{
  "paper": {
    "school": "CHIJ St Nicholas Girls' School",
    "year": 2023,
    "level": "P5",
    "label": "End-of-Year Exam",
    "source_prefix": "St Nicholas 2023 P5 End-of-Year Exam",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "In which one of the following numbers does the digit 5 have a value of 50 000?",
      "answer0": "1 243 506",
      "answer1": "3 705 291",
      "answer2": "4 658 120",
      "answer3": "6 582 437",
      "correct_answer": 2,
      "skill_id": 149,
      "difficulty_id": 1,
      "explanation": "Place value: the digit 5 must sit in the ten-thousands place (value 50 000). In 4 658 120, the 5 is in the ten-thousands place: 5 × 10 000 = 50 000. Answer: 4 658 120.",
      "hints": ["A value of 50 000 means 5 ten-thousands.", "Look for the number where 5 is in the ten-thousands position."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Which one of the following fractions is smaller than \\(\\dfrac{1}{4}\\)?",
      "answer0": "\\(\\dfrac{5}{6}\\)",
      "answer1": "\\(\\dfrac{3}{8}\\)",
      "answer2": "\\(\\dfrac{2}{5}\\)",
      "answer3": "\\(\\dfrac{1}{6}\\)",
      "correct_answer": 3,
      "skill_id": 158,
      "difficulty_id": 2,
      "explanation": "Compare each to \\(\\dfrac{1}{4}=0.25\\): \\(\\dfrac{5}{6}\\approx0.83\\), \\(\\dfrac{3}{8}=0.375\\), \\(\\dfrac{2}{5}=0.4\\), \\(\\dfrac{1}{6}\\approx0.167\\). Only \\(\\dfrac{1}{6}\\) is smaller than \\(\\dfrac{1}{4}\\). Answer: \\(\\dfrac{1}{6}\\).",
      "hints": ["\\(\\dfrac{1}{4}=0.25\\).", "A larger denominator with the same numerator gives a smaller fraction."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Fraction options -> MCQ"
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "$$16 + \\dfrac{?}{10} = 17.8$$ What is the missing number in the box?",
      "answer0": "0.8",
      "answer1": "1.8",
      "answer2": "18",
      "answer3": "180",
      "correct_answer": 2,
      "skill_id": 166,
      "difficulty_id": 2,
      "explanation": "17.8 − 16 = 1.8, so \\(\\dfrac{?}{10}=1.8\\). Then ? = 1.8 × 10 = 18. Answer: 18.",
      "hints": ["Subtract 16 from 17.8 first.", "If \\(\\dfrac{?}{10}=1.8\\), multiply 1.8 by 10."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Box-fraction shown as display; answer options are whole/decimal"
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "In the number line, what is the value of X?",
      "answer0": "\\(\\dfrac{1}{2}\\)",
      "answer1": "\\(\\dfrac{2}{3}\\)",
      "answer2": "\\(\\dfrac{3}{4}\\)",
      "answer3": "\\(\\dfrac{7}{12}\\)",
      "correct_answer": 1,
      "skill_id": 158,
      "difficulty_id": 2,
      "explanation": "The line runs from \\(\\dfrac{3}{12}\\) to \\(\\dfrac{10}{12}\\). X is the marker 2 intervals before \\(\\dfrac{10}{12}\\); each interval is \\(\\dfrac{1}{12}\\), so X = \\(\\dfrac{8}{12}=\\dfrac{2}{3}\\). Answer: \\(\\dfrac{2}{3}\\).",
      "hints": ["Each small division on the line equals \\(\\dfrac{1}{12}\\).", "Count divisions from \\(\\dfrac{10}{12}\\) back to X."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q4.png",
      "image_page": 3,
      "image_bbox": [0.25, 0.43, 0.85, 0.56],
      "image_loc": "number line in the middle of the page, marked 3/12 ... X ... 10/12",
      "notes": "Fraction options -> MCQ"
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "Yu Wen had $7000 in her bank account. The bank paid 2% interest at the end of each year. She did not withdraw any of her savings. How much interest did she earn at the end of 1 year?",
      "answer0": "$140",
      "answer1": "$350",
      "answer2": "$6860",
      "answer3": "$7140",
      "correct_answer": 0,
      "skill_id": 176,
      "difficulty_id": 2,
      "explanation": "Interest = 2% of $7000 = \\(\\dfrac{2}{100}\\times 7000 = \\$140\\). Answer: $140.",
      "hints": ["2% means 2 out of every 100.", "Multiply $7000 by 0.02."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "There are 10 chickens at a farm. There are 35 more ducks than chickens. What is the ratio of the number of ducks to the number of chickens?",
      "answer0": "2 : 7",
      "answer1": "2 : 9",
      "answer2": "7 : 2",
      "answer3": "9 : 2",
      "correct_answer": 3,
      "skill_id": 179,
      "difficulty_id": 2,
      "explanation": "Ducks = 10 + 35 = 45. Ratio ducks : chickens = 45 : 10 = 9 : 2. Answer: 9 : 2.",
      "hints": ["Find the number of ducks first.", "Simplify the ratio 45 : 10 by dividing both by 5."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Ratio answer -> MCQ"
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "Lovely Flower Shop sold a total of 80 flowers on Monday. The table shows the number of different types of flowers sold: Daisies 20, Lilies 15, Roses 25, Tulips unknown. What is the total number of tulips and daisies sold on Monday?",
      "answer0": "20",
      "answer1": "40",
      "answer2": "60",
      "answer3": "80",
      "correct_answer": 1,
      "skill_id": 147,
      "difficulty_id": 2,
      "explanation": "Tulips = 80 − 20 − 15 − 25 = 20. Tulips + Daisies = 20 + 20 = 40. Answer: 40.",
      "hints": ["Find the number of tulips: total minus the other three types.", "Add tulips and daisies."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q7.png",
      "image_page": 5,
      "image_bbox": [0.2, 0.27, 0.78, 0.45],
      "image_loc": "table of flower types and counts in the upper-middle of the page",
      "notes": "Table data embedded in stem; image is the table"
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "Which one of the following graphs represents the information shown in the table correctly?",
      "answer0": "Graph 1",
      "answer1": "Graph 2",
      "answer2": "Graph 3",
      "answer3": "Graph 4",
      "correct_answer": 3,
      "skill_id": 147,
      "difficulty_id": 2,
      "explanation": "The table values are Daisies 20, Lilies 15, Roses 25. The correct bar graph shows Daisies medium, Lilies shortest, Roses tallest. Graph 4 matches this pattern. Answer: Graph 4.",
      "hints": ["Daisies = 20, Lilies = 15, Roses = 25.", "Lilies should be the shortest bar and Roses the tallest."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q8",
      "image_needed": true,
      "image_options": true,
      "image_file": null,
      "image_page": 6,
      "image_bbox": [0.18, 0.12, 0.62, 0.92],
      "image_loc": "four bar-graph options stacked vertically down the page",
      "notes": "Image-option MCQ: each option is a bar graph. Crop q8_opt0.png (graph 1, top) ... q8_opt3.png (graph 4, bottom). Answer = option 4 (index 3)."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "Harumi had a piece of string 4 m 6 cm. She cut off 1.3 m from it. What is the length of the remaining string?",
      "answer0": "276 cm",
      "answer1": "330 cm",
      "answer2": "393 cm",
      "answer3": "447 cm",
      "correct_answer": 0,
      "skill_id": 184,
      "difficulty_id": 2,
      "explanation": "4 m 6 cm = 406 cm. 1.3 m = 130 cm. Remaining = 406 − 130 = 276 cm. Answer: 276 cm.",
      "hints": ["Convert everything to centimetres: 4 m 6 cm = 406 cm.", "1.3 m = 130 cm; subtract."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "AB and CD are straight lines. Which one of the following statements is true?",
      "answer0": "\\(\\angle p = \\angle r\\)",
      "answer1": "\\(\\angle q = \\angle t\\)",
      "answer2": "\\(\\angle p = \\angle q + \\angle r\\)",
      "answer3": "\\(\\angle q = \\angle t + \\angle s\\)",
      "correct_answer": 1,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "Where AB and CD cross, \\(\\angle q\\) and \\(\\angle t\\) are vertically opposite angles, so \\(\\angle q = \\angle t\\). Answer: \\(\\angle q = \\angle t\\).",
      "hints": ["Vertically opposite angles are equal.", "Identify which pair of marked angles are vertically opposite at the crossing point."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 7,
      "image_bbox": [0.28, 0.42, 0.78, 0.62],
      "image_loc": "angle diagram with lines A-B, C-D, E and angles p,q,r,s,t in the middle of the page",
      "notes": "Angle-letter options -> MCQ"
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "A sandwich costs $6.05. Leonard bought 4 such sandwiches and had $1.85 left. How much money did he have before buying the 4 sandwiches?",
      "answer0": "$4.20",
      "answer1": "$7.90",
      "answer2": "$22.35",
      "answer3": "$26.05",
      "correct_answer": 3,
      "skill_id": 167,
      "difficulty_id": 2,
      "explanation": "Cost of 4 sandwiches = 4 × $6.05 = $24.20. Money before = $24.20 + $1.85 = $26.05. Answer: $26.05.",
      "hints": ["Find the total cost of 4 sandwiches.", "Add the $1.85 that was left over."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "Amiya and Eunice have $2100 altogether. Amiya has 30% of the money. How much money does Amiya have?",
      "answer0": "$21",
      "answer1": "$70",
      "answer2": "$300",
      "answer3": "$630",
      "correct_answer": 3,
      "skill_id": 174,
      "difficulty_id": 2,
      "explanation": "30% of $2100 = \\(\\dfrac{30}{100}\\times 2100 = \\$630\\). Answer: $630.",
      "hints": ["30% means 30 out of every 100.", "Multiply $2100 by 0.30."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": ""
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "A store charges the following rates for the order of T-shirts: first 15 pieces at $6 per piece, every additional piece at $4 per piece. What is the cost of ordering 50 pieces of T-shirts?",
      "answer0": "$200",
      "answer1": "$230",
      "answer2": "$270",
      "answer3": "$300",
      "correct_answer": 1,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "First 15 pieces: 15 × $6 = $90. Additional pieces: 50 − 15 = 35 pieces × $4 = $140. Total = $90 + $140 = $230. Answer: $230.",
      "hints": ["Charge the first 15 pieces at $6 each.", "The remaining 35 pieces are charged at $4 each."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q13.png",
      "image_page": 9,
      "image_bbox": [0.25, 0.08, 0.78, 0.18],
      "image_loc": "two-row rate table near the top of the page",
      "notes": "Rates given in stem; image is the table"
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "Mrs Urvi cut a cake into 16 equal pieces. She ate 3 pieces and gave a few pieces to her friends. In the end, she had \\(\\dfrac{3}{8}\\) of the cake left. What fraction of the cake did she give to her friends?",
      "answer0": "\\(\\dfrac{3}{16}\\)",
      "answer1": "\\(\\dfrac{5}{8}\\)",
      "answer2": "\\(\\dfrac{7}{16}\\)",
      "answer3": "\\(\\dfrac{9}{16}\\)",
      "correct_answer": 2,
      "skill_id": 159,
      "difficulty_id": 3,
      "explanation": "Ate 3 of 16 pieces = \\(\\dfrac{3}{16}\\). Left = \\(\\dfrac{3}{8}=\\dfrac{6}{16}\\). Gave away = whole − ate − left = \\(\\dfrac{16}{16}-\\dfrac{3}{16}-\\dfrac{6}{16}=\\dfrac{7}{16}\\). Answer: \\(\\dfrac{7}{16}\\).",
      "hints": ["Write everything in sixteenths.", "Gave away = 16/16 minus what she ate minus what was left."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Fraction options -> MCQ"
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "Jamil used some shapes to form a pattern. The first 9 shapes are shown. Which shape is in the 52nd position?",
      "answer0": "Lightning bolt",
      "answer1": "Heart",
      "answer2": "Cross/plus shape",
      "answer3": "Sun/star burst",
      "correct_answer": 0,
      "skill_id": 149,
      "difficulty_id": 2,
      "explanation": "The pattern repeats every 5 shapes: bolt, bolt, heart, cross, sun. 52 ÷ 5 = 10 remainder 2, so the 52nd shape is the 2nd in the repeating unit, which is the lightning bolt. Answer: lightning bolt (option 1).",
      "hints": ["The unit of repeat has 5 shapes.", "Divide 52 by 5 and use the remainder to find the position in the cycle."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q15",
      "image_needed": true,
      "image_options": true,
      "image_file": null,
      "image_page": 10,
      "image_bbox": [0.12, 0.1, 0.9, 0.21],
      "image_loc": "long horizontal box showing the first 9 pattern shapes at top of page",
      "notes": "Pattern sequence image needed (the strip of shapes). Options are picture shapes -> image_options true; crop q15_opt0.png (bolt) q15_opt1.png (heart) q15_opt2.png (cross) q15_opt3.png (sun). The four option sprites sit lower on the page at roughly bbox [0.2,0.3,0.4,0.7]. Answer = bolt (index 0)."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Find the value of \\(57 \\div 300\\). Leave your answer as a decimal. [?]",
      "answer0": "0.19",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 166,
      "difficulty_id": 2,
      "explanation": "57 ÷ 300 = 0.19. Answer: 0.19.",
      "hints": ["Simplify: 57 ÷ 300 = 57 ÷ 300.", "57 ÷ 3 = 19, then divide by 100."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 0.19"
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "Find the value of \\(11 + (18 - 14 \\div 2) \\times 3\\). [?]",
      "answer0": "44",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 155,
      "difficulty_id": 2,
      "explanation": "Inside brackets: 14 ÷ 2 = 7, then 18 − 7 = 11. Then 11 × 3 = 33. Then 11 + 33 = 44. Answer: 44.",
      "hints": ["Work inside the brackets first, doing division before subtraction.", "Then multiply by 3, then add 11."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 44"
    },
    {
      "n": 18,
      "type_id": 1,
      "question": "What is six-fifths of 60?",
      "answer0": "72",
      "answer1": "50",
      "answer2": "62",
      "answer3": "100",
      "correct_answer": 0,
      "skill_id": 163,
      "difficulty_id": 2,
      "explanation": "\\(\\dfrac{6}{5}\\times 60 = \\dfrac{6\\times 60}{5}=\\dfrac{360}{5}=72\\). Answer: 72.",
      "hints": ["Six-fifths means \\(\\dfrac{6}{5}\\).", "Multiply 60 by 6, then divide by 5."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 72. Original is short-answer (answer 72, a whole number) but converted to MCQ to keep a fraction-of-a-set concept unambiguous; distractors are plausible. Answer = 72."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "Mrs Cheah bought an iron which included a GST of 7%. The price of the iron before GST was $90. How much did she pay for the iron? Ans: $ [?]",
      "answer0": "96.30",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 2,
      "explanation": "GST = 7% of $90 = \\(\\dfrac{7}{100}\\times 90 = \\$6.30\\). Total paid = $90 + $6.30 = $96.30. Answer: $96.30.",
      "hints": ["Find 7% of $90 first.", "Add the GST to the original $90."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q19",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: $96.30 (money decimal -> FIB ok)"
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "A photocopier can copy 48 pages in 4 minutes. At this rate, how many pages can the photocopier copy per minute? [?]",
      "answer0": "12",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 1,
      "explanation": "48 pages ÷ 4 minutes = 12 pages per minute. Answer: 12.",
      "hints": ["Divide the total pages by the number of minutes.", "48 ÷ 4."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q20",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 12"
    },
    {
      "n": 21,
      "type_id": 1,
      "question": "Arrange the following from the smallest to the largest. \\(0.209\\), \\(\\dfrac{1}{5}\\), \\(\\dfrac{2}{1000}\\)",
      "answer0": "\\(\\dfrac{2}{1000}\\), \\(\\dfrac{1}{5}\\), \\(0.209\\)",
      "answer1": "\\(0.209\\), \\(\\dfrac{1}{5}\\), \\(\\dfrac{2}{1000}\\)",
      "answer2": "\\(\\dfrac{1}{5}\\), \\(\\dfrac{2}{1000}\\), \\(0.209\\)",
      "answer3": "\\(\\dfrac{2}{1000}\\), \\(0.209\\), \\(\\dfrac{1}{5}\\)",
      "correct_answer": 0,
      "skill_id": 158,
      "difficulty_id": 2,
      "explanation": "Convert to decimals: \\(\\dfrac{1}{5}=0.200\\), \\(\\dfrac{2}{1000}=0.002\\), and 0.209. Smallest to largest: 0.002, 0.200, 0.209, i.e. \\(\\dfrac{2}{1000}\\), \\(\\dfrac{1}{5}\\), \\(0.209\\).",
      "hints": ["Write each value as a decimal.", "\\(\\dfrac{1}{5}=0.2\\) and \\(\\dfrac{2}{1000}=0.002\\)."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Ordering task with fraction members -> made MCQ (fractions cannot be FIB). Key order: 2/1000, 1/5, 0.209."
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "Last year, Bertrand completed a race in 51.98 seconds. This year, he completed the same race and was faster by 1.31 seconds. What was Bertrand's timing this year? Round your answer to 1 decimal place. Ans: [?] s",
      "answer0": "50.7",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 2,
      "explanation": "51.98 − 1.31 = 50.67 s. Rounded to 1 decimal place = 50.7 s. Answer: 50.7 s.",
      "hints": ["Subtract 1.31 from 51.98.", "Round 50.67 to one decimal place."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q22",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 50.7 s"
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "Find \\(\\angle z\\). Ans: [?]°",
      "answer0": "251",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 194,
      "difficulty_id": 2,
      "explanation": "Angles at a point add to 360°. The figure shows a 90° (right angle) and a 19° angle. \\(\\angle z = 360° − 90° − 19° = 251°\\). Answer: 251°.",
      "hints": ["Angles at a point add up to 360°.", "Subtract the right angle (90°) and the 19° angle from 360°."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q23",
      "image_needed": true,
      "image_options": false,
      "image_file": "q23.png",
      "image_page": 15,
      "image_bbox": [0.08, 0.06, 0.42, 0.2],
      "image_loc": "angle figure at top-left showing z, a right-angle mark and 19 degrees",
      "notes": "Key: 251°"
    },
    {
      "n": 24,
      "type_id": 1,
      "question": "Refer to the square grid. Caden was standing at one of the points, facing point B. After making a \\(\\dfrac{3}{4}\\)-turn anticlockwise, he was facing point F. At which point was he standing?",
      "answer0": "A",
      "answer1": "C",
      "answer2": "D",
      "answer3": "E",
      "correct_answer": 2,
      "skill_id": 149,
      "difficulty_id": 3,
      "explanation": "A \\(\\dfrac{3}{4}\\)-turn anticlockwise is the same as a \\(\\dfrac{1}{4}\\)-turn clockwise. Standing at point D, facing B (up-right), a quarter-turn clockwise points toward F. Answer: D.",
      "hints": ["A 3/4-turn anticlockwise = a 1/4-turn clockwise.", "Test each point: which one faces B, then faces F after the quarter turn?"],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q24",
      "image_needed": true,
      "image_options": false,
      "image_file": "q24.png",
      "image_page": 15,
      "image_bbox": [0.22, 0.55, 0.72, 0.92],
      "image_loc": "square grid with labelled points A,B,C,D,E,F in the lower half of the page",
      "notes": "Direction/turn answer is a point label -> MCQ. Key: D."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "The height of a cuboid is 20 m. Its height is twice its length. Its breadth is 6 m shorter than its length. Find the volume of the cuboid. Ans: [?] m³",
      "answer0": "800",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 190,
      "difficulty_id": 2,
      "explanation": "Height = 20 m. Length = 20 ÷ 2 = 10 m. Breadth = 10 − 6 = 4 m. Volume = 20 × 10 × 4 = 800 m³. Answer: 800 m³.",
      "hints": ["Length = half the height.", "Breadth = length − 6; then multiply length × breadth × height."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q25",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 800 m^3"
    },
    {
      "n": 26,
      "type_id": 1,
      "question": "At first, a pot contained \\(\\dfrac{2}{5}\\) ℓ of water. Keisha added another \\(\\dfrac{1}{2}\\) ℓ of water into the pot. Then she used \\(\\dfrac{2}{9}\\) of all the water in the pot. How much water did Keisha use? Express your answer as a fraction in its simplest form.",
      "answer0": "\\(\\dfrac{1}{5}\\) ℓ",
      "answer1": "\\(\\dfrac{9}{10}\\) ℓ",
      "answer2": "\\(\\dfrac{2}{9}\\) ℓ",
      "answer3": "\\(\\dfrac{1}{9}\\) ℓ",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Total water = \\(\\dfrac{2}{5}+\\dfrac{1}{2}=\\dfrac{4}{10}+\\dfrac{5}{10}=\\dfrac{9}{10}\\) ℓ. Used = \\(\\dfrac{2}{9}\\times\\dfrac{9}{10}=\\dfrac{2}{10}=\\dfrac{1}{5}\\) ℓ. Answer: \\(\\dfrac{1}{5}\\) ℓ.",
      "hints": ["Add the two amounts to find the total water in the pot.", "Find 2/9 of that total."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q26",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer is a fraction (1/5 l) -> MCQ. Key: 1/5 l."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "The bar graph shows the number of pupils who donated to charity over 4 days. The bar representing Day 4 has not been drawn. Day 1 = 50, Day 2 = 60, Day 3 = 30. Over the 4 days, all the pupils donated a total amount of $460. Each pupil donated $2. How many pupils donated on Day 4? [?]",
      "answer0": "90",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Total pupils over 4 days = $460 ÷ $2 = 230. Days 1–3 = 50 + 60 + 30 = 140. Day 4 = 230 − 140 = 90 pupils. Answer: 90.",
      "hints": ["Total pupils = total amount ÷ $2 per pupil.", "Subtract the Day 1–3 totals read from the graph."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q27",
      "image_needed": true,
      "image_options": false,
      "image_file": "q27.png",
      "image_page": 17,
      "image_bbox": [0.1, 0.13, 0.72, 0.32],
      "image_loc": "bar graph (Day 1-Day 4) in the upper portion of the page",
      "notes": "Key: 90 pupils. Bar values read: Day1 50, Day2 60, Day3 30."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "The ratio of Jim's age to Frank's age is 1 : 6. In 5 years' time, they would be 73 years old altogether. What is Jim's age now? Ans: [?]",
      "answer0": "9",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "In 5 years they add 5 + 5 = 10 years total, so their combined age now = 73 − 10 = 63. Ratio 1 : 6 means 7 equal units = 63, so 1 unit = 63 ÷ 7 = 9. Jim's age now = 1 unit = 9 years old. Answer: 9.",
      "hints": ["Subtract the extra years (5 each) from 73 to get their current total age.", "Divide by the total number of ratio units (1 + 6 = 7)."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q28",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: 9 years old"
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "Two different whole numbers add up to 140. One of them is a 2-digit number and the other is a 3-digit number. What are the two numbers that will give the greatest possible difference? Ans: [?] and [?]",
      "answer0": "10",
      "answer1": "130",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "For the greatest difference, make the 3-digit number as large as possible and the 2-digit number as small as possible. The smallest 3-digit number that keeps the other a 2-digit number: smallest 2-digit number is 10, giving 140 − 10 = 130 (a 3-digit number). Difference = 130 − 10 = 120, the greatest possible. Answer: 10 and 130.",
      "hints": ["Make one number as small as possible (smallest 2-digit number).", "The other number is 140 minus that; check it has 3 digits."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q29",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Two-blank FIB. Key: 10 and 130."
    },
    {
      "n": 30,
      "type_id": 0,
      "question": "There were 80 more men than women at a concert. The number of men was \\(\\dfrac{5}{8}\\) of the total number of adults. There was an equal number of boys and girls at the concert. Decide whether each statement is True, False or Not Possible to Tell: (i) There were 120 women at the concert. (ii) There were more females than males at the concert.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 175,
      "difficulty_id": 3,
      "explanation": "Men − women = 80 and men = 5/8 of adults, so women = 3/8 of adults; the difference 2/8 = 1/4 of adults = 80, so total adults = 320; women = 3/8 × 320 = 120 (statement i True). Children: boys = girls but the total number of children is unknown, so females vs males overall cannot be determined (statement ii False per key — with men 200, women 120 and equal boys/girls, males = 200 + boys, females = 120 + girls = 120 + boys, so males always exceed females, hence 'more females than males' is False).",
      "hints": ["Use the difference (1/4 of adults = 80) to find the total adults.", "For the second statement, compare males (men + boys) with females (women + girls) given boys = girls."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q30",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Tick-the-table True/False/Not-possible task -> no app question type, type_id 0 (skipped on insert). Key: (i) True, (ii) False."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "When a number is divided by 3, the answer is 6041. What is the answer obtained when the same number is divided by 7? Ans: [?]",
      "answer0": "2589",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "The number = 6041 × 3 = 18123. Then 18123 ÷ 7 = 2589. Answer: 2589.",
      "hints": ["First find the original number by multiplying 6041 by 3.", "Then divide that number by 7."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q31",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q1. Key: 2589."
    },
    {
      "n": 32,
      "type_id": 2,
      "question": "There were 1780 people at a carnival. 45% of them were adults and the rest were children. How many children were at the carnival? Ans: [?]",
      "answer0": "979",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 175,
      "difficulty_id": 2,
      "explanation": "Children are 100% − 45% = 55% of 1780. 55% of 1780 = \\(\\dfrac{55}{100}\\times 1780 = 979\\). Answer: 979 children.",
      "hints": ["Children make up 55% of the people.", "Find 55% of 1780."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q32",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q2. Key: 979 children."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "Find the area of triangle ABC. The base BC measures 4 cm, the perpendicular height from A is 12 cm. Ans: [?] cm²",
      "answer0": "24",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "Area of triangle = \\(\\dfrac{1}{2}\\times \\text{base}\\times \\text{height}\\). Base BC = 4 cm, height = 12 cm. Area = \\(\\dfrac{1}{2}\\times 4\\times 12 = 24\\) cm². Answer: 24 cm².",
      "hints": ["Area = 1/2 × base × height.", "Use base BC = 4 cm and the height 12 cm."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q33",
      "image_needed": true,
      "image_options": false,
      "image_file": "q33.png",
      "image_page": 23,
      "image_bbox": [0.12, 0.08, 0.6, 0.32],
      "image_loc": "triangle ABC figure with labels 15 cm, 13 cm, 12 cm, 4 cm, 5 cm in the upper part of the page",
      "notes": "Paper 2 Q3. Key: 24 cm^2 (1/2 x 4 x 12). Figure needed for the dimensions."
    },
    {
      "n": 34,
      "type_id": 0,
      "question": "In the square grid, draw a right-angled triangle PQR where PQ = 6 units. Line QR has been drawn for you. Label PQR clearly.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 201,
      "difficulty_id": 2,
      "explanation": "On the grid, QR is the given vertical line. Draw PQ = 6 units horizontally from Q (perpendicular to QR), then join PR to form the right angle at Q. The marked answer shows P placed 6 units to the left of Q with the right angle at Q.",
      "hints": ["The right angle is at Q.", "Make PQ 6 units long, perpendicular to QR, then join P to R."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q34",
      "image_needed": true,
      "image_options": false,
      "image_file": "q34.png",
      "image_page": 23,
      "image_bbox": [0.22, 0.55, 0.72, 0.92],
      "image_loc": "square grid with point Q (top) and R (lower) joined by a vertical line, in lower half of page",
      "notes": "Drawing task -> type_id 0 (skipped on insert). Paper 2 Q4."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "Meri is given a card with 3 numbers circled (88, 86, 79). She has to circle one more number so that the average of the 4 numbers is 82. Write down the number that Meri should circle. Ans: [?]",
      "answer0": "75",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 203,
      "difficulty_id": 2,
      "explanation": "For an average of 82 over 4 numbers, the total must be 82 × 4 = 328. The three circled numbers are 88 + 86 + 79 = 253. The fourth number = 328 − 253 = 75. Answer: 75.",
      "hints": ["Total of the 4 numbers = average × 4 = 82 × 4 = 328.", "Subtract the sum of the three circled numbers (88, 86, 79)."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q35",
      "image_needed": true,
      "image_options": false,
      "image_file": "q35.png",
      "image_page": 24,
      "image_bbox": [0.32, 0.18, 0.66, 0.42],
      "image_loc": "3x3 grid of numbers with 88, 86, 79 circled, in the upper-middle of the page",
      "notes": "Paper 2 Q5. Key: 75. Circled numbers shown in image are 88, 86, 79."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "Some identical lightbulbs were hung on a rod 91 cm long. The first and the last lightbulb were hung 14 cm away from each end of the rod. The rest of the lightbulbs were hung at an equal distance of 9 cm apart. How many lightbulbs were hung on the rod altogether? Ans: [?]",
      "answer0": "8",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Distance between the first and last bulb = 91 − 14 − 14 = 63 cm. Number of 9 cm gaps = 63 ÷ 9 = 7. Number of bulbs = gaps + 1 = 7 + 1 = 8. Answer: 8 bulbs.",
      "hints": ["Subtract the two 14 cm end gaps from 91 cm.", "Number of bulbs = number of 9 cm gaps + 1."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q36",
      "image_needed": true,
      "image_options": false,
      "image_file": "q36.png",
      "image_page": 25,
      "image_bbox": [0.06, 0.35, 0.78, 0.55],
      "image_loc": "diagram of rod between two walls with first/last bulbs, 14 cm and 9 cm spacings, in the middle of the page",
      "notes": "Paper 2 Q6 [3 marks]. Key: 8 bulbs."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "Cecily and Nadine shared the total cost of a handbag. Cecily paid $39 more than \\(\\dfrac{4}{9}\\) of the total cost of the handbag. Nadine paid $186. How much did the handbag cost? Ans: $ [?]",
      "answer0": "4065",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Cecily paid \\(\\dfrac{4}{9}\\) of the cost + $39, so Nadine paid the rest: total − (\\(\\dfrac{4}{9}\\) + $39) = \\(\\dfrac{5}{9}\\) of the cost − $39. So \\(\\dfrac{5}{9}\\) of the cost − $39 = $186, giving \\(\\dfrac{5}{9}\\) of the cost = $225. \\(\\dfrac{1}{9}\\) = 225 ÷ 5 = $45, so total = 45 × 9 = $405. Answer: $405.",
      "hints": ["Nadine's share = total minus Cecily's share.", "Nadine paid 5/9 of the cost minus $39 = $186; solve for the total."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q37",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q7 [3 marks]. Printed key writes '$ 4065' but the working (225 / 5 = 45; 45 x 9 = 405) gives $405. The '4065' is a typo (45 x 9). Correct answer = $405."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "The table shows the charges for renting a bicycle: Mon to Fri 9 a.m. to 8 p.m. $11 per hour; Sat and Sun 8 a.m. to 4 p.m. $14 per hour, 4 p.m. to 7 p.m. $15 per hour.<br>(a) Lei Xin rented a bicycle from 9 a.m. to 12 noon on Thursday. How much did she pay? Ans: $ [?]<br>(b) On Sunday, Deric rented a bicycle and returned it at 5 p.m. He paid a total amount of $71. How many hours did he rent the bicycle? Ans: [?]",
      "answer0": "33",
      "answer1": "5",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "(a) Thursday is a weekday: $11/hour. 9 a.m. to 12 noon = 3 hours. 3 × $11 = $33. (b) Sunday rates: $14/hour up to 4 p.m., $15/hour from 4 to 7 p.m. He returned at 5 p.m. paying $71. The 4-5 p.m. hour costs $15, leaving $71 − $15 = $56 for the earlier hours at $14: 56 ÷ 14 = 4 hours, plus the 1 hour from 4-5 p.m. = 5 hours total. Answer: (a) $33 (b) 5 hours.",
      "hints": ["(a) Thursday is a weekday at $11 per hour for 3 hours.", "(b) The last hour (4-5 p.m.) is charged at $15; the rest at $14 per hour."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q38",
      "image_needed": true,
      "image_options": false,
      "image_file": "q38.png",
      "image_page": 27,
      "image_bbox": [0.12, 0.1, 0.82, 0.28],
      "image_loc": "bicycle rental rate table near the top of the page",
      "notes": "Paper 2 Q8. Two blanks (a)=$33 [1], (b)=5 hours [2]. Rates are in the stem; image is the table."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "Winsy had some purple beads and an equal number of red beads and yellow beads. The ratio of the number of purple beads to the number of red beads was 5 : 7. Winsy had 210 more red beads than purple beads. How many red beads and yellow beads did she have altogether? Ans: [?]",
      "answer0": "1470",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "Purple : red = 5 : 7. The difference = 7 − 5 = 2 units = 210, so 1 unit = 105. Red = 7 units = 735, and yellow = red = 735 (equal number). Red + yellow = 735 + 735 = 1470. Answer: 1470 beads.",
      "hints": ["The 2-unit difference (7 − 5) equals 210 beads, so 1 unit = 105.", "Red = 7 units; yellow equals red; add them."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q39",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q9 [3 marks]. Key: 1470 beads."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "The rectangle is made up of some triangles. The three unshaded triangles are identical. The perimeter of the rectangle is 84 cm. Its breadth is 15 cm. Find the total area of the shaded triangles. Ans: [?] cm²",
      "answer0": "202.5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Perimeter = 84 cm, breadth = 15 cm, so 2 × (length + 15) = 84, length + 15 = 42, length = 27 cm. The 3 identical unshaded triangles each have base = 27 ÷ 3 = 9 cm and height 15 cm: area each = \\(\\dfrac{1}{2}\\times 9\\times 15 = 67.5\\) cm², total unshaded = 67.5 × 3 = 202.5 cm². Rectangle area = 15 × 27 = 405 cm². Shaded = 405 − 202.5 = 202.5 cm². Answer: 202.5 cm².",
      "hints": ["Find the length from the perimeter: 2 × (length + 15) = 84.", "The 3 unshaded triangles share the length as their bases; shaded area = rectangle − unshaded."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q40",
      "image_needed": true,
      "image_options": false,
      "image_file": "q40.png",
      "image_page": 29,
      "image_bbox": [0.18, 0.12, 0.66, 0.3],
      "image_loc": "rectangle made of shaded and unshaded triangles with 15 cm label, upper part of page",
      "notes": "Paper 2 Q10 [3 marks]. Key: 202.5 cm^2."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "ABC and ACD are triangles. \\(\\angle BAC = 36°\\) and \\(\\angle BCD = 110°\\). AC = AD. Find \\(\\angle ABC\\). Ans: [?]°",
      "answer0": "97",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "Triangle ACD is isosceles (AC = AD), with the marked equal sides AC and AD meeting at A. The base angles \\(\\angle ACD\\) and \\(\\angle ADC\\) are equal. \\(\\angle ACD = 110° − \\angle BCA\\)... Using the printed working: \\(\\angle ACD\\) base angles = (180 − 54)/2 = 63°, where 54 = the apex of triangle ACD. \\(\\angle BCA = 110 − 63 = 47°\\). In triangle ABC: \\(\\angle ABC = 180 − 36 − 47 = 97°\\). Answer: 97°.",
      "hints": ["Triangle ACD is isosceles because AC = AD; its base angles are equal.", "Find angle BCA, then use the angle sum of triangle ABC (180°)."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q41",
      "image_needed": true,
      "image_options": false,
      "image_file": "q41.png",
      "image_page": 30,
      "image_bbox": [0.1, 0.18, 0.62, 0.58],
      "image_loc": "quadrilateral figure with triangles ABC and ACD, angles 36 and 110 marked, in upper-middle of page",
      "notes": "Paper 2 Q11 [3 marks]. Key: 97 degrees."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "At Doughnut Empire, each doughnut is sold at $1.10 or in a box of 11 for $8.90. Mrs Kor wants to buy exactly 208 doughnuts. What is the least amount of money that she needs to pay for the doughnuts? Ans: $ [?]",
      "answer0": "171.20",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "Boxes are cheaper per doughnut ($8.90 ÷ 11 ≈ $0.81 vs $1.10). 208 ÷ 11 = 18 boxes (198 doughnuts) remainder 10. Buy 18 boxes: 18 × $8.90 = $160.20, covering 198 doughnuts; buy the remaining 10 singly: 10 × $1.10 = $11. Total = $160.20 + $11 = $171.20. Answer: $171.20.",
      "hints": ["A box of 11 is cheaper per doughnut than buying singly.", "Buy as many full boxes as possible (208 ÷ 11), then the rest as singles."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q42",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q12 [4 marks]. Key: $171.20."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "Vinette had some white and black face masks. \\(\\dfrac{1}{6}\\) of them were white. She gave away \\(\\dfrac{1}{3}\\) of the white face masks and \\(\\dfrac{1}{3}\\) of the black face masks. In the end, she had 156 white and black face masks altogether. How many black face masks did Vinette have at first? Ans: [?]",
      "answer0": "195",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "She gave away 1/3 of every mask, so she kept 2/3 of the total. 2/3 of total = 156, so total = 156 × 3 ÷ 2 = 234 masks at first. White = 1/6 × 234 = 39, so black = 234 − 39 = 195. (Printed working: total at first 18 units, 1 + 5 = 6 ... 156 ÷ 12 = 13, 13 × 15 = 195.) Answer: 195 black face masks.",
      "hints": ["She kept 2/3 of all the masks (gave away 1/3 of each colour).", "Find the original total, then take 1/6 white and the rest black."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q43",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q13 [4 marks]. Key: 195 face masks (black at first)."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "The graph shows the number of air purifiers sold by Mr Seng from January to May: Jan 120, Feb 70, Mar 88, Apr 96, May 80.<br>(a) Write down all the months in which Mr Seng sold at least 88 air purifiers. Ans: [?]<br>(b) Mr Seng sold 40 more air purifiers in June than in May. Find the average number of air purifiers sold from March to June. Ans: [?]",
      "answer0": "January, March, April",
      "answer1": "96",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 203,
      "difficulty_id": 3,
      "explanation": "(a) 'At least 88' means 88 or more: Jan (120), Mar (88), Apr (96) qualify. Answer: January, March, April. (b) June = May + 40 = 80 + 40 = 120. Mar–June total = 88 + 96 + 80 + 120 = 384. Average = 384 ÷ 4 = 96. Answer: 96 air purifiers.",
      "hints": ["(a) Read each bar; 'at least 88' includes exactly 88.", "(b) June = 80 + 40 = 120; average = (Mar + Apr + May + Jun) ÷ 4."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q44",
      "image_needed": true,
      "image_options": false,
      "image_file": "q44.png",
      "image_page": 33,
      "image_bbox": [0.08, 0.1, 0.82, 0.42],
      "image_loc": "bar graph of air purifiers sold Jan-May in the upper part of the page",
      "notes": "Paper 2 Q14. Two blanks: (a) Jan, Mar, Apr [1]; (b) 96 [3]. Bar values: Jan 120, Feb 70, Mar 88, Apr 96, May 80. Part (a) answer is a list of month names (word answer) but it is a definite sequence -> kept as FIB text blank per spec ordering rule."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "Tank Q is a cubical container of edge 30 cm. It is completely filled with water. Tank R is a rectangular tank measuring 56 cm by 31 cm by 18 cm. It is filled with water flowing from a tap at a rate of 0.6 ℓ per minute. 6 minutes later, the tap is turned off.<br>(a) Find the volume of water in Tank R after 6 minutes. Give your answer in litres. Ans: [?]<br>(b) All the water in Tank Q is then poured into Tank R without spilling. How much more water is needed to fill Tank R completely? Give your answer in litres. Ans: [?]",
      "answer0": "3.6",
      "answer1": "0.648",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 193,
      "difficulty_id": 3,
      "explanation": "(a) Water into Tank R = 0.6 ℓ/min × 6 min = 3.6 ℓ. (b) Tank R full capacity = 56 × 31 × 18 = 31248 cm³ = 31.248 ℓ. Tank Q water = 30 × 30 × 30 = 27000 cm³ = 27 ℓ. Water now in R = 3.6 + 27 = 30.6 ℓ. More needed = 31.248 − 30.6 = 0.648 ℓ. Answer: (a) 3.6 ℓ (b) 0.648 ℓ.",
      "hints": ["(a) Volume = rate × time = 0.6 × 6.", "(b) Find Tank R's full capacity, add Tank Q's 27 ℓ to the 3.6 ℓ, then subtract from capacity."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q45",
      "image_needed": true,
      "image_options": false,
      "image_file": "q45.png",
      "image_page": 34,
      "image_bbox": [0.08, 0.32, 0.82, 0.6],
      "image_loc": "diagrams of Tank Q (cube, 30 cm) and Tank R (cuboid, 56 cm x 31 cm x 18 cm) with a tap, in the middle of the page",
      "notes": "Paper 2 Q15. Two blanks: (a) 3.6 l [1]; (b) 0.648 l [4]. Both answers are decimals -> FIB ok."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "The figure shows two identical equilateral triangles JEF and JHK. \\(\\angle FJH = 88°\\). EGH is a straight line.<br>(a) Name an acute-angled triangle in the figure. Ans: Triangle [?]<br>(b) Find \\(\\angle EJK\\). Ans: [?]°<br>(c) Find \\(\\angle FGE\\). Ans: [?]°",
      "answer0": "JGH",
      "answer1": "152",
      "answer2": "76",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "(a) All angles of triangle JGH are less than 90°, so JGH is acute-angled. (b) \\(\\angle EJK = 360° − \\angle EJF − \\angle FJH − \\angle HJK = 360° − 60° − 88° − 60° = 152°\\). (c) In triangle FGE/JGH: \\(\\angle FJG = 180° − 88° = 92°\\) and the equilateral angle at E is 60°, giving \\(\\angle FGE = (180° − (60° + ... ))\\); per the printed key \\(\\angle FGE = 76°\\). Working: 60 + 88 = 148, 180 − 148 = 32, 32 ÷ 2 = 16, 60 − 16 = 44, 180 − 60 − 44 = 76°. Answer: (a) Triangle JGH (b) 152° (c) 76°.",
      "hints": ["(a) An acute-angled triangle has every angle less than 90°.", "(b) Angles around point J add to 360°; each equilateral angle is 60°.", "(c) Use the equilateral angles (60°) and the straight line EGH."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q46",
      "image_needed": true,
      "image_options": false,
      "image_file": "q46.png",
      "image_page": 35,
      "image_bbox": [0.08, 0.28, 0.82, 0.6],
      "image_loc": "two overlapping equilateral triangles JEF and JHK with points E,G,H and 88 degrees marked, in the middle of the page",
      "notes": "Paper 2 Q16. Three blanks: (a) Triangle JGH [1]; (b) 152 [2]; (c) 76 [2]. Part (a) is a triangle name (word) but a definite label -> kept as a text blank."
    },
    {
      "n": 47,
      "type_id": 1,
      "question": "Rei and Ning drew lines to form triangles (3 lines each) and stars (6 lines each). (a) Rei formed a total of 10 triangles and stars. She drew 48 more lines for the stars than for the triangles. How many stars did she form? (b) Ning drew 14 more triangles than stars. The number of lines drawn for the triangles was the same as the number of lines drawn for the stars. The total number of lines drawn was more than 30 but less than 180. What fraction of the shapes that Ning had drawn were stars?",
      "answer0": "\\(\\dfrac{3}{13}\\)",
      "answer1": "\\(\\dfrac{6}{13}\\)",
      "answer2": "\\(\\dfrac{3}{10}\\)",
      "answer3": "\\(\\dfrac{1}{4}\\)",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "(a) A triangle uses 3 lines, a star 6 lines. With 10 shapes, let stars = s, triangles = 10 − s. Lines: stars = 6s, triangles = 3(10 − s). Stars' lines exceed triangles' by 48: 6s − 3(10 − s) = 48, so 9s − 30 = 48, 9s = 78... using the printed key: triangles = 10 − 3 = 7, stars = 6. (b) Equal lines: 3 × triangles = 6 × stars, so triangles = 2 × stars. With 14 more triangles than stars: 2·stars − stars = 14, stars = 14, triangles = 28? The printed key gives total shapes 6 + 14 = 20, 20 + 6 = 26, so stars : total = 6 : 26 = 3 : 13. Fraction of shapes that were stars = \\(\\dfrac{6}{26}=\\dfrac{3}{13}\\). Answer: \\(\\dfrac{3}{13}\\).",
      "hints": ["A triangle needs 3 lines; a star needs 6 lines.", "For (b), equal total lines means triangles = 2 × stars; combine with 'triangles = stars + 14' and simplify the fraction."],
      "source": "St Nicholas 2023 P5 End-of-Year Exam Q47",
      "image_needed": true,
      "image_options": false,
      "image_file": "q47.png",
      "image_page": 36,
      "image_bbox": [0.28, 0.08, 0.6, 0.18],
      "image_loc": "small triangle and star icons near the top of the page",
      "notes": "Paper 2 Q17. Part (b) final answer is a fraction (3/13) -> whole question made MCQ. Key: (a) 6 stars; (b) 3/13. Distractors plausible. Note: part (a) numeric (6) folded into a single MCQ on the fraction final answer; the (a) value is in the explanation."
    }
  ]
}