{ "paper": { "school": "ACS Junior", "year": 2023, "level": "P6", "label": "Weighted Assessment 2", "source_prefix": "ACS 2023 P6 Weighted Assessment 2", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "Round 498 675 to the nearest thousand.", "answer0": "490 000", "answer1": "498 000", "answer2": "499 000", "answer3": "500 000", "correct_answer": 2, "skill_id": 2, "difficulty_id": 1, "explanation": "Look at the hundreds digit of 498 675, which is 6 (675 ≥ 500), so round the thousands up: 498 000 → 499 000. Answer: 499 000.", "hints": ["Find the thousands digit, then look at the hundreds digit.", "If the part after the thousands is 500 or more, round up."], "source": "ACS 2023 P6 Weighted Assessment 2 Q1", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "Key: option 3." }, { "n": 2, "type_id": 1, "question": "The pie chart shows the CCAs taken up by a class of 40 students. How many students take up Rugby as a CCA?", "answer0": "7", "answer1": "8", "answer2": "9", "answer3": "10", "correct_answer": 0, "skill_id": 209, "difficulty_id": 2, "explanation": "Soccer is a right angle (90°) = 1/4 of 360°, so Soccer = 1/4 × 40 = 10 students. Swimming = 8, Tennis = 5. The remaining students for Rugby and Badminton total 40 − 10 − 8 − 5 = 17. From the chart Rugby is 7 students. Answer: 7.", "hints": ["The right-angle slice (Soccer) is 1/4 of the whole circle.", "Subtract the known sectors from 40, then read off Rugby."], "source": "ACS 2023 P6 Weighted Assessment 2 Q2", "image_needed": true, "image_options": false, "image_file": "q2.png", "image_page": 2, "image_bbox": [0.5, 0.66, 0.9, 0.92], "image_loc": "pie chart on the right side of the question, lower half of page", "notes": "Key: option 1 (7). Pie chart labels: Swimming 8, Soccer (right angle), Tennis 5, Rugby, Badminton." }, { "n": 3, "type_id": 1, "question": "There are 720 beads in a box. 180 of the beads are red. What percentage of the beads are not red?", "answer0": "20%", "answer1": "25%", "answer2": "33%", "answer3": "75%", "correct_answer": 3, "skill_id": 209, "difficulty_id": 1, "explanation": "Beads not red = 720 − 180 = 540. Percentage not red = 540/720 × 100% = 75%. Answer: 75%.", "hints": ["First find how many beads are NOT red.", "Percentage = (not red ÷ total) × 100%."], "source": "ACS 2023 P6 Weighted Assessment 2 Q3", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "Key: option 4." }, { "n": 4, "type_id": 1, "question": "The figure shows a semicircle. The diameter of the semicircle is 14 cm. What is the perimeter of the figure? Take \\(\\pi = \\dfrac{22}{7}\\)", "answer0": "22 cm", "answer1": "36 cm", "answer2": "44 cm", "answer3": "58 cm", "correct_answer": 1, "skill_id": 221, "difficulty_id": 2, "explanation": "Perimeter of a semicircle = half the circumference + diameter = \\(\\dfrac{1}{2}\\times\\dfrac{22}{7}\\times14 + 14\\) = 22 + 14 = 36 cm. Answer: 36 cm.", "hints": ["Perimeter of a semicircle = half the full circumference PLUS the straight diameter.", "Half circumference = \\(\\dfrac{1}{2}\\pi d\\) = \\(\\dfrac{1}{2}\\times\\dfrac{22}{7}\\times14\\)."], "source": "ACS 2023 P6 Weighted Assessment 2 Q4", "image_needed": true, "image_options": false, "image_file": "q4.png", "image_page": 3, "image_bbox": [0.62, 0.38, 0.86, 0.52], "image_loc": "semicircle figure on the right, beside the options; '14 cm' labels the diameter", "notes": "Key: option 2." }, { "n": 5, "type_id": 1, "question": "ABCD is a trapezium. FED and AEC are straight lines.
Which of the following statements is not true?", "answer0": "\\(\\angle AEF = \\angle DEC\\)", "answer1": "\\(\\angle ABC + \\angle DCB = 180^\\circ\\)", "answer2": "\\(\\angle ADE + \\angle DAE = \\angle EFC + \\angle FCE\\)", "answer3": "\\(\\angle ABF + \\angle BFE + \\angle EDA + \\angle DAB = 360^\\circ\\)", "correct_answer": 1, "skill_id": 230, "difficulty_id": 3, "explanation": "AD is parallel to BC in the trapezium. Option 1 (vertically opposite angles) is true. Option 3 (each pair of angles sums to the same exterior, alternate angles) is true. Option 4 (angle sum of quadrilateral ABFD = 360°) is true. Option 2 claims ∠ABC + ∠DCB = 180°, but co-interior angles equal 180° only along the parallel sides (AB and DC are the non-parallel slanted sides), so this is not true. Answer: option 2.", "hints": ["Identify which pair of sides is parallel (AD ∥ BC).", "Co-interior angles add to 180° only between the two parallel lines."], "source": "ACS 2023 P6 Weighted Assessment 2 Q5", "image_needed": true, "image_options": false, "image_file": "q5.png", "image_page": 3, "image_bbox": [0.3, 0.56, 0.66, 0.74], "image_loc": "trapezium ABCD diagram with diagonals meeting at E, centred below the question text", "notes": "Key: option 2." }, { "n": 6, "type_id": 1, "question": "A string of length 5.4 m was cut into three pieces. The second piece was \\(\\dfrac{1}{3}\\) as long as the first piece. The second piece was twice as long as the third piece. How long was the second piece?", "answer0": "0.6 m", "answer1": "0.9 m", "answer2": "1.2 m", "answer3": "1.8 m", "correct_answer": 2, "skill_id": 206, "difficulty_id": 3, "explanation": "Let the second piece = 2 units. First = 3 × 2 = 6 units (second is 1/3 of first). Third = 1 unit (second is twice the third). Total = 6 + 2 + 1 = 9 units = 5.4 m, so 1 unit = 0.6 m. Second piece = 2 units = 1.2 m. Answer: 1.2 m.", "hints": ["Let the second piece be 2 units so the third piece is a whole number of units.", "First = 3 × second; add all three to equal 5.4 m."], "source": "ACS 2023 P6 Weighted Assessment 2 Q6", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "Key: option 3." }, { "n": 7, "type_id": 1, "question": "Glenn wants to pack 56 erasers and 70 rulers into as many bags as possible, with no remainder. The total number of erasers and rulers was the same in each bag. The number of erasers in each bag was the same. How many erasers were there in each bag?", "answer0": "28", "answer1": "14", "answer2": "8", "answer3": "4", "correct_answer": 3, "skill_id": 2, "difficulty_id": 3, "explanation": "The greatest number of bags is the HCF of 56 and 70. 56 = 2³ × 7, 70 = 2 × 5 × 7, so HCF = 2 × 7 = 14 bags. Erasers per bag = 56 ÷ 14 = 4. Answer: 4.", "hints": ["The greatest number of equal bags is the HCF of 56 and 70.", "Once you know the number of bags, divide the erasers by it."], "source": "ACS 2023 P6 Weighted Assessment 2 Q7", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "Key: option 4 (HCF = 14 bags, 56 ÷ 14 = 4 erasers per bag)." }, { "n": 8, "type_id": 0, "question": null, "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 209, "difficulty_id": 2, "explanation": "Printed answer key gives the answer as 25%. The question stem (a percentage question) is on a page that did not render any extractable text in the source PDF.", "hints": [], "source": "ACS 2023 P6 Weighted Assessment 2 Q8", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "STEM UNREADABLE — page 5 (printed p.287) rendered blank; only the answer (25%) is recoverable from the key. type_id 0 so it is skipped on insert rather than served without a question." }, { "n": 9, "type_id": 0, "question": null, "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 221, "difficulty_id": 2, "explanation": "Printed answer key working: 10 × 10 = 100; 1600 ÷ 100 = 16 cm. Final answer 16 cm (a length/perimeter figure question). The question stem and its figure are on a page that did not render any extractable text in the source PDF.", "hints": [], "source": "ACS 2023 P6 Weighted Assessment 2 Q9", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "STEM + FIGURE UNREADABLE — page 5 (printed p.287) rendered blank; only the key working (10×10=100, 1600÷100=16 cm) is recoverable. type_id 0 so it is skipped on insert." }, { "n": 10, "type_id": 2, "question": "The line graph shows the number of wallets sold in a shop from Monday to Saturday.
During which one-day interval was the increase in the number of wallets sold by the shop the greatest?
From [?] to [?]", "answer0": "Thursday", "answer1": "Friday", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 461, "difficulty_id": 2, "explanation": "Read the rise between consecutive days. Thu to Fri rises from about 45 to about 70, an increase of about 25 wallets, which is the steepest single-day climb on the graph. Answer: from Thursday to Friday.", "hints": ["Look for the steepest upward segment between two adjacent days.", "Compare the vertical jump for each one-day interval."], "source": "ACS 2023 P6 Weighted Assessment 2 Q10", "image_needed": true, "image_options": false, "image_file": "q10.png", "image_page": 6, "image_bbox": [0.1, 0.13, 0.92, 0.43], "image_loc": "line graph (Number of wallets sold vs Mon–Sat) in the upper portion of the page", "notes": "Key: From Thu to Fri." }, { "n": 11, "type_id": 2, "question": "The figure is made up of two squares. The length of the smaller square is 6 cm and the length of the larger square is 10 cm. Find the area of the shaded part.
[?] cm²", "answer0": "80", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 223, "difficulty_id": 3, "explanation": "The shaded triangle has a base equal to the combined width of the two squares, 6 + 10 = 16 cm, and a height of 10 cm. Area = \\(\\dfrac{1}{2}\\times16\\times10\\) = 80 cm². Answer: 80 cm².", "hints": ["The shaded region is a triangle spanning both squares.", "Area of a triangle = \\(\\dfrac{1}{2}\\times\\text{base}\\times\\text{height}\\)."], "source": "ACS 2023 P6 Weighted Assessment 2 Q11", "image_needed": true, "image_options": false, "image_file": "q11.png", "image_page": 7, "image_bbox": [0.28, 0.16, 0.66, 0.36], "image_loc": "two-squares figure with '10 cm' top and '6 cm' left labels, below the question text", "notes": "Key working: ½ × 16 × 10 = 80 cm²." }, { "n": 12, "type_id": 1, "question": "The figure is made up of 5 rectangles. What fraction of the whole figure is shaded?", "answer0": "\\(\\dfrac{3}{10}\\)", "answer1": "\\(\\dfrac{1}{4}\\)", "answer2": "\\(\\dfrac{2}{5}\\)", "answer3": "\\(\\dfrac{1}{2}\\)", "correct_answer": 0, "skill_id": 223, "difficulty_id": 3, "explanation": "Taking the whole figure as a rectangle split into 5 equal columns, the shaded part forms a triangle across the strip. Comparing the shaded area to the total gives \\(\\dfrac{3}{10}\\) of the whole figure. Answer: \\(\\dfrac{3}{10}\\).", "hints": ["The 5 rectangles tile the whole figure equally.", "Compare the shaded triangular area to the total area of all 5 rectangles."], "source": "ACS 2023 P6 Weighted Assessment 2 Q12", "image_needed": true, "image_options": false, "image_file": "q12.png", "image_page": 7, "image_bbox": [0.2, 0.55, 0.5, 0.68], "image_loc": "row of 5 rectangles with a shaded triangular band, below the question text", "notes": "Key: 3/10. Made MCQ because the answer is a fraction (FIB forbidden for fractions)." }, { "n": 13, "type_id": 1, "question": "At a musical, the ratio of the number of adults to the number of children was 7 : 4. Among the adults, the ratio of the number of men to the number of women was 1 : 2. What was the ratio of the number of women to the number of children? Express your answer in the simplest form.", "answer0": "7 : 6", "answer1": "2 : 3", "answer2": "14 : 12", "answer3": "7 : 4", "correct_answer": 0, "skill_id": 214, "difficulty_id": 3, "explanation": "Adults : children = 7 : 4. Make adults divisible by 3 (men:women = 1:2): scale to adults : children = 21 : 12. Women = 2/3 of 21 = 14. So women : children = 14 : 12 = 7 : 6. Answer: 7 : 6.", "hints": ["Scale the adults part so it divides evenly into 1 + 2 = 3 shares.", "Women are 2/3 of the adults; then simplify women : children."], "source": "ACS 2023 P6 Weighted Assessment 2 Q13", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "Key: 7 : 6. Made MCQ because the answer is a ratio (FIB forbidden for ratios)." }, { "n": 14, "type_id": 2, "question": "ABCD is a parallelogram. BC = BE, \\(\\angle ADE = 115^\\circ\\) and \\(\\angle AEB = 75^\\circ\\). Find \\(\\angle DAE\\).
[?]°", "answer0": "25", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 3, "explanation": "On straight line DEC, ∠AEC = 180° − ∠AEB = 180° − 75° = 105°, so ∠AED = 180° − 75° = 105°? Use triangle ADE: angles sum to 180°. ∠AED = 180° − ∠AEB = 105° is the angle on the line; the key uses ∠AEC = 180 − 75 − 65 = 40° then ∠DAE = 180 − 40 − 115 = 25°. So ∠DAE = 25°. Answer: 25°.", "hints": ["Angles on the straight line DEC add to 180°.", "Use the angle sum of triangle ADE = 180° with ∠ADE = 115°."], "source": "ACS 2023 P6 Weighted Assessment 2 Q14", "image_needed": true, "image_options": false, "image_file": "q14.png", "image_page": 8, "image_bbox": [0.08, 0.42, 0.7, 0.66], "image_loc": "parallelogram ABCD with point E on DC; labels 115° at D-side and 75° at E, vertices A B C D E", "notes": "Key working: 180 − 75 − 65 = 40°; 180 − 40 − 115 = 25°. Final answer 25°." }, { "n": 15, "type_id": 2, "question": "A cubical tank of edge 20 cm is \\(\\dfrac{3}{8}\\)-filled with water. Water started leaking out the tank through a crack at 60 cm³ per minute. How many minutes will it take for the tank to be completely empty?
[?] min", "answer0": "50", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 229, "difficulty_id": 2, "explanation": "Tank volume = 20 × 20 × 20 = 8000 cm³. Water in tank = \\(\\dfrac{3}{8}\\) × 8000 = 3000 cm³. Time to empty = 3000 ÷ 60 = 50 minutes. Answer: 50 min.", "hints": ["Volume of a cube = edge³.", "Find the water volume (3/8 of the tank), then divide by the leak rate."], "source": "ACS 2023 P6 Weighted Assessment 2 Q15", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "Key working: 20×20×20 = 8000; 8000÷8 = 1000; 1000×3 = 3000; 3000÷60 = 50 min." }, { "n": 16, "type_id": 2, "question": "The pie chart shows the type of books in a library. The number of Tamil books is \\(\\dfrac{1}{2}\\) the number of Malay books and there are 400 more Chinese books than Malay books. How many books are there in the library altogether?
[?]", "answer0": "2400", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 209, "difficulty_id": 3, "explanation": "Chinese = 1/3 and English = 5/12 of the total. Tamil + Malay = 1 − 1/3 − 5/12 = 12/12 − 4/12 − 5/12 = 3/12 = 1/4. Tamil is 1/2 of Malay, so Tamil : Malay = 1 : 2, giving Malay = 2/3 × 1/4 = 1/6 of total. Chinese (1/3) − Malay (1/6) = 1/6 of total = 400, so total = 400 × 6 = 2400. Answer: 2400 books.", "hints": ["Chinese is 1/3 and English is 5/12; find the fraction left for Tamil + Malay.", "Use Tamil = 1/2 Malay to split that fraction, then 'Chinese − Malay = 400'."], "source": "ACS 2023 P6 Weighted Assessment 2 Q16", "image_needed": true, "image_options": false, "image_file": "q16.png", "image_page": 9, "image_bbox": [0.32, 0.4, 0.66, 0.6], "image_loc": "pie chart with sectors Tamil, Malay, English (5/12), Chinese (1/3); below the question intro", "notes": "Key: 2400. Pie chart fractions: Chinese 1/3, English 5/12." }, { "n": 17, "type_id": 2, "question": "Kelvin has just enough money to buy 15 files. If the price of each file is reduced by 30¢ he will be able to buy 3 more files. What is the original price of each file? Give your answer in dollars.
$[?]", "answer0": "1.80", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 209, "difficulty_id": 3, "explanation": "His total money is fixed. At the reduced price he buys 15 + 3 = 18 files. The 18 extra-cheap files cost 18 × 30¢ = 540¢ less than 18 at the old price would, and that 540¢ equals the saving spread differently — using total money M: M = 15p = 18(p − 30¢). So 15p = 18p − 540¢ → 3p = 540¢ → p = 180¢ = $1.80. Answer: $1.80.", "hints": ["Total money is the same: 15 × original price = 18 × reduced price.", "Reduced price = original − 30¢; solve for the original price."], "source": "ACS 2023 P6 Weighted Assessment 2 Q17", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "Key: $1.80." }, { "n": 18, "type_id": 2, "question": "Ahmad has some 10-cent, 20-cent and 50-cent coins. There are 3 times as many 50-cent coins as 20-cent coins. The number of 50-cent coins is \\(\\dfrac{3}{5}\\) of the number of 10-cent coins. The total amount of the 50-cent and 10-cent coins Ahmad has is $84. What is the total number of 50-cent and 10-cent coins Ahmad had?
[?]", "answer0": "336", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 209, "difficulty_id": 3, "explanation": "50-cent coins = 3/5 of 10-cent coins, so 50-cent : 10-cent = 3 : 5. Let 50-cent = 3u, 10-cent = 5u. Value = 3u × $0.50 + 5u × $0.10 = $1.50u + $0.50u = $2.00u = $84, so u = 42. 50-cent coins = 3 × 42 = 126, 10-cent coins = 5 × 42 = 210. Total = 126 + 210 = 336 coins. Answer: 336.", "hints": ["Use the 3 : 5 ratio of 50-cent to 10-cent coins in units.", "Form the $84 value equation in units, solve, then add the two coin counts."], "source": "ACS 2023 P6 Weighted Assessment 2 Q18", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "Key: 336." }, { "n": 19, "type_id": 2, "question": "The figure is made up of a square, a large semicircle, a small semicircle and 2 quarter circles. The length of each side of the square is 28 cm. Find the area of the shaded part. Take \\(\\pi = \\dfrac{22}{7}\\)
[?] cm²", "answer0": "273", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 222, "difficulty_id": 3, "explanation": "Side = 28 cm; the curves are built on the 28 cm and 14 cm diameters. By rearranging the large semicircle, small semicircle and two quarter circles inside the 28 cm square, the shaded region works out to 273 cm² (using \\(\\pi=\\dfrac{22}{7}\\)). Answer: 273 cm².", "hints": ["Diameters are 28 cm (large semicircle) and 14 cm (small parts).", "Add/subtract the semicircle and quarter-circle areas against the square; use \\(\\pi=\\dfrac{22}{7}\\)."], "source": "ACS 2023 P6 Weighted Assessment 2 Q19", "image_needed": true, "image_options": false, "image_file": "q19.png", "image_page": 12, "image_bbox": [0.3, 0.14, 0.6, 0.36], "image_loc": "square with shaded curved region (large + small semicircle + 2 quarter circles); '28 cm' labels the base", "notes": "Key: 273 cm²." }, { "n": 20, "type_id": 2, "question": "Xueqing filled two types of containers, large and small, with sugar. She filled 3 large containers and 5 small containers with 7800 g of sugar. She could not fill another large container with the remaining sugar as she was short of 150 g. Instead, she filled another small container and had 450 g of sugar left.
(a) How many more grams of sugar did each large container hold than each small container?
[?]
(b) How much sugar did Xueqing have at first? Leave your answer in kilograms.
[?]", "answer0": "600", "answer1": "9", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 209, "difficulty_id": 3, "explanation": "(a) After filling 3 large + 5 small (7800 g), one more large needs 150 g more than the leftover, while one more small leaves 450 g. So large − small = 150 + 450 = 600 g. Each large holds 600 g more than each small. (b) The leftover after 3 large + 5 small fills one more small with 450 g remaining, i.e. leftover = small + 450. Also leftover = large − 150. With large = small + 600: small + 450 = (small + 600) − 150 (consistent). Working through the totals gives the starting amount = 9000 g = 9 kg. Answers: (a) 600 g, (b) 9 kg.", "hints": ["(a) Compare 'short by 150 g for a large' with 'a small leaves 450 g' — the difference is one large minus one small.", "(b) Add the sugar used for all containers plus the leftover to find the original total, then convert g to kg."], "source": "ACS 2023 P6 Weighted Assessment 2 Q20", "image_needed": false, "image_options": false, "image_file": null, "image_page": null, "image_bbox": null, "image_loc": null, "notes": "Key: (a) 600 g, (b) 9 kg. Two FIB blanks for parts (a) and (b)." } ] }