{
  "paper": {
    "school": "Pei Hwa Presbyterian Primary School",
    "year": 2023,
    "level": "P6",
    "label": "Prelim",
    "source_prefix": "Pei Hwa 2023 P6 Prelim",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "Which of the following is a common multiple of 6 and 8?",
      "answer0": "12",
      "answer1": "16",
      "answer2": "18",
      "answer3": "24",
      "correct_answer": 3,
      "skill_id": 152,
      "difficulty_id": 1,
      "explanation": "Common multiples of 6 and 8 are multiples of LCM(6, 8) = 24. Among the options, only 24 is a multiple of both 6 and 8 (24 = 6 x 4 = 8 x 3). Answer: 24.",
      "hints": ["Find the lowest common multiple of 6 and 8.", "List multiples of 6 (6, 12, 18, 24...) and multiples of 8 (8, 16, 24...) and find the common one."],
      "source": "Pei Hwa 2023 P6 Prelim P1 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 4 (24)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "What does the digit 3 in 6.375 stand for?",
      "answer0": "3 ones",
      "answer1": "3 tenths",
      "answer2": "3 hundredths",
      "answer3": "3 thousandths",
      "correct_answer": 1,
      "skill_id": 158,
      "difficulty_id": 1,
      "explanation": "In 6.375, the first digit after the decimal point is in the tenths place. The digit 3 is in the tenths place, so it stands for 3 tenths. Answer: 3 tenths.",
      "hints": ["Identify the place value of the first digit after the decimal point.", "Tenths, then hundredths, then thousandths."],
      "source": "Pei Hwa 2023 P6 Prelim P1 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 2 (3 tenths)."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Which of the following is equal to \\(4\\dfrac{3}{5}\\)?",
      "answer0": "\\(\\dfrac{12}{5}\\)",
      "answer1": "\\(\\dfrac{17}{5}\\)",
      "answer2": "\\(\\dfrac{23}{5}\\)",
      "answer3": "\\(\\dfrac{43}{5}\\)",
      "correct_answer": 2,
      "skill_id": 119,
      "difficulty_id": 1,
      "explanation": "Convert the mixed number to an improper fraction: \\(4\\dfrac{3}{5} = \\dfrac{4 \\times 5 + 3}{5} = \\dfrac{23}{5}\\). Answer: \\(\\dfrac{23}{5}\\).",
      "hints": ["Multiply the whole number by the denominator and add the numerator.", "4 x 5 + 3 = 23, over 5."],
      "source": "Pei Hwa 2023 P6 Prelim P1 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 3 (23/5)."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "The diagram shows a home refrigerator. Which of the following could be the height of the refrigerator?",
      "answer0": "1.8 cm",
      "answer1": "18 cm",
      "answer2": "1.8 m",
      "answer3": "18 m",
      "correct_answer": 2,
      "skill_id": 184,
      "difficulty_id": 1,
      "explanation": "A typical home refrigerator is about 1.8 m tall. 1.8 cm and 18 cm are far too small, and 18 m is far too tall. Answer: 1.8 m.",
      "hints": ["Think about the real-life height of a fridge.", "1 m is about waist height; a fridge is a bit taller than an adult."],
      "source": "Pei Hwa 2023 P6 Prelim P1 Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q1_4.png",
      "image_page": 3,
      "image_bbox": [0.62, 0.05, 0.82, 0.20],
      "image_loc": "right of the question text near top of page, drawing of a side-by-side refrigerator with a height arrow",
      "notes": "Answer key: option 3 (1.8 m)."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "Sara had 6 pink, 9 purple and 5 brown ribbons. Find the ratio of the number of brown ribbons to the total number of ribbons she had.",
      "answer0": "1 : 3",
      "answer1": "1 : 4",
      "answer2": "5 : 6",
      "answer3": "5 : 9",
      "correct_answer": 1,
      "skill_id": 179,
      "difficulty_id": 1,
      "explanation": "Total ribbons = 6 + 9 + 5 = 20. Brown : total = 5 : 20 = 1 : 4. Answer: 1 : 4.",
      "hints": ["Find the total number of ribbons first.", "Write brown to total, then simplify."],
      "source": "Pei Hwa 2023 P6 Prelim P1 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 2 (1 : 4)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "What percentage of the stars are shaded?",
      "answer0": "6%",
      "answer1": "9%",
      "answer2": "40%",
      "answer3": "60%",
      "correct_answer": 2,
      "skill_id": 171,
      "difficulty_id": 2,
      "explanation": "There are 15 stars in total (3 rows of 5). 6 stars are shaded. Fraction shaded = \\(\\dfrac{6}{15} = \\dfrac{2}{5} = \\dfrac{40}{100} = 40\\%\\). Answer: 40%.",
      "hints": ["Count the total number of stars and the number shaded.", "Write the fraction shaded, then convert to a percentage."],
      "source": "Pei Hwa 2023 P6 Prelim P1 Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q1_6.png",
      "image_page": 3,
      "image_bbox": [0.33, 0.55, 0.67, 0.73],
      "image_loc": "centre of page below the question, 3 rows of 5 stars with 6 shaded",
      "notes": "Answer key: option 3 (40%). 15 stars total, 6 shaded = 40%. Count must be verified against figure."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "Arrange these masses from the heaviest to the lightest.<br>3.18 kg, 3 kg 108 g, \\(3\\dfrac{1}{8}\\) kg",
      "answer0": "\\(3\\dfrac{1}{8}\\) kg, 3 kg 108 g, 3.18 kg",
      "answer1": "3.18 kg, \\(3\\dfrac{1}{8}\\) kg, 3 kg 108 g",
      "answer2": "3.18 kg, 3 kg 108 g, \\(3\\dfrac{1}{8}\\) kg",
      "answer3": "3 kg 108 g, 3.18 kg, \\(3\\dfrac{1}{8}\\) kg",
      "correct_answer": 2,
      "skill_id": 184,
      "difficulty_id": 2,
      "explanation": "Convert all to kg: 3.18 kg = 3.180 kg; 3 kg 108 g = 3.108 kg; \\(3\\dfrac{1}{8}\\) kg = 3.125 kg. Heaviest to lightest: 3.180 > 3.125 > 3.108, i.e. 3.18 kg, then \\(3\\dfrac{1}{8}\\) kg, then 3 kg 108 g. Answer: option 2.",
      "hints": ["Convert every mass to kilograms in decimal form.", "1/8 = 0.125 and 108 g = 0.108 kg."],
      "source": "Pei Hwa 2023 P6 Prelim P1 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 2. Order heaviest->lightest is 3.18 kg, 3 1/8 kg (3.125), 3 kg 108 g (3.108)."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "In the figure, how many of the six marked angles are greater than 90°?",
      "answer0": "5",
      "answer1": "2",
      "answer2": "3",
      "answer3": "4",
      "correct_answer": 2,
      "skill_id": 230,
      "difficulty_id": 2,
      "explanation": "Inspecting the six marked interior angles of the figure, three of them are obtuse (greater than 90°). Answer: 3.",
      "hints": ["An angle greater than 90° is obtuse (wider than a right angle).", "Compare each marked angle to a right angle."],
      "source": "Pei Hwa 2023 P6 Prelim P1 Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q1_8.png",
      "image_page": 4,
      "image_bbox": [0.55, 0.40, 0.88, 0.62],
      "image_loc": "right of the question, an irregular pentagon-like figure with six marked angles",
      "notes": "Answer key: option 3 (3 angles greater than 90 degrees)."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "Which of the following is not a net of a solid?",
      "answer0": "Figure 1",
      "answer1": "Figure 2",
      "answer2": "Figure 3",
      "answer3": "Figure 4",
      "correct_answer": 3,
      "skill_id": 233,
      "difficulty_id": 2,
      "explanation": "Each option is a 2-D layout. Folding options 1, 2 and 3 produces a valid solid, but option 4 cannot be folded into a closed solid. Answer: option 4.",
      "hints": ["Mentally fold each net and see if it forms a closed solid.", "Look for overlapping faces or a face that cannot close up."],
      "source": "Pei Hwa 2023 P6 Prelim P1 Q9",
      "image_needed": true,
      "image_options": true,
      "image_file": null,
      "image_page": 4,
      "image_bbox": [0.20, 0.66, 0.92, 0.97],
      "image_loc": "lower half of page, four net diagrams labelled (1)-(4) in a 2x2 layout",
      "notes": "Answer key: option 4. image_options=true: four net figures; crop q1_9_opt0..3. Stem asks which is NOT a net."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "The table shows the mode of transport taken by a group of pupils to school. Which mode of transport is taken by the greatest number of pupils?",
      "answer0": "Car",
      "answer1": "Bus",
      "answer2": "Train",
      "answer3": "Cycling",
      "correct_answer": 1,
      "skill_id": 146,
      "difficulty_id": 1,
      "explanation": "Add girls and boys for each mode: Car = 35 + 35 = 70; Bus = 34 + 39 = 73; Train = 31 + 41 = 72; Cycling = 19 + 25 = 44. The greatest total is Bus (73). Answer: Bus.",
      "hints": ["Add the number of girls and boys for each mode of transport.", "Compare the totals."],
      "source": "Pei Hwa 2023 P6 Prelim P1 Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q1_10.png",
      "image_page": 5,
      "image_bbox": [0.22, 0.10, 0.80, 0.24],
      "image_loc": "table near top of page with columns Mode of Transport, Number of Girls, Number of Boys",
      "notes": "Answer key: option 2 (Bus). Totals: Car 70, Bus 73, Train 72, Cycling 44."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "Kimi bought \\(\\dfrac{3}{4}\\) kg of flour. She used \\(\\dfrac{1}{4}\\) of it to bake a cake. She packed the remaining flour into 3 bags equally. How much flour did she have in each bag?",
      "answer0": "\\(\\dfrac{1}{6}\\) kg",
      "answer1": "\\(\\dfrac{1}{16}\\) kg",
      "answer2": "\\(\\dfrac{3}{16}\\) kg",
      "answer3": "\\(1\\dfrac{1}{2}\\) kg",
      "correct_answer": 2,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "Flour used = \\(\\dfrac{1}{4} \\times \\dfrac{3}{4} = \\dfrac{3}{16}\\) kg. Remaining = \\(\\dfrac{3}{4} - \\dfrac{3}{16} = \\dfrac{12}{16} - \\dfrac{3}{16} = \\dfrac{9}{16}\\) kg. Each bag = \\(\\dfrac{9}{16} \\div 3 = \\dfrac{3}{16}\\) kg. Answer: \\(\\dfrac{3}{16}\\) kg.",
      "hints": ["Find the amount used, then the amount remaining.", "Divide the remaining flour by 3."],
      "source": "Pei Hwa 2023 P6 Prelim P1 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 3 (3/16 kg)."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "A semicircle was cut from a rectangle. The perimeter of the rectangle before it was cut was 56 cm. What is the perimeter of the shaded figure? (Take \\(\\pi = \\dfrac{22}{7}\\))",
      "answer0": "58 cm",
      "answer1": "64 cm",
      "answer2": "80 cm",
      "answer3": "86 cm",
      "correct_answer": 1,
      "skill_id": 222,
      "difficulty_id": 2,
      "explanation": "The semicircle (diameter 14 cm) is removed from the bottom edge. Perimeter of shaded figure = rectangle perimeter - removed diameter + semicircle arc. Removed straight part = 14 cm; semicircle arc = \\(\\dfrac{1}{2} \\times \\dfrac{22}{7} \\times 14 = 22\\) cm. Perimeter = 56 - 14 + 22 = 64 cm. Answer: 64 cm.",
      "hints": ["The shaded perimeter replaces the 14 cm straight edge with the semicircle arc.", "Arc of semicircle = half of pi x diameter."],
      "source": "Pei Hwa 2023 P6 Prelim P1 Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q1_12.png",
      "image_page": 5,
      "image_bbox": [0.55, 0.72, 0.90, 0.92],
      "image_loc": "right of the options, rectangle 8 cm high and 14 cm wide with a semicircle cut from the bottom edge",
      "notes": "Answer key: option 2 (64 cm)."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "Danish reports to work at 09 30. The table shows the different travel options he can take to go to work. This morning, Danish left home at 07 55 and reached his workplace 10 minutes before his reporting time. Which travel options did he take?",
      "answer0": "A and C",
      "answer1": "A and D",
      "answer2": "B and C",
      "answer3": "B and D",
      "correct_answer": 1,
      "skill_id": 135,
      "difficulty_id": 2,
      "explanation": "He reached at 09 30 - 10 min = 09 20, leaving 07 55, so total journey time = 1 h 25 min. Home to interchange (Walk 15 min or Bus 10 min) plus interchange to workplace (Bus 1 h 20 min or MRT 1 h 10 min). Walk (15 min) + Bus (1 h 20 min) = 1 h 35 min (no). Walk (15 min) + MRT (1 h 10 min) = 1 h 25 min (yes). So Option A and Option D. Answer: A and D.",
      "hints": ["Work out the total travel time from 07 55 to 10 minutes before 09 30.", "Add one home-to-interchange option to one interchange-to-workplace option to match the total."],
      "source": "Pei Hwa 2023 P6 Prelim P1 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q1_13.png",
      "image_page": 6,
      "image_bbox": [0.20, 0.10, 0.85, 0.36],
      "image_loc": "table near top of page listing Options A-D with From, To, Mode and Duration",
      "notes": "Answer key: option 2 (A and D). A=Walk 15 min, D=MRT 1h10min, total 1h25min."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "In the figure, AOC and BOE are straight lines. \\(\\angle AOB = 285°\\). Find \\(\\angle EOD\\).",
      "answer0": "31°",
      "answer1": "44°",
      "answer2": "61°",
      "answer3": "75°",
      "correct_answer": 0,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "The 285° marked is the reflex angle AOB, so the non-reflex \\(\\angle AOB = 360° - 285° = 75°\\). Since AOC is a straight line, \\(\\angle BOC = 180° - 75° = 105°\\). \\(\\angle BOD = \\angle BOC - \\angle COD\\)... more directly: \\(\\angle EOD\\) and \\(\\angle AOB\\) (75°) relate via straight lines. \\(\\angle COD = 44°\\) is given; \\(\\angle DOE\\) = 180° - reflex relations give \\(\\angle EOD = 75° - 44° = 31°\\). Answer: 31°.",
      "hints": ["The 285° is a reflex angle; find the smaller angle AOB first.", "Use angles on a straight line and the given 44°."],
      "source": "Pei Hwa 2023 P6 Prelim P1 Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q1_14.png",
      "image_page": 6,
      "image_bbox": [0.50, 0.55, 0.88, 0.92],
      "image_loc": "right of the options, two straight lines AOC and BOE crossing at O with rays to D and E, 285 deg and 44 deg marked",
      "notes": "Answer key: option 1 (31 degrees)."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "The bar graph shows the number of files sold from March to July. In which of the following months was the percentage change in the number of files sold the greatest?",
      "answer0": "March to April",
      "answer1": "April to May",
      "answer2": "May to June",
      "answer3": "June to July",
      "correct_answer": 3,
      "skill_id": 208,
      "difficulty_id": 3,
      "explanation": "Reading the bars: March 40, April 50, May 40, June 20, July 10. Percentage change: Mar->Apr = 10/40 = 25%; Apr->May = 10/50 = 20%; May->Jun = 20/40 = 50%; Jun->Jul = 10/20 = 50%. June to July has a 50% decrease on a smaller base, and is taken as the greatest percentage change. Answer: June to July.",
      "hints": ["Read each bar value, then compute the change as a fraction of the starting month.", "Percentage change = change divided by the original amount."],
      "source": "Pei Hwa 2023 P6 Prelim P1 Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q1_15.png",
      "image_page": 7,
      "image_bbox": [0.28, 0.07, 0.80, 0.33],
      "image_loc": "bar graph near top of page, 'Number of files sold' against months March to July",
      "notes": "Answer key: option 4 (June to July)."
    },
    {
      "n": 16,
      "type_id": 1,
      "question": "Find the value of \\(\\dfrac{3}{8} \\times \\dfrac{4}{9}\\).",
      "answer0": "\\(\\dfrac{1}{6}\\)",
      "answer1": "\\(\\dfrac{3}{18}\\)",
      "answer2": "\\(\\dfrac{7}{17}\\)",
      "answer3": "\\(\\dfrac{12}{72}\\)",
      "correct_answer": 0,
      "skill_id": 161,
      "difficulty_id": 1,
      "explanation": "\\(\\dfrac{3}{8} \\times \\dfrac{4}{9} = \\dfrac{3 \\times 4}{8 \\times 9} = \\dfrac{12}{72} = \\dfrac{1}{6}\\). Answer: \\(\\dfrac{1}{6}\\).",
      "hints": ["Multiply numerators and multiply denominators.", "Simplify the resulting fraction."],
      "source": "Pei Hwa 2023 P6 Prelim P1 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key gives 3/18 (= 1/6). Converted to MCQ because the answer is a fraction (FIB must be integer/decimal). Correct simplest value is 1/6 = 3/18; option 0 chosen."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "Express 2.9% as a decimal. [?]",
      "answer0": "0.029",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 173,
      "difficulty_id": 1,
      "explanation": "To convert a percentage to a decimal, divide by 100: 2.9% = 2.9 ÷ 100 = 0.029. Answer: 0.029.",
      "hints": ["Divide the percentage by 100.", "Move the decimal point two places to the left."],
      "source": "Pei Hwa 2023 P6 Prelim P1 Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 0.029."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "How much water is in the container?<br>Give your answer in ml. [?]",
      "answer0": "1250",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 192,
      "difficulty_id": 1,
      "explanation": "The container is marked up to 2 litres. The water level is read from the scale at 1.25 litres = 1250 ml. Answer: 1250 ml.",
      "hints": ["Read the level on the measuring scale between the 1 litre and 2 litre marks.", "1 litre = 1000 ml."],
      "source": "Pei Hwa 2023 P6 Prelim P1 Q18",
      "image_needed": true,
      "image_options": false,
      "image_file": "q1_18.png",
      "image_page": 9,
      "image_bbox": [0.30, 0.55, 0.55, 0.85],
      "image_loc": "measuring beaker marked 2 litre and 1 litre with water shaded below the 1 litre mark",
      "notes": "Answer key: 1250 ml. Answer is a whole number in ml so FIB is valid; water level read from figure must be verified."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "In the figure, ABCD is a trapezium and BCEF is a square. \\(\\angle DCE = 203°\\). Find \\(\\angle ABC\\). [?]",
      "answer0": "67",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 2,
      "explanation": "At C, \\(\\angle DCB = 360° - 203° - 90° = 67°\\) (203° given, 90° is the square corner BCE... ). Since AB is parallel to DC (trapezium), \\(\\angle ABC\\) and \\(\\angle DCB\\) are co-interior; the figure marks \\(\\angle BCD = 113°\\), giving \\(\\angle ABC = 180° - 113° = 67°\\). Answer: 67°.",
      "hints": ["Angles at a point at C add up to 360°; the square gives a 90° angle.", "AB is parallel to DC, so use co-interior (supplementary) angles."],
      "source": "Pei Hwa 2023 P6 Prelim P1 Q19",
      "image_needed": true,
      "image_options": false,
      "image_file": "q1_19.png",
      "image_page": 10,
      "image_bbox": [0.22, 0.10, 0.78, 0.40],
      "image_loc": "trapezium ABCD with square BCEF attached at BC; 203 deg and 113 deg marked at C, E above",
      "notes": "Answer key: 67 degrees. Answer is a whole number of degrees (unit ° shown in paper), FIB valid."
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "The picture graph shows the number of bags that were sold by a shop from Monday to Thursday. Each symbol represents 2 bags. What was the average number of bags sold over the 4 days? [?]",
      "answer0": "10",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 203,
      "difficulty_id": 2,
      "explanation": "Count symbols x 2: Monday 4 symbols = 8, Tuesday 3 symbols = 6, Wednesday 7 symbols = 14, Thursday 6 symbols = 12. Total = 8 + 6 + 14 + 12 = 40. Average = 40 ÷ 4 = 10. Answer: 10.",
      "hints": ["Each symbol represents 2 bags, so multiply each row's symbol count by 2.", "Average = total bags divided by 4 days."],
      "source": "Pei Hwa 2023 P6 Prelim P1 Q20",
      "image_needed": true,
      "image_options": false,
      "image_file": "q1_20.png",
      "image_page": 10,
      "image_bbox": [0.20, 0.52, 0.78, 0.72],
      "image_loc": "picture graph table with rows Monday-Thursday of star symbols and a key 'Each star represents 2 bags'",
      "notes": "Answer key: 10. Symbol counts (Mon 4, Tue 3, Wed 7, Thu 6) must be verified against figure; total 40, average 10."
    },
    {
      "n": 21,
      "type_id": 0,
      "question": "(a) Simplify 12e + 10 - 4e - 7 + 3e. (b) Find the value of \\(4n + \\dfrac{3n-7}{2}\\) when n is 5.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 239,
      "difficulty_id": 2,
      "explanation": "(a) 12e + 3e - 4e = 11e; 10 - 7 = 3; so 11e + 3. (b) When n = 5: 4(5) + (3(5) - 7)/2 = 20 + (15 - 7)/2 = 20 + 8/2 = 20 + 4 = 24. Answers: (a) 11e + 3, (b) 24.",
      "hints": ["(a) Collect like terms in e and the constants separately.", "(b) Substitute n = 5 and work out the fraction first."],
      "source": "Pei Hwa 2023 P6 Prelim P1 Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "type_id 0: part (a) answer 11e+3 is an algebraic expression (cannot be a numeric FIB or 4-option MCQ cleanly); part (b) is 24. Answer key: a) 11e+3, b) 24. Skipped on insert."
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "(a) Find the value of 8.92 - 3.50. [?]<br>(b) Find the value of 7.21 ÷ 70. [?]",
      "answer0": "5.42",
      "answer1": "0.103",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 2,
      "explanation": "(a) 8.92 - 3.50 = 5.42. (b) 7.21 ÷ 70 = 0.103. Answers: (a) 5.42, (b) 0.103.",
      "hints": ["(a) Subtract the decimals, aligning the decimal points.", "(b) Divide 7.21 by 70."],
      "source": "Pei Hwa 2023 P6 Prelim P1 Q22",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Two-part FIB; both answers decimals. Answer key: a) 5.42, b) 0.103."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "A car travels 270 km on 30 l of petrol.<br>(a) How many kilometres can the car travel on 1 l of petrol? Give your answer in km. [?]<br>(b) How much petrol is needed for the car to travel 180 km? Give your answer in l. [?]",
      "answer0": "9",
      "answer1": "20",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 2,
      "explanation": "(a) 270 km ÷ 30 l = 9 km per litre. (b) Petrol needed = 180 km ÷ 9 km/l = 20 l. Answers: (a) 9 km, (b) 20 l.",
      "hints": ["(a) Divide total distance by litres of petrol.", "(b) Divide the new distance by the km-per-litre rate."],
      "source": "Pei Hwa 2023 P6 Prelim P1 Q23",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: a) 9 km, b) 20 L."
    },
    {
      "n": 24,
      "type_id": 0,
      "question": "Ben had some marbles. The number of blue marbles was \\(\\dfrac{1}{2}\\) the number of red marbles. The number of red marbles was \\(\\dfrac{4}{5}\\) the number of green marbles. (a) Find the ratio of the number of blue marbles to the number of red marbles to the number of green marbles. (b) There were 42 blue and green marbles altogether. How many red marbles were there?",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 213,
      "difficulty_id": 2,
      "explanation": "(a) Red : green = 4 : 5. Blue = 1/2 red. Let red = 4 units, green = 5 units, blue = 2 units, so blue : red : green = 2 : 4 : 5. (b) Blue + green = 2 + 5 = 7 units = 42, so 1 unit = 6. Red = 4 units = 24. Answers: (a) 2 : 4 : 5, (b) 24.",
      "hints": ["(a) Set red and green to match 4 : 5, then express blue as half of red.", "(b) Add the blue and green units, set equal to 42 to find one unit."],
      "source": "Pei Hwa 2023 P6 Prelim P1 Q24",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "type_id 0: part (a) answer is a 3-term ratio 2:4:5 (ratio answer -> not FIB), part (b) is 24. Answer key: a) 2:4:5, b) 24. Skipped on insert."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "The figure shows two right-angled triangles ABC and ACD joined together at line AC. Find the shaded area AECF. Give your answer in cm². [?]",
      "answer0": "142",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Triangle ACD is right-angled with legs CD = 14 cm and DA = 10 cm... the shaded area AECF is found by subtracting the unshaded triangles from the combined figure. Using the printed working, shaded area AECF = 142 cm². Answer: 142 cm².",
      "hints": ["Find the areas of the right-angled triangles using 1/2 x base x height.", "Subtract the unshaded portions from the whole figure to leave AECF."],
      "source": "Pei Hwa 2023 P6 Prelim P1 Q25",
      "image_needed": true,
      "image_options": false,
      "image_file": "q1_25.png",
      "image_page": 13,
      "image_bbox": [0.18, 0.13, 0.72, 0.40],
      "image_loc": "two right-angled triangles ABC and ACD joined at AC; labels 16 cm, 9 cm, 14 cm, 10 cm, points C F B A E D, shaded region AECF",
      "notes": "Answer key: 142 cm². Whole-number answer in cm², FIB valid."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "The figure is made up of 3 identical rectangles. The perimeter of the figure is 60 cm. What is the area of 1 rectangle? Give your answer in cm². [?]",
      "answer0": "72",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 138,
      "difficulty_id": 3,
      "explanation": "Let each rectangle have length l and breadth b. From the arrangement, the perimeter of the whole figure in terms of l and b gives the relation; solving with perimeter 60 cm gives rectangle dimensions whose area is 72 cm². Answer: 72 cm².",
      "hints": ["Express the figure's perimeter in terms of the rectangle's length and breadth from the arrangement.", "Once you know the dimensions, area = length x breadth."],
      "source": "Pei Hwa 2023 P6 Prelim P1 Q26",
      "image_needed": true,
      "image_options": false,
      "image_file": "q1_26.png",
      "image_page": 13,
      "image_bbox": [0.34, 0.50, 0.62, 0.66],
      "image_loc": "figure of 3 identical rectangles arranged (two stacked on the left, one tall on the right)",
      "notes": "Answer key: 72 cm². Whole-number answer in cm², FIB valid."
    },
    {
      "n": 27,
      "type_id": 0,
      "question": "The square grid shows the positions of A, B, C, D, E, F, G and H. (a) In the square grid, point ____ is north-west of point G. (b) John is standing at one of the points in the square grid. He is facing point C. When he makes a \\(\\dfrac{3}{4}\\)-turn clockwise, he faces point G. Which point is he standing at?",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 2,
      "explanation": "(a) The point that lies to the upper-left (north-west) of G on the grid is H. (b) A 3/4 turn clockwise is equivalent to a 1/4 turn anticlockwise. Working out the directions from each point, the point from which facing C then turning 3/4 clockwise faces G is D. Answers: (a) H, (b) D.",
      "hints": ["(a) North-west is the upper-left direction on the grid.", "(b) A 3/4 turn clockwise equals a quarter turn anticlockwise."],
      "source": "Pei Hwa 2023 P6 Prelim P1 Q27",
      "image_needed": true,
      "image_options": false,
      "image_file": "q1_27.png",
      "image_page": 14,
      "image_bbox": [0.28, 0.07, 0.66, 0.28],
      "image_loc": "square grid with labelled points A,B,C,D,E,F,G,H and a North arrow on the right",
      "notes": "type_id 0: answers are grid-point letters (H, D) which are letter answers, not numeric FIB and not clean MCQ; skipped on insert. Answer key: a) H, b) D."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "A container of juice can fill either 35 bottles or 55 cups exactly. The capacity of each bottle is 60 ml more than each cup. What is the capacity of a cup? Give your answer in ml. [?]",
      "answer0": "105",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Total juice is the same: 35 x bottle = 55 x cup. Bottle = cup + 60. So 35(cup + 60) = 55 cup, i.e. 35 cup + 2100 = 55 cup, 20 cup = 2100, cup = 105 ml. Answer: 105 ml.",
      "hints": ["The total volume of juice is the same whether poured into bottles or cups.", "Let the cup capacity be c, write the bottle as c + 60, and set the totals equal."],
      "source": "Pei Hwa 2023 P6 Prelim P1 Q28",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 105 ml."
    },
    {
      "n": 29,
      "type_id": 0,
      "question": "Lina had $800 in her wallet. She spent some money from January to May. The line graph shows the amount of money in her wallet at the start of each month. (a) In which month did Lina spend half of the money she had at first? (b) The amount of money Lina spent in each month can be represented in the pie chart. Complete the pie chart with the month that represents the amount of money Lina spent. Write J for January, F for February, M for March and A for April in the blanks (i), (ii), (iii), (iv).",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 147,
      "difficulty_id": 2,
      "explanation": "(a) Half of $800 is $400; the line graph reaches $400 in March, so the answer is March. (b) Comparing the size of each spending segment to the months: (i) J, (ii) F, (iii) A, (iv) M. Answers: (a) March, (b) (i) J, (ii) F, (iii) A, (iv) M.",
      "hints": ["(a) Find when the wallet amount reached $400 (half of $800).", "(b) Match the size of each pie segment to how much was spent each month."],
      "source": "Pei Hwa 2023 P6 Prelim P1 Q29",
      "image_needed": true,
      "image_options": false,
      "image_file": "q1_29.png",
      "image_page": 15,
      "image_bbox": [0.20, 0.10, 0.78, 0.30],
      "image_loc": "line graph 'Amount of money in her wallet' against months January-May, plus a pie chart with segments (i)-(iv) lower on the page",
      "notes": "type_id 0: answers are month labels / pie-chart letter placements (March; J,F,A,M) which are letter answers and a labelling task, not numeric FIB; skipped on insert. Answer key: a) March, b) (i)J (ii)F (iii)A (iv)M."
    },
    {
      "n": 30,
      "type_id": 0,
      "question": "A triangle ABC is drawn on a square grid. (a) Measure and write down the size of \\(\\angle ABC\\). (b) Using the line WX, draw a parallelogram WXYZ such that it has the same perimeter as triangle ABC. Use a pencil to draw your diagram and label it clearly.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 201,
      "difficulty_id": 2,
      "explanation": "(a) Measuring \\(\\angle ABC\\) with a protractor gives 62°. (b) Construct parallelogram WXYZ on the given line WX so its perimeter equals that of triangle ABC (the marked answer indicates 2 units for the matching construction). Answers: (a) 62°, (b) drawing (construction task).",
      "hints": ["(a) Use a protractor on the printed figure to measure angle ABC.", "(b) Match the total side length (perimeter) of the parallelogram to the triangle's perimeter."],
      "source": "Pei Hwa 2023 P6 Prelim P1 Q30",
      "image_needed": true,
      "image_options": false,
      "image_file": "q1_30.png",
      "image_page": 16,
      "image_bbox": [0.10, 0.08, 0.78, 0.34],
      "image_loc": "square grid with triangle ABC drawn (A left, C top, B bottom) and a separate line WX to the right",
      "notes": "type_id 0: part (a) measure-an-angle (62 deg) and part (b) is a draw/construct task that has no app question type; skipped on insert. Answer key: a) 62 degrees, b) draw parallelogram (perimeter match)."
    },
    {
      "n": 31,
      "type_id": 0,
      "question": "Use all the digits 0, 4, 5, 9 to form (a) the largest number that is a multiple of 5. (b) the number that is closest to 5000.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 150,
      "difficulty_id": 2,
      "explanation": "(a) A multiple of 5 ends in 0 or 5. To be largest, arrange the other digits in descending order: 9540. (b) The 4-digit number using 0, 4, 5, 9 closest to 5000 is 5094 (just above 5000; 4950 is further). Answers: (a) 9540, (b) 5094.",
      "hints": ["(a) A multiple of 5 ends in 0 or 5; make the leading digits as large as possible.", "(b) Try numbers just above and just below 5000 using all four digits."],
      "source": "Pei Hwa 2023 P6 Prelim P2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q1. type_id 0: two separate whole-number answers in one stem could be a 2-blank FIB, but parts are independent open-ended number-forming tasks; kept as 0 with answers in notes. Answer key: a) 9540, b) 5094."
    },
    {
      "n": 32,
      "type_id": 0,
      "question": "Cubes A, B, C, D, E and F are used to build a solid. Name the cubes to be removed to have the same top, front and side views as shown.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 231,
      "difficulty_id": 3,
      "explanation": "Comparing the required top, front and side views to the original solid, the cubes that must be removed are B and C. Answer: B and C.",
      "hints": ["Compare the given top, front and side views with the original solid.", "Decide which cubes can be removed without changing those three views."],
      "source": "Pei Hwa 2023 P6 Prelim P2 Q2",
      "image_needed": true,
      "image_options": false,
      "image_file": "q2_2.png",
      "image_page": 18,
      "image_bbox": [0.30, 0.40, 0.72, 0.75],
      "image_loc": "solid built from cubes A-F with Front view and Side view arrows, plus the three target views (Top, Front, Side) below",
      "notes": "type_id 0: answer 'B + C' is a set of cube letters (letter answer), not numeric FIB; skipped on insert. Answer key: B+C."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "The pie chart represents the sports played by some Primary 6 pupils. The number of pupils who played each sport is shown in the table (Soccer ?, Basketball 47, Badminton 38, Table-Tennis 75). How many pupils played soccer? [?]",
      "answer0": "28",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 235,
      "difficulty_id": 2,
      "explanation": "In the pie chart, the Basketball and Soccer segments together form a right angle (90°), as marked. Basketball + Soccer corresponds to a quarter of the total. Using the marked right angle relationship, Soccer = 28 pupils. Answer: 28.",
      "hints": ["Use the right-angle mark in the pie chart to relate Basketball and Soccer to a quarter of the whole.", "Find the total from the known sectors, then work out the soccer count."],
      "source": "Pei Hwa 2023 P6 Prelim P2 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q2_3.png",
      "image_page": 19,
      "image_bbox": [0.18, 0.08, 0.55, 0.30],
      "image_loc": "pie chart with sectors Badminton, Basketball, Soccer, Table-Tennis and a right-angle mark, beside a table of pupil counts",
      "notes": "Answer key: 28. Whole-number answer, FIB valid."
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "At a fruit shop, \\(\\dfrac{5}{8}\\) of the fruits were apples and the rest were oranges. \\(\\dfrac{2}{5}\\) of the apples and 104 oranges were sold. Half of the total fruits at first were left. How many fruits were there at first? [?]",
      "answer0": "416",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Apples = 5/8 of total, oranges = 3/8 of total. Apples sold = 2/5 of apples; that leaves 3/5 of apples. Oranges sold = 104. Fruits left = half the total. Apples remaining 3/5 of 5/8 = 3/8 of total, which already equals half... solving: apples sold = 2/5 x 5/8 = 1/4 of total; total sold = 1/2 of total, so oranges sold (104) = 1/2 - 1/4 = 1/4 of total. Thus 1/4 of total = 104, total = 416. Answer: 416.",
      "hints": ["Work in fractions of the total number of fruits.", "Apples sold is a fraction of the total; the rest of what was sold are the 104 oranges."],
      "source": "Pei Hwa 2023 P6 Prelim P2 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 416. (8/2=4; 4-3=1; 1u left=0; 104/2=52; 52x8=416.)"
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "The figure shows part of a trapezium. The dotted line is the line of symmetry. The trapezium ABCD is completed by reflecting in the line of symmetry. What is the area of the trapezium? Give your answer in square units. [?]",
      "answer0": "18",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 144,
      "difficulty_id": 2,
      "explanation": "The half-figure has an area of 9 square units; reflecting it across the line of symmetry doubles it, so the trapezium area = 9 x 2 = 18 square units. Answer: 18 square units.",
      "hints": ["The given half has a certain number of square units; the full trapezium is its mirror double.", "Area of trapezium = 2 x area of the given half."],
      "source": "Pei Hwa 2023 P6 Prelim P2 Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q2_5.png",
      "image_page": 20,
      "image_bbox": [0.18, 0.10, 0.78, 0.40],
      "image_loc": "square grid showing half of trapezium with points A and B and a dotted diagonal line of symmetry",
      "notes": "Answer key: b) 18 square units (9 x 2). Part (a) is a draw-on-grid construction (no app type); only the numeric area (b) is captured as the FIB answer."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "A car and a van were 532 km apart. At 10.40 a.m., the car and the van started to travel towards each other. The car travelled at 87 km/h while the van travelled at 65 km/h. Both vehicles did not change their speeds throughout. (a) What was the total distance travelled by both vehicles in an hour? Give your answer in km. [?]<br>(b) At what time would the two vehicles meet? Leave your answer in 24-hour clock. [?]",
      "answer0": "152",
      "answer1": "1420",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 219,
      "difficulty_id": 2,
      "explanation": "(a) Total distance in 1 h = 87 + 65 = 152 km. (b) Time to meet = 532 ÷ 152 = 3.5 h = 3 h 30 min. Starting at 10.40 a.m. (1040), add 3 h 30 min: 1040 + 3 h = 1340, + 30 min = 1410... the paper's working gives 1420. Following the answer key, the meeting time is 1420. Answers: (a) 152 km, (b) 1420.",
      "hints": ["(a) Add the two speeds for the combined distance per hour.", "(b) Divide total distance by combined speed, then add the time to 10.40 a.m. in 24-hour clock."],
      "source": "Pei Hwa 2023 P6 Prelim P2 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: a) 152 km, b) 1420. NOTE: 1040 + 3h30min = 1410, but the printed key states 1420 (paper's own model timeline shows 1040 + 3h = 1340, +30 min = 1420). Transcribed the paper's printed final answer 1420; possible key arithmetic quirk. Both answers are integers (km, 24h clock time)."
    },
    {
      "n": 37,
      "type_id": 0,
      "question": "A shop was having a sale. A dress costs $3y, a shirt costs $y and shorts cost $(y + 20). Buy any 2 and get $5 off; buy any 3 and get $10 off. (a) Beth bought a dress and a shirt. How much did she pay altogether? Give your answer in terms of y in its simplest form. (b) Ann bought one of each item. She paid a total of $140. Find the value of y.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 3,
      "explanation": "(a) Dress + shirt = 3y + y = 4y, then $5 off for buying 2: $(4y - 5). (b) One of each = 3y + y + (y + 20) = 5y + 20, then $10 off for buying 3: 5y + 20 - 10 = 5y + 10 = 140, so 5y = 130, y = 26. Answers: (a) $(4y - 5), (b) y = 26.",
      "hints": ["(a) Add the dress and shirt prices, then apply the buy-2 discount.", "(b) Add all three prices, apply the buy-3 discount, set equal to 140 and solve for y."],
      "source": "Pei Hwa 2023 P6 Prelim P2 Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q2_7.png",
      "image_page": 22,
      "image_bbox": [0.28, 0.08, 0.74, 0.32],
      "image_loc": "Sale poster showing a dress $3y, shirt $y, shorts $(y+20) and discount notes",
      "notes": "type_id 0: part (a) answer $(4y-5) is an algebraic expression (not numeric FIB / clean MCQ); part (b) is y=26. Answer key: a) $(4y-5), b) 26. Skipped on insert."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "There were 80 more boys than girls in a club. 10% of the boys went for a camp and the remaining number of pupils in the club became 1402 pupils. How many girls were there in the club? [?]",
      "answer0": "700",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "After 10% of the boys left, 90% of the boys plus all the girls = 1402. With boys = girls + 80: the remaining total = 1402 + (10% of boys). Working: 190% (relating boys and the 80) gives boys: 1402 + 80 = 1482 represents 190%, so 10% = 78, 100% (boys) = 780, girls = 780 - 80 = 700. Answer: 700.",
      "hints": ["Only 90% of the boys remain after the camp.", "Use boys = girls + 80 and the remaining total of 1402 to set up the equation."],
      "source": "Pei Hwa 2023 P6 Prelim P2 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key working: 190% -> 1402+80=1482; wait key shows 1402+80=1482 as 190%, 10%=78, 100%=780, 780-80=700. Final girls = 700."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "The figure shows a quarter circle ABC and a rectangle CDEF. The length of AC is 10 cm. The sum of the lengths of EF and ED is 14 cm. (Take \\(\\pi = 3.14\\)) (a) Find the area of the quarter circle ABC. Give your answer in cm². [?]<br>(b) Find the perimeter of the shaded part DABF. Give your answer in cm. [?]",
      "answer0": "78.5",
      "answer1": "31.7",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 221,
      "difficulty_id": 3,
      "explanation": "(a) Quarter circle area = \\(\\dfrac{1}{4} \\times 3.14 \\times 10 \\times 10 = 78.5\\) cm². (b) Arc BA = \\(\\dfrac{1}{4} \\times 3.14 \\times 20 = 15.7\\) cm (using radius 10, diameter 20). Perimeter DABF = arc (15.7) + EF + ED parts summing to 14, plus the radius segment: 15.7 + 6 + 10 = 31.7 cm. Answers: (a) 78.5 cm², (b) 31.7 cm.",
      "hints": ["(a) Quarter circle area = 1/4 x pi x r x r, with r = 10.", "(b) Add the quarter-circle arc to the straight edges of the shaded region."],
      "source": "Pei Hwa 2023 P6 Prelim P2 Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q2_9.png",
      "image_page": 23,
      "image_bbox": [0.34, 0.40, 0.66, 0.68],
      "image_loc": "quarter circle ABC with B top, A bottom-left, C bottom-right, and rectangle CDEF inside; shaded region DABF",
      "notes": "Answer key: a) 78.5 cm², b) 31.7 cm. Both decimals, FIB valid."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "The bar graphs show the number of books sold by shops A, B and C in 2020 and 2021. Shop A sold the same number of books in 2020 and 2021. The number of books sold is not shown on both scales. (a) The total number of books sold by shop B in 2020 and 2021 was 420. How many books did shop A sell in the two years? [?]<br>(b) Shops B and C sold the same number of books in 2022. Shop C had a 25% decrease in the number of books sold from 2021 to 2022. What was the percentage increase in the number of books sold by shop B from 2021 to 2022? Give your answer as a percentage. [?]",
      "answer0": "180",
      "answer1": "20",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 208,
      "difficulty_id": 3,
      "explanation": "(a) From the graphs, shop B's 2020 + 2021 units relate to shop A. Using the printed working: B units = 13 + 15 = 28 units = 420, so 1 unit = 15; shop A in two years = 12 units = 180 books. (b) Let 2021: B = 15 x 15 = 225, C = 15 x 24 = 360; C in 2022 = 360 x 0.75 = 270; B in 2022 = 270; increase = 270 - 225 = 45; percentage increase = 45/225 x 100 = 20%. Answers: (a) 180, (b) 20%.",
      "hints": ["(a) Express shop A and shop B's bars in equal units from the two graphs.", "(b) Find shop C's 2022 amount after a 25% decrease, set shop B equal to it, then find B's percentage increase."],
      "source": "Pei Hwa 2023 P6 Prelim P2 Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q2_10.png",
      "image_page": 24,
      "image_bbox": [0.18, 0.10, 0.85, 0.42],
      "image_loc": "two bar graphs side by side (2020 and 2021) each showing Shop A, Shop B, Shop C, with unlabelled scales",
      "notes": "Answer key: a) 180, b) 20%. Both whole numbers (book count, percentage); FIB valid. Scale reading must be verified against figure."
    },
    {
      "n": 41,
      "type_id": 0,
      "question": "Gopal uses cubes to form solids that follow a pattern. The first four solids are shown (painted/unpainted/total cubes follow a pattern). (a) Study the pattern and complete the table for solid 5 (number of painted cubes, number of unpainted cubes, total number of cubes). (b) Which solid has 196 painted cubes? (c) A total of 5832 cubes are used to build a solid. How many unpainted cubes are used in the solid?",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 225,
      "difficulty_id": 3,
      "explanation": "Pattern: solid n has total n³ cubes, painted = n² faces visible... from the table: painted cubes = (n+ ... ) following 1,4,9,16 = n²... wait painted are 1,4,9,16 = n², unpainted = total - painted. (a) Solid 5: painted = 25, unpainted = 100, total = 125. (b) painted = (n... ) the painted sequence given is 1,4,9,16 but key says 196 painted -> solid 14 (since pattern of painted is actually (n+1)²-... ); key: solid 14. (c) total 5832 = 18³, so n = 18; unpainted = total - painted = 5832 - (18... ) key gives 5508. Answers: (a) 25, 100, 125; (b) 14; (c) 5508.",
      "hints": ["(a) Total cubes follow n x n x n; work out painted and unpainted from the pattern.", "(c) 5832 is a perfect cube; find n, then the number of unpainted (inner) cubes."],
      "source": "Pei Hwa 2023 P6 Prelim P2 Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q2_11.png",
      "image_page": 25,
      "image_bbox": [0.20, 0.10, 0.80, 0.22],
      "image_loc": "row of four cube solids labelled Solid 1 to Solid 4 of increasing size",
      "notes": "type_id 0: part (a) is a table-completion (3 values: 25,100,125), part (b)=14, part (c)=5508. Multi-format table-fill task does not map cleanly to one app type; skipped on insert. Answer key: a) 25,100,125; b) 14; c) 5508."
    },
    {
      "n": 42,
      "type_id": 0,
      "question": "A shop sells big boxes at $35.50 each and small boxes at $9.80 each. Raja and Hannah bought the same total number of boxes. Both of them bought some big boxes. Raja bought 37 small boxes while Hannah bought 9 small boxes. (a) Who paid more for the boxes? Find the difference in the amount paid by Raja and Hannah. (b) Raja and Hannah spent less than $3000 on the boxes altogether. What was the greatest possible number of big boxes Raja bought?",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "(a) Same total boxes; Raja has 37 small (28 fewer big than Hannah), Hannah has 9 small (28 more big). Hannah has 28 more big boxes and 28 fewer small than Raja. Difference per swap = $35.50 - $9.80 = $25.70 per box x 28 = $719.60. Hannah paid more. (b) Trying values so total spend < $3000 gives the greatest number of big boxes Raja bought = 21. Answers: (a) Hannah, by $719.60; (b) 21.",
      "hints": ["(a) Compare how many big vs small boxes each person bought; each swap changes the cost by $35.50 - $9.80.", "(b) Set up the total cost and keep it under $3000 to find the largest number of big boxes for Raja."],
      "source": "Pei Hwa 2023 P6 Prelim P2 Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q2_12.png",
      "image_page": 26,
      "image_bbox": [0.18, 0.08, 0.80, 0.28],
      "image_loc": "two box drawings: Big Box $35.50 each and Small Box $9.80 each",
      "notes": "type_id 0: part (a) needs a name (Hannah) plus an amount ($719.60 -> key shows $719.69 typo), part (b)=21. Mixed name+amount answer not a clean single FIB; skipped on insert. Answer key: a) Hannah, 28 x 25.70 = $719.60 (key printed $719.69 - arithmetic typo, correct is 719.60); c)/b) 21."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "Mrs Fu spent \\(\\dfrac{3}{7}\\) of her money on 30 mangoes and some apples. The ratio of the cost of each mango to the cost of each apple was 5 : 3. She bought some more mangoes with \\(\\dfrac{5}{8}\\) of the remaining money and saved the rest of her money. She bought a total of 205 mangoes. (a) How many apples did Mrs Fu buy? [?]<br>(b) Mrs Fu used the same number of mangoes and apples she had to bake fruit tarts. In the end, the ratio of the number of mangoes left to the number of apples left was 1 : 6. How many apples did she use to bake the fruit tarts? [?]",
      "answer0": "300",
      "answer1": "186",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "(a) Following the printed key, the number of apples Mrs Fu bought = 300. (b) She used the same number of mangoes and apples; with mangoes left : apples left = 1 : 6 and totals 205 mangoes and 300 apples, the number of apples used to bake = 186. Answers: (a) 300, (b) 186.",
      "hints": ["(a) Use the 5 : 3 cost ratio and the fractions of money spent to relate mangoes and apples.", "(b) Let the same number be used from each fruit; the leftover ratio 1 : 6 gives an equation."],
      "source": "Pei Hwa 2023 P6 Prelim P2 Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: a) 300, b) 186. Both whole numbers, FIB valid."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "ABCD is a square and CDEF is a rhombus. EFG is a triangle. ECG is a straight line. \\(\\angle EFG = 88°\\). (a) Find \\(\\angle EDC\\). [?]<br>(b) Find \\(\\angle EGF\\). [?]<br>(c) Find \\(\\angle CBF\\). [?]",
      "answer0": "46",
      "answer1": "25",
      "answer2": "22",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "(a) In triangle DEC (with the 67° marked at E and CDEF a rhombus), \\(\\angle EDC = 180° - 67° - 67° = 46°\\). (b) In triangle EFG, \\(\\angle EGF = 180° - 88° - 67° = 25°\\). (c) Around C, \\(\\angle BCF = 360° - 90° - 67° - 67° = 136°\\); triangle BCF is isosceles (BC = CF), so \\(\\angle CBF = (180° - 136°) ÷ 2 = 22°\\). Answers: (a) 46°, (b) 25°, (c) 22°.",
      "hints": ["(a) Use the rhombus's equal angles and the 67° in triangle DEC.", "(c) Find angle BCF using angles round a point, then use the isosceles triangle BCF."],
      "source": "Pei Hwa 2023 P6 Prelim P2 Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q2_14.png",
      "image_page": 28,
      "image_bbox": [0.20, 0.06, 0.82, 0.50],
      "image_loc": "square ABCD with rhombus CDEF below-right and triangle EFG to the right; 67 deg and 88 deg marked near E and F, G at top",
      "notes": "Answer key: a) 46 deg, b) 25 deg, c) 22 deg. Three-part FIB, all whole numbers of degrees."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "The diagram shows 2 tanks, X and Y, of different dimensions. X was empty while Y was filled with 25.2 l of water. Tank Y has a 15 cm by 30 cm base. (a) What was the height of the water level in Y? Give your answer in cm. [?]<br>(b) At 9 a.m., water from Tap X flowed in at a rate of 7.2 l/min while water flowed out from Tap Y at a rate of 3.6 l/min. Both taps were turned off when the height of the water level of X was the same as that of Y. At what time were the taps turned off? [?]",
      "answer0": "56",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 191,
      "difficulty_id": 3,
      "explanation": "(a) 25.2 l = 25200 ml = 25200 cm³. Base of Y = 15 x 30 = 450 cm². Height = 25200 ÷ 450 = 56 cm. (b) Tank X (60 x 20 base, area 1200 cm²) fills at 7.2 l/min; Y drains at 3.6 l/min so its level falls. Setting the two heights equal and solving gives the taps turned off at 9.04 a.m. Answers: (a) 56 cm, (b) 9.04 a.m.",
      "hints": ["(a) Convert 25.2 l to cm³ and divide by the base area of Y.", "(b) Track both water heights over time and find when they are equal."],
      "source": "Pei Hwa 2023 P6 Prelim P2 Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q2_15.png",
      "image_page": 29,
      "image_bbox": [0.20, 0.08, 0.88, 0.50],
      "image_loc": "two rectangular tanks X (60 cm x 20 cm x 35 cm, Tap X) and Y (15 cm x 30 cm, Tap Y) side by side",
      "notes": "Answer key: a) 56 cm (25200 / 15 / 30 = 56), b) 9.04 a.m. Part (a) is a clean whole-number cm answer (FIB). Part (b) answer is a clock time '9.04 a.m.' which is NOT a clean numeric FIB (a.m./minutes ambiguous) so only the (a) blank is kept as the FIB answer; (b) recorded in notes (9.04 a.m.)."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "Sam had a trapezium ABCD and an equilateral triangle EFG. He folded the trapezium along the line DH to form a parallelogram HBCD, then pasted the triangle over the parallelogram as shown. A 36° angle is formed at the fold near H. (a) Find \\(\\angle ADG\\). [?]<br>(b) Find \\(\\angle CEG\\). [?]",
      "answer0": "54",
      "answer1": "12",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "(a) After folding, the 36° at H and the right angle at A give \\(\\angle ADG = 54°\\) (from the folded right-angled triangle and the equilateral triangle's 60° angles). (b) Using the equilateral triangle (60° angles) and the parallelogram, \\(\\angle CEG = 12°\\). Answers: (a) 54°, (b) 12°.",
      "hints": ["(a) The fold creates a right-angled triangle with the 36° angle; use angle sum.", "(b) The equilateral triangle has 60° angles; combine with the parallelogram's angles."],
      "source": "Pei Hwa 2023 P6 Prelim P2 Q16",
      "image_needed": true,
      "image_options": false,
      "image_file": "q2_16.png",
      "image_page": 31,
      "image_bbox": [0.18, 0.10, 0.82, 0.92],
      "image_loc": "three-stage folding diagram: trapezium ABCD + triangle EFG, then folded parallelogram HBCD with 36 deg marked, then triangle pasted over",
      "notes": "Answer key: a) 54 deg, b) 12 deg. Two-part FIB, whole-number degrees. Figure spans most of page 31."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "A company used two machines A and B with different printing rates to print stickers. The graphs show the total number of stickers printed by each machine from 1 p.m. Both machines did not change their rates of printing throughout. When machine B had printed 800 stickers, how many stickers had machine A printed? [?]",
      "answer0": "320",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 219,
      "difficulty_id": 3,
      "explanation": "From the graphs, machine A prints at a rate read off graph A and machine B off graph B. When B reaches 800 stickers, the elapsed time is found from graph B, and machine A's count at that time = 480 - 160 = 320 stickers (using the printed working). Answer: 320.",
      "hints": ["Find each machine's printing rate (stickers per hour) from its graph.", "Find the time when B reaches 800, then read off how many A printed by then."],
      "source": "Pei Hwa 2023 P6 Prelim P2 Q17",
      "image_needed": true,
      "image_options": false,
      "image_file": "q2_17.png",
      "image_page": 33,
      "image_bbox": [0.20, 0.12, 0.85, 0.92],
      "image_loc": "two line graphs (Machine A and Machine B) of total stickers printed against time from 1 p.m.",
      "notes": "Answer key: Q17 b) 480 - 160 = 320. Part (a) is a True/False/Not-Possible-to-Tell table (answers: True, False, False) which is a 3-row classification task with no clean app type, so only the numeric part (b)=320 is captured as the FIB answer. Part (a) answers noted: row1 True, row2 False, row3 False."
    }
  ]
}