{ "paper": { "school": "Ai Tong", "year": 2022, "level": "P5", "label": "Weighted Assessment 3", "source_prefix": "Ai Tong 2022 P5 Weighted Assessment 3", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 2, "question": "What is 75% of 180? [?]", "answer0": "135", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 174, "difficulty_id": 1, "explanation": "Method: find a percentage part of a whole. \\(75\\% \\times 180 = \\dfrac{75}{100} \\times 180 = 135\\). Answer: 135.", "hints": ["75% means \\(\\dfrac{75}{100}\\) of the whole.", "Multiply: \\(\\dfrac{75}{100} \\times 180\\)."], "source": "Ai Tong 2022 P5 Weighted Assessment 3 Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 135." }, { "n": 2, "type_id": 2, "question": "10.5 $\\ell$ of syrup is added to 6.8 $\\ell$ of water to form a mixture. The mixture is then poured equally into 4 similar bottles. What is the volume of the mixture in each bottle in millilitres? [?]", "answer0": "4325", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 192, "difficulty_id": 2, "explanation": "Method: total volume then convert and divide. Total = \\(10.5 + 6.8 = 17.3\\ \\ell\\). Convert: \\(17.3 \\times 1000 = 17300\\) ml. Divide: \\(17300 \\div 4 = 4325\\) ml. Answer: 4325 ml.", "hints": ["Add the two volumes first.", "1 litre = 1000 ml; convert before dividing by 4."], "source": "Ai Tong 2022 P5 Weighted Assessment 3 Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 4325 ml. Answer entered in ml as required." }, { "n": 3, "type_id": 2, "question": "Mr Tan buys a laptop that costs $2460. He also has to pay a 7% GST. How much is the GST? $[?]", "answer0": "172.20", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 176, "difficulty_id": 1, "explanation": "Method: GST is a percentage of the cost. \\(7\\% \\times 2460 = \\dfrac{7}{100} \\times 2460 = 172.20\\). Answer: $172.20.", "hints": ["GST = 7% of the laptop price.", "Compute \\(\\dfrac{7}{100} \\times 2460\\)."], "source": "Ai Tong 2022 P5 Weighted Assessment 3 Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: $172.20." }, { "n": 4, "type_id": 2, "question": "Mushrooms are sold at $2.90 per 200 g at a supermarket. What is the price of 1.8 kg of mushrooms? $[?]", "answer0": "26.10", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 2, "explanation": "Method: find how many 200 g portions, then multiply. \\(200\\ \\text{g} = 0.2\\ \\text{kg}\\). Number of portions = \\(1.8 \\div 0.2 = 9\\). Price = \\(2.90 \\times 9 = 26.10\\). Answer: $26.10.", "hints": ["Convert 200 g to kg, then find how many portions are in 1.8 kg.", "Multiply the number of portions by $2.90."], "source": "Ai Tong 2022 P5 Weighted Assessment 3 Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: $26.10." }, { "n": 5, "type_id": 2, "question": "The figure shows 3 parcels A, B and C on a balance scale. The scale shows that it is balanced. The mass of Parcel A is 108 kg. What is the average mass of the 3 parcels? [?]", "answer0": "72", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 184, "difficulty_id": 2, "explanation": "Method: balanced scale means B + C = A. Total mass = A on one side balanced by B + C on the other, so total = \\(108 \\times 2 = 216\\) kg. Average = \\(216 \\div 3 = 72\\) kg. Answer: 72 kg.", "hints": ["Balanced means the two sides have equal mass: B + C = A = 108 kg.", "Total of all 3 = 216 kg; divide by 3 for the average."], "source": "Ai Tong 2022 P5 Weighted Assessment 3 Q5", "image_needed": true, "image_options": false, "image_file": "q5.png", "image_page": 3, "image_bbox": [0.33, 0.16, 0.62, 0.31], "image_loc": "balance scale with parcels A, B, C, upper-middle of page below the question", "notes": "Answer key: 108 x 2 = 216; 216 / 3 = 72 kg." }, { "n": 6, "type_id": 2, "question": "Greg keeps $1280 in his bank account for a year. The bank pays him interest of 2.5% each year. How much money will Greg have in his bank account at the end of 1 year? $[?]", "answer0": "1312", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 176, "difficulty_id": 2, "explanation": "Method: interest then add to principal. Interest = \\(2.5\\% \\times 1280 = \\dfrac{2.5}{100} \\times 1280 = 32\\). Total = \\(1280 + 32 = 1312\\). Answer: $1312.", "hints": ["Find 2.5% of $1280 for the interest.", "Add the interest back to the original $1280."], "source": "Ai Tong 2022 P5 Weighted Assessment 3 Q6", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 1280 x 25% = 32 (key writes 25% but means 2.5%); 32 + 1280 = $1312." }, { "n": 7, "type_id": 2, "question": "Mr Mani sold an equal number of large and small pies at the prices shown and collected $1092. How many large pies did Mr Mani sell? [?]", "answer0": "65", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 2, "explanation": "Method: cost of one large + one small set, then divide. One large + one small = \\(10.90 + 5.90 = 16.80\\). Number of sets = \\(1092 \\div 16.80 = 65\\). Since equal numbers, large pies sold = 65. Answer: 65.", "hints": ["Equal numbers means group one large with one small.", "Cost per set = $10.90 + $5.90; divide the total by this."], "source": "Ai Tong 2022 P5 Weighted Assessment 3 Q7", "image_needed": true, "image_options": false, "image_file": "q7.png", "image_page": 4, "image_bbox": [0.25, 0.49, 0.64, 0.66], "image_loc": "PIES FOR SALE box showing Large $10.90 and Small $5.90, middle of page", "notes": "Answer key: 10.90 + 5.90 = 16.8; 1092 / 16.8 = 65." }, { "n": 8, "type_id": 0, "question": "The average mass of all the students in a class is 40 kg. There is an equal number of boys and girls in the class. The average mass of the boys is 50 kg. Each statement is either true, false or not possible to tell from the information given. For each statement, put a tick in the correct column.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 184, "difficulty_id": 3, "explanation": "Equal boys and girls, overall average 40 kg, boys average 50 kg, so girls average must be 30 kg (so that (50+30)/2 = 40). (1) 'Each boy has a greater mass than each girl' = FALSE (averages differ, but individual masses can overlap). (2) 'The average mass of the girls is less than 40 kg' = TRUE (girls average 30 kg). (3) 'The average mass of the class will increase if 2 more students are added' = NOT POSSIBLE TO TELL (depends on the masses of the new students).", "hints": ["Use the overall average to back-out the girls' average mass.", "Distinguish averages from individual values; new students could be any mass."], "source": "Ai Tong 2022 P5 Weighted Assessment 3 Q8", "image_needed": false, "image_options": false, "image_file": null, "notes": "Interactive tick-the-column table; no app value/sequence type so type_id 0 (skipped on insert). Answer key ticks: (1) False, (2) True, (3) Not possible to tell." }, { "n": 9, "type_id": 2, "question": "Eli worked in a restaurant for 8 hours each day from Monday to Friday. She was paid $340 in total. She was paid the same amount per hour.
(a) How much was she paid per hour? $[?]
(b) At this rate, how many hours would she have to work to be paid $2380? [?]", "answer0": "8.50", "answer1": "280", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 2, "explanation": "(a) Per day = \\(340 \\div 5 = 68\\); per hour = \\(68 \\div 8 = 8.50\\). So $8.50 per hour. (b) Hours = \\(2380 \\div 8.50 = 280\\) hours.", "hints": ["(a) She works 5 days, 8 hours each = 40 hours total.", "(b) Divide the target pay by the hourly rate."], "source": "Ai Tong 2022 P5 Weighted Assessment 3 Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: (a) 340/5=68, 68/8=$8.50; (b) 2380/8.5=280 hours." }, { "n": 10, "type_id": 2, "question": "The original price of a television was $1700. Cathy bought it at a discount of 20% and had \\(\\dfrac{4}{5}\\) of her money left. She then spent 30% of the money left on a sofa.
(a) How much was the cost of the television after the discount? $[?]
(b) How much did Cathy spend on the sofa? $[?]", "answer0": "1360", "answer1": "1632", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 175, "difficulty_id": 3, "explanation": "(a) After 20% discount she pays 80%: \\(80\\% \\times 1700 = 1360\\). So $1360. (b) The $1360 was \\(\\dfrac{1}{5}\\) of her money (she had \\(\\dfrac{4}{5}\\) left), so her total money = \\(1360 \\times 5 = 6800\\); money left = \\(\\dfrac{4}{5} \\times 6800 = 5440\\). Sofa = \\(30\\% \\times 5440 = 1632\\). So $1632.", "hints": ["(a) Paying after a 20% discount means paying 80% of the price.", "(b) The TV cost is the part of her money she used up; find her total, then the money left, then 30% of it."], "source": "Ai Tong 2022 P5 Weighted Assessment 3 Q10", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: (a) 1700 x 80% = $1360; (b) 1360 x 4 = 5440 (money left), 5440 x 30% = $1632." }, { "n": 11, "type_id": 2, "question": "The bar graph shows the number of fiction and non-fiction books four classes borrowed in a week. The bar for non-fiction books borrowed by 5C is not shown.
(a) What is the average number of fiction books borrowed by the 4 classes? Leave your answer to the nearest whole number. [?]
(b) The average number of books borrowed by 5C and 5D is 68. How many non-fiction books did 5C borrow? [?]", "answer0": "26", "answer1": "46", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 154, "difficulty_id": 3, "explanation": "(a) Fiction books: 5A=15, 5B=30, 5C=20, 5D=40. Total = \\(15+30+20+40 = 105\\); average = \\(105 \\div 4 = 26.25 \\approx 26\\). (b) 5C and 5D together = \\(68 \\times 2 = 136\\) books. Known: 5C fiction=20, 5D fiction=40, 5D non-fiction=30. So 5C non-fiction = \\(136 - 20 - 40 - 30 = 46\\).", "hints": ["(a) Read the four fiction bars, add them, divide by 4 and round.", "(b) Total for 5C and 5D = average x 2; subtract the three known bar values."], "source": "Ai Tong 2022 P5 Weighted Assessment 3 Q11", "image_needed": true, "image_options": false, "image_file": "q11.png", "image_page": 7, "image_bbox": [0.13, 0.18, 0.87, 0.40], "image_loc": "two bar graphs (Fiction books and Non-fiction books) for classes 5A-5D, upper portion of page", "notes": "Answer key: (a) 15+30+20+40=105, 105/4=26.25 -> 26; (b) 68x2=136, 136-20-40-30=46." }, { "n": 12, "type_id": 2, "question": "The rental rates of a bicycle at a neighbourhood park is shown in the table. First 1 hour: $6.80. For every additional 30 minutes or part thereof: $2.50.
(a) Keith rented a bicycle from 8 am to 10.45 am. How much did he pay for the rental? $[?]
(b) William rented a bicycle and paid $19.30 in total. What was the most number of minutes that William rented the bicycle for? [?]", "answer0": "16.80", "answer1": "210", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 3, "explanation": "(a) 8 am to 10.45 am = 2 h 45 min. First hour = $6.80, remaining 1 h 45 min = 105 min = 4 blocks of 30 min (or part thereof) = \\(2.50 \\times 4 = 10\\). Total = \\(10 + 6.80 = 16.80\\). So $16.80. (b) Extra paid beyond first hour = \\(19.30 - 6.80 = 12.50\\); number of 30-min blocks = \\(12.50 \\div 2.50 = 5\\); that is \\(5 \\times 30 = 150\\) min. Plus the first hour (60 min) = \\(150 + 60 = 210\\) minutes.", "hints": ["(a) Split the time into the first hour plus 30-minute blocks (round each part up to a full block).", "(b) Subtract the first-hour charge, divide by $2.50 to count 30-minute blocks, then add the first 60 minutes."], "source": "Ai Tong 2022 P5 Weighted Assessment 3 Q12", "image_needed": true, "image_options": false, "image_file": "q12.png", "image_page": 8, "image_bbox": [0.19, 0.15, 0.63, 0.23], "image_loc": "rental rates table (First 1 hour $6.80; every additional 30 min or part thereof $2.50), top of page below question", "notes": "Answer key: (a) 2.50x4=10, 10+6.80=$16.80; (b) 19.30-6.80=12.5, 12.5/2.5=5, 5x30=150, 150+60=210 minutes." } ] }