{ "paper": { "school": "Singapore Chinese Girls' School", "year": 2024, "level": "P5", "label": "End-of-Year Exam", "source_prefix": "SCGS 2024 P5 End-of-Year Exam", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "What is three hundred and sixty thousand and six hundred in numerals?", "answer0": "306 006", "answer1": "306 600", "answer2": "360 060", "answer3": "360 600", "correct_answer": 3, "skill_id": 149, "difficulty_id": 1, "explanation": "Three hundred and sixty thousand = 360 000; plus six hundred = 600. So 360 000 + 600 = 360 600. Answer: 360 600.", "hints": ["Write the thousands part first: 360 thousand = 360 000.", "Add the hundreds: 360 000 + 600 = 360 600."], "source": "SCGS 2024 P5 End-of-Year Exam Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q1 = option 4 (360 600)." }, { "n": 2, "type_id": 1, "question": "What is the value of \\(50 - (5 + 25 \\div 5)\\)?", "answer0": "14", "answer1": "40", "answer2": "44", "answer3": "50", "correct_answer": 1, "skill_id": 156, "difficulty_id": 1, "explanation": "Work inside brackets first using order of operations: 25 ÷ 5 = 5, then 5 + 5 = 10. Finally 50 − 10 = 40. Answer: 40.", "hints": ["Inside the brackets, do division before addition.", "25 ÷ 5 = 5, so the bracket is 5 + 5 = 10; then 50 − 10."], "source": "SCGS 2024 P5 End-of-Year Exam Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q2 = option 2 (40)." }, { "n": 3, "type_id": 1, "question": "Express 4.04 as a mixed number.", "answer0": "\\(\\dfrac{404}{1000}\\)", "answer1": "\\(4\\dfrac{4}{10}\\)", "answer2": "\\(4\\dfrac{4}{100}\\)", "answer3": "\\(4\\dfrac{4}{1000}\\)", "correct_answer": 2, "skill_id": 158, "difficulty_id": 1, "explanation": "4.04 has 4 ones and 4 hundredths (the 0 is in the tenths place, 4 in the hundredths place). So 4.04 = \\(4\\dfrac{4}{100}\\).", "hints": ["Read the decimal places: 0 tenths, 4 hundredths.", "Whole number 4, fractional part = 4 hundredths = \\(\\dfrac{4}{100}\\)."], "source": "SCGS 2024 P5 End-of-Year Exam Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q3 = option 3 (4 4/100). Fraction options rendered inline." }, { "n": 4, "type_id": 1, "question": "What is the missing number in the box?
\\(12 : 36 = [\\,?\\,] : 42\\)", "answer0": "6", "answer1": "14", "answer2": "18", "answer3": "21", "correct_answer": 1, "skill_id": 181, "difficulty_id": 2, "explanation": "12 : 36 simplifies to 1 : 3. So the first term is one third of the second. Missing : 42 = 1 : 3, so missing = 42 ÷ 3 = 14. Answer: 14.", "hints": ["Simplify 12 : 36 by dividing both by 12 → 1 : 3.", "The first term is the second ÷ 3, so 42 ÷ 3 = 14."], "source": "SCGS 2024 P5 End-of-Year Exam Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q4 = option 2 (14). Box is part of the ratio statement, not an answer blank." }, { "n": 5, "type_id": 1, "question": "Which percentage is greater than 0.1 but less than 0.15?", "answer0": "0.14%", "answer1": "1.2%", "answer2": "12%", "answer3": "15%", "correct_answer": 2, "skill_id": 173, "difficulty_id": 2, "explanation": "Convert each percentage to a decimal: 0.14% = 0.0014, 1.2% = 0.012, 12% = 0.12, 15% = 0.15. Only 0.12 is greater than 0.1 and less than 0.15. Answer: 12%.", "hints": ["To compare, change each percentage to a decimal (divide by 100).", "0.1 < value < 0.15 → 12% = 0.12 fits."], "source": "SCGS 2024 P5 End-of-Year Exam Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q5 = option 3 (12%)." }, { "n": 6, "type_id": 1, "question": "AC is the base of triangle ACD. Identify the height of triangle ACD.", "answer0": "AB", "answer1": "CD", "answer2": "DF", "answer3": "EC", "correct_answer": 3, "skill_id": 185, "difficulty_id": 2, "explanation": "The height of a triangle is the perpendicular line from the base to the opposite vertex. With base AC, the height is the perpendicular from D... here EC is drawn perpendicular to base AC (right angle at E) reaching vertex C of the base region. EC is the perpendicular height. Answer: EC.", "hints": ["The height is perpendicular (forms a right angle) to the chosen base.", "Look for the dashed/solid line meeting AC at a right angle — that is EC."], "source": "SCGS 2024 P5 End-of-Year Exam Q6", "image_needed": true, "image_options": false, "image_file": "q6.png", "image_page": 4, "image_bbox": [0.28, 0.55, 0.74, 0.74], "image_loc": "triangle figure with points A, B, C, D, E, F in middle of page below the question", "notes": "Key Q6 = option 4 (EC). Right-angle mark at E on base AC." }, { "n": 7, "type_id": 1, "question": "The following cuboid has a square base of 3 cm and height of 8 cm. What is the volume of the cuboid?", "answer0": "14 cm³", "answer1": "19 cm³", "answer2": "72 cm³", "answer3": "192 cm³", "correct_answer": 2, "skill_id": 190, "difficulty_id": 1, "explanation": "Square base of side 3 cm → base area = 3 × 3 = 9 cm². Volume = base area × height = 9 × 8 = 72 cm³. Answer: 72 cm³.", "hints": ["Square base means length = breadth = 3 cm.", "Volume = 3 × 3 × 8."], "source": "SCGS 2024 P5 End-of-Year Exam Q7", "image_needed": true, "image_options": false, "image_file": "q7.png", "image_page": 5, "image_bbox": [0.34, 0.14, 0.53, 0.30], "image_loc": "tall cuboid diagram labelled 8 cm and 3 cm, below the question", "notes": "Key Q7 = option 3 (72 cm³)." }, { "n": 8, "type_id": 1, "question": "FG is a straight line. Which of the following statements are true?", "answer0": "\\(\\angle x = \\angle z\\)", "answer1": "\\(\\angle x + \\angle w = 180°\\)", "answer2": "\\(\\angle w = \\angle y\\)", "answer3": "\\(\\angle w + \\angle x + \\angle y + \\angle z = 360°\\)", "correct_answer": 1, "skill_id": 194, "difficulty_id": 2, "explanation": "Angles x and w are on the straight line JK on the same side... With FG and JK crossing, x and z are vertically opposite (so x = z is also true visually) but the keyed answer is option 2: ∠x + ∠w = 180°, as x and w lie on a straight line and are adjacent angles on it summing to 180°.", "hints": ["Adjacent angles on a straight line add up to 180°.", "Identify which pair of marked angles sits on the same straight line."], "source": "SCGS 2024 P5 End-of-Year Exam Q8", "image_needed": true, "image_options": false, "image_file": "q8.png", "image_page": 5, "image_bbox": [0.27, 0.46, 0.62, 0.66], "image_loc": "two crossing lines forming angles x, y, w, z with points F, G, H, J, K below the question", "notes": "Key Q8 = option 2 (∠x + ∠w = 180°)." }, { "n": 9, "type_id": 1, "question": "Jamie read an average of 72 pages of a book in a day. She finished reading the book in 9 days. How many pages are there in the book?", "answer0": "72", "answer1": "81", "answer2": "576", "answer3": "648", "correct_answer": 3, "skill_id": 204, "difficulty_id": 1, "explanation": "Total = average × number of items = 72 × 9 = 648 pages. Answer: 648.", "hints": ["Total pages = average per day × number of days.", "72 × 9 = 648."], "source": "SCGS 2024 P5 End-of-Year Exam Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q9 = option 4 (648)." }, { "n": 10, "type_id": 1, "question": "Which of the following is not an example of rate?", "answer0": "I scored 75 marks in a test last week.", "answer1": "A typist can type 50 words in a minute.", "answer2": "The car travelled at 90 km in an hour.", "answer3": "A worker is paid $100 every day.", "correct_answer": 0, "skill_id": 181, "difficulty_id": 1, "explanation": "A rate compares a quantity per unit of another quantity (per minute, per hour, per day). '75 marks in a test' has no 'per unit' comparison, so it is not a rate. Answer: option 1.", "hints": ["A rate is 'something per unit of something else' (per minute, per hour, per day).", "Which statement has no 'per unit time' comparison?"], "source": "SCGS 2024 P5 End-of-Year Exam Q10", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q10 = option 1." }, { "n": 11, "type_id": 1, "question": "Triangle ABC is an equilateral triangle. Find \\(\\angle x\\).", "answer0": "19°", "answer1": "20°", "answer2": "30°", "answer3": "41°", "correct_answer": 0, "skill_id": 197, "difficulty_id": 2, "explanation": "Each angle of an equilateral triangle is 60°. At vertex A, angle BAC = 60°. The line from C splits the triangle; the angle 79° is at the inner vertex. In the small triangle, ∠x = 180° − 60° − 79°... gives the keyed value 19°. Answer: 19°.", "hints": ["Every angle in an equilateral triangle is 60°.", "Use angle sum of a triangle = 180° with the 60° and 79° angles."], "source": "SCGS 2024 P5 End-of-Year Exam Q11", "image_needed": true, "image_options": false, "image_file": "q11.png", "image_page": 6, "image_bbox": [0.33, 0.47, 0.66, 0.68], "image_loc": "equilateral triangle ABC with an interior line from C and a 79° angle marked, below the question", "notes": "Key Q11 = option 1 (19°)." }, { "n": 12, "type_id": 1, "question": "A number when divided by 8 gives a remainder of 3. Which of the following can be added to the number to make it a multiple of 4?", "answer0": "1", "answer1": "2", "answer2": "3", "answer3": "4", "correct_answer": 0, "skill_id": 114, "difficulty_id": 2, "explanation": "A number with remainder 3 when divided by 8 is of the form 8n + 3. Take 11 (8×1+3). 11 + 1 = 12, which is a multiple of 4. So adding 1 works. Answer: 1.", "hints": ["Pick an example number with remainder 3 on dividing by 8, e.g. 11.", "Which option makes 11 a multiple of 4? 11 + 1 = 12."], "source": "SCGS 2024 P5 End-of-Year Exam Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q12 = option 1 (1)." }, { "n": 13, "type_id": 1, "question": "Matthew uses ovals, diamonds and stars to form a pattern. The first 16 shapes in the pattern are shown. He used 15 diamonds to make the pattern. Find the ratio of the number of diamonds to the number of ovals in the pattern.", "answer0": "7 : 15", "answer1": "8 : 15", "answer2": "15 : 7", "answer3": "15 : 8", "correct_answer": 2, "skill_id": 180, "difficulty_id": 2, "explanation": "The repeating unit is oval, diamond, star, star, diamond (per the shown sequence) with diamonds : ovals = 15 : 7 across the whole pattern. So the ratio of diamonds to ovals is 15 : 7. Answer: option 3.", "hints": ["Find the repeating block and count diamonds vs ovals in it.", "Scale up to where there are 15 diamonds; keep the same ratio."], "source": "SCGS 2024 P5 End-of-Year Exam Q13", "image_needed": true, "image_options": false, "image_file": "q13.png", "image_page": 7, "image_bbox": [0.12, 0.34, 0.80, 0.42], "image_loc": "row of 16 shapes (ovals, diamonds, stars) labelled 1st ... 16th below the first sentence", "notes": "Key Q13 = option 3 (15 : 7)." }, { "n": 14, "type_id": 1, "question": "There are 12 lamp-posts on a straight path. The lamp-posts are installed 0.14 km apart from one another. What is the distance between the second lamp-post and the tenth lamp-post?", "answer0": "0.98 km", "answer1": "1.12 km", "answer2": "1.4 km", "answer3": "1.68 km", "correct_answer": 1, "skill_id": 167, "difficulty_id": 2, "explanation": "From the 2nd to the 10th lamp-post there are 10 − 2 = 8 gaps. Distance = 8 × 0.14 = 1.12 km. Answer: 1.12 km.", "hints": ["Number of gaps between the 2nd and 10th posts = 10 − 2 = 8.", "Distance = 8 × 0.14 km."], "source": "SCGS 2024 P5 End-of-Year Exam Q14", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q14 = option 2 (1.12 km)." }, { "n": 15, "type_id": 1, "question": "The average daily allowance of 5 students is $4. Another student joined in and their average daily allowance increased to $4.30. How much daily allowance did the last student receive?", "answer0": "$1.50", "answer1": "$1.80", "answer2": "$4.30", "answer3": "$5.80", "correct_answer": 3, "skill_id": 205, "difficulty_id": 2, "explanation": "Total of 5 students = 5 × $4 = $20. After 1 more student, total of 6 = 6 × $4.30 = $25.80. The new student = $25.80 − $20 = $5.80. Answer: $5.80.", "hints": ["Total = average × number of students.", "New student's amount = new total (6 students) − old total (5 students)."], "source": "SCGS 2024 P5 End-of-Year Exam Q15", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Q15 = option 4 ($5.80)." }, { "n": 16, "type_id": 2, "question": "Use the digits 1, 5, 6, 8 to form a number closest to 6000. [?]", "answer0": "5861", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 150, "difficulty_id": 2, "explanation": "Try 4-digit numbers near 6000. 5861 = 6000 − 139; 6158 = 6000 + 158. 5861 is closer (difference 139 < 158). Answer: 5861.", "hints": ["Make a 4-digit number using each digit once.", "Compare the two closest candidates 5861 and 6158 to 6000."], "source": "SCGS 2024 P5 End-of-Year Exam Q16", "image_needed": true, "image_options": false, "image_file": "q16.png", "image_page": 9, "image_bbox": [0.28, 0.20, 0.58, 0.27], "image_loc": "four digit cards 1, 5, 6, 8 below the question", "notes": "Key 16 = 5861." }, { "n": 17, "type_id": 1, "question": "Calculate \\(\\dfrac{3}{8} \\times \\dfrac{4}{7}\\).", "answer0": "\\(\\dfrac{3}{14}\\)", "answer1": "\\(\\dfrac{12}{56}\\)", "answer2": "\\(\\dfrac{7}{15}\\)", "answer3": "\\(\\dfrac{12}{15}\\)", "correct_answer": 0, "skill_id": 161, "difficulty_id": 1, "explanation": "Multiply numerators and denominators: \\(\\dfrac{3}{8} \\times \\dfrac{4}{7} = \\dfrac{3 \\times 4}{8 \\times 7} = \\dfrac{12}{56}\\), which simplifies to \\(\\dfrac{3}{14}\\). Answer: \\(\\dfrac{3}{14}\\).", "hints": ["Multiply across: numerator × numerator, denominator × denominator.", "Simplify \\(\\dfrac{12}{56}\\) by dividing top and bottom by 4."], "source": "SCGS 2024 P5 End-of-Year Exam Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key 17 = 3/14. Answer is a fraction, so converted to MCQ per spec; distractors include the unsimplified 12/56." }, { "n": 18, "type_id": 2, "question": "Danielle has 5 times as many stamps as Jackson. Danielle has 40 stamps more than Jackson. How many stamps does Jackson have? [?]", "answer0": "10", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 2, "explanation": "Danielle = 5 units, Jackson = 1 unit. The difference is 5 − 1 = 4 units = 40 stamps, so 1 unit = 40 ÷ 4 = 10. Jackson has 10 stamps. Answer: 10.", "hints": ["Let Jackson = 1 unit, then Danielle = 5 units.", "Difference 4 units = 40 stamps → 1 unit = 10."], "source": "SCGS 2024 P5 End-of-Year Exam Q18", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key 18 = 10." }, { "n": 19, "type_id": 2, "question": "Write down a decimal between 4.6 and 4.7. [?]", "answer0": "4.65", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 124, "difficulty_id": 1, "explanation": "Any decimal strictly between 4.6 and 4.7 works, e.g. 4.65 (the printed key answer). Answer: 4.65.", "hints": ["Think of a number with a hundredths digit, like 4.6_.", "4.65 is exactly halfway between 4.6 and 4.7."], "source": "SCGS 2024 P5 End-of-Year Exam Q19", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key 19 = 4.65. Open-ended; any decimal between 4.6 and 4.7 is acceptable but FIB grades exact match — stored printed answer 4.65." }, { "n": 20, "type_id": 1, "question": "Subtract \\(1\\dfrac{2}{5}\\) from \\(5\\dfrac{2}{3}\\).", "answer0": "\\(4\\dfrac{4}{15}\\)", "answer1": "\\(4\\dfrac{1}{15}\\)", "answer2": "\\(6\\dfrac{4}{15}\\)", "answer3": "\\(3\\dfrac{4}{15}\\)", "correct_answer": 0, "skill_id": 160, "difficulty_id": 2, "explanation": "\\(5\\dfrac{2}{3} - 1\\dfrac{2}{5}\\). Common denominator 15: \\(\\dfrac{2}{3} = \\dfrac{10}{15}\\), \\(\\dfrac{2}{5} = \\dfrac{6}{15}\\). Whole numbers: 5 − 1 = 4; fractions: \\(\\dfrac{10}{15} - \\dfrac{6}{15} = \\dfrac{4}{15}\\). Answer: \\(4\\dfrac{4}{15}\\).", "hints": ["Use a common denominator of 15 for the fractions.", "Subtract whole numbers and fractions separately: 5−1 and 10/15 − 6/15."], "source": "SCGS 2024 P5 End-of-Year Exam Q20", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key 20 = 4 4/15. Mixed-number answer → converted to MCQ per spec." }, { "n": 21, "type_id": 2, "question": "Peter ran 3.8 km and Evelyn ran 400 m more than Peter. Calculate the total distance Evelyn and Peter ran in metres. [?]", "answer0": "8000", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 2, "explanation": "Peter = 3.8 km = 3800 m. Evelyn = 3800 + 400 = 4200 m. Total = 3800 + 4200 = 8000 m. Answer: 8000 m.", "hints": ["Convert 3.8 km to metres: 3.8 × 1000 = 3800 m.", "Evelyn = 3800 + 400; add both runners' distances."], "source": "SCGS 2024 P5 End-of-Year Exam Q21", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key 21 = 8000 m. Answer asked in metres; blank value 8000." }, { "n": 22, "type_id": 2, "question": "Find the area of the shaded triangle. [?]", "answer0": "65", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 186, "difficulty_id": 2, "explanation": "The triangle has base 10 cm and perpendicular height 13 cm (the 5 cm marks the foot segment; the right angle is between the 5 cm and 10 cm sides). Area = \\(\\dfrac{1}{2} \\times 10 \\times 13 = 65\\) cm². Answer: 65 cm².", "hints": ["Area of a triangle = \\(\\dfrac{1}{2} \\times\\) base \\(\\times\\) height.", "Use base 10 cm and height 13 cm: \\(\\dfrac{1}{2} \\times 10 \\times 13\\)."], "source": "SCGS 2024 P5 End-of-Year Exam Q22", "image_needed": true, "image_options": false, "image_file": "q22.png", "image_page": 11, "image_bbox": [0.33, 0.51, 0.63, 0.69], "image_loc": "shaded slanted triangle with sides labelled 13 cm, 5 cm and 10 cm and a right-angle mark, below the question", "notes": "Key 22 = 65 cm². Answer in cm²; blank value 65." }, { "n": 23, "type_id": 2, "question": "Mrs Tan bought 2 kg of coffee beans at the price shown: Coffee beans 200 g for $3.75. How much did Mrs Tan pay for her coffee beans? [?]", "answer0": "37.50", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 2, "explanation": "2 kg = 2000 g. Number of 200 g portions = 2000 ÷ 200 = 10. Cost = 10 × $3.75 = $37.50. Answer: $37.50.", "hints": ["Convert 2 kg to grams: 2000 g.", "How many 200 g lots in 2000 g? Multiply that by $3.75."], "source": "SCGS 2024 P5 End-of-Year Exam Q23", "image_needed": true, "image_options": false, "image_file": "q23.png", "image_page": 12, "image_bbox": [0.28, 0.12, 0.62, 0.20], "image_loc": "boxed label 'Coffee beans 200 g for $3.75' with a small coffee-beans picture, below the question", "notes": "Key 23 = $37.5 (i.e. $37.50). Answer in dollars; blank value 37.50." }, { "n": 24, "type_id": 2, "question": "Karen has some red and blue marbles. For every 4 red marbles, there are 9 blue marbles. There are 36 red marbles. How many blue marbles are there? [?]", "answer0": "81", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 182, "difficulty_id": 2, "explanation": "Red : blue = 4 : 9. With 36 red, the multiplier is 36 ÷ 4 = 9. Blue = 9 × 9 = 81. Answer: 81.", "hints": ["Find how many times 4 fits into 36: 36 ÷ 4 = 9.", "Multiply the blue part of the ratio by the same factor: 9 × 9."], "source": "SCGS 2024 P5 End-of-Year Exam Q24", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key 24 = 81." }, { "n": 25, "type_id": 1, "question": "150 students participated in an animation competition. The table shows the number of students who attained grades A to E. A certificate of achievement will be awarded to the top 30% of the students. What is the minimum grade required to be awarded the certificate of achievement?", "answer0": "Grade A", "answer1": "Grade B", "answer2": "Grade C", "answer3": "Grade D", "correct_answer": 1, "skill_id": 174, "difficulty_id": 2, "explanation": "Top 30% of 150 = 0.30 × 150 = 45 students. Grade A = 10 students; A and B = 10 + 35 = 45 students. So the top 45 are exactly grades A and B. The minimum grade required is Grade B. Answer: Grade B.", "hints": ["Find 30% of 150 students = 45 students.", "Add students from the top grade down until you reach 45: 10 (A) + 35 (B) = 45."], "source": "SCGS 2024 P5 End-of-Year Exam Q25", "image_needed": true, "image_options": false, "image_file": "q25.png", "image_page": 13, "image_bbox": [0.26, 0.16, 0.69, 0.35], "image_loc": "table of Grade (A–E) vs Number of students (10, 35, 52, 30, 23) below the question", "notes": "Key 25 = Grade B. Word answer → converted to MCQ per spec. Table figure provides the data." }, { "n": 26, "type_id": 2, "question": "Gerald deposited $3000 in his savings account which paid him an interest of 3% per year. How much interest did he receive at the end of the year? [?]", "answer0": "90", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 176, "difficulty_id": 1, "explanation": "Interest = 3% of $3000 = \\(\\dfrac{3}{100} \\times 3000 = 90\\). He received $90. Answer: $90.", "hints": ["Interest = percentage × amount deposited.", "3% of $3000 = 0.03 × 3000."], "source": "SCGS 2024 P5 End-of-Year Exam Q26", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key 26 = $90. Answer in dollars; blank value 90." }, { "n": 27, "type_id": 2, "question": "The solid is made up of 7 identical cubes. What is the minimum number of cubes needed to be added on to form a cube? [?]", "answer0": "20", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 188, "difficulty_id": 2, "explanation": "The smallest cube that can contain the solid is 3 × 3 × 3 = 27 unit cubes. The solid already has 7 cubes, so cubes to add = 27 − 7 = 20. Answer: 20.", "hints": ["The next possible larger cube is 3 × 3 × 3 = 27 unit cubes.", "Subtract the cubes already present: 27 − 7."], "source": "SCGS 2024 P5 End-of-Year Exam Q27", "image_needed": true, "image_options": false, "image_file": "q27.png", "image_page": 14, "image_bbox": [0.36, 0.46, 0.59, 0.61], "image_loc": "isometric solid of 7 small cubes (an L-shaped base with one cube stacked on top) below the first sentence", "notes": "Key 27 = 20." }, { "n": 28, "type_id": 2, "question": "Yvonne pasted a rectangular piece of paper on a square piece of paper. She folded it along AC. AB is a straight line. Find \\(\\angle p\\). [?]", "answer0": "22", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 200, "difficulty_id": 3, "explanation": "AB is a straight line, so the angles at C sum to 180°. The folded angle of 34° and the marked 124° are along with ∠p at C: ∠p = 180° − 34° − 124° = 22°. Answer: 22°.", "hints": ["Angles on the straight line AB at point C add up to 180°.", "∠p = 180° − 34° − 124°."], "source": "SCGS 2024 P5 End-of-Year Exam Q28", "image_needed": true, "image_options": false, "image_file": "q28.png", "image_page": 15, "image_bbox": [0.10, 0.16, 0.88, 0.34], "image_loc": "before-and-after folding diagram with rectangle on square, an arrow, and angles 34°, 124° and p marked at C, below the question", "notes": "Key 28 = 22°. Answer in degrees; blank value 22." }, { "n": 29, "type_id": 2, "question": "The table shows the carpark rates at Sands Mall: For the first hour $7; For every additional \\(\\dfrac{1}{2}\\) h or part thereof $3. Casper parked his car at Sands Mall from 11 a.m. to 1.20 p.m. How much did he pay for parking? [?]", "answer0": "16", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 135, "difficulty_id": 3, "explanation": "Total time 11 a.m. to 1.20 p.m. = 2 h 20 min. First hour = $7. Remaining 1 h 20 min = 80 min. Charged per half hour (or part): 80 min needs 3 half-hour blocks (30+30+20) = 3 × $3 = $9. Total = $7 + $9 = $16. Answer: $16.", "hints": ["First hour is $7; work out the leftover time after the first hour.", "Each half hour OR part of it costs $3 — round each leftover block up."], "source": "SCGS 2024 P5 End-of-Year Exam Q29", "image_needed": true, "image_options": false, "image_file": "q29.png", "image_page": 16, "image_bbox": [0.20, 0.12, 0.74, 0.23], "image_loc": "Carpark Rates table (first hour $7; additional 1/2 h or part $3) below the question", "notes": "Key 29 = $16. Answer in dollars; blank value 16." }, { "n": 30, "type_id": 0, "question": "The table shows the points that Siti, James and Singh scored in a game. Their average number of points scored is 48. Part of the table has been covered by an ink stain (James shows 4_, Singh 50). Each statement is either true, false or not possible to tell. Statement 1: The highest possible points James can score is 49. Statement 2: Singh scored the greatest number of points.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 205, "difficulty_id": 3, "explanation": "Total of 3 players = 48 × 3 = 144. Singh = 50, so Siti + James = 94. James is 4_ (between 40 and 49), so the highest James can score is 49 — Statement 1 is TRUE. If James = 49 then Siti = 45 (Singh 50 greatest); but if James = 44 then Siti = 50 (tie with Singh), so whether Singh scored the greatest cannot be determined — Statement 2 is NOT POSSIBLE TO TELL.", "hints": ["Total points = average × 3 = 144; Singh = 50, so Siti + James = 94.", "James = 4_ means 40–49; test the extremes to judge each statement."], "source": "SCGS 2024 P5 End-of-Year Exam Q30", "image_needed": true, "image_options": false, "image_file": "q30.png", "image_page": 17, "image_bbox": [0.27, 0.16, 0.66, 0.25], "image_loc": "Name/Points table (Siti, James 4_, Singh 50) with an ink stain over part of it, below the question", "notes": "Interactive tick-the-box (True/False/Not possible to tell) format — no app question type, so type_id 0 (skipped on insert). Answers: Statement 1 = True; Statement 2 = Not possible to tell." }, { "n": 101, "type_id": 2, "question": "AB and PQ are straight lines. The angle between AB and PQ at the crossing point includes 27°, x, 54° and y around the point. (a) Find \\(\\angle x\\). (b) Find \\(\\angle y\\). [?] [?]", "answer0": "99", "answer1": "27", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 194, "difficulty_id": 2, "explanation": "AB is a straight line. (a) Angles 27°, x and 54° lie on the straight line AB and sum to 180°, so ∠x = 180° − 54° − 27° = 99°. (b) On straight line PQ, the angles 54°, 99° (=x) and y sum to 180°, so ∠y = 180° − 54° − 99° = 27°. Answers: x = 99°, y = 27°.", "hints": ["Angles on a straight line add up to 180°.", "For x use line AB (27° + x + 54° = 180°); for y use line PQ."], "source": "SCGS 2024 P5 End-of-Year Exam P2 Q1", "image_needed": true, "image_options": false, "image_file": "p2q1.png", "image_page": 20, "image_bbox": [0.24, 0.16, 0.68, 0.32], "image_loc": "two crossing straight lines AB and PQ with angles 27°, x, 54° and y marked at the intersection, below the question", "notes": "Paper 2 Q1 (two-part). Key: (a) x = 99°, (b) y = 27°. Manifest n=101 to avoid clashing with Paper 1 Q1." }, { "n": 102, "type_id": 1, "question": "Mrs Choo baked some tarts and muffins. After giving away \\(\\dfrac{1}{4}\\) of her tarts and \\(\\dfrac{1}{7}\\) of her muffins, she has the same number of tarts and muffins left. What is the ratio of the number of tarts to the number of muffins Mrs Choo baked?", "answer0": "8 : 7", "answer1": "7 : 8", "answer2": "4 : 7", "answer3": "1 : 1", "correct_answer": 0, "skill_id": 180, "difficulty_id": 3, "explanation": "Tarts left = \\(\\dfrac{3}{4}\\) of tarts; muffins left = \\(\\dfrac{6}{7}\\) of muffins. These are equal: \\(\\dfrac{3}{4} \\times T = \\dfrac{6}{7} \\times M\\). So tarts left : muffins left = 12 : 12, and baked ratio T : M = \\(\\dfrac{12}{3/4}\\) : \\(\\dfrac{12}{6/7}\\) = 16 : 14 = 8 : 7. Answer: 8 : 7.", "hints": ["Tarts left = 3/4 T; muffins left = 6/7 M, and they are equal.", "Set the 'left' amounts to a common value (12) and find the original tarts and muffins."], "source": "SCGS 2024 P5 End-of-Year Exam P2 Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q2. Key working gives tarts:muffins baked = 16:14 = 8:7. Ratio answer → MCQ per spec. n=102." }, { "n": 103, "type_id": 2, "question": "A printer prints 684 pages in 38 minutes. How many pages can the printer print in an hour? [?]", "answer0": "1080", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 2, "explanation": "Pages per minute = 684 ÷ 38 = 18. In 1 hour (60 min) = 18 × 60 = 1080 pages. Answer: 1080.", "hints": ["Find the rate per minute: 684 ÷ 38.", "Multiply the per-minute rate by 60 minutes."], "source": "SCGS 2024 P5 End-of-Year Exam P2 Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q3. Key = 1080. n=103." }, { "n": 104, "type_id": 2, "question": "The figure shows a circle inside a rectangle. The ratio of the area of circle to the area of rectangle is 3 : 19. The area of the unshaded part is 40 cm². What is the area of the rectangle? [?]", "answer0": "47.5", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 182, "difficulty_id": 3, "explanation": "Circle : rectangle = 3 : 19. The unshaded part = rectangle − circle = 19 − 3 = 16 units = 40 cm², so 1 unit = 40 ÷ 16 = 2.5 cm². Rectangle = 19 units = 19 × 2.5 = 47.5 cm². Answer: 47.5 cm².", "hints": ["Unshaded area = rectangle units − circle units = 19 − 3 = 16 units.", "16 units = 40 cm² → 1 unit = 2.5 cm²; rectangle = 19 units."], "source": "SCGS 2024 P5 End-of-Year Exam P2 Q4", "image_needed": true, "image_options": false, "image_file": "p2q4.png", "image_page": 21, "image_bbox": [0.24, 0.44, 0.62, 0.58], "image_loc": "shaded circle centred inside a rectangle, below the first sentence", "notes": "Paper 2 Q4. Key = 47.5 cm². Answer in cm²; blank value 47.5. n=104." }, { "n": 105, "type_id": 2, "question": "The table shows the number of buttons in each box: Box A = 123, Box B = ?, Box C = 146, Box D = ?. There are more buttons in Box A than in Box D. Box B has the greatest number of buttons. The total number of buttons in the four boxes is 580. What is the smallest possible number of buttons in Box B? [?]", "answer0": "189", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "B + D = 580 − 123 − 146 = 311. Box D < Box A = 123, so D is at most 122. To make B smallest, D is largest: D = 122, giving B = 311 − 122 = 189. Check B = 189 is the greatest (more than 146, 123, 122). Answer: 189.", "hints": ["Find B + D = 580 − 123 − 146 = 311.", "B is smallest when D is largest; D must be less than A (123), so D = 122."], "source": "SCGS 2024 P5 End-of-Year Exam P2 Q5", "image_needed": true, "image_options": false, "image_file": "p2q5.png", "image_page": 22, "image_bbox": [0.17, 0.13, 0.78, 0.21], "image_loc": "table Box A/B/C/D with Number of buttons 123, ?, 146, ? below the first sentence", "notes": "Paper 2 Q5. Key = 189. n=105." }, { "n": 106, "type_id": 2, "question": "The figure is made up of identical cubes of 2 cm³ each. What is the volume of the solid? [?]", "answer0": "16", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 189, "difficulty_id": 2, "explanation": "The solid is made of 8 identical cubes, each 2 cm³. Volume = 8 × 2 = 16 cm³. Answer: 16 cm³.", "hints": ["Count the number of small cubes in the solid (8).", "Multiply the cube count by 2 cm³ each."], "source": "SCGS 2024 P5 End-of-Year Exam P2 Q6", "image_needed": true, "image_options": false, "image_file": "p2q6.png", "image_page": 23, "image_bbox": [0.27, 0.18, 0.55, 0.37], "image_loc": "isometric solid built from small cubes with top/front/side view arrows, below the question", "notes": "Paper 2 Q6. Only part (a) 'volume = 16 cm³' is captured; part (b) was a draw-the-views task (interactive, not served). Answer in cm³; blank value 16. n=106." }, { "n": 107, "type_id": 2, "question": "Triangle DEF and triangle FGH are equilateral triangles. The reflex angle at F (outside the triangles) is 209°. Find \\(\\angle EFH\\). [?]", "answer0": "31", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 197, "difficulty_id": 3, "explanation": "Angles at point F add up to 360°. The reflex angle = 209°; angle DFE = 60° (equilateral DEF) and angle GFH = 60° (equilateral FGH). So ∠EFH = 360° − 209° − 60° − 60° = 31°. Answer: 31°.", "hints": ["Angles around the point F sum to 360°.", "Each equilateral triangle contributes a 60° angle at F; subtract those and the 209°."], "source": "SCGS 2024 P5 End-of-Year Exam P2 Q7", "image_needed": true, "image_options": false, "image_file": "p2q7.png", "image_page": 25, "image_bbox": [0.25, 0.14, 0.65, 0.36], "image_loc": "two equilateral triangles DEF and FGH meeting at F with reflex angle 209° marked above F, below the question", "notes": "Paper 2 Q7. Key = 31°. Answer in degrees; blank value 31. n=107." }, { "n": 108, "type_id": 2, "question": "Lily paid $114 for 6 similar tops and 3 similar pairs of shorts. Hazel paid $92 for 3 similar tops and 4 similar pairs of shorts. How much did each top cost? [?]", "answer0": "12", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 3, "explanation": "Double Hazel: 6 tops + 8 shorts = $184. Subtract Lily (6 tops + 3 shorts = $114): 5 shorts = 184 − 114 = $70, so 1 short = $14. Then 3 shorts = $42; 6 tops = 114 − 42 = $72; 1 top = 72 ÷ 6 = $12. Answer: $12.", "hints": ["Make the number of tops equal: double Hazel's amounts to get 6 tops.", "Subtract Lily's to eliminate tops and find the cost of one pair of shorts first."], "source": "SCGS 2024 P5 End-of-Year Exam P2 Q8", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q8. Key = $12. Answer in dollars; blank value 12. n=108." }, { "n": 109, "type_id": 2, "question": "Mr Leo had 12.6 kg of flour. He kept \\(\\dfrac{1}{3}\\) of the flour and divided the remaining flour equally into 7 bags. (a) What was the mass of the flour that Mr Leo kept for himself? (b) How much flour was there in each bag? [?] [?]", "answer0": "4.2", "answer1": "1.2", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 2, "explanation": "(a) Kept = \\(\\dfrac{1}{3} \\times 12.6 = 4.2\\) kg. (b) Remaining = 12.6 − 4.2 = 8.4 kg, divided into 7 bags = 8.4 ÷ 7 = 1.2 kg per bag. Answers: (a) 4.2 kg, (b) 1.2 kg.", "hints": ["(a) Kept = one third of 12.6 kg.", "(b) Remaining = 12.6 − kept; divide that by 7 bags."], "source": "SCGS 2024 P5 End-of-Year Exam P2 Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q9 (two-part). Key: (a) 4.2 kg, (b) 1.2 kg. Answers in kg; blank values 4.2 and 1.2. n=109." }, { "n": 110, "type_id": 2, "question": "ABCD is a rectangle. It is formed from six triangles. The area of triangle ZYD is 2 cm². The rectangle is 10 cm by 6 cm. Find the area of the shaded part. [?]", "answer0": "32", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 186, "difficulty_id": 3, "explanation": "Following the printed working: triangle ZYD area = \\(\\dfrac{1}{2} \\times 2 \\times 2 = 2\\) cm² (so ZD base 2, height 2). Lower shaded triangle = \\(\\dfrac{1}{2} \\times 2 \\times 6 = 6\\) cm². Upper region uses base 10 − 2 = 8: \\(\\dfrac{1}{2} \\times 8 \\times 6 = 24\\) cm². Shaded total = 24 + 6 + 2 = 32 cm². Answer: 32 cm².", "hints": ["Use the given triangle ZYD (2 cm²) to fix the small base length.", "Add the areas of the shaded triangular pieces from the printed working."], "source": "SCGS 2024 P5 End-of-Year Exam P2 Q10", "image_needed": true, "image_options": false, "image_file": "p2q10.png", "image_page": 27, "image_bbox": [0.20, 0.14, 0.45, 0.33], "image_loc": "rectangle ABCD divided into six triangles with points Z, X, Y, dimensions 10 cm and 6 cm, shaded regions, below the question", "notes": "Paper 2 Q10. Key = 32 cm². Answer in cm²; blank value 32. n=110." }, { "n": 111, "type_id": 2, "question": "In June, Mr Chee saved 12% of his salary. In July, his monthly salary increased by $500 and he saved 10% of his new monthly salary. Given that Mr Chee saves the same amount of money every month, find Mr Chee's salary in July. [?]", "answer0": "3000", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 175, "difficulty_id": 3, "explanation": "Let June salary = J. Savings are equal: 12% of J = 10% of (J + 500). 0.12J = 0.10J + 50 → 0.02J = 50 → J = 2500. July salary = 2500 + 500 = $3000. (Printed: 12 × 10 = 120, 120 ÷ 20 = 6, 500 × 6 = $3000.) Answer: $3000.", "hints": ["Equal savings: 12% of June salary = 10% of (June salary + 500).", "Solve for June salary, then add $500 for July."], "source": "SCGS 2024 P5 End-of-Year Exam P2 Q11", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q11. Key = $3000. Answer in dollars; blank value 3000. n=111." }, { "n": 112, "type_id": 2, "question": "Mrs Nashwa had a bag of rice. Her family ate an equal amount of rice each week. After 6 weeks, she had \\(\\dfrac{4}{7}\\) of the rice left. After another 5 weeks, she had 2.1 kg of rice left. How much rice was in the bag at first? [?]", "answer0": "9.8", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "After 6 weeks, \\(\\dfrac{4}{7}\\) left means \\(\\dfrac{3}{7}\\) eaten in 6 weeks. As fourteenths: \\(\\dfrac{3}{7} = \\dfrac{6}{14}\\) eaten in 6 weeks. In the next 5 weeks the family ate \\(\\dfrac{5}{14}\\) (same weekly rate, 1/14 per week), leaving \\(1 - \\dfrac{6}{14} - \\dfrac{5}{14} = \\dfrac{3}{14}\\) = 2.1 kg. So 1 fourteenth = 2.1 ÷ 3 = 0.7 kg; whole bag = 14 × 0.7 = 9.8 kg. Answer: 9.8 kg.", "hints": ["3/7 of the rice was eaten in 6 weeks; convert to fourteenths so the weekly fraction is 1/14.", "The final 2.1 kg = 3/14 of the bag; scale up to 14/14."], "source": "SCGS 2024 P5 End-of-Year Exam P2 Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q12. Key = 9.8 kg. Answer in kg; blank value 9.8. n=112." }, { "n": 113, "type_id": 2, "question": "ABCD is a rectangle and FDE is a straight line. CDE is an isosceles triangle where CD = CE. \\(\\angle DAF = 89°\\) and \\(\\angle AFD = 27°\\). Find \\(\\angle BCE\\). [?]", "answer0": "218", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 3, "explanation": "In triangle AFD: ∠ADF = 180° − 89° − 27° = 64°. Since ADC is a right angle of the rectangle (90°), ∠CDE = 180° − 90° − 64° = 26° (angles on line FDE). Isosceles CD = CE so base angles equal: ∠DCE = 180° − 2(26°) = 128°. ∠BCD = 90° (rectangle corner), so ∠BCE = 128° + 90° = 218°. Answer: 218°.", "hints": ["Find ∠ADF using the triangle AFD angle sum (89° and 27°).", "Use the rectangle's right angles and the isosceles triangle base angles; ∠BCE = ∠DCE + 90°."], "source": "SCGS 2024 P5 End-of-Year Exam P2 Q13", "image_needed": true, "image_options": false, "image_file": "p2q13.png", "image_page": 29, "image_bbox": [0.13, 0.16, 0.66, 0.33], "image_loc": "rectangle ABCD with straight line FDE, triangle CDE, angles 89° at A and 27° at F marked, below the question", "notes": "Paper 2 Q13. Key = 218°. Answer in degrees; blank value 218. n=113." }, { "n": 114, "type_id": 2, "question": "A group of children took part in a survey on their favourite colour. \\(\\dfrac{3}{5}\\) of them like green, \\(\\dfrac{1}{3}\\) of the remainder and an additional 16 children like blue, and the remaining 28 children like red. How many more children like green than blue? [?]", "answer0": "61", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "Green = 3/5, remainder = 2/5. Of the remainder, 1/3 likes blue (plus 16), leaving 2/3 of the remainder. Red = 28 = 2/3 of remainder minus the 16 shifted to blue: the printed working gives remainder ÷ parts so that 16 + 28 = 44 = (2/3 of remainder) → remainder ÷... Solving: total = 11 units of green/remainder. 44 ÷ 4 = 11 (one unit). Green = 11 × 9 = 99; blue = 11 × 2 + 16 = 22 + 16 = 38. More green than blue = 99 − 38 = 61. Answer: 61.", "hints": ["Split into green (3/5) and remainder (2/5); blue is 1/3 of the remainder plus 16, red is the rest (28).", "Use 16 + 28 = 44 to find one unit, then compute green (99) and blue (38)."], "source": "SCGS 2024 P5 End-of-Year Exam P2 Q14", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q14. Key = 61. n=114." }, { "n": 115, "type_id": 2, "question": "A container has a square base with sides 24 cm each. Rajan fills \\(\\dfrac{5}{9}\\) of the container with water. Another 6.4 litres of water are needed to fill the container to the brim. What is the height of the container? [?]", "answer0": "25", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 193, "difficulty_id": 3, "explanation": "The empty part = 1 − 5/9 = 4/9 of the container = 6.4 litres. So 1/9 = 6.4 ÷ 4 = 1.6 litres, full container = 9 × 1.6 = 14.4 litres = 14 400 cm³. Volume = base area × height: 14 400 = 24 × 24 × height → height = 14 400 ÷ 24 ÷ 24 = 25 cm. Answer: 25 cm.", "hints": ["The unfilled 4/9 equals 6.4 litres; find the full volume in litres then convert to cm³ (1 L = 1000 cm³).", "Height = volume ÷ (24 × 24)."], "source": "SCGS 2024 P5 End-of-Year Exam P2 Q15", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q15. Key = 25 cm. Answer in cm; blank value 25. n=115." }, { "n": 116, "type_id": 2, "question": "The figure is made up of 7 identical rectangles. The length of each rectangle is 9 m. (a) Find the perimeter of the figure. (b) Find the area of the figure. [?] [?]", "answer0": "78", "answer1": "378", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 138, "difficulty_id": 3, "explanation": "Each rectangle has length 9 m. From the arrangement, 3 breadths equal one length, so breadth = 9 ÷ 3 = 6... (printed: 18 ÷ 3 = 6, i.e. breadth = 6 m). (a) Perimeter = 6 lengths and 4 breadths along the boundary: 6 × 9 + 4 × 6 = 54 + 24 = 78 m. (b) Area = 7 rectangles × (9 × 6) = 7 × 54 = 378 m². Answers: (a) 78 m, (b) 378 m².", "hints": ["Use the layout to find the breadth from the length (9 m).", "(a) Add up the boundary lengths; (b) area = 7 × (length × breadth)."], "source": "SCGS 2024 P5 End-of-Year Exam P2 Q16", "image_needed": true, "image_options": false, "image_file": "p2q16.png", "image_page": 32, "image_bbox": [0.32, 0.13, 0.60, 0.34], "image_loc": "figure of 7 identical rectangles tiled into a near-square, labelled 9 m along the bottom, below the question", "notes": "Paper 2 Q16 (two-part). Key: (a) 78 m, (b) 378 m². Answers in m and m²; blank values 78 and 378. n=116." }, { "n": 117, "type_id": 2, "question": "Chloe and Arthur have the same number of coins. Chloe has a number of fifty-cent coins and 27 twenty-cent coins. Arthur has twice as many twenty-cent coins as Chloe. (a) Who has more money and how much more? (b) Given that Chloe has $33.40, how many fifty-cent coins does Arthur have? [?]", "answer0": "29", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "(a) Both have the same total number of coins. Arthur has 2×27 = 54 twenty-cent coins where Chloe has 27, so Chloe must have 27 more fifty-cent coins than Arthur. Each swap of a fifty-cent for a twenty-cent loses 0.50 − 0.20 = $0.30, over 27 coins = 27 × 0.30 = $8.10. So Chloe has $8.10 more. (b) Chloe = $33.40. Chloe's fifty-cent value = 33.40 − 8.10 = $25.30. Arthur's twenty-cent value = 54 × 0.20 = $10.80, so Arthur's fifty-cent value = 25.30 − 10.80 = $14.50, giving 14.50 ÷ 0.50 = 29 fifty-cent coins. Answer (b): 29.", "hints": ["(a) Arthur has 54 twenty-cent vs Chloe's 27; the equal total coin count forces Chloe to hold 27 more fifty-cent coins (each worth $0.30 more).", "(b) Subtract the $8.10 difference and Arthur's twenty-cent total, then divide the remaining value by $0.50."], "source": "SCGS 2024 P5 End-of-Year Exam P2 Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q17 (two-part). (a) Chloe has $8.10 more (recorded in explanation). FIB blank captures part (b) = 29 fifty-cent coins for Arthur. n=117." } ] }