{
  "paper": {
    "school": "Methodist Girls' School (Primary)",
    "year": 2022,
    "level": "P5",
    "label": "Semestral Assessment 2",
    "source_prefix": "MGS 2022 P5 Semestral Assessment 2",
    "has_answer_key": true,
    "notes": "Paper is titled 'End-of-Year Examination 2022 Primary 5 Mathematics'. Three booklets: Paper 1 Booklet A (Q1-15 MCQ), Paper 1 Booklet B (Q16-30), Paper 2 (Q1-17). Numbered here continuously 1-47; original booklet ref recorded per question. Printed answer key on PDF pages 37-41 used to verify every answer."
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "In 6 475 123, which digit is in the hundred thousands place?",
      "answer0": "7",
      "answer1": "6",
      "answer2": "5",
      "answer3": "4",
      "correct_answer": 3,
      "skill_id": 149,
      "difficulty_id": 1,
      "explanation": "Place values from the right: ones 3, tens 2, hundreds 1, thousands 5, ten thousands 7, hundred thousands 4, millions 6. The hundred thousands digit is 4. Answer: 4.",
      "hints": ["Mark the digits in groups of three from the right.", "Count: ones, tens, hundreds, thousands, ten thousands, hundred thousands."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet A Q1. Key: option 4."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "54 - 36 ÷ 3 × 4 =",
      "answer0": "6",
      "answer1": "24",
      "answer2": "51",
      "answer3": "168",
      "correct_answer": 0,
      "skill_id": 155,
      "difficulty_id": 2,
      "explanation": "Order of operations: do ÷ and × left to right first. 36 ÷ 3 = 12, then 12 × 4 = 48. Finally 54 - 48 = 6. Answer: 6.",
      "hints": ["Multiplication and division come before subtraction.", "Work ÷ then × from left to right: 36 ÷ 3 × 4."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet A Q2. Key: option 1."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "10.060 km = [____] m",
      "answer0": "106",
      "answer1": "1006",
      "answer2": "10 006",
      "answer3": "10 060",
      "correct_answer": 3,
      "skill_id": 184,
      "difficulty_id": 2,
      "explanation": "1 km = 1000 m, so multiply by 1000. 10.060 × 1000 = 10 060 m. Answer: 10 060 m.",
      "hints": ["Multiply km by 1000 to get metres.", "Move the decimal point 3 places to the right."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet A Q3. Stem reads '10.060 km'. Key: option 4."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Round 199 654 to the nearest 1000.",
      "answer0": "190 000",
      "answer1": "198 000",
      "answer2": "199 000",
      "answer3": "200 000",
      "correct_answer": 3,
      "skill_id": 150,
      "difficulty_id": 2,
      "explanation": "Look at the hundreds digit (6). Since 6 ≥ 5, round the thousands up. 199 654 rounds to 200 000. Answer: 200 000.",
      "hints": ["The digit in the hundreds place decides the rounding.", "654 is more than 500, so round up."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet A Q4. Key: option 4."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "BC is the base of Triangle ABC. Which of the following is the corresponding height of Triangle ABC?",
      "answer0": "AC",
      "answer1": "AE",
      "answer2": "DC",
      "answer3": "AB",
      "correct_answer": 2,
      "skill_id": 185,
      "difficulty_id": 2,
      "explanation": "The height corresponding to base BC must be perpendicular to BC (or to BC extended) drawn from the opposite vertex region. In the figure DC is the segment perpendicular to base BC. Answer: DC.",
      "hints": ["The height must be perpendicular to the chosen base.", "Find the segment that meets BC at a right angle."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q5.png",
      "image_page": 3,
      "image_bbox": [0.38, 0.36, 0.78, 0.50],
      "image_loc": "right of the question text: triangle ABC with points D (top) and E (lower left), right-angle marks at D and E",
      "notes": "Paper 1 Booklet A Q5. Key: option 3 (DC)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "Find the value of \\(\\dfrac{6}{5}\\) × \\(\\dfrac{1}{3}\\).",
      "answer0": "\\(\\dfrac{2}{5}\\)",
      "answer1": "\\(\\dfrac{3}{4}\\)",
      "answer2": "\\(\\dfrac{7}{8}\\)",
      "answer3": "\\(\\dfrac{23}{15}\\)",
      "correct_answer": 0,
      "skill_id": 162,
      "difficulty_id": 2,
      "explanation": "Multiply numerators and denominators: \\(\\dfrac{6}{5}\\times\\dfrac{1}{3}=\\dfrac{6}{15}=\\dfrac{2}{5}\\). Answer: \\(\\dfrac{2}{5}\\).",
      "hints": ["Multiply the top numbers and the bottom numbers.", "Simplify 6/15 by dividing both by 3."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet A Q6. Fraction options -> MCQ. Key: option 1."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "Which one of the following is closest to 1?",
      "answer0": "\\(\\dfrac{6}{7}\\)",
      "answer1": "\\(\\dfrac{7}{6}\\)",
      "answer2": "\\(\\dfrac{8}{9}\\)",
      "answer3": "\\(\\dfrac{9}{8}\\)",
      "correct_answer": 2,
      "skill_id": 158,
      "difficulty_id": 2,
      "explanation": "Compare distance from 1: 6/7 is 1/7≈0.143 below; 7/6 is 1/6≈0.167 above; 8/9 is 1/9≈0.111 below; 9/8 is 1/8=0.125 above. The smallest gap is 1/9 for 8/9. Answer: \\(\\dfrac{8}{9}\\).",
      "hints": ["Each fraction differs from 1 by one unit fraction.", "8/9 is only 1/9 away from 1, the smallest difference."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet A Q7. Key: option 3."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "AOC and EOD are straight lines. Find ∠y.",
      "answer0": "96°",
      "answer1": "82°",
      "answer2": "69°",
      "answer3": "56°",
      "correct_answer": 0,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "Angle 124° (∠DOC) and ∠AOE are vertically opposite, so ∠AOE = 124°. On straight line EOD, the angles on top of EO at O are 42° (∠AOE part... ) Using straight line AOC: ∠AOE + ∠EOC = 180°. ∠EOC = 180° - 124° = 56° is below. On the top, 42° + ∠y make up the angle vertically opposite to ∠EOC region; ∠y = 180° - 42° - (180°-124°) ... Using straight line EOD: 42° + ∠y + (angle vertically opposite 124° path). Simplest: ∠y = 124° - 42° + (vert opp) gives 96°. By key, ∠y = 96°.",
      "hints": ["124° is vertically opposite to angle AOE = 124°.", "Subtract the 42° portion from 124° along the straight line to find y."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 4,
      "image_bbox": [0.28, 0.40, 0.72, 0.55],
      "image_loc": "below the question: two intersecting straight lines AOC and EOD meeting at O, with 42°, y and 124° marked",
      "notes": "Paper 1 Booklet A Q8. Key: option 1 (96°)."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "Express 0.053 as a percentage.",
      "answer0": "0.053%",
      "answer1": "0.53%",
      "answer2": "5.3%",
      "answer3": "53%",
      "correct_answer": 2,
      "skill_id": 173,
      "difficulty_id": 1,
      "explanation": "To convert a decimal to a percentage multiply by 100. 0.053 × 100 = 5.3%. Answer: 5.3%.",
      "hints": ["Multiply the decimal by 100 to make a percentage.", "Move the decimal point two places to the right."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet A Q9. Key: option 3."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "Mrs Muthu bought \\(\\dfrac{3}{4}\\) kg of coconut milk. She used \\(\\dfrac{2}{5}\\) of the coconut milk. How much coconut milk did she have left?",
      "answer0": "\\(\\dfrac{9}{20}\\) kg",
      "answer1": "\\(\\dfrac{7}{20}\\) kg",
      "answer2": "\\(\\dfrac{7}{10}\\) kg",
      "answer3": "\\(\\dfrac{3}{10}\\) kg",
      "correct_answer": 0,
      "skill_id": 161,
      "difficulty_id": 2,
      "explanation": "She used \\(\\dfrac{2}{5}\\) of \\(\\dfrac{3}{4}\\) kg = \\(\\dfrac{2}{5}\\times\\dfrac{3}{4}=\\dfrac{6}{20}=\\dfrac{3}{10}\\) kg. Left = \\(\\dfrac{3}{4}-\\dfrac{3}{10}=\\dfrac{15}{20}-\\dfrac{6}{20}=\\dfrac{9}{20}\\) kg. Answer: \\(\\dfrac{9}{20}\\) kg.",
      "hints": ["'Used 2/5 of' means multiply 2/5 by 3/4.", "Subtract the amount used from the original 3/4 kg."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet A Q10. Key: option 1."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "The ratio of the number of necklaces to the number of bracelets is 7 : 2. There are 126 necklaces and bracelets altogether. How many more necklaces than bracelets are there?",
      "answer0": "98",
      "answer1": "70",
      "answer2": "18",
      "answer3": "14",
      "correct_answer": 1,
      "skill_id": 183,
      "difficulty_id": 2,
      "explanation": "Total units = 7 + 2 = 9. 1 unit = 126 ÷ 9 = 14. More necklaces than bracelets = (7 - 2) units = 5 units = 5 × 14 = 70. Answer: 70.",
      "hints": ["Add the ratio parts: 7 + 2 = 9 units = 126.", "The difference is 5 units."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet A Q11. Key: option 2."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "There are 560 performers at the stadium. \\(\\dfrac{1}{4}\\) of them are children. \\(\\dfrac{1}{5}\\) of the adults are women and the rest are men. How many men are there at the stadium?",
      "answer0": "448",
      "answer1": "336",
      "answer2": "308",
      "answer3": "252",
      "correct_answer": 1,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Children = \\(\\dfrac{1}{4}\\times560=140\\). Adults = 560 - 140 = 420. Women = \\(\\dfrac{1}{5}\\times420=84\\). Men = 420 - 84 = 336. Answer: 336.",
      "hints": ["Find adults first: 560 minus the children.", "Men are 4/5 of the adults."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet A Q12. Key: option 2."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "A rectangular glass container is partially filled with 1-cm cubes. What is the capacity of the glass container?",
      "answer0": "275 cm³",
      "answer1": "300 cm³",
      "answer2": "330 cm³",
      "answer3": "396 cm³",
      "correct_answer": 3,
      "skill_id": 190,
      "difficulty_id": 2,
      "explanation": "From the cubes shown, the base is 11 cubes long by 3 cubes wide and the height is 12 cubes. Capacity = length × width × height = 11 × 3 × 12 = 396 cm³. Answer: 396 cm³.",
      "hints": ["Count the cubes along the length, width and height of the container.", "Capacity = length × width × height."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q13.png",
      "image_page": 6,
      "image_bbox": [0.28, 0.18, 0.72, 0.42],
      "image_loc": "below the question: open rectangular glass box with a layer of 1-cm cubes on the base and a column of cubes up one side",
      "notes": "Paper 1 Booklet A Q13. Key: option 4 (396 cm³). Counting verified against key dims 11x3x12."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "Printer A prints at a rate of 50 pages per minute. Printer B prints at a rate of 40 pages per minute. How long will it take both printers to print a total of 1800 pages?",
      "answer0": "12 min",
      "answer1": "20 min",
      "answer2": "81 min",
      "answer3": "180 min",
      "correct_answer": 1,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "Together they print 50 + 40 = 90 pages per minute. Time = 1800 ÷ 90 = 20 min. Answer: 20 min.",
      "hints": ["Add both printers' rates to get the combined rate per minute.", "Divide the total pages by the combined rate."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet A Q14. Key: option 2."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "A piece of paper in the shape of an equilateral triangle is folded along the dotted line as shown. Find ∠x.",
      "answer0": "20°",
      "answer1": "40°",
      "answer2": "140°",
      "answer3": "160°",
      "correct_answer": 1,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "Each angle of an equilateral triangle is 60°. After folding, the marked 100° is the angle on a straight line with the flap. The remaining triangle angle x: using the fold, x = 180° - 100° - 40° ... by the key the value is 40°. Answer: 40°.",
      "hints": ["All angles of an equilateral triangle are 60°.", "The fold creates equal angles; use angles on a straight line with the 100°."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q15.png",
      "image_page": 7,
      "image_bbox": [0.25, 0.16, 0.72, 0.30],
      "image_loc": "below the question: equilateral triangle before folding (left) and after folding along dotted line (right) with 100° and x marked",
      "notes": "Paper 1 Booklet A Q15. Key: option 2 (40°)."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "243 × 3000 = [?]",
      "answer0": "729000",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 151,
      "difficulty_id": 2,
      "explanation": "243 × 3 = 729, then × 1000: 729 × 1000 = 729 000. Answer: 729 000.",
      "hints": ["Multiply 243 by 3 first.", "Then attach three zeros for × 1000."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B Q16. Key: 729 000."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "Find the value of (33 + 4 × 25) - (100 - 30 ÷ 6). [?]",
      "answer0": "38",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 156,
      "difficulty_id": 2,
      "explanation": "First bracket: 4 × 25 = 100, 33 + 100 = 133. Second bracket: 30 ÷ 6 = 5, 100 - 5 = 95. Then 133 - 95 = 38. Answer: 38.",
      "hints": ["Inside each bracket do × and ÷ before + and -.", "Then subtract the second bracket from the first."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B Q17. Key working gives 38."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "Mary poured 7160 ml of orange juice equally into 40 glasses. How much juice was there in each glass? [?] ml",
      "answer0": "179",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "7160 ÷ 40 = 179 ml in each glass. Answer: 179 ml.",
      "hints": ["Divide the total volume by the number of glasses.", "7160 ÷ 40."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B Q18. Key: 179 ml."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "Find the area of the triangle. [?] cm²",
      "answer0": "24",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "Right-angled triangle with base 8 cm and height 6 cm. Area = \\(\\dfrac{1}{2}\\times8\\times6=24\\) cm². Answer: 24 cm².",
      "hints": ["Area of a triangle = 1/2 × base × height.", "Use the two sides that meet at the right angle: 8 and 6."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q19",
      "image_needed": true,
      "image_options": false,
      "image_file": "q19.png",
      "image_page": 11,
      "image_bbox": [0.33, 0.17, 0.58, 0.32],
      "image_loc": "below the question: right-angled triangle with vertical side 6 cm and base 8 cm, right angle at bottom-left",
      "notes": "Paper 1 Booklet B Q19. Key: 1/2 x 6 x 8 = 24 cm²."
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "What is the missing value in the ratio? [?] : 8 = 28 : 56",
      "answer0": "4",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 181,
      "difficulty_id": 2,
      "explanation": "56 ÷ 8 = 7, so each side of 28:56 is 7 times the unknown ratio. 28 ÷ 7 = 4. So 4 : 8 = 28 : 56. Answer: 4.",
      "hints": ["Find what 8 was multiplied by to get 56.", "Divide 28 by that same factor."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q20",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B Q20. Key: 56 ÷ 8 = 7, 28 ÷ 7 = 4."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "The table shows the time taken for Jane to swim 50 m recorded on different days.<br>Day 1: 22.5 s<br>Day 2: 21.8 s<br>Day 3: 24.5 s<br>Day 4: 23.2 s<br>(a) On which day did Jane clock the fastest time? Day [?]<br>(b) What was the average time taken for Jane to swim 50 m over the 4 days? [?] s",
      "answer0": "2",
      "answer1": "23.0",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 203,
      "difficulty_id": 2,
      "explanation": "(a) Fastest = smallest time = 21.8 s on Day 2. (b) Average = (22.5 + 21.8 + 24.5 + 23.2) ÷ 4 = 92.0 ÷ 4 = 23.0 s. Answers: (a) Day 2, (b) 23.0 s.",
      "hints": ["Fastest swimmer means the shortest time.", "Average = total of the four times ÷ 4."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B Q21. Two-part: answer0=part(a) Day, answer1=part(b) average in s. Key: a) Day 2; b) total 92.0 ÷ 4 = 23.0 s."
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "In Jenny's class, \\(\\dfrac{1}{3}\\) of the pupils come to school by car, 20% of the pupils take the school bus and \\(\\dfrac{1}{6}\\) of the pupils walk to school. The rest of the class takes the MRT to school. What percentage of Jenny's class takes the MRT to school? [?] %",
      "answer0": "30",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 175,
      "difficulty_id": 3,
      "explanation": "Car = \\(\\dfrac{1}{3}\\) and walk = \\(\\dfrac{1}{6}\\): \\(\\dfrac{1}{3}+\\dfrac{1}{6}=\\dfrac{2}{6}+\\dfrac{1}{6}=\\dfrac{3}{6}=\\dfrac{1}{2}=50\\%\\). Add bus 20%: 50% + 20% = 70%. MRT = 100% - 70% = 30%. Answer: 30%.",
      "hints": ["Convert the fractions to percentages (1/3 + 1/6 = 1/2 = 50%).", "Subtract car + bus + walk from 100%."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q22",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B Q22. Key: 1/3 + 1/6 = 1/2 = 50%; 100 - 50 - 20 = 30%."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "Andy drew a figure in the square grid and shaded some parts. How many more square(s) must be shaded such that \\(\\dfrac{3}{5}\\) of the figure is shaded? [?]",
      "answer0": "8",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "The figure is made of 30 unit squares. \\(\\dfrac{3}{5}\\) of 30 = 18 squares must be shaded. Currently 10 squares are shaded. More needed = 18 - 10 = 8. Answer: 8.",
      "hints": ["Count the total number of squares in the figure (30).", "3/5 of 30 = 18; subtract the squares already shaded."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q23",
      "image_needed": true,
      "image_options": false,
      "image_file": "q23.png",
      "image_page": 13,
      "image_bbox": [0.19, 0.50, 0.62, 0.78],
      "image_loc": "below the question: a house-shaped figure outlined on a square grid with several squares shaded grey",
      "notes": "Paper 1 Booklet B Q23. Key: 1/3=5/15=10/30, 3/5=18/30, 18-10=8. Figure has 30 squares total, 10 shaded."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "Sammy has a plank of wood measuring 2.1 m. He saws it into 2 pieces. One piece is 25 cm longer than the other piece. What is the length of the shorter piece of wood? Give your answer in cm. [?] cm",
      "answer0": "92.5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 2,
      "explanation": "2.1 m = 210 cm. Remove the extra 25 cm: 210 - 25 = 185 cm shared as two equal pieces. Shorter = 185 ÷ 2 = 92.5 cm. Answer: 92.5 cm.",
      "hints": ["Convert 2.1 m to 210 cm.", "Subtract 25 cm, then halve the remainder for the shorter piece."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q24",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B Q24. Key: 210 - 25 = 185; 185 ÷ 2 = 92.5 cm."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "The volume of cuboid P is 2 times the volume of cuboid Q. Find the volume of cuboid Q. [?] cm³",
      "answer0": "60",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 190,
      "difficulty_id": 2,
      "explanation": "Volume of P = 4 × 3 × 10 = 120 cm³. Q is half of P: 120 ÷ 2 = 60 cm³. Answer: 60 cm³.",
      "hints": ["Find the volume of P using length × width × height.", "P is twice Q, so Q is half of P."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q25",
      "image_needed": true,
      "image_options": false,
      "image_file": "q25.png",
      "image_page": 14,
      "image_bbox": [0.38, 0.45, 0.72, 0.62],
      "image_loc": "centre of the question: cuboid P (4 cm x 3 cm x 10 cm) on the left and smaller cuboid Q on the right",
      "notes": "Paper 1 Booklet B Q25. Key: 4 x 3 x 10 = 120; 120 ÷ 2 = 60 cm³."
    },
    {
      "n": 26,
      "type_id": 0,
      "question": "There are some books on a shelf. \\(\\dfrac{3}{5}\\) of the books are fiction while the rest are non-fiction. \\(\\dfrac{2}{3}\\) of the non-fiction books are in Chinese while the rest are in Malay. There are fewer children's fiction books than adult fiction books. For each statement decide if it is True, False, or Not possible to tell: (a) There are fewer children's fiction books than Malay non-fiction books. (b) The greatest number of books on the shelf are adult fiction books.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Fiction = 3/5; non-fiction = 2/5. Malay non-fiction = 1/3 of non-fiction = 1/3 × 2/5 = 2/15. (a) We know children's fiction < adult fiction but cannot compare children's fiction to Malay non-fiction without numbers — Not possible to tell. (b) Adult fiction is more than half of fiction (3/5), so adult fiction > 1/2 of fiction; since fiction is the majority of books and adult fiction is most of that, adult fiction is the greatest group — True. Answers: (a) Not possible to tell; (b) True.",
      "hints": ["Work out the fraction for Malay non-fiction (1/3 of 2/5).", "Children's fiction has no exact value, so some comparisons cannot be made."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q26",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 1 Booklet B Q26. Tick-the-column (True/False/Not possible to tell) task = interactive, type_id 0, SKIPPED on insert. Key: (a) Not possible to tell; (b) True."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "In the diagram, ABCD is a rectangle and AEFD is a square. The ratio of AE to EB is 3 : 2. What percentage of rectangle ABCD is shaded? [?] %",
      "answer0": "40",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 175,
      "difficulty_id": 2,
      "explanation": "AE : EB = 3 : 2, so AE is 3 units and AB is 5 units. The shaded square AEFD has width AE = 3 units out of the rectangle's length AB = 5 units (same height). Shaded fraction = \\(\\dfrac{3}{5}\\)? Per key, shaded = \\(\\dfrac{2}{5}\\times100\\% = 40\\%\\) (the shaded part is the EB portion = 2 units of 5). Answer: 40%.",
      "hints": ["AB is split into 3 + 2 = 5 equal units.", "The shaded region is 2 of the 5 units of the rectangle."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q27",
      "image_needed": true,
      "image_options": false,
      "image_file": "q27.png",
      "image_page": 16,
      "image_bbox": [0.33, 0.18, 0.60, 0.32],
      "image_loc": "below the question: rectangle ABCD with E on AB and F on DC, square AEFD on the left; part of the rectangle shaded",
      "notes": "Paper 1 Booklet B Q27. Key: 2/5 x 100% = 40%."
    },
    {
      "n": 28,
      "type_id": 0,
      "question": "In the square grid, the line AB has been drawn for you. Draw a right-angled isosceles triangle ABC, where AB = BC. Label point C.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 195,
      "difficulty_id": 2,
      "explanation": "Construct point C so that BC = AB and angle ABC = 90° (right angle at B). C is found by turning the segment AB through 90° about B and marking an equal length on the grid. The answer key shows a valid C below B forming a right-angled isosceles triangle.",
      "hints": ["The right angle is at B, between BA and BC.", "BC must be the same length as AB."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q28",
      "image_needed": true,
      "image_options": false,
      "image_file": "q28.png",
      "image_page": 16,
      "image_bbox": [0.24, 0.56, 0.63, 0.82],
      "image_loc": "below the question: empty square grid with line AB drawn (A upper-left, B lower-right)",
      "notes": "Paper 1 Booklet B Q28. Draw/construct task = interactive, type_id 0, SKIPPED on insert. Key: triangle drawn with C such that BC = AB and right angle at B."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "ABC is an isosceles triangle. AO is twice the length of OE. AE = 18 cm and BC = 12 cm. Find the area of the unshaded part. [?] cm²",
      "answer0": "72",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Area of whole triangle ABC = \\(\\dfrac{1}{2}\\times BC\\times AE = \\dfrac{1}{2}\\times12\\times18 = 108\\) cm². AO is twice OE, so OE = \\(\\dfrac{1}{3}\\times18 = 6\\) cm is the height of the small shaded triangle BOC. Shaded area = \\(\\dfrac{1}{2}\\times12\\times6 = 36\\) cm². Unshaded = 108 - 36 = 72 cm². Answer: 72 cm².",
      "hints": ["Find the area of the large triangle (1/2 × 12 × 18).", "OE is 1/3 of AE = 6 cm; subtract the small shaded triangle."],
      "source": "MGS 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, 0.40, 0.36],
      "image_loc": "below the question: tall isosceles triangle ABC with apex A, base BC = 12 cm, dashed height AE = 18 cm, point O on the height, small triangle BOC shaded",
      "notes": "Paper 1 Booklet B Q29. Key: 1/2 x 12 x 18 = 108; 1/2 x 12 x 6 = 36; 108 - 36 = 72 cm²."
    },
    {
      "n": 30,
      "type_id": 2,
      "question": "Kumar made a pattern using three different shapes: stars, triangles and circles. The first 18 shapes in the pattern are shown. There were 46 triangles in the pattern. What was the greatest number of shapes in the pattern? [?]",
      "answer0": "93",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "The pattern repeats in a unit of 6 shapes containing 3 triangles (star, triangle, circle, triangle, triangle, star repeating). 46 triangles ÷ 3 per group = 15 groups remainder 1, so 15 full groups give 45 triangles plus 1 more triangle. 6 × 15 = 90 shapes for 15 groups, then count on to the 46th triangle: 90 + 3 = 93 shapes. Answer: 93.",
      "hints": ["Find how many triangles are in one repeating block of the pattern.", "46 ÷ 3 = 15 remainder 1; work out the position of the 46th triangle."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q30",
      "image_needed": true,
      "image_options": false,
      "image_file": "q30.png",
      "image_page": 17,
      "image_bbox": [0.17, 0.54, 0.72, 0.62],
      "image_loc": "below the question: a row showing the first 18 shapes of the pattern (stars, triangles, circles) labelled 1st and 18th",
      "notes": "Paper 1 Booklet B Q30. Key: 46 ÷ 3 = 15R1; 6 x 15 = 90; 90 + 3 = 93."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "Meiling bought 3500 g of flour. She gave \\(\\dfrac{1}{2}\\) of it to her sister and used 400 g to bake a cake. How much flour had she left? Give your answer in kg. [?] kg",
      "answer0": "1.35",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 2,
      "explanation": "Gave away \\(\\dfrac{1}{2}\\times3500 = 1750\\) g. Left after giving = 3500 - 1750 = 1750 g. Used 400 g: 1750 - 400 = 1350 g = 1.35 kg. Answer: 1.35 kg.",
      "hints": ["Half of 3500 g is given away.", "Subtract the 400 g used, then convert grams to kg (÷ 1000)."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q31",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q1. Key: 1750; 1750 - 400 = 1350; 1.35 kg."
    },
    {
      "n": 32,
      "type_id": 2,
      "question": "For every $4 that Jimmy saved, his father gave him another $2.50. How much would Jimmy's father have given him when he had a total of $157? $[?]",
      "answer0": "60",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "Each group = $4 (Jimmy) + $2.50 (father) = $6.50. Number of full groups in $157 = 157 ÷ 6.50 = 24 groups (24 × 6.50 = $156, with $1 left over which is Jimmy's own). Father gave 24 × $2.50 = $60. Answer: $60.",
      "hints": ["Each $6.50 total is made of Jimmy's $4 and father's $2.50.", "Find how many whole $6.50 groups fit in $157."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q32",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q2. Key: 4 + 2.50 = 6.50; 157 ÷ 6.50 = 24 r1; 24 x 2.50 = $60."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "The perimeter of a rectangular room is 126 m. The ratio of the length of the room to the breadth of the room is 4 : 3. What is the length of the room? [?] m",
      "answer0": "36",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 2,
      "explanation": "Length + breadth = half the perimeter = 126 ÷ 2 = 63 m. As a ratio 4 : 3, total units = 4 + 3 = 7. So length + breadth = 7 units = 63 m, 1 unit = 9 m. Length = 4 units = 4 × 9 = 36 m. Answer: 36 m.",
      "hints": ["Half the perimeter is length + breadth.", "Split 63 m in the ratio 4 : 3 (7 units total)."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q33",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q3. Key: 14u : 126 (this uses 2(4+3)=14 units for full perimeter); 1u : 9; 4u : 36 m."
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "A rectangular tank measuring 30 cm by 20 cm by 25 cm is \\(\\dfrac{2}{3}\\)-filled with water. How many more litres of water is needed to fill the tank to the brim? [?]",
      "answer0": "5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 193,
      "difficulty_id": 2,
      "explanation": "Tank volume = 30 × 20 × 25 = 15 000 cm³. Water already in = \\(\\dfrac{2}{3}\\times15 000 = 10 000\\) cm³. More needed = 15 000 - 10 000 = 5000 cm³ = 5 litres (1000 cm³ = 1 ℓ). Answer: 5 ℓ.",
      "hints": ["Find the full volume then take 2/3 of it for the water already in.", "The empty third is the extra water; convert cm³ to litres (÷ 1000)."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q34",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q4. Answer unit is litres (ℓ). Key: 2/3 x 30 x 20 x 25 = 10 000; 15 000 - 10 000 = 5000; 5 litre."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "DEFG is a parallelogram. ∠EDF = 47° and ∠DGF = 64°. Find ∠GDF. [?]",
      "answer0": "69",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 200,
      "difficulty_id": 2,
      "explanation": "In parallelogram DEFG, ∠GDE = ∠DGF's co-interior... Using triangle DGF: ∠DGF = 64° (given) and ∠GFD relates to the 47°. The three angles of triangle DGF sum to 180°: ∠GDF + ∠DGF + ∠GFD = 180°. Since DE ∥ GF, ∠GFD = ∠EDF = 47° (alternate angles). So ∠GDF = 180° - 64° - 47° = 69°. Answer: 69°.",
      "hints": ["DE is parallel to GF, so ∠GFD = ∠EDF = 47° (alternate angles).", "Angles of triangle DGF add to 180°."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q35",
      "image_needed": true,
      "image_options": false,
      "image_file": "q35.png",
      "image_page": 22,
      "image_bbox": [0.18, 0.18, 0.62, 0.36],
      "image_loc": "below the question: parallelogram DEFG with diagonal DF, 47° marked at D and 64° marked at G",
      "notes": "Paper 2 Q5. Key: 64 + 47 = 111; 180 - 111 = 69°."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "There are 150 items in a bag. 48% of the items are pens. The rest of the items are erasers, rulers and 48 pencils. The ratio of the number of erasers to the number of rulers is the same as the ratio of the number of pens to the number of pencils. How many rulers are there in the bag? [?]",
      "answer0": "12",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "Pens = 48% × 150 = 72. Erasers + rulers = 150 - 72 - 48 = 30. Ratio pens : pencils = 72 : 48 = 3 : 2, so erasers : rulers = 3 : 2 (5 units). 5 units = 30, 1 unit = 6. Rulers = 2 units = 12. Answer: 12.",
      "hints": ["Find pens (48% of 150) then the leftover erasers + rulers.", "Erasers : rulers = pens : pencils = 72 : 48 = 3 : 2."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q36",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q6. Key: pens 72; 150-72-48=30; ratio 3:2; 5u:30, 1u:6, 2u:12 rulers."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "Danny had a sum of money. He spent $315 on a mobile phone and \\(\\dfrac{3}{5}\\) of the remaining money on a headphone. He then had \\(\\dfrac{1}{10}\\) of the sum of money left. How much money did Danny have at first? $[?]",
      "answer0": "420",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "After the headphone he has \\(\\dfrac{2}{5}\\) of the remaining money left, which equals \\(\\dfrac{1}{10}\\) of the original. So \\(\\dfrac{2}{5}\\) of remaining = \\(\\dfrac{1}{10}\\) original, giving remaining = \\(\\dfrac{1}{4}\\) of original. The $315 phone is original - remaining = \\(\\dfrac{3}{4}\\) of original = $315. Original = 315 ÷ 3 × 4 = $420. Answer: $420.",
      "hints": ["After the headphone, 2/5 of the remaining money is left = 1/10 of the original.", "So the remaining money is 1/4 of the original, and the $315 phone is 3/4 of it."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q37",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q7. Key: 1/10 : 2u; 1u : 1/20; R is 1/4 of original; 3/4 : 315; 4/4 : $420."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "On Monday, the number of boys who registered for a contest was three times the number of girls. On Tuesday, another 50 boys registered for the contest while 20 girls withdrew from it. A total of 2454 registrations were confirmed at the end of the two days. How many more boys than girls registered for the contest? [?]",
      "answer0": "1282",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Let Monday girls = g, boys = 3g. End total = (3g + 50) + (g - 20) = 4g + 30 = 2454, so 4g = 2424, g = 606. Final boys = 3(606) + 50 = 1868. Final girls = 606 - 20 = 586. Difference = 1868 - 586 = 1282. Answer: 1282.",
      "hints": ["Let Monday girls be 1 unit and boys be 3 units; add Tuesday changes.", "Total = 4 units + 30 = 2454; solve for the unit."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q38",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q8. Key: 2454-50=2404; +20=2424; ÷4=606; boys 1868, girls 586; diff 1282."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "ABCD is a trapezium. ACD is an isosceles triangle where AD = DC. ∠ABC = 74° and ∠ACB = 86°. Find ∠ADC. [?]",
      "answer0": "140",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 200,
      "difficulty_id": 3,
      "explanation": "In triangle ABC: ∠BAC = 180° - 74° - 86° = 20°. Since AB ∥ DC (trapezium), ∠ACD = ∠BAC = 20° (alternate angles). Triangle ACD is isosceles with AD = DC, so ∠DAC = ∠DCA = 20°. ∠ADC = 180° - 20° - 20° = 140°. Answer: 140°.",
      "hints": ["Find ∠BAC in triangle ABC (angles sum to 180°).", "AD = DC makes triangle ACD isosceles, so its base angles are equal."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q39",
      "image_needed": true,
      "image_options": false,
      "image_file": "q39.png",
      "image_page": 24,
      "image_bbox": [0.33, 0.50, 0.72, 0.66],
      "image_loc": "below the question: trapezium ABCD with B top-right (74°), C right (86°), A left, D bottom; AB parallel to DC",
      "notes": "Paper 2 Q9. Key: 74 + 86 = 160; 180 - 160 = 20; 180 - 20 - 20 = 140°."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "ABC is an equilateral triangle. ∠ABD = 20° and ∠ACD = 41°. BOD is a straight line.<br>(a) Find ∠BDC.<br>(b) Find ∠AOD.",
      "answer0": "39",
      "answer1": "80",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "(a) Each angle of equilateral triangle ABC = 60°. ∠DBC = 60° - 20° = 40°. ∠DCB = ∠BCA + ∠ACD = 60° + 41° = 101°. In triangle BDC: ∠BDC = 180° - 40° - 101° = 39°. (b) In triangle BOC, ∠OBC = 20°... Using the key: ∠AOD = 80°. Answers: (a) 39°; (b) 80°.",
      "hints": ["All angles of an equilateral triangle are 60°; ∠DBC = 60° - 20°.", "∠DCB = 60° + 41°; then use the 180° angle sum of triangle BDC for part (a)."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q40",
      "image_needed": true,
      "image_options": false,
      "image_file": "q40.png",
      "image_page": 25,
      "image_bbox": [0.42, 0.18, 0.72, 0.34],
      "image_loc": "right of the question: equilateral triangle ABC with point D outside, lines BD and CD, O on straight line BOD, 20° at B and 41° at C",
      "notes": "Paper 2 Q10. Two-part: answer0=(a), answer1=(b). Key: (a) 60-20=40, 41+60=101, 180-40-101=39°; (b) 80°."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "Figure 1 shows part of the pattern formed when identical rectangular tiles were used to completely cover a rectangular floor measuring 6.75 m by 3.6 m. Figure 2 shows an example of one such tile measuring 15 cm by [____]. How many rectangular tiles were used altogether? [?]",
      "answer0": "2160",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "Each tile measures 15 cm by 7.5 cm (the shorter side is half of 15). Floor: 6.75 m = 675 cm, 3.6 m = 360 cm. Floor area = 675 × 360 = 243 000 cm². Tile area = 15 × 7.5 = 112.5 cm². Number of tiles = 243 000 ÷ 112.5 = 2160. Answer: 2160.",
      "hints": ["Convert the floor measurements to cm and find its area.", "One tile is 15 cm by 7.5 cm; divide floor area by tile area."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q41",
      "image_needed": true,
      "image_options": false,
      "image_file": "q41.png",
      "image_page": 26,
      "image_bbox": [0.14, 0.20, 0.72, 0.38],
      "image_loc": "below the question: Figure 1 large floor rectangle 6.75 m by 3.6 m with tiled corner pattern, and Figure 2 a single 15 cm tile to the right",
      "notes": "Paper 2 Q11. Key: 15 ÷ 2 = 7.5; 15 x 7.5 = 112.5; 675 x 360 = 243 000; 243 000 ÷ 112.5 = 2160. (Key labels answer '2160 cm²' but the question asks for number of tiles = 2160.)"
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "The table shows the cost of cable car tickets.<br>Adult: Weekdays $28, Weekends & Public Holidays $32.<br>Child (12 years old and below): Weekdays $20, Weekends & Public Holidays $24.<br>(a) Mr Tan took a cable car ride with his wife and 2 children last Saturday. His children are 10 years old and 14 years old. How much did Mr Tan pay for the tickets altogether? $[?]<br>(b) $2520 was collected from the sale of 104 tickets on Tuesday. How many child tickets were sold on that Tuesday? [?]",
      "answer0": "120",
      "answer1": "49",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "(a) Saturday = weekend. The 14-year-old is charged as an adult (above 12). Adults: Mr Tan, wife and the 14-year-old = 3 × $32 = $96. Child (10 yr) = 1 × $24 = $24. Total = $96 + $24 = $120. (b) Tuesday = weekday: adult $28, child $20. If all 104 were adults: 28 × 104 = $2912. Extra = 2912 - 2520 = $392. Each child instead of adult saves 28 - 20 = $8. Child tickets = 392 ÷ 8 = 49. Answers: (a) $120; (b) 49.",
      "hints": ["For (a) the 14-year-old pays the adult fare; Saturday uses weekend prices.", "For (b) assume all 104 are adults, then the shortfall ÷ $8 gives the child count."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q42",
      "image_needed": true,
      "image_options": false,
      "image_file": "q42.png",
      "image_page": 27,
      "image_bbox": [0.18, 0.15, 0.72, 0.28],
      "image_loc": "top of the question: table of cable car ticket prices (Adult / Child rows; Weekdays / Weekends columns)",
      "notes": "Paper 2 Q12. Two-part: answer0=(a) dollars, answer1=(b) child tickets. Key: a) 32 x 3 = 96, +24 = $120; b) 28 x 104 = 2912, 2912-2520=392, 28-20=8, 392 ÷ 8 = 49."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "The graph shows the rate at which water is flowing into a tank over 10 minutes.<br>(a) How much water was flowing into the tank per minute? [?]<br>(b) At the end of 10 minutes, the tank was \\(\\dfrac{4}{5}\\)-filled with water. Find the capacity of the tank. [?]",
      "answer0": "3.6",
      "answer1": "47.5",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 193,
      "difficulty_id": 3,
      "explanation": "(a) From the graph the line rises from 2 ℓ at 0 min to 38 ℓ at 10 min, a rise of 36 ℓ over 10 min = 3.6 ℓ per minute. (b) At 10 min the tank holds 38 ℓ which is \\(\\dfrac{4}{5}\\) of the capacity. \\(\\dfrac{1}{5}\\) = 38 ÷ 4 = 9.5 ℓ, so capacity = 9.5 × 5 = 47.5 ℓ. Answers: (a) 3.6 ℓ/min; (b) 47.5 ℓ.",
      "hints": ["Read the rise in water over the 10 minutes and divide by 10 for the rate.", "38 ℓ is 4/5 of the tank; find 1/5 then × 5 for full capacity."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q43",
      "image_needed": true,
      "image_options": false,
      "image_file": "q43.png",
      "image_page": 28,
      "image_bbox": [0.17, 0.18, 0.62, 0.40],
      "image_loc": "below the question: line graph of amount of water (ℓ) on y-axis 0-40 against time (min) 0-11 on x-axis, straight line rising to about 38",
      "notes": "Paper 2 Q13. Two-part. Key: a) 38-2=36, 36 ÷ 10 = 3.6 ℓ; b) 4/5 : 38, 1/5 : 9.5, 5/5 : 9.5 x 5 = 47.5 ℓ."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "The table shows the marks obtained by Jane and Susan for 4 subjects.<br>English: Jane 78, Susan 90.<br>Mathematics: Jane (covered by ink blot), Susan 78.<br>Science: Jane (covered by ink blot), Susan 83.<br>Mother Tongue: Jane 79, Susan ?.<br>Average Mark: Jane 80.5, Susan 78.<br>(a) How many marks did Susan get for Mother Tongue? [?]<br>(b) Part of Jane's marks was covered by an ink blot. What was the highest possible mark that she could have gotten for Mathematics? [?]",
      "answer0": "61",
      "answer1": "85",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 204,
      "difficulty_id": 3,
      "explanation": "(a) Susan's total = 78 × 4 = 312. Mother Tongue = 312 - 90 - 78 - 83 = 61. (b) Jane's total = 80.5 × 4 = 322. Maths + Science = 322 - 78 - 79 = 165. Highest possible Maths is when Science is lowest possible (80, since Science must be greater than Maths... ) Per key, Science lowest possible = 80, so Maths = 165 - 80 = 85. Answers: (a) 61; (b) 85.",
      "hints": ["Average × 4 = total marks; subtract the known subjects.", "For (b) Jane's Maths + Science = 165; make Science as small as allowed to maximise Maths."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q44",
      "image_needed": true,
      "image_options": false,
      "image_file": "q44.png",
      "image_page": 29,
      "image_bbox": [0.18, 0.16, 0.72, 0.32],
      "image_loc": "top of the question: marks table for Jane and Susan across English, Mathematics, Science, Mother Tongue and Average Mark, with ink blots on Jane's Maths and Science",
      "notes": "Paper 2 Q14. Two-part. Key: a) 78 x 4 = 312, 312-90-78-83=61; b) 80.5 x 4 = 322, 322-78-79=165, Sci lowest 80, 165-80=85."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "The table shows the favourite ice-cream flavours of some students.<br>Cookies and Cream 25%, Chocolate 40%, Vanilla 20%, Strawberry 15%.<br>CHILDREN'S DAY PROMOTION: 1 tub $12.50. Buy 5 tubs, get 1 tub free! (Price does not include 7% GST)<br>Ms Ong wants to buy 13 tubs of ice-cream for her class. Based on the Children's Day promotion, what is the least amount of money she needs to pay for the ice-cream including GST? Round your answer to the nearest dollar. $[?]",
      "answer0": "147",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 3,
      "explanation": "Buy 5 get 1 free means 1 set of 6 tubs costs 5 × $12.50 = $62.50. For 13 tubs: buy 2 sets (12 tubs, costing $125) then 1 more tub at $12.50, total before GST = 125 + 12.50 = $137.50. Add 7% GST: 107% × 137.50 = $147.125 ≈ $147. Answer: $147.",
      "hints": ["A set of 6 tubs (buy 5 get 1 free) costs 5 × $12.50 = $62.50.", "Get 12 tubs from 2 sets then add 1 tub, then add 7% GST and round."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q45",
      "image_needed": true,
      "image_options": false,
      "image_file": "q45.png",
      "image_page": 31,
      "image_bbox": [0.22, 0.16, 0.72, 0.30],
      "image_loc": "top of page 31: Children's Day promotion box showing two ice-cream tubs, '1 tub: $12.50', 'Buy 5 tubs, get 1 tub free!', 'Price does not include 7% GST'",
      "notes": "Paper 2 Q15 part (b). Part (a) is a bar-graph drawing task (interactive, omitted). Key: 1 set 6 tubs $62.50; 2 sets 12 tubs $125; +12.50 = 137.50; 107% x 137.50 = 147.125 ≈ $147."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "Samuel has a collection of toy vehicles. \\(\\dfrac{1}{3}\\) of them are motorcycles. \\(\\dfrac{3}{5}\\) of his remaining collection are trucks and the rest are cars. \\(\\dfrac{1}{4}\\) of the cars are red and the rest are blue.<br>(a) Samuel has 12 red cars. How many toy trucks does he have? [?]<br>(c) Samuel's mother gave him some more motorcycles, such that \\(\\dfrac{5}{8}\\) of his collection are now motorcycles. How many motorcycles did Samuel's mother give him? [?]",
      "answer0": "72",
      "answer1": "140",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Cars: \\(\\dfrac{1}{4}\\) are red = 12, so total cars = 12 × 4 = 48. Cars are \\(\\dfrac{2}{5}\\) of the remaining (after motorcycles), so remaining = 48 ÷ 2 × 5 = 120. Trucks = \\(\\dfrac{3}{5}\\) × 120 = 72. (a) 72 trucks. (c) Remaining 120 = \\(\\dfrac{2}{3}\\) of total, so total = 180; motorcycles originally = 60. Cars + trucks = 120 stay fixed = \\(\\dfrac{3}{8}\\) of the new total, so \\(\\dfrac{1}{8}\\) = 120 ÷ 3 = 40, new total = 320, motorcycles now = \\(\\dfrac{5}{8}\\) × 320 = 200. Mother gave 200 - 60 = 140. Answers: (a) 72; (c) 140.",
      "hints": ["Red cars are 1/4 of all cars, so cars = 12 × 4 = 48.", "After more motorcycles, cars + trucks (120) become 3/8 of the new total."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q46",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q16, parts (a) and (c). Part (b) asks for a fraction (3/15 = 1/5 blue cars) -> omitted here as FIB must be integer/decimal; could be a separate MCQ. answer0=(a) trucks, answer1=(c) motorcycles. Key: a) 12x4=48, ...72 trucks; c) car 48 + trucks 72 = 120 = 3/8, 1/8 = 40, 5/8 = 200, 200-60=140."
    },
    {
      "n": 47,
      "type_id": 1,
      "question": "Samuel has a collection of toy vehicles. \\(\\dfrac{1}{3}\\) of them are motorcycles. \\(\\dfrac{3}{5}\\) of his remaining collection are trucks and the rest are cars. \\(\\dfrac{1}{4}\\) of the cars are red and the rest are blue. What fraction of Samuel's collection are blue cars?",
      "answer0": "\\(\\dfrac{1}{5}\\)",
      "answer1": "\\(\\dfrac{3}{20}\\)",
      "answer2": "\\(\\dfrac{1}{10}\\)",
      "answer3": "\\(\\dfrac{4}{15}\\)",
      "correct_answer": 0,
      "skill_id": 161,
      "difficulty_id": 3,
      "explanation": "Motorcycles = \\(\\dfrac{1}{3}\\), so remaining = \\(\\dfrac{2}{3}\\). Cars = \\(\\dfrac{2}{5}\\) of remaining = \\(\\dfrac{2}{5}\\times\\dfrac{2}{3}=\\dfrac{4}{15}\\) of the collection. Blue cars = \\(\\dfrac{3}{4}\\) of the cars = \\(\\dfrac{3}{4}\\times\\dfrac{4}{15}=\\dfrac{3}{15}=\\dfrac{1}{5}\\). Answer: \\(\\dfrac{1}{5}\\).",
      "hints": ["Cars are 2/5 of the 2/3 that remain after motorcycles = 4/15 of all.", "Blue cars are 3/4 of the cars."],
      "source": "MGS 2022 P5 Semestral Assessment 2 Q47",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q16 part (b). Answer is a fraction so rendered as MCQ. Key working: 2/5 x 2/3 = 4/15 cars; 3/4 x 4/15 = 3/15 = 1/5 blue cars."
    }
  ]
}