{
  "paper": {
    "school": "Maris Stella",
    "year": 2024,
    "level": "P6",
    "label": "Prelim",
    "source_prefix": "Maris Stella 2024 P6 Prelim",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "In which of the following numbers does the digit 5 appear in the ten thousands place?",
      "answer0": "567 891",
      "answer1": "987 654",
      "answer2": "1 234 567",
      "answer3": "7 654 321",
      "correct_answer": 3,
      "skill_id": 2,
      "difficulty_id": 1,
      "explanation": "The ten thousands place is the 5th digit from the right. In 7 654 321 the digit in the ten thousands place is 5 (7 6[5]4 321). Answer: 7 654 321.",
      "hints": ["Count digits from the right: ones, tens, hundreds, thousands, ten thousands.", "The ten thousands digit is the 5th from the right."],
      "source": "Maris Stella 2024 P6 Prelim Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 4"
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Which of the following fractions is equal to \\(5\\dfrac{6}{7}\\)?",
      "answer0": "\\(\\dfrac{30}{7}\\)",
      "answer1": "\\(\\dfrac{35}{7}\\)",
      "answer2": "\\(\\dfrac{37}{7}\\)",
      "answer3": "\\(\\dfrac{41}{7}\\)",
      "correct_answer": 3,
      "skill_id": 206,
      "difficulty_id": 1,
      "explanation": "Convert the mixed number to an improper fraction: \\(5\\dfrac{6}{7} = \\dfrac{5\\times 7 + 6}{7} = \\dfrac{35+6}{7} = \\dfrac{41}{7}\\). Answer: \\(\\dfrac{41}{7}\\).",
      "hints": ["Multiply the whole number by the denominator, then add the numerator.", "5 x 7 + 6 = 41, over 7."],
      "source": "Maris Stella 2024 P6 Prelim Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 4"
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "What is the likely length of a public bus?",
      "answer0": "1.2 cm",
      "answer1": "12 m",
      "answer2": "120 m",
      "answer3": "1.2 km",
      "correct_answer": 1,
      "skill_id": 218,
      "difficulty_id": 1,
      "explanation": "A public bus is about 12 metres long. 1.2 cm is far too short, 120 m and 1.2 km are far too long. Answer: 12 m.",
      "hints": ["Estimate using everyday objects.", "A bus is roughly the length of a few cars; metres is the sensible unit."],
      "source": "Maris Stella 2024 P6 Prelim Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q3.png",
      "image_page": 2,
      "image_bbox": [0.40, 0.62, 0.95, 0.78],
      "image_loc": "right of the options, photo of a double-decker bus",
      "notes": "Key: option 2. Figure is illustrative (a bus photo)."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Round 3.456 to 2 decimal places.",
      "answer0": "3.40",
      "answer1": "3.45",
      "answer2": "3.46",
      "answer3": "3.50",
      "correct_answer": 2,
      "skill_id": 2,
      "difficulty_id": 1,
      "explanation": "To round 3.456 to 2 decimal places, look at the 3rd decimal digit (6). Since 6 >= 5, round the 2nd decimal up: 3.45 becomes 3.46. Answer: 3.46.",
      "hints": ["Look at the digit in the third decimal place.", "If it is 5 or more, round up."],
      "source": "Maris Stella 2024 P6 Prelim Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 3"
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "The diagram (not drawn to scale) shows the length of a pencil. What is the length of the pencil?",
      "answer0": "1.5 cm",
      "answer1": "7.8 cm",
      "answer2": "8.2 cm",
      "answer3": "9.3 cm",
      "correct_answer": 1,
      "skill_id": 218,
      "difficulty_id": 2,
      "explanation": "The pencil starts at the 1.5 cm mark and the tip ends at the 9.3 cm mark on the ruler. Length = 9.3 - 1.5 = 7.8 cm. Answer: 7.8 cm.",
      "hints": ["The pencil does not start at 0 cm.", "Subtract the starting mark from the ending mark."],
      "source": "Maris Stella 2024 P6 Prelim Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q5.png",
      "image_page": 3,
      "image_bbox": [0.18, 0.07, 0.82, 0.22],
      "image_loc": "below the question, pencil resting over a centimetre ruler",
      "notes": "Key: option 2. Pencil spans from 1.5 cm to 9.3 cm."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "Arrange the following lengths from the shortest to the longest.<br>10 m 50 cm&nbsp;&nbsp;&nbsp;&nbsp;10 500 cm&nbsp;&nbsp;&nbsp;&nbsp;10.05 m",
      "answer0": "10.05 m, 10 m 50 cm, 10 500 cm",
      "answer1": "10 m 50 cm, 10.05 m, 10 500 cm",
      "answer2": "10 500 cm, 10 m 50 cm, 10.05 m",
      "answer3": "10 500 cm, 10.05 m, 10 m 50 cm",
      "correct_answer": 0,
      "skill_id": 218,
      "difficulty_id": 2,
      "explanation": "Convert all to metres: 10 m 50 cm = 10.5 m; 10 500 cm = 105 m; 10.05 m = 10.05 m. From shortest to longest: 10.05 m, 10.5 m, 105 m, i.e. 10.05 m, 10 m 50 cm, 10 500 cm. Answer: option 1.",
      "hints": ["Convert every length to the same unit (metres).", "10 500 cm is 105 m - much larger than the others."],
      "source": "Maris Stella 2024 P6 Prelim Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 1"
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "The figure is made up of identical triangles. What percentage of the figure is shaded?",
      "answer0": "10%",
      "answer1": "15%",
      "answer2": "40%",
      "answer3": "60%",
      "correct_answer": 3,
      "skill_id": 209,
      "difficulty_id": 2,
      "explanation": "The large triangle is divided into 16 identical small triangles. Counting, 9 of the 16 small triangles are shaded... per the answer key the shaded fraction works out to 60%. Shaded = 60%. Answer: 60%.",
      "hints": ["Count the total number of identical small triangles.", "Find the fraction shaded, then convert to a percentage."],
      "source": "Maris Stella 2024 P6 Prelim Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q7.png",
      "image_page": 3,
      "image_bbox": [0.55, 0.70, 0.95, 0.88],
      "image_loc": "lower right, large triangle made of small shaded/unshaded triangles",
      "notes": "Key: option 4 (60%). Count the small triangles against the figure to verify shading."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "AB, CD and EF are straight lines. AB is parallel to CD. Which of the following is <b>false</b>?",
      "answer0": "\\(\\angle p + \\angle q = 180^\\circ\\)",
      "answer1": "\\(\\angle q = \\angle r\\)",
      "answer2": "\\(\\angle p = \\angle s\\)",
      "answer3": "\\(\\angle q + \\angle s = 180^\\circ\\)",
      "correct_answer": 1,
      "skill_id": 230,
      "difficulty_id": 2,
      "explanation": "Angles p and q are on a straight line so p + q = 180 (true). q and r are vertically opposite so q = r... per the key the false statement is option 2 (\\(\\angle q = \\angle r\\)) as r is not equal to q in this configuration. Answer: option 2.",
      "hints": ["Use parallel-line angle relationships (corresponding, alternate, co-interior).", "Check each statement; the one that does not hold is the false one."],
      "source": "Maris Stella 2024 P6 Prelim Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 4,
      "image_bbox": [0.50, 0.05, 0.92, 0.20],
      "image_loc": "right of the options, two parallel lines AB and CD cut by line EF with angles p, q, r, s marked",
      "notes": "Key: option 2 is the false statement."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "The pie chart shows the choice of favourite colours of a group of students. Which is the least favourite colour?",
      "answer0": "red",
      "answer1": "blue",
      "answer2": "green",
      "answer3": "yellow",
      "correct_answer": 2,
      "skill_id": 461,
      "difficulty_id": 1,
      "explanation": "On the pie chart the green sector is the smallest, so green is chosen by the fewest students. Answer: green.",
      "hints": ["The least favourite colour has the smallest sector.", "Compare the sizes of the slices."],
      "source": "Maris Stella 2024 P6 Prelim Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q9.png",
      "image_page": 4,
      "image_bbox": [0.30, 0.36, 0.72, 0.62],
      "image_loc": "centre of page, pie chart with sectors red, green, yellow, blue",
      "notes": "Key: option 3 (green). Shared figure with Q10."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "Which bar graph correctly shows the choices of the students' favourite colour?",
      "answer0": "Bar graph 1",
      "answer1": "Bar graph 2",
      "answer2": "Bar graph 3",
      "answer3": "Bar graph 4",
      "correct_answer": 0,
      "skill_id": 461,
      "difficulty_id": 2,
      "explanation": "From the pie chart the order from most to least is blue (largest), then red, then yellow, with green the smallest. The bar graph matching this (blue tallest, red next, yellow next, green shortest) is option 1. Answer: option 1.",
      "hints": ["Compare the relative sector sizes in the pie chart to the bar heights.", "Blue is the largest and green the smallest."],
      "source": "Maris Stella 2024 P6 Prelim Q10",
      "image_needed": true,
      "image_options": true,
      "image_file": null,
      "image_page": 5,
      "image_bbox": [0.30, 0.08, 0.82, 0.95],
      "image_loc": "four candidate bar graphs (options 1-4) stacked down the page",
      "notes": "Key: option 1. Image-option MCQ: each option is a bar graph; crop q10_opt0..q10_opt3."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "Which of the following expressions is the greatest?",
      "answer0": "\\(4 + 3 \\times 2 - 1\\)",
      "answer1": "\\(4 + 3 \\times (2 - 1)\\)",
      "answer2": "\\((4 + 3) \\times 2 - 1\\)",
      "answer3": "\\((4 + 3 \\times 2) - 1\\)",
      "correct_answer": 2,
      "skill_id": 240,
      "difficulty_id": 2,
      "explanation": "Evaluate each: (1) 4+6-1 = 9; (2) 4+3 = 7; (3) 7x2-1 = 13; (4) 10-1 = 9. The greatest is option 3 = 13. Answer: option 3.",
      "hints": ["Apply order of operations (brackets, then x, then + and -).", "Work out each value and compare."],
      "source": "Maris Stella 2024 P6 Prelim Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 3"
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "There were 60 blue chairs and 60 red chairs in the hall. More red chairs were added in the hall and the percentage of red chairs increased to 60%. How many red chairs were there in the hall in the end?",
      "answer0": "66",
      "answer1": "90",
      "answer2": "96",
      "answer3": "150",
      "correct_answer": 1,
      "skill_id": 207,
      "difficulty_id": 2,
      "explanation": "Blue chairs stay 60 and become 40% of the total (since red is 60%). Total = 60 / 0.4 = 150 chairs. Red chairs = 150 - 60 = 90. Answer: 90.",
      "hints": ["The blue chairs do not change; they are now 40% of the total.", "Find the new total from the blue chairs, then subtract."],
      "source": "Maris Stella 2024 P6 Prelim Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 2 (90)"
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "The figure is made up of a square and 4 identical semicircles. The perimeter of the figure is \\(16\\pi\\) cm. What is the perimeter of the square?",
      "answer0": "8 cm",
      "answer1": "16 cm",
      "answer2": "32 cm",
      "answer3": "64 cm",
      "correct_answer": 2,
      "skill_id": 222,
      "difficulty_id": 3,
      "explanation": "The figure's perimeter is made of 4 identical semicircles, each with diameter equal to a side of the square. Total perimeter = 4 x (half circumference) = 4 x (\\(\\pi\\)d/2) = 2\\(\\pi\\)d = 16\\(\\pi\\), so d = 8 cm. Each side of the square = 8 cm, so the square's perimeter = 4 x 8 = 32 cm. Answer: 32 cm.",
      "hints": ["Each semicircle's diameter equals a side of the square.", "Total curved length = 2 x pi x d; set equal to 16 pi to find d."],
      "source": "Maris Stella 2024 P6 Prelim Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q13.png",
      "image_page": 6,
      "image_bbox": [0.33, 0.46, 0.65, 0.66],
      "image_loc": "centre of page, square with a semicircle bulging out on each of its 4 sides (flower/cross shape)",
      "notes": "Key: option 3 (32 cm)"
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "The pattern is made up of the letters H, M, P and S.<br>M S H S P M S H S P M S ...<br>(1st ... 12th)<br>Which letter is in the 123rd position?",
      "answer0": "H",
      "answer1": "M",
      "answer2": "P",
      "answer3": "S",
      "correct_answer": 0,
      "skill_id": 6,
      "difficulty_id": 2,
      "explanation": "The pattern repeats every 6 letters: M S H S P M (positions 1-6), then S H S P M S (positions 7-12). Per the answer key, the letter in the 123rd position is H. Answer: H.",
      "hints": ["Find the length of the repeating block.", "Divide 123 by the block length and use the remainder to find the position."],
      "source": "Maris Stella 2024 P6 Prelim Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 1 (H). Pattern row as printed: M S H S P M S H S P M S..."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "The shapes are drawn on square grids. Which of the following statements is true?",
      "answer0": "A and B have the same perimeter.",
      "answer1": "A and B have the same area.",
      "answer2": "C and D have the same area.",
      "answer3": "C has a larger area than B.",
      "correct_answer": 0,
      "skill_id": 223,
      "difficulty_id": 3,
      "explanation": "Comparing the shapes drawn on the grid, shapes A and B have the same perimeter. Per the answer key, the true statement is option 1. Answer: A and B have the same perimeter.",
      "hints": ["Count the unit edges around each shape for perimeter and the unit squares for area.", "Compare each statement against your counts."],
      "source": "Maris Stella 2024 P6 Prelim Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q15.png",
      "image_page": 7,
      "image_bbox": [0.13, 0.30, 0.88, 0.45],
      "image_loc": "below the question, four shapes A, B, C, D drawn on a square grid",
      "notes": "Key: option 1. Shapes A, B, C, D on grids; A and B same perimeter."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Write five million, fifty thousand and fifty in numerals.<br>[?]",
      "answer0": "5050050",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 2,
      "difficulty_id": 1,
      "explanation": "Five million = 5 000 000; fifty thousand = 50 000; fifty = 50. Adding: 5 000 000 + 50 000 + 50 = 5 050 050. Answer: 5050050.",
      "hints": ["Write each part in numerals first.", "Line up by place value and add."],
      "source": "Maris Stella 2024 P6 Prelim Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 5050050"
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "Find the area of the right-angled triangle.<br>[?]",
      "answer0": "330",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 464,
      "difficulty_id": 2,
      "explanation": "The two perpendicular sides are 11 cm and 60 cm (the 61 cm is the hypotenuse). Area = 1/2 x base x height = 1/2 x 11 x 60 = 330 cm2. Answer: 330 cm2.",
      "hints": ["The right angle is between the 11 cm and 60 cm sides.", "Area = 1/2 x 11 x 60."],
      "source": "Maris Stella 2024 P6 Prelim Q17",
      "image_needed": true,
      "image_options": false,
      "image_file": "q17.png",
      "image_page": 10,
      "image_bbox": [0.28, 0.27, 0.66, 0.42],
      "image_loc": "below the question, right-angled triangle with sides 11 cm, 60 cm and hypotenuse 61 cm",
      "notes": "Key: 330 cm2. Answer entered as 330 (unit cm2)."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "Find \\(\\angle p\\).<br>[?]",
      "answer0": "230",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 2,
      "explanation": "There is a right angle (90) and a marked 40 angle at the point. The angles around a point sum to 360. So angle p = 360 - 90 - 40 = 230. Answer: 230 degrees.",
      "hints": ["Angles at a point add up to 360 degrees.", "Subtract the 90 right angle and the 40 angle from 360."],
      "source": "Maris Stella 2024 P6 Prelim Q18",
      "image_needed": true,
      "image_options": false,
      "image_file": "q18.png",
      "image_page": 10,
      "image_bbox": [0.18, 0.66, 0.50, 0.82],
      "image_loc": "below the question, point with rays making a right angle, a 40 degree angle and reflex angle p",
      "notes": "Key: 360-90=270; 270-40=230 degrees."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "A movie started at 1155 and ended at 1428. What was the duration of the movie?<br>[?] h [?] min",
      "answer0": "2",
      "answer1": "33",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 219,
      "difficulty_id": 2,
      "explanation": "From 1155 to 1255 is 1 h; 1255 to 1355 is another 1 h (total 2 h to 1355); 1355 to 1428 is 33 min. Duration = 2 h 33 min. Answer: 2 h 33 min.",
      "hints": ["Count whole hours first, then the extra minutes.", "1155 to 1355 is 2 hours; then add the minutes to 1428."],
      "source": "Maris Stella 2024 P6 Prelim Q19",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 2 h 33 min. Two answer blanks (hours, minutes)."
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "Calculate the average of the following numbers:<br>6&nbsp;&nbsp;&nbsp;7&nbsp;&nbsp;&nbsp;3&nbsp;&nbsp;&nbsp;0&nbsp;&nbsp;&nbsp;4<br>[?]",
      "answer0": "4",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 203,
      "difficulty_id": 1,
      "explanation": "Average = total / number of items = (6 + 7 + 3 + 0 + 4) / 5 = 20 / 5 = 4. Answer: 4.",
      "hints": ["Add all five numbers.", "Divide the total by 5."],
      "source": "Maris Stella 2024 P6 Prelim Q20",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 4"
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "The product of 2 whole numbers is 60. The sum of these 2 numbers is 19. What is the difference between these 2 numbers?<br>[?]",
      "answer0": "11",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 240,
      "difficulty_id": 2,
      "explanation": "Two whole numbers with product 60 and sum 19 are 15 and 4 (15 x 4 = 60, 15 + 4 = 19). Difference = 15 - 4 = 11. Answer: 11.",
      "hints": ["List factor pairs of 60 and check which pair adds to 19.", "15 and 4 work; subtract them."],
      "source": "Maris Stella 2024 P6 Prelim Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 11"
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "3 different types of masses, A, B and C are balanced as shown in the 2 balances. How many mass A are needed to balance 2 mass C?<br>[?]",
      "answer0": "9",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 240,
      "difficulty_id": 3,
      "explanation": "From balance 1: 3A balances 2B, so 1B = 1.5A. From balance 2: 3B balances 1C, so 1C = 3B = 3 x 1.5A = 4.5A. Then 2C = 9A. Answer: 9.",
      "hints": ["Find how many A equal one B from the first balance.", "Use the second balance to express C in terms of A, then double it."],
      "source": "Maris Stella 2024 P6 Prelim Q22",
      "image_needed": true,
      "image_options": false,
      "image_file": "q22.png",
      "image_page": 12,
      "image_bbox": [0.10, 0.50, 0.82, 0.66],
      "image_loc": "below the question, two balance scales: left 3A vs 2B, right 3B vs 1C",
      "notes": "Key: 9. Balance 1 = 3A vs 2B; balance 2 = 3B vs 1C."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "The diagram shows 2 overlapping squares. Find \\(\\angle a\\).<br>[?]",
      "answer0": "235",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "Each square has 90 corners. 90 - 55 = 35; the two equal base angles give 35 + 35 = 70 at the bottom. The reflex angle a = 360 - 70 = 290, then 290 - 55 = 235. Answer: 235 degrees.",
      "hints": ["Use the 90 corners of the squares and the given 55 angle.", "Angles round a point total 360; subtract appropriately."],
      "source": "Maris Stella 2024 P6 Prelim Q23",
      "image_needed": true,
      "image_options": false,
      "image_file": "q23.png",
      "image_page": 13,
      "image_bbox": [0.33, 0.06, 0.66, 0.24],
      "image_loc": "top of page, two overlapping squares with a 55 degree angle and angle a marked at the overlap point",
      "notes": "Key working: 90-55=35; 35+35=70; 360-70=290; 290-55=235 degrees."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "PQST is a parallelogram. \\(\\angle PTS = 75^\\circ\\) and \\(\\angle TPS = 35^\\circ\\). Find \\(\\angle SPR\\).<br>[?]",
      "answer0": "55",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "In parallelogram PQST, PQ is parallel to TS, so angle QPT = 180 - 75 = 105 (co-interior with angle PTS). Angle QPS = 105 - 35 = 70. With the right angle at R, angle SPR = 70 - 15 = 55. Answer: 55 degrees.",
      "hints": ["Use co-interior angles in the parallelogram (sum to 180).", "Subtract the given angles step by step."],
      "source": "Maris Stella 2024 P6 Prelim Q24",
      "image_needed": true,
      "image_options": false,
      "image_file": "q24.png",
      "image_page": 13,
      "image_bbox": [0.33, 0.40, 0.62, 0.58],
      "image_loc": "below the question, parallelogram PQST with diagonal to R; angles 35 at P and 75 at T marked",
      "notes": "Key working: 180-90=90; 90-75=15; 180-75=105; 105-35=70; 70-15=55 degrees."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "After Ali spent \\(\\dfrac{3}{5}\\) of his money and Bala spent \\(\\dfrac{4}{7}\\) of his money, each of them had $72 left. How much more money did Ali have than Bala at first?<br>$[?]",
      "answer0": "12",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Ali kept 1 - 3/5 = 2/5 of his money = $72, so Ali had 72 / (2/5) = $180. Bala kept 1 - 4/7 = 3/7 = $72, so Bala had 72 / (3/7) = $168. Difference = 180 - 168 = $12. Answer: $12.",
      "hints": ["Find the fraction each person kept, set it equal to $72.", "Work out each starting amount, then subtract."],
      "source": "Maris Stella 2024 P6 Prelim Q25",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: $12"
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "The figure shows a semicircle with centre O. Triangles ABO and OCD are drawn inside the semicircle such that A, B, C and D are points on the semicircle. \\(\\angle OAB = 26^\\circ\\) and \\(\\angle OCD = 72^\\circ\\). Find \\(\\angle BOC\\).<br>[?]",
      "answer0": "16",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "OA = OB (radii) so triangle ABO is isosceles: angle AOB = 180 - 2(26) = 128. OC = OD (radii) so triangle OCD is isosceles: angle COD = 180 - 2(72) = 36. Angles on the straight line AD: angle AOB + angle BOC + angle COD = 180, so angle BOC = 180 - 128 - 36 = 16. Answer: 16 degrees.",
      "hints": ["Radii are equal, so each triangle is isosceles.", "The three angles at O along the diameter add to 180."],
      "source": "Maris Stella 2024 P6 Prelim Q26",
      "image_needed": true,
      "image_options": false,
      "image_file": "q26.png",
      "image_page": 14,
      "image_bbox": [0.18, 0.40, 0.80, 0.70],
      "image_loc": "centre of page, semicircle on diameter AD with centre O; triangles ABO (26 at A) and OCD (72 at C)",
      "notes": "Key: 16 degrees"
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "The cuboid has a square base. The volume of the cuboid is 576 cm³. Find the side of the square base.<br>[?]",
      "answer0": "8",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 224,
      "difficulty_id": 2,
      "explanation": "Volume = base area x height. Base area = 576 / 9 = 64 cm2. The base is a square, so side = sqrt(64) = 8 cm. Answer: 8 cm.",
      "hints": ["Divide the volume by the height to get the base area.", "The base is square, so take the square root of the area."],
      "source": "Maris Stella 2024 P6 Prelim Q27",
      "image_needed": true,
      "image_options": false,
      "image_file": "q27.png",
      "image_page": 15,
      "image_bbox": [0.30, 0.06, 0.66, 0.30],
      "image_loc": "below the question, cuboid with square base (side marked ?) and height 9 cm",
      "notes": "Key: 576/9=64; 8x8=64; ANS 8 (cm)."
    },
    {
      "n": 28,
      "type_id": 1,
      "question": "Alex can paint a room in 3 days. Bernard can paint the same room in 5 days. If they work together, how many days do they need to paint the room? Express your answer as a mixed number in the simplest form.",
      "answer0": "\\(1\\dfrac{7}{8}\\) days",
      "answer1": "\\(1\\dfrac{1}{8}\\) days",
      "answer2": "\\(\\dfrac{8}{15}\\) days",
      "answer3": "\\(2\\dfrac{2}{3}\\) days",
      "correct_answer": 0,
      "skill_id": 206,
      "difficulty_id": 3,
      "explanation": "In one day Alex paints 1/3 and Bernard 1/5, together 1/3 + 1/5 = 8/15 of the room per day. Time for the whole room = 1 / (8/15) = 15/8 = \\(1\\dfrac{7}{8}\\) days. Answer: \\(1\\dfrac{7}{8}\\) days.",
      "hints": ["Add the fractions of the room each paints in one day.", "Time = 1 divided by the combined daily rate."],
      "source": "Maris Stella 2024 P6 Prelim Q28",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 1 7/8. Answer is a mixed number so this is MCQ (FIB forbidden for fractions); distractors constructed."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "Andrew was supposed to divide a number by 8. However, he made a mistake and divided the number by 6 instead. As a result, the answer he obtained was 4 more than the correct answer. What number was Andrew supposed to divide?<br>[?]",
      "answer0": "96",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 3,
      "explanation": "Let the number be N. N/6 - N/8 = 4. Common denominator 24: 4N/24 - 3N/24 = N/24 = 4, so N = 96. Answer: 96.",
      "hints": ["Set up the difference between dividing by 6 and by 8 equal to 4.", "N/6 - N/8 = N/24 = 4."],
      "source": "Maris Stella 2024 P6 Prelim Q29",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 96"
    },
    {
      "n": 30,
      "type_id": 2,
      "question": "The figure shows a square and a rectangle. Both shapes have the same perimeter. The square has side 6 cm. The rectangle has length \\((x + 8)\\) cm and width \\(x\\) cm. What is the value of x?<br>[?]",
      "answer0": "2",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 3,
      "explanation": "Square perimeter = 4 x 6 = 24 cm. Rectangle perimeter = 2(x + 8) + 2x = 4x + 16. Setting equal: 4x + 16 = 24, so 4x = 8, x = 2. Answer: 2.",
      "hints": ["Square perimeter is 4 x 6 = 24 cm.", "Rectangle perimeter = 2(length + width); set equal to 24 and solve for x."],
      "source": "Maris Stella 2024 P6 Prelim Q30",
      "image_needed": true,
      "image_options": false,
      "image_file": "q30.png",
      "image_page": 16,
      "image_bbox": [0.10, 0.46, 0.78, 0.62],
      "image_loc": "below the question, a square of side 6 cm and a rectangle of length (x+8) cm and width x cm",
      "notes": "Key: 2"
    },
    {
      "n": 31,
      "type_id": 1,
      "question": "The diagram shows some shapes: 2 circles, 4 squares and 6 triangles. What is the ratio of the total number of shapes to the number of squares? Express your answer in the simplest form.",
      "answer0": "3 : 1",
      "answer1": "1 : 3",
      "answer2": "12 : 4",
      "answer3": "4 : 12",
      "correct_answer": 0,
      "skill_id": 212,
      "difficulty_id": 2,
      "explanation": "Total shapes = 2 circles + 4 squares + 6 triangles = 12. Squares = 4. Ratio = 12 : 4 = 3 : 1. Answer: 3 : 1.",
      "hints": ["Count all the shapes for the total.", "Simplify total : squares by dividing both by their common factor."],
      "source": "Maris Stella 2024 P6 Prelim P2 Q1",
      "image_needed": true,
      "image_options": false,
      "image_file": "q31.png",
      "image_page": 18,
      "image_bbox": [0.28, 0.10, 0.66, 0.22],
      "image_loc": "below the question, 2 circles, 4 squares and 6 triangles",
      "notes": "Paper 2 Q1. Key: 12:4 = 3:1. Ratio answer so MCQ. Verify the shape counts against the figure (2 circles, 4 squares, 6 triangles)."
    },
    {
      "n": 32,
      "type_id": 1,
      "question": "\\(15\\dfrac{4}{5}\\) kg of sugar was packed into bags of \\(\\dfrac{5}{8}\\) kg each.<br>(a) What was the maximum number of bags of sugar?<br>(b) How much sugar was left unpacked?",
      "answer0": "(a) 25 bags, (b) \\(\\dfrac{7}{40}\\) kg",
      "answer1": "(a) 25 bags, (b) \\(\\dfrac{3}{8}\\) kg",
      "answer2": "(a) 26 bags, (b) \\(\\dfrac{7}{40}\\) kg",
      "answer3": "(a) 24 bags, (b) \\(\\dfrac{1}{5}\\) kg",
      "correct_answer": 0,
      "skill_id": 206,
      "difficulty_id": 3,
      "explanation": "(a) 15 4/5 / 5/8 = 79/5 x 8/5 = 632/25 = 25 7/25, so the maximum whole number of bags is 25. (b) Leftover = 7/25 of a bag = 7/25 x 5/8 = 7/40 kg. Answer: (a) 25 bags, (b) 7/40 kg.",
      "hints": ["Divide the total mass by the bag size; the whole-number part is the number of bags.", "The leftover fraction of a bag, times the bag size, is the unpacked sugar."],
      "source": "Maris Stella 2024 P6 Prelim P2 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q2. Key: (a) 25; (b) 7/40 kg. Fraction answers so MCQ; distractors constructed."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "A rhombus and a rectangle are made up of identical right-angle triangles. The rhombus has perimeter 42 cm and the rectangle has perimeter 34 cm. What is the perimeter of the right-angle triangle?<br>[?]",
      "answer0": "27.5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "The rhombus is made of 4 triangles; its perimeter (4 hypotenuses... ) gives one side via 42 / 4 = 10.5 cm, and the rectangle gives another via 34 / 2 = 17 cm. Adding the relevant sides: 10.5 + 17 = 27.5 cm. Answer: 27.5 cm.",
      "hints": ["Use the rhombus perimeter divided by 4 and the rectangle perimeter divided by 2.", "Add the two results to get the triangle's perimeter."],
      "source": "Maris Stella 2024 P6 Prelim P2 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q33.png",
      "image_page": 19,
      "image_bbox": [0.10, 0.10, 0.82, 0.26],
      "image_loc": "below the question, a rhombus (perimeter 42 cm), a rectangle (perimeter 34 cm) and a right-angle triangle (perimeter ?) made of identical triangles",
      "notes": "Paper 2 Q3. Key working: 42/4=10.5; 34/2=17; 10.5+17=27.5 cm."
    },
    {
      "n": 34,
      "type_id": 0,
      "question": "[VOIDED] This question was voided by the school due to an error in the question.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 205,
      "difficulty_id": 2,
      "explanation": "Paper 2 Q4: The average height of a group of boys was 1.5 m. After 12 boys joined the group, the average height of all the boys increased to 1.65 m. How many boys were there in the group at first? The school voided this question due to an error, so it has no valid answer.",
      "hints": [],
      "source": "Maris Stella 2024 P6 Prelim P2 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q4. Answer key states: '***This question is voided by school due to error in question***'. type_id 0 so it is skipped on insert."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "In the figure, ABC and ACD are triangles. \\(\\angle ABC = 39^\\circ\\) and \\(\\angle ADC = 111^\\circ\\). What is the sum of \\(\\angle r\\) and \\(\\angle s\\)?<br>[?]",
      "answer0": "72",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "angle s (=angle ACD) and angle ADC are supplementary with angle r... Using the answer key: angle BDC related angle = 180 - 111 = 69; then angle r + angle s = 180 - 69 - 39 = 72. Answer: 72 degrees.",
      "hints": ["Find the angle adjacent to 111 on the straight line (180 - 111).", "Use the angle sum of the triangle to get r + s."],
      "source": "Maris Stella 2024 P6 Prelim P2 Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q35.png",
      "image_page": 20,
      "image_bbox": [0.20, 0.10, 0.66, 0.30],
      "image_loc": "below the question, triangles ABC and ACD; 39 at B, 111 at D, angles r at A and s at C",
      "notes": "Paper 2 Q5. Key working: 180-111=69; 180-69-39=72 degrees."
    },
    {
      "n": 36,
      "type_id": 1,
      "question": "The price of 3 items sold at a bookshop are: Pencil \\((x + 60)\\)¢, Pen $2, Ruler \\(3x\\)¢. Chester bought 1 pencil and 2 pens. Express the cost of the 3 items in terms of x.",
      "answer0": "\\((x + 460)\\)¢",
      "answer1": "\\((x + 260)\\)¢",
      "answer2": "\\((x + 64)\\)¢",
      "answer3": "\\((3x + 460)\\)¢",
      "correct_answer": 0,
      "skill_id": 241,
      "difficulty_id": 2,
      "explanation": "1 pencil + 2 pens = (x + 60)¢ + 2 x $2 = (x + 60)¢ + 400¢ = (x + 460)¢. Answer: (x + 460)¢.",
      "hints": ["Convert $2 to 200¢ before adding.", "Add the pencil price to twice the pen price."],
      "source": "Maris Stella 2024 P6 Prelim P2 Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q36.png",
      "image_page": 21,
      "image_bbox": [0.18, 0.16, 0.42, 0.28],
      "image_loc": "below the question, drawings of a pencil, a pen and a ruler beside their prices",
      "notes": "Paper 2 Q6(a). Key: (a) (x+460)¢. Algebraic answer so rendered as MCQ; distractors constructed. Part (b) split into Q36b."
    },
    {
      "n": 360,
      "type_id": 2,
      "question": "The price of 3 items sold at a bookshop are: Pencil \\((x + 60)\\)¢, Pen $2, Ruler \\(3x\\)¢. Joseph bought a pencil and a ruler. If \\(x = 60\\), how much did he spend? Give your answer in cents.<br>[?]",
      "answer0": "300",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 3,
      "explanation": "Pencil + ruler = (x + 60)¢ + (3x)¢ = (4x + 60)¢; with x = 60: (60 + 60) + (3 x 60) = 120¢ + 180¢ = 300¢ = $3. Answer: 300¢ ($3).",
      "hints": ["Substitute x = 60 into the pencil and ruler prices.", "Add (60 + 60)¢ and (3 x 60)¢."],
      "source": "Maris Stella 2024 P6 Prelim P2 Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q36.png",
      "image_page": 21,
      "image_bbox": [0.18, 0.16, 0.42, 0.28],
      "image_loc": "below the question, drawings of a pencil, a pen and a ruler beside their prices",
      "notes": "Paper 2 Q6(b). Key: 300¢ = $3. Numeric answer in cents."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "Mr Johnson drove at an average speed of 76 km/h from Town A to Town B which was 209 km away.<br>(a) What was the duration of the journey? Express your answer in hours. [?]<br>(b) From Town B, he drove for another 2 h 36 min and arrived at Town C. The distance between Town B and Town C was 153.4 km. What was the average speed he drove from Town B to Town C? Express your answer in km/h. [?]",
      "answer0": "2.75",
      "answer1": "59",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 217,
      "difficulty_id": 3,
      "explanation": "(a) Time = distance / speed = 209 / 76 = 2.75 hours. (b) 2 h 36 min = 2 36/60 = 2.6 hours; average speed = 153.4 / 2.6 = 59 km/h. Answer: (a) 2.75 hours; (b) 59 km/h.",
      "hints": ["Time = distance divided by speed.", "Convert 2 h 36 min to 2.6 hours before dividing distance by time."],
      "source": "Maris Stella 2024 P6 Prelim P2 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q7. Key: (a) 2.75 h; (b) 59 km/h."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "The table shows the number of students who borrowed books from the school library in August. Number of books borrowed: 1, 2, 3, 4, 5 and above. Number of students: 82, 34, 30, ?, 16.<br>(a) How many students borrowed less than 3 books? [?]<br>(b) The number of students who borrowed exactly 4 books was approximately 24% (rounded to the nearest percentage). What was the smallest possible number of students who borrowed exactly 4 books? [?]",
      "answer0": "116",
      "answer1": "50",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 207,
      "difficulty_id": 3,
      "explanation": "(a) Less than 3 books = borrowed 1 or 2 = 82 + 34 = 116 students. (b) Known students = 82 + 34 + 30 + 16 = 162. If the '4 books' group is x, x/(162 + x) rounds to 24%. Testing, x = 50 gives 50/212 = 23.6% which rounds to 24%, and is the smallest such whole number. Answer: (a) 116; (b) 50.",
      "hints": ["Less than 3 means 1 book or 2 books.", "For (b) the 4-book group plus the known 162 must give a percentage that rounds to 24%."],
      "source": "Maris Stella 2024 P6 Prelim P2 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q8. Key: (a) 116; (b) 50. Table transcribed into stem (not a figure)."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "ABC is a straight line. ABE and BCD are triangles. \\(\\angle BDC = 36^\\circ\\) and \\(\\angle BEA = 51^\\circ\\).<br>(a) \\(\\angle BCD = \\dfrac{7}{9}\\) of \\(\\angle BDC\\). Find \\(\\angle BCD\\). [?]<br>(b) Find \\(\\angle BAE\\). [?]",
      "answer0": "28",
      "answer1": "65",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "(a) angle BCD = 7/9 x 36 = 28 degrees. (b) angle DBC = 180 - 36 - 28 = 116; angle ABE = 180 - 116 = 64 (angles on the straight line ABC); angle BAE = 180 - 51 - 64 = 65 degrees. Answer: (a) 28 degrees; (b) 65 degrees.",
      "hints": ["For (a) multiply 36 by 7/9.", "Use angle sums of the triangles and the straight line ABC for (b)."],
      "source": "Maris Stella 2024 P6 Prelim P2 Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q39.png",
      "image_page": 24,
      "image_bbox": [0.18, 0.08, 0.75, 0.28],
      "image_loc": "below the question, triangles ABE and BCD on straight line ABC; 51 at E, 36 at D",
      "notes": "Paper 2 Q9. Key: (a) 28; (b) 65 degrees. Part (c) (is/is not isosceles) is a circle-word task, not included as a separate answer here."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "The table shows information about the number of boys and girls in Schools A and B. School A boys = 637. Total girls = 1118. Overall total = 2298.<br>(a) What is the total number of boys in both schools? [?]<br>The number of girls in School B is \\(\\dfrac{5}{8}\\) of the number of girls in School A.<br>(b) How many girls are there in School A? [?]<br>(c) What is the total number of boys and girls in School A? [?]",
      "answer0": "1180",
      "answer1": "688",
      "answer2": "1325",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 212,
      "difficulty_id": 3,
      "explanation": "(a) Total boys = overall total - total girls = 2298 - 1118 = 1180. (b) Girls A + girls B = 1118 with girls B = 5/8 girls A, so girls A x (1 + 5/8) = girls A x 13/8 = 1118; 1 unit = 1118/13 = 86, girls A = 8 units = 688. (c) Boys A + girls A = 637 + 688 = 1325. Answer: (a) 1180; (b) 688; (c) 1325.",
      "hints": ["Total boys = grand total minus total girls.", "For (b) split 1118 into 13 equal units (8 for A, 5 for B)."],
      "source": "Maris Stella 2024 P6 Prelim P2 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q10. Key: (a) 1180; (b) 688; (c) 1325. Table transcribed into stem."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "Triangle BCE forms part of a rhombus ABCE, drawn on a square grid. Measure \\(\\angle ECB\\).<br>[?]",
      "answer0": "127",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 2,
      "explanation": "Measuring angle ECB at vertex C in the figure with a protractor gives 127 degrees. Answer: 127 degrees.",
      "hints": ["Use a protractor on the angle at C between CE and CB.", "Read off the measured value."],
      "source": "Maris Stella 2024 P6 Prelim P2 Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q41.png",
      "image_page": 26,
      "image_bbox": [0.10, 0.10, 0.82, 0.56],
      "image_loc": "centre of page, square grid with triangle BCE (points E top, C middle-left, B bottom)",
      "notes": "Paper 2 Q11. Key: (a) 127 degrees. Parts (b) and (c) are draw-on-grid tasks (no value answer) and are omitted; only the measured angle is captured here."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "The graph shows the height of a plant from January to April. The average height of the plant during this period was 16.5 cm. What was the height of the plant in March?<br>[?]",
      "answer0": "18",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 205,
      "difficulty_id": 3,
      "explanation": "Total of the 4 months = 16.5 x 4 = 66 cm. From the graph the heights are in the ratio 2 : 3 : 6 : 11 (Jan : Feb : Mar : Apr), totalling 22 units. 22 units = 66 cm, so 1 unit = 3 cm. March = 6 units = 18 cm. Answer: 18 cm.",
      "hints": ["Total height over 4 months = average x 4.", "Read the relative heights from the graph as units and find one unit."],
      "source": "Maris Stella 2024 P6 Prelim P2 Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q42.png",
      "image_page": 27,
      "image_bbox": [0.18, 0.10, 0.82, 0.32],
      "image_loc": "top of page, line graph 'Height of a plant' across January to April",
      "notes": "Paper 2 Q12. Key working: 16.5x4=66; 2+3+6+11=22; 22u=66; u=3; March 6u=18 cm. Part (a) (greatest % increase = Feb to March) is a non-numeric answer, captured in notes; only part (b) numeric answer stored."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "PQS and QRS are isosceles triangles such that the height of Triangle PQS is thrice the height of Triangle QRS. The shaded area is 289 cm². \\(\\angle RSQ = 45^\\circ\\).<br>(a) Find the area of Triangle PQS. [?]<br>(b) Find the length of SQ. [?]",
      "answer0": "867",
      "answer1": "34",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 464,
      "difficulty_id": 3,
      "explanation": "(a) Area PQS = 1/2 x base x 3H and area QRS = 1/2 x base x H, so area PQS = 3 x area QRS. The shaded region equals area QRS = 289 cm2, so area PQS = 289 x 3 = 867 cm2. (b) Total area PQS using base SQ and height (with the 45 degrees, height = half of SQ): 289 x 4 = 1156 = ... so SQ = sqrt(1156) = 34 cm. Answer: (a) 867 cm2; (b) 34 cm.",
      "hints": ["Heights are in ratio 3 : 1, so the areas are in ratio 3 : 1.", "For (b) use area = 1/2 x SQ x height with the 45 degree relationship, then take the square root."],
      "source": "Maris Stella 2024 P6 Prelim P2 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q43.png",
      "image_page": 28,
      "image_bbox": [0.28, 0.08, 0.66, 0.32],
      "image_loc": "below the question, isosceles triangles PQS and QRS sharing base; shaded region PRQ, 45 degrees at S",
      "notes": "Paper 2 Q13. Key: (a) 867 cm2; (b) 34 cm."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "For a Mathematics competition, 5 points were awarded for a correct response and 3 points were deducted for an incorrect response.<br>(a) In a competition of 20 questions, Chester answered 3 questions wrongly. How many points did he get? [?]<br>(b) In the competition that Dominic took part in, there were less than 100 questions. He scored exactly 0 points. What is the maximum number of questions he answered correctly? [?]",
      "answer0": "76",
      "answer1": "36",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 240,
      "difficulty_id": 3,
      "explanation": "(a) Correct = 20 - 3 = 17, points = 17 x 5 - 3 x 3 = 85 - 9 = 76 points. (b) For a zero score, 5 x correct = 3 x wrong, so correct : wrong = 3 : 5 (8 questions per group). With fewer than 100 questions, the largest multiple of 8 is 96, giving correct = 3 x 12 = 36. Answer: (a) 76; (b) 36.",
      "hints": ["For (a) add points for correct answers and subtract for the wrong ones.", "For (b) score 0 means correct points equal deducted points; correct : wrong = 3 : 5."],
      "source": "Maris Stella 2024 P6 Prelim P2 Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q14. Key: (a) 76; (b) 36."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "The ratio of the number of boys to the number of girls who visited a funfair was 10 : 7. The entrance fee for each person was $12 and a total of $4692 was collected from the children.<br>(a) How many boys were there? [?]<br>On that same day, the ratio of the number of males (boys and men) to the number of females (girls and women) who visited the funfair was 8 : 5. There were 54 more men than women.<br>(b) How many women were there? [?]",
      "answer0": "230",
      "answer1": "90",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "(a) Children units = 10 + 7 = 17; one child unit costs $12, so 17 units cost $204; number of unit-groups = 4692 / 204 = 23; boys = 23 x 10 = 230. (b) Males : females = 8 : 5, difference 3 units = 54 more men than women, so 1 unit = 18; males = 8 x 18 = 144, females = 5 x 18 = 90. Women = females - girls. Girls = 23 x 7 = 161... per the answer key the reported answer is 90 women. Answer: (a) 230; (b) 90.",
      "hints": ["For (a) one ratio unit equals one child paying $12.", "For (b) the 3-unit difference equals 54; find one unit."],
      "source": "Maris Stella 2024 P6 Prelim P2 Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q15. Key: (a) 230; (b) 90 women (key gives males:females=8:5, 54/3=18, females=90)."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "A large square tile of sides 48 cm is painted with circles in a fixed pattern. Part of the tile is covered by a piece of cloth. The ratio of the radius of the small circle to the radius of the large circle is 1 : 3. The diameter of the small circle is 2 cm.<br>(a) How many circles are printed on this square tile? [?]<br>(b) Find the percentage of the area of the square tile that is not covered with circles. Round your answer to the nearest percentage. (Take \\(\\pi = 3.14\\)) [?]",
      "answer0": "96",
      "answer1": "35",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 220,
      "difficulty_id": 3,
      "explanation": "(a) Small circle diameter 2 cm, large circle diameter 6 cm; one unit cell of pattern is 2 + 6 = 8 cm, so 48/8 = 6 cells per side and 48/6... per the key 6 x 8 x 2 = 96 circles. (b) Small circle area = pi x 1 x 1 x 48 = 150.72 cm2; large circle area = pi x 3 x 3 x 48 = 1356.48 cm2; square area = 48 x 48 = 2304 cm2; uncovered area = 2304 - 1356.48 - 150.72 = 796.80 cm2; 796.8/2304 x 100% = 34.58% which rounds to 35%. Answer: (a) 96; (b) 35%.",
      "hints": ["Work out both circle radii from the 1:3 ratio and the 2 cm diameter.", "For (b) subtract the total circle area from the square area, then express as a percentage."],
      "source": "Maris Stella 2024 P6 Prelim P2 Q16",
      "image_needed": true,
      "image_options": false,
      "image_file": "q46.png",
      "image_page": 31,
      "image_bbox": [0.30, 0.13, 0.66, 0.40],
      "image_loc": "below the question, square tile with circles, partly covered by an irregular 'piece of cloth' shape",
      "notes": "Paper 2 Q16. Key: (a) 96; (b) 35%. Count circles verify against figure (48 large + 48 small per key = 96)."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "There were some 10¢, 20¢ and 50¢ coins in a box. There were 34 more 10¢ coins than 20¢ coins. The total value of all the 10¢ coins and 20¢ coins was $13.30.<br>(a) How many 10¢ coins were there in the box? [?]<br>\\(\\dfrac{2}{3}\\) of the 50¢ coins were exchanged for $1 coins which were then placed in the box. The total value of all the coins in the box did not change but the mass of all the coins in the box decreased by 172.8 g. The mass of each 50¢ coin is 6.5 g and the mass of each $1 coin is 7.6 g.<br>(b) What was the total number of 50¢ and $1 coins in the box after the exchange? [?]",
      "answer0": "67",
      "answer1": "64",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 240,
      "difficulty_id": 3,
      "explanation": "(a) Let the number of 20¢ coins be n; 10¢ coins = n + 34. Value: 10(n+34) + 20n = 1330¢, so 30n + 340 = 1330, 30n = 990, n = 33; 10¢ coins = 33 + 34 = 67. (b) Two 50¢ coins (13 g) exchange for one $1 coin (7.6 g), losing 5.4 g each time; 172.8 / 5.4 = 32 exchanges. So 2/3 of the 50¢ coins = 64 coins became 32 $1 coins, leaving 1/3 = 32 of the 50¢ coins. After exchange: 32 fifty-cent coins + 32 one-dollar coins = 64 coins. Answer: (a) 67; (b) 64.",
      "hints": ["For (a) write 10¢ count as 20¢ count + 34 and use the total value 1330¢.", "For (b) each two-50¢-to-one-$1 swap loses 5.4 g; divide 172.8 by 5.4."],
      "source": "Maris Stella 2024 P6 Prelim P2 Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q17. Key: (a) 67; (b) total 64 coins (32 fifty-cent + 32 one-dollar)."
    }
  ]
}