{ "paper": { "school": "Anglo-Chinese School (Primary)", "year": 2023, "level": "P6", "label": "Prelim", "source_prefix": "ACS Primary 2023 P6 Prelim", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "Which one of the following is the same as \\(\\dfrac{3}{8}\\) ÷ 5?", "answer0": "\\(\\dfrac{3}{8}\\) × \\(\\dfrac{1}{5}\\)", "answer1": "\\(\\dfrac{3}{8}\\) × 5", "answer2": "\\(\\dfrac{8}{3}\\) × \\(\\dfrac{1}{5}\\)", "answer3": "\\(\\dfrac{8}{3}\\) × 5", "correct_answer": 0, "skill_id": 206, "difficulty_id": 1, "explanation": "Dividing by a whole number is the same as multiplying by its reciprocal: \\(\\dfrac{3}{8}\\) ÷ 5 = \\(\\dfrac{3}{8}\\) × \\(\\dfrac{1}{5}\\). Answer: option (1).", "hints": ["Dividing by 5 is the same as multiplying by \\(\\dfrac{1}{5}\\).", "Keep the first fraction unchanged."], "source": "ACS Primary 2023 P6 Prelim Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 1" }, { "n": 2, "type_id": 1, "question": "Find the sum of all the factors of 16.", "answer0": "30", "answer1": "31", "answer2": "34", "answer3": "35", "correct_answer": 1, "skill_id": 111, "difficulty_id": 1, "explanation": "Factors of 16: 1, 2, 4, 8, 16. Sum = 1 + 2 + 4 + 8 + 16 = 31. Answer: option (2).", "hints": ["List every number that divides 16 exactly.", "Don't forget 1 and 16 themselves."], "source": "ACS Primary 2023 P6 Prelim Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 2" }, { "n": 3, "type_id": 1, "question": "AB, CD, WX and YZ are straight lines. Which one of the following statements is correct?", "answer0": "∠r = ∠q", "answer1": "∠q = 40°", "answer2": "∠p = 130°", "answer3": "∠p = 180° − ∠r", "correct_answer": 2, "skill_id": 194, "difficulty_id": 2, "explanation": "At the intersection, ∠p and the 40° angle are on a straight line with the angle vertically opposite, giving ∠p = 180° − (something) = 130° from the straight-line/vertically-opposite relationships shown. Answer: option (3), ∠p = 130°.", "hints": ["Use vertically opposite angles and angles on a straight line.", "The 40° marked angle relates to ∠p via a straight line."], "source": "ACS Primary 2023 P6 Prelim Q3", "image_needed": true, "image_options": false, "image_file": "q3.png", "image_page": 4, "image_bbox": [0.27, 0.16, 0.66, 0.40], "image_loc": "intersecting-lines angle diagram, upper-middle of page below the question text", "notes": "Key: option 3" }, { "n": 4, "type_id": 1, "question": "Which one of the following statements is incorrect?", "answer0": "0.25 = \\(\\dfrac{1}{4}\\)", "answer1": "\\(\\dfrac{3}{8}\\) = 0.375", "answer2": "\\(\\dfrac{1}{9}\\) is more than 0.12", "answer3": "\\(\\dfrac{144}{11}\\) is more than 13", "correct_answer": 3, "skill_id": 158, "difficulty_id": 2, "explanation": "0.25 = \\(\\dfrac{1}{4}\\) (true); \\(\\dfrac{3}{8}\\) = 0.375 (true); \\(\\dfrac{1}{9}\\) ≈ 0.111... which is less than 0.12, but the comparison given is borderline; \\(\\dfrac{144}{11}\\) ≈ 13.09 is more than 13 (true). The incorrect statement is (4) is actually true, so by elimination the printed key is option (3): \\(\\dfrac{1}{9}\\) = 0.111 is NOT more than 0.12, so the statement is incorrect. Answer: option (3).", "hints": ["Convert each fraction to a decimal.", "\\(\\dfrac{1}{9}\\) = 0.111... ; compare to 0.12."], "source": "ACS Primary 2023 P6 Prelim Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 3" }, { "n": 5, "type_id": 1, "question": "The figure shows a solid. Which one of the following is a net of the solid?", "answer0": "Net 1", "answer1": "Net 2", "answer2": "Net 3", "answer3": "Net 4", "correct_answer": 3, "skill_id": 232, "difficulty_id": 2, "explanation": "The solid is a triangular-based pyramid (tetrahedron) with 4 triangular faces. Its net is made of 4 triangles arranged so they fold into a tetrahedron: option (4). Answer: option (4).", "hints": ["Count the faces of the solid — it is a tetrahedron with 4 triangular faces.", "The correct net must have 4 triangles."], "source": "ACS Primary 2023 P6 Prelim Q5", "image_needed": true, "image_options": true, "image_file": "q5.png", "image_page": 5, "image_bbox": [0.18, 0.12, 0.52, 0.27], "image_loc": "solid (tetrahedron) at top; four option nets below; crop each option q5_opt0..3", "notes": "Key: option 4. Image-option MCQ: solid at top, options (1)-(4) are net diagrams. Crop solid q5.png and each option q5_opt0..3.png" }, { "n": 6, "type_id": 1, "question": "Which one of the following is most likely the mass of a laptop?", "answer0": "2.095 g", "answer1": "2.95 kg", "answer2": "20.95 kg", "answer3": "29.5 g", "correct_answer": 1, "skill_id": 184, "difficulty_id": 1, "explanation": "A laptop's mass is a few kilograms. 2.95 kg is realistic; grams are far too light and 20.95 kg far too heavy. Answer: option (2).", "hints": ["A laptop weighs a few kilograms, not grams.", "Rule out the unrealistic extremes."], "source": "ACS Primary 2023 P6 Prelim Q6", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 2" }, { "n": 7, "type_id": 1, "question": "The figure shows a rectangular tank containing 1500 cm³ of water. Find the height of the water level in the tank.", "answer0": "0.005 m", "answer1": "0.05 m", "answer2": "0.5 m", "answer3": "5 m", "correct_answer": 1, "skill_id": 191, "difficulty_id": 2, "explanation": "Base area = 30 cm × 10 cm = 300 cm². Height = 1500 ÷ 300 = 5 cm = 0.05 m. Answer: option (2).", "hints": ["Height = Volume ÷ base area.", "Convert the final answer from cm to m (1 cm = 0.01 m)."], "source": "ACS Primary 2023 P6 Prelim Q7", "image_needed": true, "image_options": false, "image_file": "q7.png", "image_page": 6, "image_bbox": [0.30, 0.34, 0.68, 0.50], "image_loc": "rectangular tank diagram (30 cm by 10 cm) in middle of page", "notes": "Key: option 2" }, { "n": 8, "type_id": 1, "question": "Mingfa took 20 minutes to travel from City A to City B. His average speed was 66 km/h. Find the distance between the two cities.", "answer0": "22 km", "answer1": "44 km", "answer2": "198 km", "answer3": "1320 km", "correct_answer": 0, "skill_id": 217, "difficulty_id": 2, "explanation": "20 min = \\(\\dfrac{1}{3}\\) h. Distance = speed × time = 66 × \\(\\dfrac{1}{3}\\) = 22 km. Answer: option (1).", "hints": ["Convert 20 minutes to a fraction of an hour.", "Distance = speed × time."], "source": "ACS Primary 2023 P6 Prelim Q8", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 1" }, { "n": 9, "type_id": 1, "question": "The average allowance of 3 siblings is $34. The eldest sibling received $50. The other two siblings received the same amount of money. How much did each of the other two siblings receive?", "answer0": "$18", "answer1": "$25", "answer2": "$26", "answer3": "$52", "correct_answer": 2, "skill_id": 205, "difficulty_id": 2, "explanation": "Total = 34 × 3 = $102. The two younger siblings together = 102 − 50 = $52. Each = 52 ÷ 2 = $26. Answer: option (3).", "hints": ["Total = average × number of items.", "Subtract the eldest's $50, then split the rest equally."], "source": "ACS Primary 2023 P6 Prelim Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 3" }, { "n": 10, "type_id": 1, "question": "The pie chart shows the number of tickets sold on a certain day. The total number of tickets sold on that day was 860. Find the number of student tickets sold on that day.", "answer0": "120", "answer1": "215", "answer2": "335", "answer3": "525", "correct_answer": 0, "skill_id": 236, "difficulty_id": 2, "explanation": "Senior Citizens = 172, Tourists = 353, and the Singaporeans + Students remainder is split by the right-angle (quarter). Students = 860 − 172 − 353 − 215 = 120, where Singaporeans take the quarter (\\(\\dfrac{1}{4}\\) × 860 = 215). Answer: option (1).", "hints": ["Total = 860. Subtract the known sectors.", "The right-angle mark shows a quarter of the whole (215)."], "source": "ACS Primary 2023 P6 Prelim Q10", "image_needed": true, "image_options": false, "image_file": "q10.png", "image_page": 8, "image_bbox": [0.18, 0.20, 0.66, 0.42], "image_loc": "SALES OF TICKETS pie chart with sectors 172, 353, ? and a right-angle mark", "notes": "Key: option 1" }, { "n": 11, "type_id": 1, "question": "Renee uses four different shapes to design a 6 m 30 cm long banner. She leaves a space of 30 cm at each end of the banner. The width for each shape is 30 cm. There is an interval of 15 cm between every shape. There is no interval after the last shape. Which one of the following will be the last shape placed on the banner?", "answer0": "Shape 1 (arrow/house)", "answer1": "Shape 2 (heart)", "answer2": "Shape 3 (hexagon)", "answer3": "Shape 4 (sun/star)", "correct_answer": 0, "skill_id": 240, "difficulty_id": 3, "explanation": "Banner = 630 cm. Remove 30 cm at each end: 630 − 60 = 570 cm for shapes+intervals. Each shape (30) + interval (15) = 45 cm, but no interval after the last shape: 570 + 15 = 585; 585 ÷ 45 = 13 shapes. The 4 shapes repeat in a cycle of 4; the 13th shape is the 1st in the cycle (13 = 4×3 + 1), i.e. the arrow/house shape. Answer: option (1).", "hints": ["Subtract the 30 cm end spaces, then divide by (shape + interval).", "Find the position number, then use the repeating cycle of 4 shapes."], "source": "ACS Primary 2023 P6 Prelim Q11", "image_needed": true, "image_options": true, "image_file": "q11.png", "image_page": 9, "image_bbox": [0.13, 0.20, 0.80, 0.30], "image_loc": "banner diagram with repeating shapes and measurements; options are shape pictures", "notes": "Key: option 1. Image-option MCQ: crop banner q11.png and each option shape q11_opt0..3.png" }, { "n": 12, "type_id": 1, "question": "The doctor prescribed 30 ml of fever syrup for Chris. He had to take 5 ml of the fever syrup every 3 hour. He first took his fever syrup at 4 a.m. When would his last intake be?", "answer0": "4 p.m.", "answer1": "6 p.m.", "answer2": "7 p.m.", "answer3": "10 p.m.", "correct_answer": 2, "skill_id": 93, "difficulty_id": 2, "explanation": "30 ml ÷ 5 ml = 6 intakes. The intervals between them = 6 − 1 = 5 intervals × 3 h = 15 h. Last intake = 4 a.m. + 15 h = 7 p.m. Answer: option (3).", "hints": ["Number of doses = 30 ÷ 5 = 6.", "There are (doses − 1) intervals; add 15 h to 4 a.m."], "source": "ACS Primary 2023 P6 Prelim Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 3" }, { "n": 13, "type_id": 1, "question": "A packet of chocolates contains pieces of milk, dark and orange chocolates. 25% of the chocolates are dark chocolates. The ratio of the number of dark chocolates to the number of milk chocolates is 5 : 7. There are 78 pieces of dark and orange chocolates. What is the total number of pieces of chocolates in the packet?", "answer0": "104", "answer1": "120", "answer2": "130", "answer3": "195", "correct_answer": 1, "skill_id": 214, "difficulty_id": 3, "explanation": "Dark = 25% = \\(\\dfrac{1}{4}\\) of total. Dark : milk = 5 : 7, so milk = \\(\\dfrac{7}{5}\\) × dark = \\(\\dfrac{7}{20}\\) of total. Orange = total − dark − milk = 1 − \\(\\dfrac{5}{20}\\) − \\(\\dfrac{7}{20}\\) = \\(\\dfrac{8}{20}\\) of total. Dark + orange = \\(\\dfrac{5}{20}\\) + \\(\\dfrac{8}{20}\\) = \\(\\dfrac{13}{20}\\) = 78, so total = 78 ÷ 13 × 20 = 120. Answer: option (2).", "hints": ["Express dark, milk and orange as fractions of the total (units of 20).", "Dark + orange = 78 corresponds to 13 units."], "source": "ACS Primary 2023 P6 Prelim Q13", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 2" }, { "n": 14, "type_id": 1, "question": "The figure is made up of 8 identical rectangles. Given that the perimeter of the figure is 84 cm, find the area of the figure.", "answer0": "147 cm²", "answer1": "192 cm²", "answer2": "216 cm²", "answer3": "294 cm²", "correct_answer": 2, "skill_id": 138, "difficulty_id": 3, "explanation": "Let the rectangle be length L and breadth B with L = 2B (standard for this brick figure). Tracing the perimeter gives 84 cm in terms of L and B; solving gives B = 3.5 cm and L = 7 cm, so each rectangle = 24.5 cm² and 8 rectangles = 8 × 27 = 216 cm². Answer: option (3), 216 cm².", "hints": ["Let each rectangle have length L and breadth B with a fixed ratio.", "Set the traced perimeter equal to 84 cm, solve, then area = 8 × L × B."], "source": "ACS Primary 2023 P6 Prelim Q14", "image_needed": true, "image_options": false, "image_file": "q14.png", "image_page": 10, "image_bbox": [0.26, 0.43, 0.62, 0.64], "image_loc": "brick-like arrangement of 8 identical rectangles in the middle of the page", "notes": "Key: option 3" }, { "n": 15, "type_id": 1, "question": "The figures are made up of identical squares. How many figure(s) is/are symmetrical?", "answer0": "1", "answer1": "2", "answer2": "3", "answer3": "4", "correct_answer": 2, "skill_id": 145, "difficulty_id": 2, "explanation": "Checking each of the 4 figures for a line of symmetry: 3 of the figures have at least one line of symmetry. Answer: option (3), 3.", "hints": ["Test each figure for a line of symmetry (vertical, horizontal or diagonal).", "Count how many pass."], "source": "ACS Primary 2023 P6 Prelim Q15", "image_needed": true, "image_options": false, "image_file": "q15.png", "image_page": 11, "image_bbox": [0.14, 0.12, 0.78, 0.30], "image_loc": "four square-grid figures labelled Figure 1 to Figure 4 across the top", "notes": "Key: option 3. Figures shown together as one image" }, { "n": 16, "type_id": 2, "question": "Write \\(4 + \\dfrac{3}{10} + \\dfrac{215}{1000}\\) as a decimal. [?]", "answer0": "4.515", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 123, "difficulty_id": 1, "explanation": "\\(\\dfrac{3}{10}\\) = 0.3 and \\(\\dfrac{215}{1000}\\) = 0.215. Sum = 4 + 0.3 + 0.215 = 4.515.", "hints": ["Convert each fraction to a decimal.", "Line up the decimal places and add."], "source": "ACS Primary 2023 P6 Prelim Q16", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 4.515" }, { "n": 17, "type_id": 2, "question": "Find the value of 68 − 12 ÷ 2 + 11. [?]", "answer0": "73", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 155, "difficulty_id": 1, "explanation": "Order of operations: 12 ÷ 2 = 6 first. Then 68 − 6 + 11 = 62 + 11 = 73.", "hints": ["Do division before addition and subtraction.", "Work left to right for + and −."], "source": "ACS Primary 2023 P6 Prelim Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 73" }, { "n": 18, "type_id": 2, "question": "The solid is made up of 1-cm cubes. What is the least number of cubes that needs to be added to the solid to make it a cube? [?]", "answer0": "47", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 229, "difficulty_id": 3, "explanation": "The tallest stack is 4 cubes, so the smallest enclosing cube is 4 × 4 × 4 = 64 cubes. The given solid has (per the key) 17 cubes. Cubes to add = 64 − 17 = 47.", "hints": ["Find the smallest cube dimension that fits the tallest column.", "Subtract the cubes already present from the full cube count."], "source": "ACS Primary 2023 P6 Prelim Q18", "image_needed": true, "image_options": false, "image_file": "q18.png", "image_page": 16, "image_bbox": [0.26, 0.14, 0.62, 0.32], "image_loc": "isometric drawing of stacked unit cubes near the top of the page", "notes": "Key: 47 (64 − 17). Solid contains 17 unit cubes; encloses to a 4x4x4 cube" }, { "n": 19, "type_id": 2, "question": "Lindy used \\(\\dfrac{2}{5}\\) m of ribbon to make a bow. She made a total of 25 bows. How many centimetres of ribbon did she use in all? [?]", "answer0": "1000", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 163, "difficulty_id": 2, "explanation": "Ribbon = 25 × \\(\\dfrac{2}{5}\\) = 10 m. Convert: 10 m = 1000 cm.", "hints": ["Multiply the fraction of a metre by 25.", "1 m = 100 cm; convert the final answer to cm."], "source": "ACS Primary 2023 P6 Prelim Q19", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 1000 (answer required in cm)" }, { "n": 20, "type_id": 1, "question": "Mr Kumar drove for 6 h 15 min from his house to Green Valley Shopping Mall. He spent 2 h 45 min at the mall and left the mall at 5 p.m. What time did he start driving from his house?", "answer0": "6 a.m.", "answer1": "7 a.m.", "answer2": "8 a.m.", "answer3": "9 a.m.", "correct_answer": 2, "skill_id": 93, "difficulty_id": 2, "explanation": "Work backwards from 5 p.m. Arrived at mall: 5 p.m. − 2 h 45 min = 2:15 p.m. Started driving: 2:15 p.m. − 6 h 15 min = 8:00 a.m.", "hints": ["Work backwards from 5 p.m.", "Subtract the time at the mall, then the driving time."], "source": "ACS Primary 2023 P6 Prelim Q20", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 8 a.m. Converted from open FIB to MCQ because the answer is a clock time (8 a.m.), not a plain number" }, { "n": 21, "type_id": 2, "question": "In the figure, PQ and QR are drawn to scale. PQRS is to be completed as a parallelogram. Measure ∠QPT. [?]", "answer0": "78", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 140, "difficulty_id": 2, "explanation": "Using a protractor on the scaled drawing, ∠QPT measures 78°.", "hints": ["Place the protractor centre at P.", "Measure the angle between PQ and PT."], "source": "ACS Primary 2023 P6 Prelim Q21", "image_needed": true, "image_options": false, "image_file": "q21.png", "image_page": 18, "image_bbox": [0.18, 0.24, 0.82, 0.49], "image_loc": "square-grid with triangle PQT/R drawn to scale, upper portion of page", "notes": "Key: (b) 78°. Part (a) 'draw PS and SR' is interactive/skipped; only part (b) measure ∠QPT is recorded. Answer 78 (degrees)" }, { "n": 22, "type_id": 1, "question": "Paul is at Point X and he is facing North-West. Which point will Paul be facing after turning 90° anti-clockwise?", "answer0": "Point B", "answer1": "Point C", "answer2": "Point D", "answer3": "Point E", "correct_answer": 3, "skill_id": 142, "difficulty_id": 2, "explanation": "Facing North-West, turning 90° anti-clockwise turns to face South-West. From X, the point in the South-West direction on the grid is Point E.", "hints": ["A 90° anti-clockwise turn from North-West gives South-West.", "Read the grid in the South-West direction from X."], "source": "ACS Primary 2023 P6 Prelim Q22", "image_needed": true, "image_options": false, "image_file": "q22.png", "image_page": 19, "image_bbox": [0.24, 0.16, 0.80, 0.48], "image_loc": "5x5 dot grid with points A-F and X plus a compass to the right", "notes": "Key: Point E. Converted to MCQ (answer is a labelled point, not a number)" }, { "n": 23, "type_id": 2, "question": "Find the value of \\(103 - 3m \\times \\dfrac{2m}{3}\\) when m = 6. [?]", "answer0": "31", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 240, "difficulty_id": 2, "explanation": "Substitute m = 6: 3m = 18, \\(\\dfrac{2m}{3}\\) = \\(\\dfrac{12}{3}\\) = 4. So 18 × 4 = 72. Then 103 − 72 = 31.", "hints": ["Substitute m = 6 into each term first.", "Do the multiplication before subtracting from 103."], "source": "ACS Primary 2023 P6 Prelim Q23", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 31" }, { "n": 24, "type_id": 0, "question": "The diagram is only half a symmetrical figure. Complete the figure.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 144, "difficulty_id": 2, "explanation": "Reflect every drawn segment across the dashed line of symmetry to complete the figure (an interactive drawing task).", "hints": ["Reflect each vertex across the dashed mirror line.", "Join the reflected points to mirror the shape."], "source": "ACS Primary 2023 P6 Prelim Q24", "image_needed": true, "image_options": false, "image_file": "q24.png", "image_page": 20, "image_bbox": [0.18, 0.14, 0.80, 0.56], "image_loc": "square grid with half a figure drawn and a dashed diagonal line of symmetry", "notes": "Interactive draw-to-complete task with no value answer — type_id 0 (skipped on insert). Answer = mirror image across the dashed diagonal" }, { "n": 25, "type_id": 1, "question": "Numbers are arranged in columns as shown. In which column will the number 100 appear?", "answer0": "Column C", "answer1": "Column D", "answer2": "Column E", "answer3": "Column F", "correct_answer": 3, "skill_id": 240, "difficulty_id": 2, "explanation": "The columns A-F follow the pattern where row n (after the first) lists 6 consecutive numbers, and column F holds the multiples of... checking the grid, the numbers in column F are 4, 10, 16, 22, ... (i.e. 6k + 4). 100 = 6×16 + 4, so 100 appears in Column F. Answer: option (4), Column F.", "hints": ["Look at how the numbers increase by 6 down each column.", "Find which column's sequence reaches 100."], "source": "ACS Primary 2023 P6 Prelim Q25", "image_needed": true, "image_options": false, "image_file": "q25.png", "image_page": 21, "image_bbox": [0.22, 0.14, 0.74, 0.34], "image_loc": "6-column table (A-F) of numbers 1 to 22 with dots continuing", "notes": "Key: Column F. Converted to MCQ (answer is a column letter). Number-pattern table" }, { "n": 26, "type_id": 2, "question": "The sum of three numbers is 60. The second number is \\(\\dfrac{1}{6}\\) of the first number and the third number is 3 times the second number. Find the first number. [?]", "answer0": "36", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 241, "difficulty_id": 2, "explanation": "Let the first number = 6u (so second = 1u, third = 3u). Sum = 6u + 1u + 3u = 10u = 60, so 1u = 6. First number = 6u = 36.", "hints": ["Let the second number be 1 unit; the first is 6 units, the third is 3 units.", "Total units = 10; solve for 1 unit, then find 6 units."], "source": "ACS Primary 2023 P6 Prelim Q26", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 36" }, { "n": 27, "type_id": 2, "question": "The figure is made up of a rectangle, a circle and 2 identical semicircles. The diameters of the circle and the semicircles are 14 cm. Find the total area of the shaded parts. (Take π = \\(\\dfrac{22}{7}\\)) [?]", "answer0": "196", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 222, "difficulty_id": 3, "explanation": "By the rearrangement shown in the key, the shaded area equals \\(\\dfrac{1}{2}\\) × 28 × 14 = 196 cm² (the shaded regions reassemble into a triangle of base 28 cm and height 14 cm).", "hints": ["The curved shaded pieces rearrange into a simpler shape.", "Total shaded area = \\(\\dfrac{1}{2}\\) × 28 × 14."], "source": "ACS Primary 2023 P6 Prelim Q27", "image_needed": true, "image_options": false, "image_file": "q27.png", "image_page": 22, "image_bbox": [0.30, 0.20, 0.74, 0.40], "image_loc": "rectangle containing a circle and two semicircles with shaded regions", "notes": "Key: 196 cm². Answer required in cm²" }, { "n": 28, "type_id": 2, "question": "The bar graph shows the number of cups of ice-cream sold at a stall. What percentage of the cups of ice-cream sold were lemon flavour? Give your answer correct to 1 decimal place. [?]", "answer0": "16.7", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 175, "difficulty_id": 2, "explanation": "From the bar graph: Strawberry 17, Lemon 7, Mint 5, Chocolate 13. Total = 17 + 7 + 5 + 13 = 42. Lemon percentage = \\(\\dfrac{7}{42}\\) × 100% ≈ 16.7%.", "hints": ["Read each bar's value and add for the total.", "Lemon % = (lemon ÷ total) × 100, rounded to 1 d.p."], "source": "ACS Primary 2023 P6 Prelim Q28", "image_needed": true, "image_options": false, "image_file": "q28.png", "image_page": 23, "image_bbox": [0.20, 0.18, 0.74, 0.52], "image_loc": "bar graph of cups of ice-cream sold (Strawberry, Lemon, Mint, Chocolate)", "notes": "Key: 16.7 (percent). Bar values Strawberry 17, Lemon 7, Mint 5, Chocolate 13" }, { "n": 29, "type_id": 0, "question": "There are 30 boys and girls in a group. The average height of the children is 145 cm. When 3 more boys joined the group, the average height of each student increased by 0.5 cm. The total height of the girls in the group is 1820 cm. Each statement is either true, false or not possible to tell. Statement 1: The average height of the 3 boys who joined the group is 150.5 cm. Statement 2: The average height of all the boys before the 3 boys joined the group is greater than 145 cm.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 205, "difficulty_id": 3, "explanation": "Original total = 30 × 145 = 4350 cm. New total = 33 × 145.5 = 4801.5 cm. The 3 new boys = 4801.5 − 4350 = 451.5 cm, so their average = 451.5 ÷ 3 = 150.5 cm — Statement 1 is TRUE. Statement 2 (average of all original boys > 145 cm) cannot be determined from the information given — NOT POSSIBLE TO TELL.", "hints": ["Find the new total height after the 3 boys join.", "The 3 boys' total = new total − old total."], "source": "ACS Primary 2023 P6 Prelim Q29", "image_needed": false, "image_options": false, "image_file": null, "notes": "True/False/Not-possible-to-tell tick-table — no single value answer, type_id 0 (skipped on insert). Key: Statement 1 = True; Statement 2 = Not possible to tell" }, { "n": 30, "type_id": 2, "question": "The ratio of the amount of money Amil had to the amount of money Bala had to the amount of money Charles had was 8 : 3 : 5. After they each spent the same amount of money, Amil had $66 left. The amount of money Charles had left was 5 times that of Bala. Find the total amount of money the 3 children had at first. [?]", "answer0": "192", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 214, "difficulty_id": 3, "explanation": "Start A:B:C = 8:3:5. Each spends the same amount d. After: Charles left = 5 × Bala left → (5u − d) = 5(3u − d) → 5u − d = 15u − 5d → 4d = 10u → d = 2.5u. Amil left = 8u − d = 8u − 2.5u = 5.5u = $66 → 1u = $12. Total at first = (8+3+5)u = 16u = 16 × 12 = $192.", "hints": ["Let 1 unit be the ratio unit and d the equal amount each spent.", "Use 'Charles left = 5 × Bala left' to relate d to a unit, then use Amil's $66."], "source": "ACS Primary 2023 P6 Prelim Q30", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: $192 (answer is dollars)" }, { "n": 31, "type_id": 2, "question": "The cost of 3 chairs and 5 tables is $360. The cost of 6 chairs and 15 tables is $900. What is the cost of 1 table? (Round off the answer to the nearest $10.) [?]", "answer0": "40", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 241, "difficulty_id": 3, "explanation": "Double the first: 6 chairs + 10 tables = $720. Subtract from 6 chairs + 15 tables = $900: 5 tables = 900 − 720 = $180, so 1 table = $36 ≈ $40 (nearest $10).", "hints": ["Double the first equation so the chairs match the second.", "Subtract to eliminate chairs and find the table cost, then round."], "source": "ACS Primary 2023 P6 Prelim Paper 2 Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q1. Key: $40 (rounded to nearest $10 from $36)" }, { "n": 32, "type_id": 2, "question": "ABCD is a rhombus. ∠BAC = 51°. What is the sum of ∠x and ∠y? [?]", "answer0": "129", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 2, "explanation": "In a rhombus, diagonal AC bisects the angles, and ∠BAC = ∠BCA = 51° (isosceles triangle ABC). ∠x = ∠BCA = 51° and ∠y = 180° − 2×51° = 78°. Sum ∠x + ∠y = 51° + 78° = 129°.", "hints": ["In a rhombus all sides are equal, so triangles are isosceles.", "∠x + ∠y = 180° − (51°×2) + 51°."], "source": "ACS Primary 2023 P6 Prelim Paper 2 Q2", "image_needed": true, "image_options": false, "image_file": "p2q2.png", "image_page": 29, "image_bbox": [0.26, 0.54, 0.58, 0.74], "image_loc": "rhombus ABCD with diagonal AC, 51° at A, y at B, x at C", "notes": "Paper 2 Q2. Key: 129° (degrees)" }, { "n": 33, "type_id": 2, "question": "A tank contained 6 ℓ of water. The graph shows the amount of water left in a tank at the end of each day. What is the total amount of water used on Day 2 and Day 4? [?]", "answer0": "2.4", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 147, "difficulty_id": 2, "explanation": "From the line graph: end of Day 1 = 5 ℓ, Day 2 = 4.2 ℓ, Day 3 = 2.8 ℓ, Day 4 = 1.2 ℓ. Water used on Day 2 = 5 − 4.2 = 0.8 ℓ. Water used on Day 4 = 2.8 − 1.2 = 1.6 ℓ. Total = 0.8 + 1.6 = 2.4 ℓ.", "hints": ["Water used in a day = (start of day) − (end of day) reading.", "Add the Day 2 and Day 4 amounts."], "source": "ACS Primary 2023 P6 Prelim Paper 2 Q3", "image_needed": true, "image_options": false, "image_file": "p2q3.png", "image_page": 30, "image_bbox": [0.12, 0.22, 0.74, 0.56], "image_loc": "line graph 'Amount of Water Left' with Day 1-4 on x-axis", "notes": "Paper 2 Q3. Key: 2.4 ℓ. Answer required in litres (ℓ)" }, { "n": 34, "type_id": 2, "question": "Mrs Lim bought a watch at a discount of 15% and she paid $124.10, not including GST. What is the original price of the watch including 8% GST? [?]", "answer0": "157.68", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 176, "difficulty_id": 3, "explanation": "After 15% discount, $124.10 = 85% of the original. Original price = 124.10 ÷ 17 × 20 = $146. Including 8% GST: \\(\\dfrac{108}{100}\\) × 146 = $157.68.", "hints": ["$124.10 is 85% of the original price; find 100%.", "Add 8% GST to the original price."], "source": "ACS Primary 2023 P6 Prelim Paper 2 Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q4. Key: $157.68" }, { "n": 35, "type_id": 2, "question": "Mrs Sim bought a bag for $140. She paid the cashier in $10 and $5 notes. If there were fifteen notes altogether, how many $10 notes were there? [?]", "answer0": "13", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 241, "difficulty_id": 2, "explanation": "If all 15 notes were $5, total = $75. Shortfall = 140 − 75 = $65. Each $10 note adds $5 over a $5 note: number of $10 notes = 65 ÷ 5 = 13.", "hints": ["Assume all 15 notes are $5 and find the shortfall.", "Each swap of $5 to $10 adds $5."], "source": "ACS Primary 2023 P6 Prelim Paper 2 Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q5. Key: 13" }, { "n": 36, "type_id": 2, "question": "The figure is formed by joining five identical \\(\\dfrac{3}{4}\\)-circle discs. Points A, B, C, D and E are centres of each \\(\\dfrac{3}{4}\\)-circle disc. Given that the distance between B and D is 17 cm and the distance between the first and the last disc is 48 cm, find the length AB. [?]", "answer0": "12", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 222, "difficulty_id": 3, "explanation": "BD spans 2 gaps between centres, but it equals 17 cm including a diameter overlap; the working gives 48 − 17 − 17 = 14, so the radius-related span = 14, and 14 ÷ 7 = 2 leads to radius = 15.5 − 7 = 8.5; AB = 7 + 7 − 2 = 12 cm (per the printed key).", "hints": ["Use the 48 cm total and the 17 cm BD span.", "AB is found from the disc radii along the row of centres."], "source": "ACS Primary 2023 P6 Prelim Paper 2 Q6", "image_needed": true, "image_options": false, "image_file": "p2q6.png", "image_page": 32, "image_bbox": [0.16, 0.36, 0.62, 0.56], "image_loc": "row of five three-quarter-circle discs with centres A-E, 17 cm and 48 cm marked", "notes": "Paper 2 Q6. Key: AB = 12 cm" }, { "n": 37, "type_id": 2, "question": "Serena has a monthly salary of $8650. She spent \\(\\dfrac{1}{5}\\) of her money on food. The pie chart shows how she used her monthly salary (Savings $3000, Transport $865, Rent $2422, Shopping, Food). (a) How much money did Serena spend on food? (b) What percentage of her salary did she spend on shopping? Give your answer correct to nearest 1%. [?] [?]", "answer0": "1730", "answer1": "7", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 236, "difficulty_id": 2, "explanation": "(a) Food = \\(\\dfrac{1}{5}\\) × 8650 = $1730. (b) Shopping = 8650 − 3000 − 1730 − 865 − 2422 = $633. Percentage = \\(\\dfrac{633}{8650}\\) × 100% ≈ 7%.", "hints": ["(a) Food is one-fifth of the salary.", "(b) Shopping = total − all the other sectors; then express as a percentage."], "source": "ACS Primary 2023 P6 Prelim Paper 2 Q7", "image_needed": true, "image_options": false, "image_file": "p2q7.png", "image_page": 33, "image_bbox": [0.32, 0.22, 0.66, 0.44], "image_loc": "pie chart of monthly salary (Savings, Food, Transport, Rent, Shopping)", "notes": "Paper 2 Q7. Part (b) of paper (fraction \\(\\dfrac{19}{50}\\)) omitted because it is a fraction answer; recorded the value parts (a)=$1730 and (c, percentage)=7%. answer0=food $1730, answer1=shopping percentage 7" }, { "n": 38, "type_id": 2, "question": "The figure is not drawn to scale. ABEF is a parallelogram and BCDE is a trapezium. BE//CD, AB//FD and BC//AD. DF is a straight line. ∠ADF = 42° and ∠DAF = 68°. (a) Find ∠BCD. (b) Find ∠ABE. (c) Find ∠BEF. [?] [?] [?]", "answer0": "112", "answer1": "70", "answer2": "110", "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 3, "explanation": "(a) ∠BCD = 180° − 68° = 112°. (b) ∠ABE = 180° − 68° − 42° = 70°. (c) ∠BEF = 180° − 70° = 110°.", "hints": ["Use co-interior (allied) angles between the parallel lines.", "Angles in the parallelogram are supplementary along each side."], "source": "ACS Primary 2023 P6 Prelim Paper 2 Q8", "image_needed": true, "image_options": false, "image_file": "p2q8.png", "image_page": 34, "image_bbox": [0.28, 0.16, 0.60, 0.36], "image_loc": "parallelogram ABEF with trapezium BCDE, angles 68° and 42° marked", "notes": "Paper 2 Q8. Three blanks: (a) ∠BCD=112°, (b) ∠ABE=70°, (c) ∠BEF=110°" }, { "n": 39, "type_id": 2, "question": "The distance between Town A and Town B is 1260 km. Train X travels from Town A to Town B at 8.00 a.m. at an average speed of 230 km/h. At the same time, Train Y travels from Town B to Town A at an average speed of 190 km/h. (b) How far would each train have travelled when they meet on the way? Train X: [?] km Train Y: [?] km", "answer0": "690", "answer1": "570", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 219, "difficulty_id": 3, "explanation": "Combined speed = 230 + 190 = 420 km/h. Time to meet = 1260 ÷ 420 = 3 h. Train X distance = 230 × 3 = 690 km. Train Y distance = 190 × 3 = 570 km. (They meet at 11 a.m.)", "hints": ["Add the two speeds to get the closing speed.", "Time to meet = total distance ÷ combined speed; then distance = speed × time for each train."], "source": "ACS Primary 2023 P6 Prelim Paper 2 Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q9. Part (a) 'what time did they meet' = 11 a.m. omitted (clock-time answer). Recorded part (b): Train X = 690 km, Train Y = 570 km" }, { "n": 40, "type_id": 2, "question": "The table shows the charges for making an overseas call to Australia: First 15 minutes costs $2.60; every additional minute costs p ¢ per minute. Given that p = 60, find the duration of the call Mrs Jamus made, who paid $32 for a phone call. [?]", "answer0": "64", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 241, "difficulty_id": 3, "explanation": "First 15 min costs $2.60. Remaining cost = 32 − 2.60 = $29.40 = 2940¢. At p = 60¢/min, additional minutes = 2940 ÷ 60 = 49 min. Total duration = 15 + 49 = 64 min.", "hints": ["Subtract the $2.60 base charge first, then convert to cents.", "Divide by 60¢ to get the extra minutes, then add the first 15 min."], "source": "ACS Primary 2023 P6 Prelim Paper 2 Q10", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q10. Part (a) answer is in terms of p (15 + 2940/p) min — algebraic, omitted. Recorded part (b) with p=60: 64 min" }, { "n": 41, "type_id": 2, "question": "Bottles A, B and C contain 7.35 litres of oil altogether. \\(\\dfrac{1}{5}\\) of the oil in Bottle A is transferred to Bottle B. After that, \\(\\dfrac{1}{5}\\) of the oil in Bottle B is transferred to Bottle C. Now, Bottle A has twice the amount of oil in Bottle B and Bottle B has twice the amount of oil in Bottle C. (a) How much oil was transferred from Bottle A to Bottle B? (b) How much oil was in Bottle C at first? [?] [?]", "answer0": "1.05", "answer1": "0.525", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 3, "explanation": "After all transfers A:B:C = 4:2:1 (A=2B, B=2C), total 7 units = 7.35 L, so 1 unit = 1.05 L; final A=4.2, B=2.1, C=1.05. (a) Transfer from A to B = \\(\\dfrac{1}{5}\\) of original A. Working back, the oil moved from A = 1.05 L. (b) Bottle C at first = final C − amount received = 1.05 − (\\(\\dfrac{1}{5}\\) of B's content moved) = 1.05 − 0.525 = 0.525 L.", "hints": ["Final ratio A:B:C = 4:2:1; find one unit from 7.35 L.", "Work backwards through each transfer to find the original amounts."], "source": "ACS Primary 2023 P6 Prelim Paper 2 Q11", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q11. Key (a) 1.05 L, (b) 0.525 L. answer0=transfer A to B, answer1=Bottle C at first" }, { "n": 42, "type_id": 2, "question": "Marcus is playing a video game. On his first win, he obtains 3 points. For every subsequent win, he will receive 2 additional points more than his previous win. (a) Marcus gets 6 wins in a row. What will be his score for the 6th win? (b) How many times must he win the game in a row for him to achieve 99 points? [?] [?]", "answer0": "13", "answer1": "49", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 240, "difficulty_id": 2, "explanation": "(a) Score for the nth win = 3 + 2(n−1). 6th win = 3 + 2×5 = 13 points. (b) Set 3 + 2(n−1) = 99 → 2(n−1) = 96 → n−1 = 48 → n = 49.", "hints": ["Each win's score increases by 2: 3, 5, 7, 9, ...", "Use score = 3 + 2(n−1) and solve for the required value."], "source": "ACS Primary 2023 P6 Prelim Paper 2 Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q12. Key (a) 13 points, (b) 49 wins" }, { "n": 43, "type_id": 2, "question": "The figure is made up of four squares of sides 10 cm, four quadrants and eight semicircles. Find the total area of the shaded parts. (Take π = 3.14) [?]", "answer0": "200", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 223, "difficulty_id": 3, "explanation": "Per the printed working: 5×10 − \\(\\dfrac{1}{2}\\)×3.14×5×5 = 10.75; ×2 = 21.5; +10×10 = 121.5; plus \\(\\dfrac{1}{2}\\)×3.14×10×10 = 78.5; total = 121.5 + 78.5 = 200 cm².", "hints": ["Break the shaded region into square pieces and semicircle/quadrant pieces.", "Combine the rectangular and circular parts to total 200 cm²."], "source": "ACS Primary 2023 P6 Prelim Paper 2 Q13", "image_needed": true, "image_options": false, "image_file": "p2q13.png", "image_page": 39, "image_bbox": [0.26, 0.52, 0.46, 0.78], "image_loc": "shaded composite figure (4 squares, quadrants, semicircles) — use the lower black-shaded version", "notes": "Paper 2 Q13. Key: 200 cm². Use the lower (black-shaded) version of the figure for the crop" }, { "n": 44, "type_id": 2, "question": "The container is made up of 2 cuboids and a 6-cm cube. The small cuboid has a square base of side 3 cm. The dimension of the big cuboid is 16 cm by 9 cm by 5 cm. There is 864 mℓ of water in the container and the height of the water level in the small cuboid and the cube is the same. What is the height of the water level from the base of the container? [?]", "answer0": "8.2", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 229, "difficulty_id": 3, "explanation": "Big cuboid volume = 16 × 9 × 5 = 720 cm³, which the water fills. Remaining water = 864 − 720 = 144 cm³ fills the cube (6×6 base) and small cuboid (3×3 base) above 5 cm: combined base = 36 + 9 = 45 cm². Extra height = 144 ÷ 45 = 3.2 cm. Total height = 5 + 3.2 = 8.2 cm.", "hints": ["The big cuboid (720 cm³) fills first; find the leftover water.", "The leftover rises over the combined base of the cube and small cuboid."], "source": "ACS Primary 2023 P6 Prelim Paper 2 Q14", "image_needed": true, "image_options": false, "image_file": "p2q14.png", "image_page": 40, "image_bbox": [0.14, 0.26, 0.66, 0.56], "image_loc": "stepped container of 2 cuboids and a cube with dimensions labelled", "notes": "Paper 2 Q14. Key: 8.2 cm" }, { "n": 45, "type_id": 2, "question": "Simon, Marc and Wilson sat for their Math exam. The average score of Simon and Marc was 85 marks. The average score of Marc and Wilson was 91 marks. The average score of Simon and Wilson was 82 marks. (a) What was the average mark of the three boys? (b) Simon's mark was recorded incorrectly. He was given an additional of 7.5 marks. What is the correct average score of the 3 boys? [?] [?]", "answer0": "86", "answer1": "83.5", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 205, "difficulty_id": 3, "explanation": "(a) Sum of all pairs: (S+M) + (M+W) + (S+W) = 2(S+M+W) = 170 + 182 + 164 = 516, so S+M+W = 258 and average = 258 ÷ 3 = 86. (b) Correct total = 258 − 7.5 = 250.5; correct average = 250.5 ÷ 3 = 83.5.", "hints": ["Add the three pair-totals to get 2×(sum of all three).", "Subtract the wrongly added 7.5 marks before re-averaging."], "source": "ACS Primary 2023 P6 Prelim Paper 2 Q15", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q15. Key (a) 86 marks, (b) 83.5 marks" }, { "n": 46, "type_id": 2, "question": "The figure is not drawn to scale. ABE is an equilateral triangle and BCD is an isosceles triangle. ABC and BDF are straight lines and AC//EF. ∠EBD = 90° and ∠BED = 43°. (a) Find ∠CBF. (b) Find ∠BDC. (c) Find ∠EDF. [?] [?] [?]", "answer0": "30", "answer1": "75", "answer2": "133", "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 3, "explanation": "(a) ABE equilateral → ∠ABE = 60°. On straight line ABC: ∠CBF = 180° − 60° − 90° = 30°. (b) In isosceles triangle BCD with ∠DBC = 30°, base angles = (180° − 30°) ÷ 2 = 75°, so ∠BDC = 75°. (c) ∠BDE = 180° − 90° − 43° = 47°; using the straight line BDF, ∠EDF = 180° − 47° = 133°.", "hints": ["Equilateral triangle angles are 60°; use straight-line angle sums.", "Isosceles triangle BCD has two equal base angles."], "source": "ACS Primary 2023 P6 Prelim Paper 2 Q16", "image_needed": true, "image_options": false, "image_file": "p2q16.png", "image_page": 42, "image_bbox": [0.12, 0.16, 0.74, 0.38], "image_loc": "triangles ABE and BCD with straight lines and 43° angle marked", "notes": "Paper 2 Q16. Key (a) ∠CBF=30°, (b) ∠BDC=75°, (c) ∠EDF=133°" }, { "n": 47, "type_id": 2, "question": "A box contained some twenty-cent, fifty-cent and one-dollar coins. 24% of the coins are twenty-cent coins. The ratio of the number of fifty-cent coins to the number of one-dollar coins is 7 : 12. When 62.5% of the twenty-cent coins were removed, the total number of coins decreased by 15%. In the end there were 255 coins left. (a) How many twenty-cent coins were removed? (b) How many one-dollar coins were there in the box? [?] [?]", "answer0": "45", "answer1": "144", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 214, "difficulty_id": 3, "explanation": "Removed coins = 15% of original total. Twenty-cent coins removed = 62.5% of the 24% twenty-cent coins = 0.625 × 0.24 = 0.15 of total, confirming the 15% drop. The 255 left = 85% of original, so original total = 255 ÷ 85 × 100 = 300. Twenty-cent removed = 15% × 300 = 45. (b) One-dollar coins: of the 76% non-twenty-cent (228 coins) split 7:12, one-dollar = \\(\\dfrac{12}{19}\\) × 228 = 144.", "hints": ["The 255 remaining is 85% of the original total; find 100%.", "(a) twenty-cent removed = 15% of total; (b) split the 50¢:$1 coins in ratio 7:12."], "source": "ACS Primary 2023 P6 Prelim Paper 2 Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q17. Key (a) 45 coins, (b) 144 coins" } ] }