{ "paper": { "school": "CHIJ St Nicholas Girls' School (Primary)", "year": 2023, "level": "P6", "label": "Weighted Assessment 1", "source_prefix": "St Nicholas 2023 P6 Weighted Assessment 1", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 2, "question": "Mr Lee has $6000 in his bank account. The bank gives 0.3% interest at the end of each year. He does not withdraw any of his savings. What is the total amount of money he will have in the bank at the end of one year?
Ans: $[?]", "answer0": "6018", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 209, "difficulty_id": 1, "explanation": "Interest = 0.3% of $6000 = \\(\\dfrac{0.3}{100}\\times 6000 = \\$18\\). Total = $6000 + $18 = $6018.", "hints": ["0.3% means 0.3 out of 100.", "Add the interest to the original amount."], "source": "St Nicholas 2023 P6 Weighted Assessment 1 Q1", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "Answer key: $6018." }, { "n": 2, "type_id": 2, "question": "A group of 4 girls and 3 boys took a quiz. The average score of the girls was 28. The average score of the boys was 27. Find the total score of all the children.
Ans: [?]", "answer0": "193", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 204, "difficulty_id": 1, "explanation": "Total of girls = 28 \\(\\times\\) 4 = 112. Total of boys = 27 \\(\\times\\) 3 = 81. Total score = 112 + 81 = 193.", "hints": ["Total = average \\(\\times\\) number of items.", "Add the girls' total and the boys' total."], "source": "St Nicholas 2023 P6 Weighted Assessment 1 Q2", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "Answer key total = 193 (printed working shows a typo '112 + 87' but the correct sum 81+112=193 is used)." }, { "n": 3, "type_id": 2, "question": "The graph shows the number of tickets sold for a basketball match from Monday to Friday.
(a) What was the total number of tickets sold from Monday to Wednesday? [?]
(b) The usual price of a ticket was $70. On Friday, tickets were sold at a 5% discount. How much money was collected from the sale of tickets on Friday? $[?]", "answer0": "220", "answer1": "7448", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 104, "difficulty_id": 2, "explanation": "(a) From the graph: Mon = 44, Tue = 96, Wed = 80. Total = 44 + 96 + 80 = 220 tickets.
(b) Discount = 5% of $70 = \\(\\dfrac{5}{100}\\times 70 = \\$3.50\\). Sale price = $70 - $3.50 = $66.50. Friday tickets = 112. Money collected = $66.50 \\(\\times\\) 112 = $7448.", "hints": ["Read the bar heights for Mon, Tue and Wed from the graph.", "Find the discounted price first, then multiply by the number of Friday tickets."], "source": "St Nicholas 2023 P6 Weighted Assessment 1 Q3", "image_needed": true, "image_options": false, "image_file": "q3.png", "image_page": 4, "image_bbox": [0.16, 0.23, 0.82, 0.46], "image_loc": "Bar graph 'Number of tickets sold' Mon-Fri, upper portion of the page below the question text.", "notes": "Bar values read from graph: Mon 44, Tue 96, Wed 80, Thu ~38, Fri 112. Answer key: (a) 220, (b) $7448." }, { "n": 4, "type_id": 2, "question": "In a library, \\(\\dfrac{3}{4}\\) of the number of fiction books is equal to \\(\\dfrac{1}{6}\\) of the number of non-fiction books. There are 5940 fiction and non-fiction books altogether. How many fiction books are there in the library?
Ans: [?]", "answer0": "1080", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 214, "difficulty_id": 3, "explanation": "\\(\\dfrac{3}{4}\\) fiction = \\(\\dfrac{1}{6}\\) non-fiction, so \\(\\dfrac{1}{4}\\) fiction = \\(\\dfrac{1}{18}\\) non-fiction. Thus fiction : non-fiction = 4 : 18 = 2 : 9. Wait, using equal units: \\(\\dfrac{1}{4}\\) fiction equals \\(\\dfrac{1}{18}\\) non-fiction, so fiction has 4 units and non-fiction has 18 units of the same size. Total units = 4 + 18 = 22 units = 5940 books, so 1 unit = 5940 \\(\\div\\) 22 = 270. Fiction = 4 units = 270 \\(\\times\\) 4 = 1080 books.", "hints": ["Make the two given fractions share equal-sized units.", "Express fiction and non-fiction as a number of equal units, then find one unit from the total."], "source": "St Nicholas 2023 P6 Weighted Assessment 1 Q4", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "Answer key: 5940 / 22 = 270, fiction = 270 x 4 = 1080." }, { "n": 5, "type_id": 2, "question": "ABCD is a parallelogram. CFE is an isosceles triangle with CF = EF. AFC is a straight line. \\(\\angle BAF = 59^\\circ\\) and \\(\\angle ABC = 71^\\circ\\). Find \\(\\angle AFE\\).
Ans: [?]", "answer0": "118", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 3, "explanation": "In triangle ABC, \\(\\angle BAC = 59^\\circ\\) and \\(\\angle ABC = 71^\\circ\\). Since AFC is a straight line and ABCD is a parallelogram, \\(\\angle ACE = \\angle BAC = 59^\\circ\\) (alternate angles, AB \\(\\parallel\\) DC). Triangle CFE is isosceles with CF = EF, so \\(\\angle FCE = \\angle FEC = 59^\\circ\\). \\(\\angle CFE = 180^\\circ - 59^\\circ - 59^\\circ = 62^\\circ\\). \\(\\angle AFE\\) is on the straight line AFC, so \\(\\angle AFE = 180^\\circ - 62^\\circ = 118^\\circ\\).", "hints": ["Use the parallel sides of the parallelogram to find alternate angles.", "The isosceles triangle CFE has two equal base angles; AFC is a straight line."], "source": "St Nicholas 2023 P6 Weighted Assessment 1 Q5", "image_needed": true, "image_options": false, "image_file": "q5.png", "image_page": 6, "image_bbox": [0.18, 0.15, 0.78, 0.40], "image_loc": "Parallelogram ABCD with triangle CFE, angle 59 deg at A and 71 deg at B, near top of page.", "notes": "Part (b) of the printed paper is a true/false tick-table (AFED is a trapezium = False; angle ACD = angle ADC = False) which is an interactive format and is omitted; only part (a) Find angle AFE is ingested. Answer key (a): 118 deg." }, { "n": 6, "type_id": 2, "question": "At a furniture shop, office chairs are sold at the usual price of $106 each before GST. During a sale in October, the shop offered a 25% discount on the office chair.
(a) What was the discount given for each office chair? $[?]
(b) Karen had $550. What was the greatest number of chairs she could buy during the sale in October? [?]", "answer0": "26.50", "answer1": "6", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 176, "difficulty_id": 2, "explanation": "(a) Discount = 25% of $106 = \\(\\dfrac{25}{100}\\times 106 = \\$26.50\\).
(b) Sale price = $106 - $26.50 = $79.50. $550 \\(\\div\\) $79.50 = 6 remainder $73, so Karen can buy 6 chairs.", "hints": ["Discount = 25% of the usual price.", "Divide her money by the sale price and take the whole-number part."], "source": "St Nicholas 2023 P6 Weighted Assessment 1 Q6", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "Office-chair price-tag image is decorative; the $106 price is stated in the stem, so no figure is needed. Answer key: (a) $26.50, (b) 6 chairs." }, { "n": 7, "type_id": 1, "question": "Xavier spent \\(\\dfrac{2}{7}\\) of his money on a laptop and a refrigerator. The refrigerator cost 2 times as much as the laptop. He spent \\(\\dfrac{1}{3}\\) of his remaining money on a vacuum cleaner. The laptop cost $1320 less than the vacuum cleaner. What fraction of Xavier's money was spent on the laptop?", "answer0": "\\(\\dfrac{2}{21}\\)", "answer1": "\\(\\dfrac{4}{21}\\)", "answer2": "\\(\\dfrac{1}{7}\\)", "answer3": "\\(\\dfrac{2}{7}\\)", "correct_answer": 0, "skill_id": 165, "difficulty_id": 2, "explanation": "Laptop + refrigerator = \\(\\dfrac{2}{7}\\). Refrigerator = 2 \\(\\times\\) laptop, so laptop is 1 part of 3 parts: laptop = \\(\\dfrac{1}{3}\\) of \\(\\dfrac{2}{7} = \\dfrac{2}{21}\\) of his money.", "hints": ["Split the \\(\\dfrac{2}{7}\\) between laptop and refrigerator in the ratio 1 : 2.", "The laptop is one part out of three equal parts of \\(\\dfrac{2}{7}\\)."], "source": "St Nicholas 2023 P6 Weighted Assessment 1 Q7", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "Part (a) answer is a fraction (2/21) so this part is rendered as MCQ. Part (b) 'How much money did he have at first?' ($9240) is the integer money answer captured in Q7b below. Answer key (a): 2/21." }, { "n": "7b", "type_id": 2, "question": "Xavier spent \\(\\dfrac{2}{7}\\) of his money on a laptop and a refrigerator. The refrigerator cost 2 times as much as the laptop. He spent \\(\\dfrac{1}{3}\\) of his remaining money on a vacuum cleaner. The laptop cost $1320 less than the vacuum cleaner. How much money did Xavier have at first?
Ans: $[?]", "answer0": "9240", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "Let total = 21 units. Laptop + refrigerator = \\(\\dfrac{2}{7}\\) = 6 units; laptop = 2 units, refrigerator = 4 units. Remaining = 21 - 6 = 15 units. Vacuum cleaner = \\(\\dfrac{1}{3}\\) of 15 = 5 units. Laptop is $1320 less than the vacuum cleaner: 5 units - 2 units = 3 units = $1320, so 1 unit = $440. Total = 21 \\(\\times\\) $440 = $9240.", "hints": ["Use 21 units for the whole; find the laptop, refrigerator and vacuum-cleaner units.", "The difference between the vacuum cleaner and the laptop units equals $1320."], "source": "St Nicholas 2023 P6 Weighted Assessment 1 Q7", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "This is part (b) of paper Q7 (integer answer). Answer key: 3 units = $1320, 1 unit = $440, total = 440 x 21 = $9240." }, { "n": 8, "type_id": 2, "question": "Figure 1 shows a rectangular tile. Figure 2 is formed using 5 such tiles. The perimeter of Figure 2 is 360 cm.
(a) Find the perimeter of Figure 1. [?] cm
(b) The length of the rectangular tile was 3 times as long as its breadth. Find the area of the rectangular tile. [?] cm²", "answer0": "120", "answer1": "675", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 97, "difficulty_id": 3, "explanation": "(a) The perimeter of Figure 2 is made up of 3 tile-perimeters worth of edges (the 5 tiles arranged as a cross share edges so the outer boundary equals 3 single-tile perimeters). 360 \\(\\div\\) 3 = 120 cm, so the perimeter of one tile (Figure 1) is 120 cm.
(b) Length = 3 \\(\\times\\) breadth, so one tile perimeter = 2(length + breadth) = 2(3b + b) = 8b = 120 cm, giving b = 15 cm and length = 45 cm. Area = 45 \\(\\times\\) 15 = 675 cm².", "hints": ["The outer boundary of Figure 2 equals 3 single-tile perimeters.", "With length = 3 \\(\\times\\) breadth, the tile perimeter is 8 breadths."], "source": "St Nicholas 2023 P6 Weighted Assessment 1 Q8", "image_needed": true, "image_options": false, "image_file": "q8.png", "image_page": 9, "image_bbox": [0.20, 0.17, 0.80, 0.32], "image_loc": "Figure 1 (single rectangular tile) on the left and Figure 2 (cross of 5 tiles) on the right, upper-middle of the page.", "notes": "Answer key: (a) 360 / 3 = 120 cm; (b) 8 units = 120, 1 unit = 15, length = 45, area = 45 x 15 = 675 cm2." }, { "n": 9, "type_id": 2, "question": "Devi had 180 butter buns and two times as many kaya buns in the morning. In the afternoon, she baked some butter buns and sold some kaya buns. The number of kaya buns sold was 5 times of the number of butter buns baked. She had the same number of butter buns and kaya buns in the end.
(a) How many butter buns did Devi bake in the afternoon? [?]
(b) How many buns did Devi have altogether in the end? [?]
(c) The remaining buns were sold at $2.20 each and 1 bun was given free for every 3 buns bought. Mr Poh wanted to get 13 buns. How much money did he need to pay in total? $[?]", "answer0": "30", "answer1": "420", "answer2": "22", "answer3": null, "correct_answer": null, "skill_id": 241, "difficulty_id": 3, "explanation": "Morning: butter = 180, kaya = 180 \\(\\times\\) 2 = 360. Difference = 360 - 180 = 180. Let butter baked = 1 unit, then kaya sold = 5 units; the gap closes by 5 + 1 = 6 units = 180, so 1 unit = 180 \\(\\div\\) 6 = 30.
(a) Butter buns baked = 30.
(b) Butter in the end = 180 + 30 = 210; kaya in the end = 210 (equal). Altogether = 210 + 210 = 420 buns.
(c) Buy 3, get 1 free, so 4 buns per group. 13 \\(\\div\\) 4 = 3 remainder 1, so 3 free buns; Mr Poh pays for 13 - 3 = 10 buns. Working: 3 groups give 3 \\(\\times\\) 3 = 9 paid buns plus the 1 extra = 10 paid buns. 10 \\(\\times\\) $2.20 = $22.", "hints": ["The butter and kaya counts start 180 apart and must end equal.", "For every 3 buns paid, 1 is free; group the 13 buns to find how many are paid for."], "source": "St Nicholas 2023 P6 Weighted Assessment 1 Q9", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "Answer key: (a) 30; (b) 420; (c) $22. (c) printed working: 13/4 = 3R1, pays for 10 buns, 10 x 2.20 = $22." } ] }