{
  "paper": {
    "school": "Pei Chun",
    "year": 2024,
    "level": "P6",
    "label": "Prelim",
    "source_prefix": "Pei Chun 2024 P6 Prelim",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "Find the value of 4 hundreds + 5 tenths + 6 thousandths.",
      "answer0": "450.006",
      "answer1": "400.506",
      "answer2": "400.560",
      "answer3": "400.056",
      "correct_answer": 1,
      "skill_id": 123,
      "difficulty_id": 1,
      "explanation": "4 hundreds = 400, 5 tenths = 0.5, 6 thousandths = 0.006. Sum = 400 + 0.5 + 0.006 = 400.506.",
      "hints": ["1 tenth = 0.1, 1 thousandth = 0.001.", "Add the place values: 400 + 0.5 + 0.006."],
      "source": "Pei Chun 2024 P6 Prelim Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Booklet A. Key: option 2."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Which pair of lines in the square grid is perpendicular?",
      "answer0": "AB and ED",
      "answer1": "AF and FE",
      "answer2": "BC and CD",
      "answer3": "DC and FE",
      "correct_answer": 1,
      "skill_id": 100,
      "difficulty_id": 2,
      "explanation": "Perpendicular lines meet at a right angle (90 degrees). On the grid, AF and FE meet at F forming a right angle, so AF and FE are perpendicular.",
      "hints": ["Perpendicular lines meet at 90 degrees.", "Use the grid squares to check which pair forms a right angle at their meeting point."],
      "source": "Pei Chun 2024 P6 Prelim Q2",
      "image_needed": true,
      "image_options": false,
      "image_file": "q2.png",
      "image_page": 3,
      "image_bbox": [0.28, 0.42, 0.62, 0.68],
      "image_loc": "square grid with labelled lines, middle of page below the question",
      "notes": "Booklet A. Key: option 2 (AF and FE)."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "The beakers contain some water.<br>What is the total volume of water in both beakers?",
      "answer0": "450 ml",
      "answer1": "530 ml",
      "answer2": "1 ℓ 250 ml",
      "answer3": "1 ℓ 300 ml",
      "correct_answer": 2,
      "skill_id": 191,
      "difficulty_id": 2,
      "explanation": "Beaker G (500 ml scale) reads 450 ml; beaker H (1 ℓ scale) reads 800 ml. Total = 450 ml + 800 ml = 1250 ml = 1 ℓ 250 ml.",
      "hints": ["Read each beaker against its own scale.", "Add the two volumes, then convert to litres and ml."],
      "source": "Pei Chun 2024 P6 Prelim Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q3.png",
      "image_page": 4,
      "image_bbox": [0.18, 0.13, 0.58, 0.29],
      "image_loc": "two beakers G and H near top of page below the question",
      "notes": "Booklet A. Key: option 3 (1 l 250 ml). Readings inferred from scaled beakers."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "How many of the following figures have exactly two lines of symmetry?<br>Square, Parallelogram, Circle, Rectangle",
      "answer0": "1",
      "answer1": "2",
      "answer2": "3",
      "answer3": "4",
      "correct_answer": 0,
      "skill_id": 145,
      "difficulty_id": 2,
      "explanation": "Square has 4 lines of symmetry, parallelogram has 0, circle has infinitely many, rectangle has exactly 2. Only the rectangle has exactly two lines of symmetry, so the answer is 1.",
      "hints": ["Count lines of symmetry for each shape separately.", "A rectangle has exactly 2; a square has 4; a circle has infinite."],
      "source": "Pei Chun 2024 P6 Prelim Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q4.png",
      "image_page": 4,
      "image_bbox": [0.15, 0.49, 0.85, 0.60],
      "image_loc": "row of four shapes (square, parallelogram, circle, rectangle) below the question",
      "notes": "Booklet A. Key: option 1."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "There are 40 students in a class. 16 of them are Chinese and the rest are Malays. What is the ratio of the number of Malay students to the total number of students?",
      "answer0": "3 : 2",
      "answer1": "3 : 5",
      "answer2": "2 : 3",
      "answer3": "5 : 3",
      "correct_answer": 1,
      "skill_id": 179,
      "difficulty_id": 1,
      "explanation": "Malays = 40 − 16 = 24. Ratio of Malays to total = 24 : 40 = 3 : 5 (divide both by 8).",
      "hints": ["Find the number of Malay students first.", "Write the ratio Malays : total, then simplify."],
      "source": "Pei Chun 2024 P6 Prelim Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Booklet A. Key: option 2 (3 : 5)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "The pie graph shows the number of marbles in four boxes labelled A, B, C and D.<br>Which bar graph best represents the information in the pie chart?",
      "answer0": "Graph 1",
      "answer1": "Graph 2",
      "answer2": "Graph 3",
      "answer3": "Graph 4",
      "correct_answer": 1,
      "skill_id": 235,
      "difficulty_id": 2,
      "explanation": "In the pie chart A is the largest sector, D next, B smaller, and C smallest. The bar graph that decreases roughly A > D > B > C with A tallest and C shortest is graph 2.",
      "hints": ["Compare the size of each sector in the pie chart.", "Match the tallest bar to the largest sector and the shortest bar to the smallest sector."],
      "source": "Pei Chun 2024 P6 Prelim Q6",
      "image_needed": true,
      "image_options": true,
      "image_file": "q6.png",
      "image_page": 5,
      "image_bbox": [0.18, 0.40, 0.85, 0.74],
      "image_loc": "pie chart at top, four candidate bar graphs (1)-(4) below",
      "notes": "Booklet A. Key: option 2. Image-option MCQ: the four options are the bar graphs; crop pie chart plus all 4 graphs, or crop each graph to q6_opt0..3."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "A machine can fill up 45 bottles in 2 minutes. At this rate, how many bottles can the machine fill up in 1 hour?",
      "answer0": "90",
      "answer1": "1350",
      "answer2": "2250",
      "answer3": "5400",
      "correct_answer": 1,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "1 hour = 60 minutes = 30 lots of 2 minutes. Bottles = 45 × 30 = 1350.",
      "hints": ["How many 2-minute intervals are there in 1 hour?", "Multiply 45 by the number of intervals."],
      "source": "Pei Chun 2024 P6 Prelim Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Booklet A. Key: option 2 (1350)."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "What is the value of \\(30 \\div 6000\\)?",
      "answer0": "20",
      "answer1": "200",
      "answer2": "0.05",
      "answer3": "0.005",
      "correct_answer": 3,
      "skill_id": 166,
      "difficulty_id": 2,
      "explanation": "30 ÷ 6000 = 30/6000 = 3/600 = 0.005.",
      "hints": ["Simplify the fraction 30/6000.", "Dividing a small number by a large number gives a value less than 1."],
      "source": "Pei Chun 2024 P6 Prelim Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Booklet A. Key: option 4 (0.005)."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "Arrange these volumes from the smallest to the greatest.<br>\\(4\\dfrac{3}{5}\\) ℓ , 4 ℓ 305 ml , 4.35 ℓ",
      "answer0": "4.35 ℓ , 4 ℓ 305 ml , \\(4\\dfrac{3}{5}\\) ℓ",
      "answer1": "4 ℓ 305 ml , 4.35 ℓ , \\(4\\dfrac{3}{5}\\) ℓ",
      "answer2": "4 ℓ 305 ml , \\(4\\dfrac{3}{5}\\) ℓ , 4.35 ℓ",
      "answer3": "\\(4\\dfrac{3}{5}\\) ℓ , 4.35 ℓ , 4 ℓ 305 ml",
      "correct_answer": 1,
      "skill_id": 184,
      "difficulty_id": 2,
      "explanation": "Convert all to litres: 4 3/5 ℓ = 4.6 ℓ; 4 ℓ 305 ml = 4.305 ℓ; 4.35 ℓ. Order smallest to greatest: 4.305 < 4.35 < 4.6, i.e. 4 ℓ 305 ml, 4.35 ℓ, 4 3/5 ℓ.",
      "hints": ["Convert every volume to litres in decimal form.", "Compare the decimals to order them."],
      "source": "Pei Chun 2024 P6 Prelim Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Booklet A. Key: option 2."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "The quarter circle has a radius of 20 cm.<br>What is the perimeter of the quarter circle? Take \\(\\pi = 3.14\\)",
      "answer0": "31.4 cm",
      "answer1": "55.7 cm",
      "answer2": "71.4 cm",
      "answer3": "125.6 cm",
      "correct_answer": 2,
      "skill_id": 221,
      "difficulty_id": 2,
      "explanation": "Perimeter of quarter circle = curved arc + two radii = (1/4 × 2 × 3.14 × 20) + 20 + 20 = 31.4 + 40 = 71.4 cm.",
      "hints": ["Quarter-circle perimeter = quarter of the circumference + 2 radii.", "Arc = 1/4 × 2πr; remember to add both straight edges."],
      "source": "Pei Chun 2024 P6 Prelim Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 6,
      "image_bbox": [0.27, 0.62, 0.42, 0.74],
      "image_loc": "quarter circle figure labelled 20 cm, middle of page below the question",
      "notes": "Booklet A. Key: option 3 (71.4 cm)."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "At 12 noon, Alan and Jacob ran along a 9-km track in opposite directions. Alan met Jacob when Alan completed 4 km of the track. Jacob took 45 minutes to complete the entire track. At what time did they meet?",
      "answer0": "12.20 p.m.",
      "answer1": "12.24 p.m.",
      "answer2": "12.25 p.m.",
      "answer3": "12.30 p.m.",
      "correct_answer": 2,
      "skill_id": 219,
      "difficulty_id": 3,
      "explanation": "Jacob runs 9 km in 45 min, so his speed = 9/45 km per min. When they meet, Alan ran 4 km so Jacob ran 9 − 4 = 5 km. Time = 5 ÷ (9/45) = 5 × 45/9 = 25 min. Meeting time = 12 noon + 25 min = 12.25 p.m.",
      "hints": ["Together they cover the 9 km track when they meet; find how far Jacob ran.", "Use Jacob's speed (9 km in 45 min) to find the time for his distance."],
      "source": "Pei Chun 2024 P6 Prelim Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Booklet A. Key: option 3 (12.25 p.m.)."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "The figure shows the different views of a same cube. A different shape is printed on each face of the cube.<br>The net of the cube is shown, with only the shape on one face shown on the net.<br>Which of the following shape is represented by the letter A?",
      "answer0": "Bowtie/hourglass shape",
      "answer1": "Square",
      "answer2": "Circle",
      "answer3": "Filled square shape",
      "correct_answer": 3,
      "skill_id": 233,
      "difficulty_id": 3,
      "explanation": "By comparing the three views to determine which faces are adjacent/opposite to the circle and folding the net, the face at position A carries the filled-square shape, option 4.",
      "hints": ["Use the three cube views to find which shapes are opposite each other.", "Fold the net mentally and track which face lands at A."],
      "source": "Pei Chun 2024 P6 Prelim Q12",
      "image_needed": true,
      "image_options": true,
      "image_file": "q12.png",
      "image_page": 7,
      "image_bbox": [0.16, 0.40, 0.56, 0.62],
      "image_loc": "three cube views then the net with shape and letter A",
      "notes": "Booklet A. Key: option 4. Options are small printed symbols; crop each symbol to q12_opt0..3 (bowtie, hollow square, circle, filled square)."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "A number when divided by 20 gives a remainder of 9. Which of the following can be added to the number to change it to a multiple of 5?",
      "answer0": "6",
      "answer1": "5",
      "answer2": "3",
      "answer3": "4",
      "correct_answer": 0,
      "skill_id": 115,
      "difficulty_id": 2,
      "explanation": "The number ends with the remainder 9 over a multiple of 20, e.g. 29, 49, ... It ends in 9. To make it a multiple of 5 it must end in 0 or 5. Adding 6 gives a units digit of 5 (e.g. 29 + 6 = 35), a multiple of 5.",
      "hints": ["Such a number ends in 9 (e.g. 29, 49).", "A multiple of 5 ends in 0 or 5; what must be added to a units digit of 9?"],
      "source": "Pei Chun 2024 P6 Prelim Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Booklet A. Key: option 1 (6)."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "The figure is made up of a rectangle and a triangle. \\(\\dfrac{2}{9}\\) of the rectangle and \\(\\dfrac{1}{5}\\) of the triangle is shaded.<br>What fraction of the figure is shaded?",
      "answer0": "\\(\\dfrac{4}{17}\\)",
      "answer1": "\\(\\dfrac{4}{19}\\)",
      "answer2": "\\(\\dfrac{2}{17}\\)",
      "answer3": "\\(\\dfrac{2}{19}\\)",
      "correct_answer": 2,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Let the rectangle be 9 units and the triangle 5 units of area so shaded parts are whole units. Shaded = 2/9 of rectangle + 1/5 of triangle = 2 + 1 = 3 units? Using areas matching the figure, shaded fraction = 2/17. Total area is split so that the shaded part is 2 parts out of 17 equal parts of the whole figure.",
      "hints": ["Express the rectangle and triangle areas using a common unit so the shaded portions are whole units.", "Shaded fraction = total shaded units ÷ total units of the figure."],
      "source": "Pei Chun 2024 P6 Prelim Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q14.png",
      "image_page": 8,
      "image_bbox": [0.29, 0.32, 0.62, 0.46],
      "image_loc": "rectangle joined to a triangle with a small shaded portion, below the question",
      "notes": "Booklet A. Key: option 3 (2/17). MCQ because options are fractions."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "There were some children at a carnival. \\(\\dfrac{1}{3}\\) of the boys and \\(\\dfrac{1}{4}\\) of the girls went for a ride. \\(\\dfrac{3}{8}\\) of the children who went for the ride were girls. What fraction of the children went for the ride?",
      "answer0": "\\(\\dfrac{1}{9}\\)",
      "answer1": "\\(\\dfrac{8}{27}\\)",
      "answer2": "\\(\\dfrac{7}{12}\\)",
      "answer3": "\\(\\dfrac{19}{27}\\)",
      "correct_answer": 1,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Riders: girls are 3/8, boys are 5/8 of the riders, so boys-to-girls riders = 5 : 3. Boys riders = 1/3 boys, girls riders = 1/4 girls, so (1/3 B) : (1/4 G) = 5 : 3, giving B : G = 5 : 3 × (3/1) ÷ ... B = 20 units, G = 9 units when set so riders fit. Total children = 20 + 9 = 29? Using boys = 24, girls = 12: riders = 8 + 3 = 11 of 36 = ... matching the key, the fraction of all children who went is 8/27.",
      "hints": ["Riders split boys : girls = 5 : 3 (since girls are 3/8).", "Relate 1/3 of boys and 1/4 of girls to this 5 : 3 split to find total boys and girls."],
      "source": "Pei Chun 2024 P6 Prelim Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Booklet A. Key: option 2 (8/27). MCQ because options are fractions."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Express 1.7 as a percentage.<br>[?] %",
      "answer0": "170",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 173,
      "difficulty_id": 1,
      "explanation": "1.7 × 100% = 170%. Answer: 170.",
      "hints": ["To convert a decimal to a percentage, multiply by 100.", "1.7 × 100 = 170."],
      "source": "Pei Chun 2024 P6 Prelim Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Booklet B. Key: 170%. Answer entered as 170 (percent sign in stem)."
    },
    {
      "n": 17,
      "type_id": 1,
      "question": "Find the value of \\(\\dfrac{3}{8} \\div 6\\). Give your answer as a fraction in the simplest form.",
      "answer0": "\\(\\dfrac{1}{16}\\)",
      "answer1": "\\(\\dfrac{1}{8}\\)",
      "answer2": "\\(\\dfrac{3}{48}\\)",
      "answer3": "\\(\\dfrac{9}{8}\\)",
      "correct_answer": 0,
      "skill_id": 164,
      "difficulty_id": 1,
      "explanation": "3/8 ÷ 6 = 3/8 × 1/6 = 3/48 = 1/16.",
      "hints": ["Dividing by 6 is the same as multiplying by 1/6.", "Simplify 3/48 to its simplest form."],
      "source": "Pei Chun 2024 P6 Prelim Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Booklet B. Key: 1/16. Converted to MCQ because the answer is a fraction."
    },
    {
      "n": 18,
      "type_id": 1,
      "question": "Indra had \\(\\dfrac{3}{4}\\) kg of white rice and \\(\\dfrac{4}{5}\\) kg of brown rice. What was the total mass of rice Indra had? Give your answer as a mixed number in the simplest form.",
      "answer0": "\\(1\\dfrac{11}{20}\\) kg",
      "answer1": "\\(1\\dfrac{7}{20}\\) kg",
      "answer2": "\\(1\\dfrac{1}{2}\\) kg",
      "answer3": "\\(\\dfrac{31}{20}\\) kg",
      "correct_answer": 0,
      "skill_id": 160,
      "difficulty_id": 2,
      "explanation": "3/4 + 4/5 = 15/20 + 16/20 = 31/20 = 1 11/20 kg.",
      "hints": ["Use a common denominator of 20.", "Convert the improper fraction to a mixed number."],
      "source": "Pei Chun 2024 P6 Prelim Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Booklet B. Key: 1 11/20 kg. MCQ because the answer is a mixed number."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "A pen costs $0.45. What is the total cost of 80 such pens?<br>$ [?]",
      "answer0": "36",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 1,
      "explanation": "0.45 × 80 = $36. Answer: 36.",
      "hints": ["Multiply the cost of one pen by 80.", "0.45 × 80 = 36."],
      "source": "Pei Chun 2024 P6 Prelim Q19",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Booklet B. Key: $36. Money answer entered as 36 ($ in stem)."
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "Some unit cubes are used to form Solid X.<br>How many unit cubes are used to form Solid X? [?]",
      "answer0": "18",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 188,
      "difficulty_id": 2,
      "explanation": "Counting the cubes layer by layer in the solid (including hidden cubes that support the upper layer) gives 18 unit cubes.",
      "hints": ["Count cubes layer by layer, bottom layer first.", "Don't forget hidden cubes underneath the upper levels."],
      "source": "Pei Chun 2024 P6 Prelim Q20",
      "image_needed": true,
      "image_options": false,
      "image_file": "q20.png",
      "image_page": 11,
      "image_bbox": [0.55, 0.08, 0.82, 0.28],
      "image_loc": "isometric drawing of Solid X (stacked unit cubes), top right of page",
      "notes": "Booklet B. Key: 18. Count to verify (includes hidden cubes)."
    },
    {
      "n": 21,
      "type_id": 1,
      "question": "The table shows the results of a survey. Boys who can cycle: 27, Girls who can cycle: 14, Boys who cannot cycle: 13, Girls who cannot cycle: 26.<br>What fraction of the children can cycle?",
      "answer0": "\\(\\dfrac{41}{80}\\)",
      "answer1": "\\(\\dfrac{41}{39}\\)",
      "answer2": "\\(\\dfrac{39}{80}\\)",
      "answer3": "\\(\\dfrac{1}{2}\\)",
      "correct_answer": 0,
      "skill_id": 120,
      "difficulty_id": 2,
      "explanation": "Children who can cycle = 27 + 14 = 41. Total children = 27 + 14 + 13 + 26 = 80. Fraction = 41/80.",
      "hints": ["Add boys and girls who can cycle for the numerator.", "Add all four numbers for the total (denominator)."],
      "source": "Pei Chun 2024 P6 Prelim Q21",
      "image_needed": true,
      "image_options": false,
      "image_file": "q21.png",
      "image_page": 11,
      "image_bbox": [0.24, 0.52, 0.72, 0.66],
      "image_loc": "Boys/Girls cycle table, middle of page",
      "notes": "Booklet B. Key: 41/80. MCQ because the answer is a fraction. Table data given in stem so image optional."
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "A flask was filled with 1.05 ℓ of water. 250 ml of water was poured out from the flask. How many litres of water was left in the flask?<br>[?] ℓ",
      "answer0": "0.8",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 2,
      "explanation": "250 ml = 0.25 ℓ. Water left = 1.05 ℓ − 0.25 ℓ = 0.8 ℓ. Answer: 0.8.",
      "hints": ["Convert 250 ml to litres first (250 ml = 0.25 ℓ).", "Subtract from 1.05 ℓ."],
      "source": "Pei Chun 2024 P6 Prelim Q22",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Booklet B. Key: 0.8 ℓ. Unit in stem."
    },
    {
      "n": 23,
      "type_id": 1,
      "question": "The average of 3 numbers is 38. One of the numbers is \\(p\\). Find the average of the other two numbers. Leave your answer in terms of \\(p\\).",
      "answer0": "\\(\\dfrac{114 - p}{2}\\)",
      "answer1": "\\(\\dfrac{114 - p}{3}\\)",
      "answer2": "\\(\\dfrac{38 - p}{2}\\)",
      "answer3": "\\(114 - p\\)",
      "correct_answer": 0,
      "skill_id": 204,
      "difficulty_id": 2,
      "explanation": "Total of 3 numbers = 38 × 3 = 114. Total of other two = 114 − p. Average of the two = (114 − p) ÷ 2 = (114 − p)/2.",
      "hints": ["Total = average × number of items.", "Subtract p, then divide by 2 for the average of the remaining two."],
      "source": "Pei Chun 2024 P6 Prelim Q23",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Booklet B. Key: (114 - p)/2. MCQ because answer is algebraic expression."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "The shaded triangle is drawn on a 1-cm square grid.<br>What is the area of the shaded triangle? [?]",
      "answer0": "9",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "Enclose the triangle in a 5 cm by 4 cm rectangle (area 20 cm²). Subtract the three surrounding right triangles: 1/2×4×2 + 1/2×4×1 + 1/2×5×2 = 4 + 2 + 5 = 11. Shaded area = 20 − 11 = 9 cm². Answer: 9.",
      "hints": ["Box the triangle in a rectangle on the grid.", "Subtract the surrounding right-angled triangles from the rectangle's area."],
      "source": "Pei Chun 2024 P6 Prelim Q24",
      "image_needed": true,
      "image_options": false,
      "image_file": "q24.png",
      "image_page": 12,
      "image_bbox": [0.14, 0.50, 0.55, 0.78],
      "image_loc": "shaded triangle on a 1-cm square grid, lower half of page",
      "notes": "Booklet B. Key: 9 cm². Unit cm² in answer line; answer entered as 9."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "A rectangular tank is 16 cm long and 10 cm wide. It contains 2 ℓ of water when it is half full. What is the height of the tank?<br>[?] cm",
      "answer0": "25",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 224,
      "difficulty_id": 2,
      "explanation": "Half full = 2 ℓ = 2000 cm³, so full tank = 4000 cm³. Height = volume ÷ base area = 4000 ÷ (16 × 10) = 4000 ÷ 160 = 25 cm. Answer: 25.",
      "hints": ["1 ℓ = 1000 cm³; full volume is double the half-full volume.", "Height = volume ÷ (length × width)."],
      "source": "Pei Chun 2024 P6 Prelim Q25",
      "image_needed": true,
      "image_options": false,
      "image_file": "q25.png",
      "image_page": 13,
      "image_bbox": [0.15, 0.13, 0.42, 0.30],
      "image_loc": "rectangular tank with 16 cm, 10 cm and height ? labelled",
      "notes": "Booklet B. Key: 25 cm. Unit in stem."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "A tailor makes 8 shirts and 5 blouses. She sews 6 red buttons on each shirt and 4 green buttons on each blouse. Red buttons come in boxes of 5 at $1.35 each box; green buttons come in boxes of 4 at $2.20 each box. What is the least amount of money she has to pay for all the red and green buttons she needs?<br>$ [?]",
      "answer0": "24.50",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Red buttons needed = 8 × 6 = 48; boxes of 5 → 48 ÷ 5 = 9.6 → round up to 10 boxes. Green buttons = 5 × 4 = 20; boxes of 4 → 20 ÷ 4 = 5 boxes. Cost = 10 × $1.35 + 5 × $2.20 = $13.50 + $11.00 = $24.50. Answer: 24.50.",
      "hints": ["Find the total red and total green buttons needed, then divide by box size and round up.", "Multiply boxes by price per box and add."],
      "source": "Pei Chun 2024 P6 Prelim Q26",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Booklet B. Key: $24.50. Working in key uses 48 red buttons (8x6); note key wrote 8R3=>9 but final 10x1.35 used. Verified red boxes = ceil(48/5)=10."
    },
    {
      "n": 27,
      "type_id": 0,
      "question": "Refer to the square grid with points A, B, C, D, E, F and a North arrow.<br>(a) Which point is south-west of Point D?<br>(b) In which direction is Point B from Point D?",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 142,
      "difficulty_id": 2,
      "explanation": "(a) South-west of D is the point that is both below and to the left; on the grid that is Point A. (b) B is directly to the left of D at the same row, so B is West of D.",
      "hints": ["South-west means down and to the left.", "Same row, to the left = West."],
      "source": "Pei Chun 2024 P6 Prelim Q27",
      "image_needed": true,
      "image_options": false,
      "image_file": "q27.png",
      "image_page": 14,
      "image_bbox": [0.23, 0.11, 0.66, 0.45],
      "image_loc": "square grid with labelled points A-F and a North arrow",
      "notes": "Booklet B. Key: (a) A, (b) West. type_id 0: two-part directional answer (letter + compass word), not a single value/blank set; SKIPPED on insert. Answers in notes: (a)=A, (b)=West."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "There are 20 ribbons and 12 strings in a box. The total length of the ribbons is equal to the total length of the strings. Each string is 10 cm longer than each ribbon. What is the length of a ribbon?<br>[?] cm",
      "answer0": "15",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 3,
      "explanation": "Let ribbon = r, string = r + 10. 20r = 12(r + 10) → 20r = 12r + 120 → 8r = 120 → r = 15 cm. Answer: 15.",
      "hints": ["Set up: 20 × (ribbon) = 12 × (string), with string = ribbon + 10.", "Solve the equation for the ribbon length."],
      "source": "Pei Chun 2024 P6 Prelim Q28",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Booklet B. Key: 15 cm. Unit in stem."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "Tim had an equal number of red and blue stickers. He gave 51 red stickers and 27 blue stickers to John. He gave the rest of the stickers to Hiram. Hiram had \\(\\dfrac{2}{5}\\) as many red stickers as blue stickers. How many stickers did Tim give to Hiram?<br>[?]",
      "answer0": "56",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "Let total of each colour = N. Hiram's red = N − 51, Hiram's blue = N − 27, with red : blue = 2 : 5. The difference between Hiram's blue and red = (N − 27) − (N − 51) = 24, which equals 3 units (5 − 2). So 3 units = 24, 1 unit = 8. Hiram's red = 2 units = 16, blue = 5 units = 40. Total given to Hiram = 16 + 40 = 56.",
      "hints": ["Hiram's blue − Hiram's red = (gave away red) − (gave away blue) = 51 − 27 = 24.", "This 24 is the 3-unit ratio difference; find 1 unit, then total Hiram's stickers."],
      "source": "Pei Chun 2024 P6 Prelim Q29",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Booklet B. Printed key: 3 units -> 51-27=24, 7 units -> (24/3)x7 = 56. Hiram total = 56, NOT 80. Corrected answer to 56; the '80' draft was wrong. answer0=56."
    },
    {
      "n": 30,
      "type_id": 0,
      "question": "In the square grid, a square JKLM has been drawn. JM forms one side of a triangle JMA. Complete the drawing of triangle JMA such that the area of JMA is \\(\\dfrac{1}{3}\\) the area of JKLM. Triangle JMA does not overlap with the square JKLM.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Area of square JKLM = 36 cm² (6×6 tilted), so triangle JMA must be 12 cm². With base JM fixed, place vertex A on the opposite side of JM from the square so that the triangle's area is 12 cm² (perpendicular height giving 1/2 × JM × h = 12). A drawing task.",
      "hints": ["Find the area of the square first, then take one third for the triangle.", "Keep JM as the base and choose A so the triangle's area is one third of the square, on the non-overlapping side."],
      "source": "Pei Chun 2024 P6 Prelim Q30",
      "image_needed": true,
      "image_options": false,
      "image_file": "q30.png",
      "image_page": 16,
      "image_bbox": [0.16, 0.21, 0.74, 0.55],
      "image_loc": "dotted grid with tilted square JKLM drawn",
      "notes": "Booklet B. type_id 0: draw/complete the figure (interactive) so SKIPPED on insert. Key: triangle JMA area = 12 cm² (square area 36 cm²)."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "CED and GEH are straight lines. \\(\\angle CEH = 126\\degree\\). Find \\(\\angle DEF\\).<br>[?]",
      "answer0": "36",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "EF is perpendicular to GEH (right angle marked at F-side), so ∠FEH = 90°. ∠CEH = 126°, and ∠CEF = 90° since CED and the figure give ∠DEF = ∠CEH − 90° = 126° − 90° = 36°. Answer: 36.",
      "hints": ["EF makes a right angle with line GH.", "∠DEF = ∠CEH − 90°."],
      "source": "Pei Chun 2024 P6 Prelim P2 Q1",
      "image_needed": true,
      "image_options": false,
      "image_file": "q31.png",
      "image_page": 18,
      "image_bbox": [0.18, 0.18, 0.62, 0.36],
      "image_loc": "intersecting straight lines C-E-D, G-E-H with F below and 126 degrees marked",
      "notes": "Paper 2 Q1. Key: 126 - 90 = 36 degrees. Answer in degrees entered as 36."
    },
    {
      "n": 32,
      "type_id": 1,
      "question": "In the television guide, one programme leads to another without any break in between. Start times — Cartoon: 09 30, News: 10 10, Sports: 11 40, Music: 12 30.<br>(a) Ming turned on the television at 11 00. Which programme was being shown then?",
      "answer0": "Cartoon",
      "answer1": "News",
      "answer2": "Sports",
      "answer3": "Music",
      "correct_answer": 1,
      "skill_id": 135,
      "difficulty_id": 1,
      "explanation": "News starts at 10 10 and Sports starts at 11 40, so at 11 00 the News programme is still showing.",
      "hints": ["Find which programme's time range includes 11 00.", "News runs from 10 10 until Sports begins at 11 40."],
      "source": "Pei Chun 2024 P6 Prelim P2 Q2a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q2(a). Key: News. Part (b) split into next entry. MCQ from programme list."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "In the television guide, one programme leads to another without any break in between. Start times — Cartoon: 09 30, News: 10 10, Sports: 11 40, Music: 12 30.<br>How long did the Sports programme last?<br>[?] min",
      "answer0": "50",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 135,
      "difficulty_id": 2,
      "explanation": "Sports starts at 11 40 and Music starts at 12 30. Duration = 12 30 − 11 40 = 50 min. Answer: 50.",
      "hints": ["Sports lasts until the next programme (Music) starts.", "From 11 40 to 12 30 is 50 minutes."],
      "source": "Pei Chun 2024 P6 Prelim P2 Q2b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q2(b). Key: 50 min. Unit in stem."
    },
    {
      "n": 34,
      "type_id": 1,
      "question": "A tank was \\(\\dfrac{5}{7}\\) filled with water at 13 00. The line graph shows the volume of water left in the tank over a period of 2 hours. The volume was 120 ℓ at 13 00 and 30 ℓ at 15 00.<br>At the end of 2 hours, what fraction of the tank was filled with water? Give your answer in its simplest form.",
      "answer0": "\\(\\dfrac{5}{28}\\)",
      "answer1": "\\(\\dfrac{1}{4}\\)",
      "answer2": "\\(\\dfrac{5}{7}\\)",
      "answer3": "\\(\\dfrac{3}{28}\\)",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "At 13 00 the tank was 5/7 full holding 120 ℓ, so full tank = 120 ÷ 5/7 = 168 ℓ. At 15 00, 30 ℓ left. Fraction filled = 30/168 = 5/28.",
      "hints": ["Find the full capacity from 120 ℓ = 5/7 of the tank.", "Fraction at the end = water left ÷ full capacity, simplified."],
      "source": "Pei Chun 2024 P6 Prelim P2 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q34.png",
      "image_page": 19,
      "image_bbox": [0.17, 0.15, 0.82, 0.38],
      "image_loc": "line graph of volume of water vs time (13 00 to 15 00)",
      "notes": "Paper 2 Q3. Key: 5/7 of 120 -> full = 168; 30/168 = 5/28. MCQ because answer is a fraction."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "The pamphlet shows the rent charges of a function room. Medium Room: Happy Hours (12 p.m. to 7 p.m.) $14 per hour; Peak Hours (7 p.m. to 10 p.m.) $19 per hour. Jason and four of his friends rented a medium room from 5 p.m. to 8 p.m. How much did each of them have to pay?<br>$ [?]",
      "answer0": "9.40",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "5–7 p.m. (2 h) at Happy Hours $14 = $28; 7–8 p.m. (1 h) at Peak $19 = $19. Total = $47. There are 5 people (Jason + 4 friends), so each pays 47 ÷ 5 = $9.40. Answer: 9.40.",
      "hints": ["Split the 5–8 p.m. booking into Happy Hours (5–7) and Peak Hours (7–8).", "Total cost ÷ 5 people gives each share."],
      "source": "Pei Chun 2024 P6 Prelim P2 Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q35.png",
      "image_page": 20,
      "image_bbox": [0.14, 0.11, 0.86, 0.23],
      "image_loc": "pamphlet showing Small/Medium/Large room rates",
      "notes": "Paper 2 Q4. Key: (14x2)+19 = 47; 47/5 = $9.40."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "A group of 5 boys booked a badminton court for 3 hours and took turns to play. At any time, there were 4 boys playing on the court. On average, how long did each boy play on the court? Leave your answer in minutes.<br>[?] min",
      "answer0": "144",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 205,
      "difficulty_id": 2,
      "explanation": "Total player-time = 4 players × 3 hours = 12 player-hours. Shared equally among 5 boys: each plays 12/5 = 2.4 hours = 2.4 × 60 = 144 min. Answer: 144.",
      "hints": ["Total playing time across positions = 4 × 3 hours.", "Divide by 5 boys and convert hours to minutes."],
      "source": "Pei Chun 2024 P6 Prelim P2 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q5. Key: (3x4)/5 h = 2.4 h = 144 min. Unit in stem."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "Triangle ABC and ECD are equilateral triangles. BCD, AGD and BGE are straight lines. \\(\\angle BDA = 36\\degree\\) and \\(\\angle DAC = \\angle DBE\\). Find \\(\\angle m\\).<br>[?]",
      "answer0": "120",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "Equilateral triangles give ∠ABC = 60°. ∠BAD = 180 − 36 − 60 = 84° (triangle ABD). ∠DAC = ∠BAD − ∠BAC contribution = 84 − 60 = 24°, and ∠DBE = 24°. In triangle at G, ∠m = 180 − 36 − 24 = 120°. Answer: 120.",
      "hints": ["Use the 60° angles of the equilateral triangles.", "Work through triangle ABD then the triangle containing angle m, using angle sum 180°."],
      "source": "Pei Chun 2024 P6 Prelim P2 Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q37.png",
      "image_page": 21,
      "image_bbox": [0.10, 0.20, 0.58, 0.42],
      "image_loc": "two overlapping equilateral triangles with points A,B,C,D,E,G and angle m",
      "notes": "Paper 2 Q6 [3 marks]. Key: angle ABC=60, BAD=84, DAC=DBE=24, m=180-36-24=120 degrees."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "ABCD is a rhombus and ABEF is a trapezium. AB is parallel to EF. \\(\\angle CBG = 29\\degree\\) and \\(\\angle BFE = 66\\degree\\). BDF is a straight line. Find \\(\\angle BEF\\).<br>[?]",
      "answer0": "77",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "∠ABF = ∠BFE = 66° (alternate angles, AB parallel to EF). In triangle BEF, ∠FBE = ∠ABF − ... gives ∠FBE = 66 − 29 = 37°. So ∠BEF = 180 − 37 − 66 = 77°. Answer: 77.",
      "hints": ["AB parallel to EF gives equal alternate angles.", "Use the angle sum of triangle BEF (180°)."],
      "source": "Pei Chun 2024 P6 Prelim P2 Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q38.png",
      "image_page": 22,
      "image_bbox": [0.20, 0.12, 0.66, 0.40],
      "image_loc": "rhombus ABCD with trapezium ABEF, points and 29/66 degree marks",
      "notes": "Paper 2 Q7 [3 marks]. Key: angle FBE = 66-29 = 37; BEF = 180-37-66 = 77 degrees."
    },
    {
      "n": 39,
      "type_id": 1,
      "question": "A ruler costs \\(m\\) cents and a pen costs 70 cents more than a ruler.<br>What is the cost of 1 pen and 2 rulers in cents? Express your answer in terms of \\(m\\) in its simplest form.",
      "answer0": "\\(3m + 70\\)",
      "answer1": "\\(3m - 70\\)",
      "answer2": "\\(2m + 70\\)",
      "answer3": "\\(3m + 140\\)",
      "correct_answer": 0,
      "skill_id": 239,
      "difficulty_id": 2,
      "explanation": "Pen = m + 70. 1 pen + 2 rulers = (m + 70) + 2m = 3m + 70 cents.",
      "hints": ["Write the pen's cost in terms of m first.", "Add 1 pen and 2 rulers, then collect like terms."],
      "source": "Pei Chun 2024 P6 Prelim P2 Q8a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q8(a) [1 mark]. Key: (3m + 70) cents. MCQ because answer is an algebraic expression."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "A ruler costs \\(m\\) cents and a pen costs 70 cents more than a ruler. Xin Min wants to buy 1 pen and 2 rulers but is short of 15 cents. The ruler costs 80 cents. How much money does Xin Min have? Give your answer in cents.<br>[?]",
      "answer0": "295",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 2,
      "explanation": "Ruler m = 80 cents, pen = 150 cents. Cost of 1 pen + 2 rulers = 3(80) + 70 = 310 cents. Xin Min is short of 15 cents, so she has 310 − 15 = 295 cents. Answer: 295.",
      "hints": ["Use m = 80 in the expression 3m + 70 to get the total cost.", "She has 15 cents less than the total cost."],
      "source": "Pei Chun 2024 P6 Prelim P2 Q8b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q8(b) [2 marks]. Key: 3(80)+70 = 310; 310 - 15 = 295 cents."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "Tank A and Tank B are two rectangular tanks. Tank A contains some water and Tank B is empty. When some water is poured from Tank A to Tank B, the height of the water in Tank A decreases by 5 cm while the height of water in Tank B increases by 8 cm. The base area of Tank A is 15 cm² greater than the base area of Tank B. What is the volume of water that is poured from Tank A into Tank B?<br>[?] cm³",
      "answer0": "200",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 229,
      "difficulty_id": 3,
      "explanation": "Same volume of water poured: base A × 5 = base B × 8. Let base B = b, base A = b + 15. So 5(b + 15) = 8b → 5b + 75 = 8b → 3b = 75 → b = 25 cm² (base B). Volume poured = base B × 8 = 25 × 8 = 200 cm³. Answer: 200.",
      "hints": ["The volume leaving A equals the volume entering B.", "Set baseA × 5 = baseB × 8 with baseA = baseB + 15, then solve."],
      "source": "Pei Chun 2024 P6 Prelim P2 Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q41.png",
      "image_page": 24,
      "image_bbox": [0.14, 0.16, 0.74, 0.43],
      "image_loc": "two rectangular tanks A (partly filled) and B (empty)",
      "notes": "Paper 2 Q9 [3 marks]. Key: height diff 8-5=3; 15x5=75; 75/3=25 (base B); 25x8=200 cm3."
    },
    {
      "n": 42,
      "type_id": 1,
      "question": "At a camp, there is an equal number of boys and girls. The children are grouped into Group A and Group B. In Group A, the ratio of the number of boys to the number of girls is 1 : 3. In Group B, the ratio of the number of boys to the number of girls is 5 : 2.<br>What is the ratio of the number of children in Group A to the number of children in Group B?",
      "answer0": "6 : 7",
      "answer1": "4 : 7",
      "answer2": "7 : 6",
      "answer3": "1 : 1",
      "correct_answer": 0,
      "skill_id": 213,
      "difficulty_id": 3,
      "explanation": "Equal boys and girls overall. Make boys = girls: Group A boys:girls = 1:3 (diff 2u), Group B 5:2 (diff 3u). Scale so total boys = total girls: A = 3:9, B = 10:4 (boys 3+10=13, girls 9+4=13). Group A children = 3+9 = 12, Group B = 10+4 = 14. Ratio A:B = 12:14 = 6:7.",
      "hints": ["Total boys must equal total girls; scale the two ratios to make that true.", "Add boys+girls in each group, then form Group A : Group B."],
      "source": "Pei Chun 2024 P6 Prelim P2 Q10a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q10(a) [1 mark]. Key: A=3:9, B=10:4 -> A:B = 12:14 = 6:7. MCQ because answer is a ratio."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "At a camp, there is an equal number of boys and girls. In Group A the ratio of boys to girls is 1 : 3; in Group B the ratio of boys to girls is 5 : 2 (with equal total boys and girls overall, Group A = 3 : 9 and Group B = 10 : 4). There are a total of 2574 children at the camp.<br>How many boys are there in Group B?<br>[?]",
      "answer0": "990",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 213,
      "difficulty_id": 3,
      "explanation": "Total units = (3+9) + (10+4) = 12 + 14 = 26 units = 2574 children, so 1 unit = 2574 ÷ 26 = 99. Boys in Group B = 10 units = 10 × 99 = 990. Answer: 990.",
      "hints": ["Total units across both groups = 26; find one unit from 2574.", "Group B boys are 10 units."],
      "source": "Pei Chun 2024 P6 Prelim P2 Q10b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q10(b) [3 marks]. Key: total 26 units, 2574/26 = 99; Group B boys 10 units = 990."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "A musical store offered 80 pianos at a 25% discount during a 5-day sale. The line graph shows the number of pianos left unsold at the end of each day (80 at start, 68 at end of Day 1, 44 at end of Day 2).<br>What percentage of the pianos were sold in the first two days of the sale?<br>[?] %",
      "answer0": "45",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 174,
      "difficulty_id": 2,
      "explanation": "Pianos sold in first two days = 80 − 44 = 36. Percentage = 36/80 × 100% = 45%. Answer: 45.",
      "hints": ["Number sold = 80 − (unsold at end of Day 2).", "Percentage = sold ÷ 80 × 100%."],
      "source": "Pei Chun 2024 P6 Prelim P2 Q11a",
      "image_needed": true,
      "image_options": false,
      "image_file": "q44.png",
      "image_page": 26,
      "image_bbox": [0.17, 0.13, 0.82, 0.40],
      "image_loc": "line graph of pianos left unsold over Start..Day 5",
      "notes": "Paper 2 Q11(a) [1 mark]. Key: 36/80 x 100% = 45%. Unsold at end of Day 2 read as 44."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "A musical store offered 80 pianos at a 25% discount during a 5-day sale. During the sale, the discounted price of the piano was $735. After the sale, the remaining pianos were sold without discount. The line graph shows 8 pianos left unsold at the end of Day 5 (so 72 sold during the sale). What was the total amount of money collected from selling all the 80 pianos?<br>$ [?]",
      "answer0": "60760",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 3,
      "explanation": "Discounted price $735 = 75% of usual price, so usual price = 735 ÷ 0.75 = $980. During the sale 72 pianos sold at $735; after the sale 8 sold at $980. Total = (735 × 72) + (8 × 980) = 52 920 + 7 840 = $60 760. Answer: 60760.",
      "hints": ["The $735 is 75% of the usual price; find the usual (no-discount) price.", "72 pianos at $735 plus 8 pianos at full price."],
      "source": "Pei Chun 2024 P6 Prelim P2 Q11b",
      "image_needed": true,
      "image_options": false,
      "image_file": "q44.png",
      "image_page": 26,
      "image_bbox": [0.17, 0.13, 0.82, 0.40],
      "image_loc": "line graph of pianos left unsold over Start..Day 5 (8 left at Day 5)",
      "notes": "Paper 2 Q11(b) [3 marks]. Key: 75%->735, 100%->980; (735x72)+(8x980)=52920+7840=$60760. Uses same graph as Q44."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "The pie chart shows the different types of fruit sold at a stall last month. The shop sold 800 fruits in total. Half of the fruits sold were oranges. The shop sold 40 more apples than pears. The durians made up 17% of the fruits sold.<br>How many durians did the shop sell?<br>[?]",
      "answer0": "136",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 236,
      "difficulty_id": 2,
      "explanation": "Durians = 17% of 800 = 0.17 × 800 = 136. Answer: 136.",
      "hints": ["Durians are 17% of the total.", "17% of 800 = 0.17 × 800."],
      "source": "Pei Chun 2024 P6 Prelim P2 Q12a",
      "image_needed": true,
      "image_options": false,
      "image_file": "q46.png",
      "image_page": 27,
      "image_bbox": [0.30, 0.13, 0.66, 0.42],
      "image_loc": "pie chart of fruit types (Apples, Oranges, Pears, Durians 17%)",
      "notes": "Paper 2 Q12(a) [1 mark]. Key: 8 x 17 = 136."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "The pie chart shows the different types of fruit sold at a stall last month. The shop sold 800 fruits in total. Half of the fruits sold were oranges. The shop sold 40 more apples than pears. The durians made up 17% of the fruits sold (136 durians).<br>What percentage of the fruits sold last month were pears?<br>[?] %",
      "answer0": "14",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 236,
      "difficulty_id": 3,
      "explanation": "Oranges = half = 400. Durians = 136. Apples + pears = 800 − 400 − 136 = 264, with apples 40 more than pears: pears = (264 − 40) ÷ 2 = 112. Percentage = 112/800 × 100% = 14%. Answer: 14.",
      "hints": ["Apples + pears = 800 − oranges − durians.", "Apples = pears + 40; solve for pears then find the percentage."],
      "source": "Pei Chun 2024 P6 Prelim P2 Q12b",
      "image_needed": true,
      "image_options": false,
      "image_file": "q46.png",
      "image_page": 27,
      "image_bbox": [0.30, 0.13, 0.66, 0.42],
      "image_loc": "pie chart of fruit types (Apples, Oranges, Pears, Durians 17%)",
      "notes": "Paper 2 Q12(b) [3 marks]. Key: (800-400-136-40)/2 = 112; 112/800 x 100% = 14%. Uses same pie chart as Q46."
    },
    {
      "n": 48,
      "type_id": 2,
      "question": "In the figure, ABCD is a parallelogram. E is a point on AB and EDF is a straight line. \\(\\angle BAD = 137\\degree\\), \\(\\angle EDA = 18\\degree\\) and \\(\\angle DCF = 15\\degree\\).<br>Find \\(\\angle BED\\).<br>[?]",
      "answer0": "155",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "In triangle AED, ∠DEA = 180 − ∠BAD − ∠EDA = 180 − 137 − 18 = 25°. ∠BED and ∠DEA are angles on a straight line AB, so ∠BED = 180 − 25 = 155°. Answer: 155.",
      "hints": ["Use triangle AED angle sum to find ∠DEA.", "∠BED is the supplement of ∠DEA on line AB."],
      "source": "Pei Chun 2024 P6 Prelim P2 Q13a",
      "image_needed": true,
      "image_options": false,
      "image_file": "q48.png",
      "image_page": 28,
      "image_bbox": [0.20, 0.15, 0.78, 0.32],
      "image_loc": "parallelogram ABCD with E on AB and straight line EDF, angles marked",
      "notes": "Paper 2 Q13(a) [2 marks]. Key: angle DEA = 180-155=25; BED = 180-25 = 155 degrees."
    },
    {
      "n": 49,
      "type_id": 2,
      "question": "In the figure, ABCD is a parallelogram. E is a point on AB and EDF is a straight line. \\(\\angle BAD = 137\\degree\\), \\(\\angle EDA = 18\\degree\\) and \\(\\angle DCF = 15\\degree\\).<br>Find \\(\\angle CFD\\).<br>[?]",
      "answer0": "10",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "∠CDA = 180 − 137 = 43° (co-interior angles of parallelogram). ∠CDF = ∠CDA − ∠EDA = 43 − 18 = 25°. ∠CDF and ∠CDA... ∠CDF along line EDF gives ∠CDF (interior of triangle CDF) = 180 − 25 = 155°. In triangle CDF, ∠CFD = 180 − 155 − 15 = 10°. Answer: 10.",
      "hints": ["Find ∠CDA in the parallelogram, then ∠CDF using ∠EDA.", "Use triangle CDF angle sum with ∠DCF = 15°."],
      "source": "Pei Chun 2024 P6 Prelim P2 Q13b",
      "image_needed": true,
      "image_options": false,
      "image_file": "q48.png",
      "image_page": 28,
      "image_bbox": [0.20, 0.15, 0.78, 0.32],
      "image_loc": "parallelogram ABCD with E on AB and straight line EDF, angles marked",
      "notes": "Paper 2 Q13(b) [2 marks]. Key: CDA=43, CDF=25, angle CDF(triangle)=155, CFD=180-155-15=10 degrees. Uses same figure as Q48."
    },
    {
      "n": 50,
      "type_id": 2,
      "question": "Jill had a roll of lace. He used \\(\\dfrac{4}{7}\\) of the lace to make 15 similar blouses and 7 similar skirts. The length of the lace used for 5 blouses was the same as the length of the lace used for 3 skirts.<br>How many skirts can he make with the same length of lace used for 15 similar blouses?<br>[?]",
      "answer0": "9",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "5 blouses = 3 skirts (equal lace), so 15 blouses = 3 × 3 = 9 skirts. Answer: 9.",
      "hints": ["Use the relation 5 blouses = 3 skirts.", "Scale up: 15 blouses is 3 times 5 blouses."],
      "source": "Pei Chun 2024 P6 Prelim P2 Q14a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q14(a) [1 mark]. Key: 5b=3s, 15b=9 skirts."
    },
    {
      "n": 51,
      "type_id": 2,
      "question": "Jill had a roll of lace. He used \\(\\dfrac{4}{7}\\) of the lace to make 15 similar blouses and 7 similar skirts. The length of the lace used for 5 blouses was the same as the length of the lace used for 3 skirts (so 15 blouses use the same lace as 9 skirts).<br>What is the greatest number of skirts he can make with \\(\\dfrac{5}{6}\\) of the remaining lace?<br>[?]",
      "answer0": "10",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "15 blouses + 7 skirts = 9 skirts + 7 skirts = 16 skirts' worth of lace = 4/7 of the roll. So 4/7 of roll = 16 skirts, meaning 1/7 = 4 skirts, and the whole roll = 28 skirts. Remaining lace = 3/7 of roll = 12 skirts. 5/6 of remaining = 5/6 × 12 = 10 skirts. Answer: 10.",
      "hints": ["Convert the 15 blouses into skirts, then total the used lace in 'skirts'.", "Find the whole roll in skirts, take the remaining 3/7, then 5/6 of it."],
      "source": "Pei Chun 2024 P6 Prelim P2 Q14b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q14(b) [3 marks]. Key: 4/7 -> 8 units? Printed: 8u -> 9+7=16; 5u -> (16/8)x5 = 10 skirts."
    },
    {
      "n": 52,
      "type_id": 2,
      "question": "Figure X and Figure Y are made up of identical right-angled triangles. The perimeter of Figure X is 46 cm. The perimeter of Figure Y is 96 cm. The length of AB is 17 cm.<br>What is the length of CD?<br>[?] cm",
      "answer0": "7",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 138,
      "difficulty_id": 3,
      "explanation": "Figure X (one triangle, a rectangle outline) perimeter 46 cm, with AB (hypotenuse) = 17 cm, so the two legs sum: 46 ÷ 2 = 23 = length + breadth; one leg = 23 − 17 ... working from key: 91 − 17×4 = 28, then 28 ÷ 4 = 7 cm. CD = 7 cm. Answer: 7.",
      "hints": ["Relate the perimeters of Figures X and Y to the triangle's sides and AB.", "Use the printed working: 91 − 17×4 = 28, then ÷ 4."],
      "source": "Pei Chun 2024 P6 Prelim P2 Q15a",
      "image_needed": true,
      "image_options": false,
      "image_file": "q52.png",
      "image_page": 30,
      "image_bbox": [0.18, 0.14, 0.80, 0.40],
      "image_loc": "Figure X (rectangle with diagonal AB) and Figure Y (pinwheel of triangles, CD marked)",
      "notes": "Paper 2 Q15(a) [1 mark]. Key: 91 - 17x4 = 28; 28/4 = 7 cm. (91 = 46 + 96 - ... per printed working.)"
    },
    {
      "n": 53,
      "type_id": 2,
      "question": "Figure X and Figure Y are made up of identical right-angled triangles. The perimeter of Figure X is 46 cm. The perimeter of Figure Y is 96 cm. The length of AB is 17 cm, and CD is 7 cm.<br>What is the area of 1 right-angled triangle?<br>[?] cm²",
      "answer0": "60",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "From the perimeters, the triangle's legs are base B and height H with H = B + 7. Half-perimeter of Figure X: 46 ÷ 2 = 23 = H + B, and H = B + 7 → 23 = (B + 7) + B → 2B = 16 → B = 8, H = 15. Area = 1/2 × 8 × 15 = 60 cm². Answer: 60.",
      "hints": ["The two legs differ by 7 (the value of CD) and sum to 23.", "Area of a right triangle = 1/2 × base × height."],
      "source": "Pei Chun 2024 P6 Prelim P2 Q15b",
      "image_needed": true,
      "image_options": false,
      "image_file": "q52.png",
      "image_page": 30,
      "image_bbox": [0.18, 0.14, 0.80, 0.40],
      "image_loc": "Figure X (rectangle with diagonal AB) and Figure Y (pinwheel of triangles)",
      "notes": "Paper 2 Q15(b) [3 marks]. Key: 46/2=23, H=B+7, B=8, H=15; area = 1/2 x 8 x 15 = 60 cm2. Uses same figures as Q52."
    },
    {
      "n": 54,
      "type_id": 2,
      "question": "Joseph has some red, blue and orange beads. 28% of the beads are blue. There are 25 more blue beads than orange beads. There were 289 red beads.<br>How many blue beads are there altogether?<br>[?]",
      "answer0": "168",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 207,
      "difficulty_id": 3,
      "explanation": "Blue = 28%, orange = 28% − 25 beads (blue is 25 more than orange). Red = 289 = 100% − 28% − orange%. Red and orange together = 100 − 28 = 72% but orange = blue − 25. Using the key: 289 − 25 = 264 = 4.4 units (44% combined adjustment) → 1 unit (1%) = 60, so blue = 2.8 units = 28 × 6 = 168. Answer: 168.",
      "hints": ["Express blue and orange both in terms of the 28% unit; orange = blue − 25.", "Red is the remaining percentage; set up an equation to find 1% of the beads."],
      "source": "Pei Chun 2024 P6 Prelim P2 Q16a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q16(a) [2 marks]. Key: B=2.8u, O=2.8u-25, R=289; 289-25=264; 4.4u=264; 1u=60; 2.8u=168 blue beads."
    },
    {
      "n": 55,
      "type_id": 2,
      "question": "Joseph has some red, blue and orange beads. 28% of the beads are blue (168 blue beads). There are 25 more blue beads than orange beads. There were 289 red beads.<br>After Joseph bought more blue beads, the percentage of blue beads increased to 64%. How many blue beads did he buy?<br>[?]",
      "answer0": "600",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 208,
      "difficulty_id": 3,
      "explanation": "Red + orange stay the same = 289 + (168 − 25) = 289 + 143 = 432. After buying, these are 100 − 64 = 36% of the new total, so total = 432 ÷ 36% = 1200. New blue = 64% × 1200 = 768. Blue bought = 768 − 168 = 600. Answer: 600.",
      "hints": ["Red + orange beads don't change; after the purchase they form 36% of the new total.", "Find the new total, then the new blue count, then subtract the original 168."],
      "source": "Pei Chun 2024 P6 Prelim P2 Q16b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q16(b) [3 marks]. Key: red+orange = 29x9+289 = 432 (=36%); 1%=12; 64%=768; 768-168=600 blue beads bought."
    },
    {
      "n": 56,
      "type_id": 2,
      "question": "The figure is made up of 5 identical quarter circles. The figure spans 13 cm, 8 cm, 7 cm, 8 cm, 13 cm across the bottom.<br>Find the radius of a quarter circle.<br>[?] cm",
      "answer0": "17",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 221,
      "difficulty_id": 3,
      "explanation": "Along the top span: 13 + 7 + 13 = 33 cm. Along the gaps: 8 + 8 = 16 cm. The radius = 33 − 16 = 17 cm. Answer: 17.",
      "hints": ["Add the larger horizontal segments, then subtract the two 8 cm gaps.", "Radius = (13 + 7 + 13) − (8 + 8)."],
      "source": "Pei Chun 2024 P6 Prelim P2 Q17a",
      "image_needed": true,
      "image_options": false,
      "image_file": "q56.png",
      "image_page": 32,
      "image_bbox": [0.12, 0.11, 0.66, 0.34],
      "image_loc": "figure of 5 interlocking quarter circles with 13/8/7/8/13 cm labels",
      "notes": "Paper 2 Q17(a) [2 marks]. Key: 13+7+13 = 33; 8+8 = 16; 33-16 = 17 cm."
    },
    {
      "n": 57,
      "type_id": 2,
      "question": "The figure is made up of 5 identical quarter circles, each of radius 17 cm.<br>Find the perimeter of the figure. Take \\(\\pi = 3.14\\). Round your answer to the nearest 1 decimal place.<br>[?] cm",
      "answer0": "267.45",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 222,
      "difficulty_id": 3,
      "explanation": "Curved parts = 5 quarter arcs = 5/4 × 2πr = 5/4 × 3.14 × 17 × 2 = 133.45 cm. Straight parts = 17×5 + 13×2 + 7 + 8×2 = 85 + 26 + 7 + 16 = 134 cm. Perimeter = 134 + 133.45 = 267.45 cm. (Already to 1 d.p.) Answer: 267.45.",
      "hints": ["Curved length = 5 quarter-circle arcs = 5/4 of a full circumference.", "Add the straight edges from the printed working, then total."],
      "source": "Pei Chun 2024 P6 Prelim P2 Q17b",
      "image_needed": true,
      "image_options": false,
      "image_file": "q56.png",
      "image_page": 32,
      "image_bbox": [0.12, 0.11, 0.66, 0.34],
      "image_loc": "figure of 5 interlocking quarter circles with 13/8/7/8/13 cm labels",
      "notes": "Paper 2 Q17(b) [2 marks]. Key: curved = 5/4 x 3.14 x 17 x 2 = 133.45; straight = 17x5 + 13x2 + 7 + 8x2 = 134; total 267.45 cm. Uses same figure as Q56."
    }
  ]
}