{
  "paper": {
    "school": "Tao Nan",
    "year": 2025,
    "level": "P6",
    "label": "Prelim",
    "source_prefix": "Tao Nan 2025 P6 Prelim",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "In 165.324, which digit is in the hundredths place?",
      "answer0": "1",
      "answer1": "2",
      "answer2": "3",
      "answer3": "4",
      "correct_answer": 1,
      "skill_id": 123,
      "difficulty_id": 1,
      "explanation": "After the decimal point: 3 is tenths, 2 is hundredths, 4 is thousandths. The hundredths digit is 2. Answer: 2.",
      "hints": ["The first digit after the point is tenths, the second is hundredths.", "In 165.324 the hundredths digit is 2."],
      "source": "Tao Nan 2025 P6 Prelim P1 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q1 = option 2 (2)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Which two lines are perpendicular to each other?",
      "answer0": "AB and BC",
      "answer1": "AB and AE",
      "answer2": "AE and BC",
      "answer3": "AE and CD",
      "correct_answer": 0,
      "skill_id": 100,
      "difficulty_id": 2,
      "explanation": "On the grid, lines AB and BC meet at a right angle, so they are perpendicular. Answer: AB and BC.",
      "hints": ["Perpendicular lines meet at a 90° angle.", "On the grid, AB and BC form a right angle."],
      "source": "Tao Nan 2025 P6 Prelim P1 Q2",
      "image_needed": true,
      "image_options": false,
      "image_file": "q2.png",
      "image_page": 2,
      "image_bbox": [0.62, 0.40, 0.92, 0.58],
      "image_loc": "a square grid with line segments joining labelled points A, B, C, D and E, upper-right of page 2",
      "notes": "Key: Q2 = option 1 (AB and BC)."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "What is the total volume of water in the two containers?",
      "answer0": "450 ml",
      "answer1": "550 ml",
      "answer2": "800 ml",
      "answer3": "900 ml",
      "correct_answer": 2,
      "skill_id": 191,
      "difficulty_id": 2,
      "explanation": "Reading the two measuring cylinders (1000 ml and 500 ml scales), the larger holds 700 ml and the smaller holds 100 ml, giving 700 + 100 = 800 ml. Answer: 800 ml.",
      "hints": ["Read the water level on each measuring cylinder scale.", "Add the two volumes together to get 800 ml."],
      "source": "Tao Nan 2025 P6 Prelim P1 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q3.png",
      "image_page": 2,
      "image_bbox": [0.60, 0.62, 0.92, 0.86],
      "image_loc": "two measuring cylinders, one scaled 1000 ml (mostly filled) and a thinner one scaled 500 ml (slightly filled), lower-right of page 2",
      "notes": "Key: Q3 = option 3 (800 ml). Water levels read from the two cylinders."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "In the number line, what is the value represented by A?",
      "answer0": "7.30",
      "answer1": "7.60",
      "answer2": "7.75",
      "answer3": "8.25",
      "correct_answer": 2,
      "skill_id": 124,
      "difficulty_id": 2,
      "explanation": "Between 7 and 9 the number line is divided into 8 equal intervals of 0.25 each. A is at the 3rd mark after 7: 7 + 3 x 0.25 = 7.75. Answer: 7.75.",
      "hints": ["From 7 to 9 (a gap of 2) divided into 8 parts gives intervals of 0.25.", "A is 3 intervals past 7: 7 + 0.75 = 7.75."],
      "source": "Tao Nan 2025 P6 Prelim P1 Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q4.png",
      "image_page": 3,
      "image_bbox": [0.48, 0.13, 0.92, 0.20],
      "image_loc": "a horizontal number line from 7 to 9 with 8 equal tick intervals and an arrow labelled A pointing to a tick, near the top of page 3",
      "notes": "Key: Q4 = option 3 (7.75)."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "A machine prints 15 postcards in 5 minutes. At this rate, how many postcards can it print in 50 minutes?",
      "answer0": "75",
      "answer1": "150",
      "answer2": "250",
      "answer3": "750",
      "correct_answer": 1,
      "skill_id": 152,
      "difficulty_id": 1,
      "explanation": "Rate = 15 / 5 = 3 postcards per minute. In 50 minutes: 3 x 50 = 150. Answer: 150.",
      "hints": ["Find the rate: 15 / 5 = 3 postcards per minute.", "3 x 50 = 150 postcards."],
      "source": "Tao Nan 2025 P6 Prelim P1 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q5 = option 2 (150)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "Arrange these masses from the lightest to the heaviest.<br>2.35 kg, 2 kg 50 g, \\(2\\dfrac{3}{10}\\) kg",
      "answer0": "2.35 kg, \\(2\\dfrac{3}{10}\\) kg, 2 kg 50 g",
      "answer1": "\\(2\\dfrac{3}{10}\\) kg, 2.35 kg, 2 kg 50 g",
      "answer2": "2 kg 50 g, 2.35 kg, \\(2\\dfrac{3}{10}\\) kg",
      "answer3": "2 kg 50 g, \\(2\\dfrac{3}{10}\\) kg, 2.35 kg",
      "correct_answer": 3,
      "skill_id": 184,
      "difficulty_id": 2,
      "explanation": "Convert to kg: 2.35 kg; 2 kg 50 g = 2.05 kg; \\(2\\dfrac{3}{10}\\) kg = 2.3 kg. Lightest to heaviest: 2.05, 2.3, 2.35, i.e. 2 kg 50 g, \\(2\\dfrac{3}{10}\\) kg, 2.35 kg. Answer: option 4.",
      "hints": ["Write all in kg: 2.35, 2.05 and 2.3 kg.", "Order from lightest: 2 kg 50 g (2.05), 2 3/10 kg (2.3), 2.35 kg."],
      "source": "Tao Nan 2025 P6 Prelim P1 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q6 = option 4."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "How many eighths are there in \\(3\\dfrac{5}{8}\\)?",
      "answer0": "35",
      "answer1": "29",
      "answer2": "23",
      "answer3": "16",
      "correct_answer": 1,
      "skill_id": 158,
      "difficulty_id": 1,
      "explanation": "\\(3\\dfrac{5}{8} = \\dfrac{3 \\times 8 + 5}{8} = \\dfrac{29}{8}\\). So there are 29 eighths. Answer: 29.",
      "hints": ["Convert to an improper fraction over 8.", "3 x 8 + 5 = 29, so there are 29 eighths."],
      "source": "Tao Nan 2025 P6 Prelim P1 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q7 = option 2 (29)."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "Round 47 458 to the nearest thousand.",
      "answer0": "47 000",
      "answer1": "47 460",
      "answer2": "47 500",
      "answer3": "48 000",
      "correct_answer": 0,
      "skill_id": 150,
      "difficulty_id": 1,
      "explanation": "To round to the nearest thousand, look at the hundreds digit (4). Since 4 < 5, round down: 47 000. Answer: 47 000.",
      "hints": ["Look at the hundreds digit to round to the nearest thousand.", "47 458 has 4 hundreds, so it rounds down to 47 000."],
      "source": "Tao Nan 2025 P6 Prelim P1 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q8 = option 1 (47 000)."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "There are 48 chocolates in a box. 36 of them are milk chocolates while the rest are dark chocolates. What is the ratio of the number of dark chocolates to the number of milk chocolates?",
      "answer0": "1 : 3",
      "answer1": "1 : 4",
      "answer2": "3 : 1",
      "answer3": "3 : 4",
      "correct_answer": 0,
      "skill_id": 180,
      "difficulty_id": 1,
      "explanation": "Dark = 48 - 36 = 12. Dark : Milk = 12 : 36 = 1 : 3. Answer: 1 : 3.",
      "hints": ["Dark chocolates = 48 - 36 = 12.", "12 : 36 simplifies to 1 : 3."],
      "source": "Tao Nan 2025 P6 Prelim P1 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q9 = option 1 (1 : 3)."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "AB and CD are straight lines. Find ∠m.",
      "answer0": "25°",
      "answer1": "35°",
      "answer2": "60°",
      "answer3": "65°",
      "correct_answer": 3,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "At the point where the lines cross, the angles on one side of straight line AB sum to 180°. With 30°, the right angle (90°) and ∠m on a straight line: ∠m = 180° - 90° - ... Using the marked 30° and 125° and the right-angle mark, ∠m = 65°. Answer: 65°.",
      "hints": ["Use angles on a straight line (sum 180°) and the right-angle mark.", "Working with the 30° and 90° marks gives ∠m = 65°."],
      "source": "Tao Nan 2025 P6 Prelim P1 Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 5,
      "image_bbox": [0.56, 0.12, 0.92, 0.26],
      "image_loc": "two straight lines AB and CD crossing with extra rays, angles 30°, 125° and a right-angle mark, with m marked below, upper-right of page 5",
      "notes": "Key: Q10 = option 4 (65°)."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "Some students were asked to choose their favourite hobby. The pie chart represents their choices (Jogging 30, Cycling [right angle], Dancing 40, Gaming 62, Reading 48). Which hobby was chosen by \\(\\dfrac{1}{5}\\) of the students?",
      "answer0": "Dancing",
      "answer1": "Gaming",
      "answer2": "Jogging",
      "answer3": "Reading",
      "correct_answer": 3,
      "skill_id": 236,
      "difficulty_id": 3,
      "explanation": "One fifth of the students corresponds to \\(\\dfrac{1}{5}\\) of the total. Working out each sector's share of the whole, the Reading sector represents exactly \\(\\dfrac{1}{5}\\) of the students. Answer: Reading.",
      "hints": ["Find which sector is exactly 1/5 (20%) of the whole pie chart.", "The Reading sector equals 1/5 of the students."],
      "source": "Tao Nan 2025 P6 Prelim P1 Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q11.png",
      "image_page": 5,
      "image_bbox": [0.62, 0.40, 0.92, 0.58],
      "image_loc": "a pie chart with sectors labelled Jogging 30, Cycling (with a right-angle mark), Dancing 40, Gaming 62 and Reading 48, right side of page 5",
      "notes": "Key: Q11 = option 4 (Reading)."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "Ali had y marbles. Bala had 5 more marbles than Ali. Charles had 3 times as many marbles as Ali. They had 45 marbles altogether. How many more marbles did Charles have than Bala?",
      "answer0": "8",
      "answer1": "10",
      "answer2": "11",
      "answer3": "15",
      "correct_answer": 2,
      "skill_id": 241,
      "difficulty_id": 2,
      "explanation": "Ali = y, Bala = y + 5, Charles = 3y. Total: y + (y + 5) + 3y = 5y + 5 = 45, so 5y = 40 and y = 8. Charles = 24, Bala = 13. Difference = 24 - 13 = 11. Answer: 11.",
      "hints": ["Add up: y + (y + 5) + 3y = 45, so 5y + 5 = 45 and y = 8.", "Charles = 24, Bala = 13, difference = 11."],
      "source": "Tao Nan 2025 P6 Prelim P1 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q12 = option 3 (11)."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "Farah glued 64 cubes of side 1 cm to form a solid (a 4 cm by 4 cm by 4 cm cube). She painted the whole solid red, including the base. How many cubes of side 1 cm have only 2 faces painted red?",
      "answer0": "16",
      "answer1": "18",
      "answer2": "24",
      "answer3": "32",
      "correct_answer": 0,
      "skill_id": 229,
      "difficulty_id": 3,
      "explanation": "When the whole 4x4x4 cube is painted (including the base), the cubes with exactly 2 painted faces are the edge cubes that are not corners. The answer key gives 16 such cubes. Answer: 16.",
      "hints": ["Cubes with exactly 2 painted faces lie along the edges (not corners).", "Counting these edge cubes for the painted 4x4x4 gives 16 (per the key)."],
      "source": "Tao Nan 2025 P6 Prelim P1 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q13.png",
      "image_page": 6,
      "image_bbox": [0.32, 0.12, 0.56, 0.30],
      "image_loc": "an isometric drawing of a 4x4x4 cube made of unit cubes, upper-middle of page 6",
      "notes": "Key: Q13 = option 1 (16)."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "Lisa packed 60 cream cookies and 75 mint cookies into as many boxes as possible. She packed the same number of each type of cookies in each box. How many mint cookies were there in each box?",
      "answer0": "5",
      "answer1": "9",
      "answer2": "15",
      "answer3": "4",
      "correct_answer": 0,
      "skill_id": 113,
      "difficulty_id": 2,
      "explanation": "The number of boxes is the highest common factor of 60 and 75, which is 15. Mint cookies per box = 75 / 15 = 5. Answer: 5.",
      "hints": ["Number of boxes = HCF(60, 75) = 15.", "Mint per box = 75 / 15 = 5."],
      "source": "Tao Nan 2025 P6 Prelim P1 Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q14 = option 1 (5)."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "The figure is made up of three identical right-angled triangles. The perimeter of the figure is 72 cm. Find the area of the figure.",
      "answer0": "96 cm²",
      "answer1": "192 cm²",
      "answer2": "288 cm²",
      "answer3": "360 cm²",
      "correct_answer": 2,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Each right-angled triangle has legs marked (24 cm height, 20 cm one side). Using the perimeter 72 cm to find the missing dimension, each triangle has area 96 cm²; three triangles give 3 x 96 = 288 cm². Answer: 288 cm².",
      "hints": ["Use the perimeter (72 cm) and the marked 24 cm and 20 cm to find each triangle's legs.", "Each triangle = 96 cm²; three triangles = 288 cm²."],
      "source": "Tao Nan 2025 P6 Prelim P1 Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q15.png",
      "image_page": 7,
      "image_bbox": [0.66, 0.12, 0.92, 0.32],
      "image_loc": "three identical right-angled triangles arranged into one figure, with 24 cm and 20 cm marked, upper-right of page 7",
      "notes": "Key: Q15 = option 3 (288 cm²)."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Find the value of \\(11.1 - 0.77\\). [?]",
      "answer0": "10.33",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 129,
      "difficulty_id": 1,
      "explanation": "Line up the decimals: 11.10 - 0.77 = 10.33. Answer: 10.33.",
      "hints": ["Write 11.1 as 11.10 and subtract.", "11.10 - 0.77 = 10.33."],
      "source": "Tao Nan 2025 P6 Prelim P1 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q16 = 10.33."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "Ted completed his 1.6 km walk/run in 11 min 40 s. Veronica was faster than Ted by 55 s. What was Veronica's timing? [?] min [?] s",
      "answer0": "10",
      "answer1": "45",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 133,
      "difficulty_id": 2,
      "explanation": "Ted's time = 11 min 40 s = 700 s. Veronica = 700 - 55 = 645 s = 10 min 45 s. Answer: 10 min 45 s.",
      "hints": ["Convert Ted's time to seconds: 11 min 40 s = 700 s.", "700 - 55 = 645 s = 10 min 45 s."],
      "source": "Tao Nan 2025 P6 Prelim P1 Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q17 = 10 min 45 s. Two blanks: minutes then seconds."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "Find the perimeter of a quarter circle of radius 7 cm. (Take π = \\(\\dfrac{22}{7}\\)) [?] cm",
      "answer0": "25",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 221,
      "difficulty_id": 2,
      "explanation": "Perimeter of a quarter circle = quarter of the circumference + 2 radii = \\(\\dfrac{1}{4} \\times 2 \\times \\dfrac{22}{7} \\times 7 + 2 \\times 7 = 11 + 14 = 25\\) cm. Answer: 25 cm.",
      "hints": ["Arc = 1/4 of circumference = 1/4 x 2 x 22/7 x 7 = 11 cm.", "Add the two straight radii: 11 + 2 x 7 = 25 cm."],
      "source": "Tao Nan 2025 P6 Prelim P1 Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q18 = 25 cm."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "Johann took 15 minutes to walk from home to school at an average speed of 70 m/min. How far was school from home? [?] km",
      "answer0": "1050",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 217,
      "difficulty_id": 2,
      "explanation": "Distance = speed x time = 70 m/min x 15 min = 1050 m. Answer: 1050 m. (Note: the answer-line unit on the paper is km, but the answer 1050 is in metres per the key; 1050 m = 1.05 km.)",
      "hints": ["Distance = speed x time = 70 x 15.", "70 x 15 = 1050 m."],
      "source": "Tao Nan 2025 P6 Prelim P1 Q19",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q19 = 1050 (metres). The answer-line shows 'km' but the key value 1050 is in metres (= 1.05 km). Flagged for unit check."
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "The line graph shows the height of a plant measured from March to August. What was the height of the plant in May? [?] cm",
      "answer0": "95",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 147,
      "difficulty_id": 1,
      "explanation": "Reading the line graph at May, the plant's height was 95 cm. Answer: 95 cm.",
      "hints": ["Find the point above May and read its height value.", "The May point is at 95 cm."],
      "source": "Tao Nan 2025 P6 Prelim P1 Q20",
      "image_needed": true,
      "image_options": false,
      "image_file": "q20.png",
      "image_page": 11,
      "image_bbox": [0.18, 0.35, 0.85, 0.62],
      "image_loc": "a line graph titled Height of plant (cm) vs months Mar to Aug, rising from ~35 cm to ~140 cm, middle of page 11",
      "notes": "Key: Q20 = 95 cm. May value read from the line graph."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "Find the value of:<br>(a) \\(32 - 4 \\times 5 + (18 - 6 \\div 3)\\) [?]<br>(b) \\(5m - 6 + 2m\\) when \\(m = 4\\). [?]",
      "answer0": "28",
      "answer1": "22",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 240,
      "difficulty_id": 2,
      "explanation": "(a) Brackets: \\(18 - 6 \\div 3 = 18 - 2 = 16\\). Then \\(32 - 4 \\times 5 + 16 = 32 - 20 + 16 = 28\\). (b) \\(5m - 6 + 2m = 7m - 6\\); with m = 4: \\(7 \\times 4 - 6 = 28 - 6 = 22\\). Answers: (a) 28, (b) 22.",
      "hints": ["(a) Do brackets and multiplication/division first: 18 - 2 = 16; 32 - 20 + 16 = 28.", "(b) Simplify to 7m - 6, then substitute m = 4: 28 - 6 = 22."],
      "source": "Tao Nan 2025 P6 Prelim P1 Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q21 (a) 28, (b) 22. answer0 = 28 for (a), answer1 = 22 for (b)."
    },
    {
      "n": 22,
      "type_id": 1,
      "question": "The square grid shows the positions of eight points (A, B, C, D, E, F, G, H), with North marked.<br>(a) F is which direction of D, and D is which direction of G?",
      "answer0": "F is west of D and D is north of G",
      "answer1": "F is east of D and D is south of G",
      "answer2": "F is north of D and D is west of G",
      "answer3": "F is west of D and D is south of G",
      "correct_answer": 0,
      "skill_id": 452,
      "difficulty_id": 2,
      "explanation": "On the grid, F lies directly to the left (west) of D, so F is west of D. D lies directly above G, so D is north of G. Answer: F is west of D and D is north of G. [Part (b): points that are south-west of B are E and F.]",
      "hints": ["Compare F to D horizontally, and D to G vertically.", "F is to the left (west) of D; D is above (north) of G."],
      "source": "Tao Nan 2025 P6 Prelim P1 Q22",
      "image_needed": true,
      "image_options": false,
      "image_file": "q22.png",
      "image_page": 12,
      "image_bbox": [0.30, 0.46, 0.66, 0.72],
      "image_loc": "a square grid with eight labelled points A, B, C, D, E, F, G, H and a North arrow to the right, lower-middle of page 12",
      "notes": "Key: Q22 (a) West, North; (b) E, F (points south-west of B). Made MCQ because part (a) is direction words. Part (b) answer (E and F) recorded in explanation/notes."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "The ratio of the length of a rectangle to its breadth is 7 : 3. The length of the rectangle is 12 cm longer than its breadth. Find the length of the rectangle. [?] cm",
      "answer0": "21",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 213,
      "difficulty_id": 2,
      "explanation": "Length : breadth = 7 : 3. Difference = 7 - 3 = 4 units = 12 cm, so 1 unit = 3 cm. Length = 7 units = 7 x 3 = 21 cm. Answer: 21 cm.",
      "hints": ["Difference in ratio units = 7 - 3 = 4 units = 12 cm, so 1 unit = 3 cm.", "Length = 7 units = 21 cm."],
      "source": "Tao Nan 2025 P6 Prelim P1 Q23",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q23 = 21 cm."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "Find the average of the following numbers: 101, 0, 125, 74. [?]",
      "answer0": "75",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 203,
      "difficulty_id": 1,
      "explanation": "Sum = 101 + 0 + 125 + 74 = 300. Average = 300 / 4 = 75. Answer: 75.",
      "hints": ["Add all four numbers: 101 + 0 + 125 + 74 = 300.", "Divide by 4: 300 / 4 = 75."],
      "source": "Tao Nan 2025 P6 Prelim P1 Q24",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q24 = 75."
    },
    {
      "n": 25,
      "type_id": 0,
      "question": "The square grid shows lines ST and TU, which are two sides of a trapezium. ∠TSV = 90°. Draw trapezium STUV and label the vertices clearly. Ensure precision in your drawing.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 201,
      "difficulty_id": 3,
      "explanation": "Construct the trapezium by drawing SV perpendicular to ST (since ∠TSV = 90°) and completing the fourth vertex V so that STUV is a trapezium. (See the answer key diagram for the exact placement.)",
      "hints": ["Draw SV at 90° to ST (because ∠TSV = 90°).", "Complete the trapezium so VU is parallel to the correct side."],
      "source": "Tao Nan 2025 P6 Prelim P1 Q25",
      "image_needed": true,
      "image_options": false,
      "image_file": "q25.png",
      "image_page": 13,
      "image_bbox": [0.20, 0.52, 0.80, 0.82],
      "image_loc": "a dashed square grid with two line segments ST and TU drawn and labelled S, T, U, lower part of page 13",
      "notes": "Interactive draw-the-trapezium task - type_id 0, skipped on insert. Construction shown in the key diagram."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "Pamela builds a solid using 8 cubes of side 1 cm (the side view is shown). Pamela wants to build a cuboid of sides 3 cm by 3 cm by 4 cm. How many more cubes does she need? [?]",
      "answer0": "28",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 224,
      "difficulty_id": 2,
      "explanation": "A 3 cm by 3 cm by 4 cm cuboid needs 3 x 3 x 4 = 36 unit cubes. She already has 8, so she needs 36 - 8 = 28 more. Answer: 28. [Part (a) was 'draw the top view on the grid', a drawing task.]",
      "hints": ["The target cuboid uses 3 x 3 x 4 = 36 unit cubes.", "She has 8, so she needs 36 - 8 = 28 more."],
      "source": "Tao Nan 2025 P6 Prelim P1 Q26",
      "image_needed": true,
      "image_options": false,
      "image_file": "q26.png",
      "image_page": 14,
      "image_bbox": [0.18, 0.12, 0.50, 0.28],
      "image_loc": "an isometric drawing of a solid made of 8 unit cubes with Front view and Side view arrows, upper-left of page 14",
      "notes": "Key: Q26 (b) = 28. Part (a) 'draw the top view' is a drawing task (omitted); this FIB captures part (b), the numeric answer."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "Mrs Chong has 2 rolls of ribbon each \\(\\dfrac{9}{10}\\) m long. She cuts the ribbon into equal pieces to make bows. Each piece is \\(\\dfrac{1}{5}\\) m long. How many bows can she make? [?]",
      "answer0": "8",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "Each \\(\\dfrac{9}{10}\\) m roll gives \\(\\dfrac{9}{10} \\div \\dfrac{1}{5} = \\dfrac{9}{10} \\times 5 = 4\\dfrac{1}{2}\\), so 4 full bows per roll. With 2 rolls: 4 x 2 = 8 bows. Answer: 8. (The leftover half-pieces cannot form whole bows.)",
      "hints": ["Per roll: (9/10) / (1/5) = 4.5, so 4 full bows.", "2 rolls give 4 x 2 = 8 bows."],
      "source": "Tao Nan 2025 P6 Prelim P1 Q27",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q27 = 8."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "After a 10% discount, the price of an admission ticket to the amusement park is $45. Children are given a further discount of $3. What is the percentage discount for one child ticket? [?]%",
      "answer0": "16",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Usual price: $45 is 90% of it, so usual = 45 / 0.9 = $50. Child pays $45 - $3 = $42. Total discount off the usual $50 = $50 - $42 = $8. Percentage = \\(\\dfrac{8}{50} \\times 100\\% = 16\\%\\). Answer: 16%.",
      "hints": ["Usual price = $45 / 0.9 = $50; child pays $45 - $3 = $42.", "Discount = $50 - $42 = $8; 8/50 x 100% = 16%."],
      "source": "Tao Nan 2025 P6 Prelim P1 Q28",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q28 = 16%."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "At a movie marathon, John watched movies one after another without any break in between. He started the first movie at 18 30. The durations are: 1st 1 h 20 min, 2nd 50 min, 3rd 1 h 30 min, 4th 2 h 5 min. At what time did he start to watch the 4th movie? (Give your answer in 24-hour clock) [?] [?]",
      "answer0": "22",
      "answer1": "10",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 135,
      "difficulty_id": 2,
      "explanation": "Start 18 30. After 1st (1 h 20 min) -> 19 50. After 2nd (50 min) -> 20 40. After 3rd (1 h 30 min) -> 22 10. So the 4th movie starts at 22 10. Answer: 2210 (22 h 10 min).",
      "hints": ["Add each movie's duration in turn from 18 30.", "18 30 + 1 h 20 + 50 min + 1 h 30 = 22 10."],
      "source": "Tao Nan 2025 P6 Prelim P1 Q29",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q29 = 22 10 (22:10 in 24-hour clock). Two blanks: hours (22) then minutes (10). Movie durations placed in stem as plain text."
    },
    {
      "n": 30,
      "type_id": 2,
      "question": "The table shows the first 3 rows of a number pattern (Row 1: A=3, B=4, C=5, D=6; Row 2: A=10, B=9, C=8, D=7; Row 3: A=11, B=12, C=13, D=14; the pattern continues). In which column and which row will number 498 appear? Column [?], Row [?]",
      "answer0": "A",
      "answer1": "124",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 108,
      "difficulty_id": 3,
      "explanation": "Each row holds 4 numbers; the largest number in row n is 8 x ceil(n/2)... working the pattern, 498 falls in row 124, column A. Answer: Column A, Row 124.",
      "hints": ["Each row contains 4 consecutive numbers; the direction alternates each row.", "Tracking the pattern, 498 lands in Column A, Row 124."],
      "source": "Tao Nan 2025 P6 Prelim P1 Q30",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q30 = Column A, Row 124. answer0 = A (column), answer1 = 124 (row). Column answer is a letter; recorded as the first blank."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "A baker had 300 eggs at first. In the morning, he used some eggs. In the afternoon, he used \\(\\dfrac{1}{3}\\) of the remaining eggs. After that, there were 60 eggs left. How many eggs did the baker use in the morning? [?]",
      "answer0": "210",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "After the afternoon, \\(\\dfrac{2}{3}\\) of the remaining eggs = 60, so \\(\\dfrac{1}{3}\\) = 30 and the whole remaining (after the morning) = 90. Eggs used in the morning = 300 - 90 = 210. Answer: 210.",
      "hints": ["The 60 left is 2/3 of what remained after the morning, so the remainder = 90.", "Morning use = 300 - 90 = 210."],
      "source": "Tao Nan 2025 P6 Prelim P2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: P2 Q1 working 2/3 remaining = 60, remaining = 90, 300 - 90 = 210."
    },
    {
      "n": 32,
      "type_id": 0,
      "question": "There are 7 shaded squares in the figure. Shade 5 more squares to form a symmetric figure with AB as the line of symmetry.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 145,
      "difficulty_id": 3,
      "explanation": "Reflect each shaded square across the diagonal line AB; shade the 5 reflected squares that are not yet shaded so the whole figure becomes symmetric about AB. (See the answer key diagram for the exact squares.)",
      "hints": ["Reflect each shaded square across line AB.", "Shade the reflections that are still unshaded (5 of them)."],
      "source": "Tao Nan 2025 P6 Prelim P2 Q2",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q2.png",
      "image_page": 18,
      "image_bbox": [0.30, 0.55, 0.66, 0.86],
      "image_loc": "a square grid with diagonal line AB (A bottom-left, B top-right) and 7 shaded squares scattered on it, lower part of page 18",
      "notes": "Interactive shade-the-grid task (no value answer) - type_id 0, skipped on insert. Completed symmetric shading shown in the key diagram."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "There were 50 red pens and 230 blue pens. After an equal number of red and blue pens were added, the ratio of the number of red pens to the number of blue pens became 1 : 3. How many red pens were there in the end? [?]",
      "answer0": "90",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "The difference (blue - red) stays 230 - 50 = 180 even after adding equal numbers. After, red : blue = 1 : 3, so the difference = 2 units = 180, meaning 1 unit = 90. Red in the end = 1 unit = 90. Answer: 90.",
      "hints": ["Adding equal numbers keeps the difference (180) the same.", "After, 3 - 1 = 2 units = 180, so 1 unit (red) = 90."],
      "source": "Tao Nan 2025 P6 Prelim P2 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: P2 Q3 working difference unchanged 180 = 2 units, 1 unit = 90, red end = 90."
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "Siti had 35 marbles and Ted had more marbles than her. After giving Siti m marbles, Ted had 20 more marbles than Siti. How many marbles did Ted have at first? Give your answer in terms of m in the simplest form. [?]",
      "answer0": "2m + 55",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 239,
      "difficulty_id": 3,
      "explanation": "After Ted gives away m marbles, Siti has 35 + m and Ted has 20 more than Siti, i.e. (35 + m) + 20 = 55 + m. Ted at first = (55 + m) + m = 2m + 55. Answer: 2m + 55.",
      "hints": ["After the gift: Siti = 35 + m, Ted = (35 + m) + 20.", "Ted at first = Ted now + m given = (55 + m) + m = 2m + 55."],
      "source": "Tao Nan 2025 P6 Prelim P2 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: P2 Q4 = 2m + 55 (algebraic answer)."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "A cyclist and a motorist started travelling at the same time from point A to point B. The motorist's average speed was 16 km/h faster than the cyclist. When the motorist reached point B in 12 minutes, the cyclist had only travelled \\(\\dfrac{3}{5}\\) of the distance. What was the cyclist's average speed in km/h? [?] km/h",
      "answer0": "24",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 219,
      "difficulty_id": 3,
      "explanation": "In 12 min (= 1/5 h) the motorist covers the full distance; the cyclist covers 3/5 of it, so the cyclist's extra-needed 2/5 of the distance corresponds to the speed gap. The motorist's extra distance in 1/5 h = 16 x 1/5 = 3.2 km = 2/5 of the distance, so 1/5 of distance = 1.6 km and 3/5 (cyclist's distance) = 4.8 km. Cyclist's speed = 4.8 / (1/5) = 24 km/h. Answer: 24 km/h.",
      "hints": ["The motorist's extra distance (16 x 1/5 = 3.2 km) equals the 2/5 of the distance the cyclist is short.", "Cyclist's distance = 3/5 = 4.8 km in 1/5 h, so speed = 24 km/h."],
      "source": "Tao Nan 2025 P6 Prelim P2 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: P2 Q5 working 16 x 1/5 = 3.2 (= 2/5 of dist); 3/5 dist = 4.8 km; 4.8 / (1/5) = 24 km/h."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "A box contained some yellow cubes and 72 blue cubes. 40% of the cubes were yellow. After some red cubes were added into the box, 32% of the cubes were yellow. How many red cubes were there? [?]",
      "answer0": "30",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "At first yellow = 40%, so blue = 60% = 72 cubes, giving 1% = 1.2 and total = 120, yellow = 48. After adding red, yellow (still 48) = 32%, so total = 48 / 0.32 = 150. Red added = 150 - 120 = 30. Answer: 30.",
      "hints": ["Blue is 60% = 72, so total at first = 120 and yellow = 48.", "Yellow stays 48 = 32% of new total, so new total = 150; red = 150 - 120 = 30."],
      "source": "Tao Nan 2025 P6 Prelim P2 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: P2 Q6 working 12 units = 72 (blue), 1 unit = 6, 5 units = 30 red."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "The figure shows the net of a cuboid with 2 square faces. The ratio of the length to the breadth is 3 : 2. The perimeter of the figure is 128 cm. Find the volume of the cuboid. [?] cm³",
      "answer0": "768",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 229,
      "difficulty_id": 3,
      "explanation": "Length = 3 units, breadth = 2 units. Counting the net's outline, the perimeter = 2 units x 10 + 3 units x 4 = 32 units = 128 cm, so 1 unit = 4 cm. Then length = 12 cm, breadth = 8 cm, and the square face has side 8 cm. Volume = 8 x 8 x 12 = 768 cm³. Answer: 768 cm³.",
      "hints": ["From the net, perimeter = 32 units = 128 cm, so 1 unit = 4 cm.", "Breadth = 8 cm (square face), length = 12 cm; volume = 8 x 8 x 12 = 768 cm³."],
      "source": "Tao Nan 2025 P6 Prelim P2 Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q7.png",
      "image_page": 21,
      "image_bbox": [0.46, 0.16, 0.86, 0.42],
      "image_loc": "the net of a cuboid (a staircase arrangement of rectangles with 2 square faces), upper-right of page 21",
      "notes": "Key: P2 Q7 working perimeter 32 units = 128; 1 unit = 4; volume = 8 x 8 x 12 = 768 cm³."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "After Aini gave \\(\\dfrac{1}{6}\\) of her stickers away and Bala gave \\(\\dfrac{1}{4}\\) of his stickers away, both of them had the same number of stickers left. The total number of stickers Aini and Bala gave away was 2280. How many stickers did Bala have at first? [?]",
      "answer0": "5700",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Aini left = \\(\\dfrac{5}{6}\\) of hers, Bala left = \\(\\dfrac{3}{4}\\) of his; these are equal. Making the 'left' equal: Aini left = \\(\\dfrac{15}{18}\\), Bala left = \\(\\dfrac{15}{20}\\). Aini gave \\(\\dfrac{1}{6} = \\dfrac{3}{18}\\) (3 units), Bala gave \\(\\dfrac{1}{4} = \\dfrac{5}{20}\\) (5 units). Total given = 3 + 5 = 8 units = 2280, so 1 unit = 285. Bala at first = 20 units = 20 x 285 = 5700. Answer: 5700.",
      "hints": ["Set Aini's and Bala's 'left' amounts equal and express both in the same units.", "Given away: 3 + 5 = 8 units = 2280, so 1 unit = 285; Bala = 20 units = 5700."],
      "source": "Tao Nan 2025 P6 Prelim P2 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: P2 Q8 working 8 units = 2280, 1 unit = 285, Bala = 20 units = 5700."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "At a concert, there were 30% more women than men and 25% more boys than girls. There were 250 people at the concert with as many males as females. How many girls were there at the concert? [?]",
      "answer0": "60",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Females = males = 250 / 2 = 125 each. Women : men = 130 : 100 (30% more); girls : boys = 100 : 125 (25% more boys). Setting up: women + girls = 125 (females) and men + boys = 125 (males). Solving the two equations (per the key) gives 1 unit = 0.5, women = 65, so girls = 125 - 65 = 60. Answer: 60.",
      "hints": ["Females = males = 125 each (as many males as females, total 250).", "Solve women + girls = 125 and men + boys = 125 with the 30%/25% ratios to get girls = 60."],
      "source": "Tao Nan 2025 P6 Prelim P2 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: P2 Q9 working 250/2 = 125; solving the equations gives women = 65, girls = 125 - 65 = 60."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "The figure shows two rectangular tanks X and Y at first. Tank X contained 432 cm³ of water and tank Y was empty. Tank X has height 9 cm; tank Y has base 8 cm by 3 cm. Water dripped at a rate of 3 cm³ per second from a leaking tap at the bottom of tank X into tank Y. How long did it take for the height of the water level in tank Y to be 3 cm above that of tank X? [?] s",
      "answer0": "64",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 193,
      "difficulty_id": 3,
      "explanation": "Base area of X = 432 / 9 = 48 cm². Base area of Y = 8 x 3 = 24 cm². When Y's water level is 3 cm above X's: let X's final height = h, Y's height = h + 3. Volume conserved: 48h + 24(h + 3) = 432, so 72h + 72 = 432, 72h = 360, h = 5. Volume that leaked to Y = 48 x (9 - 5) = 192 cm³. Time = 192 / 3 = 64 s. Answer: 64 s.",
      "hints": ["Base areas: X = 432/9 = 48 cm², Y = 8 x 3 = 24 cm².", "Solve for the levels, find the volume moved (192 cm³), divide by 3 cm³/s = 64 s."],
      "source": "Tao Nan 2025 P6 Prelim P2 Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q10.png",
      "image_page": 24,
      "image_bbox": [0.30, 0.15, 0.70, 0.40],
      "image_loc": "tank X (raised on a stand, height 9 cm) with a leaking tap dripping into tank Y (base 8 cm by 3 cm) below, upper-middle of page 24",
      "notes": "Key: P2 Q10 working base X = 48, base Y = 24, height in X = 5, volume to Y = 192, 192/3 = 64 s."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "The line graph shows the volume of water the Tan family used from January to June (Jan 35, Feb 48, Mar 28, Apr 40, May 50, Jun 24, in m³).<br>(a) What was the percentage increase in the water used from April to May? [?]%<br>(b) Charges: first 40 m³ at $3.50 per m³, every additional m³ at $4.50 per m³. How much did the Tan family pay for their water bill in May? $[?]",
      "answer0": "25",
      "answer1": "185",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 208,
      "difficulty_id": 3,
      "explanation": "(a) April = 40 m³, May = 50 m³, increase = 10 m³; percentage = \\(\\dfrac{10}{40} \\times 100\\% = 25\\%\\). (b) May used 50 m³: first 40 m³ at $3.50 = $140; next 10 m³ at $4.50 = $45; total = $140 + $45 = $185. Answers: (a) 25%, (b) $185.",
      "hints": ["(a) Increase = 50 - 40 = 10 m³; 10/40 x 100% = 25%.", "(b) 40 x $3.50 + 10 x $4.50 = $140 + $45 = $185."],
      "source": "Tao Nan 2025 P6 Prelim P2 Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q11.png",
      "image_page": 25,
      "image_bbox": [0.18, 0.13, 0.85, 0.42],
      "image_loc": "a line graph titled Amount of water used (m³) vs months Jan to Jun, with points around 35, 48, 28, 40, 50, 24, upper part of page 25",
      "notes": "Key: P2 Q11 (a) 25%, (b) $185. answer0 = 25 for (a), answer1 = 185 for (b). Apr and May values (40, 50) read from the line graph; tariff in stem."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "ABCD is a parallelogram and CFDE is a rhombus. ∠ADG = 12°. ∠DFC = 74° is marked at F. Find ∠w (at the top near E/H). [?]°",
      "answer0": "127",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "In the rhombus CFDE, ∠DEC = ∠DFC = 74° (opposite angles equal). The triangle at the top (E, H, G) gives ∠EHG = (180° - 74°) / 2 = 53°. ∠w = 180° - 53° = 127° (angles on a straight line). Answer: 127°.",
      "hints": ["In the rhombus, ∠DEC = ∠DFC = 74°.", "∠EHG = (180° - 74°) / 2 = 53°; ∠w = 180° - 53° = 127°."],
      "source": "Tao Nan 2025 P6 Prelim P2 Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q12.png",
      "image_page": 26,
      "image_bbox": [0.28, 0.13, 0.66, 0.42],
      "image_loc": "parallelogram ABCD with a rhombus CFDE overlaid; apex E at top with w marked near H, 12° marked at the left near D, and 74° marked at F at the bottom, upper part of page 26",
      "notes": "Key: P2 Q12 (a) ∠w = 127°. Part (b) 'Find ∠y' was 'Not labelled in question paper' per the answer key, so only part (a) is captured."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "1 m white lines are painted on roads as lane markings. The 7 white lines before a traffic light crossing are 1 m apart while the other white lines are 3 m apart. The distance between two traffic light crossings along a straight stretch of two-lane road is 493 m.<br>(a) How many 1 m white lines are there between the two traffic light crossings? [?]<br>(b) George and Hariz started jogging at the same time but in opposite directions from one traffic light crossing to the other. George's speed was 5 m/s and Hariz's speed was 4 m/s. After jogging for 1 minute, how far apart were George and Hariz from each other? [?] m",
      "answer0": "127",
      "answer1": "47",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 219,
      "difficulty_id": 3,
      "explanation": "(a) Removing the 13 m at the start (7 one-metre lines), the remaining 480 m is in 1 m + 3 m = 4 m repeating groups: 480 / 4 = 120 lines; plus the original 7 = 127 one-metre lines. (b) In 1 min (60 s) they move apart at 5 + 4 = 9 m/s, covering 9 x 60 = 540 m; but the road is only 493 m, so after passing each other they are 540 - 493 = 47 m apart. Answers: (a) 127, (b) 47 m.",
      "hints": ["(a) After the first 13 m, 480 m splits into 4 m groups: 480/4 = 120, plus 7 = 127 lines.", "(b) Combined speed 9 m/s x 60 s = 540 m; 540 - 493 = 47 m apart."],
      "source": "Tao Nan 2025 P6 Prelim P2 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q13.png",
      "image_page": 27,
      "image_bbox": [0.16, 0.18, 0.85, 0.32],
      "image_loc": "a photo/diagram of a road with white lane lines, two arrows for direction, '1 m' and '3 m' spacing marked, between two traffic-light crossings, upper part of page 27",
      "notes": "Key: P2 Q13 (a) 127, (b) 47 m. answer0 = 127 for (a), answer1 = 47 for (b)."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "The bar graph shows the number of books borrowed over five days (Mon 65, Tue 90, Wed 85, Thu 40; the bar for Friday is not shown).<br>(a) 30% of the books borrowed from Monday to Thursday were non-fiction. The number of fiction books borrowed: Mon 45, Tue 57, Thu 28 (Wednesday not shown). How many fiction books were borrowed on Wednesday? [?]<br>(b) The number of books borrowed from Monday to Wednesday is 4 times as many as the number borrowed on Thursday and Friday. Find the number of books borrowed on Friday. [?]",
      "answer0": "66",
      "answer1": "20",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "(a) Mon-Thu total borrowed = 65 + 90 + 85 + 40 = 280; fiction = 70% of 280 = 196. Known fiction = 45 + 57 + 28 = 130, so Wednesday fiction = 196 - 130 = 66. (b) Mon-Wed = 65 + 90 + 85 = 240 = 4 x (Thu + Fri), so Thu + Fri = 60; Friday = 60 - 40 = 20. Answers: (a) 66, (b) 20.",
      "hints": ["(a) Fiction Mon-Thu = 70% of 280 = 196; subtract the known 130 to get Wednesday = 66.", "(b) Mon-Wed = 240 = 4 x (Thu + Fri), so Thu + Fri = 60; Friday = 60 - 40 = 20."],
      "source": "Tao Nan 2025 P6 Prelim P2 Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q14.png",
      "image_page": 28,
      "image_bbox": [0.16, 0.12, 0.72, 0.32],
      "image_loc": "a vertical bar graph titled Number of books borrowed for Mon-Fri (Friday bar missing, shown with a '?'), upper part of page 28",
      "notes": "Key: P2 Q14 (a) 66, (b) 20. answer0 = 66 for (a), answer1 = 20 for (b). Daily totals read from the bar graph; fiction table in stem."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "The average height of a group of 3 girls and 5 boys was 160 cm. The average height of the 3 girls was 12 cm less than the average height of the 5 boys. Find the average height of the 5 boys. [?] cm",
      "answer0": "164.5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 205,
      "difficulty_id": 3,
      "explanation": "Total height of all 8 = 160 x 8 = 1280 cm. If boys' average = b, girls' average = b - 12. Total = 5b + 3(b - 12) = 8b - 36 = 1280, so 8b = 1316 and b = 164.5 cm. Answer: 164.5 cm.",
      "hints": ["Total height = 160 x 8 = 1280 cm.", "5b + 3(b - 12) = 1280 gives 8b = 1316, b = 164.5 cm."],
      "source": "Tao Nan 2025 P6 Prelim P2 Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: P2 Q15 working 160 x 8 = 1280; 1280 + 12 x 3 = 1316; 1316 / 8 = 164.5 cm."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "Mr Abdul received some Majulah Singapura vouchers in denominations of $2, $5 and $10. There were as many $10 vouchers as $5 vouchers. The ratio of the number of $2 vouchers to the number of $10 vouchers was 3 : 2. The value of all the vouchers was $1260.<br>(a) What was the total value of the $2 vouchers he received? $[?]<br>(b) Later he had 4 $2 vouchers, 2 $5 vouchers and 1 $10 voucher left. He bought food from 3 stalls (Stall A $8, Stall B $9, Stall C $11). Vouchers used at each stall cannot exceed the cost of the food. What was the least amount he could have paid in cash? $[?]",
      "answer0": "210",
      "answer1": "2",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 213,
      "difficulty_id": 3,
      "explanation": "(a) $5 and $10 vouchers are equal in count (ratio 1 : 1), and $2 : $10 = 3 : 2. Take a group of 2 $5 + 2 $10 + 3 $2 = $10 + $20 + $6 = $36 per set. $1260 / $36 = 35 sets. Total value of $2 vouchers = 35 x (3 x $2) = $210. (b) Pay max vouchers without exceeding each food cost: Stall A $8 -> use $5 + $2 = $7, cash $1; Stall B $9 -> $5 + $2 + $2 = $9, cash $0; Stall C $11 -> use $10, cash $1. Least cash = $1 + $1 = $2. Answers: (a) $210, (b) $2.",
      "hints": ["(a) One set (2 $5 + 2 $10 + 3 $2) = $36; $1260 / $36 = 35 sets; $2 total = 35 x $6 = $210.", "(b) Cover as much of each food cost with vouchers (not exceeding it); least cash = $1 + $0 + $1 = $2."],
      "source": "Tao Nan 2025 P6 Prelim P2 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: P2 Q16 (a) $210, (b) $2. answer0 = 210 for (a), answer1 = 2 for (b). Stall costs placed in stem."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "(a) Figure 1 shows three identical rectangles. The area of the shaded triangle is 256 cm². Find the difference in area between the shaded and unshaded parts. [?] cm²<br>(b) Figure 2 is formed by three similar-sized circles and three similar-sized squares. Line AB passes through the centre of the three circles. The area of each square is 256 cm². Find the difference in area between the shaded and unshaded parts. (Take π = 3.14) [?] cm²",
      "answer0": "1024",
      "answer1": "748.8",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 222,
      "difficulty_id": 3,
      "explanation": "(a) The shaded triangle is \\(\\dfrac{1}{6}\\) of the three identical rectangles, so the unshaded part is \\(\\dfrac{5}{6}\\). Difference = \\(\\dfrac{5}{6} - \\dfrac{1}{6} = \\dfrac{4}{6}\\) of the total. Since 1/6 = 256 cm², the difference = 256 x 4 = 1024 cm². (b) Square side = \\(\\sqrt{256} = 16\\) cm, so the circle radius = 16 cm. Working the shaded vs unshaded parts (7 quarter-circles + 1 square shaded, etc.): 4 quarters = 1 circle = 3.14 x 16 x 16 = 803.84 cm²; the 'boomerang' (square minus quarter-circle) = 256 - 1/4 x 803.84 = 55.04 cm²; difference = 803.84 - 55.04 = 748.8 cm². Answers: (a) 1024 cm², (b) 748.8 cm².",
      "hints": ["(a) Shaded = 1/6, unshaded = 5/6; difference = 4/6; since 1/6 = 256, difference = 1024 cm².", "(b) Circle radius = sqrt(256) = 16 cm; compute 1 circle (803.84) minus the boomerang (55.04) = 748.8 cm²."],
      "source": "Tao Nan 2025 P6 Prelim P2 Q17",
      "image_needed": true,
      "image_options": false,
      "image_file": "p2q17.png",
      "image_page": 31,
      "image_bbox": [0.36, 0.15, 0.88, 0.34],
      "image_loc": "Figure 1 (three identical rectangles with a shaded triangle stretching diagonally across) near the top, and Figure 2 (three circles each with an inscribed square along line AB, parts shaded) in the middle of page 31",
      "notes": "Key: P2 Q17 (a) 1024 cm², (b) 748.8 cm². answer0 = 1024 for (a), answer1 = 748.8 for (b). Both figures (Figure 1 and Figure 2) are on page 31; bbox covers both - the cropper may need two crops (q47a / q47b)."
    }
  ]
}