of 6 cups)",
      "image_options": false,
      "image_file": "q46.png",
      "notes": "No answer key -- solved. Answer in cm."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "Nelson used some sticks to form figures in a pattern. The number of sticks per figure is 3, 7, 10, 14, 17, ... for Figures 1, 2, 3, 4, 5.<br>(a) How many sticks are there in Figure 6 and Figure 7? [?] (Figure 6), [?] (Figure 7)<br>(b) How many sticks are there in Figure 107? [?]<br>(c) Nelson used 2327 sticks to form a figure. Which Figure number did he form? [?]",
      "answer0": "21",
      "answer1": "24",
      "answer2": "374",
      "answer3": "665",
      "correct_answer": null,
      "skill_id": 240,
      "difficulty_id": 3,
      "explanation": "The sticks go up by +4, +3, +4, +3, ... (3, 7, 10, 14, 17, 21, 24, ...). (a) Figure 6 = 17 + 4 = 21; Figure 7 = 21 + 3 = 24. (b) Group figures in pairs (each pair adds 7 sticks): Figure (2k−1) = 7k − 4 and Figure (2k) = 7k. Figure 107 is odd: 107 = 2(54) − 1, so sticks = 7 × 54 − 4 = 378 − 4 = 374. (c) For an even figure 2k: 7k = 2327 is not whole. For an odd figure 2k−1: 7k − 4 = 2327 → 7k = 2331 → k = 333, figure number = 2(333) − 1 = 665. So Figure 665.",
      "hints": ["The increases alternate +4, +3.", "Group figures in pairs (each pair adds 7 sticks)."],
      "source": "Henry Park 2024 P6 Term Review 2 P2 Q17",
      "image_needed": true,
      "image_page": 31,
      "image_bbox": [0.04, 0.1, 0.92, 0.24],
      "image_loc": "Figures 1-5 of the stick pattern",
      "image_options": false,
      "image_file": "q47.png",
      "notes": "No answer key -- solved. NOTE: (a) Fig6=21, Fig7=24 are confident; the closed form gives (b) Figure 107 = 374 sticks and (c) 2327 sticks -> Figure 665. answer0=Fig6, answer1=Fig7, answer2=Fig107 sticks (374), answer3=figure number for 2327 sticks (665). [answer2/answer3 corrected from initial draft]"
    }
  ]
}