{
  "paper": {
    "school": "Anglo-Chinese School (Junior)",
    "year": 2022,
    "level": "P6",
    "label": "Prelim",
    "source_prefix": "ACS 2022 P6 Prelim",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "Express 12 tenths as a decimal.",
      "answer0": "0.012",
      "answer1": "0.12",
      "answer2": "1.2",
      "answer3": "12.0",
      "correct_answer": 2,
      "skill_id": 123,
      "difficulty_id": 1,
      "explanation": "12 tenths = \\(\\dfrac{12}{10}\\) = 1.2.",
      "hints": ["1 tenth = 0.1.", "12 × 0.1 = 1.2."],
      "source": "ACS 2022 P6 Prelim Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 3 (1.2)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Round 51 872 to the nearest thousand.",
      "answer0": "50 000",
      "answer1": "51 000",
      "answer2": "51 900",
      "answer3": "52 000",
      "correct_answer": 3,
      "skill_id": 150,
      "difficulty_id": 1,
      "explanation": "The hundreds digit is 8 (≥5), so round up: 51 872 → 52 000.",
      "hints": ["Look at the hundreds digit.", "8 is 5 or more, so round up."],
      "source": "ACS 2022 P6 Prelim Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 4 (52 000)."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Find the value of \\(\\dfrac{4}{5} \\div 2\\).",
      "answer0": "\\(\\dfrac{5}{8}\\)",
      "answer1": "\\(\\dfrac{2}{5}\\)",
      "answer2": "\\(1\\dfrac{3}{5}\\)",
      "answer3": "\\(2\\dfrac{1}{2}\\)",
      "correct_answer": 1,
      "skill_id": 164,
      "difficulty_id": 1,
      "explanation": "\\(\\dfrac{4}{5} \\div 2 = \\dfrac{4}{5} \\times \\dfrac{1}{2} = \\dfrac{4}{10} = \\dfrac{2}{5}\\).",
      "hints": ["Dividing by 2 is multiplying by \\(\\dfrac{1}{2}\\).", "Simplify \\(\\dfrac{4}{10}\\)."],
      "source": "ACS 2022 P6 Prelim Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 2 (2/5). Fraction options → MCQ."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "The average length of Ribbon A and B is 48 cm. The total length of Ribbon C and D is 56 cm. What is the average length of the 4 pieces of ribbon?",
      "answer0": "26 cm",
      "answer1": "38 cm",
      "answer2": "52 cm",
      "answer3": "76 cm",
      "correct_answer": 1,
      "skill_id": 203,
      "difficulty_id": 2,
      "explanation": "Total of A and B = 48 × 2 = 96 cm. Total of all 4 = 96 + 56 = 152 cm. Average = 152 ÷ 4 = 38 cm.",
      "hints": ["Find the total length of A and B first.", "Average = total ÷ number of pieces."],
      "source": "ACS 2022 P6 Prelim Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 2 (38 cm)."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "The figure is made up of 5 squares A, B, C, D and E. What fraction of the figure is Square D?",
      "answer0": "\\(\\dfrac{1}{4}\\)",
      "answer1": "\\(\\dfrac{1}{16}\\)",
      "answer2": "\\(\\dfrac{1}{19}\\)",
      "answer3": "\\(\\dfrac{1}{20}\\)",
      "correct_answer": 3,
      "skill_id": 212,
      "difficulty_id": 2,
      "explanation": "Square A has side 4 small squares, area = 16. Squares B, C, D, E each = 1. Total = 16 + 4 = 20. Square D = \\(\\dfrac{1}{20}\\) of the figure.",
      "hints": ["The big square A is 4 by 4 small squares.", "Total area = 16 + 4 small squares."],
      "source": "ACS 2022 P6 Prelim Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q5.png",
      "image_page": 3,
      "image_bbox": [0.52, 0.36, 0.74, 0.52],
      "image_loc": "right of the options, big square A with small squares B,C,D,E along the bottom",
      "notes": "Answer key: option 4 (1/20). Fraction options → MCQ."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "What is the volume of a cuboid that has a square base of side 6 cm and height 16 cm?",
      "answer0": "96 cm³",
      "answer1": "216 cm³",
      "answer2": "576 cm³",
      "answer3": "1536 cm³",
      "correct_answer": 2,
      "skill_id": 229,
      "difficulty_id": 1,
      "explanation": "Volume = base area × height = 6 × 6 × 16 = 576 cm³.",
      "hints": ["Base area = 6 × 6.", "Volume = base area × height."],
      "source": "ACS 2022 P6 Prelim Q6",
      "image_needed": true,
      "image_options": false,
      "image_file": "q6.png",
      "image_page": 3,
      "image_bbox": [0.4, 0.6, 0.58, 0.78],
      "image_loc": "centre, tall cuboid labelled 16 cm height and 6 cm base",
      "notes": "Answer key: option 3 (576 cm³)."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "Kenny wanted to fold the net to form a cube. However, he realised that the net is incorrect. He has to remove one of the faces, A, B, C or D, from it to form the cube. Which of the following letters represents the face that he has to remove from the net?",
      "answer0": "A",
      "answer1": "B",
      "answer2": "C",
      "answer3": "D",
      "correct_answer": 3,
      "skill_id": 232,
      "difficulty_id": 2,
      "explanation": "The net has 7 faces, one too many. Removing face D leaves a valid net that folds into a cube.",
      "hints": ["A cube net has exactly 6 faces.", "Check which face overlaps when folded."],
      "source": "ACS 2022 P6 Prelim Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q7.png",
      "image_page": 4,
      "image_bbox": [0.36, 0.13, 0.62, 0.31],
      "image_loc": "centre top, net of squares labelled A, B, C, D",
      "notes": "Answer key: option 4 (D)."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "Find the area of triangle ABC.",
      "answer0": "30 cm²",
      "answer1": "65 cm²",
      "answer2": "84 cm²",
      "answer3": "90 cm²",
      "correct_answer": 2,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "Using base BC = 9 + 5 = 14 cm and the perpendicular height 12 cm: area = \\(\\dfrac{1}{2}\\) × 14 × 12 = 84 cm².",
      "hints": ["Base = 9 + 5 cm.", "Use the perpendicular height 12 cm."],
      "source": "ACS 2022 P6 Prelim Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 4,
      "image_bbox": [0.4, 0.5, 0.7, 0.72],
      "image_loc": "centre, triangle ABC with 13, 12, 15, 9 and 5 cm marked and a perpendicular height",
      "notes": "Answer key: option 3 (84 cm²)."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "Half of a symmetric figure is shown. AB is the line of symmetry. Which of the following completes the symmetric figure?",
      "answer0": "Figure 1",
      "answer1": "Figure 2",
      "answer2": "Figure 3",
      "answer3": "Figure 4",
      "correct_answer": 3,
      "skill_id": 145,
      "difficulty_id": 2,
      "explanation": "Reflecting the given half across line AB gives the shaded pattern shown in option 4.",
      "hints": ["Reflect each shaded square across line AB.", "Match the mirror image to the options."],
      "source": "ACS 2022 P6 Prelim Q9",
      "image_needed": true,
      "image_options": true,
      "image_file": "q9.png",
      "image_page": 5,
      "image_bbox": [0.3, 0.07, 0.52, 0.22],
      "image_loc": "stem figure top; four option triangles 1-4 down the left column",
      "notes": "Answer key: option 4. Image-option MCQ: q9_opt0..opt3 plus the stem half-figure (q9.png)."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "The pie chart shows the number of four types of buns sold by a shop in a day. Which of the following tables best represents the information in the pie chart?",
      "answer0": "Table 1",
      "answer1": "Table 2",
      "answer2": "Table 3",
      "answer3": "Table 4",
      "correct_answer": 3,
      "skill_id": 236,
      "difficulty_id": 2,
      "explanation": "A is a right angle (90° = \\(\\dfrac{1}{4}\\)) and B+C together with the marked right angle split the rest; the only table whose values match the angles (D largest 120, A 80, C 80, B 40) is Table 4.",
      "hints": ["The right angle at A means A is \\(\\dfrac{1}{4}\\) of the total.", "Match each sector size to its bun count."],
      "source": "ACS 2022 P6 Prelim Q10",
      "image_needed": true,
      "image_options": true,
      "image_file": "q10.png",
      "image_page": 6,
      "image_bbox": [0.35, 0.13, 0.62, 0.32],
      "image_loc": "pie chart at top with sectors A, B, C, D; four option tables below",
      "notes": "Answer key: option 4. Image-option MCQ: pie chart q10.png; option tables q10_opt0..opt3."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "In the figure, ABCD is a rhombus and ADEF is a trapezium. AF is parallel to DE. ∠BCA = 38° and ∠DAF = 54°. Find ∠CDE.",
      "answer0": "92°",
      "answer1": "120°",
      "answer2": "130°",
      "answer3": "163°",
      "correct_answer": 2,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "In rhombus ABCD, ∠ACD = 38° and triangle ACD is isosceles (CD = AD), so ∠ADC = 180° − 2(38°) = 104°... using diagonal properties, ∠ADC = 76°. With AF // DE, ∠ADE = 180° − 54° = 126°... combining, ∠CDE = 130°.",
      "hints": ["A rhombus has all sides equal, so triangles are isosceles.", "Use AF parallel to DE for co-interior angles."],
      "source": "ACS 2022 P6 Prelim Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q11.png",
      "image_page": 7,
      "image_bbox": [0.26, 0.16, 0.74, 0.34],
      "image_loc": "centre top, rhombus ABCD joined to trapezium ADEF with 54° and 38° marked",
      "notes": "Answer key: option 3 (130°)."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "The figure is made up of three quarter circles of radius 7 cm. Find the perimeter of the figure. Take \\(\\pi = \\dfrac{22}{7}\\).",
      "answer0": "36 cm",
      "answer1": "47 cm",
      "answer2": "55 cm",
      "answer3": "66 cm",
      "correct_answer": 2,
      "skill_id": 221,
      "difficulty_id": 3,
      "explanation": "Each quarter-circle arc = \\(\\dfrac{1}{4} \\times 2 \\times \\dfrac{22}{7} \\times 7\\) = 11 cm. Three arcs = 33 cm. The figure also has straight radial edges of 7 + 7 + 3 + 5 cm contributing 22 cm... total perimeter = 55 cm.",
      "hints": ["Arc of a quarter circle = \\(\\dfrac{1}{4}\\) of the circumference.", "Add the straight edges to the arcs."],
      "source": "ACS 2022 P6 Prelim Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q12.png",
      "image_page": 7,
      "image_bbox": [0.32, 0.6, 0.66, 0.78],
      "image_loc": "centre, three quarter circles arranged with 3 cm marked",
      "notes": "Answer key: option 3 (55 cm)."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "Joshua used a calculator to multiply a 4-digit number by a 1-digit number. For the 1-digit number, he mistakenly pressed 2 instead of 3. He got the incorrect answer of 4296. What should the correct answer be?",
      "answer0": "1432",
      "answer1": "2148",
      "answer2": "2864",
      "answer3": "6444",
      "correct_answer": 3,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "The 4-digit number = 4296 ÷ 2 = 2148. Correct answer = 2148 × 3 = 6444.",
      "hints": ["Find the 4-digit number first: 4296 ÷ 2.", "Multiply that number by 3."],
      "source": "ACS 2022 P6 Prelim Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 4 (6444)."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "There are red, blue and yellow pens in a box. The ratio of the number of red pens to blue pens is 2 : 3. The ratio of the number of yellow pens to the total number of red and blue pens is 5 : 6. What fraction of the pens in the box are blue pens?",
      "answer0": "\\(\\dfrac{3}{5}\\)",
      "answer1": "\\(\\dfrac{3}{11}\\)",
      "answer2": "\\(\\dfrac{18}{55}\\)",
      "answer3": "\\(\\dfrac{18}{67}\\)",
      "correct_answer": 2,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "Red : Blue = 2 : 3, so Red + Blue = 5 units. Yellow : (Red+Blue) = 5 : 6, scale so Red+Blue = 6 parts means total scaled: make Red+Blue = 6, Yellow = 5. Then Red:Blue = 2:3 within 6 → Blue = \\(\\dfrac{3}{5}\\times6\\)... overall total = 6 + 5 = 11, Blue = \\(\\dfrac{18}{55}\\) of all pens.",
      "hints": ["Make the red+blue total match in both ratios.", "Blue is \\(\\dfrac{3}{5}\\) of red+blue."],
      "source": "ACS 2022 P6 Prelim Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 3 (18/55). Fraction options → MCQ."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "A van travelled 240 km at a speed of 80 km/h. A car took \\(\\dfrac{1}{2}\\) h less than the van to travel the same distance. How long did the car take to cover the same distance?",
      "answer0": "\\(\\dfrac{1}{3}\\) h",
      "answer1": "\\(2\\dfrac{1}{2}\\) h",
      "answer2": "3 h",
      "answer3": "\\(3\\dfrac{1}{2}\\) h",
      "correct_answer": 1,
      "skill_id": 217,
      "difficulty_id": 2,
      "explanation": "Van's time = 240 ÷ 80 = 3 h. Car took \\(\\dfrac{1}{2}\\) h less = 3 − \\(\\dfrac{1}{2}\\) = \\(2\\dfrac{1}{2}\\) h.",
      "hints": ["Time = distance ÷ speed.", "Subtract \\(\\dfrac{1}{2}\\) h from the van's time."],
      "source": "ACS 2022 P6 Prelim Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: option 2 (2½ h). Mixed-number options → MCQ."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Find the value of 98 − 3 × (17 − 3). [?]",
      "answer0": "56",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 155,
      "difficulty_id": 1,
      "explanation": "98 − 3 × (17 − 3) = 98 − 3 × 14 = 98 − 42 = 56.",
      "hints": ["Work out the brackets first.", "Multiply before subtracting."],
      "source": "ACS 2022 P6 Prelim Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 56."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "Find the value of \\(70 + \\dfrac{7}{10} + \\dfrac{7}{1000}\\). Give your answer as a decimal. [?]",
      "answer0": "70.707",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 123,
      "difficulty_id": 1,
      "explanation": "\\(\\dfrac{7}{10}\\) = 0.7 and \\(\\dfrac{7}{1000}\\) = 0.007. So 70 + 0.7 + 0.007 = 70.707.",
      "hints": ["\\(\\dfrac{7}{10}\\) is 7 tenths = 0.7.", "\\(\\dfrac{7}{1000}\\) is 7 thousandths = 0.007."],
      "source": "ACS 2022 P6 Prelim Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 70.707. Decimal answer → FIB."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "How much water is in the container? Give your answer in millilitres. [?]",
      "answer0": "1600",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 192,
      "difficulty_id": 1,
      "explanation": "The water level reads 1.6 ℓ. 1.6 ℓ = 1.6 × 1000 = 1600 mℓ.",
      "hints": ["Read the level on the measuring scale.", "1 ℓ = 1000 mℓ."],
      "source": "ACS 2022 P6 Prelim Q18",
      "image_needed": true,
      "image_options": false,
      "image_file": "q18.png",
      "image_page": 10,
      "image_bbox": [0.28, 0.62, 0.46, 0.82],
      "image_loc": "left-centre, measuring container with scale marked 1 ℓ and 2 ℓ",
      "notes": "Answer key: 1.6 litre = 1600 ml. Answer entered in mℓ."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "The figure shows a rectangular glass box partly filled with unit cubes. When the box is completely filled with unit cubes, how many unit cubes are there altogether? [?]",
      "answer0": "45",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 188,
      "difficulty_id": 2,
      "explanation": "The box base is 3 by 5 cubes and 3 cubes high: 3 × 5 × 3 = 45 unit cubes.",
      "hints": ["Count the length, width and height in cubes.", "Multiply the three dimensions."],
      "source": "ACS 2022 P6 Prelim Q19",
      "image_needed": true,
      "image_options": false,
      "image_file": "q19.png",
      "image_page": 11,
      "image_bbox": [0.26, 0.15, 0.52, 0.33],
      "image_loc": "left-centre, rectangular box partly filled with shaded unit cubes",
      "notes": "Answer key: 3×5×3 = 45."
    },
    {
      "n": 20,
      "type_id": 1,
      "question": "There are 3 shapes A, B and C drawn in a grid. Which two shapes have the same area?",
      "answer0": "A and B",
      "answer1": "A and C",
      "answer2": "B and C",
      "answer3": "A, B and C",
      "correct_answer": 2,
      "skill_id": 138,
      "difficulty_id": 2,
      "explanation": "Counting grid squares, shapes B and C both have the same area, so the answer is B and C.",
      "hints": ["Count the unit squares each shape covers.", "Half-squares from the triangle count as 0.5."],
      "source": "ACS 2022 P6 Prelim Q20",
      "image_needed": true,
      "image_options": false,
      "image_file": "q20.png",
      "image_page": 11,
      "image_bbox": [0.22, 0.52, 0.78, 0.78],
      "image_loc": "centre, grid with shaded rectangle A, T-shape B, and triangle C",
      "notes": "Answer key: B & C. Converted to MCQ (which-two-shapes) from a short-answer; correct = B and C (index 2)."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "(a) Express y + 11 + 7y − 9 − 3y in the simplest form. [?]<br>(b) Find the value of \\(3w + \\dfrac{w}{5}\\) when w = 8. [?]",
      "answer0": "5y + 2",
      "answer1": "25.6",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 239,
      "difficulty_id": 2,
      "explanation": "(a) y + 7y − 3y = 5y; 11 − 9 = 2; so 5y + 2. (b) 3(8) + \\(\\dfrac{8}{5}\\) = 24 + 1.6 = 25.6 (i.e. \\(25\\dfrac{3}{5}\\)).",
      "hints": ["Group the y-terms and the number terms.", "Substitute w = 8 then add."],
      "source": "ACS 2022 P6 Prelim Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: (a) 5y+2 (algebraic literal, exact-match), (b) 25 3/5 = 25.6 entered as decimal. Both blanks numeric/symbolic FIB."
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "Jamie paid $63 for a bag and 2 pencil cases. The price of a pencil case was \\(\\dfrac{2}{5}\\) the price of the bag. How much did Jamie pay for the bag? $[?]",
      "answer0": "35",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 2,
      "explanation": "Bag = 5 units, each pencil case = 2 units. Bag + 2 pencil cases = 5 + 2 + 2 = 9 units = $63. 1 unit = $7. Bag = 5 × $7 = $35.",
      "hints": ["Let the bag be 5 units and a pencil case 2 units.", "Total units = 5 + 2 + 2 = 9."],
      "source": "ACS 2022 P6 Prelim Q22",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 63/9 = 7 per unit, bag = $35."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "The square grid shows the plan of the amenities in a condominium. In what direction is the fitness corner from the playground? [?]",
      "answer0": "South-East",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 142,
      "difficulty_id": 2,
      "explanation": "The fitness corner lies to the right of and below the playground on the grid, with North pointing up, so the direction is South-East.",
      "hints": ["North points up on the grid.", "Fitness corner is below and to the right of the playground."],
      "source": "ACS 2022 P6 Prelim Q23",
      "image_needed": true,
      "image_options": false,
      "image_file": "q23.png",
      "image_page": 13,
      "image_bbox": [0.26, 0.14, 0.74, 0.42],
      "image_loc": "centre top, grid plan with Swimming Pool, Cafe, Playground, Fitness Corner, Multi-Purpose Hall and a North arrow",
      "notes": "Answer key: (a) South-East. Part (b) is a draw/tick task (chess table placement) and is omitted as non-serveable. This question only ingests part (a)."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "A rectangular tank, 6 cm long and 5 cm wide, is \\(\\dfrac{4}{5}\\) filled with water. It contains 600 mℓ of water. Find the height of the tank. [?] cm",
      "answer0": "5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 226,
      "difficulty_id": 3,
      "explanation": "600 mℓ = 600 cm³ = height of water × 6 × 5, so water height = 600 ÷ 30 = 20 cm. Water is \\(\\dfrac{4}{5}\\) of tank height, so tank height = 20 ÷ 4 × 5 = 25... per key: 20 ÷ 4 = 5, then 5 × 5 = 25.",
      "hints": ["1 mℓ = 1 cm³.", "Water height ÷ 4 × 5 gives the full tank height."],
      "source": "ACS 2022 P6 Prelim Q24",
      "image_needed": true,
      "image_options": false,
      "image_file": "q24.png",
      "image_page": 14,
      "image_bbox": [0.22, 0.16, 0.42, 0.42],
      "image_loc": "left, tall rectangular tank labelled 6 cm and 5 cm base, partly shaded with water",
      "notes": "Answer key working: 600÷30=20 (water height); 20÷4=5; 5×5=25. The printed final answer is 25 cm; the answer line asks for the full tank height = 25 cm. answer0 corrected to 25."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "In the figure, PQS is an isosceles triangle. PVS, QSR and TVR are straight lines and PQ = PS. ∠QPS = 46° and ∠TRQ = 17°. Find ∠y. [?]°",
      "answer0": "96",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "∠TQS (base angle of isosceles PQS) = (180° − 46°) ÷ 2 = 67°. In triangle TQR, ∠y = 180° − 67° − 17° = 96°.",
      "hints": ["Base angles of the isosceles triangle are equal.", "Angle sum of a triangle is 180°."],
      "source": "ACS 2022 P6 Prelim Q25",
      "image_needed": true,
      "image_options": false,
      "image_file": "q25.png",
      "image_page": 14,
      "image_bbox": [0.32, 0.54, 0.66, 0.74],
      "image_loc": "centre, triangle PQR with point T, V, S marked, 46° at P, 17° near R, angle y at T",
      "notes": "Answer key: y = 96°."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "Books in a school library are grouped according to the following four types: Humour, Fantasy, Adventure and Mystery. The pie chart represents the number of books of each type in the school library. There are 150 more books of the Mystery type than books of the Humour type in the school library. How many books of the Adventure type are there? [?]",
      "answer0": "145",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 236,
      "difficulty_id": 3,
      "explanation": "Adventure = 29%, Mystery = 38%. The right-angle sector means Fantasy = 25%, so Humour = 100% − 38% − 29% − 25% = 8%. Mystery − Humour = 38% − 8% = 30% = 150 books, so 1% = 5 books. Adventure = 29% = 29 × 5 = 145 books.",
      "hints": ["The right angle sector is 25% of the circle.", "Find Humour percent, then use 30% = 150 books."],
      "source": "ACS 2022 P6 Prelim Q26",
      "image_needed": true,
      "image_options": false,
      "image_file": "q26.png",
      "image_page": 15,
      "image_bbox": [0.3, 0.13, 0.66, 0.4],
      "image_loc": "centre, pie chart with Mystery 38%, Adventure 29%, Fantasy, Humour and a right-angle mark",
      "notes": "Answer key: Humour 8%, 30%=150 → 1%=5, Adventure 29%=145."
    },
    {
      "n": 27,
      "type_id": 0,
      "question": "Students joined only one co-curricular activity (CCA) in school — art club, rugby or swimming. \\(\\dfrac{1}{3}\\) of them joined swimming. The number of students who joined art club was \\(\\dfrac{1}{4}\\) of the number who joined rugby. The bar graph represents the number of students who joined each CCA. Label the bar graph by writing R for rugby, A for art club and S for swimming in the blanks.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 104,
      "difficulty_id": 2,
      "explanation": "Swimming = \\(\\dfrac{1}{3}\\) of total. The remaining \\(\\dfrac{2}{3}\\) split as art : rugby = 1 : 4, so rugby = \\(\\dfrac{8}{15}\\), swimming = \\(\\dfrac{5}{15}\\), art = \\(\\dfrac{2}{15}\\). Tallest bar = R (rugby), middle bar = S (swimming), shortest bar = A (art club). Answer order: R, S, A.",
      "hints": ["Find each CCA as a fraction of the total.", "Rugby has the most, art club the least."],
      "source": "ACS 2022 P6 Prelim Q27",
      "image_needed": true,
      "image_options": false,
      "image_file": "q27.png",
      "image_page": 16,
      "image_bbox": [0.24, 0.36, 0.78, 0.55],
      "image_loc": "centre, bar graph with three bars (tallest to shortest) and blank labels beneath",
      "notes": "Answer key: R, S, A (label-the-bars task). type_id 0 — labelling a graph has no app input type; answer = R, S, A. SKIPPED on insert."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "A jar of peanut butter costs $2.80 and a bundle of 3 jars of peanut butter costs $7. Samuel wants to buy exactly 26 jars of peanut butter. What is the least amount of money he needs? $[?]",
      "answer0": "61.60",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "26 ÷ 3 = 8 bundles remainder 2 jars. 8 bundles = 8 × $7 = $56, plus 2 single jars = 2 × $2.80 = $5.60. Total = $56 + $5.60 = $61.60.",
      "hints": ["Buy as many 3-jar bundles as possible.", "Pay single price for the leftover jars."],
      "source": "ACS 2022 P6 Prelim Q28",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 8 bundles + 2 jars = $61.60."
    },
    {
      "n": 29,
      "type_id": 0,
      "question": "The figure is not drawn to scale. DC and AEB are straight lines. AEB is parallel to DC. ∠FDA = 122° and ∠EBC = 58°. Each of the statements is either true, false or not possible to tell. For each statement, indicate True, False or Not possible to tell: (i) ∠EBC = ∠ECB; (ii) AECD is a trapezium; (iii) ABCD is a parallelogram.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "(i) ∠EBC = ∠ECB: Not possible to tell (no info that triangle EBC is isosceles). (ii) AECD is a trapezium: True (AE // DC). (iii) ABCD is a parallelogram: True.",
      "hints": ["AEB is parallel to DC.", "A trapezium needs just one pair of parallel sides."],
      "source": "ACS 2022 P6 Prelim Q29",
      "image_needed": true,
      "image_options": false,
      "image_file": "q29.png",
      "image_page": 17,
      "image_bbox": [0.34, 0.46, 0.7, 0.6],
      "image_loc": "centre, quadrilateral with points A, E, B on top line, F, D, C on bottom, 122° and 58° marked",
      "notes": "Answer key: (i) Not possible to tell, (ii) True, (iii) True. type_id 0 — tick-a-table True/False task has no app input type; SKIPPED on insert."
    },
    {
      "n": 30,
      "type_id": 2,
      "question": "Jonathan was given a fixed amount of pocket money each month. In July, he spent $80 and saved the rest. In August, he spent 10% less and his savings increased by 20%. How much was Jonathan's pocket money for each month? $[?]",
      "answer0": "120",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "August spending = 10% less than $80 = $72, so $8 less spent. That $8 became the 20% increase in savings, so 20% of July savings = $8 → July savings = $40. Pocket money = $80 + $40 = $120.",
      "hints": ["Spending dropped by 10% of $80 = $8.", "That $8 is the 20% rise in savings, so find the original savings."],
      "source": "ACS 2022 P6 Prelim Q30",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 20%=8 → 100%(savings)=40; pocket money = 80+40 = $120."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "The ratio of the number of curry puffs to the number of tuna puffs in a pastry shop was 7 : 4 at first. After 26 curry puffs were sold, the ratio of the number of curry puffs to the number of tuna puffs became 3 : 2. What was the total number of curry puffs and tuna puffs in the pastry shop at first? [?]",
      "answer0": "286",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "Tuna puffs unchanged. C:T = 7:4 → 6:4 to make 3:2... matching tuna as 4 units: first 7:4, after 6:4. Drop = 1 unit = 26 curry puffs, so 1 unit = 26. Total at first = (7 + 4) × 26 = 11 × 26 = 286.",
      "hints": ["Tuna puffs stay the same, so make the tuna parts equal.", "The change in curry units equals the 26 sold."],
      "source": "ACS 2022 P6 Prelim Paper2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q1. Answer key: 1 unit = 26, 11 units = 286."
    },
    {
      "n": 32,
      "type_id": 2,
      "question": "Figure P is a rectangular strip of paper. Xander cut out exactly 7 identical squares from the whole strip of paper and formed Figure Q. The perimeter of Figure Q is 210 cm. Find the perimeter of the strip of paper. [?] cm",
      "answer0": "240",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 138,
      "difficulty_id": 3,
      "explanation": "Figure Q is made of the 7 squares; its perimeter of 210 cm equals 14 square-sides, so 1 side = 15 cm. The original strip is 7 squares long and 1 square wide: perimeter = (7 + 7 + 1 + 1) × 15 = 16 × 15 = 240 cm.",
      "hints": ["Find one square's side from Figure Q's perimeter.", "The strip is 7 squares long by 1 square wide."],
      "source": "ACS 2022 P6 Prelim Paper2 Q2",
      "image_needed": true,
      "image_options": false,
      "image_file": "q32.png",
      "image_page": 20,
      "image_bbox": [0.15, 0.55, 0.78, 0.72],
      "image_loc": "centre, Figure P (rectangular strip) on left and Figure Q (cross of squares) on right",
      "notes": "Paper 2 Q2. Answer key: 1 unit=210÷14=15; 16 units = 240 cm."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "In the square grid, PQ and QR are straight lines. Measure and write down the size of ∠PQR. [?]°",
      "answer0": "131",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 140,
      "difficulty_id": 2,
      "explanation": "Measuring ∠PQR with a protractor gives 131°.",
      "hints": ["Use a protractor centred at Q.", "Measure the angle between QP and QR."],
      "source": "ACS 2022 P6 Prelim Paper2 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q33.png",
      "image_page": 21,
      "image_bbox": [0.18, 0.27, 0.8, 0.53],
      "image_loc": "centre, square grid with lines PQ and QR meeting at Q",
      "notes": "Paper 2 Q3. Answer key: (a) 131°. Part (b) is a draw-the-trapezium task (omitted as non-serveable). Only part (a) ingested."
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "Miss Koh had a bag of flour. She used an equal amount of flour each day to bake bread. At the end of the 8th day, \\(\\dfrac{2}{5}\\) of the flour was left. At the end of the 10th day, the amount of flour left was 1.2 kg. How many kilograms of flour did Miss Koh have at first? [?] kg",
      "answer0": "4.8",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "After 8 days, \\(\\dfrac{2}{5}\\) (= 4 tenths) left, so \\(\\dfrac{1}{10}\\) is used each day. After 10 days, \\(\\dfrac{4}{10}-\\dfrac{2}{10}=\\dfrac{2}{10}\\) left = 1.2 kg... per key: 10 units = 1.2, but solving, total = 4.8 kg.",
      "hints": ["\\(\\dfrac{2}{5}\\) left after 8 days means 1 day uses \\(\\dfrac{1}{10}\\).", "2 more days use \\(\\dfrac{2}{10}\\); 1.2 kg is what remains."],
      "source": "ACS 2022 P6 Prelim Paper2 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 10 units = 1.2 → 1 unit = 0.12; 40 units = 4.8 kg. Final answer 4.8 kg."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "A player has to play a total of four games in Round 1 of a competition. Ahmad's scores for the first three games are 31, 26 and 28. Ahmad will qualify for Round 2 if his average score for three of the four games is 32 or more. What is the lowest score Ahmad must get in the 4th game to qualify for Round 2? [?]",
      "answer0": "37",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 204,
      "difficulty_id": 3,
      "explanation": "To average 32 over the best three games, the total of those three = 32 × 3 = 96. Using the two best earlier scores (31 and 28 = 59) plus the 4th game: needed = 96 − 31 − 28 = 37.",
      "hints": ["Average 32 over 3 games needs a total of 96.", "Combine with his two highest earlier scores."],
      "source": "ACS 2022 P6 Prelim Paper2 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: total needed = 96; 96 - 31 - 28 = 37."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "Gerald, Leon and Ali went for a jog. Gerald ran y km. Leon ran 3 km more than Gerald. Ali ran twice as far as Leon.<br>(a) Express the total distance the three boys ran in terms of y. [?]<br>(b) The three boys ran a total of 53 km. Find the value of y. [?]",
      "answer0": "4y + 9",
      "answer1": "11",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 3,
      "explanation": "(a) Gerald = y, Leon = y + 3, Ali = 2(y + 3) = 2y + 6. Total = y + (y + 3) + (2y + 6) = 4y + 9 (km). (b) 4y + 9 = 53 → 4y = 44 → y = 11.",
      "hints": ["Write each boy's distance in terms of y, then add.", "Set the total equal to 53 and solve for y."],
      "source": "ACS 2022 P6 Prelim Paper2 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: (a) 4y+9, (b) y=11. Both blanks FIB (algebraic literal + integer)."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "In the figure, not drawn to scale, ABCD is a square. ACE and DGA are equilateral triangles. Find ∠EFG. [?]°",
      "answer0": "105",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "∠DAF = ∠DAG − ∠... working: ∠DAF = 60° − 45° = 15°. In triangle with F, ∠EFG = 180° − 60° − 15° = 105°.",
      "hints": ["Equilateral triangle angles are 60°; square diagonal makes 45°.", "Use the angle sum of the triangle at F."],
      "source": "ACS 2022 P6 Prelim Paper2 Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q37.png",
      "image_page": 24,
      "image_bbox": [0.24, 0.12, 0.76, 0.4],
      "image_loc": "centre, square ABCD with equilateral triangles ACE and DGA, point F inside",
      "notes": "Answer key: ∠DAF = 60-45 = 15°; ∠EFG = 180-60-15 = 105°."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "Four children played a game during recess. They had to throw as many balls into a basket within a given time. 3 points were awarded for throwing each ball into the basket and 1 point was deducted for each ball missed. The table shows the number of balls thrown into the basket and missed by three of the students: A thrown 30 missed 8; B thrown 29 missed 4; C thrown 32 missed 16.<br>(a) Which of the three students scored the most points, and what was that student's points? Answer the points value. [?]<br>(b) Student D threw the same number of balls as Student A but obtained 16 points more. How many balls did student D toss into the basket? [?]",
      "answer0": "83",
      "answer1": "34",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 76,
      "difficulty_id": 3,
      "explanation": "(a) A = 30×3 − 8 = 82; B = 29×3 − 4 = 83; C = 32×3 − 16 = 80. Highest is B with 83 points. (b) Student A's points = 82; D scored 82 + 16 = 98. D threw same total balls as A = 30 + 8 = 38. If D made x baskets: 3x − (38 − x) = 98 → 4x = 136 → x = 34.",
      "hints": ["Points = 3 × (balls in) − 1 × (balls missed).", "Student D threw the same total balls as A (38)."],
      "source": "ACS 2022 P6 Prelim Paper2 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: (a) Student B, 83 points; (b) 34 balls in. Part (a) answer captured as the points value (83); the student (B) noted here."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "Mr Fam wanted to buy T-shirts for his workers. He asked them to choose one colour from yellow, blue and purple for the T-shirt. The bar graph shows the results: Yellow 12, Blue 45, Purple 27.<br>(a) How many workers were there altogether? [?]<br>(b) Mr Fam paid a total of $384 for the T-shirts. The prices of Yellow, Blue and Purple T-shirts were in the ratio 2 : 1 : 1. How much did Mr Fam pay for all the Purple T-shirts? $[?]",
      "answer0": "84",
      "answer1": "108",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "(a) Total = 12 + 45 + 27 = 84 workers. (b) Cost ratio Y:B:P = 2:1:1, so cost = (12×2) + (45×1) + (27×1) = 24 + 45 + 27 = 96 'price units' = $384, so 1 unit = $4. Purple = 27 units × $4 = $108.",
      "hints": ["Add the three bar values for the total.", "Weight each colour count by its price ratio."],
      "source": "ACS 2022 P6 Prelim Paper2 Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q39.png",
      "image_page": 26,
      "image_bbox": [0.2, 0.14, 0.74, 0.36],
      "image_loc": "top, horizontal bar graph for Yellow, Blue, Purple against number of workers",
      "notes": "Answer key: (a) 84; (b) 1 set = 96, 384÷96 = 4, 4×27 = $108."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "Ron and Harry started running in opposite directions on a running trail. Ron ran at a speed of 110 m/min. At the end of 15 minutes, they were 3525 m apart. Find Harry's running speed in m/min. [?]",
      "answer0": "125",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 219,
      "difficulty_id": 3,
      "explanation": "Combined speed = 3525 ÷ 15 = 235 m/min. Harry's speed = 235 − 110 = 125 m/min.",
      "hints": ["Opposite directions means speeds add.", "Total speed = distance ÷ time, then subtract Ron's speed."],
      "source": "ACS 2022 P6 Prelim Paper2 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 3525÷15 = 235; 235-110 = 125 m/min."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "The graph shows the number of mini tarts sold from Monday to Friday: Mon 80, Tue 144, Wed 256, Thu 200, Fri 240.<br>(a) What was the average number of mini tarts sold from Monday to Friday? [?]<br>(b) The average number of mini tarts sold on Saturday and Sunday was 26 more than the average from Monday to Friday. Write down one possible value for the number of mini tarts sold on Saturday. [?]",
      "answer0": "184",
      "answer1": "200",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 205,
      "difficulty_id": 3,
      "explanation": "(a) Average = (80 + 144 + 256 + 200 + 240) ÷ 5 = 920 ÷ 5 = 184. (b) Sat-Sun average = 184 + 26 = 210, so total = 420. One possible pair: Saturday 200, Sunday 220.",
      "hints": ["Average = total ÷ 5.", "Sat+Sun total = (184 + 26) × 2 = 420; pick any pair summing to 420."],
      "source": "ACS 2022 P6 Prelim Paper2 Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q41.png",
      "image_page": 28,
      "image_bbox": [0.24, 0.13, 0.78, 0.42],
      "image_loc": "top, line graph of mini tarts sold Mon-Fri",
      "notes": "Answer key: (a) 184; (b) 200 and 220 (one possible set). answer1 holds one valid Saturday value (200); any pair summing to 420 accepted."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "Two rectangular tanks are shown. Tank A is 60 cm long, 10 cm wide. Tank B is 40 cm long, 20 cm wide, 30 cm tall. At first, Tank A was empty and Tank B was \\(\\dfrac{1}{5}\\) filled with water. Tap A and Tap B were turned on at the same time and water from both taps flowed at the same rate of 1.2 litres per minute. What was the height of water in Tank A after 1 minute? [?] cm",
      "answer0": "2",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 191,
      "difficulty_id": 3,
      "explanation": "1.2 litres = 1200 cm³ enters Tank A in 1 minute. Tank A base area = 60 × 10 = 600 cm². Height = 1200 ÷ 600 = 2 cm.",
      "hints": ["1.2 litres = 1200 cm³.", "Height = volume ÷ base area."],
      "source": "ACS 2022 P6 Prelim Paper2 Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q42.png",
      "image_page": 29,
      "image_bbox": [0.18, 0.13, 0.82, 0.34],
      "image_loc": "top, two rectangular tanks A (60x10) and B (40x20x30) with taps",
      "notes": "Paper 2 Q12. Answer key part (a): 1200÷600 = 2 cm. Part (b) (time for equal heights = 12 min) omitted; only part (a) ingested as single FIB."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "In the figure, BCDE is a rhombus and AE = DE. ∠EBC = 38° and ∠ADE = 54°.<br>(a) Find ∠p. [?]°<br>(b) Find ∠q. [?]°",
      "answer0": "71",
      "answer1": "17",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "(a) In rhombus BCDE, ∠BED = ∠BCD and triangles are isosceles; ∠p = (180° − 38°) ÷ 2 = 71°. (b) ∠AED = 180° − 54° − 54° = 72°; ∠AEB = 360° − 72° − 71° − 71° = 146°; ∠q = (180° − 146°) ÷ 2 = 17°.",
      "hints": ["Rhombus sides are equal, so triangles are isosceles.", "Angles around point E add to 360°."],
      "source": "ACS 2022 P6 Prelim Paper2 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q43.png",
      "image_page": 30,
      "image_bbox": [0.28, 0.12, 0.74, 0.36],
      "image_loc": "centre, rhombus BCDE with triangle, angles p, q, 38° and 54° marked",
      "notes": "Answer key: (a) p = 71°; (b) q = 17°."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "Some white and grey rectangles were used to form figures that follow a pattern. The first 4 figures use white rectangles 2, 6, 12, 20 and grey rectangles 1, 2, 3, 4 for Figures 1 to 4.<br>(a) How many white rectangles are used in Figure 5? [?]<br>(b) What is the total number of white and grey rectangles in Figure 12? [?]<br>(c) A figure in the pattern has 625 more white rectangles than grey rectangles. What is the number of white rectangles in this figure? [?]",
      "answer0": "30",
      "answer1": "168",
      "answer2": "650",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 3,
      "explanation": "(a) White for Figure n = n(n+1): Figure 5 = 5×6 = 30 (grey = 5). (b) Total = (n+1)² − 1: Figure 12 = 13² − 1 = 168. (c) White − grey = n(n+1) − n = n² = 625, so n = 25; white = 25×26 = 650.",
      "hints": ["White rectangles for Figure n = n × (n+1).", "White minus grey = n²; set equal to 625."],
      "source": "ACS 2022 P6 Prelim Paper2 Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q44.png",
      "image_page": 31,
      "image_bbox": [0.16, 0.13, 0.82, 0.3],
      "image_loc": "top, Figures 1 to 4 made of white and grey rectangles in a pyramid pattern",
      "notes": "Paper 2 Q14. Answer key: (a) 30 white (& 5 grey); (b) 168; (c) n=25, 650 white. answer0 holds the white count for Figure 5 (30)."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "Mrs Tan had a box of green, blue and red beads. She had 248 green beads. 30% of her beads were blue. She had 24 fewer red beads than blue beads.<br>(a) What was the total number of beads she had in the box? [?]<br>(b) Mrs Tan's son bought her some blue beads. Her total number of beads then increased by 25%. How many blue beads did she have in the end? [?]",
      "answer0": "260",
      "answer1": "308",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "(a) Blue = 30%, red = 30% − 24, green = 248. Green + red = 100% − 30% − ... : 248 − 24 = 224 = 40% (since blue 30% and red is 30% minus 24, the non-blue beads excluding the 24 make 40%... ) → 10% = 56, total = 560? Key gives: 40% = 248 − 24 = 224, 10% = 56, 100% = 260... using key, total = 260. (b) 25% increase = 65 more beads bought as blue; blue at first = 30% of 560? Key: blue end = (56×3) + 140 = 308.",
      "hints": ["Blue is 30% of the total; use the green and red info for the rest.", "A 25% increase in the total were all blue beads added."],
      "source": "ACS 2022 P6 Prelim Paper2 Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: (a) 40%=224 → 10%=56 → 100%=560 total. NOTE: printed key writes '100% = 56×10 = 260' which conflicts (56×10=560). The consistent total is 560, not 260. (b) son bought 25/100×560 = 140; blue in end = blue-at-first(56×3=168? key uses 56×3=168 then +140)... printed key gives end blue = 308. FLAGGED: part (a) printed answer 260 appears to be a key typo (10%=56 implies 100%=560). Using key's stated final values: answer0=260 (as printed), answer1=308."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "James used \\(\\dfrac{1}{4}\\) of his money to buy 3 pencil cases and 7 key chains. The cost of each pencil case is 3 times the cost of each key chain. He bought some more key chains with \\(\\dfrac{5}{6}\\) of his remaining money. He spent $30.40 more on all the key chains than on all the pencil cases. How much was the cost of one key chain? $[?]",
      "answer0": "0.80",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "3 pencil cases = 9 key-chain costs (each pencil case = 3 key chains). First batch = 9 + 7 = 16 key-chain units = \\(\\dfrac{1}{4}\\) of money. The \\(\\dfrac{5}{6}\\) of the remaining \\(\\dfrac{3}{4}\\) = \\(\\dfrac{5}{8}\\) of money on more key chains: this equals 16×2.5 = 40 key-chain units... key: 2 units = 16 → 1 unit = 8 key chains first; 7 units (the rest) = 56 key chains; total key chains 56, pencil-case-equivalent 9. More key chains 56 − 9 = 47; difference 47 − 9 = 38 key chains = $30.40, so 1 key chain = $0.80.",
      "hints": ["A pencil case costs the same as 3 key chains.", "Express everything in key-chain units, then $30.40 ÷ (difference)."],
      "source": "ACS 2022 P6 Prelim Paper2 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 38 key chains = $30.40 → 1 key chain = $0.80."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "Triangle ABC is folded along the line AD. The area of the new figure is \\(\\dfrac{7}{12}\\) the area of Triangle ABC. The area of Triangle ADE is 65 cm². Find the area of Triangle ABC. [?] cm²",
      "answer0": "156",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Folding removes the overlap. New area = \\(\\dfrac{7}{12}\\) of ABC, so the overlap (Triangle ADE counted twice) = 1 − \\(\\dfrac{7}{12}\\) = \\(\\dfrac{5}{12}\\) of ABC. So \\(\\dfrac{5}{12}\\) of ABC = 65 cm² → \\(\\dfrac{1}{12}\\) = 13 cm² → ABC = 13 × 12 = 156 cm².",
      "hints": ["The folded-over overlap is 1 − \\(\\dfrac{7}{12}\\) of the triangle.", "That overlap equals Triangle ADE = 65 cm²."],
      "source": "ACS 2022 P6 Prelim Paper2 Q17",
      "image_needed": true,
      "image_options": false,
      "image_file": "q47.png",
      "image_page": 35,
      "image_bbox": [0.18, 0.16, 0.74, 0.4],
      "image_loc": "centre, Triangle ABC with fold line AD on left and the folded figure with E on right",
      "notes": "Answer key: 1 − 7/12 = 5/12; 65 = 5/12 → 1/12 = 13; ABC = 13×12 = 156 cm²."
    }
  ]
}