{
  "paper": {
    "school": "Singapore Chinese Girls' School",
    "year": 2025,
    "level": "P6",
    "label": "Prelim",
    "source_prefix": "SCGS 2025 P6 Prelim",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "What is the value of the digit 4 in 347 082?",
      "answer0": "400",
      "answer1": "4000",
      "answer2": "40 000",
      "answer3": "400 000",
      "correct_answer": 2,
      "skill_id": 105,
      "difficulty_id": 1,
      "explanation": "In 347 082, the digit 4 is in the ten-thousands place, so its value is 40 000.",
      "hints": ["Identify the place value of the digit 4.", "4 is the ten-thousands digit."],
      "source": "SCGS 2025 P6 Prelim Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: Q1 = 3 (1-based) -> option index 2 (40 000)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "700 + 40 + 0.5 + 0.004 = [blank]",
      "answer0": "74.540",
      "answer1": "704.504",
      "answer2": "740.504",
      "answer3": "740.540",
      "correct_answer": 2,
      "skill_id": 124,
      "difficulty_id": 1,
      "explanation": "700 + 40 + 0.5 + 0.004 = 740.504 (hundreds, tens, tenths, thousandths).",
      "hints": ["Add the whole numbers and the decimals by place value.", "0.5 is 5 tenths and 0.004 is 4 thousandths."],
      "source": "SCGS 2025 P6 Prelim Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "MCQ as printed (the line is part of the equation, not an answer blank). Answer key: Q2 = 3 (1-based) -> option index 2 (740.504)."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Which of the following is the smallest fraction?",
      "answer0": "Option 1",
      "answer1": "Option 2",
      "answer2": "Option 3",
      "answer3": "Option 4",
      "correct_answer": 3,
      "skill_id": 162,
      "difficulty_id": 2,
      "explanation": "Comparing the four printed fractions, option 4 has the smallest value.",
      "hints": ["Convert the fractions to a common denominator or to decimals.", "The smallest fraction has the least value."],
      "source": "SCGS 2025 P6 Prelim Q3",
      "image_needed": true,
      "image_options": true,
      "image_page": 2,
      "image_bbox": [0.18, 0.6, 0.5, 0.78],
      "image_loc": "four fraction options (1)-(4) listed down the page (printed as math, not text-renderable here)",
      "image_file": null,
      "notes": "Image-option MCQ: the four options are printed fractions not rendered in the PDF text layer. Crop each option to q3_opt0.png .. q3_opt3.png. Answer key: Q3 = 4 (1-based) -> option index 3."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "The figure shows a trapezium. Which of the following statements is correct?",
      "answer0": "\\(\\angle b\\) < 90°",
      "answer1": "\\(\\angle a\\) = \\(\\angle c\\)",
      "answer2": "\\(\\angle a\\) + \\(\\angle b\\) = 180°",
      "answer3": "\\(\\angle a\\) + \\(\\angle c\\) > \\(\\angle b\\) + \\(\\angle d\\)",
      "correct_answer": 2,
      "skill_id": 200,
      "difficulty_id": 2,
      "explanation": "The trapezium has one pair of parallel sides (the top and bottom). \\(\\angle a\\) and \\(\\angle b\\) are co-interior angles between the parallel sides, so \\(\\angle a\\) + \\(\\angle b\\) = 180°.",
      "hints": ["Identify the pair of parallel sides (the arrows).", "Co-interior angles on the same side add up to 180°."],
      "source": "SCGS 2025 P6 Prelim Q4",
      "image_needed": true,
      "image_page": 3,
      "image_bbox": [0.22, 0.12, 0.66, 0.3],
      "image_loc": "trapezium with marked angles a, b, c, d and parallel-side arrows",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: Q4 = 3 (1-based) -> option index 2 (\\(\\angle a\\) + \\(\\angle b\\) = 180°)."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "In the number line, what is the decimal represented by A?",
      "answer0": "2.50",
      "answer1": "2.55",
      "answer2": "3.20",
      "answer3": "3.25",
      "correct_answer": 3,
      "skill_id": 124,
      "difficulty_id": 2,
      "explanation": "The number line runs from 2 to 4 divided into 8 equal parts, so each mark is 0.25. A is at the 5th mark: 2 + 5 × 0.25 = 3.25.",
      "hints": ["Find the value of each interval between 2 and 4.", "Count the marks from 2 to A."],
      "source": "SCGS 2025 P6 Prelim Q5",
      "image_needed": true,
      "image_page": 3,
      "image_bbox": [0.2, 0.52, 0.86, 0.64],
      "image_loc": "number line from 2 to 4 with arrow marked A",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: Q5 = 4 (1-based) -> option index 3 (3.25)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "In the square grid, how many shapes have both parallel and perpendicular lines?",
      "answer0": "1",
      "answer1": "2",
      "answer2": "3",
      "answer3": "0",
      "correct_answer": 1,
      "skill_id": 100,
      "difficulty_id": 2,
      "explanation": "Checking each shape on the grid for sides that are both parallel and perpendicular, 2 of the shapes have both kinds of lines.",
      "hints": ["A shape qualifies only if it has at least one pair of parallel lines AND one pair of perpendicular lines.", "Check each shape against the grid lines."],
      "source": "SCGS 2025 P6 Prelim Q6",
      "image_needed": true,
      "image_page": 4,
      "image_bbox": [0.18, 0.12, 0.88, 0.27],
      "image_loc": "row of shapes drawn on a square grid",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: Q6 = 2 (1-based) -> option index 1 (2)."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "Simplify 20 + 5y + 8 − 2y − 7 + 3.",
      "answer0": "18 + 3y",
      "answer1": "18 + 7y",
      "answer2": "24 + 3y",
      "answer3": "24 + 7y",
      "correct_answer": 2,
      "skill_id": 238,
      "difficulty_id": 2,
      "explanation": "Constants: 20 + 8 − 7 + 3 = 24. y-terms: 5y − 2y = 3y. So the expression simplifies to 24 + 3y.",
      "hints": ["Group the number terms and the y terms separately.", "20 + 8 − 7 + 3 and 5y − 2y."],
      "source": "SCGS 2025 P6 Prelim Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: Q7 = 3 (1-based) -> option index 2 (24 + 3y)."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "Mrs Devi has a piece of square paper. She cut out a new shape from the piece of square paper. The new shape has the same perimeter as the original square paper. Which one of the following could be the new shape?",
      "answer0": "Shape 1",
      "answer1": "Shape 2",
      "answer2": "Shape 3",
      "answer3": "Shape 4",
      "correct_answer": 0,
      "skill_id": 220,
      "difficulty_id": 3,
      "explanation": "A notch cut straight in and back out keeps the perimeter the same only if the cut edges add back exactly what was removed. Shape 1's cut preserves the original square's perimeter.",
      "hints": ["A cut that goes in and comes straight back out keeps the perimeter unchanged.", "Compare the boundary length of each cut shape to the original square."],
      "source": "SCGS 2025 P6 Prelim Q8",
      "image_needed": true,
      "image_options": true,
      "image_page": 5,
      "image_bbox": [0.3, 0.32, 0.52, 0.88],
      "image_loc": "original square at top, then four cut-out shapes labelled (1)-(4) down the page",
      "image_file": null,
      "notes": "Image-option MCQ: the four options are pictures of cut shapes. Crop each to q8_opt0.png .. q8_opt3.png. Answer key: Q8 = 1 (1-based) -> option index 0 (Shape 1)."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "The bar graph shows the number of students participating in CCA activities after school. 8 more students participated in English Drama Club than in Art Club. How many more students participated in Dance than in Netball?",
      "answer0": "6",
      "answer1": "8",
      "answer2": "3",
      "answer3": "12",
      "correct_answer": 0,
      "skill_id": 104,
      "difficulty_id": 2,
      "explanation": "Use the '8 more in English Drama than Art Club' to find the scale of one unit on the graph, then read the Dance and Netball bars; the difference is 6 students.",
      "hints": ["Use the given clue (8 more) to work out the value of each gridline.", "Read the Dance and Netball bars and subtract."],
      "source": "SCGS 2025 P6 Prelim Q9",
      "image_needed": true,
      "image_page": 6,
      "image_bbox": [0.18, 0.13, 0.92, 0.38],
      "image_loc": "bar graph of students in CCA activities (English Drama Club, Netball, Dance, Art Club)",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: Q9 = 1 (1-based) -> option index 0 (6)."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "Two boxes were placed on a weighing scale (total reading 9520 g). One box is 5.2 kg. What is the mass of box B?",
      "answer0": "4320 g",
      "answer1": "4500 g",
      "answer2": "9000 g",
      "answer3": "9468 g",
      "correct_answer": 0,
      "skill_id": 184,
      "difficulty_id": 2,
      "explanation": "Total = 9520 g. The other box = 5.2 kg = 5200 g. Box B = 9520 − 5200 = 4320 g.",
      "hints": ["Convert 5.2 kg to grams.", "Subtract from the total reading of 9520 g."],
      "source": "SCGS 2025 P6 Prelim Q10",
      "image_needed": true,
      "image_page": 6,
      "image_bbox": [0.54, 0.66, 0.92, 0.8],
      "image_loc": "weighing scale showing two boxes (B and 5.2 kg) with total reading 9520 g",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: Q10 = 1 (1-based) -> option index 0 (4320 g)."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "The figure shows a prism. Which one of the following is a net of the prism?",
      "answer0": "Net 1",
      "answer1": "Net 2",
      "answer2": "Net 3",
      "answer3": "Net 4",
      "correct_answer": 0,
      "skill_id": 232,
      "difficulty_id": 3,
      "explanation": "The prism has two triangular ends and three rectangular faces. Net 1 folds correctly to form this prism.",
      "hints": ["A prism net has 2 matching triangles (the ends) and 3 rectangles.", "Mentally fold each net to check it forms the given prism."],
      "source": "SCGS 2025 P6 Prelim Q11",
      "image_needed": true,
      "image_options": true,
      "image_page": 7,
      "image_bbox": [0.24, 0.1, 0.9, 0.75],
      "image_loc": "prism figure at top, then four nets in a 2x2 layout labelled (1)-(4)",
      "image_file": null,
      "notes": "Image-option MCQ: the four options are pictures of nets. Crop each to q11_opt0.png .. q11_opt3.png. Answer key: Q11 = 1 (1-based) -> option index 0 (Net 1)."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "A gardener has a plot of land used only for growing vegetables and flowers. In March, 500 m² was used for growing vegetables, and the rest was used for growing flowers. In June, the vegetable plot area increased by 20%, while the flower plot area decreased by 50%. Every part of the land was used for growing either vegetables or flowers, and the total land area remained the same. Find the total area of the plot of land.",
      "answer0": "100 m²",
      "answer1": "200 m²",
      "answer2": "600 m²",
      "answer3": "700 m²",
      "correct_answer": 3,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Vegetable area increased by 20% of 500 = 100 m². Since total area is unchanged, the flower area must decrease by 100 m², and that 100 m² is 50% of the original flower area, so flowers = 200 m². Total = 500 + 200 = 700 m².",
      "hints": ["Find the increase in the vegetable area (20% of 500).", "That increase equals the 50% decrease in flowers; work out the flower area, then the total."],
      "source": "SCGS 2025 P6 Prelim Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: Q12 = 4 (1-based) -> option index 3 (700 m²)."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "Dora had \\(\\dfrac{4}{5}\\) kg of flour. She used \\(\\dfrac{1}{2}\\) kg to bake a cake and \\(\\dfrac{1}{6}\\) of the remainder to bake cookies. How much flour had she left?",
      "answer0": "\\(\\dfrac{2}{15}\\) kg",
      "answer1": "\\(\\dfrac{1}{4}\\) kg",
      "answer2": "\\(\\dfrac{1}{3}\\) kg",
      "answer3": "\\(\\dfrac{3}{10}\\) kg",
      "correct_answer": 1,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "After the cake: 4/5 − 1/2 = 8/10 − 5/10 = 3/10 kg remaining. Cookies use 1/6 of the remainder, so 5/6 is left: 5/6 × 3/10 = 15/60 = 1/4 kg.",
      "hints": ["Subtract the cake's flour from the start.", "5/6 of the remainder is left after cookies."],
      "source": "SCGS 2025 P6 Prelim Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: Q13 = 2 (1-based) -> option index 1 (1/4 kg)."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "The table shows the number of different fruits in a basket at first: Apple 25, Orange 40, Mango 40, Pears 10. After 15 rotten apples were removed and 15 oranges were added to the basket, which pie chart best represents the final distribution of fruits in the basket in the end?",
      "answer0": "Pie chart 1",
      "answer1": "Pie chart 2",
      "answer2": "Pie chart 3",
      "answer3": "Pie chart 4",
      "correct_answer": 2,
      "skill_id": 236,
      "difficulty_id": 3,
      "explanation": "Final counts: Apple 25 − 15 = 10, Orange 40 + 15 = 55, Mango 40, Pears 10 (total 115). Pie chart 3 shows these proportions (Orange the largest, Apple and Pears small and equal).",
      "hints": ["Work out the final number of each fruit after the changes.", "Match the relative sizes (Orange largest, Apple = Pears = 10) to a pie chart."],
      "source": "SCGS 2025 P6 Prelim Q14",
      "image_needed": true,
      "image_options": true,
      "image_page": 9,
      "image_bbox": [0.16, 0.36, 0.9, 0.88],
      "image_loc": "four pie charts labelled (1)-(4) of fruit distribution (Apple, Orange, Mango, Pears)",
      "image_file": null,
      "notes": "Image-option MCQ: the four options are pie charts. Crop each to q14_opt0.png .. q14_opt3.png. Final counts Apple 10, Orange 55, Mango 40, Pears 10. Answer key: Q14 = 3 (1-based) -> option index 2 (Pie chart 3)."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "The picture shows a strip of paper with a pattern. There are 28 shaded rectangles altogether. What is the greatest possible number of unshaded rectangles I can have in this strip of paper?",
      "answer0": "15",
      "answer1": "39",
      "answer2": "42",
      "answer3": "45",
      "correct_answer": 2,
      "skill_id": 240,
      "difficulty_id": 3,
      "explanation": "From the repeating pattern, each shaded rectangle is followed by a fixed maximum number of unshaded rectangles. With 28 shaded rectangles, the greatest possible number of unshaded rectangles is 42.",
      "hints": ["Identify the repeating block of shaded and unshaded rectangles.", "Multiply the unshaded-per-block by the number of blocks, plus any extra at the ends."],
      "source": "SCGS 2025 P6 Prelim Q15",
      "image_needed": true,
      "image_page": 10,
      "image_bbox": [0.24, 0.18, 0.82, 0.26],
      "image_loc": "horizontal strip of paper with a pattern of shaded and unshaded rectangles",
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: Q15 = 3 (1-based) -> option index 2 (42)."
    },
    {
      "n": 16,
      "type_id": 1,
      "question": "Write one hundred and six thousand and forty-five in numerals.",
      "answer0": "106 045",
      "answer1": "160 045",
      "answer2": "106 450",
      "answer3": "1 006 045",
      "correct_answer": 0,
      "skill_id": 105,
      "difficulty_id": 1,
      "explanation": "One hundred and six thousand = 106 000; forty-five = 45. Together: 106 045.",
      "hints": ["Write the thousands part first (106 thousand).", "Add forty-five for the last part."],
      "source": "SCGS 2025 P6 Prelim Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Booklet B Q16. Converted to MCQ (write-in-numerals word task -> MCQ per spec word-answer rule). Answer key: 106 045 (option index 0)."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "Find the value of 9107 ÷ 7.<br>[?]",
      "answer0": "1301",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 156,
      "difficulty_id": 1,
      "explanation": "9107 ÷ 7 = 1301 (7 × 1301 = 9107).",
      "hints": ["Use long division.", "Check: 7 × 1301 = 9107."],
      "source": "SCGS 2025 P6 Prelim Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Booklet B Q17. Answer key: 9107 ÷ 7 = 1301."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "Round 81.473 to the nearest hundredth.<br>[?]",
      "answer0": "81.47",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 124,
      "difficulty_id": 1,
      "explanation": "The thousandths digit of 81.473 is 3, which is less than 5, so round down. 81.473 rounds to 81.47.",
      "hints": ["Look at the thousandths digit to decide rounding.", "3 is less than 5, so the hundredths digit stays the same."],
      "source": "SCGS 2025 P6 Prelim Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Booklet B Q18. Answer key: 81.473 = 81.47 (nearest hundredth)."
    },
    {
      "n": 19,
      "type_id": 1,
      "question": "Find the value of \\(\\dfrac{5}{6}\\) ÷ 10. Give your answer as a fraction in the simplest form.",
      "answer0": "\\(\\dfrac{1}{12}\\)",
      "answer1": "\\(\\dfrac{5}{60}\\)",
      "answer2": "\\(\\dfrac{1}{2}\\)",
      "answer3": "\\(\\dfrac{50}{6}\\)",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "5/6 ÷ 10 = 5/6 × 1/10 = 5/60 = 1/12.",
      "hints": ["Dividing by 10 is the same as multiplying by 1/10.", "Simplify 5/60."],
      "source": "SCGS 2025 P6 Prelim Q19",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Booklet B Q19. Converted to MCQ (fraction answer 1/12). Answer key: 5/6 x 1/10 = 1/12 (option index 0)."
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "The figure is not drawn to scale. AEB and CED are straight lines. The angle 104° is marked between CE and EB, and 67° between EA and EF. Find \\(\\angle\\)DEF.<br>[?]°",
      "answer0": "37",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 100,
      "difficulty_id": 2,
      "explanation": "\\(\\angle\\)AEC = 180° − 104° = 76° (angles on straight line AEB)... using vertical angles, \\(\\angle\\)DEF = 104° − 67° = 37°.",
      "hints": ["AEB and CED are straight lines, so use vertically opposite angles.", "\\(\\angle\\)DEF = 104° − 67°."],
      "source": "SCGS 2025 P6 Prelim Q20",
      "image_needed": true,
      "image_page": 13,
      "image_bbox": [0.28, 0.42, 0.62, 0.66],
      "image_loc": "two straight lines AEB and CED crossing at E with ray F and marked angles 104° and 67°",
      "image_options": false,
      "image_file": null,
      "notes": "Booklet B Q20. Answer key: angle DEF = 104 - 67 = 37°."
    },
    {
      "n": 21,
      "type_id": 1,
      "question": "The square grid shows the position of the different places in a neighborhood (Hawker Centre, Park, Market, Playground, Pet shop, School, Home). In which direction is the school from the market?",
      "answer0": "South-East",
      "answer1": "South-West",
      "answer2": "North-East",
      "answer3": "East",
      "correct_answer": 0,
      "skill_id": 452,
      "difficulty_id": 2,
      "explanation": "Using the North arrow and the grid positions, the School lies down and to the right of the Market, i.e. South-East.",
      "hints": ["Use the North arrow to orient the grid.", "South-East is down and to the right."],
      "source": "SCGS 2025 P6 Prelim Q21",
      "image_needed": true,
      "image_page": 14,
      "image_bbox": [0.3, 0.18, 0.74, 0.46],
      "image_loc": "square grid of neighbourhood places with a North arrow",
      "image_options": false,
      "image_file": null,
      "notes": "Booklet B Q21(a). Converted to MCQ (compass-direction word answer). Answer key: South-East (option index 0). Part (b) split to next entry."
    },
    {
      "n": 22,
      "type_id": 1,
      "question": "The square grid shows the position of the different places in a neighborhood (Hawker Centre, Park, Market, Playground, Pet shop, School, Home). Alyssa stood at one of the places facing the hawker centre. After she turned 135° anti-clockwise, she faced the home. Which place was Alyssa at?",
      "answer0": "Park",
      "answer1": "Market",
      "answer2": "Pet shop",
      "answer3": "Playground",
      "correct_answer": 2,
      "skill_id": 452,
      "difficulty_id": 3,
      "explanation": "From the Pet shop, facing the Hawker Centre and turning 135° anti-clockwise points towards the Home, so Alyssa was at the Pet shop.",
      "hints": ["Find the place from which facing the hawker centre and turning 135° anti-clockwise lands on home.", "Test each candidate place using the grid directions."],
      "source": "SCGS 2025 P6 Prelim Q21",
      "image_needed": true,
      "image_page": 14,
      "image_bbox": [0.3, 0.18, 0.74, 0.46],
      "image_loc": "square grid of neighbourhood places with a North arrow",
      "image_options": false,
      "image_file": null,
      "notes": "Booklet B Q21(b). Converted to MCQ (place-name word answer). Answer key: Pet shop (option index 2)."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "A leaking tap drips water. The volume of 4 drops of water is 3 mℓ of water. If 5 drops of water leaks out of the tap every second, how many mℓ of water leaks out of the tap in one minute?<br>[?] mℓ",
      "answer0": "225",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 192,
      "difficulty_id": 2,
      "explanation": "In one minute (60 s) at 5 drops/s, the tap drips 60 × 5 = 300 drops. Each drop = 3/4 mℓ. Volume = 300 × 3/4 = 225 mℓ. (Or 60 × 5 × 3/4 = 225 mℓ.)",
      "hints": ["Find the number of drops in one minute.", "Each drop is 3/4 mℓ; multiply."],
      "source": "SCGS 2025 P6 Prelim Q22",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Booklet B Q22. Answer key: 60 x 5 x 3/4 = 225 ml."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "The total distance between Town A and Town B is 80 km. At 08 00, a car left Town A for Town B, driving at a constant speed of 90 km/h. At the same time, a bus left Town B for Town A, driving at a constant speed of 60 km/h. At what time would the car and the bus pass each other?<br>[?]",
      "answer0": "08 32",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 219,
      "difficulty_id": 3,
      "explanation": "Combined speed = 90 + 60 = 150 km/h. Time to meet = 80 ÷ 150 = 8/15 h = 8/15 × 60 = 32 min. 32 minutes after 08 00 is 08 32.",
      "hints": ["Add the two speeds (they close the gap together).", "Time = distance ÷ combined speed; convert to minutes and add to 08 00."],
      "source": "SCGS 2025 P6 Prelim Q23",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Booklet B Q23. Answer is a 24-hour clock time (08 32). Answer key: combined 150 km/h; 80/150 = 8/15 h = 32 min; 08 00 + 32 min = 08 32."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "The ratio of the number of beads in Box X to the number of beads in Box Y was 3 : 7 at first. After 35 beads were removed from Box Y, the number of beads in Box X is \\(\\dfrac{2}{3}\\) that of Box Y. How many beads were there in Box X?<br>[?]",
      "answer0": "42",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 213,
      "difficulty_id": 3,
      "explanation": "Box X is unchanged. At first X : Y = 3 : 7, scale to X : Y = 6 : 14. After removal X is 2/3 of Y, i.e. X : Y = 6 : 9. So Box Y dropped from 14 to 9 units = 5 units = 35 beads, giving 1 unit = 7. Box X = 6 units = 6 × 7 = 42 beads.",
      "hints": ["Box X stays the same, so keep its units constant in both ratios.", "The 35 removed beads equal the change in Box Y's units."],
      "source": "SCGS 2025 P6 Prelim Q24",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Booklet B Q24. Answer key: before 6:14, after 6:9; 14-9 = 5 units = 35; 1u = 7; X = 6u = 42 beads."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "To create a symmetric pattern with PQ as the line of symmetry, some squares have already been shaded. What is the <u>minimum</u> number of additional squares that need to be shaded to achieve a symmetrical pattern?<br>[?]",
      "answer0": "6",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 145,
      "difficulty_id": 3,
      "explanation": "Reflecting the shaded squares across the vertical line PQ, the squares whose mirror images are not yet shaded must be added. The minimum number of additional squares needed is 6.",
      "hints": ["For each shaded square, its mirror image across PQ must also be shaded.", "Count only the mirror squares that are not already shaded."],
      "source": "SCGS 2025 P6 Prelim Q25",
      "image_needed": true,
      "image_page": 16,
      "image_bbox": [0.22, 0.18, 0.78, 0.52],
      "image_loc": "grid with some shaded squares and a vertical line of symmetry PQ",
      "image_options": false,
      "image_file": null,
      "notes": "Booklet B Q25. Answer key: minimum 6 additional squares."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "There are some cookies in a jar. The cookies can be put into packets of 6 or 8 with no cookies left over. When the cookies are put into packets of 10, there are 2 cookies left over. What is the smallest possible number of cookies in the jar?<br>[?]",
      "answer0": "72",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 115,
      "difficulty_id": 3,
      "explanation": "The number must be a common multiple of 6 and 8, so a multiple of LCM(6, 8) = 24: 24, 48, 72, 96... The remainder when divided by 10 must be 2. Checking: 24→4, 48→8, 72→2. So the smallest is 72.",
      "hints": ["The number is a multiple of the LCM of 6 and 8.", "Test those multiples for a remainder of 2 when divided by 10."],
      "source": "SCGS 2025 P6 Prelim Q26",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Booklet B Q26. Answer key: LCM(6,8) = 24; multiples 24,48,72...; 72 mod 10 = 2; smallest = 72."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "The figure shows a pattern of identical shaded rectangles. Reading along AB the lengths are 20 cm, 10 cm, 15 cm, 10 cm, 20 cm in repeating fashion. What is the length of AB? Give your answer in m.<br>[?] m",
      "answer0": "1.25",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 184,
      "difficulty_id": 3,
      "explanation": "Let the length of one rectangle be u cm. From the pattern, AB = 2u + 20 + 15 + 20 = 3u + 10 + 10, so 2u + 55 = 3u + 20, giving u = 35. Then AB = 2 × 35 + 55 = 125 cm = 1.25 m.",
      "hints": ["Express AB two ways in terms of the rectangle length u and solve.", "Convert the final length from cm to m."],
      "source": "SCGS 2025 P6 Prelim Q27",
      "image_needed": true,
      "image_page": 17,
      "image_bbox": [0.24, 0.45, 0.88, 0.58],
      "image_loc": "strip AB with a pattern of identical shaded rectangles and measurements 20 cm, 15 cm, 10 cm",
      "image_options": false,
      "image_file": null,
      "notes": "Booklet B Q27. Answer key: 2u+55 = 3u+20; u = 35; AB = 125 cm = 1.25 m."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "The number of boys to the number of girls in a class was 2 : 3. 25% of the boys wear spectacles and 50% of the girls wear spectacles. There were 6 more girls who wear spectacles than boys who wear spectacles. How many boys and girls were there in the class altogether?<br>[?]",
      "answer0": "30",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Boys : girls = 2 : 3. Boys with spectacles = 25% of 2 units = 0.5 units; girls with spectacles = 50% of 3 units = 1.5 units. Difference = 1.5 − 0.5 = 1 unit = 6, so 1 unit = 6. Total = (2 + 3) units = 5 × 6 = 30 students.",
      "hints": ["Express boys and girls as 2 units and 3 units.", "Find the spectacle-wearers as fractions of those units; their difference is 6."],
      "source": "SCGS 2025 P6 Prelim Q28",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Booklet B Q28. Answer key: 1.5u - 0.5u = 1u = 6; total = 5 x 6 = 30 students."
    },
    {
      "n": 30,
      "type_id": 0,
      "question": "There are cats and dogs at a pet shelter. The number of dogs is twice the number of cats. The average age of all the cats is 3 years. The average age of all the dogs is 5 years.<br>Each statement is either true, false or not possible to tell from the information given. For each statement, put a tick in the correct column.<br>(i) The average age of all animals at the shelter is 4 years.<br>(ii) If a new cat that is 6 years old joins the shelter, the average age of cats will increase.<br>(iii) The oldest dog is older than the youngest cat.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 205,
      "difficulty_id": 3,
      "explanation": "Let cats = n, dogs = 2n. Average of all = (3n + 5×2n)/(3n) = (3 + 10)/3 = 13/3 ≈ 4.33 years, not 4, so (i) is False. (ii) A 6-year-old cat is above the cat average of 3, so the cat average increases — True. (iii) The oldest dog is older than 5 years while the youngest cat is younger than 3 years, so the oldest dog is older than the youngest cat — True.",
      "hints": ["Use units: dogs = 2 × cats; compute the overall average.", "For (ii) a value above the current average raises it; for (iii) compare possible extremes."],
      "source": "SCGS 2025 P6 Prelim Q29",
      "image_needed": true,
      "image_page": 18,
      "image_bbox": [0.2, 0.5, 0.92, 0.78],
      "image_loc": "True/False/Not-possible-to-tell tick table with three statements",
      "image_options": false,
      "image_file": null,
      "notes": "Booklet B Q29. type_id 0 (tick-table) - skipped on insert. Answer key ticks: (i) False, (ii) True, (iii) True. (Average of all animals = (3+2x5)/3 = 13/3 = 4 1/3 years.)"
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "The figure shows two rectangular tanks, X (10 cm by 8 cm by 20 cm) and Y (20 cm by 3 cm). Water in Tank X was filled to the brim and Tank Y was empty. Water was poured from Tank X into Tank Y such that water level in Tank X was \\(\\dfrac{1}{2}\\) that of Tank Y. What was the new water level in Tank X?<br>[?] cm",
      "answer0": "8",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 191,
      "difficulty_id": 3,
      "explanation": "Total water = full Tank X = 10 × 8 × 20 = 1600 cm³. Let the new level in Tank X be u cm, so the level in Tank Y is 2u cm. Combined volume: 10 × 8 × u + 20 × 3 × 2u = 80u + 120u = 200u = 1600, so u = 8 cm.",
      "hints": ["The total water equals the full volume of Tank X.", "Let Tank X's new level be u and Tank Y's be 2u; set the volumes' sum equal to the total."],
      "source": "SCGS 2025 P6 Prelim Q30",
      "image_needed": true,
      "image_page": 19,
      "image_bbox": [0.24, 0.2, 0.82, 0.4],
      "image_loc": "two rectangular tanks X (10x8x20) and Y (20x...x3) drawings",
      "image_options": false,
      "image_file": null,
      "notes": "Booklet B Q30. Answer key: total water 1600 cm^3; 80u + 120u = 200u = 1600; u = 8 cm."
    },
    {
      "n": 32,
      "type_id": 2,
      "question": "John was fixing a puzzle. The number of pieces he had fixed to the number of pieces he had not fixed was 1 : 3. After fixing another 165 pieces of the puzzle, he had fixed 80% of the puzzle. How many pieces of puzzle were there?<br>[?]",
      "answer0": "300",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "At first, fixed : not fixed = 1 : 3, so 1/(1+3) = 1/4 = 25% was fixed. After fixing 165 more, 80% was fixed, so the 165 pieces are 80% − 25% = 55% of the puzzle. 55% = 165, so 5% = 15, and 100% = 15 × 20 = 300 pieces.",
      "hints": ["The 1 : 3 ratio means 25% was fixed at first.", "165 pieces is the difference 80% − 25% = 55%."],
      "source": "SCGS 2025 P6 Prelim P2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q1. Answer key: 25% at first; 80% - 25% = 55% = 165; 5% = 15; 100% = 300."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "The figure is made up of 2 quarter circles, a half circle and 2 identical squares (each side 21 cm). Find the perimeter of the shaded part. (Take \\(\\pi\\) = \\(\\dfrac{22}{7}\\))<br>[?] cm",
      "answer0": "120",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 222,
      "difficulty_id": 3,
      "explanation": "Perimeter = 21 (straight side) + quarter-circle arc + quarter-circle arc + half-circle arc. Quarter arc of radius 21 = 1/2 × 2 × 22/7 × 21 = 66 cm (two of them) and a half circle arc = 1/2 × 2 × 22/7 × 21/2... Computing per the key: 21 + 1/2 × 2 × 22/7 × 21 + 1/2 × 2 × 22/7 × 21/2 = 21 + 66 + 33 = 120 cm.",
      "hints": ["Add the straight edge to the arc lengths of the quarter and half circles.", "Arc length = fraction × 2\\(\\pi r\\) with \\(\\pi\\) = 22/7."],
      "source": "SCGS 2025 P6 Prelim P2 Q2",
      "image_needed": true,
      "image_page": 22,
      "image_bbox": [0.2, 0.5, 0.58, 0.78],
      "image_loc": "shaded figure of 2 quarter circles, a half circle and 2 squares with 21 cm marked",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q2. Answer key: perimeter = 21 + 1/2 x 2 x 22/7 x 21 + 1/2 x 2 x 22/7 x 21/2 = 21 + 66 + 33 = 120 cm."
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "Ravindran took \\(\\dfrac{1}{4}\\) h to walk from home to the market. He then increased his speed and took 10 min to walk from the market back to his home. If the distance between his home and the market is 1.2 km, what was his average speed for the whole journey?<br>[?] km/h",
      "answer0": "5.76",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 219,
      "difficulty_id": 3,
      "explanation": "Total distance = 2 × 1.2 = 2.4 km. Total time = 1/4 h + 10 min = 1/4 h + 10/60 h = 5/12 h. Average speed = 2.4 ÷ 5/12 = 2.4 × 12/5 = 5.76 km/h.",
      "hints": ["Total distance is there and back (2.4 km).", "Add the two times (convert 10 min to hours) and divide."],
      "source": "SCGS 2025 P6 Prelim P2 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q3. Answer key: total distance 2.4 km; total time 5/12 h; 2.4 / (5/12) = 5.76 km/h."
    },
    {
      "n": 35,
      "type_id": 0,
      "question": "In the figure, AB is one side of a trapezium ABCD. Draw a trapezium ABCD in the square grid such that AB = AD, BC = \\(\\dfrac{1}{2}\\) AD and \\(\\angle\\)ABC = 90°. Label the trapezium ABCD.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 201,
      "difficulty_id": 3,
      "explanation": "Draw AD equal to AB from A, then BC perpendicular to AB at B (right angle) with BC = 1/2 AD; join C to D to complete the trapezium ABCD (see printed key figure).",
      "hints": ["Set AD equal to AB, then make BC a right angle at B.", "BC is half the length of AD."],
      "source": "SCGS 2025 P6 Prelim P2 Q4",
      "image_needed": true,
      "image_page": 23,
      "image_bbox": [0.26, 0.55, 0.62, 0.9],
      "image_loc": "square grid with line AB drawn (A lower left, B upper right)",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q4. type_id 0 (draw trapezium on grid). Answer: trapezium ABCD as drawn in the printed key."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "A player has to play a total of five games in Round 1 of a competition. Bala's scores for his first four games are: Game 1 = 15, Game 2 = 24, Game 3 = 14, Game 4 = 20. Bala will qualify for Round 2 if his average score for four of the five games is 20 or more. What is the lowest score Bala must get in Game 5 to qualify for Round 2?<br>[?]",
      "answer0": "21",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 204,
      "difficulty_id": 3,
      "explanation": "To qualify, the best four of the five games must average 20, i.e. total 20 × 4 = 80. Dropping the lowest score (Game 3 = 14), the other three known games (15 + 24 + 20 = 59) plus Game 5 must reach 80, so Game 5 = 80 − 24 − 20 − 15 = 21.",
      "hints": ["The best four games must total 20 × 4 = 80.", "Drop the lowest of the known scores and solve for Game 5."],
      "source": "SCGS 2025 P6 Prelim P2 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q5. Answer key: total to qualify = 80; 80 - 24 - 20 - 15 = 21."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "A jug contained \\(\\dfrac{5}{6}\\) ℓ of fruit tea. A cup had a capacity of \\(\\dfrac{2}{9}\\) ℓ. Jason poured the fruit tea into cups, filling as many cups completely as possible. How many cups could Jason fill completely?<br>[?]",
      "answer0": "3",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "5/6 ÷ 2/9 = 5/6 × 9/2 = 45/12 = 15/4 = 3 3/4. So Jason can fill 3 full cups.",
      "hints": ["Divide the total volume by the cup capacity.", "Take only the whole-number part for completely filled cups."],
      "source": "SCGS 2025 P6 Prelim P2 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q6(a). Answer key: 5/6 / (2/9) = 15/4 = 3 3/4; 3 cups."
    },
    {
      "n": 38,
      "type_id": 1,
      "question": "A jug contained \\(\\dfrac{5}{6}\\) ℓ of fruit tea. A cup had a capacity of \\(\\dfrac{2}{9}\\) ℓ. Jason filled 3 cups completely. What volume of fruit tea was left? Give your answer in litres.",
      "answer0": "\\(\\dfrac{1}{6}\\) ℓ",
      "answer1": "\\(\\dfrac{2}{9}\\) ℓ",
      "answer2": "\\(\\dfrac{3}{4}\\) ℓ",
      "answer3": "\\(\\dfrac{1}{4}\\) ℓ",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "He filled 3 3/4 cups' worth, leaving 3/4 of a cup. Volume left = 3/4 × 2/9 = 6/36 = 1/6 ℓ.",
      "hints": ["The leftover is the fractional part of a cup (3/4) times the cup capacity.", "3/4 × 2/9."],
      "source": "SCGS 2025 P6 Prelim P2 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q6(b). Converted to MCQ (fraction answer 1/6 ℓ). Answer key: 3/4 x 2/9 = 1/6 (option index 0)."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "Mdm Kamisah bought two dresses with a discount coupon. The first dress had a 10% discount, and the second dress had a 20% discount. She paid $259.42 which includes a GST of 9%. Both dresses had the same original price before discount. How much was the original price of each dress (excluding GST)?<br>$[?]",
      "answer0": "140",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "First dress = 90% of price, second = 80% of price, total = 170% of one price. Total before GST = $259.42 ÷ 109% = $238. So 170% of one price = $238, giving one price = $238 ÷ 170% = $140.",
      "hints": ["Remove the 9% GST first (divide by 109%).", "The two discounted dresses total 90% + 80% = 170% of one original price."],
      "source": "SCGS 2025 P6 Prelim P2 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q7. Answer key: before GST = 259.42 / 109% = 238; 90%+80% = 170%; 238 / 170% = $140."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "The 2 graphs show the number of students who joined two different CCAs, the Robotics Club and the Drama Club, from 2020 to 2024. In 2022, if 3 students left the Drama Club to join the Robotics Club, how many students would the Robotics Club have? <br>[?]",
      "answer0": "23",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 147,
      "difficulty_id": 2,
      "explanation": "From the graphs, in 2022 Robotics Club had 20 students. After 3 join: 20 + 3 = 23 students.",
      "hints": ["Read the 2022 value on the Robotics Club graph.", "Add the 3 students who joined."],
      "source": "SCGS 2025 P6 Prelim P2 Q8",
      "image_needed": true,
      "image_page": 27,
      "image_bbox": [0.16, 0.17, 0.92, 0.5],
      "image_loc": "two line graphs of students in Robotics Club and Drama Club, 2020-2024",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q8(a) part 1 (Robotics Club). Answer key: 20 + 3 = 23. (Drama Club part = 17 - 3 = 14, recorded next.)"
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "The 2 graphs show the number of students who joined the Robotics Club and the Drama Club, from 2020 to 2024. In 2022, if 3 students left the Drama Club to join the Robotics Club, how many students would the Drama Club have?<br>[?]",
      "answer0": "14",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 147,
      "difficulty_id": 2,
      "explanation": "From the graphs, in 2022 the Drama Club had 17 students. After 3 leave: 17 − 3 = 14 students.",
      "hints": ["Read the 2022 value on the Drama Club graph.", "Subtract the 3 students who left."],
      "source": "SCGS 2025 P6 Prelim P2 Q8",
      "image_needed": true,
      "image_page": 27,
      "image_bbox": [0.16, 0.17, 0.92, 0.5],
      "image_loc": "two line graphs of students in Robotics Club and Drama Club, 2020-2024",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q8(a) part 2 (Drama Club). Answer key: 17 - 3 = 14."
    },
    {
      "n": 42,
      "type_id": 1,
      "question": "The 2 graphs show the number of students who joined the Robotics Club and the Drama Club, from 2020 to 2024. Both the Robotics and Drama Club membership increased between 2020 and 2021. Comparing this percentage increase, which CCA had a higher percentage increase?",
      "answer0": "Robotics Club",
      "answer1": "Drama Club",
      "answer2": "Both equal",
      "answer3": "Neither increased",
      "correct_answer": 0,
      "skill_id": 208,
      "difficulty_id": 3,
      "explanation": "Robotics: from 10 (2020) to 24 (2021), increase = (24 − 10)/10 = 140%. Drama: from 6 to 13, increase = (13 − 6)/6 = 116 2/3%. The Robotics Club had the higher percentage increase.",
      "hints": ["Compute each club's percentage increase = (rise ÷ 2020 value) × 100%.", "Compare the two percentages."],
      "source": "SCGS 2025 P6 Prelim P2 Q8",
      "image_needed": true,
      "image_page": 27,
      "image_bbox": [0.16, 0.17, 0.92, 0.5],
      "image_loc": "two line graphs of students in Robotics Club and Drama Club, 2020-2024",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q8(b). Converted to MCQ (which-club word answer). Answer key: Robotics Club (140% vs 116 2/3%) -> option index 0."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "The table shows the prices of admission tickets to Mandai Wildlife Reserve: Child $3\\(y\\), Adult $60, Senior Citizen $(3\\(y\\) − 15), Family Package (2 adults and 2 children) $(4\\(y\\) + 100). A family group consisting of 2 adults, 2 children and 1 senior citizen buy their admission tickets using a family package. How much do they pay? Express your answer in terms of \\(y\\).",
      "answer0": "$(7\\(y\\) + 85)",
      "answer1": "$(7\\(y\\) + 100)",
      "answer2": "$(4\\(y\\) + 85)",
      "answer3": "$(3\\(y\\) + 85)",
      "correct_answer": 0,
      "skill_id": 240,
      "difficulty_id": 2,
      "explanation": "Family package (2 adults + 2 children) = $(4y + 100). Add 1 senior citizen = $(3y − 15). Total = (4y + 100) + (3y − 15) = 7y + 85.",
      "hints": ["Add the family package price and the senior citizen price.", "(4y + 100) + (3y − 15)."],
      "source": "SCGS 2025 P6 Prelim P2 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q9(a). Converted to MCQ (algebraic expression in y). Answer key: $(4y+100) + $(3y-15) = $(7y+85) -> option index 0."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "The table shows admission ticket prices: Child $3\\(y\\), Adult $60, Family Package (2 adults and 2 children) $(4\\(y\\) + 100). The zoo offers a 10% discount off the family package. If \\(y\\) = $18 and the family uses the family package, how much will a family consisting of 2 adults and 2 children pay after the discount?<br>$[?]",
      "answer0": "154.80",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 207,
      "difficulty_id": 2,
      "explanation": "Family package = 4y + 100 = 4(18) + 100 = $172. After 10% discount: $172 × 90% = $154.80.",
      "hints": ["Substitute y = 18 into the family package price.", "Apply the 10% discount (pay 90%)."],
      "source": "SCGS 2025 P6 Prelim P2 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q9(b). Answer key: 4(18)+100 = 172; 172 x 90% = $154.80."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "Michelle stacked her cubes to make a figure. She wants to add more cubes so that her figure matches the given top view, front view and side view. What is the minimum number of cubes Michelle needs to add?<br>[?]",
      "answer0": "4",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 229,
      "difficulty_id": 3,
      "explanation": "Comparing the existing figure to the required top, front and side views, the minimum number of cubes that must be added to match all three views is 4.",
      "hints": ["The completed figure must match all three given views.", "Add cubes only where a view requires a cube that is currently missing."],
      "source": "SCGS 2025 P6 Prelim P2 Q10",
      "image_needed": true,
      "image_page": 29,
      "image_bbox": [0.22, 0.1, 0.86, 0.5],
      "image_loc": "isometric figure of stacked cubes with Front/Side view arrows, plus required Top/Front/Side view grids",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q10(a). Answer key: minimum cubes to add = 4."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "A large water tank contained some water at first. Tap A was turned on to fill up the tank at a rate of 12 ℓ/min. After 6 min, Tap B was also turned on to drain the water at a rate of 8.5 ℓ/min. Both taps continued to turn on for the next 10 min. In the end, there was 165 ℓ of water in the tank. How much water was in the tank at first?<br>[?] ℓ",
      "answer0": "58",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 192,
      "difficulty_id": 3,
      "explanation": "Net inflow = (Tap A filling for the whole 6 + 10 = 16 min) − (Tap B draining for 10 min) = 12 × (6 + 10) − 8.5 × 10 = 192 − 85 = 107 ℓ. Water at first = 165 − 107 = 58 ℓ.",
      "hints": ["Tap A runs for 16 min; Tap B drains for 10 min.", "Net inflow = total in − total out; subtract from the final 165 ℓ."],
      "source": "SCGS 2025 P6 Prelim P2 Q10",
      "image_needed": true,
      "image_page": 30,
      "image_bbox": [0.54, 0.2, 0.92, 0.4],
      "image_loc": "water tank with Tap A (fill) at top and Tap B (drain) at the side",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q10(b). Answer key: net inflow = 12x(6+10) - 8.5x10 = 107; 165 - 107 = 58 l."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "The figure is not drawn to scale. ABCD is a rhombus, CDE is an equilateral triangle and AEDF is a trapezium. Given that AE ∥ DF and \\(\\angle\\)BCE = 42°, find \\(\\angle\\)BAE.<br>[?]°",
      "answer0": "21",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "In triangle CDE, \\(\\angle\\)CDE = \\(\\angle\\)DCE = 60° (equilateral). In rhombus ABCD, \\(\\angle\\)ADE = 180° − 60° − 60° − 42° = 18°, and \\(\\angle\\)BAD = \\(\\angle\\)BCD = 60° + 42° = 102°. In triangle ADE (isosceles), \\(\\angle\\)DAE = (180° − 18°) ÷ 2 = 81°. So \\(\\angle\\)BAE = 102° − 81° = 21°.",
      "hints": ["Use the equilateral triangle CDE (all 60°).", "Find \\(\\angle\\)BAD and \\(\\angle\\)DAE, then subtract."],
      "source": "SCGS 2025 P6 Prelim P2 Q11",
      "image_needed": true,
      "image_page": 31,
      "image_bbox": [0.3, 0.16, 0.92, 0.42],
      "image_loc": "rhombus ABCD with equilateral triangle CDE and trapezium AEDF, marked angle 42°",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q11. Answer key: angle ADE = 18; angle BAD = 102; angle DAE = 81; angle BAE = 102 - 81 = 21°."
    },
    {
      "n": 48,
      "type_id": 2,
      "question": "A string of rectangular lights is being placed along a wall with a total length of 12 m. Each rectangular light is 8 cm wide, and consecutive rectangular lights are each 30 cm apart. The lights must be spaced evenly. What is the maximum number of lights that can be placed along this wall?<br>[?]",
      "answer0": "32",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 184,
      "difficulty_id": 3,
      "explanation": "12 m = 1200 cm. Each light (8 cm) plus a gap (30 cm) = 38 cm per repeating unit. 1200 ÷ 38 = 31 remainder 22 cm. The 22 cm fits one more light (8 cm) with a 14 cm leftover, so the maximum number of lights = 31 + 1 = 32.",
      "hints": ["Each light-plus-gap unit is 8 + 30 = 38 cm.", "Divide 1200 by 38 and add the final light that fits in the remainder."],
      "source": "SCGS 2025 P6 Prelim P2 Q12",
      "image_needed": true,
      "image_page": 32,
      "image_bbox": [0.18, 0.18, 0.92, 0.35],
      "image_loc": "wall strip with rectangular lights (8 cm wide) spaced 30 cm apart and distance y at the end",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q12(a). Answer key: 1200 / 38 = 31 R22; max lights = 31 + 1 = 32."
    },
    {
      "n": 49,
      "type_id": 2,
      "question": "A string of rectangular lights (each 8 cm wide, 30 cm apart, placed evenly) is on a 12 m wall, with 32 lights placed. What is the distance y (the gap at the end), as shown in the diagram?<br>[?] cm",
      "answer0": "14",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 184,
      "difficulty_id": 2,
      "explanation": "After 31 units of 38 cm (= 1178 cm) and the final light (8 cm), the leftover from the 22 cm remainder is y = 22 − 8 = 14 cm.",
      "hints": ["The leftover space (22 cm) after the last full unit holds one more light (8 cm).", "y = 22 − 8."],
      "source": "SCGS 2025 P6 Prelim P2 Q12",
      "image_needed": true,
      "image_page": 32,
      "image_bbox": [0.18, 0.18, 0.92, 0.35],
      "image_loc": "wall strip with rectangular lights (8 cm wide) spaced 30 cm apart and distance y at the end",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q12(b). Answer key: y = 22 - 8 = 14 cm."
    },
    {
      "n": 50,
      "type_id": 2,
      "question": "The figure is made up of two quarter circles and a rectangle overlapping one another. The radius of the larger quarter circle is equal to the length of the rectangle. The radius of the smaller quarter circle is equal to the breadth of the rectangle. The length of the rectangle is 26 cm, and its breadth is 13 cm. Find the difference in area between the shaded parts, H and G. (Take \\(\\pi\\) = 3.14)<br>[?] cm²",
      "answer0": "59.995",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 223,
      "difficulty_id": 3,
      "explanation": "Difference [H] − [G] = (big quarter circle, radius 26) − (rectangle) − (small quarter circle, radius 13) = 0.25 × 3.14 × 26² − 26 × 13 − 0.25 × 3.14 × 13² = 530.66 − 338 − 132.665 = 59.995 cm².",
      "hints": ["Express [H] − [G] in terms of the big quarter circle, the rectangle, and the small quarter circle.", "Compute each area with \\(\\pi\\) = 3.14 and subtract."],
      "source": "SCGS 2025 P6 Prelim P2 Q13",
      "image_needed": true,
      "image_page": 33,
      "image_bbox": [0.3, 0.26, 0.66, 0.5],
      "image_loc": "two quarter circles and a rectangle overlapping with shaded parts H and G, 26 cm and 13 cm marked",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q13. Answer key: 0.25x3.14x26^2 - 26x13 - 0.25x3.14x13^2 = 59.995 cm^2."
    },
    {
      "n": 51,
      "type_id": 1,
      "question": "A company offered 120 soft toys at a discount of 20% during a 5-day sale. The bar graph shows the number of soft toys left unsold at the end of each day (Day 1 = 110, Day 2 = 84). What fraction of the soft toys were sold in Day 2?",
      "answer0": "\\(\\dfrac{13}{60}\\)",
      "answer1": "\\(\\dfrac{26}{60}\\)",
      "answer2": "\\(\\dfrac{13}{120}\\)",
      "answer3": "\\(\\dfrac{1}{5}\\)",
      "correct_answer": 0,
      "skill_id": 161,
      "difficulty_id": 2,
      "explanation": "Soft toys sold on Day 2 = 110 − 84 = 26. Fraction = 26/120 = 13/60.",
      "hints": ["Find the drop in unsold toys from Day 1 to Day 2.", "Write that as a fraction of 120 and simplify."],
      "source": "SCGS 2025 P6 Prelim P2 Q14",
      "image_needed": true,
      "image_page": 34,
      "image_bbox": [0.18, 0.13, 0.82, 0.36],
      "image_loc": "horizontal bar graph of soft toys left unsold (Day 1 to Day 5)",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q14(a). Converted to MCQ (fraction answer 13/60). Answer key: 110 - 84 = 26; 26/120 = 13/60 (option index 0)."
    },
    {
      "n": 52,
      "type_id": 0,
      "question": "A company offered 120 soft toys at a discount of 20% during a 5-day sale. The bar graph shows the number of soft toys left unsold at the end of each day. After the 5-day sales, the ratio of number of soft toys sold to the total number of soft toys was 4 : 5. Draw and shade the bar representing the number of soft toys left unsold on Day 5.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 104,
      "difficulty_id": 2,
      "explanation": "Sold : total = 4 : 5, so unsold = 1/5 of 120 = 24. Draw and shade the Day 5 bar to reach 24 on the 'number left unsold' axis.",
      "hints": ["Unsold is 1/5 of the total (since sold is 4/5).", "1/5 of 120 = 24; draw the bar to 24."],
      "source": "SCGS 2025 P6 Prelim P2 Q14",
      "image_needed": true,
      "image_page": 34,
      "image_bbox": [0.18, 0.13, 0.82, 0.36],
      "image_loc": "horizontal bar graph of soft toys left unsold (Day 1 to Day 5), Day 5 bar to be drawn",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q14(b). type_id 0 (draw/shade the bar). Answer key: Day 5 unsold = 1/5 x 120 = 24 (draw bar to 24)."
    },
    {
      "n": 53,
      "type_id": 2,
      "question": "A company offered 120 soft toys at a discount of 20% during a 5-day sale. After the sale, 24 soft toys were left unsold. The usual price of one soft toy was $80. What was the amount of money collected during the 5-day sale?<br>$[?]",
      "answer0": "6144",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 207,
      "difficulty_id": 3,
      "explanation": "Soft toys sold = 120 − 24 = 96. Each sold at 20% discount = $80 × 80% = $64. Money collected = 96 × $80 × 80% = $6144.",
      "hints": ["Find the number sold (120 − 24).", "Each sells at 80% of $80; multiply."],
      "source": "SCGS 2025 P6 Prelim P2 Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q14(c). Answer key: 120 - 24 = 96; 96 x $80 x 80% = $6144."
    },
    {
      "n": 54,
      "type_id": 2,
      "question": "The figure is not drawn to scale. A triangular piece of paper is folded as shown. The angles 78°, 110° and 82° are marked. Find \\(\\angle\\)x.<br>[?]°",
      "answer0": "35",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 196,
      "difficulty_id": 3,
      "explanation": "When the paper is folded, an isosceles triangle is formed at the 110° vertex, so \\(\\angle\\)x = (180° − 110°) ÷ 2 = 70° ÷ 2 = 35°.",
      "hints": ["Folding creates two equal angles at the fold vertex.", "\\(\\angle\\)x = (180° − 110°) ÷ 2."],
      "source": "SCGS 2025 P6 Prelim P2 Q15",
      "image_needed": true,
      "image_page": 35,
      "image_bbox": [0.2, 0.13, 0.82, 0.4],
      "image_loc": "folded triangular paper with marked angles 78°, x, 110°, 82° and y",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q15(a). Answer key: angle x = (180-110)/2 = 35°."
    },
    {
      "n": 55,
      "type_id": 2,
      "question": "The figure is not drawn to scale. A triangular piece of paper is folded as shown. The angles 78°, 110° and 82° are marked. Find \\(\\angle\\)y.<br>[?]°",
      "answer0": "86",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 196,
      "difficulty_id": 3,
      "explanation": "(180° − 78°) ÷ 2 = 51° (isosceles fold at the 78° vertex). 180° − 82° − 51° = 47°. By the fold's symmetry, \\(\\angle\\)y = 180° − 47° − 47° = 86°.",
      "hints": ["Use the isosceles fold at the 78° vertex to find an angle.", "Combine angles using straight lines and the fold symmetry."],
      "source": "SCGS 2025 P6 Prelim P2 Q15",
      "image_needed": true,
      "image_page": 35,
      "image_bbox": [0.2, 0.13, 0.82, 0.4],
      "image_loc": "folded triangular paper with marked angles 78°, x, 110°, 82° and y",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q15(b). Answer key: (180-78)/2 = 51; 180-82-51 = 47; y = 180-47-47 = 86°."
    },
    {
      "n": 56,
      "type_id": 2,
      "question": "Figure 1 shows a rectangle WXYZ with a length of 48 cm. The shaded region in Figure 2 shows the remaining part of the rectangle after 8 identical isosceles triangles were cut out. The perimeter of Figure 2 is 112 cm longer than the perimeter of rectangle WXYZ. What was the length of WP?<br>[?] cm",
      "answer0": "12",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 187,
      "difficulty_id": 3,
      "explanation": "The 8 triangles are cut evenly along the 48 cm top, so each triangle base = 48 ÷ 4 = 12 cm... WP is the half-base/first segment: WP = 48 ÷ 4 = 12 cm.",
      "hints": ["The triangle bases divide the 48 cm length evenly.", "WP is one of these equal divisions: 48 ÷ 4."],
      "source": "SCGS 2025 P6 Prelim P2 Q16",
      "image_needed": true,
      "image_page": 36,
      "image_bbox": [0.18, 0.17, 0.82, 0.34],
      "image_loc": "rectangle WXYZ (Figure 1, 48 cm) and Figure 2 with 8 isosceles triangles cut out, WP marked",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q16(a). Answer key: WP = 48 / 4 = 12 cm."
    },
    {
      "n": 57,
      "type_id": 2,
      "question": "Figure 1 shows a rectangle WXYZ with a length of 48 cm. The shaded region in Figure 2 shows the remaining part after 8 identical isosceles triangles were cut out. The perimeter of Figure 2 is 112 cm longer than the perimeter of rectangle WXYZ. What was the perimeter of each isosceles triangle that was cut out?<br>[?] cm",
      "answer0": "38",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 195,
      "difficulty_id": 3,
      "explanation": "Each triangle cut adds (its two equal slanted sides − its base) to the perimeter. The total extra perimeter is 112 cm over 8 triangles, so the two equal sides minus the base = 112 ÷ 8 = 14 cm. With the base WP-related length 12 cm, each triangle's perimeter = 14 + 2 × 12 = 38 cm.",
      "hints": ["The extra perimeter (112 cm) is shared over 8 triangles.", "Combine that with the base length (from part a) to get one triangle's perimeter."],
      "source": "SCGS 2025 P6 Prelim P2 Q16",
      "image_needed": true,
      "image_page": 36,
      "image_bbox": [0.18, 0.17, 0.82, 0.34],
      "image_loc": "rectangle WXYZ (Figure 1, 48 cm) and Figure 2 with 8 isosceles triangles cut out",
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q16(b). Answer key: 112/8 = 14; perimeter = 14 + 2x12 = 38 cm."
    },
    {
      "n": 58,
      "type_id": 2,
      "question": "In a bookshop, for every 3 files sold, 1 pencil case was sold. The total amount collected was $1176. The amount collected from files was $147 more than the amount collected from pencil cases. Each pencil case was sold for $3 more than a file. How many pencil cases were sold?<br>[?]",
      "answer0": "98",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 240,
      "difficulty_id": 3,
      "explanation": "Amount from files = (1176 + 147) ÷ 2 = $661.50; amount from pencil cases = (1176 − 147) ÷ 2 = $514.50. For every 3 files there is 1 pencil case, so files come in blocks of 3: one block of files = $661.50 ÷ 3 = $220.50; one block of pencil cases = $514.50. Each pencil case costs $3 more than a file, so the number of pencil cases = (514.50 − 220.50) ÷ 3 = 294 ÷ 3 = 98.",
      "hints": ["Split the total into file money and pencil-case money using the $147 difference.", "Use the 3 files : 1 pencil case ratio and the $3 price difference to find the count."],
      "source": "SCGS 2025 P6 Prelim P2 Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q17. Answer key: files = (1176+147)/2 = 661.50; pencil cases = (1176-147)/2 = 514.50; (514.50 - 220.50)/3 = 98 pencil cases."
    }
  ]
}