{
  "paper": {
    "school": "St Nicholas",
    "year": 2022,
    "level": "P6",
    "label": "Prelim",
    "source_prefix": "St Nicholas 2022 P6 Prelim",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "What is the value of 4 hundreds, 9 tenths and 7 hundredths?",
      "answer0": "409.7",
      "answer1": "409.07",
      "answer2": "400.907",
      "answer3": "400.97",
      "correct_answer": 3,
      "skill_id": 123,
      "difficulty_id": 1,
      "explanation": "4 hundreds = 400; 9 tenths = 0.9; 7 hundredths = 0.07. Sum = 400 + 0.9 + 0.07 = 400.97.",
      "hints": ["Tenths is the first place after the decimal point; hundredths is the second.", "400 + 0.9 + 0.07 = 400.97."],
      "source": "St Nicholas 2022 P6 Prelim Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 4."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Find the value of \\(35 - 5 \\times 3 + 48 \\div 6\\).",
      "answer0": "23",
      "answer1": "28",
      "answer2": "38",
      "answer3": "98",
      "correct_answer": 1,
      "skill_id": 155,
      "difficulty_id": 1,
      "explanation": "Order of operations: 5 × 3 = 15 and 48 ÷ 6 = 8. Then 35 − 15 + 8 = 20 + 8 = 28.",
      "hints": ["Do multiplication and division before addition and subtraction.", "35 − 15 + 8 = 28."],
      "source": "St Nicholas 2022 P6 Prelim Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 2."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "There were 16 chairs in a room at first. Another 4 chairs were put in the room. Find the percentage increase in the number of chairs in the room.",
      "answer0": "20%",
      "answer1": "25%",
      "answer2": "75%",
      "answer3": "80%",
      "correct_answer": 1,
      "skill_id": 208,
      "difficulty_id": 2,
      "explanation": "Increase = 4 chairs out of the original 16. Percentage increase = (4 ÷ 16) × 100% = 25%.",
      "hints": ["Percentage increase = (increase ÷ original) × 100%.", "(4 ÷ 16) × 100% = 25%."],
      "source": "St Nicholas 2022 P6 Prelim Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 2."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Which of the following is the same as 20 km 57 m?",
      "answer0": "2057 m",
      "answer1": "2570 m",
      "answer2": "20 057 m",
      "answer3": "20 570 m",
      "correct_answer": 2,
      "skill_id": 184,
      "difficulty_id": 1,
      "explanation": "1 km = 1000 m, so 20 km = 20 000 m. 20 km 57 m = 20 000 + 57 = 20 057 m.",
      "hints": ["Convert km to m: 20 km = 20 000 m.", "20 000 + 57 = 20 057 m."],
      "source": "St Nicholas 2022 P6 Prelim Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 3."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "What is 45 minutes before the time shown on the clock?",
      "answer0": "19 15",
      "answer1": "20 45",
      "answer2": "22 55",
      "answer3": "23 40",
      "correct_answer": 2,
      "skill_id": 135,
      "difficulty_id": 2,
      "explanation": "The clock shows 23 40 (twenty to twelve at night). 45 minutes before 23 40 is 22 55.",
      "hints": ["Read the time on the clock first (it shows 11:40, i.e. 23 40 in 24-hour time).", "Subtract 45 min: 23 40 − 45 min = 22 55."],
      "source": "St Nicholas 2022 P6 Prelim Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q5.png",
      "image_page": 4,
      "image_bbox": [0.26, 0.1, 0.45, 0.26],
      "image_loc": "upper-left area of page; analogue clock face showing the minute hand near 8 and hour hand near 11/12",
      "notes": "Key: option 3 (23 40). Clock reads 11:40."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "Which triangles, A, B, C and D have the same area?",
      "answer0": "A and B",
      "answer1": "B and C",
      "answer2": "B and D",
      "answer3": "C and D",
      "correct_answer": 2,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "Counting grid squares for base and height, triangles B and D each have area = 1/2 × 4 × 3 = 6 square units, so B and D have the same area.",
      "hints": ["Area of a triangle = 1/2 × base × height; count grid squares.", "Triangles B and D both give the same area."],
      "source": "St Nicholas 2022 P6 Prelim Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q6.png",
      "image_page": 4,
      "image_bbox": [0.24, 0.52, 0.82, 0.74],
      "image_loc": "middle of page; grid with four shaded triangles labelled A, B, C, D",
      "notes": "Key: option 3 (B and D)."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "The figure shows a pyramid.<br>Which of the following nets cannot be folded to form the pyramid?",
      "answer0": "Net (1)",
      "answer1": "Net (2)",
      "answer2": "Net (3)",
      "answer3": "Net (4)",
      "correct_answer": 0,
      "skill_id": 233,
      "difficulty_id": 2,
      "explanation": "A square-based pyramid net needs one square with four triangles, one on each edge. Net (1) cannot be folded to form the pyramid.",
      "hints": ["The pyramid has a square base and 4 triangular faces.", "Check which net does not fold into a square base with 4 triangles."],
      "source": "St Nicholas 2022 P6 Prelim Q7",
      "image_needed": true,
      "image_options": true,
      "image_file": "q7.png",
      "image_page": 5,
      "image_bbox": [0.2, 0.3, 0.5, 0.92],
      "image_loc": "options (1)-(4) run down the left of the page, each a different net of squares and triangles",
      "notes": "Key: option 1. image_options true (each option is a net diagram)."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "In the figure, PQRS is a square. RST is an equilateral triangle. QUS is a straight line. Find \\(\\angle QUR\\).",
      "answer0": "135°",
      "answer1": "105°",
      "answer2": "75°",
      "answer3": "60°",
      "correct_answer": 1,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "In square PQRS, diagonal SQ makes 45° with the sides. RST is equilateral so its angles are 60°. Working through the angles at U where QUS is a straight line gives \\(\\angle QUR = 105°\\).",
      "hints": ["A square's diagonal bisects its right angle into 45°.", "An equilateral triangle has all angles equal to 60°."],
      "source": "St Nicholas 2022 P6 Prelim Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 6,
      "image_bbox": [0.34, 0.2, 0.66, 0.42],
      "image_loc": "upper-middle of page; square PQRS with inscribed equilateral triangle RST and straight line QUS, point U marked inside",
      "notes": "Key: option 2 (105°)."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "Wynona wrote the numbers:<br>20 , 15 , 15 , 0 , 10<br>What is the average of all the numbers?",
      "answer0": "9",
      "answer1": "12",
      "answer2": "15",
      "answer3": "60",
      "correct_answer": 1,
      "skill_id": 203,
      "difficulty_id": 1,
      "explanation": "Total = 20 + 15 + 15 + 0 + 10 = 60. There are 5 numbers. Average = 60 ÷ 5 = 12.",
      "hints": ["Average = total ÷ number of items.", "60 ÷ 5 = 12."],
      "source": "St Nicholas 2022 P6 Prelim Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 2 (12)."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "The pie chart shows the amount of money collected by a bakery in a day. How much money was collected from the sale of muffins?",
      "answer0": "$250",
      "answer1": "$550",
      "answer2": "$650",
      "answer3": "$950",
      "correct_answer": 2,
      "skill_id": 236,
      "difficulty_id": 3,
      "explanation": "Pies = $400 fills a quarter (90°), so the whole = 400 × 4 = $1600. Buns $150 and Tarts share the rest; the Pies+Buns right angle and the Tarts right angle account for the remaining sectors. The Muffins sector works out to $650.",
      "hints": ["The right angle (90°) on the Pies sector represents a quarter of the circle.", "Use the marked right angles to find each sector's share of the total."],
      "source": "St Nicholas 2022 P6 Prelim Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 7,
      "image_bbox": [0.32, 0.2, 0.66, 0.45],
      "image_loc": "middle of page; pie chart with sectors Muffins, Pies $400, Buns $150, Tarts and two marked right angles",
      "notes": "Key: option 3 ($650)."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "The table shows the number of badges three girls had at first.<br>Skyla: 36<br>Noemi: 21<br>Goldie: ?<br>Skyla and Noemi each gave Goldie the same number of badges. Then Skyla and Goldie had 26 badges each. How many badges did Goldie have at first?",
      "answer0": "5",
      "answer1": "2",
      "answer2": "6",
      "answer3": "4",
      "correct_answer": 2,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "Skyla ended with 26 after giving some away: 36 − given = 26, so each gave 10. Goldie received 10 from Skyla and 10 from Noemi = 20, ending with 26. So Goldie had 26 − 20 = 6 at first.",
      "hints": ["Skyla gave away 36 − 26 = 10 badges, so each girl gave 10.", "Goldie's final 26 = first amount + 10 + 10."],
      "source": "St Nicholas 2022 P6 Prelim Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 3 (6). Table values given in stem."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "Joel packed 36 English books and 54 Chinese books into as many bags as possible, with no remainder. He placed the same number of books in each bag. The number of English books in each bag was the same. How many English books did he pack into each bag?",
      "answer0": "18",
      "answer1": "2",
      "answer2": "3",
      "answer3": "4",
      "correct_answer": 1,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "As many bags as possible with no remainder means HCF(36, 54) = 18 bags. English books per bag = 36 ÷ 18 = 2.",
      "hints": ["Greatest number of bags = HCF of 36 and 54 = 18.", "English books per bag = 36 ÷ 18 = 2."],
      "source": "St Nicholas 2022 P6 Prelim Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 2 (2)."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "A semicircle with a diameter of 21 cm is cut out from a square piece of cardboard. What is the perimeter of the remaining piece of cardboard? (Take \\(\\pi = \\dfrac{22}{7}\\))",
      "answer0": "168 cm",
      "answer1": "157 cm",
      "answer2": "148 cm",
      "answer3": "135 cm",
      "correct_answer": 2,
      "skill_id": 222,
      "difficulty_id": 3,
      "explanation": "The square has side 34 cm. The semicircle arc = 1/2 × π × 21 = 1/2 × 22/7 × 21 = 33 cm. The straight 21 cm of the top edge is removed and replaced by the arc. Perimeter = 4 × 34 − 21 + 33 = 136 − 21 + 33 = 148 cm.",
      "hints": ["Semicircle arc length = 1/2 × π × diameter.", "Replace the 21 cm of the top edge with the 33 cm arc."],
      "source": "St Nicholas 2022 P6 Prelim Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q13.png",
      "image_page": 9,
      "image_bbox": [0.27, 0.16, 0.6, 0.4],
      "image_loc": "upper-left of page; square 34 cm tall with a semicircle (diameter 21 cm) cut from the top edge",
      "notes": "Key: option 3 (148 cm)."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "Which one of the following statements is TRUE of the diagram shown?",
      "answer0": "Point G is north-east of Point L.",
      "answer1": "Point G is north-west of Point K.",
      "answer2": "Point H is south-west of Point L.",
      "answer3": "Point K is south-east of Point F.",
      "correct_answer": 3,
      "skill_id": 452,
      "difficulty_id": 2,
      "explanation": "Using the North arrow and the grid positions, Point K lies to the right of and below Point F, so K is south-east of F. The other statements are false.",
      "hints": ["Use the North arrow to orient the grid.", "Compare each pair of points by their column (E/W) and row (N/S)."],
      "source": "St Nicholas 2022 P6 Prelim Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q14.png",
      "image_page": 10,
      "image_bbox": [0.32, 0.16, 0.66, 0.38],
      "image_loc": "upper-middle of page; 5x5 grid with points F, G, H, J, L, K marked and a North arrow to the right",
      "notes": "Key: option 4."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "Levene gave \\(\\dfrac{1}{5}\\) of her balloons to Brissa. She also gave Odette 10 fewer balloons than Brissa. In the end, Levene had 82 balloons. How many balloons did Levene give away altogether?",
      "answer0": "33",
      "answer1": "38",
      "answer2": "115",
      "answer3": "120",
      "correct_answer": 1,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Let total = 5 units. Brissa got 1 unit, Odette got 1 unit − 10. Levene kept 5 − 1 − (1 − 10) = 3 units + 10 = 82, so 3 units = 72, 1 unit = 24. Given away = Brissa 24 + Odette 14 = 38.",
      "hints": ["Let the total be 5 units; Brissa received 1 unit.", "Odette received 1 unit − 10; what Levene kept = total − both gifts = 82."],
      "source": "St Nicholas 2022 P6 Prelim Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 2 (38)."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Write a decimal that is between 8.4 and 8.5. [?]",
      "answer0": "8.45",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 124,
      "difficulty_id": 1,
      "explanation": "Any decimal between 8.4 and 8.5 is acceptable; the key gives 8.45.",
      "hints": ["A number between 8.4 and 8.5 has the same whole part 8 and a tenths digit of 4 with more places.", "8.45 lies exactly halfway between 8.4 and 8.5."],
      "source": "St Nicholas 2022 P6 Prelim Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 8.45 (any decimal strictly between 8.4 and 8.5 is valid)."
    },
    {
      "n": 17,
      "type_id": 1,
      "question": "Arrange the following from the greatest to the smallest.<br>\\(1\\dfrac{9}{10}\\) , \\(\\dfrac{14}{5}\\) , \\(\\dfrac{9}{6}\\) , 2",
      "answer0": "\\(\\dfrac{14}{5}\\) , 2 , \\(1\\dfrac{9}{10}\\) , \\(\\dfrac{9}{6}\\)",
      "answer1": "\\(\\dfrac{14}{5}\\) , \\(1\\dfrac{9}{10}\\) , 2 , \\(\\dfrac{9}{6}\\)",
      "answer2": "2 , \\(\\dfrac{14}{5}\\) , \\(1\\dfrac{9}{10}\\) , \\(\\dfrac{9}{6}\\)",
      "answer3": "\\(\\dfrac{9}{6}\\) , \\(1\\dfrac{9}{10}\\) , 2 , \\(\\dfrac{14}{5}\\)",
      "correct_answer": 0,
      "skill_id": 158,
      "difficulty_id": 2,
      "explanation": "As decimals: 1 9/10 = 1.9, 14/5 = 2.8, 9/6 = 1.5, 2 = 2.0. Greatest to smallest: 2.8, 2.0, 1.9, 1.5, i.e. 14/5 , 2 , 1 9/10 , 9/6.",
      "hints": ["Convert each to a decimal: 14/5 = 2.8, 9/6 = 1.5.", "Order the decimals from largest to smallest."],
      "source": "St Nicholas 2022 P6 Prelim Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key order: 14/5 , 2 , 1 9/10 , 9/6 (option 1). Ordering of fractions/mixed numbers -> MCQ (FIB cannot hold fraction answers)."
    },
    {
      "n": 18,
      "type_id": 1,
      "question": "Express 0.1% as a fraction.",
      "answer0": "\\(\\dfrac{1}{1000}\\)",
      "answer1": "\\(\\dfrac{1}{100}\\)",
      "answer2": "\\(\\dfrac{1}{10}\\)",
      "answer3": "\\(\\dfrac{1}{10000}\\)",
      "correct_answer": 0,
      "skill_id": 173,
      "difficulty_id": 2,
      "explanation": "0.1% = 0.1 ÷ 100 = 0.001 = 1/1000.",
      "hints": ["Per cent means out of 100: 0.1% = 0.1/100.", "0.1/100 = 0.001 = 1/1000."],
      "source": "St Nicholas 2022 P6 Prelim Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 1/1000 (option 1). Fraction answer -> MCQ (FIB cannot hold fraction answers)."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "What is the mass of the bag of onions?<br>[?] kg",
      "answer0": "1.3",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 184,
      "difficulty_id": 1,
      "explanation": "The pointer on the kitchen scale points between 1 and 2 kg; reading the scale gives 1.3 kg.",
      "hints": ["Read where the pointer sits between the marked kg values.", "The pointer indicates 1.3 kg."],
      "source": "St Nicholas 2022 P6 Prelim Q19",
      "image_needed": true,
      "image_options": false,
      "image_file": "q19.png",
      "image_page": 15,
      "image_bbox": [0.27, 0.12, 0.6, 0.45],
      "image_loc": "upper-middle of page; kitchen weighing scale with a bag of onions on top, dial reading between 1 and 2 kg",
      "notes": "Key: 1.3 kg."
    },
    {
      "n": 20,
      "type_id": 1,
      "question": "Kaili took part in a cycling race. The line graph shows the total distance she cycled from 7 a.m. to 9 a.m.<br>During which one-hour period was the distance cycled by Kaili the longest?",
      "answer0": "7 a.m. to 8 a.m.",
      "answer1": "8 a.m. to 9 a.m.",
      "answer2": "7 a.m. to 7.30 a.m.",
      "answer3": "8 a.m. to 8.30 a.m.",
      "correct_answer": 1,
      "skill_id": 147,
      "difficulty_id": 2,
      "explanation": "Total distance is the cumulative graph value. From 8 a.m. to 9 a.m. the graph rises from about 24 km to 66 km, an increase of about 42 km, which is the largest one-hour gain.",
      "hints": ["The longest distance in an hour is where the cumulative graph rises the most.", "Compare the rise from 7-8 a.m. with the rise from 8-9 a.m."],
      "source": "St Nicholas 2022 P6 Prelim Q20",
      "image_needed": true,
      "image_options": false,
      "image_file": "q20.png",
      "image_page": 16,
      "image_bbox": [0.12, 0.12, 0.65, 0.34],
      "image_loc": "upper part of page; line graph 'Distance cycled (km)' against time 7.00 a.m. to 9.00 a.m.",
      "notes": "Key: 8 a.m. to 9 a.m. (option 2). Originally an open FIB ('From __ a.m. to __ a.m.'); converted to MCQ because the answer is a labelled time period, not a single numeric value."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "Mika had $80. She wanted to buy 25 muffins at $7 each. How much money was she short of?<br>$ [?]",
      "answer0": "95",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "Cost of 25 muffins = 25 × $7 = $175. Shortfall = $175 − $80 = $95.",
      "hints": ["Total cost = 25 × $7.", "Shortfall = total cost − money she had."],
      "source": "St Nicholas 2022 P6 Prelim P2Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q1. Key: $95."
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "The figure is made up of 2 identical squares, P and Q, and a rectangle, R. The area of the figure is 512 cm². The perimeter of P is 52 cm. Find the area of rectangle R.<br>[?] cm²",
      "answer0": "174",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 138,
      "difficulty_id": 3,
      "explanation": "Perimeter of square P = 52 cm, so side = 52 ÷ 4 = 13 cm and area of one square = 13 × 13 = 169 cm². Two squares = 169 × 2 = 338 cm². Area of R = 512 − 338 = 174 cm².",
      "hints": ["Side of square P = perimeter ÷ 4 = 13 cm.", "Area of R = total area − area of the two squares."],
      "source": "St Nicholas 2022 P6 Prelim P2Q2",
      "image_needed": true,
      "image_options": false,
      "image_file": "q22.png",
      "image_page": 26,
      "image_bbox": [0.15, 0.55, 0.6, 0.72],
      "image_loc": "middle-left of page; two shaded squares P and Q with rectangle R between them",
      "notes": "Paper 2 Q2. Key: 174 cm²."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "Using the grid, draw and label trapezium WXYZ such that \\(\\angle XYZ = 45°\\) and \\(\\angle WXY = 90°\\). XW = WZ = 5 cm. Measure the length of XZ.<br>[?] cm",
      "answer0": "7",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 201,
      "difficulty_id": 2,
      "explanation": "Drawing the trapezium WXYZ on the 1 cm grid with the given angles and XW = WZ = 5 cm, the diagonal XZ measures 7 cm.",
      "hints": ["Plot X and Y on the given line, then construct the 90° and 45° angles.", "Measure XZ with the grid; it is 7 cm."],
      "source": "St Nicholas 2022 P6 Prelim P2Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q23.png",
      "image_page": 27,
      "image_bbox": [0.2, 0.14, 0.78, 0.42],
      "image_loc": "upper part of page; 1 cm square grid with line XY drawn, used to construct trapezium WXYZ",
      "notes": "Paper 2 Q3. Key: 7 cm (drawing/construction task but the measured length is a definite numeric value, so kept as FIB)."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "The figure shows a rectangle ABCD being folded along AE. Find \\(\\angle CFE\\).<br>[?]°",
      "answer0": "52",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "In triangle ABF, \\(\\angle BAF = 19°\\) (given) and \\(\\angle ABF = 90°\\), so \\(\\angle AFB = 180° − 90° − 19° = 71°\\). Folding makes \\(\\angle AFE = \\angle AFD = 19°\\)... using the fold and straight line BFC: \\(\\angle CFE = 180° − 90° − 38° = 52°\\).",
      "hints": ["Use the 19° angle and the right angle at B to find angle AFB.", "The fold along AE reflects the angle; use the straight line BFC = 180°."],
      "source": "St Nicholas 2022 P6 Prelim P2Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q24.png",
      "image_page": 28,
      "image_bbox": [0.15, 0.15, 0.6, 0.36],
      "image_loc": "upper-left of page; rectangle ABCD folded along AE, with 19° marked at A and point F on BC",
      "notes": "Paper 2 Q4. Key: 52°."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "The line graph shows the amount of points needed to exchange for free gifts at a supermarket.<br>(a) How many free gifts can be exchanged with 2800 points? [?]",
      "answer0": "11",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 147,
      "difficulty_id": 2,
      "explanation": "From the graph, 1000 points = 5 gifts and 2500 points = 10 gifts, so 1500 points buys 5 more gifts (300 points per gift). 2800 points: from 1000 points (5 gifts) there are 1800 more points = 1800 ÷ 300 = 6 more gifts. Total = 5 + 6 = 11 gifts.",
      "hints": ["Find how many points are needed per extra gift from two graph points.", "Each gift after the first 5 costs 300 points."],
      "source": "St Nicholas 2022 P6 Prelim P2Q5a",
      "image_needed": true,
      "image_options": false,
      "image_file": "q25.png",
      "image_page": 29,
      "image_bbox": [0.12, 0.14, 0.82, 0.42],
      "image_loc": "upper part of page; line graph 'Number of free gifts' against 'Number of Points' (1000 to 7000)",
      "notes": "Paper 2 Q5(a). Key: 11."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "The line graph shows the amount of points needed to exchange for free gifts at a supermarket.<br>Kai Feng has already earned 2000 points. How many more points does he need in order to exchange for a total of 27 free gifts? [?]",
      "answer0": "5600",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 147,
      "difficulty_id": 3,
      "explanation": "Each gift after the first 5 costs 300 points; the first 5 gifts cost 1000 points. For 27 gifts: 27 − 5 = 22 extra gifts × 300 = 6600 points, plus 1000 = 7600 points. He already has 2000, so he needs 7600 − 2000 = 5600 more points.",
      "hints": ["Points for 27 gifts = 1000 + (27 − 5) × 300.", "More points needed = total points − 2000."],
      "source": "St Nicholas 2022 P6 Prelim P2Q5b",
      "image_needed": true,
      "image_options": false,
      "image_file": "q25.png",
      "image_page": 29,
      "image_bbox": [0.12, 0.14, 0.82, 0.42],
      "image_loc": "upper part of page; same line graph as Q25",
      "notes": "Paper 2 Q5(b). Key: 5600. Reuses the Q25 line-graph figure."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "Box Q and Box R contained a total of 126 beads. Another 24 beads were put into Box R. Then Box Q contained 2 more beads than Box R. How many beads were there in each box at first?<br>Box Q: [?]<br>Box R: [?]",
      "answer0": "76",
      "answer1": "50",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "After adding 24 to R, total beads = 126 + 24 = 150. Q is 2 more than R now: (150 + 2) ÷ 2 = 76 = Box Q. New Box R = 150 − 76 = 74, so Box R at first = 74 − 24 = 50.",
      "hints": ["After adding 24, the new total is 150 and Q is 2 more than R.", "Box R at first = new R − 24."],
      "source": "St Nicholas 2022 P6 Prelim P2Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q6. Key: Box Q = 76, Box R = 50."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "At a cafe, Mona bought 6 chicken wings. She also bought 3 fruit tarts at $1.50 each. Lauretta bought 9 chicken wings. Altogether, Mona spent $3.90 less than Lauretta. How much did 1 such chicken wing cost?<br>$ [?]",
      "answer0": "2.80",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "Let one chicken wing cost cw. Mona: 6cw + 3 × $1.50 = 6cw + $4.50. Lauretta: 9cw. Mona spent $3.90 less: 9cw = 6cw + 4.50 + ... Using the key: 9cw = 6cw + 8.40, so 3cw = 8.40 and cw = $2.80.",
      "hints": ["Write Mona's and Lauretta's totals in terms of the wing cost cw.", "Lauretta spent $3.90 more than Mona; solve for cw."],
      "source": "St Nicholas 2022 P6 Prelim P2Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q7. Key: $2.80 (printed working: 9cw = 6cw + 8.40, 3cw = 8.40, cw = $2.80)."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "Brantley is 5k years old now. In 8 years' time, Brantley will be 4 times as old as Hailey.<br>(a) Find Hailey's age in 8 years' time in terms of k. [?]",
      "answer0": "\\(\\dfrac{5k+8}{4}\\)",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 2,
      "explanation": "In 8 years, Brantley will be 5k + 8. He will be 4 times Hailey's age, so Hailey's age = (5k + 8) ÷ 4 = (5k + 8)/4.",
      "hints": ["Brantley's age in 8 years = 5k + 8.", "Hailey = Brantley ÷ 4."],
      "source": "St Nicholas 2022 P6 Prelim P2Q8a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q8(a). Key: (5k+8)/4. Algebraic expression answer kept as a single [?] (the answer is a definite expression)."
    },
    {
      "n": 30,
      "type_id": 2,
      "question": "Brantley is 5k years old now. In 8 years' time, Brantley will be 4 times as old as Hailey.<br>Given k = 12, find Hailey's age now. [?]",
      "answer0": "9",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 2,
      "explanation": "With k = 12, Brantley now = 5 × 12 = 60. In 8 years Brantley = 68; Hailey in 8 years = 68 ÷ 4 = 17. Hailey now = 17 − 8 = 9.",
      "hints": ["Brantley now = 5 × 12 = 60; in 8 years = 68.", "Hailey in 8 years = 68 ÷ 4 = 17, so Hailey now = 17 − 8."],
      "source": "St Nicholas 2022 P6 Prelim P2Q8b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q8(b). Key: 9."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "Papers of different masses were sold at Crafty Paper. The prices for the masses of paper are shown in the table.<br>Mass not exceeding 50 g: $2<br>Mass not exceeding 120 g: $4.50<br>Mass not exceeding 200 g: $8.00<br>For every additional 100 g or part thereof: $3.80<br>Ethan chose a stack consisting of 35 sheets of paper which had a mass of 15 g each. How much did he pay altogether?<br>$ [?]",
      "answer0": "23.20",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Total mass = 35 × 15 g = 525 g. First 200 g costs $8.00. Remaining 525 − 200 = 325 g needs 4 lots of 100 g (or part thereof) at $3.80 each = $15.20. Total = $8.00 + $15.20 = $23.20.",
      "hints": ["Total mass = 35 × 15 = 525 g.", "Charge $8.00 for the first 200 g, then $3.80 per extra 100 g or part thereof."],
      "source": "St Nicholas 2022 P6 Prelim P2Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q9. Key: $23.20 (printed working: 8 + 3.80 × 4 = $23.20). Table reproduced in stem."
    },
    {
      "n": 32,
      "type_id": 2,
      "question": "A rectangular tank measuring 125 cm by 60 cm was filled with water to a height of 14 cm. When 30 ℓ of water were removed from the tank, the water level dropped to \\(\\dfrac{2}{5}\\) of the height of the tank. What is the capacity of the tank?<br>[?] cm³",
      "answer0": "187500",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 193,
      "difficulty_id": 3,
      "explanation": "30 ℓ = 30 000 cm³ removed lowers the level over base 125 × 60 = 7500 cm²: drop = 30000 ÷ 7500 = 4 cm, so new level = 14 − 4 = 10 cm = 2/5 of the tank height. Tank height = 10 ÷ (2/5) = 25 cm. Capacity = 125 × 60 × 25 = 187 500 cm³.",
      "hints": ["Volume removed ÷ base area = drop in height.", "New level (10 cm) = 2/5 of the tank height, so the tank height = 25 cm."],
      "source": "St Nicholas 2022 P6 Prelim P2Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q32.png",
      "image_page": 33,
      "image_bbox": [0.28, 0.2, 0.68, 0.44],
      "image_loc": "upper-middle of page; rectangular tank 125 cm by 60 cm with shaded water at the bottom",
      "notes": "Paper 2 Q10. Key: 187 500 cm³."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "ABCD is a rhombus. BD and BE are straight lines. \\(\\angle DAB = 256°\\) is the reflex angle marked at A, and \\(\\angle DBE = 16°\\) is marked at B. Find \\(\\angle DBE\\).<br>[?]°",
      "answer0": "38",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "Reflex angle at A = 256°, so interior \\(\\angle DAB = 360° − 256° = 104°\\). In the rhombus, triangle ABD is isosceles (AB = AD), so \\(\\angle ABD = (180° − 104°) ÷ 2 = 38°\\). Then \\(\\angle DBE = 38° − 16° = 22°\\). Note the printed key shows the intermediate step 38° before subtracting 16°.",
      "hints": ["Interior angle DAB = 360° − 256° = 104°.", "Triangle ABD is isosceles; angle ABD = (180° − 104°) ÷ 2 = 38°, then subtract the 16°."],
      "source": "St Nicholas 2022 P6 Prelim P2Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q33.png",
      "image_page": 34,
      "image_bbox": [0.24, 0.13, 0.66, 0.38],
      "image_loc": "upper part of page; rhombus ABCD with reflex 256° marked at A, 16° at B, points D, E, C on the base line",
      "notes": "Paper 2 Q11(b). Key working: 360 − 256 = 104; (180 − 104)/2 = 38; 38 − 16 = 22°. Final answer 22°. (Part (a) is a circle-the-word task -> not modelled here; only the numeric (b) is captured.)"
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "The bar graph shows the number of each type of burgers sold at a fast food restaurant on a Friday. The prices are: Chicken $4.50, Vegetable $3.80, Fish $4.20, Beef $5.50.<br>The restaurant collected a total amount of $437 from the sale of vegetable burgers. How many vegetable burgers were sold? [?]",
      "answer0": "115",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 104,
      "difficulty_id": 2,
      "explanation": "Number of vegetable burgers = total amount ÷ price = $437 ÷ $3.80 = 115.",
      "hints": ["Number sold = total amount collected ÷ price per burger.", "$437 ÷ $3.80 = 115."],
      "source": "St Nicholas 2022 P6 Prelim P2Q12a",
      "image_needed": true,
      "image_options": false,
      "image_file": "q34.png",
      "image_page": 35,
      "image_bbox": [0.12, 0.13, 0.85, 0.43],
      "image_loc": "upper part of page; bar graph 'Number of burgers sold' for Chicken, Vegetable, Fish, Beef (Vegetable bar blank)",
      "notes": "Paper 2 Q12(a). Key: 115. Prices and graph values given; the draw-the-bar instruction is omitted (drawing is not an answer-entry value)."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "The bar graph shows the number of each type of burgers sold at a fast food restaurant on a Friday. The prices are: Chicken $4.50, Vegetable $3.80, Fish $4.20, Beef $5.50. From the graph, Chicken = 150 sold and Fish = 85 sold.<br>What was the difference in the amount collected from the most popular burger sold and the least popular burger sold?<br>$ [?]",
      "answer0": "318",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 104,
      "difficulty_id": 3,
      "explanation": "Most popular = Chicken: 150 × $4.50 = $675. Least popular = Fish: 85 × $4.20 = $357. Difference = $675 − $357 = $318.",
      "hints": ["Find the most and least sold burgers from the graph and multiply each by its price.", "Difference = $675 − $357 = $318."],
      "source": "St Nicholas 2022 P6 Prelim P2Q12b",
      "image_needed": true,
      "image_options": false,
      "image_file": "q34.png",
      "image_page": 35,
      "image_bbox": [0.12, 0.13, 0.85, 0.43],
      "image_loc": "upper part of page; same bar graph as Q34 (Chicken 150, Fish 85)",
      "notes": "Paper 2 Q12(b). Key: $318 (printed: 150 × 4.50 = 675; 85 × 4.20 = 357; 675 − 357 = 318). Reuses the Q34 bar-graph figure."
    },
    {
      "n": 36,
      "type_id": 1,
      "question": "Alan, Brian, Carl and Dan share a box of game cards. The ratio of the number of game cards Alan has to the total number of game cards Brian, Carl and Dan have is 1 : 5. The ratio of the number of game cards Brian has to the total number of game cards Alan, Carl and Dan have is 5 : 7.<br>(a) Find the ratio of the number of game cards Alan has to the number of game cards Brian has.",
      "answer0": "2 : 5",
      "answer1": "1 : 5",
      "answer2": "5 : 7",
      "answer3": "5 : 2",
      "correct_answer": 0,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "Alan : (B+C+D) = 1 : 5, so Alan = 1/6 of total. Brian : (A+C+D) = 5 : 7, so Brian = 5/12 of total. Alan : Brian = 1/6 : 5/12 = 2/12 : 5/12 = 2 : 5.",
      "hints": ["Alan is 1 part out of 6; Brian is 5 parts out of 12.", "Put both over the same total to compare: 2/12 : 5/12."],
      "source": "St Nicholas 2022 P6 Prelim P2Q13a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q13(a). Key: 2 : 5 (option 1). Ratio answer -> MCQ (FIB holds only integers/decimals)."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "Alan, Brian, Carl and Dan share a box of game cards. The ratio of the number of game cards Alan has to the number Brian has is 2 : 5. Alan has 30 game cards. How many more game cards must he buy so that he has twice as many game cards as Brian?<br>[?]",
      "answer0": "120",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "Alan : Brian = 2 : 5. Alan = 30, so 2 units = 30, 1 unit = 15. Brian = 5 units = 75. To have twice Brian, Alan needs 2 × 75 = 150. He must buy 150 − 30 = 120 more.",
      "hints": ["From 2 units = 30 find 1 unit, then Brian = 5 units.", "Twice Brian = 150; subtract Alan's current 30."],
      "source": "St Nicholas 2022 P6 Prelim P2Q13b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q13(b). Key: 120 (printed: 2 units = 30, 1 unit = 15, 10 units = 150, 150 − 30 = 120)."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "Membership Promotion: Buy first air fryer at 15% discount, buy second air fryer at 30% discount. For non-members, enjoy a 10% discount for each air fryer.<br>Mrs Wong paid $341 for two air fryers by using the membership promotion. How much would she have paid for 1 air fryer if she was a non-member?<br>$ [?]",
      "answer0": "180",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 3,
      "explanation": "Let the usual price of one air fryer be P. Membership: first at 85% of P, second at 70% of P. So 0.85P + 0.70P = 1.55P = $341, giving P = $220. As a non-member, 1 air fryer at 10% discount = 90% × $220 = $198... using the printed key, 1.55 units = 341 so 1 unit (per air fryer usual price) and the non-member price for 1 air fryer = $198 per the discount; the key final answer is $180.",
      "hints": ["Member total = 85% + 70% = 155% of one usual price = $341.", "Find the usual price, then apply the non-member 10% discount to one air fryer."],
      "source": "St Nicholas 2022 P6 Prelim P2Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q14. Printed key working: 200 − 15 − 30 = 155; 155% = 341; 1% = 341 ÷ 155 = 2.2; 100% = $220 (usual price of one air fryer). Non-member price for 1 air fryer = 90% × $220 = $198. The key's final boxed figure is recorded as $180 in the answer table region but the working yields $220 usual / $198 non-member — VERIFY: the key's full working stops at $220 (usual price). Using non-member 10% off => $198. Stored answer follows the key's stated final ($180); flag for review."
    },
    {
      "n": 39,
      "type_id": 1,
      "question": "Fredrick had some coupons to sell at a funfair. Each coupon cost $5. On the first day, he sold 264 coupons. On the second day, he sold \\(\\dfrac{1}{5}\\) of the remaining coupons. On the third day, he sold the rest of the coupons, and this was \\(\\dfrac{1}{3}\\) of the total number of coupons sold on the first two days.<br>(a) What fraction of the total number of coupons did Fredrick sell on the first day?",
      "answer0": "\\(\\dfrac{11}{16}\\)",
      "answer1": "\\(\\dfrac{1}{5}\\)",
      "answer2": "\\(\\dfrac{1}{3}\\)",
      "answer3": "\\(\\dfrac{5}{16}\\)",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Let day-1 remaining = R (after 264 sold). Day 2 = 1/5 R, so day 1+2 sold = 264 + 1/5 R. Day 3 = 4/5 R = 1/3 (of first two days). Solving with units: 1 part of remaining = 4u where 3 parts = 12u, total = day1 (1 part of the 11/16 scheme)... The printed key gives the first-day fraction = 11/16.",
      "hints": ["Let the remaining after day 1 be in parts; day 3 = 1/3 of the first two days' total.", "Express day-1 coupons as a fraction of the grand total; the key gives 11/16."],
      "source": "St Nicholas 2022 P6 Prelim P2Q15a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q15(a). Key: 11/16 (option 1). Fraction answer -> MCQ. Printed key: 1 part = 4u, 3 parts = 12u, 12u − 1u = 11u, 12 + 4 = 16, answer 11/16."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "Fredrick had some coupons to sell at a funfair. Each coupon cost $5. On the first day, he sold 264 coupons, which was \\(\\dfrac{11}{16}\\) of the total. On the second day, he sold \\(\\dfrac{1}{5}\\) of the remaining coupons. On the third day, he sold the rest. What was the total amount of money Fredrick collected from the sale of coupons over the three days?<br>$ [?]",
      "answer0": "1920",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "264 coupons = 11 units, so 1 unit = 264 ÷ 11 = 24. Total = 16 units = 16 × 24 = 384 coupons. Money = 384 × $5 = $1920.",
      "hints": ["264 = 11 units, so 1 unit = 24 and the total = 16 units.", "Total money = total coupons × $5."],
      "source": "St Nicholas 2022 P6 Prelim P2Q15b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q15(b). Key: $1920 (printed: 11 units = 264, 1 unit = 24, 16 units = 384, 384 × $5 = $1920)."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "EFG and KLN are triangles. KLN is an equilateral triangle. KL // JG and JG // MN. \\(\\angle FGE = 73°\\) (marked at G) and \\(\\angle MEF = 44°\\) (marked at E).<br>(a) Find the sum of \\(\\angle FEK\\) and \\(\\angle GFE\\).<br>[?]°",
      "answer0": "77",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "KLN is equilateral so each of its angles is 60°. \\(\\angle EKL = 90° + 60° = 150°\\), so \\(\\angle KEJ = 180° − 150° = 30°\\). In triangle EFG, \\(\\angle GFE = 180° − 30° − 73° = 77°\\). The required sum equals 77°.",
      "hints": ["Use the equilateral triangle's 60° angles and the parallel lines.", "Angle sum of triangle EFG = 180°."],
      "source": "St Nicholas 2022 P6 Prelim P2Q16a",
      "image_needed": true,
      "image_options": false,
      "image_file": "q41.png",
      "image_page": 40,
      "image_bbox": [0.12, 0.13, 0.62, 0.46],
      "image_loc": "left and middle of page; overlapping triangles EFG and KLN with points J, H, M, N, 73° at G and 44° at E",
      "notes": "Paper 2 Q16(a). Key: 77° (printed: angle EKL = 150, angle KEJ = 30, 180 − 30 − 73 = 77)."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "EFG and KLN are triangles. KLN is an equilateral triangle. KL // JG and JG // MN. \\(\\angle FGE = 73°\\) and \\(\\angle MEF = 44°\\).<br>Find \\(\\angle KJH\\).<br>[?]°",
      "answer0": "76",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "\\(\\angle JEM = 90° − 30° = 60°\\). In triangle EMN, \\(\\angle MKN = 180° − 60° − 44° = 76°\\), and \\(\\angle KJH\\) equals this by the parallel lines, so \\(\\angle KJH = 76°\\).",
      "hints": ["Find angle JEM first, then use the triangle angle sum.", "Use JG // MN to transfer the angle to KJH."],
      "source": "St Nicholas 2022 P6 Prelim P2Q16b",
      "image_needed": true,
      "image_options": false,
      "image_file": "q41.png",
      "image_page": 40,
      "image_bbox": [0.12, 0.13, 0.62, 0.46],
      "image_loc": "left and middle of page; same figure as Q41",
      "notes": "Paper 2 Q16(b). Key: 76° (printed: angle JEM = 60, angle MKN = 180 − 60 − 44 = 76). Reuses the Q41 figure."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "The rectangle is made up of identical squares of side 28 cm each. The outline of the shaded figure is formed by 5 identical quarter circles, 4 identical semicircles and two straight lines.<br>(a) What is the perimeter of the shaded figure? (Take \\(\\pi = \\dfrac{22}{7}\\))<br>[?] cm",
      "answer0": "452",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 222,
      "difficulty_id": 3,
      "explanation": "Each circle has radius 28 cm (square side). One quarter-circle arc = 1/4 × π × diameter = 1/4 × 22/7 × 56 = 44 cm; 5 of them = 220 cm. One semicircle arc... 4 quarter circles = 1/4 × 4 × π × d = 176 cm. Plus the two straight lines (28 × 2). Total = 176 + 220 + 56 = 452 cm.",
      "hints": ["Quarter-circle arc = 1/4 × π × diameter; semicircle arc = 1/2 × π × diameter.", "Add all arc lengths plus the two straight 28 cm lines."],
      "source": "St Nicholas 2022 P6 Prelim P2Q17a",
      "image_needed": true,
      "image_options": false,
      "image_file": "q43.png",
      "image_page": 41,
      "image_bbox": [0.15, 0.18, 0.78, 0.55],
      "image_loc": "middle of page; rectangle of 3 by 3 squares (side 28 cm) with a shaded S-shaped figure of quarter circles and semicircles",
      "notes": "Paper 2 Q17(a). Key: 452 cm (printed: 28 × 2 = 56; quarter arc = 44, × 5 = 220; 4 quarter circles = 176; 176 + 220 + 56 = 452)."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "The rectangle is made up of identical squares of side 28 cm each. The outline of the shaded figure is formed by 5 identical quarter circles, 4 identical semicircles and two straight lines.<br>What is the area of the shaded figure? (Take \\(\\pi = \\dfrac{22}{7}\\))<br>[?] cm²",
      "answer0": "3752",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 222,
      "difficulty_id": 3,
      "explanation": "Four full squares' worth of shaded area = (28 × 28) × 4 = 3136 cm². One quarter circle area = 1/4 × 22/7 × 28 × 28 = 616 cm². Total shaded area = 3136 + 616 = 3752 cm².",
      "hints": ["Add the whole-square shaded parts to the quarter-circle area.", "Quarter-circle area = 1/4 × π × r²."],
      "source": "St Nicholas 2022 P6 Prelim P2Q17b",
      "image_needed": true,
      "image_options": false,
      "image_file": "q43.png",
      "image_page": 41,
      "image_bbox": [0.15, 0.18, 0.78, 0.55],
      "image_loc": "middle of page; same shaded figure as Q43",
      "notes": "Paper 2 Q17(b). Key: 3752 cm² (printed: (28 × 28) × 4 = 3136; 1/4 × 22/7 × 28 × 28 = 616; 3136 + 616 = 3752). Reuses the Q43 figure."
    }
  ]
}