{ "paper": { "school": "Maha Bodhi", "year": 2022, "level": "P5", "label": "Weighted Assessment 2", "source_prefix": "Maha Bodhi 2022 P5 Weighted Assessment 2", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "Which of the following numbers is a factor of both 48 and 54?", "answer0": "9", "answer1": "8", "answer2": "3", "answer3": "4", "correct_answer": 2, "skill_id": 151, "difficulty_id": 1, "explanation": "Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54. A common factor must divide both. 3 divides 48 (48 ÷ 3 = 16) and divides 54 (54 ÷ 3 = 18). 9 divides 54 but not 48; 8 divides 48 but not 54; 4 divides 48 but not 54. Answer: 3 (option 3).", "hints": ["List the factors of each number separately.", "Look for a number that appears in both factor lists."], "source": "Maha Bodhi 2022 P5 Weighted Assessment 2 Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: option 3 = 3." }, { "n": 2, "type_id": 1, "question": "What is the value of \\(84 - (18 \\times 2) \\div 6 + 3\\)?", "answer0": "11", "answer1": "75", "answer2": "80", "answer3": "81", "correct_answer": 3, "skill_id": 155, "difficulty_id": 2, "explanation": "Apply order of operations. Brackets first: \\(18 \\times 2 = 36\\). Then division: \\(36 \\div 6 = 6\\). Then left to right: \\(84 - 6 + 3 = 78 + 3 = 81\\). Answer: 81 (option 4).", "hints": ["Do the brackets, then division, before addition and subtraction.", "Work the addition and subtraction from left to right."], "source": "Maha Bodhi 2022 P5 Weighted Assessment 2 Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: option 4 = 81." }, { "n": 3, "type_id": 1, "question": "Which of the following fractions is closest to 1?", "answer0": "\\(\\dfrac{3}{4}\\)", "answer1": "\\(\\dfrac{4}{3}\\)", "answer2": "\\(\\dfrac{5}{6}\\)", "answer3": "\\(\\dfrac{6}{5}\\)", "correct_answer": 2, "skill_id": 158, "difficulty_id": 2, "explanation": "Find how far each fraction is from 1. \\(\\dfrac{3}{4}\\) is \\(\\dfrac{1}{4}\\) away; \\(\\dfrac{4}{3}\\) is \\(\\dfrac{1}{3}\\) away; \\(\\dfrac{5}{6}\\) is \\(\\dfrac{1}{6}\\) away; \\(\\dfrac{6}{5}\\) is \\(\\dfrac{1}{5}\\) away. The smallest gap is \\(\\dfrac{1}{6}\\), so \\(\\dfrac{5}{6}\\) is closest to 1. Answer: \\(\\dfrac{5}{6}\\) (option 3).", "hints": ["Work out the difference between each fraction and 1.", "The closest fraction has the smallest difference from 1."], "source": "Maha Bodhi 2022 P5 Weighted Assessment 2 Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: option 3 = 5/6." }, { "n": 4, "type_id": 1, "question": "Express \\(30\\,\\ell\\,35\\) ml in ml.", "answer0": "30 350 ml", "answer1": "30 035 ml", "answer2": "3 350 ml", "answer3": "3 035 ml", "correct_answer": 1, "skill_id": 192, "difficulty_id": 1, "explanation": "1 litre = 1000 ml, so 30 litres = 30 000 ml. Add the extra 35 ml: \\(30\\,000 + 35 = 30\\,035\\) ml. Answer: 30 035 ml (option 2).", "hints": ["1 litre equals 1000 ml.", "Convert the litres to ml, then add the leftover ml."], "source": "Maha Bodhi 2022 P5 Weighted Assessment 2 Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: option 2 = 30 035 ml." }, { "n": 5, "type_id": 1, "question": "\\(24 : 42 = \\square : 56\\)
What is the missing number in the box?", "answer0": "38", "answer1": "32", "answer2": "7", "answer3": "4", "correct_answer": 1, "skill_id": 181, "difficulty_id": 2, "explanation": "Simplify \\(24 : 42\\) by dividing both by 6: \\(4 : 7\\). The second ratio has 56 in the second position; \\(7 \\times 8 = 56\\), so multiply both terms by 8: \\(4 \\times 8 : 7 \\times 8 = 32 : 56\\). The missing number is 32. Answer: 32 (option 2).", "hints": ["Simplify 24 : 42 to its lowest terms first.", "Find what the simplified ratio is multiplied by to get 56 in the second term."], "source": "Maha Bodhi 2022 P5 Weighted Assessment 2 Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: option 2 = 32." }, { "n": 6, "type_id": 1, "question": "ABCD is a square of side 12 cm. EC is \\(\\dfrac{1}{3}\\) the length of DC. Find the area of triangle BCE.", "answer0": "24 cm²", "answer1": "48 cm²", "answer2": "72 cm²", "answer3": "144 cm²", "correct_answer": 0, "skill_id": 186, "difficulty_id": 2, "explanation": "DC = 12 cm, so \\(EC = \\dfrac{1}{3} \\times 12 = 4\\) cm. Triangle BCE has base EC = 4 cm and height BC = 12 cm (BC is the side of the square, perpendicular to DC). Area \\(= \\dfrac{1}{2} \\times 4 \\times 12 = 24\\) cm². Answer: 24 cm² (option 1).", "hints": ["The base of triangle BCE is EC, one-third of DC.", "Area of a triangle = 1/2 × base × height; the height is the square's side BC."], "source": "Maha Bodhi 2022 P5 Weighted Assessment 2 Q6", "image_needed": true, "image_options": false, "image_file": "q6.png", "image_page": 3, "image_bbox": [0.30, 0.18, 0.52, 0.32], "image_loc": "Square ABCD with shaded triangle BCE, upper-left area of page below the question text.", "notes": "Answer key: option 1 = 24 cm²." }, { "n": 7, "type_id": 1, "question": "What is the sum of the first two common multiples of 4 and 6?", "answer0": "24", "answer1": "36", "answer2": "48", "answer3": "60", "correct_answer": 1, "skill_id": 151, "difficulty_id": 2, "explanation": "The common multiples of 4 and 6 are multiples of the LCM, 12: 12, 24, 36, ... The first two are 12 and 24. Their sum is \\(12 + 24 = 36\\). Answer: 36 (option 2).", "hints": ["The common multiples of 4 and 6 are multiples of their LCM (12).", "Add the first two common multiples together."], "source": "Maha Bodhi 2022 P5 Weighted Assessment 2 Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: option 2 = 36." }, { "n": 8, "type_id": 1, "question": "Grace bought a 2 m long ribbon. \\(\\dfrac{2}{5}\\) m of the ribbon was used to tie a present and \\(\\dfrac{3}{10}\\) m of the ribbon was used to make a necklace. How much of the ribbon was left?", "answer0": "\\(\\dfrac{3}{5}\\) m", "answer1": "\\(\\dfrac{7}{10}\\) m", "answer2": "\\(1\\dfrac{2}{5}\\) m", "answer3": "\\(1\\dfrac{3}{10}\\) m", "correct_answer": 3, "skill_id": 165, "difficulty_id": 2, "explanation": "Total used \\(= \\dfrac{2}{5} + \\dfrac{3}{10} = \\dfrac{4}{10} + \\dfrac{3}{10} = \\dfrac{7}{10}\\) m. Ribbon left \\(= 2 - \\dfrac{7}{10} = 1\\dfrac{10}{10} - \\dfrac{7}{10} = 1\\dfrac{3}{10}\\) m. Answer: \\(1\\dfrac{3}{10}\\) m (option 4).", "hints": ["Add the two fractions used, using a common denominator of 10.", "Subtract the total used from the whole 2 m."], "source": "Maha Bodhi 2022 P5 Weighted Assessment 2 Q8", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: option 4 = 1 3/10 m." }, { "n": 9, "type_id": 1, "question": "Michael sorted \\(7\\dfrac{2}{3}\\) kg of recyclable materials in the morning. He sorted \\(3\\dfrac{1}{6}\\) kg less recyclable materials in the afternoon. How much recyclable materials did he sort altogether?", "answer0": "\\(4\\dfrac{1}{2}\\) kg", "answer1": "\\(10\\dfrac{5}{6}\\) kg", "answer2": "\\(10\\dfrac{1}{3}\\) kg", "answer3": "\\(12\\dfrac{1}{6}\\) kg", "correct_answer": 3, "skill_id": 160, "difficulty_id": 2, "explanation": "Afternoon \\(= 7\\dfrac{2}{3} - 3\\dfrac{1}{6} = 7\\dfrac{4}{6} - 3\\dfrac{1}{6} = 4\\dfrac{3}{6} = 4\\dfrac{1}{2}\\) kg. Altogether \\(= 7\\dfrac{2}{3} + 4\\dfrac{1}{2} = 7\\dfrac{4}{6} + 4\\dfrac{3}{6} = 11\\dfrac{7}{6} = 12\\dfrac{1}{6}\\) kg. Answer: \\(12\\dfrac{1}{6}\\) kg (option 4).", "hints": ["First find the afternoon amount: morning minus 3 1/6.", "Add the morning and afternoon amounts using a common denominator of 6."], "source": "Maha Bodhi 2022 P5 Weighted Assessment 2 Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: option 4 = 12 1/6 kg." }, { "n": 10, "type_id": 1, "question": "Mr Tang gave monthly allowance to his elder daughter and younger son in the ratio 5 : 3. His daughter received $50 more than his son. How much allowance did Mr Tang give to his children altogether each month?", "answer0": "$75", "answer1": "$80", "answer2": "$200", "answer3": "$400", "correct_answer": 2, "skill_id": 183, "difficulty_id": 2, "explanation": "The ratio is daughter : son = 5 : 3, a difference of \\(5 - 3 = 2\\) units. This difference equals $50, so 1 unit = \\(50 \\div 2 = \\$25\\). Total units = \\(5 + 3 = 8\\), so altogether = \\(8 \\times \\$25 = \\$200\\). Answer: $200 (option 3).", "hints": ["The difference in ratio units (5 - 3 = 2) corresponds to the $50 difference.", "Find the value of one unit, then multiply by the total number of units (8)."], "source": "Maha Bodhi 2022 P5 Weighted Assessment 2 Q10", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: option 3 = $200." }, { "n": 11, "type_id": 2, "question": "\\(16 \\times 300 = [?] \\times 600\\)", "answer0": "8", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 151, "difficulty_id": 1, "explanation": "Work out the left side: \\(16 \\times 300 = 4800\\). The right side is \\([?] \\times 600 = 4800\\), so \\([?] = 4800 \\div 600 = 8\\). Answer: 8.", "hints": ["Calculate 16 × 300 first.", "Divide that product by 600 to find the missing number."], "source": "Maha Bodhi 2022 P5 Weighted Assessment 2 Q11", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 8." }, { "n": 12, "type_id": 1, "question": "Find the product of \\(\\dfrac{7}{9}\\) and \\(\\dfrac{3}{4}\\). Leave your answer in its simplest form.", "answer0": "\\(\\dfrac{7}{12}\\)", "answer1": "\\(\\dfrac{21}{36}\\)", "answer2": "\\(\\dfrac{10}{13}\\)", "answer3": "\\(\\dfrac{21}{13}\\)", "correct_answer": 0, "skill_id": 161, "difficulty_id": 1, "explanation": "Multiply numerators and denominators: \\(\\dfrac{7}{9} \\times \\dfrac{3}{4} = \\dfrac{7 \\times 3}{9 \\times 4} = \\dfrac{21}{36}\\). Simplify by dividing top and bottom by 3: \\(\\dfrac{7}{12}\\). Answer: \\(\\dfrac{7}{12}\\) (option 1).", "hints": ["Multiply the numerators together and the denominators together.", "Simplify by cancelling the common factor of 3."], "source": "Maha Bodhi 2022 P5 Weighted Assessment 2 Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 7/12. Originally a fill-in question, converted to MCQ because the answer is a fraction (FIB answers must be integers/decimals only)." }, { "n": 13, "type_id": 2, "question": "A cuboid is 5 m long, 2 m wide and 7 m high. What is the volume of the cuboid? [?] m³", "answer0": "70", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 190, "difficulty_id": 1, "explanation": "Volume of a cuboid = length × width × height = \\(5 \\times 2 \\times 7 = 70\\) m³. Answer: 70 m³.", "hints": ["Volume of a cuboid = length × width × height.", "Multiply 5 × 2 × 7."], "source": "Maha Bodhi 2022 P5 Weighted Assessment 2 Q13", "image_needed": true, "image_options": false, "image_file": "q13.png", "image_page": 5, "image_bbox": [0.20, 0.62, 0.45, 0.82], "image_loc": "Cuboid diagram labelled 7 m high, 5 m long, 2 m wide, lower-left of page.", "notes": "Answer key: 70 m³. Unit m³ is given outside the blank." }, { "n": 14, "type_id": 1, "question": "Mrs Low baked 34 muffins. 22 of them were chocolate muffins and the rest were banana muffins. What is the ratio of the number of chocolate muffins to the number of banana muffins? Leave your answer in its simplest form.", "answer0": "11 : 6", "answer1": "22 : 12", "answer2": "6 : 11", "answer3": "22 : 34", "correct_answer": 0, "skill_id": 179, "difficulty_id": 1, "explanation": "Banana muffins = \\(34 - 22 = 12\\). Ratio chocolate : banana = \\(22 : 12\\). Simplify by dividing both by 2: \\(11 : 6\\). Answer: 11 : 6 (option 1).", "hints": ["Find the number of banana muffins by subtracting from the total.", "Write chocolate : banana, then simplify by dividing both terms by 2."], "source": "Maha Bodhi 2022 P5 Weighted Assessment 2 Q14", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 11 : 6. Originally a fill-in question, converted to MCQ because the answer is a ratio (FIB answers must be integers/decimals only)." }, { "n": 15, "type_id": 2, "question": "Melody mixed water and syrup in the ratio 7 : 2 to make a drink. She used 98 ml of water. How many millilitres of drink did she make? [?] ml", "answer0": "126", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 183, "difficulty_id": 2, "explanation": "Water is 7 units = 98 ml, so 1 unit = \\(98 \\div 7 = 14\\) ml. The drink is water + syrup = \\(7 + 2 = 9\\) units. Total = \\(9 \\times 14 = 126\\) ml. Answer: 126 ml.", "hints": ["Water represents 7 units; find the value of 1 unit.", "The whole drink is 9 units (7 + 2)."], "source": "Maha Bodhi 2022 P5 Weighted Assessment 2 Q15", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key working: 7u = 98, 1u = 14, 9 units × 14 = 126 ml." }, { "n": 16, "type_id": 2, "question": "Mr Tan is at a bookshop. He wants to buy pens that cost $2 each. For every 3 pens bought, he gets 1 pen free. Mr Tan would like to buy a pen for each of his 41 pupils. What is the least amount of money Mr Tan has to pay for all the pens? $[?]", "answer0": "62", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "Each set = 3 bought + 1 free = 4 pens, costing \\(3 \\times \\$2 = \\$6\\). To get 41 pens: \\(41 \\div 4 = 10\\) sets remainder 1. 10 sets give 40 pens for \\(10 \\times \\$6 = \\$60\\). 1 more pen must be bought for $2. Total = \\(\\$60 + \\$2 = \\$62\\). Answer: $62.", "hints": ["One 'set' is 4 pens (3 paid + 1 free) costing $6.", "Find how many full sets cover the 41 pens, then pay for any leftover pens."], "source": "Maha Bodhi 2022 P5 Weighted Assessment 2 Q16", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key working: 1 set = 4 pens = $6; 41 ÷ 4 = 10 R1; $6×10 = $60; $60 + $2 = $62." }, { "n": 17, "type_id": 2, "question": "Raju paid $180 for a calculator, an e-dictionary and 10 files. The 10 files cost half as much as the calculator. The e-dictionary costs 3 times as much as the 10 files. How much did each file cost? $[?]", "answer0": "3", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "Let the 10 files = 1 unit. Calculator = 2 units (files are half the calculator). E-dictionary = 3 units (3 times the files). Total = \\(1 + 2 + 3 = 6\\) units = $180, so 1 unit = \\(180 \\div 6 = \\$30\\). The 10 files cost $30, so each file = \\(30 \\div 10 = \\$3\\). Answer: $3.", "hints": ["Let the 10 files be 1 unit; express the calculator and e-dictionary in units.", "Total 6 units = $180; find 1 unit, then divide the files' cost by 10."], "source": "Maha Bodhi 2022 P5 Weighted Assessment 2 Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key working: 180 ÷ 6 = 30 (files); 30 ÷ 10 = $3 each file. (Key shows 180÷3=60, 60÷2=30, 30÷10=$3 — same final answer $3.)" }, { "n": 18, "type_id": 2, "question": "Anna had some $2 and $5 notes in the ratio of 3 : 1. The total value of the notes is $99. How many pieces of $5 notes did Anna have? [?]", "answer0": "9", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 183, "difficulty_id": 3, "explanation": "Ratio of $2 notes : $5 notes = 3 : 1. One 'set' = 3 two-dollar notes + 1 five-dollar note, worth \\(3 \\times \\$2 + 1 \\times \\$5 = \\$6 + \\$5 = \\$11\\). Number of sets = \\(99 \\div 11 = 9\\). Each set has 1 five-dollar note, so $5 notes = \\(9 \\times 1 = 9\\). Answer: 9.", "hints": ["Work out the value of one 'set' (3 two-dollar notes + 1 five-dollar note).", "Divide the total $99 by the value of one set to find the number of sets."], "source": "Maha Bodhi 2022 P5 Weighted Assessment 2 Q18", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key working: value of 1 set = $2×3 + $5 = $11; 99 ÷ 11 = 9 sets; $5 notes = 9 × 1 = 9." }, { "n": 19, "type_id": 2, "question": "Alan had some cards at first. He gave \\(\\dfrac{1}{2}\\) of them to Ben and \\(\\dfrac{1}{8}\\) of the remainder to Colin. He then bought another 153 cards and had as many cards as he had at first. How many cards did he give Ben? [?]", "answer0": "136", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "Let the cards at first = 1 whole (16 units). He gave \\(\\dfrac{1}{2}\\) = 8 units to Ben, leaving 8 units. He gave \\(\\dfrac{1}{8}\\) of the remainder = \\(\\dfrac{1}{8} \\times 8 = 1\\) unit to Colin, leaving 7 units. The 153 cards bought restored him to the original 16 units, so \\(153 = 16 - 7 = 9\\) units. 1 unit = \\(153 \\div 9 = 17\\) cards. Ben got 8 units = \\(8 \\times 17 = 136\\) cards. Answer: 136.", "hints": ["Split the first amount into 16 equal units so the halves and eighths are whole units.", "The 153 cards equal the units he no longer had; find one unit, then Ben's 8 units."], "source": "Maha Bodhi 2022 P5 Weighted Assessment 2 Q19", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 136." }, { "n": 20, "type_id": 2, "question": "The rectangle is made up of four triangles. The area of three of the triangles are 81 cm², 104 cm² and 63 cm². What is the area of the shaded triangle? [?] cm²", "answer0": "40", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 186, "difficulty_id": 3, "explanation": "When a point inside a rectangle is joined to the four corners, the two pairs of opposite triangles have equal total areas (each pair sums to half the rectangle). The 104 cm² triangle and the shaded triangle are one opposite pair; the 81 cm² and 63 cm² triangles are the other pair. So shaded + 104 = 81 + 63 = 144, giving shaded = \\(144 - 104 = 40\\) cm². Answer: 40 cm².", "hints": ["For a point joined to all four corners of a rectangle, opposite triangles add up to the same total.", "Shaded + 104 = 81 + 63; solve for the shaded area."], "source": "Maha Bodhi 2022 P5 Weighted Assessment 2 Q20", "image_needed": true, "image_options": false, "image_file": "q20.png", "image_page": 10, "image_bbox": [0.22, 0.17, 0.62, 0.33], "image_loc": "Rectangle divided into four triangles by an interior point; labels 81 cm², 104 cm², 63 cm² and a shaded triangle on the left.", "notes": "Answer key: 40 cm²." } ] }