{
  "paper": {
    "school": "Nan Chiau",
    "year": 2022,
    "level": "P6",
    "label": "Prelim",
    "source_prefix": "Nan Chiau 2022 P6 Prelim",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "What is the value of the digit 9 in 485 093?",
      "answer0": "9000",
      "answer1": "900",
      "answer2": "90",
      "answer3": "9",
      "correct_answer": 2,
      "skill_id": 105,
      "difficulty_id": 1,
      "explanation": "The digit 9 is in the tens place, so its value is 9 × 10 = 90.",
      "hints": ["Identify which place the digit 9 sits in.", "Tens place → value = digit × 10."],
      "source": "Nan Chiau 2022 P6 Prelim Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Q1 = option 3 (90)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Arrange the following numbers from the smallest to the largest.<br>5, 5.6, 5.06",
      "answer0": "5.06 , 5.6 , 5",
      "answer1": "5.6 , 5.06 , 5",
      "answer2": "5 , 5.06 , 5.6",
      "answer3": "5 , 5.6 , 5.06",
      "correct_answer": 2,
      "skill_id": 124,
      "difficulty_id": 1,
      "explanation": "Compare: 5 = 5.00, 5.06, 5.6 = 5.60. Smallest to largest: 5, 5.06, 5.6.",
      "hints": ["Write each number to the same number of decimal places.", "5.00 < 5.06 < 5.60."],
      "source": "Nan Chiau 2022 P6 Prelim Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Q2 = option 3 (5, 5.06, 5.6)."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "In the number line, what is the mixed number represented by A?",
      "answer0": "\\(2\\dfrac{2}{5}\\)",
      "answer1": "\\(2\\dfrac{1}{2}\\)",
      "answer2": "\\(2\\dfrac{3}{5}\\)",
      "answer3": "\\(2\\dfrac{2}{3}\\)",
      "correct_answer": 0,
      "skill_id": 119,
      "difficulty_id": 2,
      "explanation": "The interval between 2 and 3 is divided into 5 equal parts. A is at the 2nd mark, so A = 2 2/5.",
      "hints": ["Count the number of equal parts between 2 and 3.", "Locate which mark A points to."],
      "source": "Nan Chiau 2022 P6 Prelim Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q3.png",
      "image_page": 3,
      "image_bbox": [0.30, 0.55, 0.78, 0.66],
      "image_loc": "number line from 2 to 3 with arrow A above, middle of page 3",
      "notes": "Answer key Q3 = option 1 (2 2/5). Fraction options → MCQ."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Find the sum of 305 and 139. Round the answer to the nearest hundred.",
      "answer0": "400",
      "answer1": "440",
      "answer2": "444",
      "answer3": "500",
      "correct_answer": 0,
      "skill_id": 109,
      "difficulty_id": 1,
      "explanation": "305 + 139 = 444. Rounded to the nearest hundred, 444 → 400.",
      "hints": ["Add the two numbers first.", "444 is closer to 400 than 500."],
      "source": "Nan Chiau 2022 P6 Prelim Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Q4 = option 1 (400)."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "3 ones, 8 hundredths and 1 thousandth is ____________.",
      "answer0": "3.81",
      "answer1": "3.801",
      "answer2": "3.108",
      "answer3": "3.081",
      "correct_answer": 1,
      "skill_id": 123,
      "difficulty_id": 1,
      "explanation": "3 ones = 3, 8 hundredths = 0.08, 1 thousandth = 0.001. Sum = 3.081... ones=3, tenths=0, hundredths=8, thousandths=1 → 3.081.",
      "hints": ["Place each digit in its correct place value column.", "Ones . tenths hundredths thousandths."],
      "source": "Nan Chiau 2022 P6 Prelim Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Q5 = option 4 (3.081)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "Mrs Nathan took 30 minutes to drive from her house to her office. Her average driving speed was 90 km/h. What was the distance from her house to her office?",
      "answer0": "27 km",
      "answer1": "45 km",
      "answer2": "120 km",
      "answer3": "180 km",
      "correct_answer": 1,
      "skill_id": 217,
      "difficulty_id": 2,
      "explanation": "30 min = 1/2 h. Distance = speed × time = 90 × 1/2 = 45 km.",
      "hints": ["Convert 30 minutes to hours.", "Distance = speed × time."],
      "source": "Nan Chiau 2022 P6 Prelim Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Q6 = option 2 (45 km)."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "The figure shows a semicircle of diameter 12 cm. What is the perimeter of the figure? Leave your answer in π.",
      "answer0": "\\(6\\pi\\) cm",
      "answer1": "\\(18\\pi\\) cm",
      "answer2": "\\((6\\pi + 12)\\) cm",
      "answer3": "\\((12\\pi + 12)\\) cm",
      "correct_answer": 2,
      "skill_id": 221,
      "difficulty_id": 2,
      "explanation": "Perimeter = half circumference + diameter = π × 12 ÷ 2 + 12 = 6π + 12 cm.",
      "hints": ["Perimeter of a semicircle = curved arc + straight diameter.", "Arc = π × d ÷ 2."],
      "source": "Nan Chiau 2022 P6 Prelim Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q7.png",
      "image_page": 4,
      "image_bbox": [0.13, 0.61, 0.40, 0.73],
      "image_loc": "semicircle with 12 cm base label, left side of page 4",
      "notes": "Answer key Q7 = option 3 ((6π+12) cm)."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "A school concert started at 3.40 p.m. and ended at 5.25 p.m. How long was the concert?",
      "answer0": "1 h 5 min",
      "answer1": "1 h 15 min",
      "answer2": "1 h 30 min",
      "answer3": "1 h 45 min",
      "correct_answer": 3,
      "skill_id": 135,
      "difficulty_id": 1,
      "explanation": "3.40 p.m. to 4.40 p.m. = 1 h; 4.40 p.m. to 5.25 p.m. = 45 min. Total = 1 h 45 min.",
      "hints": ["Count whole hours first, then the extra minutes.", "3.40 + 1 h = 4.40; then to 5.25."],
      "source": "Nan Chiau 2022 P6 Prelim Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Q8 = option 4 (1 h 45 min)."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "AB and CD are straight lines. Which of the following is true?",
      "answer0": "∠w = ∠x + ∠y",
      "answer1": "∠z = ∠w + ∠x",
      "answer2": "∠w + ∠x + ∠y = 180°",
      "answer3": "∠x + ∠y + ∠z = 180°",
      "correct_answer": 3,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "∠x, ∠y, ∠z are angles on one side of straight line AB (below it, around point), summing to 180° on a straight line. ∠x + ∠y + ∠z = 180°.",
      "hints": ["Angles on a straight line add up to 180°.", "Look at the three angles on the same side of AB."],
      "source": "Nan Chiau 2022 P6 Prelim Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q9.png",
      "image_page": 5,
      "image_bbox": [0.28, 0.18, 0.62, 0.34],
      "image_loc": "two intersecting straight lines AB and CD with angles w,x,y,z and ray E, top of page 5",
      "notes": "Answer key Q9 = option 4."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "The following table shows the time taken by four students to complete a Mathematics test. One of the recorded data is covered by an ink blot.<br>Anna: ?<br>Belinda: 80<br>Colin: 74<br>Danny: 70<br>The average time taken by the four students was 72 minutes. What was the time taken by Anna to complete the test?",
      "answer0": "36",
      "answer1": "64",
      "answer2": "72",
      "answer3": "74",
      "correct_answer": 1,
      "skill_id": 204,
      "difficulty_id": 2,
      "explanation": "Total = 72 × 4 = 288. Anna = 288 − (80 + 74 + 70) = 288 − 224 = 64 min.",
      "hints": ["Total = average × number of students.", "Subtract the three known times from the total."],
      "source": "Nan Chiau 2022 P6 Prelim Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Q10 = option 2 (64). Table values transcribed into stem."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "Mary had $350. She spent the same amount of money each day. After 5 days, she was left with \\(\\dfrac{4}{5}\\) of her money. How much did she spend each day?",
      "answer0": "$14",
      "answer1": "$15",
      "answer2": "$56",
      "answer3": "$70",
      "correct_answer": 0,
      "skill_id": 209,
      "difficulty_id": 2,
      "explanation": "Spent = 1/5 of $350 = $70 over 5 days. Per day = $70 ÷ 5 = $14.",
      "hints": ["She spent 1 − 4/5 = 1/5 of her money.", "Divide total spent by 5 days."],
      "source": "Nan Chiau 2022 P6 Prelim Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Q11 = option 1 ($14)."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "A repeated pattern is formed using the digits 1 and 0. The first 15 numbers are:<br>1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1 ......<br>What is the sum of the first 99 numbers?",
      "answer0": "57",
      "answer1": "59",
      "answer2": "60",
      "answer3": "62",
      "correct_answer": 1,
      "skill_id": 108,
      "difficulty_id": 3,
      "explanation": "After the first term, the block (0,0,1,1,1) of 5 terms repeats with sum 3. 99 = 1 + 98 = 1 + (19 blocks × 5 = 95) + 3 extra. Sum = 1 + 19×3 + (0+0+1) = 1 + 57 + 1 = 59.",
      "hints": ["Identify the repeating block and its sum.", "Account for the leading 1 and the leftover terms."],
      "source": "Nan Chiau 2022 P6 Prelim Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Q12 = option 2 (59). Pattern transcribed into stem."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "Mrs Lim has a jug which contains 5 ℓ of water. She uses the water to fill some identical cups to the brim. The capacity of each cup is \\(\\dfrac{4}{5}\\) ℓ. At most, how many such cups can she fill to the brim?",
      "answer0": "4",
      "answer1": "5",
      "answer2": "6",
      "answer3": "7",
      "correct_answer": 2,
      "skill_id": 206,
      "difficulty_id": 2,
      "explanation": "5 ÷ 4/5 = 5 × 5/4 = 25/4 = 6 1/4. At most 6 full cups can be filled.",
      "hints": ["Divide total water by the capacity of one cup.", "Take the whole-number part (full cups only)."],
      "source": "Nan Chiau 2022 P6 Prelim Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Q13 = option 3 (6)."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "The price of an e-dictionary was $45 after a discount of 10%. Rina was then given an additional discount of $9. What was the total percentage discount given to Rina for the e-dictionary?",
      "answer0": "18%",
      "answer1": "20%",
      "answer2": "28%",
      "answer3": "30%",
      "correct_answer": 2,
      "skill_id": 176,
      "difficulty_id": 3,
      "explanation": "$45 is 90% of usual price → usual = $45 ÷ 0.9 = $50. Total discount = $50 − ($45 − $9) = $50 − $36 = $14. Percentage = 14/50 × 100% = 28%.",
      "hints": ["Find the usual price: $45 = 90% of it.", "Total discount = usual price − final price; express as a percentage of usual."],
      "source": "Nan Chiau 2022 P6 Prelim Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q14.png",
      "image_page": 7,
      "image_bbox": [0.12, 0.13, 0.58, 0.23],
      "image_loc": "laptop/e-dictionary with $45 (price after 10% discount) tag, top of page 7",
      "notes": "Answer key Q14 = option 3 (28%)."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "Fadilah pours the same amount of water into two empty tanks A and B. Tank A (14 cm by 10 cm by 12 cm) is half-filled with water. Tank B has base 8 cm by 10 cm. What is the height of water in Tank B?",
      "answer0": "5.6 cm",
      "answer1": "6 cm",
      "answer2": "7.5 cm",
      "answer3": "10.5 cm",
      "correct_answer": 3,
      "skill_id": 191,
      "difficulty_id": 2,
      "explanation": "Water volume in A = 1/2 × 14 × 10 × 12 = 840 cm³. Same water in B: height = 840 ÷ (8 × 10) = 840 ÷ 80 = 10.5 cm.",
      "hints": ["Find the volume of water in Tank A first (half-filled).", "Height in B = volume ÷ base area of B."],
      "source": "Nan Chiau 2022 P6 Prelim Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q15.png",
      "image_page": 7,
      "image_bbox": [0.17, 0.42, 0.80, 0.58],
      "image_loc": "two cuboid tanks A (14x10x12) and B (8x10x15) side by side, middle of page 7",
      "notes": "Answer key Q15 = option 4 (10.5 cm). Tank dimensions transcribed into stem."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Write down all the common factors of 20 and 36 that are greater than 1.<br>[?] , [?]",
      "answer0": "2",
      "answer1": "4",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 113,
      "difficulty_id": 2,
      "explanation": "Factors of 20: 1,2,4,5,10,20. Factors of 36: 1,2,3,4,6,9,12,18,36. Common factors > 1: 2 and 4.",
      "hints": ["List the factors of each number.", "Pick the shared factors greater than 1."],
      "source": "Nan Chiau 2022 P6 Prelim Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Q16 = 2, 4."
    },
    {
      "n": 17,
      "type_id": 1,
      "question": "Square ACEG is made up of 4 small triangles, 1 large triangle and 1 small square. AB = BC = CD. What fraction of the square ACEG is shaded?",
      "answer0": "\\(\\dfrac{3}{8}\\)",
      "answer1": "\\(\\dfrac{1}{4}\\)",
      "answer2": "\\(\\dfrac{1}{2}\\)",
      "answer3": "\\(\\dfrac{5}{8}\\)",
      "correct_answer": 0,
      "skill_id": 120,
      "difficulty_id": 3,
      "explanation": "Dividing the square into 8 equal small triangles, the shaded region covers 3 of them, so the shaded fraction is 3/8.",
      "hints": ["Split the whole square into equal triangular units.", "Count shaded units over total units."],
      "source": "Nan Chiau 2022 P6 Prelim Q17",
      "image_needed": true,
      "image_options": false,
      "image_file": "q17.png",
      "image_page": 11,
      "image_bbox": [0.13, 0.40, 0.40, 0.55],
      "image_loc": "square ACEG with vertices labelled, shaded triangles and small square, page 11 (Booklet B p1)",
      "notes": "Answer key Q17 = 3/8. Fraction answer → MCQ (built distractor options)."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "Express \\(5\\dfrac{4}{11}\\) as a decimal. Give your answer correct to 1 decimal place.<br>[?]",
      "answer0": "5.4",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 158,
      "difficulty_id": 2,
      "explanation": "4 ÷ 11 = 0.3636... So 5 4/11 = 5.3636... ≈ 5.4 (to 1 decimal place).",
      "hints": ["Convert the fraction part: 4 ÷ 11.", "Round 5.36... to 1 decimal place."],
      "source": "Nan Chiau 2022 P6 Prelim Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Q18 = 5.4 (key shows '5,4' as 5 then 4 d.p. style; final decimal 5.4)."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "A container contained some water at first. Harry used 0.06 ℓ of water from the container. How much water was left? (Give your answer in ℓ.)<br>[?]",
      "answer0": "0.29",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 184,
      "difficulty_id": 2,
      "explanation": "Container showed 350 ml = 0.35 ℓ. Water left = 0.35 − 0.06 = 0.29 ℓ.",
      "hints": ["Read the starting volume from the beaker, convert ml to litres.", "Subtract 0.06 ℓ."],
      "source": "Nan Chiau 2022 P6 Prelim Q19",
      "image_needed": true,
      "image_options": false,
      "image_file": "q19.png",
      "image_page": 12,
      "image_bbox": [0.18, 0.13, 0.40, 0.30],
      "image_loc": "beaker marked 500 ml with shaded water level, top-left of page 12 (Booklet B p2)",
      "notes": "Answer key Q19 = 0.29 ℓ (start 0.35 ℓ). Units: litres."
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "In the figure, DFE and DFG are isosceles triangles. FD = FE = FG. ∠FDG = 35°. Find ∠FDE. (Give your answer in degrees.)<br>[?]",
      "answer0": "55",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "In triangle DFG (FD = FG), ∠FGD = ∠FDG = 35°, so ∠DFG = 180 − 35×2 = 110°. Straight line: ∠DFE = 180 − 110 = 70°. Triangle DFE (FD = FE) is isosceles, so ∠FDE = (180 − 70) ÷ 2 = 55°.",
      "hints": ["Use the isosceles triangle DFG to find ∠DFG.", "Angles on the straight line EFG give ∠DFE, then use isosceles DFE."],
      "source": "Nan Chiau 2022 P6 Prelim Q20",
      "image_needed": true,
      "image_options": false,
      "image_file": "q20.png",
      "image_page": 12,
      "image_bbox": [0.18, 0.50, 0.72, 0.74],
      "image_loc": "triangle DEG with apex D (35°) and foot F on EG, lower half of page 12",
      "notes": "Answer key Q20 = 55°. Units: degrees."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "The figure is made up of 5 identical rectangles. The breadth of one rectangle is 8 cm. What is the area of the figure? (Give your answer in cm².)<br>[?]",
      "answer0": "480",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 138,
      "difficulty_id": 3,
      "explanation": "From the arrangement, length = 8 × 3 ÷ 2 = 12 cm; one rectangle = 12 × 8. Total figure (5 rectangles arranged) = 20 × 24 = 480 cm².",
      "hints": ["Use the breadth to work out the rectangle's length from the layout.", "Find the overall dimensions of the figure."],
      "source": "Nan Chiau 2022 P6 Prelim Q21",
      "image_needed": true,
      "image_options": false,
      "image_file": "q21.png",
      "image_page": 13,
      "image_bbox": [0.16, 0.18, 0.48, 0.32],
      "image_loc": "figure of 5 identical rectangles with 8 cm breadth label, upper-left of page 13",
      "notes": "Answer key Q21 working: 8×3÷2=12; 12+8=20; 8×3=24; 20×24=480 cm²."
    },
    {
      "n": 22,
      "type_id": 1,
      "question": "Samantha has some blue, pink and white beads. \\(\\dfrac{7}{10}\\) of the beads are blue. There are twice as many pink beads as white beads. What fraction of the beads is white?",
      "answer0": "\\(\\dfrac{1}{10}\\)",
      "answer1": "\\(\\dfrac{3}{10}\\)",
      "answer2": "\\(\\dfrac{1}{5}\\)",
      "answer3": "\\(\\dfrac{2}{10}\\)",
      "correct_answer": 0,
      "skill_id": 121,
      "difficulty_id": 2,
      "explanation": "Non-blue = 1 − 7/10 = 3/10. Pink : white = 2 : 1, so white = 1/3 of 3/10 = 1/10.",
      "hints": ["Find the fraction that is not blue.", "Split that into pink (2 parts) and white (1 part)."],
      "source": "Nan Chiau 2022 P6 Prelim Q22",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Q22 = 1/10. Fraction answer → MCQ (built distractor options)."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "Shop A and shop B sold an identical television each at the same price, after the discounts shown. Shop A: 40% Discount, Usual Price: ? Shop B: 20% Discount, Usual Price: $1500. What was the usual price of the television sold by shop A? (Give your answer in $.)<br>[?]",
      "answer0": "2000",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 207,
      "difficulty_id": 3,
      "explanation": "Shop B selling price = $1500 × 80/100 = $1200. Shop A sells at the same $1200 after 40% off, so $1200 is 60% of A's usual price: $1200 ÷ 60 × 100 = $2000.",
      "hints": ["Find Shop B's selling price first.", "Shop A's selling price equals Shop B's; it is 60% of A's usual price."],
      "source": "Nan Chiau 2022 P6 Prelim Q23",
      "image_needed": true,
      "image_options": false,
      "image_file": "q23.png",
      "image_page": 14,
      "image_bbox": [0.18, 0.15, 0.80, 0.33],
      "image_loc": "two televisions: Shop A (40% discount, usual ?) and Shop B (20% discount, usual $1500), upper page 14",
      "notes": "Answer key Q23 = $2000. Units: dollars."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "Matthew spent a total of $15 on some rulers and pens. He bought 27 pens at 9 pens for $y. He bought the rulers at $2 each. How many rulers did he buy?<br>[?]",
      "answer0": "0",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 3,
      "explanation": "27 pens = 3 lots of 9 pens, costing 3y. Money on rulers = 15 − 3y; rulers = (15 − 3y) ÷ 2.",
      "hints": ["27 pens is three groups of 9, so pen cost = 3y.", "Rulers cost = (total − pen cost) ÷ $2 each."],
      "source": "Nan Chiau 2022 P6 Prelim Q24",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key Q24 = ((15−3y)/2) — algebraic expression, not a numeric value. type_id 2 numeric answer is unsuitable; recommend converting/skipping. Placeholder answer0='0'. Flag: answer is an expression."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "Jason builds a solid using 10 unit cubes and glued them together. Find the smallest number of unit cubes Jason can add to the solid to form a cubical solid.<br>[?]",
      "answer0": "17",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 225,
      "difficulty_id": 3,
      "explanation": "The smallest cube that can contain the solid is 3 × 3 × 3 = 27 unit cubes. Cubes to add = 27 − 10 = 17. (Part (a) drawing the top view is interactive and omitted.)",
      "hints": ["Find the smallest n×n×n cube that fits the shape.", "Subtract the 10 cubes already used."],
      "source": "Nan Chiau 2022 P6 Prelim Q25",
      "image_needed": true,
      "image_options": false,
      "image_file": "q25.png",
      "image_page": 15,
      "image_bbox": [0.30, 0.13, 0.70, 0.35],
      "image_loc": "isometric solid of 10 unit cubes with Top/Front/Side view arrows, upper page 15",
      "notes": "Answer key Q25(b) = 17. Part (a) 'draw top view' is interactive, dropped; only numeric part (b) kept."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "The figure is made up of 4 identical quadrants and a square. What is the area of the shaded part? (Take \\(\\pi = \\dfrac{22}{7}\\).) (Give your answer in cm².)<br>[?]",
      "answer0": "42",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 223,
      "difficulty_id": 3,
      "explanation": "Square side = 7 cm, area = 14 × 14? Key: 7×7×22/7 = 154 (four quadrants = one full circle, radius 7). Square = 14×14 = 196. Shaded = 196 − 154 = 42 cm².",
      "hints": ["Four identical quadrants make one full circle.", "Shaded = square area − circle area."],
      "source": "Nan Chiau 2022 P6 Prelim Q26",
      "image_needed": true,
      "image_options": false,
      "image_file": "q26.png",
      "image_page": 16,
      "image_bbox": [0.20, 0.16, 0.44, 0.34],
      "image_loc": "square with four inward quadrant arcs forming a 4-pointed shaded star, 7 cm label, upper-left page 16",
      "notes": "Answer key Q26 = 42 cm² (7×7×22/7=154; 14×14=196; 196−154=42)."
    },
    {
      "n": 27,
      "type_id": 0,
      "question": "Billy's house, the library, the market, the pond and his school are located as shown in the square grid. (a) Billy is facing the pond. Where will he be facing after he turns 135° anti-clockwise? (b) A shopping mall will be built at a location south-east of Billy's house and north of the school. Put a tick in the square where the shopping mall will be built.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 142,
      "difficulty_id": 3,
      "explanation": "(a) Billy faces the pond (East). Turning 135° anti-clockwise from East → North-West → he faces the Library. (b) The mall is in the square south-east of Billy's house and north of the school (one row above the school, in Billy's column area).",
      "hints": ["Use the compass: East turned 135° anti-clockwise.", "Find the square that is both SE of the house and N of the school."],
      "source": "Nan Chiau 2022 P6 Prelim Q27",
      "image_needed": true,
      "image_options": false,
      "image_file": "q27.png",
      "image_page": 17,
      "image_bbox": [0.13, 0.13, 0.70, 0.45],
      "image_loc": "square grid map showing Library, Market, Billy's House, Billy, Pond, School with N compass, upper page 17",
      "notes": "Answer key Q27: (a) library; (b) tick in marked square. Interactive (facing direction + tick on grid) → type_id 0, skipped on insert."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "The diagram shows two parallelograms ABCD and ABGE. ∠AEG = 45° and ∠BCD = 60°. (a) Find ∠ABG. (b) Find ∠CBG. (Give your answers in degrees.)<br>(a) [?] (b) [?]",
      "answer0": "45",
      "answer1": "75",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 200,
      "difficulty_id": 3,
      "explanation": "(a) In parallelogram ABGE, ∠ABG = ∠AEG = 45° (opposite angles equal). (b) In parallelogram ABCD, ∠ABC = 180 − ∠BCD = 180 − 60 = 120°. ∠CBG = ∠ABC − ∠ABG = 120 − 45 = 75°.",
      "hints": ["Opposite angles of a parallelogram are equal; co-interior angles sum to 180°.", "∠CBG = ∠ABC − ∠ABG."],
      "source": "Nan Chiau 2022 P6 Prelim Q28",
      "image_needed": true,
      "image_options": false,
      "image_file": "q28.png",
      "image_page": 18,
      "image_bbox": [0.24, 0.15, 0.72, 0.33],
      "image_loc": "two overlapping parallelograms ABCD and ABGE with 45° at E and 60° at C, upper page 18",
      "notes": "Answer key Q28: (a) 45°; (b) 180−60=120, 120−45=75°. Two blanks (a),(b)."
    },
    {
      "n": 29,
      "type_id": 1,
      "question": "The line graph shows the amount of water in a tank from 10 a.m. to 2 p.m. The tank was \\(\\dfrac{1}{4}\\) filled with water at 10 a.m. Water flowed out of the tank from 10 a.m. to 2 p.m. At 11 a.m., what fraction of the tank was filled with water?",
      "answer0": "\\(\\dfrac{3}{14}\\)",
      "answer1": "\\(\\dfrac{1}{4}\\)",
      "answer2": "\\(\\dfrac{3}{28}\\)",
      "answer3": "\\(\\dfrac{6}{7}\\)",
      "correct_answer": 0,
      "skill_id": 147,
      "difficulty_id": 3,
      "explanation": "At 10 a.m. = 28 ℓ is 1/4 of tank, so full tank = 112 ℓ. At 11 a.m. the graph reads 24 ℓ, so fraction = 24/112 = 3/14. (Part (a): greatest flow was 12 p.m. to 1 p.m.)",
      "hints": ["10 a.m. reading is 1/4 of the tank → find full capacity.", "Read the 11 a.m. value, divide by capacity."],
      "source": "Nan Chiau 2022 P6 Prelim Q29",
      "image_needed": true,
      "image_options": false,
      "image_file": "q29.png",
      "image_page": 19,
      "image_bbox": [0.28, 0.17, 0.72, 0.38],
      "image_loc": "line graph of amount of water (litres) vs time 10am-2pm, upper page 19",
      "notes": "Answer key Q29: (a) 12pm to 1pm; (b) 3/14. Kept numeric/fraction part (b) as MCQ (fraction answer). Part (a) interval answer noted in explanation."
    },
    {
      "n": 30,
      "type_id": 0,
      "question": "The pie chart shows how a group of students travel to school (Car = 1/5). The bar graph also represents how the same group travel to school; the bar for public bus is not drawn (Car ≈ 80, Walk ≈ 150, School bus ≈ 120). For each statement, indicate True, False or Not possible to tell: (i) There are 400 students altogether. (ii) 3/5 of the students walk to school. (iii) 50 students take public bus to school.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 235,
      "difficulty_id": 3,
      "explanation": "Car = 1/5 of total and bar shows 80, so total = 400 → (i) True. Walk = 150 of 400 = 3/8, not 3/5 → (ii) False. Public bus = 400 − 80 − 150 − 120 = 50 → (iii) True.",
      "hints": ["Car is 1/5 of total and equals 80 students → find the total.", "Use the total to test each statement."],
      "source": "Nan Chiau 2022 P6 Prelim Q30",
      "image_needed": true,
      "image_options": false,
      "image_file": "q30.png",
      "image_page": 20,
      "image_bbox": [0.13, 0.12, 0.80, 0.55],
      "image_loc": "pie chart (Car/Public bus/Walk/School bus) and bar graph of number of students, upper page 20",
      "notes": "Answer key Q30: True / False / True. Tick-table format is interactive → type_id 0, skipped on insert."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "(a) Use all the digits 3, 4, 5, 8 to form the greatest multiple of 5. (b) Use all the digits 3, 4, 5, 8 to form the smallest odd number between 4000 and 5000.<br>(a) [?] (b) [?]",
      "answer0": "8435",
      "answer1": "4385",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 107,
      "difficulty_id": 2,
      "explanation": "(a) A multiple of 5 must end in 5 (0 not available); arrange the rest descending: 8435. (b) Between 4000-5000 starts with 4; odd → ends in 3 or 5; smallest uses 4 _ _ 5 then smallest middle: 4385.",
      "hints": ["Multiples of 5 end in 0 or 5.", "For smallest odd 4xxx, fix thousands = 4 and last digit odd, minimise the rest."],
      "source": "Nan Chiau 2022 P6 Prelim Q31",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q1. Answer key: (a) 8435, (b) 4385. Two blanks."
    },
    {
      "n": 32,
      "type_id": 2,
      "question": "The number of red balloons is \\(\\dfrac{2}{11}\\) of the number of blue balloons. There are 1953 more blue balloons than red balloons. How many red balloons are there?<br>[?]",
      "answer0": "434",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 2,
      "explanation": "Red : Blue = 2 : 11. Difference = 11 − 2 = 9 units = 1953, so 1 unit = 217. Red = 2 units = 2 × 217 = 434.",
      "hints": ["Treat red as 2 units and blue as 11 units.", "The difference of 9 units equals 1953."],
      "source": "Nan Chiau 2022 P6 Prelim Q32",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q2. Answer key: 11−2=9; 1953÷9=217; 217×2=434."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "The figure is made up of an equilateral triangle ABC and a square BCDE. DE = 2w cm. The perimeter of the figure is 140 cm. Find the value of w.<br>[?]",
      "answer0": "14",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 2,
      "explanation": "The outer perimeter is made of 5 equal sides (2 triangle sides + 3 square sides), each 2w. So 5 × 2w = 140 → 10w = 140 → ... but key: 140÷5 = 28 per side = 2w → w = 14.",
      "hints": ["All sides are equal length 2w; count how many form the outer perimeter.", "5 sides × 2w = 140."],
      "source": "Nan Chiau 2022 P6 Prelim Q33",
      "image_needed": true,
      "image_options": false,
      "image_file": "q33.png",
      "image_page": 23,
      "image_bbox": [0.13, 0.65, 0.45, 0.80],
      "image_loc": "equilateral triangle ABC joined to square BCDE with 2w cm label, lower page 23 (Paper 2 p1)",
      "notes": "Paper 2 Q3. Answer key derives 28 per side, w = 14."
    },
    {
      "n": 34,
      "type_id": 0,
      "question": "In the square grid, line BC has been drawn. (a) Draw a line parallel to line BC, passing through Point A. (b) Draw a right-angled triangle BCD, such that line BC = CD and BC is perpendicular to line CD.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 101,
      "difficulty_id": 2,
      "explanation": "(a) Draw through A a line with the same gradient as BC (parallel). (b) At C, draw CD perpendicular to BC with CD = BC, then join BD to form right-angled triangle BCD.",
      "hints": ["Parallel lines have the same slope on the grid.", "Perpendicular means a 90° turn at C; keep CD equal in length to BC."],
      "source": "Nan Chiau 2022 P6 Prelim Q34",
      "image_needed": true,
      "image_options": false,
      "image_file": "q34.png",
      "image_page": 24,
      "image_bbox": [0.13, 0.22, 0.70, 0.48],
      "image_loc": "square grid with points A, B, C and line BC drawn, middle of page 24 (Paper 2 p2)",
      "notes": "Paper 2 Q4. Drawing/construction task → interactive, type_id 0, skipped on insert."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "The graph shows the fare a taxi company charges for the first 10 kilometres. John took a taxi and travelled for 9 km. How much did he pay? (Give your answer in $.)<br>[?]",
      "answer0": "28.50",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 147,
      "difficulty_id": 3,
      "explanation": "From the graph the line rises from ($2 at 6 km region); key: (33 − 24) ÷ 2 = 4.5 per km on the linear part; fare at 9 km = 24 + 4.5 = $28.50.",
      "hints": ["Find the rate per km from two points on the straight section.", "Add the per-km charge to the reading at 8 km."],
      "source": "Nan Chiau 2022 P6 Prelim Q35",
      "image_needed": true,
      "image_options": false,
      "image_file": "q35.png",
      "image_page": 25,
      "image_bbox": [0.22, 0.13, 0.72, 0.38],
      "image_loc": "taxi fare ($) vs distance (km) line graph, upper page 25 (Paper 2 p3)",
      "notes": "Paper 2 Q5. Answer key: (33−24)÷2=4.5; 24+4.5=$28.50. Units: dollars."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "Simon could buy 9 notebooks and 54 pencils with $64.80. With that same amount of money, he could buy 24 notebooks. He then decided to buy only pencils. What was the most number of pencils Simon could buy with $64.80?<br>[?]",
      "answer0": "86",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 118,
      "difficulty_id": 3,
      "explanation": "1 notebook = $64.80 ÷ 24 = $2.70. Cost of 54 pencils = 64.80 − 9 × 2.70 = 64.80 − 24.30 = $40.50; 1 pencil = 40.50 ÷ 54 = $0.75. Pencils with $64.80 = 64.80 ÷ 0.75 = 86.4 → at most 86.",
      "hints": ["Find the price of one notebook from the 24-notebook fact.", "Use that to find the pencil price, then divide $64.80 by it."],
      "source": "Nan Chiau 2022 P6 Prelim Q36",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q6 [3m]. Answer key derives ≈86 pencils."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "Two machines, X and Y, cut shapes. Machine X cuts 12 pieces per second; Machine Y cuts 20 pieces every 3 seconds. Machine X started cutting at 08 00 and stopped at 08 30. Machine Y cut shapes for 45 minutes. How many shapes were cut in total by the two machines?<br>[?]",
      "answer0": "39600",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Machine X: 30 min = 1800 s × 12 = 21600. Machine Y: 45 min = 2700 s; rate 20/3 per s; 2700 ÷ 3 = 900 × 20 = 18000. Total = 21600 + 18000 = 39600.",
      "hints": ["Convert each cutting time to seconds.", "Add the two machine outputs."],
      "source": "Nan Chiau 2022 P6 Prelim Q37",
      "image_needed": true,
      "image_options": false,
      "image_file": "q37.png",
      "image_page": 27,
      "image_bbox": [0.16, 0.13, 0.62, 0.24],
      "image_loc": "two machines X and Y with rate labels, upper page 27 (Paper 2 p5)",
      "notes": "Paper 2 Q7 [3m]. Answer key: 720×30=21600; 60÷3=20; 20×20=400; 400×45=18000; total 39600. Machine images decorative; can omit if not needed."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "PQRS is a parallelogram. TSR and QVU are straight lines. PST and SRU are isosceles triangles. PT = PS and SR = SU. ∠PST (at S, in triangle PST) = 68° and ∠VRU = 62°, ∠RUS = 22°. (a) Find ∠RSU. (b) Find ∠UQR. (Give your answers in degrees.)<br>(a) [?] (b) [?]",
      "answer0": "56",
      "answer1": "28",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "(a) Triangle SRU is isosceles (SR = SU) with base angle ∠VRU = 62°, so ∠RSU = 180 − 62×2 = 56°. (b) ∠PST = 68° → ∠PTS = 68°, so ∠TPS = 180 − 68×2... key uses 180−68=112, 180−112=68, then ∠UQR = 180 − 68 − 62 − 22 = 28°.",
      "hints": ["Use the isosceles triangle SRU for part (a).", "Use parallelogram and straight-line angle properties for part (b)."],
      "source": "Nan Chiau 2022 P6 Prelim Q38",
      "image_needed": true,
      "image_options": false,
      "image_file": "q38.png",
      "image_page": 28,
      "image_bbox": [0.20, 0.18, 0.70, 0.48],
      "image_loc": "parallelogram PQRS with triangles PST and SRU, angles 68°, 62°, 22°, upper-middle page 28 (Paper 2 p6)",
      "notes": "Paper 2 Q8. Answer key: (a) 180−62×2=56°; (b) 180−68=112, 180−112=68, 180−68−62−22=28°. Two blanks."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "The bar graph shows the number of cups of tea sold by a shop from June to September (scale not shown). (a) What was the percentage increase in the number of cups of tea sold from July to August? (b) The average number of cups of tea sold per month from June to September was 845. How many cups of tea were sold in September?<br>(a) [?] (b) [?]",
      "answer0": "37.5",
      "answer1": "520",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 208,
      "difficulty_id": 3,
      "explanation": "(a) From the bars (Jul = 8 units, Aug = 11 units): increase = (11−8)/8 × 100% = 3/8 × 100% = 37.5%. (b) Total = 845 × 4 = 3380. Units sum (3+8+11+4) = 26 → 1 unit = 3380 ÷ 26 = 130; Sep = 4 units = ... key gives 730×4 path; September = 520.",
      "hints": ["Percentage increase = increase ÷ original × 100%.", "Use total = average × 4 to find September's value."],
      "source": "Nan Chiau 2022 P6 Prelim Q39",
      "image_needed": true,
      "image_options": false,
      "image_file": "q39.png",
      "image_page": 29,
      "image_bbox": [0.26, 0.14, 0.78, 0.38],
      "image_loc": "bar graph of cups of tea sold Jun-Sep (no scale), upper page 29 (Paper 2 p7)",
      "notes": "Paper 2 Q9. Answer key: (a) (11−8)/8×100%=37.5%; (b) 845×4=3380; 3380÷(3+8+11+4)=130; September=520. Two blanks; (a) is a decimal percentage."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "In the figure, the diameters of three different semicircles form the sides of a right-angled triangle ABC. AB = 12 cm, BC = 16 cm and AC = 20 cm. Find the total area of the shaded parts. (Take \\(\\pi = 3.14\\).) (Give your answer in cm².)<br>[?]",
      "answer0": "192",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 222,
      "difficulty_id": 3,
      "explanation": "Triangle area = 12×16÷2 = 96. Semicircles on AB (r=6), BC (r=8), AC (r=10). Shaded = (semicircle on AB) + (semicircle on BC) + triangle − (semicircle on AC). Key: 50π − (50π − 96) + 96 = 192 cm².",
      "hints": ["Area of triangle = 1/2 × base × height.", "Add the two small semicircles and triangle, subtract the large semicircle (on the hypotenuse)."],
      "source": "Nan Chiau 2022 P6 Prelim Q40",
      "image_needed": true,
      "image_options": false,
      "image_file": "q40.png",
      "image_page": 30,
      "image_bbox": [0.24, 0.14, 0.66, 0.32],
      "image_loc": "right-angled triangle ABC with three semicircles on its sides, shaded regions, upper page 30 (Paper 2 p8)",
      "notes": "Paper 2 Q10 [4m]. Answer key: triangle 96; r=6 semi=18π, r=8 semi=32π(=50π with AB), r=10 semi=50π; result 192 cm²."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "Anne, Beth and Crystal bought a present. The ratio of the amount Anne paid to the total amount Beth and Crystal paid was 3 : 5. The ratio of the amount Crystal paid to the total amount Anne and Beth paid was 2 : 3. Crystal paid $21 more than Beth. How much did the person who paid the least pay for the present?<br>[?]",
      "answer0": "27",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "A : (B+C) = 3 : 5 → A = 15, B+C = 25 (total 40). C : (A+B) = 2 : 3 → C = 16, A+B = 24 (total 40). So A = 15, C = 16, B = 40 − 15 − 16 = 9. C − B = 16 − 9 = 7 units = $21 → 1 unit = $3. Beth pays least = 9 units = $27.",
      "hints": ["Make both ratios share the same total (8 parts and 5 parts → common total 40).", "Find each person's units, then use C − B = $21."],
      "source": "Nan Chiau 2022 P6 Prelim Q41",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q11 [3m]. Answer key: A=15,C=16,B=9 (of 40); 16−9=7; 21÷7=3; 9×3=$27. Beth paid the least, $27. The question asks who paid least + amount; here numeric answer = 27 (Beth). Person noted in explanation/notes."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "Mrs Raja made some pineapple tarts and nutella tarts. She sold \\(\\dfrac{7}{10}\\) of her tarts. 75% of the tarts sold were nutella tarts. She sold 350 pineapple tarts. 30% of the unsold tarts were pineapple tarts. How many pineapple tarts were not sold?<br>[?]",
      "answer0": "180",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Sold = 7/10 of total; pineapple sold = 25% of sold = 350 → sold = 1400, total = 2000. Unsold = 3/10 of 2000 = 600. Pineapple unsold = 30% of 600 = 180.",
      "hints": ["Pineapple tarts sold = 25% of all sold; use 350 to find total sold.", "Unsold = 3/10 of total; take 30% of that."],
      "source": "Nan Chiau 2022 P6 Prelim Q42",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q12 [3m]. Answer key: 100−75=25; 7/10×25/100=7/40; 1−7/10=3/10; 3/10×30/100=9/100; 350÷7×40÷100×9=180."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "In a shop, erasers and pencils are sold only in boxes. A box of 3 erasers costs $5.20; a box of 5 pencils costs $6.65. (a) Mrs Lim wants to get 40 erasers and 78 pencils for her students. What is the least amount of money she will need to spend on the erasers and pencils? (Give your answer in $.) (b) Mr Wong spent $328.30 to buy a total of 57 boxes of erasers and pencils. How many boxes of pencils did he buy?<br>(a) [?] (b) [?]",
      "answer0": "179.20",
      "answer1": "22",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 131,
      "difficulty_id": 3,
      "explanation": "(a) 40 erasers → 40÷3 = 13 R1 → 14 boxes × $5.20 = $72.80. 78 pencils → 78÷5 = 15 R3 → 16 boxes × $6.65 = $106.40. Total = $179.20. (b) If all 57 were eraser boxes: 57×5.20 = $296.40; extra $328.30 − 296.40 = $31.90; each swap to pencil box adds 6.65 − 5.20 = $1.45; 31.90 ÷ 1.45 = 22 pencil boxes.",
      "hints": ["Round up the number of boxes needed for each item.", "(b) Assume all eraser boxes first, then swap; each swap adds $1.45."],
      "source": "Nan Chiau 2022 P6 Prelim Q43",
      "image_needed": true,
      "image_options": false,
      "image_file": "q43.png",
      "image_page": 33,
      "image_bbox": [0.18, 0.12, 0.62, 0.24],
      "image_loc": "box of 3 erasers ($5.20) and box of 5 pencils ($6.65), upper page 33 (Paper 2 p11)",
      "notes": "Paper 2 Q13. Answer key: (a) 14×5.2=72.8, 16×6.65+72.8=$179.20; (b) 296.4, 328.3−296.4=31.9, 1.45, 31.9÷1.45=22. Two blanks; (a) dollars."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "JKLM is a parallelogram, folded along line OP. ∠MJL... ∠KJ at J = 70°, ∠MPO = 105°. (a) Find ∠x (∠KLO at L). (b) Find ∠LOP. (Give your answers in degrees.)<br>(a) [?] (b) [?]",
      "answer0": "75",
      "answer1": "72.5",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "(a) In parallelogram, ∠JLM = 180 − 70 = 110° (co-interior); using the fold, ∠x = 360 − 110 − 70 − 105 = 75°. (b) Fold makes triangle isosceles: ∠LPO = (180 − 105) ÷ 2 = 37.5°; ∠LOP = 180 − 37.5 − 70 = 72.5°.",
      "hints": ["Use co-interior angles of the parallelogram and angles around a point.", "The fold creates equal angles; use the isosceles property."],
      "source": "Nan Chiau 2022 P6 Prelim Q44",
      "image_needed": true,
      "image_options": false,
      "image_file": "q44.png",
      "image_page": 34,
      "image_bbox": [0.18, 0.13, 0.62, 0.33],
      "image_loc": "parallelogram JKLM folded along OP, angles 70°, x, 105°, upper page 34 (Paper 2 p12)",
      "notes": "Paper 2 Q14. Answer key: (a) 180−70=110, 360−110−70−105=75°; (b) (180−105)÷2=37.5, 180−37.5−70=72.5°. Part (c) 'circle the words' (is not/is not) is interactive and dropped. (a) is a whole number, (b) a decimal."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "Mrs Sim baked some cookies and packed all the cookies in 14 small boxes and 3 large boxes. She filled each small box with the same number of cookies and each large box with the same number of cookies. There were 4 more cookies in each large box than in each small box. \\(\\dfrac{7}{9}\\) of the cookies baked were packed in the small boxes. How many cookies were there in each small box?<br>[?]",
      "answer0": "12",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Small boxes hold 7/9 of cookies, large boxes hold 2/9. Per box: small boxes share 7/9 over 14 boxes; large share 2/9 over 3 boxes. Key: difference 4 × 3 = 12 / (path) gives each small box = 12 cookies.",
      "hints": ["Let small-box total = 7 units, large-box total = 2 units (of 9).", "Use 'each large has 4 more than each small' with 14 small and 3 large boxes."],
      "source": "Nan Chiau 2022 P6 Prelim Q45",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q15 [5m]. Answer key: 7/9÷14 vs 2/9÷3; 1−7/9=2/9; (2/9 over 3) − (7/9 over 14)=1/18 per-box gap; 4×3=12; (12×8)÷6÷3=... final each small box = 12."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "An empty L-shaped container has a tap turned on, with water flowing in at 0.8 litres per minute. The tap was turned off 6 minutes later. The container's upright part is 10 cm by 6 cm; the base part is 30 cm long, 10 cm wide and 12 cm tall. (a) Find the height of the water level from the base of the container. (Give your answer in cm.) (b) All the water was then poured into a cubical tank with a base area of 289 cm². How much more water was needed to fill the tank to its brim? (Give your answer in cm³.)<br>(a) [?] (b) [?]",
      "answer0": "32",
      "answer1": "113",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 229,
      "difficulty_id": 3,
      "explanation": "Water = 0.8 × 6 = 4.8 ℓ = 4800 cm³. Base section volume = 12 × 10 × 30 = 3600; remaining 4800 − 3600 = 1200 fills the upright (cross-section 10×6=60): 1200 ÷ 60 = 20 cm above. Total height = 20 + 12 = 32 cm. (b) Cubical tank base 289 cm² → side 17 cm, volume 17³ = 4913; more water = 4913 − 4800 = 113 cm³.",
      "hints": ["Volume of water = flow rate × time (convert litres to cm³).", "(b) Cubical tank: side = √base area; volume = side³."],
      "source": "Nan Chiau 2022 P6 Prelim Q46",
      "image_needed": true,
      "image_options": false,
      "image_file": "q46.png",
      "image_page": 36,
      "image_bbox": [0.22, 0.13, 0.70, 0.40],
      "image_loc": "L-shaped container with tap, dimensions 10cm, 6cm, 30cm, 12cm, 10cm, upper page 36 (Paper 2 p14)",
      "notes": "Paper 2 Q16. Answer key: (a) 800×6=4800; 4800−12×10×30=1200; 1200÷10÷6=20; 20+12=32cm; (b) 289=17² (cube side 17), 17³−4800=113cm³. Two blanks."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "Four identical right-angled triangles are used to form the figure shown. BC = 9 cm. The perimeter of the figure is 72 cm. (a) Find the perimeter of each right-angled triangle. (Give your answer in cm.) (b) AC is 6 cm shorter than the total lengths of AB and BC. Find the area of the figure. (Give your answer in cm².)<br>(a) [?] (b) [?]",
      "answer0": "36",
      "answer1": "216",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 138,
      "difficulty_id": 3,
      "explanation": "(a) The figure's perimeter (72) is made of the outer slant sides; with BC=9 contributing, perimeter of each triangle = (72 + 8×9)/4 = (72+72)/4 = 36 cm. (b) AB + BC + AC = 36; AC = (AB+BC) − 6. With BC=9: AB+BC = (36+6)÷2 = 21, so AB = 12. Area of figure = 4 × (1/2 × AB × BC) = 12 × 9 × 2 = 216 cm².",
      "hints": ["(a) Relate the figure's perimeter to the triangle sides using BC = 9.", "(b) Use AC = (AB+BC) − 6 with the triangle perimeter to find AB, then area = 4 triangles."],
      "source": "Nan Chiau 2022 P6 Prelim Q47",
      "image_needed": true,
      "image_options": false,
      "image_file": "q47.png",
      "image_page": 37,
      "image_bbox": [0.13, 0.13, 0.58, 0.40],
      "image_loc": "four identical right-angled triangles forming a windmill/star figure, BC=9cm label, upper page 37 (Paper 2 p15)",
      "notes": "Paper 2 Q17. Answer key: (a) (72+8×9)÷4=36cm; (b) (36+6)÷2−9=12, 12×9×2=216cm². Two blanks."
    }
  ]
}