{ "paper": { "school": "Nan Hua", "year": 2022, "level": "P5", "label": "Weighted Assessment 3", "source_prefix": "Nan Hua 2022 P5 Weighted Assessment 3", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 2, "question": "The ratio of the number of girls to the total number of students in a class is 17 : 40. What percentage of the students in the class are boys? [?]", "answer0": "57.5", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 173, "difficulty_id": 2, "explanation": "Boys make up the part of the class that is not girls. Number of boys (in ratio units) = 40 - 17 = 23. So boys are \\(\\dfrac{23}{40}\\) of the class. As a percentage: \\(\\dfrac{23}{40} \\times 100\\% = 57.5\\%\\).", "hints": ["The whole class is 40 units; girls are 17 units, so boys are 40 - 17 units.", "Convert the fraction of boys to a percentage by multiplying by 100%."], "source": "Nan Hua 2022 P5 Weighted Assessment 3 Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer 57.5% verified against printed key (40-17=23; 23/40=57.5%). Unit % in stem." }, { "n": 2, "type_id": 2, "question": "Xavier had some stamps. He gave away 22% of his stamps and was left with 312 of his stamps. How many stamps did he have at first? [?]", "answer0": "400", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 175, "difficulty_id": 2, "explanation": "The 312 stamps left represent 100% - 22% = 78% of his stamps. So 1% = 312 ÷ 78 = 4 stamps. The original total is 100% = 4 × 100 = 400 stamps.", "hints": ["The stamps left over are 100% - 22% of the original amount.", "Find 1% first, then multiply by 100 to get the whole."], "source": "Nan Hua 2022 P5 Weighted Assessment 3 Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer 400 verified against printed key (78%=312; 1%=4; 100%=400)." }, { "n": 3, "type_id": 2, "question": "The figure is made up of identical squares. How many more squares should be shaded so that 60% of the figure is shaded? [?]", "answer0": "11", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 174, "difficulty_id": 2, "explanation": "The figure has 30 identical squares. 60% of 30 = \\(\\dfrac{60}{100} \\times 30 = 18\\) squares need to be shaded in total. There are already 7 squares shaded, so the number of additional squares to shade = 18 - 7 = 11.", "hints": ["Find how many squares make up 60% of the whole figure first.", "Subtract the squares already shaded from the number needed."], "source": "Nan Hua 2022 P5 Weighted Assessment 3 Q3", "image_needed": true, "image_options": false, "image_file": "q3.png", "image_page": 2, "image_bbox": [0.38, 0.19, 0.58, 0.33], "image_loc": "Grid of identical squares (5 columns x 6 rows = 30) with 7 squares shaded, centred near top of page 2 below the question.", "notes": "Answer 11 verified against printed key (60/100=18/30; 18-7=11). Figure shows a 30-square grid with 7 already shaded; the count is required to solve." }, { "n": 4, "type_id": 2, "question": "Sheryl wants to buy a smart phone that costs $699 before 7% GST. How much GST does Sheryl have to pay? $[?]", "answer0": "48.93", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 176, "difficulty_id": 1, "explanation": "GST is 7% of the price. GST = \\(7\\% \\times \\$699 = 0.07 \\times 699 = \\$48.93\\).", "hints": ["GST is a percentage of the price before tax.", "Multiply $699 by 7% (0.07)."], "source": "Nan Hua 2022 P5 Weighted Assessment 3 Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer $48.93 verified against printed key ($699 x 7% = $48.93). Decorative phone image in paper is not needed to solve." }, { "n": 5, "type_id": 2, "question": "Mr Lim has $45 500 in his savings account. He earns 2.2% interest each year. How much will Mr Lim have in his account at the end of 1 year? $[?]", "answer0": "46501", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 176, "difficulty_id": 2, "explanation": "Interest earned in 1 year = 2.2% of $45 500 = 0.022 × 45 500 = $1001. Total in account = $45 500 + $1001 = $46 501.", "hints": ["Find the interest first: 2.2% of the savings amount.", "Add the interest to the original amount."], "source": "Nan Hua 2022 P5 Weighted Assessment 3 Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer $46501 verified against printed key ($45500 x 2.2% = $1001; $45500 + $1001 = $46501)." }, { "n": 6, "type_id": 2, "question": "Jack had 1300 stamps in his stamp collection. 55% of his stamps were Singapore stamps and the remaining stamps were from Malaysia, Indonesia and Thailand. How many Malaysia stamps did Jack collect if there were equal number of stamps from Malaysia, Indonesia and Thailand? [?]", "answer0": "195", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 175, "difficulty_id": 2, "explanation": "Remaining (non-Singapore) stamps = 100% - 55% = 45% of 1300 = 0.45 × 1300 = 585 stamps. These are shared equally among Malaysia, Indonesia and Thailand, so Malaysia = 585 ÷ 3 = 195 stamps.", "hints": ["First find the percentage and number of stamps that are NOT Singapore stamps.", "Divide the remaining stamps equally among the 3 countries."], "source": "Nan Hua 2022 P5 Weighted Assessment 3 Q6", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer 195 verified against printed key (45% of 1300 = 585; 585/3 = 195)." }, { "n": 7, "type_id": 2, "question": "The table shows how Lucas divided his time during his visit to the Science Centre.
Butterflies Up-Close: 30 min
Earth Alive: 40 min
Future Makers: 45 min
Phobia: The Science Of Fear: 50 min
The Tinkering Studio: 30 min
Smart Nation Playscape: 45 min
What percentage of his time at the Science Centre did Lucas spend in the 'Future Makers' and 'Smart Nation Playscape' exhibitions altogether? [?]", "answer0": "37.5", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 171, "difficulty_id": 2, "explanation": "Total time = 30 + 40 + 45 + 50 + 30 + 45 = 240 min. Future Makers + Smart Nation Playscape = 45 + 45 = 90 min. Percentage = \\(\\dfrac{90}{240} \\times 100\\% = 37.5\\%\\).", "hints": ["Add up all the durations to find the total time at the Science Centre.", "Express the two named exhibitions' time as a fraction of the total, then convert to a percentage."], "source": "Nan Hua 2022 P5 Weighted Assessment 3 Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Table transcribed as text. Answer 37.5% verified against printed key (total 240min; 90/240 = 3/8 = 37.5%). Unit % in stem." }, { "n": 8, "type_id": 2, "question": "Mdm Jeya receives a monthly salary of $6300. She spends 30% of her salary on her apartment rent and saves \\(\\dfrac{3}{7}\\) of her salary in the bank. Mdm Jeya spends the rest of her monthly salary on food and transport. How much does Mdm Jeya spend on food and transport every month? $[?]", "answer0": "1710", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 175, "difficulty_id": 3, "explanation": "Rent = 30% of $6300 = 0.30 × 6300 = $1890. Savings = \\(\\dfrac{3}{7}\\) of $6300 = $2700. Food and transport is the rest = $6300 - $1890 - $2700 = $1710.", "hints": ["Find the amount spent on rent (30%) and the amount saved (3/7) separately.", "Subtract both amounts from the total monthly salary."], "source": "Nan Hua 2022 P5 Weighted Assessment 3 Q8", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer $1710 verified against printed key (rent $1890; savings $2700; 6300-1890-2700=1710)." }, { "n": 9, "type_id": 2, "question": "The usual price of a laptop was $1580. Wayne bought the laptop at a discount of 20%.
(a) What was the discounted price of the laptop? $[?]
(b) There was a 7% GST on the discounted price. How much did Wayne pay for the laptop? $[?]", "answer0": "1264", "answer1": "1352.48", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 176, "difficulty_id": 2, "explanation": "(a) Discount = 20% of $1580 = 0.20 × 1580 = $316. Discounted price = $1580 - $316 = $1264. (b) GST = 7% of $1264 = 0.07 × 1264 = $88.48. Amount paid = $1264 + $88.48 = $1352.48.", "hints": ["For (a), find the discount amount first, then subtract it from the usual price.", "For (b), add 7% GST to the discounted price from (a)."], "source": "Nan Hua 2022 P5 Weighted Assessment 3 Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Two-part question. (a) $1264 and (b) $1352.48 both verified against printed key. Decorative laptop image not needed to solve." }, { "n": 10, "type_id": 2, "question": "The selling price of each Model Z car was $168 000. For every car that Mr Fadil sold, he earned 1.2% of the selling price. In July, Mr Fadil earned a total of $8064 from selling Model Z cars. How many Model Z cars did Mr Fadil sell in July? [?]", "answer0": "4", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 175, "difficulty_id": 2, "explanation": "Earnings per car = 1.2% of $168 000 = 0.012 × 168 000 = $2016. Number of cars sold = total earnings ÷ earnings per car = $8064 ÷ $2016 = 4 cars.", "hints": ["Find how much Mr Fadil earns from selling just one car (1.2% of $168 000).", "Divide the total earnings by the earnings per car."], "source": "Nan Hua 2022 P5 Weighted Assessment 3 Q10", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer 4 cars verified against printed key ($168000 x 1.2% = $2016; $8064/$2016 = 4)." } ] }