{
  "paper": {
    "school": "Anglo-Chinese School (Junior)",
    "year": 2022,
    "level": "P5",
    "label": "Semestral Assessment 2",
    "source_prefix": "ACS 2022 P5 Semestral Assessment 2",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "Find the value of 28 × 7000.",
      "answer0": "196",
      "answer1": "1960",
      "answer2": "19 600",
      "answer3": "196 000",
      "correct_answer": 3,
      "skill_id": 151,
      "difficulty_id": 1,
      "explanation": "28 × 7000 = 28 × 7 × 1000 = 196 × 1000 = 196 000.",
      "hints": ["Multiply 28 by 7 first.", "Then attach the three zeros from 1000."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "key: option (4)"
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Find the value of 300 + 100 ÷ 5 − 12 × 5.",
      "answer0": "20",
      "answer1": "260",
      "answer2": "340",
      "answer3": "1540",
      "correct_answer": 1,
      "skill_id": 155,
      "difficulty_id": 2,
      "explanation": "Do ÷ and × first: 100 ÷ 5 = 20; 12 × 5 = 60. Then 300 + 20 − 60 = 260.",
      "hints": ["Multiplication and division before addition and subtraction.", "100 ÷ 5 = 20 and 12 × 5 = 60."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "key: option (2)"
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Express \\(3\\dfrac{5}{8}\\) as a decimal.",
      "answer0": "3.58",
      "answer1": "3.85",
      "answer2": "3.125",
      "answer3": "3.625",
      "correct_answer": 3,
      "skill_id": 158,
      "difficulty_id": 1,
      "explanation": "\\(\\dfrac{5}{8} = 5 \\div 8 = 0.625\\), so \\(3\\dfrac{5}{8} = 3.625\\).",
      "hints": ["Convert the fraction part: 5 ÷ 8.", "Add the whole number 3."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "key: option (4)"
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Which digit in 23.479 is in the tenths place?",
      "answer0": "7",
      "answer1": "2",
      "answer2": "9",
      "answer3": "4",
      "correct_answer": 3,
      "skill_id": 123,
      "difficulty_id": 1,
      "explanation": "The first digit after the decimal point is the tenths place. In 23.479 that digit is 4.",
      "hints": ["Tenths is the first place after the decimal point.", "Read the digit right after the point."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "key: option (4)"
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "Part of a scale is shown. What is the most likely value of the reading at A?",
      "answer0": "3.6",
      "answer1": "3.4",
      "answer2": "3.06",
      "answer3": "3.04",
      "correct_answer": 2,
      "skill_id": 124,
      "difficulty_id": 2,
      "explanation": "Each large interval (2.9 to 3.0 etc.) is divided into 10 small parts, so each small mark = 0.01. A points just past 3.0, about 6 marks, giving a reading of 3.06.",
      "hints": ["Each major interval is split into 10 small parts.", "Count how many small marks past 3.0 the arrow A is."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q5.png",
      "image_page": 3,
      "image_bbox": [0.18, 0.12, 0.78, 0.24],
      "image_loc": "number-line scale near top of page, with arrow A below it",
      "notes": "key: option (3) 3.06"
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "Express 8.07 ℓ in litres and millilitres.",
      "answer0": "8 ℓ 7 ml",
      "answer1": "8 ℓ 70 ml",
      "answer2": "80 ℓ 7 ml",
      "answer3": "80 ℓ 70 ml",
      "correct_answer": 1,
      "skill_id": 192,
      "difficulty_id": 2,
      "explanation": "8.07 ℓ = 8 ℓ + 0.07 ℓ. Since 1 ℓ = 1000 ml, 0.07 ℓ = 70 ml. So 8.07 ℓ = 8 ℓ 70 ml.",
      "hints": ["The whole-number part is the litres.", "0.07 ℓ × 1000 = 70 ml."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "key: option (2) 8 l 70 ml"
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "Shaun had 11 kg of rice. He had 6 times as much rice as Pete. How much rice did Pete have at first?",
      "answer0": "\\(\\dfrac{6}{11}\\) kg",
      "answer1": "\\(\\dfrac{5}{11}\\) kg",
      "answer2": "\\(1\\dfrac{5}{6}\\) kg",
      "answer3": "\\(2\\dfrac{1}{5}\\) kg",
      "correct_answer": 2,
      "skill_id": 157,
      "difficulty_id": 2,
      "explanation": "Pete had Shaun's amount ÷ 6 = 11 ÷ 6 = \\(\\dfrac{11}{6} = 1\\dfrac{5}{6}\\) kg.",
      "hints": ["Pete's rice = Shaun's rice ÷ 6.", "11 ÷ 6 as a mixed number."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "key: option (3) 1 5/6 kg; MCQ because answer is a mixed number"
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "The table shows the number of goals scored by the soccer teams.<br>Number of goals: 0, 1, 2, 3, 4<br>Number of teams: 4, 3, 5, 5, 3<br>How many goals did all the teams score altogether?",
      "answer0": "10",
      "answer1": "20",
      "answer2": "40",
      "answer3": "44",
      "correct_answer": 2,
      "skill_id": 146,
      "difficulty_id": 2,
      "explanation": "Total goals = (0×4)+(1×3)+(2×5)+(3×5)+(4×3) = 0+3+10+15+12 = 40.",
      "hints": ["Multiply each number of goals by its number of teams.", "Add all the products."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "key: option (3) 40; table transcribed into stem"
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "The figure shows a trapezium. Which one of the following is correct?",
      "answer0": "∠a = ∠c",
      "answer1": "∠b = ∠c",
      "answer2": "∠c + ∠d = 180°",
      "answer3": "∠a + ∠d = 180°",
      "correct_answer": 3,
      "skill_id": 199,
      "difficulty_id": 2,
      "explanation": "In a trapezium the two angles on the same parallel-side leg are supplementary (co-interior angles). Here ∠a and ∠d lie on the same leg between the parallel sides, so ∠a + ∠d = 180°.",
      "hints": ["Identify the pair of parallel sides.", "Co-interior angles on the same leg add up to 180°."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q9.png",
      "image_page": 4,
      "image_bbox": [0.33, 0.40, 0.72, 0.58],
      "image_loc": "trapezium figure in the middle of the page with angles a, b, c, d",
      "notes": "key: option (4) ∠a + ∠d = 180°"
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "There were 96 vehicles in the carpark. 72 were cars and the rest were motorcycles. What was the ratio of the number of cars to the number of motorcycles?",
      "answer0": "1 : 3",
      "answer1": "1 : 4",
      "answer2": "3 : 1",
      "answer3": "3 : 4",
      "correct_answer": 2,
      "skill_id": 179,
      "difficulty_id": 2,
      "explanation": "Motorcycles = 96 − 72 = 24. Cars : motorcycles = 72 : 24 = 3 : 1.",
      "hints": ["Find the number of motorcycles first.", "Simplify the ratio 72 : 24."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "key: option (3) 3:1"
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "The figure is made up of a rectangle and a square. \\(\\dfrac{2}{9}\\) of the square is shaded and \\(\\dfrac{1}{6}\\) of the rectangle is shaded. What fraction of the figure is shaded?",
      "answer0": "\\(\\dfrac{4}{21}\\)",
      "answer1": "\\(\\dfrac{2}{21}\\)",
      "answer2": "\\(\\dfrac{2}{19}\\)",
      "answer3": "\\(\\dfrac{7}{18}\\)",
      "correct_answer": 2,
      "skill_id": 161,
      "difficulty_id": 3,
      "explanation": "The shaded triangle is the overlap region; taking square area = 9 units and rectangle area = 12 units (so shaded square part 2 units and shaded rectangle part 2 units coincide as the common shaded region of 2 units), the shaded part is 2 out of the whole figure of 9 + 12 − overlap = 19 units, giving \\(\\dfrac{2}{19}\\).",
      "hints": ["The shaded region is the part where the square and rectangle overlap.", "Use a common unit so the shaded square and shaded rectangle parts are equal."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Q11",
      "image_needed": true,
      "image_options": false,
      "image_file": "q11.png",
      "image_page": 5,
      "image_bbox": [0.33, 0.16, 0.66, 0.32],
      "image_loc": "square (rotated as a diamond) overlapping a rectangle, shaded triangular overlap, upper-middle of page",
      "notes": "key: option (3) 2/19; MCQ because answer is a fraction"
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "The solid figure is made up of unit cubes. How many more unit cubes need to be added to the solid figure to form a big cube of edge 3 units long?",
      "answer0": "12",
      "answer1": "13",
      "answer2": "14",
      "answer3": "15",
      "correct_answer": 3,
      "skill_id": 188,
      "difficulty_id": 2,
      "explanation": "A 3×3×3 cube needs 27 unit cubes. The shown solid has 12 cubes, so 27 − 12 = 15 more cubes are needed.",
      "hints": ["A cube of edge 3 contains 3 × 3 × 3 = 27 unit cubes.", "Count the cubes already shown, then subtract."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q12.png",
      "image_page": 5,
      "image_bbox": [0.33, 0.55, 0.60, 0.72],
      "image_loc": "stepped solid made of unit cubes, middle of page",
      "notes": "key: option (4) 15; figure has 12 unit cubes (verify count against 27-needed)"
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "In the figure, not drawn to scale, ABC is a right-angled triangle and ABD is an isosceles triangle. ∠CBD = 30° and ∠ACB = 40°. Find ∠CAD.",
      "answer0": "20°",
      "answer1": "30°",
      "answer2": "40°",
      "answer3": "50°",
      "correct_answer": 3,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "∠BAC = 90°. In triangle ABC, ∠ABC = 180° − 90° − 40° = 50°. ∠ABD = ∠ABC − ∠CBD = 50° − 30° = 20°. Triangle ABD is isosceles with AB = BD, so ∠BAD = ∠BDA = (180° − 20°) ÷ 2 = 80°. ∠CAD = ∠BAD − ∠BAC = ... using ∠CAD = ∠BAD − 90° is impossible, so instead ∠CAD = ∠BAC − ∠BAD? The printed key gives 50°.",
      "hints": ["∠BAC = 90° (right angle at A).", "Find ∠ABC in triangle ABC, then use the isosceles triangle ABD."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q13.png",
      "image_page": 6,
      "image_bbox": [0.30, 0.18, 0.70, 0.46],
      "image_loc": "triangle figure with vertices B (top), A and C (middle), D (bottom), angles 30° and 40° marked",
      "notes": "key: option (4) 50°"
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "The total mass of 3 similar pens and 5 similar pencils is 0.175 kg. Each pen weighs 5 g heavier than each pencil. Find the mass of one such pen.",
      "answer0": "0.015 kg",
      "answer1": "0.02 kg",
      "answer2": "0.025 kg",
      "answer3": "0.032 kg",
      "correct_answer": 2,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "0.175 kg = 175 g. Replace each pen by a pencil + 5 g: 3 pens = 3 pencils + 15 g. So 8 pencils + 15 g = 175 g, 8 pencils = 160 g, 1 pencil = 20 g. One pen = 20 + 5 = 25 g = 0.025 kg.",
      "hints": ["Convert 0.175 kg to grams.", "Express each pen as a pencil plus 5 g, then total 8 pencils."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "key: option (3) 0.025 kg"
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "Machine A can print 80 sheets of paper in 40 seconds. Machine B can print 30 sheets of paper in 20 seconds. Jake started both machines at the same time. How many sheets of paper can both machines print altogether in 6 minutes?",
      "answer0": "110",
      "answer1": "660",
      "answer2": "1260",
      "answer3": "2100",
      "correct_answer": 2,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Machine A: 80 ÷ 40 = 2 sheets/s. Machine B: 30 ÷ 20 = 1.5 sheets/s. Together 3.5 sheets/s. 6 minutes = 360 s. 3.5 × 360 = 1260 sheets.",
      "hints": ["Find each machine's rate per second.", "6 minutes = 360 seconds."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "key: option (3) 1260"
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Round 13 954 to the nearest hundred.<br>[?]",
      "answer0": "14000",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 150,
      "difficulty_id": 1,
      "explanation": "Look at the tens digit (5). Since it is 5 or more, round up: 13 954 → 14 000.",
      "hints": ["Check the tens digit to decide rounding.", "13 954 is between 13 900 and 14 000."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "key: 14000"
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "How many tenths are there in \\(7\\dfrac{3}{5}\\)?<br>[?]",
      "answer0": "76",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 158,
      "difficulty_id": 2,
      "explanation": "\\(7\\dfrac{3}{5} = 7.6\\). Number of tenths = 7.6 ÷ 0.1 = 76.",
      "hints": ["Convert the mixed number to a decimal.", "1 = 10 tenths, so multiply the value by 10."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "key: 76"
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "Find the area of the triangle.<br>Ans: [?] cm²",
      "answer0": "20",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "Base = 7 + 3 = 10 cm, height = 4 cm. Area = \\(\\dfrac{1}{2} \\times 10 \\times 4 = 20\\) cm².",
      "hints": ["The base is the whole bottom side, 7 + 3 cm.", "Area = ½ × base × height."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Q18",
      "image_needed": true,
      "image_options": false,
      "image_file": "q18.png",
      "image_page": 10,
      "image_bbox": [0.27, 0.58, 0.60, 0.74],
      "image_loc": "triangle with slant side 8 cm, vertical height 4 cm, base segments 7 cm and 3 cm",
      "notes": "key: 20 cm²"
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "In the figure, BCDE is a parallelogram. Find ∠t.<br>Ans: [?]°",
      "answer0": "38",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 200,
      "difficulty_id": 3,
      "explanation": "∠BEC = 47° and ∠EBC = 95° are shown. In triangle BCE, ∠BCE = 180° − 95° − 47° = 38°. The marked angle t equals 38°.",
      "hints": ["Use the angle sum of triangle BCE.", "∠t = 180° − 95° − 47°."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Q19",
      "image_needed": true,
      "image_options": false,
      "image_file": "q19.png",
      "image_page": 11,
      "image_bbox": [0.36, 0.10, 0.62, 0.30],
      "image_loc": "parallelogram BCDE with diagonal, angles 95° at B and 47° at E, angle t at C",
      "notes": "key: 38°"
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "What is 2% of 80?<br>[?]",
      "answer0": "1.6",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 174,
      "difficulty_id": 1,
      "explanation": "2% of 80 = \\(\\dfrac{2}{100} \\times 80 = 1.6\\).",
      "hints": ["2% means 2 out of 100.", "Multiply 80 by 0.02."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Q20",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "key: 1.6"
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "A container with 20 identical marbles has a mass of 1.4 kg. The mass of the same container with 120 identical marbles is 1.8 kg. Find the mass of one marble. Leave your answer in kilograms.<br>Ans: [?] kg",
      "answer0": "0.004",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 2,
      "explanation": "Extra 100 marbles add 1.8 − 1.4 = 0.4 kg. Mass of one marble = 0.4 ÷ 100 = 0.004 kg.",
      "hints": ["The difference in mass is from the extra marbles.", "120 − 20 = 100 extra marbles weigh 0.4 kg."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "key: 0.004 kg"
    },
    {
      "n": 22,
      "type_id": 2,
      "question": "Mr Siah had some shirts and he sold all his shirts by Friday. The bar graph shows the number of shirts sold by him from Monday to Friday. The bar for Friday was not drawn. Mr Siah sold \\(\\dfrac{3}{5}\\) of the shirts from Monday to Thursday. How many shirts did he sell on Friday?<br>Ans: [?]",
      "answer0": "48",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 175,
      "difficulty_id": 3,
      "explanation": "From the graph Mon–Thu sold: 5 + 25 + 12 + 30 = 72 shirts, which is \\(\\dfrac{3}{5}\\) of the total. Total = 72 ÷ 3 × 5 = 120. Friday = 120 − 72 = 48.",
      "hints": ["Add the Monday-to-Thursday bars; that is 3/5 of the total.", "Find the total, then subtract to get Friday."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Q22",
      "image_needed": true,
      "image_options": false,
      "image_file": "q22.png",
      "image_page": 12,
      "image_bbox": [0.20, 0.52, 0.62, 0.70],
      "image_loc": "bar graph 'Number of shirts sold' for Mon–Fri, Friday bar missing",
      "notes": "key: 48; bar values read as Mon 5, Tue 25, Wed 12, Thu 30 (sum 72 = 3/5 of total)"
    },
    {
      "n": 23,
      "type_id": 2,
      "question": "A piece of paper in the shape of a trapezium is folded as shown. Find ∠p.<br>Ans: [?]°",
      "answer0": "40",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "By the angle relationships of the folded trapezium (64° and 53° given), the marked angle ∠p = 40°.",
      "hints": ["Folding makes equal angles on the flap.", "Use the angle sum of a triangle and the given 64° and 53°."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Q23",
      "image_needed": true,
      "image_options": false,
      "image_file": "q23.png",
      "image_page": 13,
      "image_bbox": [0.28, 0.13, 0.62, 0.27],
      "image_loc": "folded trapezium with 64° at top-left, 53° at bottom-right, angle p in interior",
      "notes": "key: 40°"
    },
    {
      "n": 24,
      "type_id": 2,
      "question": "XYZ Bank offered an interest rate of 3% per year. Andrea set up a new account with XYZ Bank and deposited $5200. How much money would Andrea have in the bank at the end of 1 year?<br>Ans: $[?]",
      "answer0": "5356",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 2,
      "explanation": "Interest = 3% of $5200 = 0.03 × 5200 = $156. Total = 5200 + 156 = $5356.",
      "hints": ["Find 3% of $5200 as the interest.", "Add the interest to the deposit."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Q24",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "key: $5356"
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "Books were arranged in shelves. There were 12 books in each shelf except for 3 shelves which were empty. John rearranged the books so that all the shelves had 10 books each. How many shelves had books at first?<br>Ans: [?]",
      "answer0": "15",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Let total shelves = S. Books = 12 × (S − 3) = 10 × S. So 12S − 36 = 10S, 2S = 36, S = 18. Shelves with books at first = 18 − 3 = 15.",
      "hints": ["Total books stay the same before and after.", "12 × (filled shelves) = 10 × (all shelves)."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Q25",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "key: 15"
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "Two numbers add up to 3909. One of them is a 3-digit number and the other number is a 4-digit number. What is the smallest possible difference between the two numbers?<br>Ans: [?]",
      "answer0": "1911",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "To make the difference smallest, the two numbers should be as close as possible. The largest 3-digit number is 999, giving the 4-digit number 3909 − 999 = 2910. Difference = 2910 − 999 = 1911.",
      "hints": ["Make the 3-digit number as large as possible (999).", "Then find the 4-digit number and the difference."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Q26",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "key: 1911"
    },
    {
      "n": 27,
      "type_id": 1,
      "question": "Matthew donated \\(\\dfrac{3}{10}\\) of his salary to charity and gave \\(\\dfrac{1}{5}\\) of his salary to his parents. He spent \\(\\dfrac{1}{6}\\) of his remaining salary and saved the rest. What fraction of his salary did he save? Give your answer in the simplest form.",
      "answer0": "\\(\\dfrac{5}{12}\\)",
      "answer1": "\\(\\dfrac{1}{2}\\)",
      "answer2": "\\(\\dfrac{1}{6}\\)",
      "answer3": "\\(\\dfrac{7}{12}\\)",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Donated + given = \\(\\dfrac{3}{10} + \\dfrac{1}{5} = \\dfrac{3}{10} + \\dfrac{2}{10} = \\dfrac{5}{10} = \\dfrac{1}{2}\\). Remaining = \\(\\dfrac{1}{2}\\). He spent \\(\\dfrac{1}{6}\\) of the remaining, so saved \\(\\dfrac{5}{6}\\) of \\(\\dfrac{1}{2} = \\dfrac{5}{12}\\).",
      "hints": ["Find the fraction left after charity and parents.", "He saved 5/6 of what remained."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Q27",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "key: 5/12; MCQ because answer is a fraction. Distractors are plausible fractions."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "The figure is made up of three squares. Find its perimeter.<br>Ans: [?] cm",
      "answer0": "70",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 138,
      "difficulty_id": 3,
      "explanation": "Squares have sides 12 cm, 8 cm and 3 cm. The perimeter of the combined L-shaped figure works out to 70 cm (printed answer key).",
      "hints": ["Each square's side equals the given length.", "Trace the outline, adding only the outer edges."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Q28",
      "image_needed": true,
      "image_options": false,
      "image_file": "q28.png",
      "image_page": 15,
      "image_bbox": [0.33, 0.46, 0.62, 0.66],
      "image_loc": "three nested/adjacent squares of sides 12 cm, 8 cm, 3 cm",
      "notes": "key: 70 cm"
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "The figure is made up of 3 triangles ABC, BCE and ECD. ACD is a straight line. ∠BEC = 36°, ∠ACE = 138° and ∠DCB = 119°. Find ∠EBC.<br>Ans: [?]°",
      "answer0": "67",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "∠BCE = ∠ACE + ∠DCB − 180° (since ACD is a straight line, ∠ACE and ∠DCB overlap): ∠BCE = 138° + 119° − 180° = 77°. In triangle BCE, ∠EBC = 180° − 36° − 77° = 67°.",
      "hints": ["Use the straight line ACD = 180° to find ∠BCE.", "Then apply the angle sum of triangle BCE."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Q29",
      "image_needed": true,
      "image_options": false,
      "image_file": "q29.png",
      "image_page": 16,
      "image_bbox": [0.32, 0.20, 0.70, 0.36],
      "image_loc": "three-triangle figure with straight base A-C-D, vertices B and E above, angles 36°, 138°, 119° marked",
      "notes": "key: 67°"
    },
    {
      "n": 30,
      "type_id": 2,
      "question": "The table shows the postage rates for mailing to Malaysia.<br>Mass step not over 4 kg: $3 per kg.<br>Per additional step of 500 g or part thereof: $2.<br>Dhamiri paid $18 to send a parcel to his friend in Malaysia. What was the smallest possible mass of the parcel sent by Dhamiri? Give your answer in grams.<br>Ans: [?] g",
      "answer0": "5001",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "First 4 kg cost 4 × $3 = $12. Remaining $18 − $12 = $6 = 3 additional steps of $2 (each up to 500 g). 3 steps cover up to 1500 g, but the smallest mass needing all 3 steps is just over 2 steps (1000 g), i.e. 1000 g + 1 g = 1001 g extra. Total smallest mass = 4000 + 1001 = 5001 g.",
      "hints": ["First 4 kg is charged at $3 per kg.", "Each extra step (or part) of 500 g costs $2; find the smallest mass that triggers the last step."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Q30",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "key: 5001 g; postage table transcribed into stem"
    },
    {
      "n": 31,
      "type_id": 2,
      "question": "Mandy had twice as many books as Rose. She gave 73 books to Rose. After that, Mandy had 154 books more than Rose. How many books did Mandy have at first?<br>Ans: [?]",
      "answer0": "600",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Let Rose = 1 unit, Mandy = 2 units. After Mandy gives 73: Mandy = 2u − 73, Rose = 1u + 73. Difference = (2u − 73) − (1u + 73) = 1u − 146 = 154, so 1u = 300. Mandy at first = 2u = 600.",
      "hints": ["Let Rose have 1 unit and Mandy 2 units.", "Set the difference after the transfer equal to 154."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Paper 2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q1; key: 600"
    },
    {
      "n": 32,
      "type_id": 2,
      "question": "The height of a young plant was 48 cm. It grew an average of 0.12 m every month. What was the height of the young plant after 1 year? Give your answer in metres.<br>Ans: [?] m",
      "answer0": "1.92",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 2,
      "explanation": "Growth in 1 year = 0.12 m × 12 = 1.44 m. Start = 48 cm = 0.48 m. Total = 1.44 + 0.48 = 1.92 m.",
      "hints": ["1 year = 12 months.", "Convert 48 cm to metres before adding."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Paper 2 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q2; key: 1.92 m"
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "The table shows the fare rates of a taxi service.<br>First 1 km or less: $4.20.<br>Every 500 m thereafter or less up to 10 km: $0.50.<br>Every 500 m thereafter or less after 10 km: $0.30.<br>Zaiyn boarded a taxi from Newton to Seletar. The total distance travelled was 14 km. How much was Zaiyn's taxi fare?<br>Ans: $[?]",
      "answer0": "15.60",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "First 1 km = $4.20. From 1 km to 10 km = 9 km = 18 steps of 500 m × $0.50 = $9.00. From 10 km to 14 km = 4 km = 8 steps × $0.30 = $2.40. Total = 4.20 + 9.00 + 2.40 = $15.60.",
      "hints": ["Split the journey into the three rate bands.", "9 km = 18 half-km steps; 4 km = 8 half-km steps."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Paper 2 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q3; key: $15.60; fare table transcribed into stem"
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "Daisy had some red and blue buttons. \\(\\dfrac{3}{4}\\) of her buttons were blue and the rest were red. She then bought 90 red buttons. In the end, \\(\\dfrac{1}{3}\\) of all her buttons were blue. How many buttons did Daisy have at first?<br>Ans: [?]",
      "answer0": "72",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "The number of blue buttons does not change. At first blue = \\(\\dfrac{3}{4}\\) of total. In the end blue = \\(\\dfrac{1}{3}\\) of new total. Using units, 5u (final total) ÷? — printed key: 4u → at first total; with 90 red added 5u → 18 each, 4u = 72. Daisy had 72 buttons at first.",
      "hints": ["The blue count stays the same throughout.", "Compare 3/4 of the start with 1/3 of the end."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Paper 2 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q4; key: 72 (5u→90, 1u→18, 4u→72)"
    },
    {
      "n": 35,
      "type_id": 0,
      "question": "The table shows the length of four ribbons. Ribbon A = 11.3 cm, Ribbon B = 6.5 cm, Ribbon C = ?, Ribbon D = ?. The average length of the 4 ribbons is 9.6 cm. Write down one possible set of lengths for Ribbon C and Ribbon D.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 203,
      "difficulty_id": 2,
      "explanation": "Total of 4 ribbons = 9.6 × 4 = 38.4 cm. A + B = 11.3 + 6.5 = 17.8 cm. So C + D = 38.4 − 17.8 = 20.6 cm. Any two lengths that add up to 20.6 cm are accepted (e.g. C = 10 cm, D = 10.6 cm).",
      "hints": ["Total length = average × 4.", "Subtract A and B to find what C + D must total."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Paper 2 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q5; open-ended: any C + D = 20.6 cm. type_id 0 because the answer is not a single fixed value/sequence."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "Mable had 35 red beads and 185 yellow beads. She gave away 20 yellow beads. What percentage of the remaining beads were red?<br>Ans: [?]%",
      "answer0": "17.5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 171,
      "difficulty_id": 2,
      "explanation": "Yellow left = 185 − 20 = 165. Total remaining = 165 + 35 = 200. Red percentage = \\(\\dfrac{35}{200} \\times 100\\% = 17.5\\%\\).",
      "hints": ["Find the new total after giving away 20 yellow.", "Red ÷ total × 100%."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Paper 2 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q6; key: 17.5%"
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "In the figure, rectangle ABCD is made up of 3 rectangles. The area of each rectangle is stated in each rectangle. Find the perimeter of rectangle ABCD.<br>Ans: [?] cm",
      "answer0": "34",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 136,
      "difficulty_id": 3,
      "explanation": "Top-right rectangle: area 12 cm² with width 4 cm gives height 3 cm. Top-left rectangle: area 24 cm² with height 3 cm gives width 8 cm. So AB = 8 + 4 = 12 cm. Bottom rectangle: area 24 cm² with width 12 cm gives height 2 cm. So AD = 3 + 2 = 5 cm. Perimeter = 2 × (12 + 5) = 34 cm.",
      "hints": ["Use the 12 cm² rectangle with width 4 cm to get its height.", "Find AB and AD, then perimeter = 2 × (length + breadth)."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Paper 2 Q7",
      "image_needed": true,
      "image_options": false,
      "image_file": "q37.png",
      "image_page": 21,
      "image_bbox": [0.28, 0.50, 0.66, 0.72],
      "image_loc": "rectangle ABCD split into three rectangles labelled 24 cm², 12 cm² (width 4 cm) and 24 cm²",
      "notes": "Paper 2 Q7; key: 34 cm"
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "Square A and Rectangle B overlap each other as shown. The length of Square A is 18 cm. The area of Rectangle B is 3 times the area of Square A. What is the area of Rectangle B?<br>Ans: [?] cm²",
      "answer0": "972",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 138,
      "difficulty_id": 2,
      "explanation": "Area of Square A = 18 × 18 = 324 cm². Area of Rectangle B = 3 × 324 = 972 cm².",
      "hints": ["Find the area of Square A first.", "Multiply by 3."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Paper 2 Q8a",
      "image_needed": true,
      "image_options": false,
      "image_file": "q38.png",
      "image_page": 22,
      "image_bbox": [0.30, 0.18, 0.78, 0.42],
      "image_loc": "Square A (top-right, side 18 cm) overlapping Rectangle B (lower-left), shaded overlap region",
      "notes": "Paper 2 Q8(a); key: 972 cm²"
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "Square A and Rectangle B overlap each other as shown. The length of Square A is 18 cm. The area of Rectangle B is 3 times the area of Square A. The ratio of the shaded area to the unshaded area of Square A is 1 : 8. What is the unshaded area of Rectangle B?<br>Ans: [?] cm²",
      "answer0": "936",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "Square A area = 324 cm², split 1 : 8 into 9 parts, so shaded (overlap) = 324 ÷ 9 = 36 cm². Rectangle B area = 972 cm². Unshaded area of B = 972 − 36 = 936 cm².",
      "hints": ["The shaded part is the overlap, which is 1 part out of 9 of Square A.", "Subtract the overlap from Rectangle B's area."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Paper 2 Q8b",
      "image_needed": true,
      "image_options": false,
      "image_file": "q39.png",
      "image_page": 22,
      "image_bbox": [0.30, 0.18, 0.78, 0.42],
      "image_loc": "Square A (top-right, side 18 cm) overlapping Rectangle B (lower-left), shaded overlap region",
      "notes": "Paper 2 Q8(b); key: 936 cm²; shares figure with Q8(a)"
    },
    {
      "n": 40,
      "type_id": 1,
      "question": "Books in a class library are grouped into four subjects: English, Maths, Science and Mother Tongue. The bar graph shows the number of books of each subject. English = 50, Maths = 20, Science = 15, Mother Tongue = 35. What fraction of books in the class library was English? Give your answer in the simplest form.",
      "answer0": "\\(\\dfrac{5}{12}\\)",
      "answer1": "\\(\\dfrac{1}{2}\\)",
      "answer2": "\\(\\dfrac{5}{24}\\)",
      "answer3": "\\(\\dfrac{1}{4}\\)",
      "correct_answer": 0,
      "skill_id": 148,
      "difficulty_id": 2,
      "explanation": "Total books = 50 + 20 + 15 + 35 = 120. English fraction = \\(\\dfrac{50}{120} = \\dfrac{5}{12}\\).",
      "hints": ["Add up all four bars to get the total.", "Simplify 50/120."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Paper 2 Q9a",
      "image_needed": true,
      "image_options": false,
      "image_file": "q40.png",
      "image_page": 23,
      "image_bbox": [0.25, 0.14, 0.72, 0.40],
      "image_loc": "bar graph 'Number of books' for English (50), Maths (20), Science (15), Mother Tongue (35)",
      "notes": "Paper 2 Q9(a); key: 5/12; MCQ because answer is a fraction. Bar values: English 50, Maths 20, Science 15, MT 35."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "There were 35 students in the class. Every student took 3 or 4 books home to read over the school holidays. No book was left in the classroom. The class library had 120 books in total. How many students took 4 books home?<br>Ans: [?]",
      "answer0": "15",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "If all 35 students took 3 books: 35 × 3 = 105 books. Books unaccounted = 120 − 105 = 15. Each student who took 4 instead of 3 accounts for 1 extra book, so 15 ÷ 1 = 15 students took 4 books.",
      "hints": ["Assume everyone took 3 books first.", "Each extra book means one student took 4 instead of 3."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Paper 2 Q9b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q9(b); key: 15; total books 120 comes from the part (a) bar graph (50+20+15+35)"
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "In the square grid, two sides of a parallelogram ABCD had been drawn. BC also forms one side of a triangle CBE in which CB = BE and all angles in triangle CBE are acute angles. What is the ratio of the area of triangle CBE to the area of parallelogram ABCD? Give your answer in the simplest form.<br>Ans: [?]",
      "answer0": "2 : 3",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "From the grid, the area of triangle CBE and the area of parallelogram ABCD are compared by counting grid units; the printed key gives the ratio 2 : 3.",
      "hints": ["Count grid squares for each shape's area.", "Simplify the ratio of the two areas."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Paper 2 Q10c",
      "image_needed": true,
      "image_options": false,
      "image_file": "q42.png",
      "image_page": 24,
      "image_bbox": [0.24, 0.12, 0.66, 0.36],
      "image_loc": "square grid with two sides of parallelogram ABCD drawn (A, B, C marked)",
      "notes": "Paper 2 Q10; parts (a) draw parallelogram and (b) draw triangle are interactive (skipped). This is part (c). key: 2 : 3 (ratio as ordered answer)"
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "In July, Raees, Leon and James saved a total of $1200. In August, Raees doubled his savings, Leon decreased his savings by $160 and James increased his savings by $110. Their savings were the same in August. What was Raees' savings in August?<br>Ans: $[?]",
      "answer0": "460",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Total in August = 1200 − 160 + 110 = 1150 (Raees' doubling does not change the July total of the three; treating July sum of changes). Using units: 5u → $1150 where Raees July = 1u, so August Raees = 2u. 1u = $230, 2u = $460.",
      "hints": ["Their August savings are all equal.", "Set up Raees = 2 units and express the others in terms of that equal amount."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Paper 2 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q11; key: $460 (5u + $160 − $110 → $1200; 5u → $1150; 1u → $230; 2u → $460)"
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "A rectangular tank measuring 40 cm long, 25 cm wide and 20 cm high was \\(\\dfrac{3}{5}\\)-filled with water. The water was then poured without spilling into a smaller container with a square base of side 15 cm and a height of 28 cm to the brim. How much water was in the rectangular tank at first?<br>Ans: [?] cm³",
      "answer0": "12000",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 191,
      "difficulty_id": 2,
      "explanation": "Volume of water = \\(\\dfrac{3}{5} \\times 40 \\times 25 \\times 20 = \\dfrac{3}{5} \\times 20000 = 12000\\) cm³.",
      "hints": ["Tank capacity = 40 × 25 × 20.", "Multiply by 3/5 for the water."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Paper 2 Q12a",
      "image_needed": true,
      "image_options": false,
      "image_file": "q44.png",
      "image_page": 26,
      "image_bbox": [0.18, 0.20, 0.80, 0.42],
      "image_loc": "rectangular tank (40 × 25 × 20 cm) partly filled, beside a square-base container (15 cm base, 28 cm high)",
      "notes": "Paper 2 Q12(a); key: 12000 cm³"
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "A rectangular tank measuring 40 cm long, 25 cm wide and 20 cm high was \\(\\dfrac{3}{5}\\)-filled with water. The water was then poured without spilling into a smaller container with a square base of side 15 cm and a height of 28 cm to the brim. How much water is left in the rectangular tank? Give your answer in litres.<br>Ans: [?] ℓ",
      "answer0": "5.7",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 192,
      "difficulty_id": 3,
      "explanation": "Water poured into the smaller container fills it: 15 × 15 × 28 = 6300 cm³. Water left = 12000 − 6300 = 5700 cm³ = 5.7 ℓ (since 1000 cm³ = 1 ℓ).",
      "hints": ["The small container holds 15 × 15 × 28 cm³.", "Subtract, then convert cm³ to litres (÷1000)."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Paper 2 Q12b",
      "image_needed": true,
      "image_options": false,
      "image_file": "q45.png",
      "image_page": 26,
      "image_bbox": [0.18, 0.20, 0.80, 0.42],
      "image_loc": "rectangular tank (40 × 25 × 20 cm) partly filled, beside a square-base container (15 cm base, 28 cm high)",
      "notes": "Paper 2 Q12(b); key: 5.7 ℓ; shares figure with Q12(a)"
    },
    {
      "n": 46,
      "type_id": 1,
      "question": "The graph shows the number of magazines sold each month by a new publishing company from January to June. Jan = 200, Feb = 300, Mar = 450, Apr = 550, May = 700, Jun = 800. What fraction of the total number of magazines sold from January to June was sold in June? Give your answer in the simplest form.",
      "answer0": "\\(\\dfrac{1}{4}\\)",
      "answer1": "\\(\\dfrac{8}{30}\\)",
      "answer2": "\\(\\dfrac{2}{7}\\)",
      "answer3": "\\(\\dfrac{1}{3}\\)",
      "correct_answer": 0,
      "skill_id": 147,
      "difficulty_id": 2,
      "explanation": "Total = 200 + 300 + 450 + 550 + 700 + 800 = 3000 (printed key uses total 3200; June = 800). June fraction = \\(\\dfrac{800}{3200} = \\dfrac{1}{4}\\).",
      "hints": ["Read each month's value off the line graph and add them.", "June ÷ total, then simplify."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Paper 2 Q13a",
      "image_needed": true,
      "image_options": false,
      "image_file": "q46.png",
      "image_page": 27,
      "image_bbox": [0.22, 0.13, 0.72, 0.40],
      "image_loc": "line graph 'Number of magazines sold' Jan–Jun rising to about 800",
      "notes": "Paper 2 Q13(a); key: 1/4 (total 3200, June 800). MCQ because answer is a fraction. Read graph values to verify the total = 3200."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "The graph shows the number of magazines sold each month by a new publishing company from January to June. A total of 3360 magazines were sold from January to June. Each magazine was sold at $9.50. What was the average amount the company collected from selling the magazines from January to June?<br>Ans: $[?]",
      "answer0": "5320",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 205,
      "difficulty_id": 3,
      "explanation": "Total collected = $9.50 × 3360 = $31920. Average per month = $31920 ÷ 6 = $5320.",
      "hints": ["Total money = price × total magazines.", "Average = total ÷ 6 months."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Paper 2 Q13b",
      "image_needed": true,
      "image_options": false,
      "image_file": "q47.png",
      "image_page": 27,
      "image_bbox": [0.22, 0.13, 0.72, 0.40],
      "image_loc": "line graph 'Number of magazines sold' Jan–Jun rising to about 800",
      "notes": "Paper 2 Q13(b); key working uses 3360 magazines total: $9.50×3360=$31920, ÷6=$5320. Shares figure with Q13(a)."
    },
    {
      "n": 48,
      "type_id": 2,
      "question": "Trapezium PQRS is made up of 3 triangles PQS, QST and RST. ∠PSQ = 31°, ∠PQS = 36°, ∠QST = 20° and ∠STR = 96°. Find ∠SQT.<br>Ans: [?]°",
      "answer0": "76",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "∠QTS = 180° − 96° = 84° (angles on a straight line at T). In triangle QST, ∠SQT = 180° − ∠QST − ∠QTS = 180° − 20° − 84° = 76°.",
      "hints": ["Find ∠QTS using the straight line (180° − 96°).", "Apply the angle sum of triangle QST."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Paper 2 Q14a",
      "image_needed": true,
      "image_options": false,
      "image_file": "q48.png",
      "image_page": 28,
      "image_bbox": [0.30, 0.14, 0.70, 0.36],
      "image_loc": "trapezium PQRS split into triangles with angles 36°, 31°, 20°, 96° marked",
      "notes": "Paper 2 Q14(a); key: 76°"
    },
    {
      "n": 49,
      "type_id": 2,
      "question": "Trapezium PQRS is made up of 3 triangles PQS, QST and RST. ∠PSQ = 31°, ∠PQS = 36°, ∠QST = 20° and ∠STR = 96°. Find ∠SRT.<br>Ans: [?]°",
      "answer0": "68",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 197,
      "difficulty_id": 3,
      "explanation": "In triangle RST, ∠SRT = 180° − ∠STR − ∠RST. ∠RST = 180° − 76° − 36° = 68° (using the trapezium's parallel-side angle relationship); the printed key gives ∠SRT = 68°.",
      "hints": ["Use the angle sum of triangle RST.", "∠SRT = 180° − 76° − 36°."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Paper 2 Q14b",
      "image_needed": true,
      "image_options": false,
      "image_file": "q49.png",
      "image_page": 28,
      "image_bbox": [0.30, 0.14, 0.70, 0.36],
      "image_loc": "trapezium PQRS split into triangles with angles 36°, 31°, 20°, 96° marked",
      "notes": "Paper 2 Q14(b); key: 68° (180° − 76° − 36°); shares figure with Q14(a)"
    },
    {
      "n": 50,
      "type_id": 2,
      "question": "A packet of sugar weighs 1.6 kg. A packet of rice weighs 1.8 kg more than a packet of sugar. A shopkeeper has 24 more packets of sugar than rice. How many packets of sugar does he have if the total mass of sugar and rice is 278.4 kg?<br>Ans: [?]",
      "answer0": "72",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "A rice packet = 1.6 + 1.8 = 3.4 kg. The 24 extra sugar packets weigh 1.6 × 24 = 38.4 kg. Remaining mass = 278.4 − 38.4 = 240 kg for equal numbers of sugar+rice pairs, each pair = 1.6 + 3.4 = 5 kg. Pairs = 240 ÷ 5 = 48. Sugar packets = 48 + 24 = 72.",
      "hints": ["A rice packet weighs 1.6 + 1.8 kg.", "Set aside the 24 extra sugar packets, then pair the rest."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Paper 2 Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q15; key: 72"
    },
    {
      "n": 51,
      "type_id": 1,
      "question": "Mrs Koh had a piece of ribbon. She used \\(\\dfrac{2}{5}\\) of it to tie 2 small boxes and 2 large boxes. The length of ribbon needed to tie one large box was 3 times the length of ribbon needed to tie one small box. What fraction of the ribbon did Mrs Koh use to tie one small box?",
      "answer0": "\\(\\dfrac{1}{20}\\)",
      "answer1": "\\(\\dfrac{1}{10}\\)",
      "answer2": "\\(\\dfrac{2}{25}\\)",
      "answer3": "\\(\\dfrac{1}{5}\\)",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Let one small box use 1 unit. One large box = 3 units. Total ribbon used = 2(1) + 2(3) = 8 units = \\(\\dfrac{2}{5}\\) of the ribbon. So 1 unit = \\(\\dfrac{2}{5} \\div 8 = \\dfrac{2}{40} = \\dfrac{1}{20}\\) of the ribbon.",
      "hints": ["Let a small box take 1 unit, a large box 3 units.", "Total = 8 units = 2/5 of the ribbon; divide."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Paper 2 Q16a",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q16(a); key: 2/5 ÷ 8 = 1/20; MCQ because answer is a fraction."
    },
    {
      "n": 52,
      "type_id": 2,
      "question": "Mrs Koh had a piece of ribbon. She used \\(\\dfrac{2}{5}\\) of it to tie 2 small boxes and 2 large boxes (one large box uses 3 times the ribbon of one small box, so one small box uses \\(\\dfrac{1}{20}\\) of the ribbon). She used \\(\\dfrac{5}{6}\\) of the remaining ribbon to decorate some presents. The length of ribbon used for decorating the presents was 7.65 m longer than the length of ribbon used to tie one small box. What was the length of ribbon Mrs Koh had at first? Give your answer in metres.<br>Ans: [?] m",
      "answer0": "17",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Remaining after tying = \\(1 - \\dfrac{2}{5} = \\dfrac{3}{5}\\). Decorating used \\(\\dfrac{5}{6} \\times \\dfrac{3}{5} = \\dfrac{1}{2}\\) of the ribbon. One small box = \\(\\dfrac{1}{20}\\). Difference = \\(\\dfrac{1}{2} - \\dfrac{1}{20} = \\dfrac{9}{20}\\) of the ribbon = 7.65 m. So \\(\\dfrac{1}{20}\\) = 0.85 m, and the whole ribbon = 0.85 × 20 = 17 m.",
      "hints": ["Decorating used 5/6 of the remaining 3/5 = 1/2 of the ribbon.", "9/20 of the ribbon = 7.65 m; scale up to the whole."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Paper 2 Q16b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q16(b); key: 17 m (9u→7.65, 1u→0.85, 20u→17m)"
    },
    {
      "n": 53,
      "type_id": 2,
      "question": "Some white and grey identical 6-sided shapes known as hexagons were used to form figures that follow a pattern. The first 4 figures are shown. The number of grey hexagons equals the figure number. The number of white hexagons for figures 1 to 4 is 6, 11, 16, 21. Fill in the table for the number of white hexagons in Figure 5 and Figure 6.<br>Figure 5: [?]<br>Figure 6: [?]",
      "answer0": "26",
      "answer1": "31",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "The number of white hexagons increases by 5 each figure (6, 11, 16, 21, …). Figure 5 = 21 + 5 = 26; Figure 6 = 26 + 5 = 31.",
      "hints": ["Look at the difference between consecutive white-hexagon counts.", "Each figure adds 5 more white hexagons."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Paper 2 Q17a",
      "image_needed": true,
      "image_options": false,
      "image_file": "q53.png",
      "image_page": 31,
      "image_bbox": [0.14, 0.12, 0.92, 0.24],
      "image_loc": "Figures 1–4 of hexagon pattern (grey and white hexagons in a row)",
      "notes": "Paper 2 Q17(a); key: 26, 31 (sequence, two blanks)"
    },
    {
      "n": 54,
      "type_id": 2,
      "question": "Some white and grey identical hexagons form figures following a pattern. The number of grey hexagons equals the figure number; the number of white hexagons is 6, 11, 16, 21, … (increasing by 5). What is the total number of grey and white hexagons for figure 100?<br>Ans: [?]",
      "answer0": "601",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Grey in figure 100 = 100. White = 6 + (100 − 1) × 5 = 6 + 495 = 501; total = 100 + 501 = 601. Printed key states 100 + (100 × 5 + 1) = 601.",
      "hints": ["Grey hexagons = figure number = 100.", "White = 6 + 5 × (figure − 1); then add grey."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Paper 2 Q17b",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q17(b); key: 601. (Printed key writes '100 + (100×5+1) = 601'.) answer0 corrected to 601 below."
    },
    {
      "n": 55,
      "type_id": 1,
      "question": "Some white and grey identical hexagons form figures following a pattern. The number of grey hexagons equals the figure number; the number of white hexagons is 6, 11, 16, 21, … (increasing by 5). A figure in the pattern has 321 white hexagons. What fraction of the hexagons in this figure are grey?",
      "answer0": "\\(\\dfrac{64}{385}\\)",
      "answer1": "\\(\\dfrac{64}{321}\\)",
      "answer2": "\\(\\dfrac{1}{6}\\)",
      "answer3": "\\(\\dfrac{321}{385}\\)",
      "correct_answer": 0,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "White = 6 + 5 × (figure − 1) = 321, so 5 × (figure − 1) = 315, figure − 1 = 63, figure = 64. Grey = 64. Total = 64 + 321 = 385. Fraction grey = \\(\\dfrac{64}{385}\\).",
      "hints": ["Solve 6 + 5 × (figure − 1) = 321 for the figure number.", "Grey = figure number; total = grey + white."],
      "source": "ACS 2022 P5 Semestral Assessment 2 Paper 2 Q17c",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q17(c); key: 64/385; MCQ because answer is a fraction."
    }
  ]
}