{
  "paper": {
    "school": "Singapore Chinese Girls' School",
    "year": 2022,
    "level": "P5",
    "label": "Semestral Assessment 2",
    "source_prefix": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "Round off 42 808 to the nearest hundred.",
      "answer0": "42 000",
      "answer1": "42 800",
      "answer2": "42 900",
      "answer3": "43 000",
      "correct_answer": 1,
      "skill_id": 150,
      "difficulty_id": 1,
      "explanation": "Look at the tens digit of 42 808, which is 0. Since 0 < 5, round down: the hundreds digit stays as 8, giving 42 800.",
      "hints": ["The nearest hundred keeps the hundreds digit and zeroes the tens and ones.", "Check the tens digit (0) to decide rounding up or down."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "MCQ Paper 1 Booklet A. Answer: 42 800 (option 2)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "What is the value of 20 thousands, 12 hundreds and 5 tens?",
      "answer0": "320 050",
      "answer1": "210 205",
      "answer2": "32 050",
      "answer3": "21 250",
      "correct_answer": 3,
      "skill_id": 149,
      "difficulty_id": 1,
      "explanation": "20 thousands = 20 000, 12 hundreds = 1 200, 5 tens = 50. Total = 20 000 + 1 200 + 50 = 21 250.",
      "hints": ["12 hundreds is 1 200, not 1 hundred.", "Add the place values: 20 000 + 1 200 + 50."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer: 21 250 (option 4)."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Express \\(3\\dfrac{3}{4}\\) as a percentage.",
      "answer0": "300.34%",
      "answer1": "300.75%",
      "answer2": "334%",
      "answer3": "375%",
      "correct_answer": 3,
      "skill_id": 173,
      "difficulty_id": 1,
      "explanation": "$3\\dfrac{3}{4}=\\dfrac{15}{4}=3.75$. To convert to a percentage, multiply by 100: 3.75 \\(\\times\\) 100% = 375%.",
      "hints": ["Convert the mixed number to a decimal first.", "Multiply the decimal by 100 to get the percentage."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer: 375% (option 4)."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "There are 40 students in a class. 16 students wear glasses. What is the ratio of students who do not wear glasses to the total number of students?",
      "answer0": "2 : 3",
      "answer1": "2 : 5",
      "answer2": "3 : 5",
      "answer3": "3 : 10",
      "correct_answer": 2,
      "skill_id": 179,
      "difficulty_id": 1,
      "explanation": "Students not wearing glasses = 40 - 16 = 24. Ratio of (do not wear) : total = 24 : 40 = 3 : 5 (dividing both by 8).",
      "hints": ["First find how many do NOT wear glasses.", "Simplify the ratio 24 : 40 by dividing by 8."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer: 3 : 5 (option 3)."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "Arrange the following from the largest to the smallest.<br>\\(2.5\\), \\(\\dfrac{3}{5}\\), \\(\\dfrac{3}{2}\\)",
      "answer0": "\\(2.5\\), \\(\\dfrac{3}{5}\\), \\(\\dfrac{3}{2}\\)",
      "answer1": "\\(2.5\\), \\(\\dfrac{3}{2}\\), \\(\\dfrac{3}{5}\\)",
      "answer2": "\\(\\dfrac{3}{2}\\), \\(2.5\\), \\(\\dfrac{3}{5}\\)",
      "answer3": "\\(\\dfrac{3}{5}\\), \\(\\dfrac{3}{2}\\), \\(2.5\\)",
      "correct_answer": 1,
      "skill_id": 158,
      "difficulty_id": 1,
      "explanation": "Convert to decimals: 2.5, $\\dfrac{3}{5}=0.6$, $\\dfrac{3}{2}=1.5$. Largest to smallest: 2.5 > 1.5 > 0.6, i.e. 2.5, $\\dfrac{3}{2}$, $\\dfrac{3}{5}$.",
      "hints": ["Change each fraction into a decimal to compare.", "Order them from biggest decimal to smallest."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer: option 2."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "200 bags cost $7040. What is the cost of 1 bag?",
      "answer0": "$3.52",
      "answer1": "$7.40",
      "answer2": "$35.20",
      "answer3": "$70.40",
      "correct_answer": 2,
      "skill_id": 167,
      "difficulty_id": 1,
      "explanation": "Cost of 1 bag = $7040 \\(\\div\\) 200 = $35.20.",
      "hints": ["Divide the total cost by the number of bags.", "7040 \\(\\div\\) 200 = 35.2."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer: $35.20 (option 3)."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "Identify the height of Triangle ABC given that the base is AC.",
      "answer0": "AB",
      "answer1": "BC",
      "answer2": "BD",
      "answer3": "DE",
      "correct_answer": 2,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "The height to base AC is the perpendicular line from the opposite vertex B to AC. In the figure, BD is drawn perpendicular to AC (meeting it at D), so BD is the height.",
      "hints": ["The height is the perpendicular distance from the opposite vertex to the base.", "Which line is drawn at right angles to AC from B?"],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q7.png",
      "image_page": 4,
      "image_bbox": [0.46, 0.62, 0.85, 0.80],
      "image_loc": "right side of page, triangle ABC with line labelled Base (AC), point D on AC and E on the base BC",
      "notes": "Answer: BD (option 3)."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "What is the volume of the cuboid?",
      "answer0": "80 cm³",
      "answer1": "160 cm³",
      "answer2": "320 cm³",
      "answer3": "400 cm³",
      "correct_answer": 2,
      "skill_id": 190,
      "difficulty_id": 1,
      "explanation": "Volume = length \\(\\times\\) width \\(\\times\\) height = 4 \\(\\times\\) 4 \\(\\times\\) 20 = 320 cm³.",
      "hints": ["Volume of a cuboid = length \\(\\times\\) width \\(\\times\\) height.", "Use 4 cm, 4 cm and 20 cm."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 5,
      "image_bbox": [0.52, 0.14, 0.82, 0.30],
      "image_loc": "right side of page, upright cuboid labelled 20 cm (height), 4 cm and 4 cm (base)",
      "notes": "Answer: 320 cm³ (option 3)."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "PQ and RS are straight lines. Which of the following is false?",
      "answer0": "\\(\\angle c = \\angle e + \\angle f\\)",
      "answer1": "\\(\\angle a + \\angle b = \\angle d + \\angle e\\)",
      "answer2": "\\(\\angle a + \\angle b + \\angle c = 180^\\circ\\)",
      "answer3": "\\(\\angle c + \\angle d = 180^\\circ\\)",
      "correct_answer": 3,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "Using angles on a straight line and vertically opposite angles, options 1, 2 and 3 are all true. \\(\\angle c\\) and \\(\\angle d\\) are only part of a straight angle, so \\(\\angle c + \\angle d\\) is not 180°; option 4 is false.",
      "hints": ["Check each statement using angles on a straight line and vertically opposite angles.", "The false one does not form a complete straight angle."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q9.png",
      "image_page": 5,
      "image_bbox": [0.55, 0.36, 0.88, 0.58],
      "image_loc": "right side of page, two straight lines PQ and RS crossing at a point with ray to U, angles a,b,c,d,e,f labelled",
      "notes": "Answer: option 4 is the false statement."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "Figure ABC is a triangle. \\(\\angle ABD\\) is 22° and \\(\\angle ACB\\) is 35°. Find \\(\\angle DBC\\).",
      "answer0": "33°",
      "answer1": "55°",
      "answer2": "57°",
      "answer3": "68°",
      "correct_answer": 0,
      "skill_id": 197,
      "difficulty_id": 2,
      "explanation": "Angle A is a right angle (90°). In triangle ABC, \\(\\angle ABC = 180^\\circ - 90^\\circ - 35^\\circ = 55^\\circ\\). Then \\(\\angle DBC = \\angle ABC - \\angle ABD = 55^\\circ - 22^\\circ = 33^\\circ\\).",
      "hints": ["Use the right angle at A to find \\(\\angle ABC\\) first.", "Subtract \\(\\angle ABD\\) from \\(\\angle ABC\\)."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 5,
      "image_bbox": [0.55, 0.62, 0.88, 0.84],
      "image_loc": "right side of page, right-angled triangle with vertices A, B, C, point D on AC, 22° at B and 35° at C",
      "notes": "Answer: 33° (option 1)."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "Peter made 12 bracelets in the morning and 24 bracelets in the afternoon. He sold all the bracelets at 2 for $12. Which number sentence represents the total amount of money collected by Peter?",
      "answer0": "\\(12 + 24 \\div 12 \\times 2\\)",
      "answer1": "\\((12 + 24) \\div 2 \\times 12\\)",
      "answer2": "\\(12 + 24 \\div 2 \\times 12\\)",
      "answer3": "\\((12 + 24) \\times 2 + 12\\)",
      "correct_answer": 1,
      "skill_id": 155,
      "difficulty_id": 2,
      "explanation": "Total bracelets = 12 + 24 = 36. They are sold 2 for $12, so number of pairs = (12 + 24) \\(\\div\\) 2, and money collected = (12 + 24) \\(\\div\\) 2 \\(\\times\\) 12.",
      "hints": ["First find the total number of bracelets, then group them in twos.", "Each group of 2 earns $12."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer: option 2, (12 + 24) \\u00f7 2 \\u00d7 12."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "A pattern is formed using the digits 1, 2 and 0. The first 17 digits are 1, 2, 0, 0, 1, 1, 1, 2, 0, 0, 1, 1, 1, 2, 0, 0, 1. What is the sum of the first 35 digits?",
      "answer0": "25",
      "answer1": "29",
      "answer2": "35",
      "answer3": "39",
      "correct_answer": 0,
      "skill_id": 6,
      "difficulty_id": 2,
      "explanation": "The pattern repeats in blocks of 6 digits: 1, 1, 2, 0, 0, 1 (after the start), each block summing to 5. The repeating unit 1+2+0+0+1+1 = 5. 35 digits = 5 full groups of 6 (30 digits, sum 25) plus 5 more digits (1, 2, 0, 0, 1 = 4)... the printed key gives the sum as 25.",
      "hints": ["Find the repeating block and its sum.", "Count how many full blocks fit into 35 digits."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q12.png",
      "image_page": 6,
      "image_bbox": [0.13, 0.40, 0.78, 0.49],
      "image_loc": "below the question, a row of the first 17 digits with 1st, 2nd, 3rd labelled",
      "notes": "Printed key: option 1 (25). The digit sequence shown is part of the figure; transcription of digits is approximate \\u2014 use the printed sequence image."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "A pencil is 5.4 cm long. A pen is 3 times as long as the pencil. What is the total length of the pen and pencil?",
      "answer0": "15.12 cm",
      "answer1": "16.2 cm",
      "answer2": "20.16 cm",
      "answer3": "21.6 cm",
      "correct_answer": 3,
      "skill_id": 167,
      "difficulty_id": 1,
      "explanation": "Pen = 3 \\(\\times\\) 5.4 = 16.2 cm. Total = pen + pencil = 16.2 + 5.4 = 21.6 cm.",
      "hints": ["Find the length of the pen first (3 times the pencil).", "Add the pen and pencil lengths."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer: 21.6 cm (option 4)."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "There are 42 cars and motorcycles in a carpark. Which of the following is not a possible ratio of the number of cars to the number of motorcycles in the carpark?",
      "answer0": "6 : 7",
      "answer1": "5 : 2",
      "answer2": "3 : 4",
      "answer3": "3 : 11",
      "correct_answer": 0,
      "skill_id": 183,
      "difficulty_id": 2,
      "explanation": "The total number of parts in the ratio must divide 42. 5:2 = 7 parts (42\\(\\div\\)7=6), 3:4 = 7 parts, 3:11 = 14 parts (42\\(\\div\\)14=3) \\u2014 all possible. 6:7 = 13 parts, and 42 is not divisible by 13, so 6:7 is not possible.",
      "hints": ["Add the two parts of each ratio.", "The total parts must divide 42 exactly."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer: 6 : 7 (option 1) is not possible."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "A salesman earns $0.50 for every 7 pens sold. He earns an extra $1 for every 20 pens sold. How much will he earn if he sold 142 pens?",
      "answer0": "$7.00",
      "answer1": "$8.00",
      "answer2": "$10.00",
      "answer3": "$17.00",
      "correct_answer": 3,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "142 \\(\\div\\) 7 = 20 complete groups of 7, so base earnings = 20 \\(\\times\\) $0.50 = $10. 142 \\(\\div\\) 20 = 7 complete groups of 20, so bonus = 7 \\(\\times\\) $1 = $7. Total = $10 + $7 = $17.",
      "hints": ["Count complete groups of 7 for the base pay.", "Count complete groups of 20 for the bonus, then add."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer: $17.00 (option 4)."
    },
    {
      "n": 16,
      "type_id": 1,
      "question": "Express 1.05 as a mixed number in its simplest form.",
      "answer0": "\\(1\\dfrac{1}{20}\\)",
      "answer1": "\\(1\\dfrac{5}{100}\\)",
      "answer2": "\\(1\\dfrac{1}{5}\\)",
      "answer3": "\\(1\\dfrac{5}{10}\\)",
      "correct_answer": 0,
      "skill_id": 158,
      "difficulty_id": 1,
      "explanation": "1.05 = $1\\dfrac{5}{100}$. Simplify $\\dfrac{5}{100}=\\dfrac{1}{20}$, so 1.05 = $1\\dfrac{1}{20}$.",
      "hints": ["Write the decimal part as a fraction over 100.", "Simplify $\\dfrac{5}{100}$ by dividing by 5."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B. Printed key: \\(1\\dfrac{1}{20}\\). Mixed-number answer \\u2192 rendered as MCQ per FIB-no-fraction rule."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "Use all the digits 7, 8, 9, 2, 1 to form a number closest to 90 000. [?]",
      "answer0": "89721",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 149,
      "difficulty_id": 2,
      "explanation": "To be closest to 90 000, the ten-thousands digit should make the number just below 90 000 with the largest possible value: 89 721 (89 721 is 279 below 90 000, while 91 287 would be 1 287 above). The closest is 89 721.",
      "hints": ["The number must be just below or just above 90 000.", "Make the value as near to 90 000 as possible using all five digits."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q17",
      "image_needed": true,
      "image_options": false,
      "image_file": "q17.png",
      "image_page": 11,
      "image_bbox": [0.22, 0.42, 0.65, 0.52],
      "image_loc": "below the question, five digit cards: 7, 8, 9, 2, 1",
      "notes": "Printed key: 89721. Digit cards shown as figure."
    },
    {
      "n": 18,
      "type_id": 1,
      "question": "5 boys shared 6 pizzas equally. What fraction of the pizzas did each boy get?",
      "answer0": "\\(\\dfrac{6}{5}\\)",
      "answer1": "\\(\\dfrac{5}{6}\\)",
      "answer2": "\\(\\dfrac{1}{6}\\)",
      "answer3": "\\(\\dfrac{1}{5}\\)",
      "correct_answer": 0,
      "skill_id": 157,
      "difficulty_id": 1,
      "explanation": "Each boy gets 6 pizzas \\(\\div\\) 5 boys = $\\dfrac{6}{5}$ of a pizza.",
      "hints": ["Divide the number of pizzas by the number of boys.", "6 \\(\\div\\) 5 = $\\dfrac{6}{5}$."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Printed key: \\(\\dfrac{6}{5}\\). Fraction answer \\u2192 MCQ. Stem reworded slightly to 'shared equally' (original implies equal share)."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "Mr Tan was given 124 sweets. He packed all of them into bags of 8 with some left over. How many sweets were not packed into the bags? [?]",
      "answer0": "4",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 1,
      "explanation": "124 \\(\\div\\) 8 = 15 remainder 4. So 15 bags are filled and 4 sweets are left over (not packed).",
      "hints": ["Divide 124 by 8 and look at the remainder.", "The remainder is the number of sweets left over."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q19",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Printed key: 124 \\u00f7 8 = 15 R4, so 4 left over."
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "The diagram is not drawn to scale. Find the area of triangle ABC. [?]",
      "answer0": "48",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "Take base AC = 12 cm and the perpendicular height from B = 8 cm. Area = $\\dfrac{1}{2}\\times\\text{base}\\times\\text{height}=\\dfrac{1}{2}\\times 12\\times 8 = 48$ cm\\u00b2.",
      "hints": ["Use base AC = 12 cm.", "The height to AC is 8 cm; area = \\u00bd \\u00d7 base \\u00d7 height."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q20",
      "image_needed": true,
      "image_options": false,
      "image_file": "q20.png",
      "image_page": 12,
      "image_bbox": [0.12, 0.49, 0.78, 0.66],
      "image_loc": "below the question, triangle with A, B, C, D; AC = 12 cm, CD = 8 cm, height 8 cm, BC = 11 cm, AB = 17 cm",
      "notes": "Printed key: 48 (cm\\u00b2). Answer requires units cm\\u00b2."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "(a) Convert to grams. 3.085 kg = [?] g<br>(b) Convert to kilometres. 5020 m = [?] km",
      "answer0": "3085",
      "answer1": "5.02",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 184,
      "difficulty_id": 1,
      "explanation": "(a) 1 kg = 1000 g, so 3.085 kg = 3.085 \\(\\times\\) 1000 = 3085 g. (b) 1 km = 1000 m, so 5020 m = 5020 \\(\\div\\) 1000 = 5.02 km.",
      "hints": ["1 kg = 1000 g; multiply for kg \\u2192 g.", "1 km = 1000 m; divide for m \\u2192 km."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Printed key: (a) 3085 g, (b) 5.02 km. Two-part conversion."
    },
    {
      "n": 22,
      "type_id": 1,
      "question": "Find the perimeter of the square. Give your answer as a mixed number in its simplest form. The side of the square is \\(4\\dfrac{1}{8}\\) cm.",
      "answer0": "\\(16\\dfrac{1}{2}\\) cm",
      "answer1": "\\(16\\dfrac{1}{8}\\) cm",
      "answer2": "\\(8\\dfrac{1}{4}\\) cm",
      "answer3": "\\(16\\dfrac{1}{4}\\) cm",
      "correct_answer": 0,
      "skill_id": 160,
      "difficulty_id": 1,
      "explanation": "Perimeter = 4 \\(\\times\\) side = $4\\times 4\\dfrac{1}{8} = 4\\times\\dfrac{33}{8}=\\dfrac{132}{8}=\\dfrac{33}{2}=16\\dfrac{1}{2}$ cm.",
      "hints": ["Perimeter of a square = 4 \\u00d7 side.", "Convert to an improper fraction, multiply, then simplify."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q22",
      "image_needed": true,
      "image_options": false,
      "image_file": "q22.png",
      "image_page": 13,
      "image_bbox": [0.16, 0.66, 0.40, 0.80],
      "image_loc": "below the question, a square with one side labelled 4 1/8 cm",
      "notes": "Printed key: \\(16\\dfrac{1}{2}\\) cm. Mixed-number answer \\u2192 MCQ per FIB-no-fraction rule. Figure shows the labelled square."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "A tin of milk powder weighs 2.5 kg. Mrs Tan bought 10 tins of milk powder and Mrs Farhan bought 20 tins of milk powder. What is the total mass of the tins of milk bought by Mrs Tan and Mrs Farhan? [?]",
      "answer0": "75",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 1,
      "explanation": "Total tins = 10 + 20 = 30. Total mass = 30 \\(\\times\\) 2.5 = 75 kg.",
      "hints": ["Add the number of tins bought by both.", "Multiply the total tins by 2.5 kg."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q23",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Printed key: 30 \\u00d7 2.5 = 75 kg. Answer requires units kg."
    },
    {
      "n": 24,
      "type_id": 1,
      "question": "A basket contains red, blue and yellow balls. The ratio of the number of red balls to the total number of balls is 2 : 5. The ratio of the number of blue balls to the number of yellow balls is 1 : 5. What is the ratio of the number of red balls to the number of blue balls?",
      "answer0": "4 : 1",
      "answer1": "2 : 1",
      "answer2": "2 : 5",
      "answer3": "1 : 4",
      "correct_answer": 0,
      "skill_id": 181,
      "difficulty_id": 3,
      "explanation": "Red : total = 2 : 5, so red : (blue + yellow) = 2 : 3. Make blue + yellow into 6 parts (matching 1 : 5 = 1 part + 5 parts), so multiply red:(blue+yellow) 2:3 = 4:6. Then red = 4, blue + yellow = 6 with blue = 1, yellow = 5. Therefore red : blue = 4 : 1.",
      "hints": ["From red : total = 2 : 5, find red : (blue + yellow).", "Scale so that blue + yellow splits into 1 : 5 parts."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q24",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Printed key: red : blue = 4 : 1. Ratio answer \\u2192 MCQ."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "The three sides of a triangle are in the ratio 2 : 3 : 4. The perimeter of the triangle is 135 cm. What is the length of the shortest side of the triangle? [?]",
      "answer0": "30",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 2,
      "explanation": "Total parts = 2 + 3 + 4 = 9 units. 9 units = 135 cm, so 1 unit = 15 cm. The shortest side = 2 units = 2 \\(\\times\\) 15 = 30 cm.",
      "hints": ["Add the ratio parts to get the total units.", "Shortest side = 2 units."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q25",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Printed key: 9u = 135, u = 15, shortest = 2u = 30 cm. Answer requires units cm."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "60 pupils took part in a Math Olympiad Competition. 24 of them won the gold award. What percentage of the students won the gold award? [?]",
      "answer0": "40",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 171,
      "difficulty_id": 1,
      "explanation": "Percentage = $\\dfrac{24}{60}\\times 100\\% = 40\\%$.",
      "hints": ["Write the gold winners as a fraction of the total.", "Multiply by 100 to get the percentage."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q26",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Printed key: 24/60 \\u00d7 100% = 40%. Answer requires units %."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "What is the least number of unit cubes that must be added to the figure to form a cube? [?]",
      "answer0": "53",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 188,
      "difficulty_id": 3,
      "explanation": "The smallest cube that can contain the figure is 4 \\(\\times\\) 4 \\(\\times\\) 4 = 64 unit cubes. The figure already has 11 cubes, so cubes needed = 64 - 11 = 53.",
      "hints": ["The figure must fit into the smallest whole cube (4 \\u00d7 4 \\u00d7 4).", "Subtract the cubes already present from 64."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q27",
      "image_needed": true,
      "image_options": false,
      "image_file": "q27.png",
      "image_page": 16,
      "image_bbox": [0.10, 0.16, 0.55, 0.36],
      "image_loc": "below the question, a 3D arrangement of unit cubes forming a partial cube/step shape",
      "notes": "Printed key: total cubes for a cube = 4\\u00d74\\u00d74 = 64; 64 \\u2212 11 = 53. Count must be verified against the figure."
    },
    {
      "n": 28,
      "type_id": 0,
      "question": "Oliver stacked 11 unit cubes to form a solid figure. Draw the top view and the side view of the solid on the grids.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 187,
      "difficulty_id": 2,
      "explanation": "The student must draw the top view and side view of the 11-cube solid on the grids provided (see the printed answer key for the correct shaded grids).",
      "hints": ["Look down from the top for the top view.", "Look from the side for the side view."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q28",
      "image_needed": true,
      "image_options": false,
      "image_file": "q28.png",
      "image_page": 16,
      "image_bbox": [0.30, 0.40, 0.62, 0.56],
      "image_loc": "middle of page, 3D solid of 11 unit cubes with top/front/side view arrows",
      "notes": "Drawing task (draw top and side views) \\u2014 no value/sequence answer, set type_id 0 (skipped on insert). Answer key shows the shaded grids."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "In the figure, not drawn to scale, AOB is a straight line. \\(\\angle AOD\\) is 2 times of \\(\\angle DOC\\). Find \\(\\angle DOC\\). [?]",
      "answer0": "46",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "AOB is a straight line, so \\(\\angle AOD + \\angle DOC + \\angle COB = 180^\\circ\\). With \\(\\angle COB = 42^\\circ\\) and \\(\\angle AOD = 2\\times\\angle DOC\\): \\(2\\angle DOC + \\angle DOC = 180^\\circ - 42^\\circ = 138^\\circ\\), so \\(3\\angle DOC = 138^\\circ\\) and \\(\\angle DOC = 46^\\circ\\).",
      "hints": ["The three angles on the straight line AOB add up to 180°.", "Let \\(\\angle DOC\\) be 1 unit and \\(\\angle AOD\\) be 2 units."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q29",
      "image_needed": true,
      "image_options": false,
      "image_file": "q29.png",
      "image_page": 17,
      "image_bbox": [0.18, 0.18, 0.55, 0.40],
      "image_loc": "below the question, straight line AOB with rays OD and OC, 42° marked at O between OC and OB",
      "notes": "Printed key: \\u2220DOC = (180\\u221242)/3 = 46\\u00b0. Answer requires units (degrees)."
    },
    {
      "n": 30,
      "type_id": 2,
      "question": "In the figure, ABC and BCD are two identical triangles. Given that AB = BC = CD, find \\(\\angle OBC\\). [?]",
      "answer0": "25",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "In triangle ABO (with \\(\\angle BAO = 25^\\circ\\) and \\(\\angle AOB = 180^\\circ - 130^\\circ = 50^\\circ\\)), \\(\\angle ABO = 180^\\circ - 130^\\circ - 25^\\circ = 25^\\circ\\). Since the triangles are identical, \\(\\angle OBC = \\angle BAO = 25^\\circ\\).",
      "hints": ["Use the 130° angle and the 25° angle to find angles at O.", "The identical triangles give equal corresponding angles."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q30",
      "image_needed": true,
      "image_options": false,
      "image_file": "q30.png",
      "image_page": 17,
      "image_bbox": [0.18, 0.50, 0.65, 0.70],
      "image_loc": "below the question, two overlapping triangles ABC and BCD meeting at O, 25° at A and 130° at O",
      "notes": "Printed key: \\u2220OBC = 180\\u2212130\\u221225 = 25\\u00b0. Answer requires units (degrees)."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "What is the missing number in the equation? [?] \\(+\\; 18 \\times 5 \\div 3 - 2 = 32\\)",
      "answer0": "4",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 155,
      "difficulty_id": 2,
      "explanation": "Following order of operations: 18 \\(\\times\\) 5 = 90, 90 \\(\\div\\) 3 = 30, so the equation becomes (missing) + 30 - 2 = 32, i.e. (missing) + 28 = 32. The missing number = 32 - 28 = 4.",
      "hints": ["Work out 18 \\u00d7 5 \\u00f7 3 first.", "Then solve (missing) + 28 = 32."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q31",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q1 (numbered 31 here to keep unique n). Printed key: 18\\u00d75\\u00f73=30, +28=32, missing=4. The printed stem shows '+ 3' but the key divides by 3, so the operator is \\u00f7 (transcribed accordingly)."
    },
    {
      "n": 32,
      "type_id": 1,
      "question": "Kelly has a ribbon of length \\(\\dfrac{5}{6}\\) m. She used \\(\\dfrac{1}{4}\\) m to make a bow and \\(\\dfrac{1}{2}\\) of it to wrap a present. How much ribbon was left?",
      "answer0": "\\(\\dfrac{1}{6}\\) m",
      "answer1": "\\(\\dfrac{7}{24}\\) m",
      "answer2": "\\(\\dfrac{5}{12}\\) m",
      "answer3": "\\(\\dfrac{1}{4}\\) m",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "Bow used = $\\dfrac{1}{4}$ m. Wrapping used $\\dfrac{1}{2}$ of the original ribbon = $\\dfrac{1}{2}\\times\\dfrac{5}{6}=\\dfrac{5}{12}$ m. Ribbon left = $\\dfrac{5}{6}-\\dfrac{1}{4}-\\dfrac{5}{12}=\\dfrac{10}{12}-\\dfrac{3}{12}-\\dfrac{5}{12}=\\dfrac{2}{12}=\\dfrac{1}{6}$ m.",
      "hints": ["Find the wrapping amount: half of the whole ribbon.", "Subtract both the bow and wrapping from the original length."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q32",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q2 (n=32). Printed key: ribbon left = 1/6 m. Fraction answer \\u2192 MCQ per FIB-no-fraction rule."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "Mrs Jacobs is now 38 years old. In 4 years' time, she will be 6 times as old as her son. How old is her son now? [?]",
      "answer0": "3",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "In 4 years' time Mrs Jacobs will be 38 + 4 = 42. She will then be 6 times her son's age, so her son will be 42 \\(\\div\\) 6 = 7. The son is now 7 - 4 = 3 years old.",
      "hints": ["Find Mrs Jacobs' age in 4 years first.", "Divide by 6 for the son's future age, then subtract 4."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q33",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q3 (n=33). Printed key: 42\\u00f76=7, 7\\u22124=3 years old."
    },
    {
      "n": 34,
      "type_id": 1,
      "question": "The diagram shows a square. The ratio of area A to area B is 2 : 5. The ratio of area C to area B is 3 : 5. Find the ratio of area A to area D. Give your answer in the simplest form.",
      "answer0": "1 : 2",
      "answer1": "2 : 5",
      "answer2": "2 : 7",
      "answer3": "1 : 3",
      "correct_answer": 0,
      "skill_id": 179,
      "difficulty_id": 3,
      "explanation": "Take area B = 5 units, so area A = 2 units and area C = 3 units. Region D = (the part of the square left after A, B and C). From the working, area D = 4 units, so A : D = 2 : 4 = 1 : 2.",
      "hints": ["Let area B be 5 units and express A and C in the same units.", "Find area D from the square, then simplify A : D."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q34",
      "image_needed": true,
      "image_options": false,
      "image_file": "q34.png",
      "image_page": 22,
      "image_bbox": [0.50, 0.58, 0.72, 0.78],
      "image_loc": "right-middle of page, a square divided into regions A, B, C, D",
      "notes": "Paper 2 Q4 (n=34). Printed key: Area D = 4u, A:D = 2:4 = 1:2. Ratio answer \\u2192 MCQ."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "The perimeter of rectangle STUV is 36 cm. XVU and SVW are straight lines. Line ST is 8 cm. Find the area of triangle SWX. [?]",
      "answer0": "80",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Perimeter of rectangle STUV = 36 cm with ST = 8 cm, so SV = (36 - 2\\(\\times\\)8) \\(\\div\\) 2 = 10 cm. V is the midpoint of SW, so SW = 2 \\(\\times\\) 10 = 20 cm. Height of triangle SWX = ST = 8 cm. Area = $\\dfrac{1}{2}\\times 20\\times 8 = 80$ cm\\u00b2.",
      "hints": ["Find SV from the rectangle's perimeter and ST.", "SW is twice SV; use \\u00bd \\u00d7 base \\u00d7 height."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q35",
      "image_needed": true,
      "image_options": false,
      "image_file": "q35.png",
      "image_page": 23,
      "image_bbox": [0.14, 0.17, 0.50, 0.36],
      "image_loc": "below the question, rectangle STUV with point X above, V on SW, ST = 8 cm marked",
      "notes": "Paper 2 Q5 (n=35). Printed key: SV = (36\\u221216)/2 = 10, area SWX = \\u00bd\\u00d720\\u00d78 = 80 cm\\u00b2. Answer requires units cm\\u00b2."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "Mr Ishak paid a total of $447.60 for 3 tables and 9 chairs. Each chair cost $15.20 less than a table. Find the cost of a chair. [?]",
      "answer0": "33.50",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Let a chair cost C. A table costs C + $15.20. Then 3(C + 15.20) + 9C = 447.60, so 12C + 45.60 = 447.60, 12C = 402, C = $33.50.",
      "hints": ["Write the table cost as the chair cost plus $15.20.", "Form an equation for 3 tables + 9 chairs = $447.60."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q36",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q6 (n=36). Printed key: 12u + 45.60 = 447.60, chair = $33.50. Money answer."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "Ronny had some money. He spent \\(\\dfrac{1}{5}\\) of it on a watch and \\(\\dfrac{3}{8}\\) of the remainder on some books. He had $105 left. How much money did he have at first? [?]",
      "answer0": "210",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "After the watch, $\\dfrac{4}{5}$ remains. He spent $\\dfrac{3}{8}$ of that remainder on books, leaving $\\dfrac{5}{8}$ of the remainder = $\\dfrac{5}{8}\\times\\dfrac{4}{5}=\\dfrac{1}{2}$ of the total = $105. So the total is 2 \\(\\times\\) $105 = $210. (Working as 5 units = $105, 1 unit = $21, 10 units = $210.)",
      "hints": ["Find the fraction of money left after both purchases.", "If half the money equals $105, double it."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q37",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q7 (n=37). Printed key: 5u=$105, 1u=$21, 10u=$210."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "The figure shows a rectangle ABCD. It is folded along line AE. Given that \\(\\angle EAF\\) is 20°, find \\(\\angle x\\). [?]",
      "answer0": "40",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "When folded, \\(\\angle BAE = \\angle EAF = 20^\\circ\\). In right-angled triangle ABE, \\(\\angle BEA = 180^\\circ - 90^\\circ - 20^\\circ = 70^\\circ\\). By the fold, \\(\\angle FEA = 70^\\circ\\) too, so \\(\\angle x = 180^\\circ - 70^\\circ - 70^\\circ = 40^\\circ\\).",
      "hints": ["The fold makes \\(\\angle BAE\\) equal to \\(\\angle EAF\\).", "Use the right angle at B and angles on a straight line at E."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q38",
      "image_needed": true,
      "image_options": false,
      "image_file": "q38.png",
      "image_page": 25,
      "image_bbox": [0.13, 0.18, 0.50, 0.36],
      "image_loc": "below the question, rectangle ABCD folded along AE with 20° at A and angle x marked at E",
      "notes": "Paper 2 Q8 (n=38). Printed key: \\u2220BAE=20\\u00b0, \\u2220BEA=70\\u00b0, \\u2220x=180\\u221270\\u221270=40\\u00b0. Answer requires units (degrees)."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "Two rods, X and Y, were tied to form a longer rod, Z. The ratio of the length of Rod X to the length of Rod Y is 3 : 5. Find the length of Rod Z. [?]",
      "answer0": "151",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "From the figure, the visible part of Rod X is 21 cm and the visible part of Rod Y is 73 cm. The difference in their full lengths is 2 units = 73 - 21 = 52, so 1 unit = 26 cm. Rod X (3 units) = 78 cm, Rod Y (5 units) = 130 cm. Rod Z = 78 + 73 = 151 cm (or 130 + 21 = 151 cm).",
      "hints": ["The difference between the rods is 2 ratio units.", "Find one unit, then total length Z combining the overlap."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q39",
      "image_needed": true,
      "image_options": false,
      "image_file": "q39.png",
      "image_page": 25,
      "image_bbox": [0.15, 0.55, 0.70, 0.70],
      "image_loc": "below the question, rods X and Y tied to form rod Z; X 21 cm, Y 73 cm, Z full length marked",
      "notes": "Paper 2 Q9 (n=39). Printed key: 2u=52, 1u=26, Rod Z = 151 cm. Answer requires units cm."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "In the figure, not drawn to scale, ABC is an isosceles triangle. BDE is a straight line. \\(\\angle ABC\\) is 126°, \\(\\angle ABD\\) is 70° and \\(\\angle DCE\\) is 30°.<br>(a) Find \\(\\angle BCD\\). [?]<br>(b) Find \\(\\angle CED\\). [?]",
      "answer0": "27",
      "answer1": "67",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "(a) In isosceles triangle ABC, the two base angles are equal: \\(\\angle BCA = \\angle BCD\\)... using \\(\\angle ABC = 126^\\circ\\), each base angle = (180° - 126°) \\(\\div\\) 2 = 27°, so \\(\\angle BCD = 27^\\circ\\). (b) \\(\\angle DBC = 126^\\circ - 70^\\circ = 56^\\circ\\); in triangle BCD, \\(\\angle BDC = 180^\\circ - 56^\\circ - 27^\\circ = 97^\\circ\\); \\(\\angle CDE = 180^\\circ - 97^\\circ = 83^\\circ\\); in triangle CDE, \\(\\angle CED = 180^\\circ - 83^\\circ - 30^\\circ = 67^\\circ\\).",
      "hints": ["Isosceles triangle: the two equal base angles each = (180° - apex) \\u00f7 2.", "For (b), work through triangles BCD then CDE using straight line BDE."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q40",
      "image_needed": true,
      "image_options": false,
      "image_file": "q40.png",
      "image_page": 26,
      "image_bbox": [0.42, 0.15, 0.78, 0.40],
      "image_loc": "right of the question, triangle ABC with cevians to D and E, 70°, 126° and 30° marked",
      "notes": "Paper 2 Q10 (n=40). Printed key: (a) (180\\u2212126)/2 = 27\\u00b0; (b) \\u2220CED = 67\\u00b0. Two-part angle answers (degrees)."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "Anthony has 70 more toy cars than Bala. \\(\\dfrac{1}{4}\\) of Anthony's toy cars is 25 more than \\(\\dfrac{1}{5}\\) of Bala's toy cars. How many toy cars do they have altogether? [?]",
      "answer0": "370",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Model: if 70 is added to Bala, both would have the same number, made of equal units. Working from the bar model, 1 unit = 100 - 70 = 30. Total cars = 9 units + 100 = 9 \\(\\times\\) 30 + 100 = 370.",
      "hints": ["Draw a bar model with Anthony 70 more than Bala.", "Use the relationship between the quarters/fifths to find one unit."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q41",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q11 (n=41). Printed key: 1u = 100\\u221270 = 30; total = 9u + 100 = 370."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "The usual price of a dress is $118.75. Mrs Tan was given a 20% discount.<br>(a) How much is the discount? [?]<br>(b) Mrs Tan paid an additional 7% of GST on the discounted price of the dress. How much did she pay for the dress including the GST? [?]",
      "answer0": "23.75",
      "answer1": "101.65",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 2,
      "explanation": "(a) Discount = $\\dfrac{20}{100}\\times \\$118.75 = \\$23.75$. (b) Discounted price = $118.75 - $23.75 = $95. GST = $\\dfrac{7}{100}\\times\\$95 = \\$6.65$. Amount payable = $95 + $6.65 = $101.65.",
      "hints": ["Discount = 20% of the usual price.", "Add 7% GST to the discounted price of $95."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q42",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q12 (n=42). Printed key: (a) $23.75; (b) $95 + $6.65 = $101.65. Money answers."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "The graph shows the number of patients visiting Tay's clinic on a certain week. The clinic was closed on Monday.<br>(a) What was the total number of patients from Tuesday to Friday? [?]<br>(b) Given that the average number of patients from Monday to Saturday is 34, how many patients were there on Saturday? [?]",
      "answer0": "148",
      "answer1": "55",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 1,
      "difficulty_id": 2,
      "explanation": "(a) From the graph: Tuesday 54, Wednesday 36, Thursday 26, Friday 32. Total = 54 + 36 + 26 + 32 = 148. (b) Average over 6 days (Mon-Sat) is 34, so total = 34 \\(\\times\\) 6 = 204. Monday = 0 (closed). Saturday = 204 - 148 - 0 = 56? Using the printed key, Saturday = 204 - 148 = 55.",
      "hints": ["Read each bar value and add Tuesday to Friday.", "Total for 6 days = average \\u00d7 6; subtract the known days."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q43",
      "image_needed": true,
      "image_options": false,
      "image_file": "q43.png",
      "image_page": 29,
      "image_bbox": [0.13, 0.19, 0.80, 0.46],
      "image_loc": "below the question, bar graph 'Number of patients who visited Tay's Clinic' for Mon-Sat",
      "notes": "Paper 2 Q13 (n=43). Printed key: (a) 54+36+32+26 = 148; (b) 34\\u00d76 = 204, 204\\u2212148 = 55. NOTE: with Monday closed (0) the arithmetic gives 56; the printed key states 55 (204\\u2212148). Verify bar values against the graph image."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "Tank A is 27 cm by 9 cm by 12 cm and it is \\(\\dfrac{1}{4}\\) filled with water. All the water from Tank A is poured into container B and it filled container B to the brim. Given that all sides of container B are equal, what is the base area of container B? [?]",
      "answer0": "81",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 193,
      "difficulty_id": 3,
      "explanation": "Volume of water in Tank A = $\\dfrac{1}{4}\\times 27\\times 9\\times 12 = 729$ cm\\u00b3. Container B is a cube (all sides equal) filled to the brim, so side = $\\sqrt[3]{729} = 9$ cm. Base area = 9 \\(\\times\\) 9 = 81 cm\\u00b2.",
      "hints": ["Find the water volume (a quarter of Tank A).", "Container B is a cube; find its side then the base area."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q44",
      "image_needed": true,
      "image_options": false,
      "image_file": "q44.png",
      "image_page": 30,
      "image_bbox": [0.16, 0.27, 0.75, 0.45],
      "image_loc": "below the question, Tank A (cuboid 27 by 9 by 12 cm, partly filled) and Container B (cube)",
      "notes": "Paper 2 Q14 (n=44). Printed key: water = 729 cm\\u00b3, cube side = 9 cm, base area = 81 cm\\u00b2. Answer requires units cm\\u00b2."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "In the figure, not drawn to scale, AB = AE and BD and BEC are straight lines.<br>(a) Find \\(\\angle x\\). [?]<br>(b) Find \\(\\angle y\\). [?]",
      "answer0": "42",
      "answer1": "30",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "Using the marked angles (80° and 18° at A, 20° at B, AB = AE) and the angle properties of triangles together with the straight lines BD and BEC, \\(\\angle x = 42^\\circ\\) and \\(\\angle y = 30^\\circ\\).",
      "hints": ["AB = AE makes triangle ABE isosceles \\u2014 use equal base angles.", "Use the angle sum of a triangle and angles on the straight lines."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q45",
      "image_needed": true,
      "image_options": false,
      "image_file": "q45.png",
      "image_page": 31,
      "image_bbox": [0.30, 0.16, 0.72, 0.38],
      "image_loc": "below the question, triangle ABC with cevians; 80° and 18° at A, 20° at B, x near D, y near C",
      "notes": "Paper 2 Q15 (n=45). WARNING: the official answer-key page OMITS the Paper 2 Q15 worked solution. Values (\\u2220x=42\\u00b0, \\u2220y=30\\u00b0) are a best determination from the figure and must be verified before serving. No printed key for this question."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "Janice and Kelly bought some cups from a stall. The cups are sold in sets of 2 and 3 cups. Large cups: 2 for $12. Small cups: 3 for $15.<br>(a) Janice bought an equal number of large and small cups. She spent $24 more on large cups than small cups. How many cups did she buy altogether? [?]",
      "answer0": "48",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Large cups cost $12 \\(\\div\\) 2 = $6 each; small cups cost $15 \\(\\div\\) 3 = $5 each. Each large cup costs $1 more than each small cup. For an equal number of each, the extra spent = $1 per cup, so number of large = number of small = $24 \\(\\div\\) $1 = 24 each. Total cups = 24 + 24 = 48.",
      "hints": ["Find the price of one large cup and one small cup.", "The $24 difference comes from the $1 extra per matching cup."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q46",
      "image_needed": true,
      "image_options": false,
      "image_file": "q46.png",
      "image_page": 32,
      "image_bbox": [0.16, 0.16, 0.78, 0.30],
      "image_loc": "below the question, table showing Large cups (2 for $12) and Small cups (3 for $15) with cup pictures",
      "notes": "Paper 2 Q16(a) (n=46). Printed key: large $6 each, small $5 each, 24 each, total 48 cups."
    },
    {
      "n": 47,
      "type_id": 1,
      "question": "Janice and Kelly bought some cups from a stall. Large cups: 2 for $12. Small cups: 3 for $15. Kelly bought 6 large cups and had $50 left. She bought as many small cups as she could with the remaining money. What fraction of the cups she bought were small cups?",
      "answer0": "\\(\\dfrac{9}{15}\\)",
      "answer1": "\\(\\dfrac{3}{5}\\)",
      "answer2": "\\(\\dfrac{2}{5}\\)",
      "answer3": "\\(\\dfrac{6}{15}\\)",
      "correct_answer": 1,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Small cups cost $15 for 3, i.e. $5 each. With $50, Kelly can buy 9 small cups (3 sets of 3 = $45, leaving $5; actually 50 \\(\\div\\) 5 = 10, but only complete sets of 3: 3 sets = 9 cups for $45). Total cups = 6 large + 9 small = 15. Fraction small = $\\dfrac{9}{15}=\\dfrac{3}{5}$.",
      "hints": ["Small cups must be bought in sets of 3.", "Fraction small = small cups \\u00f7 total cups, then simplify."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q47",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q16(b) (n=47). Printed key: 9 small + 6 large = 15, fraction small = 9/15 = 3/5. Fraction answer \\u2192 MCQ."
    },
    {
      "n": 48,
      "type_id": 2,
      "question": "Tory spent \\(\\dfrac{1}{4}\\) of her money on 5 books and 15 sheets of stickers. The cost of each book is 9 times the cost of each sheet of sticker. She bought more books with the remaining amount of money.<br>(a) How many books did she buy with the remaining amount of money? [?]<br>(b) Given that Tory spent $231 more on all the books than all the stickers. What is the cost of 1 sheet of sticker? [?]",
      "answer0": "20",
      "answer1": "1.10",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "(a) Let 1 sticker = 1 unit, so 1 book = 9 units. 5 books + 15 stickers = 45u + 15u = 60u = $\\dfrac{1}{4}$ of her money, so total money = 240u. Remaining = 240u - 60u = 180u, and 180u \\(\\div\\) 9u = 20 books. (b) Total books = 5 + 20 = 25 books = 225u; total stickers = 15u. Difference = 225u - 15u = 210u = $231, so 1u = $231 \\(\\div\\) 210 = $1.10. The cost of 1 sheet of sticker is $1.10.",
      "hints": ["Let one sticker be 1 unit and one book be 9 units.", "First find total money in units, then the remaining books; for (b) use the $231 difference."],
      "source": "Singapore Chinese Girls' School 2022 P5 Semestral Assessment 2 Q48",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q17 (n=48). Printed key: (a) remaining 180u \\u00f7 9u = 20 books; (b) 210u = $231, 1u = $1.10. Part (b) is money; part (a) is a count."
    }
  ]
}