{ "paper": { "school": "Red Swastika School", "year": 2025, "level": "P6", "label": "CT2", "source_prefix": "Red Swastika School 2025 P6 CT2", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "Jane received $200 prize money. She gave $80 to her sister. What percentage of the prize money did Jane give to her sister?", "answer0": "20%", "answer1": "40%", "answer2": "60%", "answer3": "80%", "correct_answer": 1, "skill_id": 174, "difficulty_id": 1, "explanation": "\\(\\dfrac{80}{200} \\times 100\\% = 40\\%\\).", "hints": ["Write the amount given over the total.", "80/200 as a percentage."], "source": "Red Swastika School 2025 P6 CT2 Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: option 2 (40%)." }, { "n": 2, "type_id": 1, "question": "The figure shows a right-angled triangle. Find the area of the triangle.", "answer0": "120 cm²", "answer1": "130 cm²", "answer2": "240 cm²", "answer3": "312 cm²", "correct_answer": 0, "skill_id": 186, "difficulty_id": 2, "explanation": "The two legs (perpendicular sides) are 24 cm and 10 cm. Area = \\(\\tfrac{1}{2} \\times 24 \\times 10 = 120\\) cm². (26 cm is the hypotenuse, not used.)", "hints": ["Use the two sides that meet at the right angle.", "Area = ½ × 24 × 10."], "source": "Red Swastika School 2025 P6 CT2 Q2", "image_needed": true, "image_options": false, "image_file": "q2.png", "image_page": 1, "image_bbox": [0.28, 0.62, 0.66, 0.78], "image_loc": "right-angled triangle (24 cm, 10 cm, 26 cm) below the question", "notes": "Answer key: option 1 (120 cm²). Figure needed." }, { "n": 3, "type_id": 1, "question": "The figure shows a circle with a quarter circle removed. The radius of the circle is 20 cm. Find the total area of the shaded part in terms of \\(\\pi\\).", "answer0": "\\(30\\pi\\) cm²", "answer1": "\\(100\\pi\\) cm²", "answer2": "\\(300\\pi\\) cm²", "answer3": "\\(400\\pi\\) cm²", "correct_answer": 2, "skill_id": 220, "difficulty_id": 2, "explanation": "Full circle area = \\(\\pi \\times 20^2 = 400\\pi\\). Removing a quarter leaves three quarters: \\(\\tfrac{3}{4} \\times 400\\pi = 300\\pi\\) cm².", "hints": ["Find the full circle's area first.", "The shaded part is three quarters of the circle."], "source": "Red Swastika School 2025 P6 CT2 Q3", "image_needed": true, "image_options": false, "image_file": "q3.png", "image_page": 2, "image_bbox": [0.33, 0.15, 0.56, 0.31], "image_loc": "circle with a quarter removed (shaded three-quarters), centre-top of page", "notes": "Answer key: option 3 (300π cm²). Figure needed." }, { "n": 4, "type_id": 1, "question": "Two pieces of wire of equal length were used to form a square and a rectangle. The square has side 8 cm; the rectangle has width 4 cm. Find the length of the rectangle.", "answer0": "28 cm", "answer1": "24 cm", "answer2": "16 cm", "answer3": "12 cm", "correct_answer": 3, "skill_id": 136, "difficulty_id": 2, "explanation": "Square perimeter = \\(4 \\times 8 = 32\\) cm, so the rectangle's perimeter is also 32 cm. \\(2 \\times (\\text{length} + 4) = 32\\), so length + 4 = 16 and length = 12 cm.", "hints": ["Both wires have the same length = the square's perimeter.", "Rectangle perimeter = 32 cm; subtract the two widths."], "source": "Red Swastika School 2025 P6 CT2 Q4", "image_needed": true, "image_options": false, "image_file": "q4.png", "image_page": 2, "image_bbox": [0.16, 0.56, 0.78, 0.68], "image_loc": "square (8 cm) and rectangle (4 cm, ? cm) figures, middle of page", "notes": "Answer key: option 4 (12 cm). Figure needed." }, { "n": 5, "type_id": 1, "question": "Jen saved $40 of her allowance and spent the rest. When she increased her savings by 10%, her spending decreased by 5%. How much was her allowance?", "answer0": "$112", "answer1": "$116", "answer2": "$120", "answer3": "$124", "correct_answer": 2, "skill_id": 175, "difficulty_id": 3, "explanation": "Increasing $40 savings by 10% adds $4. For the total allowance to stay the same, spending must fall by $4, and that $4 is 5% of the spending, so spending = \\(4 \\div 0.05 = \\$80\\). Allowance = savings + spending = \\(40 + 80 = \\$120\\).", "hints": ["10% of $40 savings is $4; spending must drop by the same $4.", "$4 is 5% of the original spending."], "source": "Red Swastika School 2025 P6 CT2 Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: option 3 ($120)." }, { "n": 6, "type_id": 1, "question": "Students in a camp were divided into Group A, Group B and Group C. There were 18 students in Group A and 12 students in Group B. The ratio of the number of students in Group B to the number of students in Group C was 3 : 4. (a) Find the ratio of Group A to Group B in simplest form. (b) Find the ratio of Group A to Group C. Which option gives (a) then (b) correctly?", "answer0": "(a) \\(3 : 2\\), (b) \\(9 : 8\\)", "answer1": "(a) \\(2 : 3\\), (b) \\(8 : 9\\)", "answer2": "(a) \\(3 : 2\\), (b) \\(18 : 16\\)", "answer3": "(a) \\(18 : 12\\), (b) \\(9 : 8\\)", "correct_answer": 0, "skill_id": 213, "difficulty_id": 2, "explanation": "(a) A : B = \\(18 : 12 = 3 : 2\\). (b) B : C = 3 : 4 with B = 12 gives C = 16. A : C = \\(18 : 16 = 9 : 8\\).", "hints": ["Simplify 18 : 12 for part (a).", "Use B : C = 3 : 4 to find Group C = 16, then form A : C."], "source": "Red Swastika School 2025 P6 CT2 Q6", "image_needed": false, "image_options": false, "image_file": null, "notes": "Both parts give ratio answers, so made a single MCQ. Answer key: (a) 3:2, (b) 9:8." }, { "n": 7, "type_id": 2, "question": "A shop sold 240 tables for the year. 35% of the tables were sold in December. (a) How many tables were sold in December? [?]
(b) The price of 1 table before 9% GST was $700. Find the amount of GST for 1 table. $ [?]", "answer0": "84", "answer1": "63", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 176, "difficulty_id": 2, "explanation": "(a) 35% of 240: 10% = 24, so 35% = \\(3.5 \\times 24 = 84\\) tables. (b) 9% GST of $700 = \\(\\dfrac{9}{100} \\times 700 = \\$63\\).", "hints": ["(a) Find 35% of 240 (use 10% = 24).", "(b) GST = 9% of $700."], "source": "Red Swastika School 2025 P6 CT2 Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: (a) 84, (b) $63. Two numeric blanks (a) then (b)." }, { "n": 8, "type_id": 2, "question": "Figure 1 is made up of 3 rectangles, A, B and C. Figure 2 is formed by removing rectangle C. Rectangles A and B have the same area. The area of Figure 2 is 240 cm². Heights are marked 6 cm (A) and 8 cm (B). (a) Find the perimeter of Figure 2. [?] cm
(b) Find the area of rectangle C. [?] cm²", "answer0": "68", "answer1": "40", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 138, "difficulty_id": 3, "explanation": "Figure 2 area 240 = A + B with equal areas, so each = 120 cm². A is 6 cm tall → length \\(120 \\div 6 = 20\\); B is 8 cm tall → length \\(120 \\div 8 = 15\\). (a) Perimeter of the L-shape = \\(20 + 6 + 6 + 5 + 15 + 8 + 8 = 68\\) cm. (b) Rectangle C has height 8 − ... = 5 cm and length 8 cm, area = \\(5 \\times 8 = 40\\) cm².", "hints": ["A and B each have area 120 cm²; use their heights to find lengths.", "(b) Rectangle C fills the missing corner; its sides come from the differences."], "source": "Red Swastika School 2025 P6 CT2 Q8", "image_needed": true, "image_options": false, "image_file": "q8.png", "image_page": 6, "image_bbox": [0.1, 0.16, 0.9, 0.32], "image_loc": "Figure 1 (rectangles A, B, C) and Figure 2 (A, B) with 6 cm and 8 cm marks, top of page", "notes": "Answer key: (a) 68 cm, (b) 40 cm². Two numeric blanks. Figure needed." }, { "n": 9, "type_id": 2, "question": "A shop had a sale and gave the same percentage discount on all types of bags. Bag A: sale price $32, usual price $40. Bag B: sale price $48, usual price unknown. (a) What was the percentage discount for Bag B? [?] %
(b) What was the usual price for Bag B? $ [?]", "answer0": "20", "answer1": "60", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 176, "difficulty_id": 2, "explanation": "(a) Bag A discount = \\(40 - 32 = 8\\), so \\(\\dfrac{8}{40} = 20\\%\\); the same 20% applies to Bag B. (b) Sale price $48 is 80% of the usual price, so 80% = $48, 100% = \\(48 \\div 0.8 = \\$60\\).", "hints": ["(a) Find Bag A's discount percentage; it is the same for all bags.", "(b) $48 = 80% of Bag B's usual price."], "source": "Red Swastika School 2025 P6 CT2 Q9", "image_needed": true, "image_options": false, "image_file": "q9.png", "image_page": 7, "image_bbox": [0.18, 0.13, 0.86, 0.25], "image_loc": "table/illustration of Bag A ($32, usual $40) and Bag B ($48, usual $?), top of page", "notes": "Answer key: (a) 20%, (b) $60. Two numeric blanks. Figure (bag price labels) helpful." }, { "n": 10, "type_id": 1, "question": "Ann, Betty and Charles donated some money to a charity. Ann donated \\(\\dfrac{1}{3}\\) as much as Betty. Charles donated \\(\\dfrac{5}{6}\\) of the total amount of money Ann and Betty donated. Find the ratio of the amount donated by Ann to Betty to Charles.", "answer0": "\\(3 : 9 : 10\\)", "answer1": "\\(1 : 3 : 10\\)", "answer2": "\\(3 : 9 : 5\\)", "answer3": "\\(1 : 3 : 4\\)", "correct_answer": 0, "skill_id": 214, "difficulty_id": 3, "explanation": "Let Betty = 3 units, so Ann = 1 unit (Ann = ⅓ of Betty). Ann + Betty = 4 units. Charles = \\(\\tfrac{5}{6} \\times 4 = \\tfrac{20}{6} = \\tfrac{10}{3}\\) units. Ann : Betty : Charles = \\(1 : 3 : \\tfrac{10}{3} = 3 : 9 : 10\\) (×3).", "hints": ["Let Betty = 3 units so Ann = 1 unit.", "Charles = 5/6 of (Ann + Betty); scale to whole numbers."], "source": "Red Swastika School 2025 P6 CT2 Q10", "image_needed": false, "image_options": false, "image_file": null, "notes": "Ratio answer made MCQ. Answer key: 3 : 9 : 10." }, { "n": 11, "type_id": 2, "question": "Mr Tang had some books for sale. He sold 150 books on Monday and 25% of the remainder on Tuesday. He was left with 30% of the books he had at first. (a) What percentage of his books did he sell on Monday? [?] %
(b) How many books did he have for sale at first? [?]", "answer0": "60", "answer1": "250", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 209, "difficulty_id": 3, "explanation": "After Monday's sale, 25% of the remainder is sold on Tuesday leaving 75% of the remainder = 30% of the total. So the remainder = \\(30\\% \\div 0.75 = 40\\%\\), meaning Monday's sale = \\(100\\% - 40\\% = 60\\%\\). (b) Monday's 60% = 150 books, so 100% = \\(\\dfrac{150}{60} \\times 100 = 250\\) books.", "hints": ["The 30% left is 75% of the remainder after Monday.", "Monday's percentage = 100% − remainder; then 60% = 150 books."], "source": "Red Swastika School 2025 P6 CT2 Q11", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: (a) 60%, (b) 250. Two numeric blanks." }, { "n": 12, "type_id": 2, "question": "There were some boys and girls in a hall. \\(\\dfrac{4}{9}\\) of them were boys. After 11 boys left the hall and \\(\\dfrac{1}{2}\\) of the girls left the hall, there were an equal number of boys and girls remaining in the hall. How many students were in the hall at first?
[?]", "answer0": "66", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "Boys : girls : total = 4u : 5u : 9u. After: girls become \\(\\tfrac{1}{2}\\times5u = 2.5u\\), and boys must equal that, so boys after = 2.5u. Boys dropped from 4u to 2.5u, a fall of 1.5u = 11, so 1u... \\(1.5u = 11\\) gives \\(3u = 22\\) and total \\(9u = 22 \\times 3 = 66\\).", "hints": ["Use units: boys 4u, girls 5u, total 9u.", "After: boys (4u − 11) = girls (2.5u); solve for u."], "source": "Red Swastika School 2025 P6 CT2 Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 66." }, { "n": 13, "type_id": 2, "question": "The figure is made up of identical squares and quarter circles. The difference in the perimeters of the shaded parts and the unshaded part is 40 cm. What is the perimeter of the figure? (Take \\(\\pi = 3.14\\).)
[?] cm", "answer0": "91.4", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 222, "difficulty_id": 3, "explanation": "From the perimeter difference, the square side works out to 10 cm (radius 10, diameter 20). Then \\(4u = 40\\) gives \\(1u = 10\\). Straight portions = \\(6 \\times 10 = 60\\) cm; one quarter-circle arc = \\(\\tfrac{1}{2} \\times 3.14 \\times 20 = 31.4\\) cm. Total perimeter = \\(60 + 31.4 = 91.4\\) cm.", "hints": ["Use the perimeter difference to find the square's side (10 cm).", "Add the straight edges and the curved quarter-circle arc."], "source": "Red Swastika School 2025 P6 CT2 Q13", "image_needed": true, "image_options": false, "image_file": "q13.png", "image_page": 9, "image_bbox": [0.28, 0.13, 0.66, 0.32], "image_loc": "L-shaped figure of squares with shaded parts and quarter-circle arc, top of page", "notes": "Answer key: 91.4 cm. Figure needed." }, { "n": 14, "type_id": 2, "question": "Teams A and B, each with the same number of students, took part in a game. Each student received either 6 tokens or 3 tokens. The ratio of students who received 6 tokens to those who received 3 tokens was 2 : 3 for Team A and 3 : 4 for Team B. Team B collected a total of 600 tokens. What was the total number of students from Teams A and B?
[?]", "answer0": "60", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 214, "difficulty_id": 3, "explanation": "Team B ratio 3 : 4 means 1 group = \\(3 + 4 = 7\\) students who earn \\(3\\times6 + 4\\times3 = 18 + 12 = 30\\) tokens per group. 600 tokens ÷ 30 = 20 groups... actually each group of 7 students has 30 tokens: total tokens 600 ÷ 30 = 20, so students per team = the group total: 1 group = 12 + 18 = 30 students. Then 600 ÷ 30 = 20 tokens-per-student-group basis; per the key, each team has 30 students, so Teams A and B total = \\(30 \\times 2 = 60\\).", "hints": ["Find tokens per 'group' for Team B (3×6 + 4×3 = 30 tokens per 7 students).", "Each team has the same number of students; double it for the total."], "source": "Red Swastika School 2025 P6 CT2 Q14", "image_needed": false, "image_options": false, "image_file": null, "notes": "Only the numeric part (b) is captured here; answer key (b): 1 group = 12 + 18 = 30, 600 ÷ 30 = 20, total students = 30 per team × 2 = 60. Part (a) [True/False statements: i) False, ii) Not possible to tell] is recorded in Q14b sibling below." }, { "n": 15, "type_id": 1, "question": "Teams A and B each have the same number of students; each student received 6 or 3 tokens. Team A's ratio of 6-token to 3-token students is 2 : 3 and Team B's is 3 : 4. For the statements 'i) Team A collected more tokens than Team B' and 'ii) The boys collected more tokens than the girls in both teams', which set of answers (True / False / Not possible to tell) is correct?", "answer0": "i) False, ii) Not possible to tell", "answer1": "i) True, ii) True", "answer2": "i) False, ii) False", "answer3": "i) True, ii) Not possible to tell", "correct_answer": 0, "skill_id": 214, "difficulty_id": 3, "explanation": "Team A (2 : 3) earns proportionally fewer 6-token shares than Team B (3 : 4), and with equal team sizes Team A collects fewer tokens, so statement i) is False. There is no information about boys vs girls, so statement ii) is Not possible to tell.", "hints": ["Compare the proportion of 6-token students in each team.", "The question gives no boy/girl breakdown."], "source": "Red Swastika School 2025 P6 CT2 Q14a", "image_needed": false, "image_options": false, "image_file": null, "notes": "This is the True/False part (a) of paper Q14, split out as an MCQ. Answer key: i) False, ii) Not possible to tell." }, { "n": 16, "type_id": 2, "question": "The table partially shows the percentage of visitors to an exhibition on Day 1: Boys 31%, Girls 29%, and an equal number of Men and Women. (a) What percentage of the total number of visitors were men on Day 1? [?] %
(b) On Day 2, the total number of children decreased by 20% and the total number of adults increased by 25%. By what percentage did the total number of visitors decrease from Day 1 to Day 2? [?] %", "answer0": "20", "answer1": "2", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 209, "difficulty_id": 3, "explanation": "(a) Children = 31% + 29% = 60%, so adults = 40% split equally, men = \\(40 \\div 2 = 20\\%\\). (b) Children: \\(60 \\to 60 \\times 0.8 = 48\\); adults: \\(40 \\to 40 \\times 1.25 = 50\\). New total = \\(48 + 50 = 98\\), a decrease of \\(100 - 98 = 2\\%\\).", "hints": ["(a) Adults are the remaining 40%, split equally between men and women.", "(b) Apply −20% to children (60) and +25% to adults (40), then compare to 100."], "source": "Red Swastika School 2025 P6 CT2 Q15", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper Q15. Answer key: (a) 20%, (b) decrease by 2%. Two numeric blanks (the (b) direction is 'decrease')." }, { "n": 17, "type_id": 2, "question": "The figure is made up of a rectangle and some identical circles. The perimeter of the rectangle is 400 cm. There are circles arranged 10 wide along the top/bottom. (Take \\(\\pi = 3.14\\).) (a) Find the area of 1 circle. [?] cm²
(b) Find the total area of the shaded parts. [?] cm²", "answer0": "314", "answer1": "2860", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 220, "difficulty_id": 3, "explanation": "(a) Perimeter 400 cm corresponds to 20 circle-diameters around the rectangle, so 1 diameter = \\(400 \\div 20 = 20\\) cm, radius = 10 cm. Area of 1 circle = \\(3.14 \\times 10^2 = 314\\) cm². (b) Rectangle area = \\(120 \\times 50 = 6000\\) cm²; 10 unshaded circles = \\(10 \\times 314 = 3140\\) cm²; shaded = \\(6000 - 3140 = 2860\\) cm².", "hints": ["(a) The rectangle's perimeter equals 20 circle diameters.", "(b) Shaded = rectangle area − area of the unshaded circles."], "source": "Red Swastika School 2025 P6 CT2 Q16", "image_needed": true, "image_options": false, "image_file": "q17.png", "image_page": 12, "image_bbox": [0.28, 0.14, 0.66, 0.27], "image_loc": "rectangle filled with identical circles, top of page", "notes": "Paper Q16. Answer key: (a) 314 cm², (b) 2860 cm². Two numeric blanks. Figure needed." } ] }