{
  "paper": {
    "school": "Nan Hua",
    "year": 2025,
    "level": "P6",
    "label": "Timed Practice 2",
    "source_prefix": "Nan Hua 2025 P6 Timed Practice 2",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "\\(60\\,000 + 5000 + 400 + 3 = \\) ______",
      "answer0": "65 430",
      "answer1": "65 403",
      "answer2": "65 043",
      "answer3": "60 543",
      "correct_answer": 1,
      "skill_id": 149,
      "difficulty_id": 1,
      "explanation": "Add the place values: 60 000 + 5 000 + 400 + 3 = 65 403 (no tens, so 0 in the tens place). Answer: 65 403.",
      "hints": ["Line up the digits by place value.", "There are no tens, so place a 0 in the tens column: 65 403."],
      "source": "Nan Hua 2025 P6 Timed Practice 2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q1 = option 2 (65 403)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "What is the missing number in the box?<br>\\(2\\dfrac{5}{6} = \\dfrac{\\Box}{6}\\)",
      "answer0": "10",
      "answer1": "12",
      "answer2": "17",
      "answer3": "25",
      "correct_answer": 2,
      "skill_id": 158,
      "difficulty_id": 1,
      "explanation": "Convert the mixed number to an improper fraction: \\(2\\dfrac{5}{6} = \\dfrac{2 \\times 6 + 5}{6} = \\dfrac{17}{6}\\). The box is 17. Answer: 17.",
      "hints": ["Multiply the whole number by the denominator and add the numerator.", "2 x 6 + 5 = 17, so the box is 17."],
      "source": "Nan Hua 2025 P6 Timed Practice 2 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q2 = option 3 (17)."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Which number is the largest?",
      "answer0": "1.44",
      "answer1": "1.45",
      "answer2": "1.054",
      "answer3": "1.405",
      "correct_answer": 1,
      "skill_id": 124,
      "difficulty_id": 1,
      "explanation": "Compare by place value: 1.450 > 1.440 > 1.405 > 1.054. The largest is 1.45. Answer: 1.45.",
      "hints": ["Compare the tenths first, then hundredths and thousandths.", "1.45 has the largest hundredths digit; it is the biggest."],
      "source": "Nan Hua 2025 P6 Timed Practice 2 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q3 = option 2 (1.45)."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "What is the length of the bolt?",
      "answer0": "5.6 cm",
      "answer1": "5.8 cm",
      "answer2": "7.1 cm",
      "answer3": "7.2 cm",
      "correct_answer": 0,
      "skill_id": 85,
      "difficulty_id": 1,
      "explanation": "The bolt starts at the 1.5 cm mark and ends at the 7.1 cm mark on the ruler. Length = 7.1 - 1.5 = 5.6 cm. Answer: 5.6 cm.",
      "hints": ["Read where the bolt starts and where it ends on the ruler.", "Length = end reading - start reading = 7.1 - 1.5 = 5.6 cm."],
      "source": "Nan Hua 2025 P6 Timed Practice 2 Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q4.png",
      "image_page": 2,
      "image_bbox": [0.28, 0.15, 0.72, 0.30],
      "image_loc": "a bolt lying along a centimetre ruler (0 to 8 cm), with dashed lines marking the bolt's start and end, centred below the question on page 2",
      "notes": "Key: Q4 = option 1 (5.6 cm). Bolt measured against ruler from ~1.5 cm to ~7.1 cm."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "What is 5% of 2000?",
      "answer0": "10",
      "answer1": "100",
      "answer2": "1000",
      "answer3": "10 000",
      "correct_answer": 1,
      "skill_id": 174,
      "difficulty_id": 1,
      "explanation": "5% of 2000 = \\(\\dfrac{5}{100} \\times 2000 = 100\\). Answer: 100.",
      "hints": ["5% means 5 out of every 100.", "5/100 x 2000 = 100."],
      "source": "Nan Hua 2025 P6 Timed Practice 2 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q5 = option 2 (100)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "Which of the following shows \\(\\dfrac{1}{5}\\) of the figure shaded?",
      "answer0": "Figure 1",
      "answer1": "Figure 2",
      "answer2": "Figure 3",
      "answer3": "Figure 4",
      "correct_answer": 3,
      "skill_id": 120,
      "difficulty_id": 2,
      "explanation": "Only Figure 4 has exactly one of its five equal parts shaded, representing \\(\\dfrac{1}{5}\\). Answer: Figure 4.",
      "hints": ["Look for the figure divided into 5 equal parts with exactly 1 shaded.", "Figure 4 shows 1 out of 5 equal parts shaded."],
      "source": "Nan Hua 2025 P6 Timed Practice 2 Q6",
      "image_needed": true,
      "image_options": true,
      "image_file": null,
      "image_page": 2,
      "image_bbox": [0.22, 0.71, 0.85, 0.87],
      "image_loc": "four labelled option figures (1)-(4) in a row near the bottom of page 2: a hexagon, an oval, a grid of rectangles, and a row of triangles, each with some parts shaded",
      "notes": "Key: Q6 = option 4. Image-option MCQ: each option (1)-(4) is a separate shaded figure; crop each to q6_opt0..q6_opt3."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "Arrange these distances from the longest to the shortest.<br>2.25 km, 2 km 55 m, \\(2\\dfrac{1}{5}\\) km",
      "answer0": "2 km 55 m, \\(2\\dfrac{1}{5}\\) km, 2.25 km",
      "answer1": "2 km 55 m, 2.25 km, \\(2\\dfrac{1}{5}\\) km",
      "answer2": "\\(2\\dfrac{1}{5}\\) km, 2.25 km, 2 km 55 m",
      "answer3": "2.25 km, \\(2\\dfrac{1}{5}\\) km, 2 km 55 m",
      "correct_answer": 3,
      "skill_id": 184,
      "difficulty_id": 2,
      "explanation": "Convert to km: 2.25 km = 2.25 km; 2 km 55 m = 2.055 km; \\(2\\dfrac{1}{5}\\) km = 2.2 km. Longest to shortest: 2.25 km, 2.2 km, 2.055 km, i.e. 2.25 km, \\(2\\dfrac{1}{5}\\) km, 2 km 55 m. Answer: option 4.",
      "hints": ["Write all three in kilometres: 2.25, 2.055 and 2.2 km.", "Order from biggest to smallest: 2.25, 2.2 (= 2 1/5), 2.055 (= 2 km 55 m)."],
      "source": "Nan Hua 2025 P6 Timed Practice 2 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q7 = option 4."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "A group of senior citizens was asked in a survey to choose one game they enjoy from Uno, Chess, Toss-a-ring and Bingo. The table represents their choices.<br>Uno 5%<br>Chess 15%<br>Toss-a-ring 25%<br>Bingo ?<br>What percentage of the senior citizens chose Chess and Bingo?",
      "answer0": "15%",
      "answer1": "55%",
      "answer2": "70%",
      "answer3": "80%",
      "correct_answer": 2,
      "skill_id": 175,
      "difficulty_id": 2,
      "explanation": "The four percentages total 100%. Bingo = 100% - 5% - 15% - 25% = 55%. Chess and Bingo = 15% + 55% = 70%. Answer: 70%.",
      "hints": ["First find Bingo: 100% - (5% + 15% + 25%) = 55%.", "Chess + Bingo = 15% + 55% = 70%."],
      "source": "Nan Hua 2025 P6 Timed Practice 2 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q8 = option 3 (70%). Table values placed in stem as plain text."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "Box A has 100 markers, of which 6% are red. Box B has 200 markers, of which 9% are red. What is the ratio of the total number of red markers in Box A and B to the total number of markers in Box A and B?",
      "answer0": "1 : 3",
      "answer1": "1 : 20",
      "answer2": "2 : 3",
      "answer3": "2 : 25",
      "correct_answer": 3,
      "skill_id": 180,
      "difficulty_id": 2,
      "explanation": "Red in A = 6% of 100 = 6; red in B = 9% of 200 = 18; total red = 24. Total markers = 100 + 200 = 300. Ratio = 24 : 300 = 2 : 25. Answer: 2 : 25.",
      "hints": ["Red markers: 6% of 100 = 6 and 9% of 200 = 18, total 24.", "24 : 300 simplifies to 2 : 25."],
      "source": "Nan Hua 2025 P6 Timed Practice 2 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q9 = option 4 (2 : 25). Table values placed in stem as plain text."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "The figure is made up of 6 identical rectangles. Find the area of the shaded triangle.",
      "answer0": "72 cm²",
      "answer1": "96 cm²",
      "answer2": "144 cm²",
      "answer3": "192 cm²",
      "correct_answer": 1,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "The 6 identical rectangles form a large rectangle 24 cm wide and 2 rows tall. The shaded triangle has base 24 cm and height equal to the full height of the large rectangle (2 rectangle-heights = 8 cm). Area = \\(\\dfrac{1}{2} \\times 24 \\times 8 = 96\\) cm². Answer: 96 cm².",
      "hints": ["The triangle's base is the 24 cm width; its height is the full height of the figure.", "Area of triangle = 1/2 x base x height = 1/2 x 24 x 8 = 96 cm²."],
      "source": "Nan Hua 2025 P6 Timed Practice 2 Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 4,
      "image_bbox": [0.28, 0.47, 0.82, 0.65],
      "image_loc": "a large rectangle made of 6 identical smaller rectangles (3 columns x 2 rows) with a shaded triangle from the top-left corner to the bottom-right, base labelled 24 cm, centred on page 4",
      "notes": "Key: Q10 = option 2 (96 cm²). Figure shows 6 identical rectangles with a shaded triangle; base 24 cm."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "Figure 1 shows a parallelogram with a perimeter of 50 cm. Figure 2 is formed using 3 such parallelograms and it has a perimeter of 108 cm. Find the length of AB.",
      "answer0": "7 cm",
      "answer1": "9 cm",
      "answer2": "14 cm",
      "answer3": "42 cm",
      "correct_answer": 0,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "Three parallelograms have total perimeter 3 x 50 = 150 cm. When joined to form Figure 2, the perimeter is 108 cm, so 150 - 108 = 42 cm is hidden inside as joins. Each join hides 2 copies of the short side AB, and there are 3 joins worth of overlap = 6 x AB = 42 cm, so AB = 7 cm. Answer: 7 cm.",
      "hints": ["Total perimeter of 3 separate parallelograms = 3 x 50 = 150 cm.", "150 - 108 = 42 cm is hidden at the joins = 6 x AB, so AB = 7 cm."],
      "source": "Nan Hua 2025 P6 Timed Practice 2 Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q11.png",
      "image_page": 5,
      "image_bbox": [0.18, 0.16, 0.74, 0.34],
      "image_loc": "Figure 1 (single parallelogram with side AB marked) on the left and Figure 2 (three parallelograms arranged in a pinwheel/Y shape) on the right, near the top of page 5",
      "notes": "Key: Q11 = option 1 (7 cm)."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "Find the value of \\(\\dfrac{11}{12} \\div 3\\).",
      "answer0": "\\(\\dfrac{11}{36}\\)",
      "answer1": "\\(\\dfrac{11}{4}\\)",
      "answer2": "\\(\\dfrac{33}{12}\\)",
      "answer3": "\\(\\dfrac{11}{15}\\)",
      "correct_answer": 0,
      "skill_id": 164,
      "difficulty_id": 1,
      "explanation": "Dividing a fraction by a whole number multiplies the denominator: \\(\\dfrac{11}{12} \\div 3 = \\dfrac{11}{12 \\times 3} = \\dfrac{11}{36}\\). Answer: \\(\\dfrac{11}{36}\\).",
      "hints": ["Dividing by 3 is multiplying by 1/3.", "11/12 x 1/3 = 11/36."],
      "source": "Nan Hua 2025 P6 Timed Practice 2 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q12 = 11/36. Made MCQ because the answer is a fraction (FIB is integer/decimal only)."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "7 lines are drawn in the square grid. Name two lines that are parallel to each other.",
      "answer0": "CD and FE",
      "answer1": "AB and CD",
      "answer2": "BC and DE",
      "answer3": "AG and BF",
      "correct_answer": 0,
      "skill_id": 100,
      "difficulty_id": 2,
      "explanation": "On the square grid, lines CD and FE have the same gradient (run and rise), so they are parallel. Answer: CD and FE.",
      "hints": ["Parallel lines have the same slope (same horizontal and vertical run on the grid).", "Lines CD and FE rise and run by the same amounts, so they are parallel."],
      "source": "Nan Hua 2025 P6 Timed Practice 2 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q13.png",
      "image_page": 6,
      "image_bbox": [0.19, 0.50, 0.78, 0.78],
      "image_loc": "a square grid with 7 line segments drawn and labelled with points A, B, C, D, E, F, G, near the middle of page 6",
      "notes": "Key: Q13 = CD and FE. Made MCQ because the answer is a pair of line labels (letter answers are fragile as FIB); requires the grid figure to read the line positions."
    },
    {
      "n": 14,
      "type_id": 2,
      "question": "In the programme guide, one movie leads to another without any break in between.<br>5.45 pm — A Little Princess<br>7.20 pm — Wonder<br>9.15 pm — The Secret Garden<br>What is the duration of the movie \"Wonder\"? [?] h [?] min",
      "answer0": "1",
      "answer1": "55",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 93,
      "difficulty_id": 2,
      "explanation": "\"Wonder\" starts at 7.20 pm and the next movie starts at 9.15 pm. Duration = 7.20 pm to 9.15 pm = 1 h 55 min. Answer: 1 h 55 min.",
      "hints": ["Wonder runs from its start (7.20 pm) to the start of the next movie (9.15 pm).", "7.20 pm to 9.20 pm is 2 h, minus 5 min = 1 h 55 min."],
      "source": "Nan Hua 2025 P6 Timed Practice 2 Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q14 = 1 h 55 min. Two blanks: hours then minutes. Schedule placed in stem as plain text."
    },
    {
      "n": 15,
      "type_id": 2,
      "question": "A toaster has a sale price of $56 and a usual price of $80. What is the percentage discount for the toaster? [?]%",
      "answer0": "30",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 2,
      "explanation": "Discount = $80 - $56 = $24. Percentage discount = \\(\\dfrac{24}{80} \\times 100\\% = 30\\%\\). Answer: 30%.",
      "hints": ["Discount amount = usual price - sale price = $80 - $56 = $24.", "Percentage discount = 24/80 x 100% = 30%."],
      "source": "Nan Hua 2025 P6 Timed Practice 2 Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q15.png",
      "image_page": 7,
      "image_bbox": [0.30, 0.49, 0.68, 0.66],
      "image_loc": "a drawing of a toaster with a banner reading SALE PRICE $56 and text Usual Price: $80, centred below the question on page 7",
      "notes": "Key: Q15 = 30%. The sale price ($56) and usual price ($80) are read from the toaster figure; included in stem so the question is answerable without the image."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "The bar graph shows the number of items sold in an electrical store in a month. How many more fans than washing machines were sold? [?]",
      "answer0": "55",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 104,
      "difficulty_id": 2,
      "explanation": "From the bar graph, fans = 95 and washing machines = 40. Difference = 95 - 40 = 55. Answer: 55.",
      "hints": ["Read the heights of the Fans and Washing machines bars.", "Fans (95) - Washing machines (40) = 55."],
      "source": "Nan Hua 2025 P6 Timed Practice 2 Q16",
      "image_needed": true,
      "image_options": false,
      "image_file": "q16.png",
      "image_page": 8,
      "image_bbox": [0.30, 0.13, 0.85, 0.40],
      "image_loc": "a vertical bar graph titled Number of items sold with bars for Fans, Ovens, Washing machines and Refrigerators, near the top of page 8",
      "notes": "Key: Q16 working 95 - 40 = 55. Values read from the bar graph (Fans 95, Washing machines 40)."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "(a) Round 32.047 to one decimal place. [?]<br>(b) Write down one decimal between \\(\\dfrac{1}{10}\\) and \\(\\dfrac{1}{5}\\). [?]",
      "answer0": "32.0",
      "answer1": "0.15",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 128,
      "difficulty_id": 2,
      "explanation": "(a) The second decimal digit of 32.047 is 4 (less than 5), so it rounds down: 32.0. (b) \\(\\dfrac{1}{10} = 0.1\\) and \\(\\dfrac{1}{5} = 0.2\\); a decimal between them is 0.15. Answers: (a) 32.0, (b) 0.15.",
      "hints": ["(a) Look at the hundredths digit (4) to decide rounding to 1 d.p.", "(b) 1/10 = 0.1 and 1/5 = 0.2; any decimal in between, e.g. 0.15, works."],
      "source": "Nan Hua 2025 P6 Timed Practice 2 Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q17 (a) 32.0, (b) 0.15. Part (b) accepts any decimal strictly between 0.1 and 0.2; key uses 0.15."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "A machine started packing snacks at 8 a.m. at the rate of 300 packets per hour. After every 8 hours, it was stopped for 2 hours. How many packets can it pack by 11 p.m. on the same day? [?]",
      "answer0": "3900",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "From 8 a.m. to 11 p.m. is 15 hours. It packs for 8 h, stops 2 h (8 a.m.-6 p.m. = 10 h used, 8 h packing), then packs again from 6 p.m. to 11 p.m. = 5 more hours. Total packing time = 8 + 5 = 13 hours. Packets = 13 x 300 = 3900. Answer: 3900.",
      "hints": ["8 a.m. to 11 p.m. is 15 hours; subtract the 2-hour break.", "Packing hours = 8 + 5 = 13; 13 x 300 = 3900 packets."],
      "source": "Nan Hua 2025 P6 Timed Practice 2 Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q18 = 3900."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "A swimmer has to swim a total of 3 races in a competition. The timing for Ryan's first two races are 4.6 min and 4.1 min. Ryan's average timing is 4.3 min for the 3 races. What is the timing for his 3rd race? [?] min",
      "answer0": "4.2",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 204,
      "difficulty_id": 2,
      "explanation": "Total time for 3 races = average x number = 4.3 x 3 = 12.9 min. Third race = 12.9 - 4.6 - 4.1 = 4.2 min. Answer: 4.2 min.",
      "hints": ["Total of all 3 races = average x 3 = 4.3 x 3 = 12.9 min.", "12.9 - 4.6 - 4.1 = 4.2 min for the 3rd race."],
      "source": "Nan Hua 2025 P6 Timed Practice 2 Q19",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q19 working 4.3 x 3 = 12.9; 12.9 - 4.6 - 4.1 = 4.2 min. Table values placed in stem."
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "The figure is made up of a square and 2 triangles. The area of the square is 100 cm². Find the shaded area of the figure. [?] cm²",
      "answer0": "125",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "The square has area 100 cm², so its side = 10 cm. The top edge spans 35 cm, so the two triangle bases together = 35 - 10 = 25 cm, each triangle has height equal to the square's side 10 cm. The two shaded triangles total area = \\(\\dfrac{1}{2} \\times 25 \\times 10 = 125\\) cm². Answer: 125 cm².",
      "hints": ["Square area 100 cm² gives side 10 cm (the height of the triangles).", "Combined triangle base = 35 - 10 = 25 cm; area = 1/2 x 25 x 10 = 125 cm²."],
      "source": "Nan Hua 2025 P6 Timed Practice 2 Q20",
      "image_needed": true,
      "image_options": false,
      "image_file": "q20.png",
      "image_page": 10,
      "image_bbox": [0.28, 0.51, 0.72, 0.68],
      "image_loc": "a figure made of a white central square with a shaded triangle on each side, total top width labelled 35 cm, centred on page 10",
      "notes": "Key: Q20 = 125 cm². Top width 35 cm read from figure; square side 10 cm from area 100 cm²."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "A pattern is formed using the letters B, C and D. The first 21 letters are B B C B D D B B B C B D D B B B C B D D B. The letter D appears 50 times in the pattern. What is the smallest possible number of letter B appearing in the pattern? [?]",
      "answer0": "99",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 108,
      "difficulty_id": 3,
      "explanation": "The pattern repeats in a block where D appears 2 times and B appears 4 times per block. For D to appear 50 times, there are 50 / 2 = 25 complete blocks, giving 25 x 4 = 100 B's. The smallest possible count ends just after the last D, removing 1 trailing B: 100 - 1 = 99. Answer: 99.",
      "hints": ["In each repeating block D appears twice; 50 / 2 = 25 blocks.", "Each block has 4 B's: 25 x 4 = 100, minus 1 trailing B for the smallest count = 99."],
      "source": "Nan Hua 2025 P6 Timed Practice 2 Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q21 working 50/2 = 25; 25 x 4 = 100; 100 - 1 = 99."
    },
    {
      "n": 22,
      "type_id": 0,
      "question": "There are 6 shaded shapes in the square grid. Shade the least number of shapes such that AB is the line of symmetry.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 145,
      "difficulty_id": 3,
      "explanation": "Reflect each of the 6 shaded shapes across the diagonal line AB; any reflected shape not already shaded must be shaded so the whole figure is symmetric about AB. (See the answer key diagram for the exact additional shaded squares.)",
      "hints": ["Reflect each shaded shape across the line AB.", "Shade only the reflections that are not already shaded."],
      "source": "Nan Hua 2025 P6 Timed Practice 2 Q22",
      "image_needed": true,
      "image_options": false,
      "image_file": "q22.png",
      "image_page": 11,
      "image_bbox": [0.27, 0.49, 0.78, 0.85],
      "image_loc": "a 6x6 dashed square grid with diagonal line AB from top-left (A) to bottom-right (B) and 6 shaded shapes scattered on the grid, on page 11",
      "notes": "Interactive shade-the-grid task (no value answer) - type_id 0, skipped on insert. Answer is a completed symmetric shading shown in the key diagram."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "Bala glued 7 unit cubes to form a solid (shown with Top view, Front view and Side view). Bala painted the whole solid, including the base, green. How many of the 7 cubes had exactly four of their faces painted green? [?]",
      "answer0": "2",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 224,
      "difficulty_id": 3,
      "explanation": "When the whole solid (including the base) is painted, a cube with exactly 4 painted faces is one that is glued to other cubes on exactly 2 of its faces. Counting the cubes in this 7-cube arrangement, 2 cubes have exactly 4 faces exposed. Answer: 2.",
      "hints": ["A cube has 6 faces; 4 painted means 2 faces are glued (hidden).", "Find the cubes touching neighbours on exactly 2 faces: there are 2 of them."],
      "source": "Nan Hua 2025 P6 Timed Practice 2 Q23",
      "image_needed": true,
      "image_options": false,
      "image_file": "q23.png",
      "image_page": 12,
      "image_bbox": [0.33, 0.15, 0.55, 0.37],
      "image_loc": "an isometric drawing of 7 unit cubes glued into an L/T-shaped solid, with arrows labelling Top view, Front view and Side view, near the top of page 12",
      "notes": "Key: Q23 (b) = 2. Part (a) was 'draw the side view on the grid' (a drawing task, omitted here); this FIB captures part (b), the numeric answer."
    },
    {
      "n": 24,
      "type_id": 0,
      "question": "A parallelogram ABCD is drawn on a square grid. EF is one side of a triangle EFG. The sum of ∠EFG and ∠ADC is 180°. FG is twice as long as BC. Draw triangle EFG on the square grid with a pencil and label it clearly.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 200,
      "difficulty_id": 3,
      "explanation": "Since ∠EFG + ∠ADC = 180°, angle EFG supplements angle ADC of the parallelogram. With EF given, draw FG twice the length of BC (using the grid's run/rise of BC) at angle EFG, then join G to E to complete the triangle. (See the answer key diagram for the exact placement.)",
      "hints": ["∠EFG = 180° - ∠ADC, so use the supplement of the parallelogram's angle at D.", "Make FG twice the length of side BC, copying BC's grid steps, then complete triangle EFG."],
      "source": "Nan Hua 2025 P6 Timed Practice 2 Q24",
      "image_needed": true,
      "image_options": false,
      "image_file": "q24.png",
      "image_page": 13,
      "image_bbox": [0.22, 0.18, 0.78, 0.55],
      "image_loc": "a dashed square grid showing parallelogram ABCD on the left and a partial line EF (with E and F labelled) on the right, on page 13",
      "notes": "Interactive draw-the-triangle task (no value answer) - type_id 0, skipped on insert. Construction shown in the key diagram."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "Aleemah had an album of local and foreign stamps in the ratio 3 : 4. She gave away an equal number of local and foreign stamps. The total number of stamps she gave away is 40. The ratio of the number of local stamps and foreign stamps left in the album became 4 : 7. How many local stamps did she have at first? [?]",
      "answer0": "36",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "She gave away 40 stamps equally, so 20 local and 20 foreign. Let local : foreign = 3a : 4a at first. After: (3a - 20) : (4a - 20) = 4 : 7. So 7(3a - 20) = 4(4a - 20); 21a - 140 = 16a - 80; 5a = 60; a = 12. Local at first = 3 x 12 = 36. Answer: 36.",
      "hints": ["She gave away 20 local and 20 foreign (40 split equally).", "Set (3a - 20):(4a - 20) = 4:7, solve to get a = 12, so local = 3 x 12 = 36."],
      "source": "Nan Hua 2025 P6 Timed Practice 2 Q25",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key working shown is partial (10u = 40, u = y, 9u = 36); solving the ratio gives local at first = 36."
    }
  ]
}