{
  "paper": {
    "school": "Singapore Chinese Girls' School",
    "year": 2023,
    "level": "P6",
    "label": "Prelim",
    "source_prefix": "SCGS 2023 P6 Prelim",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "In 65<u>2</u> 009, what does the digit 2 stand for?",
      "answer0": "20",
      "answer1": "200",
      "answer2": "2000",
      "answer3": "20 000",
      "correct_answer": 2,
      "skill_id": 2,
      "difficulty_id": 1,
      "explanation": "The digit 2 is in the thousands place, so it stands for 2 × 1000 = 2000. Answer: 2000.",
      "hints": ["Identify which place value column the digit 2 sits in.", "65<u>2</u> 009 — the 2 is in the thousands place."],
      "source": "SCGS 2023 P6 Prelim Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 3 (2000)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Round off 49.456 to the nearest tenth.",
      "answer0": "50.0",
      "answer1": "49.5",
      "answer2": "49.4",
      "answer3": "49.0",
      "correct_answer": 1,
      "skill_id": 2,
      "difficulty_id": 1,
      "explanation": "The tenths digit is 4; the next digit (hundredths) is 5, so round up: 49.456 → 49.5. Answer: 49.5.",
      "hints": ["The tenths place is the first digit after the decimal point.", "Look at the hundredths digit to decide whether to round up."],
      "source": "SCGS 2023 P6 Prelim Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 2 (49.5)."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Which one of the following is closest to 1?",
      "answer0": "\\(\\dfrac{6}{7}\\)",
      "answer1": "\\(\\dfrac{7}{8}\\)",
      "answer2": "\\(\\dfrac{10}{9}\\)",
      "answer3": "\\(\\dfrac{12}{11}\\)",
      "correct_answer": 3,
      "skill_id": 206,
      "difficulty_id": 2,
      "explanation": "Distance from 1: \\(\\dfrac{6}{7}\\) is \\(\\dfrac{1}{7}\\approx0.143\\); \\(\\dfrac{7}{8}\\) is \\(\\dfrac{1}{8}=0.125\\); \\(\\dfrac{10}{9}\\) is \\(\\dfrac{1}{9}\\approx0.111\\); \\(\\dfrac{12}{11}\\) is \\(\\dfrac{1}{11}\\approx0.091\\). The smallest gap is \\(\\dfrac{12}{11}\\). Answer: \\(\\dfrac{12}{11}\\).",
      "hints": ["For each fraction, find how far it is from 1.", "The fraction with the smallest difference from 1 is the closest."],
      "source": "SCGS 2023 P6 Prelim Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 4 (12/11)."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "In the given figure, how many pairs of lines are perpendicular to each other?",
      "answer0": "1",
      "answer1": "2",
      "answer2": "3",
      "answer3": "4",
      "correct_answer": 1,
      "skill_id": 230,
      "difficulty_id": 2,
      "explanation": "Examining each junction in the figure on the grid, exactly 2 pairs of lines meet at right angles. Answer: 2.",
      "hints": ["Perpendicular lines meet at a right angle (90°). Use the grid squares to check.", "Count each pair where two line segments form a 90° corner."],
      "source": "SCGS 2023 P6 Prelim Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q4.png",
      "image_page": 4,
      "image_bbox": [0.54, 0.11, 0.88, 0.30],
      "image_loc": "right of the question, a polygon drawn on a square grid (top of page 4)",
      "notes": "Key: option 2 (2 pairs)."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "In the number line, which mixed number is represented by X?",
      "answer0": "\\(2\\dfrac{2}{3}\\)",
      "answer1": "\\(2\\dfrac{5}{6}\\)",
      "answer2": "\\(3\\dfrac{1}{6}\\)",
      "answer3": "\\(3\\dfrac{2}{3}\\)",
      "correct_answer": 3,
      "skill_id": 206,
      "difficulty_id": 2,
      "explanation": "The number line runs from 2 to 4 in 6 equal intervals, so each mark is \\(\\dfrac{1}{3}\\). X is at the 5th mark from 2, i.e. 2 + \\(\\dfrac{5}{3}\\) = \\(3\\dfrac{2}{3}\\). Answer: \\(3\\dfrac{2}{3}\\).",
      "hints": ["Count the equal intervals between 2 and 4 to find the value of each step.", "Locate X and add that many steps to 2."],
      "source": "SCGS 2023 P6 Prelim Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q5.png",
      "image_page": 4,
      "image_bbox": [0.50, 0.36, 0.80, 0.47],
      "image_loc": "right side, a number line from 2 to 4 with X marked near 4",
      "notes": "Key: option 4 (3 2/3)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "The table shows the number of pupils with the following Math scores.<br>Prizes were given to the top 8 pupils. Gwen won a prize. What was the lowest she could have scored?",
      "answer0": "88",
      "answer1": "90",
      "answer2": "91",
      "answer3": "95",
      "correct_answer": 2,
      "skill_id": 461,
      "difficulty_id": 2,
      "explanation": "Counting from the highest scores: 100 (1) + 98 (2) + 95 (3) = 6 pupils; adding 91 (2 pupils) gives 8 pupils. So the top 8 must include the two scoring 91. The lowest a prize-winner could have scored is 91. Answer: 91.",
      "hints": ["List the pupils from the highest score downward and keep a running total.", "Find the score at which the running total reaches 8."],
      "source": "SCGS 2023 P6 Prelim Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q6.png",
      "image_page": 4,
      "image_bbox": [0.14, 0.58, 0.88, 0.69],
      "image_loc": "two-row table of Math scores (85-100) and number of pupils, middle of page 4",
      "notes": "Key: option 3 (91). Scores 85:5, 88:3, 90:2, 91:2, 95:3, 98:2, 100:1."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "The figure is not drawn to scale. PQRT is a parallelogram. ∠TPQ = 115° and ∠SQP = 43°. Find ∠RQS.",
      "answer0": "22°",
      "answer1": "48°",
      "answer2": "50°",
      "answer3": "72°",
      "correct_answer": 0,
      "skill_id": 230,
      "difficulty_id": 2,
      "explanation": "In parallelogram PQRT, co-interior angles ∠TPQ + ∠PQR = 180°, so ∠PQR = 180° − 115° = 65°. ∠RQS = ∠PQR − ∠SQP = 65° − 43° = 22°. Answer: 22°.",
      "hints": ["Adjacent angles of a parallelogram add up to 180°, so find ∠PQR first.", "∠RQS = ∠PQR − ∠SQP."],
      "source": "SCGS 2023 P6 Prelim Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q7.png",
      "image_page": 5,
      "image_bbox": [0.14, 0.10, 0.72, 0.32],
      "image_loc": "parallelogram PQRT with angles 115° at P and 43° at Q, top of page 5",
      "notes": "Key: option 1 (22°)."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "Arrange these values from the largest to the smallest.<br>1.005 \\(m\\ell\\)   1 \\(\\ell\\) 50 \\(m\\ell\\)   1550 \\(m\\ell\\)   \\(1\\dfrac{1}{2}\\) \\(\\ell\\)",
      "answer0": "\\(1\\dfrac{1}{2}\\) \\(\\ell\\), 1.005 \\(\\ell\\), 1 \\(\\ell\\) 50 \\(m\\ell\\), 1550 \\(m\\ell\\)",
      "answer1": "\\(1\\dfrac{1}{2}\\) \\(\\ell\\), 1550 \\(m\\ell\\), 1.005 \\(\\ell\\), 1 \\(\\ell\\) 50 \\(m\\ell\\)",
      "answer2": "1550 \\(m\\ell\\), \\(1\\dfrac{1}{2}\\) \\(\\ell\\), 1 \\(\\ell\\) 50 \\(m\\ell\\), 1.005 \\(\\ell\\)",
      "answer3": "1 \\(\\ell\\) 50 \\(m\\ell\\), 1.005 \\(\\ell\\), 1550 \\(m\\ell\\), \\(1\\dfrac{1}{2}\\) \\(\\ell\\)",
      "correct_answer": 2,
      "skill_id": 5,
      "difficulty_id": 3,
      "explanation": "Convert all to ml. The four values given are 1.005 ml, 1 l 50 ml = 1050 ml, 1550 ml, and 1½ l = 1500 ml. But the options use 1.005 l = 1005 ml. Comparing 1550, 1500, 1050, 1005 ml: largest to smallest is 1550 ml > 1½ l > 1 l 50 ml > 1.005 l. Answer: option 3.",
      "hints": ["Convert every measurement to the same unit (millilitres) before comparing.", "1 l 50 ml = 1050 ml; 1½ l = 1500 ml; 1.005 l = 1005 ml."],
      "source": "SCGS 2023 P6 Prelim Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 3. Options restate units (e.g. 1.005 l = 1005 ml). Ordering largest to smallest: 1550 ml, 1.5 l, 1 l 50 ml, 1.005 l."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "The figure shows a prism.<br>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": 3,
      "skill_id": 230,
      "difficulty_id": 2,
      "explanation": "A triangular prism has 2 triangular faces and 3 rectangular faces. The correct net (option 4) shows three rectangles in a row with the two triangles attached so they fold to form the triangular prism. Answer: Net 4.",
      "hints": ["A triangular prism has 2 triangles and 3 rectangles.", "Check that the two triangular faces are positioned so they fold onto opposite ends."],
      "source": "SCGS 2023 P6 Prelim Q9",
      "image_needed": true,
      "image_options": true,
      "image_file": "q9.png",
      "image_page": 6,
      "image_bbox": [0.30, 0.10, 0.62, 0.27],
      "image_loc": "triangular prism near top of page 6; four candidate nets labelled (1)-(4) below it",
      "notes": "Key: option 4. image_options=true: crop the prism (q9.png) and the four nets as q9_opt0..q9_opt3 from page 6."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "The pie chart shows the mode of transport taken by Primary Six students to school. \\(\\dfrac{1}{2}\\) of the students take the train to school.<br>Which of the following bar graphs best represents the information in the pie chart?",
      "answer0": "Bar graph 1",
      "answer1": "Bar graph 2",
      "answer2": "Bar graph 3",
      "answer3": "Bar graph 4",
      "correct_answer": 0,
      "skill_id": 461,
      "difficulty_id": 2,
      "explanation": "Train = \\(\\dfrac{1}{2}\\) (tallest), Bus = \\(\\dfrac{3}{20}\\). The Bus–Car corner is a right angle, so Bus + Car = \\(\\dfrac{1}{4}\\), giving Car = \\(\\dfrac{1}{4}-\\dfrac{3}{20}=\\dfrac{1}{10}\\); the remaining Walk = \\(\\dfrac{1}{2}-\\dfrac{1}{4}=\\dfrac{1}{4}\\)... re-reading the chart, Walk is the smallest sector. Bar graph 1 shows Train tallest, then Car, then Bus, with Walk shortest, matching the pie chart. Answer: Bar graph 1.",
      "hints": ["Train is half, so its bar must be the tallest by far.", "Compare the relative sizes of the Bus, Car and Walk sectors to the bar heights."],
      "source": "SCGS 2023 P6 Prelim Q10",
      "image_needed": true,
      "image_options": true,
      "image_file": "q10.png",
      "image_page": 7,
      "image_bbox": [0.30, 0.12, 0.70, 0.36],
      "image_loc": "pie chart (Train/Bus/Car/Walk) top of page 7; four bar graphs labelled (1)-(4) below",
      "notes": "Key: option 1. image_options=true: crop pie chart (q10.png) and four bar graphs as q10_opt0..q10_opt3 from page 7."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "The total mass of Ben and Jerry is 100 kg. Jerry weighs 7.8 kg lighter than Ben. How heavy is Jerry?",
      "answer0": "(100 ÷ 2 + 7.8) kg",
      "answer1": "(100 − 7.8 ÷ 2) kg",
      "answer2": "\\((100 + \\dfrac{7.8}{2})\\) kg",
      "answer3": "\\((\\dfrac{100 - 7.8}{2})\\) kg",
      "correct_answer": 3,
      "skill_id": 240,
      "difficulty_id": 2,
      "explanation": "Remove the 7.8 kg difference so the two are equal: 100 − 7.8 is twice Jerry's mass. Jerry = \\(\\dfrac{100-7.8}{2}\\) kg. Answer: option 4.",
      "hints": ["Subtract the difference from the total to make both masses equal.", "Then halve the result to get the lighter person's (Jerry's) mass."],
      "source": "SCGS 2023 P6 Prelim Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 4."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "Adam Electronics Store gave a storewide discount of 20% during its annual sale. As a member of the store, Ming Hui is entitled to an additional 10% discount on the discounted price. He bought a camera. Usual Price: $2000.<br>How much did Ming Hui pay for the camera?",
      "answer0": "$600",
      "answer1": "$1400",
      "answer2": "$1440",
      "answer3": "$1600",
      "correct_answer": 2,
      "skill_id": 209,
      "difficulty_id": 2,
      "explanation": "After 20% off: $2000 × 0.8 = $1600. After a further 10% off: $1600 × 0.9 = $1440. Answer: $1440.",
      "hints": ["Apply the 20% discount first to get the sale price.", "Then take 10% off that sale price (not off the original)."],
      "source": "SCGS 2023 P6 Prelim Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 3 ($1440). Camera/price-tag image is decorative; usual price $2000 stated in stem."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "The figure shows 4 points (A, B, C and D) in a square grid.<br>Which of the following statements is <b>false</b>?",
      "answer0": "D is south of B.",
      "answer1": "D is south-west of C.",
      "answer2": "A is north-west of D.",
      "answer3": "B is north-west of C.",
      "correct_answer": 2,
      "skill_id": 230,
      "difficulty_id": 2,
      "explanation": "Reading positions on the grid (N is up): D is directly below B (south of B — true); D is below-left of C (south-west — true); B is above-left of C (north-west — true); A is below-left of D, so A is south-west of D, NOT north-west. So the false statement is 'A is north-west of D.' Answer: option 3.",
      "hints": ["North is up, so compare each pair's left/right and up/down positions on the grid.", "Check statement (3): is A actually above-and-left of D, or below-and-left?"],
      "source": "SCGS 2023 P6 Prelim Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q13.png",
      "image_page": 9,
      "image_bbox": [0.20, 0.11, 0.66, 0.38],
      "image_loc": "square grid with points A, B, C, D and a North arrow to its right, top of page 9",
      "notes": "Key: option 3 (A is north-west of D)."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "Study the table. Which algebraic expression is for Row \\(n\\), Column C?",
      "answer0": "\\(n + 4\\)",
      "answer1": "\\(n + 14\\)",
      "answer2": "\\(4n + 2\\)",
      "answer3": "\\(4n\\)",
      "correct_answer": 2,
      "skill_id": 238,
      "difficulty_id": 2,
      "explanation": "Column C values are Row 1: 6, Row 2: 10, Row 3: 14, increasing by 4 each row. The pattern is 4n + 2 (check: 4×1+2=6, 4×2+2=10, 4×3+2=14). Answer: 4n + 2.",
      "hints": ["Find the difference between consecutive Column C values — that is the coefficient of n.", "Test your expression against Row 1 (should give 6)."],
      "source": "SCGS 2023 P6 Prelim Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q14.png",
      "image_page": 10,
      "image_bbox": [0.14, 0.13, 0.78, 0.31],
      "image_loc": "grid table with columns A-D and rows 1-3 then Row n, top of page 10",
      "notes": "Key: option 3 (4n + 2). Column C: 6, 10, 14."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "A baker can either bake 100 big cookies or 150 small cookies using the same amount of ingredients. After baking 80 big cookies, what is the maximum number of small cookies he can bake with the remaining ingredients?",
      "answer0": "20",
      "answer1": "30",
      "answer2": "70",
      "answer3": "120",
      "correct_answer": 1,
      "skill_id": 209,
      "difficulty_id": 2,
      "explanation": "Baking 80 big cookies uses \\(\\dfrac{80}{100}=\\dfrac{4}{5}\\) of the ingredients, leaving \\(\\dfrac{1}{5}\\). That \\(\\dfrac{1}{5}\\) can make \\(\\dfrac{1}{5}\\times150 = 30\\) small cookies. Answer: 30.",
      "hints": ["Find what fraction of the ingredients 80 big cookies use (out of 100).", "Apply the leftover fraction to the 150 small-cookie capacity."],
      "source": "SCGS 2023 P6 Prelim Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 2 (30)."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Find the value of 82 hundreds, 4 tenths and 7 thousandths. [?]",
      "answer0": "8200.407",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 2,
      "difficulty_id": 1,
      "explanation": "82 hundreds = 8200; 4 tenths = 0.4; 7 thousandths = 0.007. Sum = 8200 + 0.4 + 0.007 = 8200.407. Answer: 8200.407.",
      "hints": ["82 hundreds = 82 × 100.", "Add the tenths (0.4) and thousandths (0.007) to the whole-number part."],
      "source": "SCGS 2023 P6 Prelim Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 8200.407."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "Hui Ling paid $5 for 20 pencils. What was the cost of each pencil in cents? [?]",
      "answer0": "25",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 206,
      "difficulty_id": 1,
      "explanation": "$5 = 500 cents. Cost per pencil = 500 ÷ 20 = 25 cents. Answer: 25 cents.",
      "hints": ["Convert $5 to cents first ($1 = 100 cents).", "Divide the total cents by the number of pencils."],
      "source": "SCGS 2023 P6 Prelim Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 25c. Answer unit is cents."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "Find the value of 7 − 3.18. [?]",
      "answer0": "3.82",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 2,
      "difficulty_id": 1,
      "explanation": "7.00 − 3.18 = 3.82. Answer: 3.82.",
      "hints": ["Write 7 as 7.00 and align the decimal points.", "Subtract: 7.00 − 3.18."],
      "source": "SCGS 2023 P6 Prelim Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 3.82."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "A ribbon is 148.6 m long. It is cut into 200 equal pieces. How long is each piece of ribbon? [?]",
      "answer0": "0.743",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 2,
      "difficulty_id": 1,
      "explanation": "148.6 ÷ 200 = 0.743 m. Answer: 0.743 m.",
      "hints": ["Divide the total length by the number of pieces.", "148.6 ÷ 200."],
      "source": "SCGS 2023 P6 Prelim Q19",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 0.743 m. Answer unit is metres."
    },
    {
      "n": 20,
      "type_id": 1,
      "question": "Find the value of \\(\\dfrac{4}{9} \\div \\dfrac{2}{5}\\). Give your answer as a mixed number in its simplest form.",
      "answer0": "\\(1\\dfrac{1}{9}\\)",
      "answer1": "\\(\\dfrac{8}{45}\\)",
      "answer2": "\\(1\\dfrac{2}{9}\\)",
      "answer3": "\\(\\dfrac{10}{9}\\)",
      "correct_answer": 0,
      "skill_id": 206,
      "difficulty_id": 2,
      "explanation": "\\(\\dfrac{4}{9} \\div \\dfrac{2}{5} = \\dfrac{4}{9} \\times \\dfrac{5}{2} = \\dfrac{20}{18} = \\dfrac{10}{9} = 1\\dfrac{1}{9}\\). Answer: \\(1\\dfrac{1}{9}\\).",
      "hints": ["To divide by a fraction, multiply by its reciprocal.", "Simplify \\(\\dfrac{20}{18}\\) and write it as a mixed number."],
      "source": "SCGS 2023 P6 Prelim Q20",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 1 1/9. Originally FIB in the paper but the answer is a mixed number, so converted to MCQ (FIB answers must be integers/decimals)."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "A can of mushroom soup costs $3.20 and a bundle of 3 cans of mushroom soup costs $8. Diane wants to buy 20 cans of mushroom soup. What is the least amount of money she needs? $[?]",
      "answer0": "54.40",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 2,
      "explanation": "A bundle (3 cans) costs $8, i.e. about $2.67/can — cheaper than $3.20 each. Buy 6 bundles = 18 cans = 6 × $8 = $48, then 2 single cans = 2 × $3.20 = $6.40. Total = $48 + $6.40 = $54.40. Answer: $54.40.",
      "hints": ["A bundle of 3 is cheaper per can than a single can, so buy as many bundles as possible.", "20 = 6 bundles (18 cans) + 2 single cans."],
      "source": "SCGS 2023 P6 Prelim Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: $54.40. Answer unit is dollars."
    },
    {
      "n": 22,
      "type_id": 1,
      "question": "Siti has a string that is 5 m long. She cuts the string into equal pieces, each measuring \\(\\dfrac{3}{5}\\) m. Find the length of the remaining piece of string. Express your answer in metres.",
      "answer0": "\\(\\dfrac{1}{5}\\) m",
      "answer1": "\\(\\dfrac{2}{5}\\) m",
      "answer2": "\\(\\dfrac{3}{5}\\) m",
      "answer3": "\\(\\dfrac{4}{5}\\) m",
      "correct_answer": 0,
      "skill_id": 206,
      "difficulty_id": 2,
      "explanation": "5 ÷ \\(\\dfrac{3}{5}\\) = 5 × \\(\\dfrac{5}{3}\\) = \\(\\dfrac{25}{3}\\) = 8 pieces remainder \\(\\dfrac{1}{3}\\) of a piece. Remaining = \\(\\dfrac{1}{3}\\times\\dfrac{3}{5}=\\dfrac{1}{5}\\) m. Answer: \\(\\dfrac{1}{5}\\) m.",
      "hints": ["Divide 5 by \\(\\dfrac{3}{5}\\) to find how many whole pieces, and the leftover fraction of a piece.", "The remainder length = leftover fraction × \\(\\dfrac{3}{5}\\) m."],
      "source": "SCGS 2023 P6 Prelim Q22",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 1/5 m. Answer is a fraction, so MCQ (FIB answers must be integers/decimals)."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "Last month, Rachel saved $90 and spent the rest of her pocket money. If she increased her spendings by 40%, her savings would decrease by 20%. How much was her pocket money? $[?]",
      "answer0": "135",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Savings would decrease by 20% of $90 = $18, so the extra spending is $18. That $18 is the 40% increase in spending, so original spending = $18 ÷ 0.4 = $45. Pocket money = savings + spending = $90 + $45 = $135. Answer: $135.",
      "hints": ["The increase in spending equals the decrease in savings (total is fixed).", "20% of $90 = $18, and this $18 is 40% of the original spending."],
      "source": "SCGS 2023 P6 Prelim Q23",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: $135. Answer unit is dollars."
    },
    {
      "n": 24,
      "type_id": 1,
      "question": "Jane is \\(p\\) years old. She is twice as old as her brother. How old is her brother in 8 years' time? Express your answer in terms of \\(p\\).",
      "answer0": "\\(\\dfrac{p}{2} + 8\\)",
      "answer1": "\\(2p + 8\\)",
      "answer2": "\\(\\dfrac{p}{2} - 8\\)",
      "answer3": "\\(\\dfrac{p+8}{2}\\)",
      "correct_answer": 0,
      "skill_id": 241,
      "difficulty_id": 2,
      "explanation": "Jane is twice the brother's age, so the brother is now \\(\\dfrac{p}{2}\\) years old. In 8 years he will be \\(\\dfrac{p}{2} + 8\\) years old. Answer: \\(\\dfrac{p}{2} + 8\\) years old.",
      "hints": ["If Jane is twice as old, the brother is half of Jane's age.", "Add 8 for '8 years' time'."],
      "source": "SCGS 2023 P6 Prelim Q24",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: p/2 + 8 years old. Algebraic answer, so MCQ."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "30 students shared a box of stickers equally. 6 students gave up their shares and their stickers were distributed equally to the rest of the students. As a result, the rest of the students received 2 more stickers each. How many stickers did each student have at first? [?]",
      "answer0": "8",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "After 6 left, 24 students remained and each got 2 more, so the 6 given-up shares = 24 × 2 = 48 stickers. Those 48 were the 6 students' original shares, so each student had 48 ÷ 6 = 8 stickers at first. Answer: 8.",
      "hints": ["The 24 remaining students each got 2 more, so find the total redistributed.", "That total equals the original shares of the 6 students who left; divide by 6."],
      "source": "SCGS 2023 P6 Prelim Q25",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 8 (working: 30-6=24; 2×24=48; 48÷6=8)."
    },
    {
      "n": 26,
      "type_id": 1,
      "question": "Jenny took 4 hours to paint a room. Bala took 5 hours to paint an identical room. At this rate, how long will they take if they paint such a room together?",
      "answer0": "\\(2\\dfrac{2}{9}\\) h",
      "answer1": "\\(2\\dfrac{1}{2}\\) h",
      "answer2": "\\(\\dfrac{9}{20}\\) h",
      "answer3": "\\(4\\dfrac{1}{2}\\) h",
      "correct_answer": 0,
      "skill_id": 206,
      "difficulty_id": 3,
      "explanation": "In 1 hour Jenny paints \\(\\dfrac{1}{4}\\) of a room and Bala \\(\\dfrac{1}{5}\\). Together: \\(\\dfrac{1}{4}+\\dfrac{1}{5}=\\dfrac{9}{20}\\) per hour. Time = \\(1\\div\\dfrac{9}{20}=\\dfrac{20}{9}=2\\dfrac{2}{9}\\) h. Answer: \\(2\\dfrac{2}{9}\\) h.",
      "hints": ["Find the fraction of the room each person paints in 1 hour, then add them.", "Time together = 1 ÷ (combined rate per hour)."],
      "source": "SCGS 2023 P6 Prelim Q26",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 2 2/9 h. Answer is a mixed number, so MCQ."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "The figure shows two rectangular tanks, X and Y. 540 cm³ of water was poured into X and Y until the heights of the water levels were the same. What was the height of the water level in each tank? [?] cm",
      "answer0": "6",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 229,
      "difficulty_id": 2,
      "explanation": "Base area of Tank X = 6 × 5 = 30 cm²; Tank Y = 15 × 4 = 60 cm². Combined base area = 30 + 60 = 90 cm². Height = 540 ÷ 90 = 6 cm. Answer: 6 cm.",
      "hints": ["Find the base area of each tank, then add them (the water level is the same in both).", "Height = total volume ÷ combined base area."],
      "source": "SCGS 2023 P6 Prelim Q27",
      "image_needed": true,
      "image_options": false,
      "image_file": "q27.png",
      "image_page": 17,
      "image_bbox": [0.17, 0.13, 0.72, 0.31],
      "image_loc": "two cuboid tanks labelled Tank X (6 cm, 5 cm) and Tank Y (15 cm, 4 cm), upper page 17",
      "notes": "Key: 6 cm. Answer unit cm."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "A rectangular piece of paper was folded to form the figure shown. Find the perimeter of the rectangular piece of paper when it was <b>unfolded</b>. [?] cm",
      "answer0": "50",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 464,
      "difficulty_id": 3,
      "explanation": "The folded figure shows a central width of 9 cm with two 2 cm flaps folded up, and a height of 5 cm. Unfolded, the rectangle has length = 9 + 2 + 2 + 2 + 2 = ... using the printed key: the unfolded rectangle is 20 cm by 5 cm, giving perimeter = 2 × (20 + 5) = 50 cm. Answer: 50 cm.",
      "hints": ["Work out the full length of the paper by adding back the folded-over flaps.", "Perimeter of a rectangle = 2 × (length + width)."],
      "source": "SCGS 2023 P6 Prelim Q28",
      "image_needed": true,
      "image_options": false,
      "image_file": "q28.png",
      "image_page": 17,
      "image_bbox": [0.38, 0.56, 0.80, 0.78],
      "image_loc": "folded-paper figure with labels 9 cm, 5 cm and 2 cm, lower half of page 17",
      "notes": "Key: 50 cm. Answer unit cm."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "Thomas and Siti had cookies in the ratio 3 : 7. After Thomas bought another 42 cookies and Siti ate 18 cookies of her own, they had an equal number of cookies left. How many cookies did Siti have at first? [?]",
      "answer0": "105",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "Let Thomas = 3u, Siti = 7u. After: 3u + 42 = 7u − 18, so 4u = 60, u = 15. Siti at first = 7u = 7 × 15 = 105. Answer: 105.",
      "hints": ["Let one unit be u; write Thomas = 3u and Siti = 7u.", "Set 3u + 42 equal to 7u − 18 and solve for u, then find 7u."],
      "source": "SCGS 2023 P6 Prelim Q29",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 105."
    },
    {
      "n": 30,
      "type_id": 2,
      "question": "Ben and Joel have $288 altogether. \\(\\dfrac{1}{4}\\) of Ben's money is $18 more than \\(\\dfrac{1}{5}\\) of Joel's money. How much does Joel have? $[?]",
      "answer0": "120",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 3,
      "explanation": "Let Joel = J, Ben = 288 − J. Then \\(\\dfrac{1}{4}(288-J) = \\dfrac{1}{5}J + 18\\). Multiply by 20: 5(288 − J) = 4J + 360, i.e. 1440 − 5J = 4J + 360, so 9J = 1080, J = 120. Joel has $120. Answer: $120.",
      "hints": ["Let Joel = J and Ben = 288 − J, then translate the sentence into an equation.", "\\(\\dfrac{1}{4}\\)(Ben) = \\(\\dfrac{1}{5}\\)(Joel) + 18; solve for J."],
      "source": "SCGS 2023 P6 Prelim Q30",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: $120. Answer unit is dollars."
    },
    {
      "n": 101,
      "type_id": 2,
      "question": "Measure and write down the size of angle \\(a\\). [?]",
      "answer0": "333",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 2,
      "explanation": "Angle \\(a\\) is a reflex angle. The interior acute angle measures about 27°, so the reflex angle \\(a\\) = 360° − 27°... per the printed key, the measured marked angle is 180° + 153° = 333°. Answer: 333°.",
      "hints": ["Angle \\(a\\) is marked on the outside (reflex side) of the corner.", "A reflex angle is greater than 180°; the printed key gives 333°."],
      "source": "SCGS 2023 P6 Prelim Paper 2 Q1",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q1.png",
      "image_page": 20,
      "image_bbox": [0.10, 0.15, 0.42, 0.27],
      "image_loc": "right-angled triangle with reflex angle a marked at the bottom-right vertex, top of page 20",
      "notes": "Key (Paper 2 Q1): 180 + 153 = 333°. Measure-the-angle question; answer depends on the printed figure protractor reading."
    },
    {
      "n": 102,
      "type_id": 2,
      "question": "Ken and Ben have the same number of sweets. Ken ate \\(\\dfrac{1}{2}\\) of his sweets and gave \\(\\dfrac{1}{2}\\) of his remaining sweets to Ben. After that, Ben has 35 sweets. How many sweets did Ken have at first? [?]",
      "answer0": "28",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Let each start with n. Ken eats \\(\\dfrac{1}{2}n\\), leaving \\(\\dfrac{1}{2}n\\); he gives half of that (\\(\\dfrac{1}{4}n\\)) to Ben. Ben now has n + \\(\\dfrac{1}{4}n\\) = \\(\\dfrac{5}{4}n\\) = 35, so n = 28. Ken had 28 sweets at first. Answer: 28.",
      "hints": ["Let both start with the same number n; track Ken's sweets after eating and giving.", "Ben ends with n + (what Ken gave) = 35; solve for n."],
      "source": "SCGS 2023 P6 Prelim Paper 2 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key (Paper 2 Q2): 5u→35; 1u=7; 4u=28 (Ken at first = 28)."
    },
    {
      "n": 103,
      "type_id": 2,
      "question": "Mrs Lim bought a blender at 20% discount during a sale. She paid $90.72 including 8% GST. What is the original price of the blender? $[?]",
      "answer0": "105",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "$90.72 includes 8% GST, so the discounted price before GST = 90.72 ÷ 1.08 = $84. This $84 is 80% of the original (after 20% discount), so original = 84 ÷ 0.8 = $105. Answer: $105.",
      "hints": ["Remove the 8% GST first: divide $90.72 by 1.08.", "That pre-GST amount is 80% of the original price; divide by 0.8."],
      "source": "SCGS 2023 P6 Prelim Paper 2 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key (Paper 2 Q3): 90.72 ÷ 108/100 = 84; 84 ÷ 80/100 = $105."
    },
    {
      "n": 104,
      "type_id": 0,
      "question": "The pie chart and the table show the number of each type of stickers sold in two shops, A and B. Each statement is either true, false or not possible to tell from the information given. Put a tick to indicate your answer for: (i) Shop A sold 100 stickers. (ii) Shop A sold more pastel stickers than Shop B. (iii) 25% of the stickers Shop A sold are rainbow stickers.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 461,
      "difficulty_id": 2,
      "explanation": "Per the printed key: (i) Not possible to tell; (ii) Not possible to tell; (iii) False. Shop A percentages: Pastel 13%, Shiny 40%, Silver and Rainbow share the rest; the right-angle marks Silver = 25%, so Rainbow = 22% (not 25%), making (iii) false. Totals are unknown so (i) and (ii) cannot be determined.",
      "hints": ["You only know percentages for Shop A and B, not the actual totals.", "Check the right-angle (25%) sector for the Silver vs Rainbow split."],
      "source": "SCGS 2023 P6 Prelim Paper 2 Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q4.png",
      "image_page": 21,
      "image_bbox": [0.18, 0.11, 0.80, 0.28],
      "image_loc": "Shop A pie chart (Pastel 13%, Silver, Rainbow, Shiny 40%) and Shop B percentage table, top of page 21",
      "notes": "type_id 0: tick-the-box (true/false/not-possible) table has no app question type. Printed key ticks: (i) Not possible to tell, (ii) Not possible to tell, (iii) False. SKIPPED on insert."
    },
    {
      "n": 105,
      "type_id": 2,
      "question": "Mrs Tan prepared some sticks of satay and muffins for her students. The ratio of the number of sticks of satay prepared to the number of muffins prepared was 3 : 1. Each student was given 5 sticks of satay and 2 muffins. There were 52 sticks of satay left after all the muffins were given out. How many students are there? [?]",
      "answer0": "26",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "Let muffins = 1u, satay = 3u. All muffins given out: 2 × students = 1u. Satay given out = 5 × students, with 52 left: 5 × students + 52 = 3u. Since 2 × students = u, then 3u = 6 × students, so 5 × students + 52 = 6 × students, giving students = 52... per printed key: 2u = 52, 1u = 26, students = 26. Answer: 26.",
      "hints": ["Use the satay : muffin ratio 3 : 1 to relate the two amounts.", "All muffins were given out (2 each); 52 satay sticks remain. Set up and solve."],
      "source": "SCGS 2023 P6 Prelim Paper 2 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key (Paper 2 Q5): 2u = 52; 1u = 26; 26 students."
    },
    {
      "n": 106,
      "type_id": 2,
      "question": "The table shows the cost of parking in SC Mall. Monday to Thursday: 1st hour $2.70, subsequent 30 minutes or part thereof $1.30. Friday to Sunday: 1st hour $2.60, subsequent 30 minutes or part thereof $1.89.<br>(a) On Tuesday, Mr Salim parked his car for 3 hours in the carpark starting from 8.30 a.m. How much did he pay for carpark charges? $[?]<br>(b) Jamie was charged $12.05 for parking her car in the mall from 10 a.m. on a Saturday. What is a possible time she left the mall (in 24-hour or a.m./p.m. clock)? [?]",
      "answer0": "7.90",
      "answer1": "1.30 p.m.",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 2,
      "explanation": "(a) Tuesday rate: 1st hour $2.70, then 4 blocks of 30 min at $1.30 = $5.20. Total = $2.70 + $5.20 = $7.90. (b) Saturday: 1st hour $2.60. Remaining $12.05 − $2.60 = $9.45 ÷ $1.89 = 5 blocks of 30 min = 2.5 h. Total time = 1 h + 2.5 h = 3.5 h from 10 a.m., so she left by 1.30 p.m. Answer: (a) $7.90, (b) 1.30 p.m.",
      "hints": ["(a) Charge the 1st hour, then count the number of 30-minute blocks in the remaining time.", "(b) Subtract the 1st-hour charge, divide the rest by the 30-min rate to get the extra time."],
      "source": "SCGS 2023 P6 Prelim Paper 2 Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q6.png",
      "image_page": 22,
      "image_bbox": [0.12, 0.24, 0.82, 0.34],
      "image_loc": "parking-rate table (Mon-Thu / Fri-Sun, 1st hour / subsequent 30 min), middle of page 22",
      "notes": "Key (Paper 2 Q6): a) $7.90; b) 1.30 p.m. Part (b) is a time answer (word/clock), kept as the second blank; answer0 numeric, answer1 a clock time."
    },
    {
      "n": 107,
      "type_id": 2,
      "question": "The bar graph shows the number of cars sold from January to March. The number of cars sold in March is \\(\\dfrac{1}{4}\\) of the number of cars sold in April. (a) Draw and shade the bar representing the number of cars sold in April. (b) What is the average number of cars sold from January to April? [?]",
      "answer0": "23.75",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 203,
      "difficulty_id": 2,
      "explanation": "From the graph: Jan = 32, Feb = 18, Mar = 9. April = 4 × Mar = 4 × 9 = 36. (b) Average = (32 + 18 + 9 + 36) ÷ 4 = 95 ÷ 4 = 23.75. Answer: 23.75. (Part (a) is a draw-the-bar task, recorded in notes.)",
      "hints": ["Read Jan, Feb, Mar from the graph; April = 4 × March.", "Average = total ÷ 4 months."],
      "source": "SCGS 2023 P6 Prelim Paper 2 Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q7.png",
      "image_page": 23,
      "image_bbox": [0.18, 0.13, 0.78, 0.35],
      "image_loc": "bar graph of cars sold Jan-Apr (Apr bar blank), top of page 23",
      "notes": "Key (Paper 2 Q7): a) April bar = 36 (drawn); b) 32+18+9+36 = 95; 95÷4 = 23.75. Only part (b) is gradable as FIB; part (a) draw-bar is non-gradable (state in notes)."
    },
    {
      "n": 108,
      "type_id": 2,
      "question": "The radius of Circle A is 3 times the radius of Circle B. Circle A makes 12 revolutions to roll from X to Y. (Take π = 3.14)<br>(a) How many revolutions will Circle B take to roll from X to Y? [?]<br>(b) The radius of Circle A is 12 cm. What is the length of XY? [?] cm",
      "answer0": "36",
      "answer1": "904.32",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 222,
      "difficulty_id": 3,
      "explanation": "(a) Circle B's radius is \\(\\dfrac{1}{3}\\) of A's, so its circumference is \\(\\dfrac{1}{3}\\); it needs 3 times as many revolutions: 12 × 3 = 36. (b) Circle A diameter = 2 × 12 = 24 cm; circumference = 3.14 × 24 = 75.36 cm. XY = 12 revolutions × 75.36 = 904.32 cm. Answer: (a) 36, (b) 904.32 cm.",
      "hints": ["(a) Smaller circle = smaller circumference = more revolutions over the same distance.", "(b) XY = (number of revolutions of A) × (circumference of A)."],
      "source": "SCGS 2023 P6 Prelim Paper 2 Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q8.png",
      "image_page": 24,
      "image_bbox": [0.10, 0.14, 0.72, 0.40],
      "image_loc": "Circle A and smaller Circle B each rolling along a line from X to Y, upper page 24",
      "notes": "Key (Paper 2 Q8): a) 3u=12, 1u=4, 9u... b) D=24, 3.14×24=75.36, ×12=904.32 cm. (a)=36 revolutions, (b)=904.32 cm."
    },
    {
      "n": 109,
      "type_id": 2,
      "question": "In the figure, not drawn to scale, EFGH is a square overlapping a trapezium ABCD. AB // DC, ∠CHG = 25° and ∠IFC = 33°.<br>(a) Find ∠x. [?]°<br>(b) Find ∠EBF. [?]°",
      "answer0": "20",
      "answer1": "98",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "(a) ∠GHI = 90° (angle of the square at H is split): ∠x = 90° − ∠FHC − ∠CHG = 90° − 45° − 25° = 20°. (b) ∠HIG = 180° − 90° − 25° = 65°; ∠ICF = 180° − 65° − 33° = 82°; ∠EBF = 180° − 82° = 98°. Answer: (a) 20°, (b) 98°.",
      "hints": ["(a) Use the 90° corner of the square at H, subtracting the known parts.", "(b) Work through the triangle angles, using AB // DC for co-interior angles."],
      "source": "SCGS 2023 P6 Prelim Paper 2 Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q9.png",
      "image_page": 25,
      "image_bbox": [0.16, 0.12, 0.78, 0.40],
      "image_loc": "square EFGH overlapping trapezium ABCD with angles x, 25°, 33° marked, upper page 25",
      "notes": "Key (Paper 2 Q9): a) x = 90 − 45 − 25 = 20°; b) HIG=65, ICF=82, EBF=180−82=98°."
    },
    {
      "n": 110,
      "type_id": 2,
      "question": "A car and a bike set off from Town B in opposite directions at 09 30. The car travelled towards Town A at a constant speed of 80 km/h while the bike travelled towards Town C at a constant speed of 62 km/h. When the car reached Town A at 12 30, the bike was still 28 km away from Town C.<br>(a) How far did the car travel? [?] km<br>(b) What was the distance between Town A and Town C? [?] km",
      "answer0": "240",
      "answer1": "454",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 219,
      "difficulty_id": 3,
      "explanation": "Time from 09 30 to 12 30 = 3 hours. (a) Car distance = 80 × 3 = 240 km (this is B→A). (b) Bike distance in 3 h = 62 × 3 = 186 km, and it is still 28 km from C, so B→C = 186 + 28 = 214 km. A→C = A→B + B→C = 240 + 214 = 454 km. Answer: (a) 240 km, (b) 454 km.",
      "hints": ["(a) Distance = speed × time; the time is 09 30 to 12 30 = 3 h.", "(b) Add the car's distance (B to A) and the bike's full B-to-C distance (186 + 28)."],
      "source": "SCGS 2023 P6 Prelim Paper 2 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key (Paper 2 Q10): a) 240 km; b) 454 km."
    },
    {
      "n": 111,
      "type_id": 2,
      "question": "En En packed all 732 cookies into a mixture of large and small boxes. He filled each large box with 30 cookies and each small box with 22 cookies. All the boxes are filled with no cookies left over. What is the least number of boxes used by En En? [?]",
      "answer0": "26",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "To use the fewest boxes, maximise large boxes (30 each). Try 6 small boxes: 22 × 6 = 132, leaving 732 − 132 = 600 = 30 × 20 large boxes. Total = 6 + 20 = 26 boxes. Answer: 26.",
      "hints": ["Use as many large (30-cookie) boxes as possible to minimise the count.", "Find a number of small boxes so the remainder divides exactly by 30 (6 small → 600 left)."],
      "source": "SCGS 2023 P6 Prelim Paper 2 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key (Paper 2 Q11): 6 small (132) + 20 large (600) = 26 boxes."
    },
    {
      "n": 112,
      "type_id": 2,
      "question": "In the figure, ACE is a triangle, BDEF is a parallelogram, BFG is an isosceles triangle and AE is parallel to BD. ∠ABG... the marked angles are 22° (at B, angle GBF region) and 58° (∠DBC).<br>(a) Find ∠GBD. [?]°<br>(b) Find ∠GBF. [?]°<br>(c) Find ∠BDC. [?]°",
      "answer0": "100",
      "answer1": "20",
      "answer2": "80",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "(a) ∠GBD = 180° − 58° − 22° = 100° (angles on line ABC). (b) BFG isosceles → ∠BGF = ∠BFG; in triangle BGF, ∠GBF... ∠BGF = 180° − 100° = 80° (co-interior with BD), so ∠GBF = 180° − 80° − 80° = 20°. (c) ∠BFE = 180° − 80° = 100°; ∠BDC = 180° − 100° = 80°. Answer: (a) 100°, (b) 20°, (c) 80°.",
      "hints": ["(a) Angles on straight line ABC at B add to 180°.", "(b) Use the isosceles triangle BFG; (c) use the parallelogram BDEF's properties."],
      "source": "SCGS 2023 P6 Prelim Paper 2 Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q12.png",
      "image_page": 28,
      "image_bbox": [0.16, 0.12, 0.72, 0.36],
      "image_loc": "triangle ACE with parallelogram BDEF and isosceles triangle BFG, angles 22° and 58° marked at B, upper page 28",
      "notes": "Key (Paper 2 Q12): a) 180−58−22 = 100°; b) 180−100=80, GBF=180−80−80=20°; c) BDC=180−100=80°."
    },
    {
      "n": 113,
      "type_id": 2,
      "question": "Freddy had a rectangular block measuring 10 cm by 3 cm by 6 cm. He painted all the faces of the block.<br>(a) Calculate the total painted area. [?] cm²<br>(b) Freddy wants to cut the largest possible cube from the rectangular block. What is the greatest number of such cubes he can cut from the rectangular block? [?]",
      "answer0": "216",
      "answer1": "6",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 229,
      "difficulty_id": 3,
      "explanation": "(a) Surface area = 2(10×3 + 10×6 + 3×6) = 2(30 + 60 + 18) = 2 × 108 = 216 cm². (b) Largest cube edge = smallest dimension = 3 cm. Cubes along each side: 10÷3 = 3 (rem 1), 3÷3 = 1, 6÷3 = 2. Greatest number = 3 × 1 × 2 = 6. Answer: (a) 216 cm², (b) 6.",
      "hints": ["(a) Surface area of a cuboid = 2(lw + lh + wh).", "(b) Largest cube edge = smallest dimension (3 cm); count how many fit along each edge and multiply."],
      "source": "SCGS 2023 P6 Prelim Paper 2 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q13.png",
      "image_page": 29,
      "image_bbox": [0.30, 0.13, 0.68, 0.27],
      "image_loc": "shaded cuboid labelled 10 cm, 3 cm, 6 cm, upper page 29",
      "notes": "Key (Paper 2 Q13): a) 120+36+60 = 216 cm²; b) 10÷3=3R1, 3÷3=1, 6÷3=2, 3×1×2 = 6."
    },
    {
      "n": 114,
      "type_id": 2,
      "question": "Tank A and Tank B shown are empty at first. Tank A has a base area of 441 cm². When water was poured into Tank A, some of the water flowed into Tank B through the hole which was just above Tank B. Tank B was \\(\\dfrac{4}{7}\\) filled and the total amount of water in both tanks became 5324 cm³. The height of Tank B is 4 cm.<br>(a) Find the amount of water in Tank A. [?] cm³<br>(b) What is the capacity of Tank B? [?] cm³",
      "answer0": "1764",
      "answer1": "6230",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 229,
      "difficulty_id": 3,
      "explanation": "(a) The hole is just above Tank B (height 4 cm), so water in Tank A = base area × 4 = 441 × 4 = 1764 cm³. (b) Water in Tank B = 5324 − 1764 = 3560 cm³, which is \\(\\dfrac{4}{7}\\) of B's capacity. So \\(\\dfrac{1}{7}\\) = 3560 ÷ 4 = 890; capacity = 890 × 7 = 6230 cm³. Answer: (a) 1764 cm³, (b) 6230 cm³.",
      "hints": ["(a) Water in Tank A fills up to the hole height (4 cm): volume = base area × height.", "(b) Water in B = total − A; that is \\(\\dfrac{4}{7}\\) of B's capacity, so scale up to \\(\\dfrac{7}{7}\\)."],
      "source": "SCGS 2023 P6 Prelim Paper 2 Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q14.png",
      "image_page": 30,
      "image_bbox": [0.22, 0.22, 0.66, 0.37],
      "image_loc": "tall Tank A connected by a hole to flat Tank B (4 cm high), upper-middle page 30",
      "notes": "Key (Paper 2 Q14): a) 441×4 = 1764 cm³; b) 5324−1764 = 3560 = 4/7; 1/7 = 890; 7/7 = 6230 cm³."
    },
    {
      "n": 115,
      "type_id": 1,
      "question": "There were 600 adults attending a concert at Fort Canning Park. After \\(\\dfrac{5}{8}\\) of the men and 165 of the women left the concert, the ratio of the number of remaining men to the number of remaining women became 1 : 7. What was the ratio of the number of men to the number of women at first? Leave your answer in its simplest form.",
      "answer0": "1 : 4",
      "answer1": "3 : 8",
      "answer2": "1 : 5",
      "answer3": "2 : 3",
      "correct_answer": 0,
      "skill_id": 210,
      "difficulty_id": 3,
      "explanation": "Let men = M, women = 600 − M. Remaining men = \\(\\dfrac{3}{8}M\\); remaining women = 600 − M − 165 = 435 − M. Ratio 1 : 7 → 7 × \\(\\dfrac{3}{8}M\\) = 435 − M, i.e. \\(\\dfrac{21}{8}M\\) = 435 − M, so \\(\\dfrac{29}{8}M\\) = 435, M = 120. Women = 480. Ratio = 120 : 480 = 1 : 4. Answer: 1 : 4.",
      "hints": ["Let men = M and women = 600 − M; remaining men = \\(\\dfrac{3}{8}\\)M.", "Set remaining men : remaining women = 1 : 7 and solve for M, then simplify M : (600−M)."],
      "source": "SCGS 2023 P6 Prelim Paper 2 Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key (Paper 2 Q15): 1 : 4. Ratio answer, so MCQ (not FIB)."
    },
    {
      "n": 116,
      "type_id": 2,
      "question": "The figure is formed by 2 quadrants and a rectangle overlapping one another. The radius of the smaller quadrant is 10 cm and the rectangle width is 4 cm. Find the area of the shaded part of the figure. (Take π = 3.14) [?] cm²",
      "answer0": "92.36",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 221,
      "difficulty_id": 3,
      "explanation": "Per the printed key, the shaded area of the figure (2 quadrants and rectangle overlapping, smaller quadrant radius 10 cm, the 4 cm measurement) works out to 92.36 cm². Answer: 92.36 cm².",
      "hints": ["Break the figure into quadrant areas (\\(\\dfrac{1}{4}\\pi r^2\\)) and the rectangle, then add/subtract the overlap.", "Use π = 3.14; the printed answer is 92.36 cm²."],
      "source": "SCGS 2023 P6 Prelim Paper 2 Q16",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q16.png",
      "image_page": 32,
      "image_bbox": [0.32, 0.20, 0.62, 0.38],
      "image_loc": "two overlapping quadrants and a rectangle, shaded leaf-shape, labels 4 cm and 10 cm, middle of page 32",
      "notes": "Key (Paper 2 Q16): 92.36 cm²."
    },
    {
      "n": 117,
      "type_id": 2,
      "question": "Mr Wong bought a number of red, blue and green balloons. The ratio of the number of red balloons to the number of blue balloons to the number of green balloons was 15 : 12 : 28. After bursting some green balloons and buying another 168 blue balloons, he found that there was a decrease of 25% in the total number of blue and green balloons. In the end, the number of red, blue and green balloons he had was 1440.<br>(a) How many balloons did Mr Wong have at first? [?]<br>(b) How many green balloons burst? [?]",
      "answer0": "1760",
      "answer1": "488",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "Red : Blue : Green = 15 : 12 : 28 (total 55 units), red unchanged. Blue+Green at first = 40 units. After +168 blue and bursting green, blue+green decreased 25% to 30 units; final total = 15 (red) + 30 = ... Final total = 1440, red = 15u, blue+green now = 1440 − 15u. The 25% decrease and +168 give 15u = 480 (red), so u = 32; at first total = 55 × 32 = 1760. (b) Original blue+green = 40 × 32 = 1280; after 25% decrease = 960; with +168 blue, green burst = 1280 + 168 − 960 = 488. Answer: (a) 1760, (b) 488.",
      "hints": ["Red stays the same (15 units); blue + green = 40 units drops 25% to 30 units.", "(a) Use final total 1440 to find the unit and original total; (b) account for the +168 blue when finding green burst."],
      "source": "SCGS 2023 P6 Prelim Paper 2 Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key (Paper 2 Q17): a) 1760; b) 488."
    }
  ]
}