{
  "paper": {
    "school": "ACS Primary",
    "year": 2022,
    "level": "P4",
    "label": "Semestral Assessment 1",
    "source_prefix": "ACS Primary 2022 P4 Semestral Assessment 1",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "Which one of the following numbers have the greatest value?",
      "answer0": "83 714", "answer1": "87 341", "answer2": "87 431", "answer3": "83 741",
      "correct_answer": 2,
      "skill_id": 107,
      "difficulty_id": 1,
      "explanation": "Compare digit by digit from the left. 87 431 and 87 341 both start with 87; 87 431 has 4 hundreds vs 3 hundreds, so 87 431 is the greatest.",
      "hints": ["Line up all four numbers by place value.", "Compare the ten-thousands digit first, then thousands, then hundreds."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key=option (3)=87 431."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Which one of the following number when rounded off to the nearest hundred is 6000?",
      "answer0": "6138", "answer1": "6087", "answer2": "5986", "answer3": "5092",
      "correct_answer": 2,
      "skill_id": 109,
      "difficulty_id": 2,
      "explanation": "Round each to the nearest hundred: 6138->6100, 6087->6100, 5986->6000, 5092->5100. Only 5986 rounds to 6000.",
      "hints": ["Look at the tens digit to decide rounding the hundreds.", "5986: the nearest hundreds are 5900 and 6000; 86 is past 50 so it rounds up to 6000."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key=option (3)=5986."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Which one of the following is not a common factor of 18 and 36?",
      "answer0": "6", "answer1": "18", "answer2": "3", "answer3": "36",
      "correct_answer": 3,
      "skill_id": 113,
      "difficulty_id": 2,
      "explanation": "Common factors of 18 and 36 are 1, 2, 3, 6, 9, 18. 36 is a factor of 36 but not of 18, so 36 is not a common factor.",
      "hints": ["A common factor must divide both 18 and 36 exactly.", "Does 36 divide 18 without remainder? No."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key=option (4)=36."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "2 3/7 = [?]/7\nWhat is the missing number in the box?",
      "answer0": "17", "answer1": "14", "answer2": "6", "answer3": "5",
      "correct_answer": 0,
      "skill_id": 119,
      "difficulty_id": 1,
      "explanation": "Convert the mixed number to an improper fraction: 2 3/7 = (2x7 + 3)/7 = 17/7. The missing numerator is 17.",
      "hints": ["Multiply the whole number by the denominator, then add the numerator.", "2 x 7 + 3 = 17."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key=option (1)=17. Box shown over the 7 in stem."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "A sticker printer can print 7680 stickers in 6 hours. How many stickers can the printer print in 4 hours?",
      "answer0": "1280", "answer1": "1920", "answer2": "2560", "answer3": "5120",
      "correct_answer": 3,
      "skill_id": 118,
      "difficulty_id": 2,
      "explanation": "Stickers per hour = 7680 / 6 = 1280. In 4 hours = 1280 x 4 = 5120.",
      "hints": ["First find how many stickers are printed in 1 hour.", "7680 / 6 = 1280, then multiply by 4."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key=option (4)=5120."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "5/12 + 1/4 =",
      "answer0": "1/2", "answer1": "1/4", "answer2": "3/8", "answer3": "8/12",
      "correct_answer": 3,
      "skill_id": 121,
      "difficulty_id": 2,
      "explanation": "Make the denominators the same: 1/4 = 3/12. Then 5/12 + 3/12 = 8/12.",
      "hints": ["Convert 1/4 to twelfths.", "1/4 = 3/12, so 5/12 + 3/12 = 8/12."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key=option (4)=8/12 (option left unsimplified to match the printed choice)."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "Which of the following is a multiple of both 4 and 6?",
      "answer0": "46", "answer1": "36", "answer2": "28", "answer3": "16",
      "correct_answer": 1,
      "skill_id": 115,
      "difficulty_id": 2,
      "explanation": "A multiple of both 4 and 6 must be a multiple of 12. 36 = 12 x 3 is divisible by both 4 and 6. 46, 28, 16 are not.",
      "hints": ["A common multiple of 4 and 6 is a multiple of 12.", "Which option is in the 12 times table? 36 = 12 x 3."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key=option (2)=36."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "Which of the following mixed numbers is represented by the letter N in the number line shown?",
      "answer0": "4 4/5", "answer1": "4 3/5", "answer2": "4 2/5", "answer3": "4 1/2",
      "correct_answer": 1,
      "skill_id": 119,
      "difficulty_id": 2,
      "explanation": "The interval from 4 to 5 is divided into 5 equal parts (fifths). N is on the 3rd mark after 4, so N = 4 3/5.",
      "hints": ["Count how many equal parts lie between 4 and 5.", "N sits on the 3rd small mark, so it is 4 and 3 fifths."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 4,
      "image_bbox": [0.18, 0.36, 0.78, 0.45],
      "image_loc": "number line from 4 to 5 with arrow marked N below it, upper-middle of page",
      "notes": "Key=option (2)=4 3/5."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "How many one-fifths are there in 6 wholes?",
      "answer0": "30", "answer1": "11", "answer2": "6", "answer3": "5",
      "correct_answer": 0,
      "skill_id": 119,
      "difficulty_id": 1,
      "explanation": "Each whole contains 5 one-fifths. 6 wholes = 6 x 5 = 30 one-fifths.",
      "hints": ["1 whole = 5 fifths.", "6 x 5 = 30."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key=option (1)=30."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "The area of the square carpet is 36 m². What is the perimeter of the square carpet?",
      "answer0": "6 m", "answer1": "9 m", "answer2": "24 m", "answer3": "81 m",
      "correct_answer": 2,
      "skill_id": 137,
      "difficulty_id": 2,
      "explanation": "Side of the square = square root of 36 = 6 m. Perimeter = 4 x 6 = 24 m.",
      "hints": ["Area of a square = side x side, so find the side first.", "6 x 6 = 36, so side = 6 m; perimeter = 4 x 6."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 5,
      "image_bbox": [0.37, 0.17, 0.52, 0.27],
      "image_loc": "small square labelled '36 m²', upper-middle of page beside the question",
      "notes": "Key=option (3)=24 m."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "The perimeter of a rectangle is 108 cm. The length of the rectangle is 12 cm longer than its breadth. What is the breadth of the rectangle?",
      "answer0": "21 cm", "answer1": "24 cm", "answer2": "84 cm", "answer3": "96 cm",
      "correct_answer": 0,
      "skill_id": 136,
      "difficulty_id": 2,
      "explanation": "Length + breadth = 108 / 2 = 54 cm. Since length = breadth + 12, then 2 x breadth + 12 = 54, so 2 x breadth = 42, breadth = 21 cm.",
      "hints": ["Half the perimeter equals length + breadth.", "54 - 12 = 42, then divide by 2."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key=option (1)=21 cm."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "The figure is made up of 2 rectangles, X and Y, and a square Z. Find the area of square Z.",
      "answer0": "18 cm²", "answer1": "27 cm²", "answer2": "36 cm²", "answer3": "81 cm²",
      "correct_answer": 3,
      "skill_id": 138,
      "difficulty_id": 2,
      "explanation": "The left side is 12 cm tall. Rectangle Y is 3 cm and rectangle X is 3 cm, so the height of square Z = 12 - 3 - 3 = 6... but Z spans from the top down to the top of X. Z's side = 12 - 3 = 9 cm. Area of Z = 9 x 9 = 81 cm².",
      "hints": ["The total left height is 12 cm; X takes the bottom 3 cm.", "Square Z's side = 12 - 3 = 9 cm, then 9 x 9."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q12.png",
      "image_page": 6,
      "image_bbox": [0.22, 0.16, 0.52, 0.30],
      "image_loc": "composite figure of square Z on top-left, rectangles X (bottom) and Y (right), labelled 12 cm, 3 cm, 3 cm",
      "notes": "Key=option (4)=81 cm². Z side = 12 - 3 = 9 cm."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "What is the size of ∠WYX in degree?",
      "answer0": "55°", "answer1": "65°", "answer2": "120°", "answer3": "180°",
      "correct_answer": 0,
      "skill_id": 140,
      "difficulty_id": 2,
      "explanation": "Read the protractor. Ray YW points to 120° and ray YX points to 65° on the same (inner) scale, so ∠WYX = 120° - 65° = 55°.",
      "hints": ["Read the protractor reading for both arms YW and YX.", "Subtract the two readings: 120 - 65 = 55."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q13.png",
      "image_page": 6,
      "image_bbox": [0.18, 0.48, 0.80, 0.68],
      "image_loc": "protractor with rays to W and X from vertex Y on baseline V-Z, middle of page",
      "notes": "Key=option (1)=55°."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "The perimeter of the rectangle EFGH is 56 cm. The breadth EH is 9 cm, find the length of EF.",
      "answer0": "18 cm", "answer1": "19 cm", "answer2": "38 cm", "answer3": "47 cm",
      "correct_answer": 1,
      "skill_id": 136,
      "difficulty_id": 2,
      "explanation": "Length + breadth = 56 / 2 = 28 cm. EF = 28 - 9 = 19 cm.",
      "hints": ["Half the perimeter equals length + breadth.", "28 - 9 = 19."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q14.png",
      "image_page": 7,
      "image_bbox": [0.27, 0.17, 0.62, 0.30],
      "image_loc": "rectangle EFGH with breadth 9 cm marked on left side and '?' on top edge EF",
      "notes": "Key=option (2)=19 cm."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "In the figure, which angle/s is/are greater than a right angle?",
      "answer0": "∠b only", "answer1": "∠a and ∠d", "answer2": "∠c and ∠d", "answer3": "∠a, ∠c and ∠d",
      "correct_answer": 2,
      "skill_id": 99,
      "difficulty_id": 2,
      "explanation": "Compare each marked angle to a right angle (90°). Angles c and d are obtuse (greater than 90°), while a is acute and b is acute. So ∠c and ∠d are greater than a right angle.",
      "hints": ["A right angle is 90° (a square corner).", "Look for the angles that open wider than a square corner: c and d."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q15",
      "image_needed": true,
      "image_options": false,
      "image_file": "q15.png",
      "image_page": 7,
      "image_bbox": [0.34, 0.47, 0.76, 0.62],
      "image_loc": "irregular quadrilateral with angles labelled a, b, c, d at its vertices, middle of page",
      "notes": "Key=option (3)=∠c and ∠d. skill_id 99 (right angles, greater/smaller than a right angle, P3 carry-over)."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Write ninety-seven thousand and two in figures.\n[?]",
      "answer0": "97002", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 106,
      "difficulty_id": 1,
      "explanation": "Ninety-seven thousand = 97 000, and two = 2. Together: 97 002.",
      "hints": ["97 thousand fills the thousands places.", "Add 2 in the ones place: 97 002."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key=97002. Numeric answer, kept as FIB."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "Arrange the following numbers in ascending order.\n2879, 2798, 2897, 2789\n[?], [?], [?], [?]",
      "answer0": "2789", "answer1": "2798", "answer2": "2879", "answer3": "2897",
      "correct_answer": null,
      "skill_id": 107,
      "difficulty_id": 1,
      "explanation": "Ascending = smallest to largest. Compare by place value: 2789 < 2798 < 2879 < 2897.",
      "hints": ["All start with 27, so compare the tens and ones.", "Order: 2789, 2798, 2879, 2897."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key=2789, 2798, 2879, 2897 (ascending)."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "Find the value of 3 - 3/8.\n[?]",
      "answer0": "21/8", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 121,
      "difficulty_id": 1,
      "explanation": "3 = 24/8. Then 24/8 - 3/8 = 21/8 (or 2 5/8).",
      "hints": ["Write 3 as eighths: 3 = 24/8.", "24/8 - 3/8 = 21/8."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key=21/8."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "The number, when divided by 9, has a quotient of 406 and a remainder of 4. What is the number?\n[?]",
      "answer0": "3658", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 117,
      "difficulty_id": 2,
      "explanation": "Number = quotient x divisor + remainder = 406 x 9 + 4 = 3654 + 4 = 3658.",
      "hints": ["Number = quotient x divisor + remainder.", "406 x 9 = 3654, then add 4."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q19",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key working: 406 x 9 = 3654; 3654 + 4 = 3658."
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "Write 17/6 as a mixed number.\n[?]",
      "answer0": "2 5/6", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 119,
      "difficulty_id": 1,
      "explanation": "17 / 6 = 2 remainder 5, so 17/6 = 2 5/6.",
      "hints": ["Divide 17 by 6 to get the whole number part.", "17 = 6 x 2 + 5, so 2 with 5/6 left over."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q20",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key=2 5/6."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "I am a common multiple of 6 and 9. I am greater than 28 but lesser than 40. What number am I?\n[?]",
      "answer0": "36", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 115,
      "difficulty_id": 2,
      "explanation": "Common multiples of 6 and 9 are multiples of 18: 18, 36, 54... The only one between 28 and 40 is 36.",
      "hints": ["Common multiples of 6 and 9 are multiples of 18.", "Which multiple of 18 is between 28 and 40? 36."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key=36."
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "Using a protractor, measure and write down the size of ∠a in the figure.\n[?]°",
      "answer0": "143", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 140,
      "difficulty_id": 2,
      "explanation": "Measuring the marked obtuse angle ∠a with a protractor gives 143°.",
      "hints": ["Place the protractor centre on the vertex of angle a.", "Read along the arm; the angle is obtuse, about 143°."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q22",
      "image_needed": true,
      "image_options": false,
      "image_file": "q22.png",
      "image_page": 12,
      "image_bbox": [0.27, 0.43, 0.82, 0.54],
      "image_loc": "open angle drawn with vertex at lower middle, marked 'a', two rays going up-left and up-right",
      "notes": "Key=143 (degrees). Answer is a measured value; stored as numeric FIB."
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "Arrange the following fractions from the greatest to the smallest.\n[?], [?], [?]",
      "answer0": "7/10", "answer1": "2/5", "answer2": "3/8", "answer3": null,
      "correct_answer": null,
      "skill_id": 121,
      "difficulty_id": 2,
      "explanation": "Convert to a common comparison: 7/10 = 0.70, 2/5 = 0.40, 3/8 = 0.375. Greatest to smallest: 7/10, 2/5, 3/8.",
      "hints": ["Turn each fraction into a decimal to compare.", "0.70 > 0.40 > 0.375."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q23",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key=7/10, 2/5, 3/8 (greatest to smallest). The three fractions themselves are not legible in the scan but the key lists them."
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "James bought 5 pencils and 2 markers for $27. 1 marker cost twice as much as a pencil. How much did a marker cost?\n$[?]",
      "answer0": "6", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 118,
      "difficulty_id": 2,
      "explanation": "1 marker = 2 pencils. So 2 markers = 4 pencils. Total in pencil-units = 5 + 4 = 9 pencils = $27, so 1 pencil = $27 / 9 = $3. A marker = 2 x $3 = $6.",
      "hints": ["Replace each marker with 2 pencils to make everything in pencils.", "9 pencils cost $27, so 1 pencil = $3; a marker = 2 x $3."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q24",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key working: 27 / 9 = 3; 3 x 2 = 6. Answer $6."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "4 + 9/10 is equivalent to [?] tenths.",
      "answer0": "49",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 123,
      "difficulty_id": 2,
      "explanation": "4 = 40 tenths. 40 tenths + 9 tenths = 49 tenths.",
      "hints": ["Each whole has 10 tenths.", "4 wholes = 40 tenths, add the 9 tenths."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q25",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key=49."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "Benjamin bought 397 bags of marbles. Each bag contains 17 marbles. How many marbles does he have altogether?\n[?]",
      "answer0": "6749", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 116,
      "difficulty_id": 2,
      "explanation": "Total marbles = 397 x 17 = 6749.",
      "hints": ["Multiply the number of bags by marbles per bag.", "397 x 17 = 6749."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q26",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key=397 x 17 = 6749."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "The map shows some places around Sue's neighbourhood.\nComplete the table.\nSue is facing MRT Station; if Sue turns 135° clockwise, Sue will be facing [?]. Sue is facing Hawker Centre; if Sue turns [?], Sue will be facing Playground.",
      "answer0": "Hospital", "answer1": "90° clockwise", "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 142,
      "difficulty_id": 3,
      "explanation": "(a) Facing MRT Station (N). A 135° clockwise turn (each 45° = one of the 8 compass directions) moves N -> NE (45) -> E (90) -> SE (135). The place to the SE is Hospital. (b) Facing Hawker Centre (SW); to face Playground (NW) turn 90° clockwise (SW -> W -> NW).",
      "hints": ["Each 45° turn moves to the next of the 8 compass points.", "(a) From North, 135° clockwise lands on South-East. (b) From SW to NW is a 90° clockwise turn."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q27",
      "image_needed": true,
      "image_options": false,
      "image_file": "q27.png",
      "image_page": 14,
      "image_bbox": [0.30, 0.41, 0.78, 0.58],
      "image_loc": "neighbourhood grid map with Playground/MRT/School on top, Police Station/Sue/Sue's home in middle, Hawker Centre/Shopping Mall/Hospital at bottom, and a North arrow to the right",
      "notes": "Key: a) Hospital, b) 90° clockwise. answer1 is the word/direction blank for (b)."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "The figure is made up of unit squares. How many more squares must be shaded so that 3/4 of the figure is shaded?\n[?]",
      "answer0": "17", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 120,
      "difficulty_id": 3,
      "explanation": "The grid is 6 x 6 = 36 unit squares. 3/4 of 36 = 27 squares must be shaded. Currently 10 are shaded (6 x 6 = 36; 36 x 3/4 = 27; 27 - 10 = 17). So 17 more must be shaded.",
      "hints": ["Count the total squares and how many are already shaded.", "3/4 of 36 = 27 needed; subtract those already shaded (10)."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q28",
      "image_needed": true,
      "image_options": false,
      "image_file": "q28.png",
      "image_page": 15,
      "image_bbox": [0.37, 0.21, 0.65, 0.40],
      "image_loc": "6 by 6 grid of unit squares with some squares shaded, middle of page",
      "notes": "Key working: 6 x 6 = 36; 36 x 3/4 = 27; 27 - 10 = 17. Count to verify: 10 shaded currently."
    },
    {
      "n": 29,
      "type_id": 0,
      "question": "On the grid, draw a square using the given line.",
      "answer0": null, "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 143,
      "difficulty_id": 2,
      "explanation": "Use the given diagonal/side line as one side of a square and construct the other three equal sides at right angles on the grid. The key shows a tilted square drawn on the given segment.",
      "hints": [],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q29",
      "image_needed": true,
      "image_options": false,
      "image_file": "q29.png",
      "image_page": 15,
      "image_bbox": [0.27, 0.51, 0.73, 0.76],
      "image_loc": "blank square grid with one short diagonal line drawn on it, lower-middle of page",
      "notes": "Interactive draw-a-square task; no value answer. type_id 0 (skipped on insert). Key shows a tilted square constructed on the given line."
    },
    {
      "n": 30,
      "type_id": 2,
      "question": "Two factors of 27 are 1 and 27. What are the other two factors of 27?\n[?] and [?]",
      "answer0": "3", "answer1": "9", "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 111,
      "difficulty_id": 1,
      "explanation": "Factors of 27 are 1, 3, 9, 27. Besides 1 and 27, the other two are 3 and 9.",
      "hints": ["List all numbers that divide 27 exactly.", "27 = 3 x 9, so 3 and 9 are factors."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q30",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key=3 and 9."
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "Find the area of the figure shown.\n[?]",
      "answer0": "673",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 138,
      "difficulty_id": 3,
      "explanation": "Whole rectangle = 37 x 25 = 925 cm². The notch (rectangle removed) has length 37 - 16 = 21 cm and height 25 - 13 = 12 cm, area 21 x 12 = 252 cm². Figure area = 925 - 252 = 673 cm².",
      "hints": ["Take the big rectangle (37 x 25) and subtract the missing corner.", "Notch = (37-16) x (25-13) = 21 x 12 = 252; 925 - 252 = 673."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q31",
      "image_needed": true,
      "image_options": false,
      "image_file": "q31.png",
      "image_page": 16,
      "image_bbox": [0.23, 0.43, 0.78, 0.66],
      "image_loc": "L-shaped figure ABCDEF labelled 37 cm top, 25 cm left, 13 cm right, 16 cm bottom",
      "notes": "Key working: 37 x 25 = 925; 21 x 12 = 252; 925 - 252 = 673. Answer 673 cm²."
    },
    {
      "n": 32,
      "type_id": 2,
      "question": "The figure is made up of 7 identical squares. Given that GH is 16 cm, find the area of the figure.\n[?]",
      "answer0": "448",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 138,
      "difficulty_id": 3,
      "explanation": "GH spans 2 square sides = 16 cm, so each square's side = 16 / 2 = 8 cm. Area of one square = 8 x 8 = 64 cm². Total = 7 x 64 = 448 cm².",
      "hints": ["GH covers 2 square sides, so 1 side = 16 / 2.", "Each square = 8 x 8 = 64; times 7 squares."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q32",
      "image_needed": true,
      "image_options": false,
      "image_file": "q32.png",
      "image_page": 17,
      "image_bbox": [0.28, 0.19, 0.58, 0.37],
      "image_loc": "staircase arrangement of 7 identical squares with vertical 16 cm (GH) marked on the right edge spanning 2 squares",
      "notes": "Key working: 16 / 2 = 8; 8 x 8 = 64; 64 x 7 = 448. Answer 448 cm²."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "3/8 of Elle's magnets is 24. How many magnets does she have?\n[?]",
      "answer0": "64", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 120,
      "difficulty_id": 2,
      "explanation": "3/8 = 24, so 1/8 = 24 / 3 = 8. The whole (8/8) = 8 x 8 = 64 magnets.",
      "hints": ["First find 1/8 by dividing 24 by 3.", "1/8 = 8, so the whole 8/8 = 8 x 8 = 64."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q33",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key working: 24 / 3 = 8; 8 x 8 = 64."
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "A picture measuring 14 cm by 5 cm is mounted on a cardboard leaving some shaded border around it. Find the area of the shaded border.\n[?]",
      "answer0": "110",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 138,
      "difficulty_id": 3,
      "explanation": "Cardboard area = 20 x 9 = 180 cm². Picture area = 14 x 5 = 70 cm². Border = 180 - 70 = 110 cm².",
      "hints": ["Find the whole cardboard area, then subtract the picture.", "20 x 9 = 180; 14 x 5 = 70; 180 - 70 = 110."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q34",
      "image_needed": true,
      "image_options": false,
      "image_file": "q34.png",
      "image_page": 18,
      "image_bbox": [0.22, 0.19, 0.74, 0.35],
      "image_loc": "outer cardboard rectangle 20 cm by 9 cm with inner picture 14 cm by 5 cm, patterned shaded border between them",
      "notes": "Key working: 20 x 9 = 180; 14 x 5 = 70; 180 - 70 = 110. Answer 110 cm²."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "Find the perimeter of the figure.\n[?]",
      "answer0": "94",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 138,
      "difficulty_id": 3,
      "explanation": "For a rectilinear figure the horizontal sides add to twice the full width and the vertical sides add to twice the full height. Summing all edges: 26 + 4 + 9 + 4 + 9 + 4 + 26 + 12 = 94 cm.",
      "hints": ["Add up the length of every side around the figure.", "Key sum: 26 + 4 + 9 + 4 + 9 + 4 + 26 + 12 = 94."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q35",
      "image_needed": true,
      "image_options": false,
      "image_file": "q35.png",
      "image_page": 19,
      "image_bbox": [0.27, 0.18, 0.74, 0.36],
      "image_loc": "rectilinear figure with a notch on the right; labelled 26 cm top, 26 cm bottom, 12 cm left, 4 cm and 9 cm on the step",
      "notes": "Key: 26 + 4 + 9 + 4 + 9 + 4 + 26 + 12 = 94. Answer 94 cm."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "Mrs Ong has 2776 stamps. She kept 368 stamps for herself and gave away the rest to a group of friends. Each friend received 8 stamps. How many friends did she give the stamps?\n[?]",
      "answer0": "301", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 118,
      "difficulty_id": 2,
      "explanation": "Stamps given away = 2776 - 368 = 2408. Number of friends = 2408 / 8 = 301.",
      "hints": ["First find how many stamps were given away.", "2776 - 368 = 2408; 2408 / 8 = 301."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q36",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key working: 2776 - 368 = 2408; 2408 / 8 = 301."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "Charles walked 3/4 km to reach his home. Steve walked 1/3 km further to reach his home. What was the total distance both boys walked? (Leave your answer as a fraction)\n[?]",
      "answer0": "1 5/6",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 122,
      "difficulty_id": 2,
      "explanation": "Steve walked 3/4 + 1/3 km. Total of both = 3/4 + (3/4 + 1/3) = 3/4 + 3/4 + 1/3. Using the key's method: 3/4 + 3/4 = 1 1/2; 1 1/2 + 1/3 = 1 5/6 km.",
      "hints": ["Steve walked Charles's distance plus 1/3 more.", "Add 3/4 + 3/4 + 1/3 = 1 5/6 km."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q37",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key working: 3/4 + 3/4 = 1 1/2; 1 1/2 + 1/3 = 1 5/6 km."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "During a carnival, John collected $4032 from the sale of chicken burgers and $6874 from sausage burgers. How many more sausage burgers than chicken burgers were sold?\nChicken Burger: $8\nSausage Burger: $7\n[?]",
      "answer0": "478", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 118,
      "difficulty_id": 3,
      "explanation": "Chicken burgers sold = 4032 / 8 = 504. Sausage burgers sold = 6874 / 7 = 982. Difference = 982 - 504 = 478.",
      "hints": ["Divide each total by its burger price to get the count.", "4032/8 = 504; 6874/7 = 982; 982 - 504 = 478."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q38",
      "image_needed": true,
      "image_options": false,
      "image_file": "q38.png",
      "image_page": 21,
      "image_bbox": [0.52, 0.23, 0.82, 0.35],
      "image_loc": "'Carnival' price box listing Chicken Burger $8 and Sausage Burger $7 with small burger and hotdog drawings, right side",
      "notes": "Key working: 4032/8 = 504; 6874/7 = 982; 982 - 504 = 478. Prices are in the figure box."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "Peter and John had the same amount of money at first. After Peter spent $156 and John spent $12, John had 4 times as much money left as Peter. How much did John have at first?\n$[?]",
      "answer0": "204", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 118,
      "difficulty_id": 3,
      "explanation": "Both started equal. The difference between what they spent = 156 - 12 = 144, which equals the difference in money left (3 units, since John has 4 units and Peter 1 unit). So 3 units = 144, 1 unit = 48 (Peter's remainder). John at first = Peter's start = 48 + 156 = $204.",
      "hints": ["Same start means the gap in remainders equals the gap in spending: 156 - 12 = 144.", "John(4 units) - Peter(1 unit) = 3 units = 144; 1 unit = 48; start = 48 + 156 = 204."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q39",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key working: 156 - 12 = 144; 144 / 3 = 48; 48 + 156 = $204."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "Mary had 374 pens and pencils. After she sold 1/4 of the pens and 108 pencils, she had an equal number of pens and pencils left. How many pens did she have at first?\n[?]",
      "answer0": "152", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 118,
      "difficulty_id": 3,
      "explanation": "Using the key's method: 374 - 108 = 266 (total left plus the sold pens accounted as units). 266 / 7 = 38 (one unit, where pens = 4 units and pencils-side gives 3 units after removing 108). Pens at first = 38 x 4 = 152.",
      "hints": ["Model pens as 4 units (she sold 1 unit = 1/4).", "374 - 108 = 266; 266 / 7 = 38; pens = 38 x 4 = 152."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q40",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key working: 374 - 108 = 266; 266 / 7 = 38; 38 x 4 = 152."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "Mrs Tan invited her friends to her party. Her friends either brought 2 or 3 children with them to the party. There were 12 more friends who brought 3 children than those who brought 2 children. The total number of children at the party was 91. How many of Mrs Tan's friends brought 3 children to the party?\n[?]",
      "answer0": "23", "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 118,
      "difficulty_id": 3,
      "explanation": "The 12 extra 3-child friends bring 12 x 3 = 36 children. Remaining children = 91 - 36 = 55, shared by equal numbers of 2-child and 3-child friends (5 children per matched pair). 55 / 5 = 11 friends in each group. Friends who brought 3 children = 11 + 12 = 23.",
      "hints": ["Set aside the 12 extra 3-child friends: 12 x 3 = 36 children.", "91 - 36 = 55; 55 / 5 = 11; then 11 + 12 = 23."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q41",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key working: 12 x 3 = 36; 91 - 36 = 55; 55 / 5 = 11; 11 + 12 = 23."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "Rectangles ABFG and DEGH are identical. The area of each rectangle ABFG and DEGH is 176 cm² and the shaded square CFGH has an area of 64 cm². Find the perimeter of the rectangle DEGH.\n[?]",
      "answer0": "60",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 136,
      "difficulty_id": 3,
      "explanation": "Square CFGH area 64 = 8 x 8, so one side = 8 cm (this is the shorter side / breadth of the rectangle). Rectangle area 176 = breadth x length, so length = 176 / 8 = 22 cm. Perimeter of DEGH = 2 x (22 + 8) = 2 x 30 = 60 cm.",
      "hints": ["The square's side (square root of 64 = 8) is the rectangle's breadth.", "Length = 176 / 8 = 22; perimeter = 2 x (22 + 8) = 60."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q42",
      "image_needed": true,
      "image_options": false,
      "image_file": "q42.png",
      "image_page": 24,
      "image_bbox": [0.33, 0.23, 0.62, 0.41],
      "image_loc": "two identical rectangles ABFG (vertical, top) and DEGH (horizontal) overlapping at shaded square CFGH labelled 64 cm², with vertices A B C D E F G H marked",
      "notes": "Key working: 64 = 8 x 8; 176 / 8 = 22; 22 + 8 = 30; 30 x 2 = 60 cm."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "1/4 of the bottle is filled with orange juice. After Andrew refilled with 800 ml of orange juice, it became 7/12 full. Find the capacity of the bottle in terms of ml.\n[?]",
      "answer0": "2400",
      "answer1": null, "answer2": null, "answer3": null,
      "correct_answer": null,
      "skill_id": 122,
      "difficulty_id": 3,
      "explanation": "Increase in fraction = 7/12 - 1/4 = 7/12 - 3/12 = 4/12 = 1/3 of the bottle. This 1/3 equals 800 ml... using the key's method: 800 / 4 = 200 ml per twelfth; capacity = 200 x 12 = 2400 ml.",
      "hints": ["The 800 ml fills the extra fraction 7/12 - 3/12 = 4/12.", "800 / 4 = 200 ml per 1/12; full bottle = 200 x 12 = 2400 ml."],
      "source": "ACS Primary 2022 P4 Semestral Assessment 1 Q43",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key working: 800 / 4 = 200; 200 x 12 = 2400 ml."
    }
  ]
}