{ "paper": { "school": "CHIJ St Nicholas Girls'", "year": 2025, "level": "P6", "label": "WA1", "source_prefix": "CHIJ St Nicholas Girls' 2025 P6 WA1", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "Vani baked 720 cookies. She packed 18 cookies into each of the 25 bags. What fraction of the cookies baked were packed into the 25 bags? Leave your answer in the simplest form.", "answer0": "\\(\\dfrac{5}{8}\\)", "answer1": "\\(\\dfrac{5}{6}\\)", "answer2": "\\(\\dfrac{3}{8}\\)", "answer3": "\\(\\dfrac{18}{25}\\)", "correct_answer": 0, "skill_id": 171, "difficulty_id": 2, "explanation": "Cookies packed = 18 x 25 = 450. Fraction packed = \\(\\dfrac{450}{720}\\). Simplify by dividing by 90: \\(\\dfrac{450}{720} = \\dfrac{5}{8}\\). Answer: \\(\\dfrac{5}{8}\\).", "hints": ["Find how many cookies were packed: 18 x 25.", "\\(\\dfrac{450}{720}\\) simplifies to \\(\\dfrac{5}{8}\\)."], "source": "CHIJ St Nicholas Girls' 2025 P6 WA1 Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: Q1 = 5/8. MCQ because answer is a fraction. Distractor options added. [2 marks]" }, { "n": 2, "type_id": 2, "question": "Two groups of pupils, X and Y, visited a museum. There was an equal number of pupils in both groups. 35 pupils from Group X joined Group Y. In the end, there were 121 pupils in Group Y. How many pupils visited the museum altogether?
[?]", "answer0": "172", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 2, "explanation": "Group Y had 121 after gaining 35, so Group Y started with 121 - 35 = 86. Both groups were equal, so each had 86. Total = 86 x 2 = 172 pupils. Answer: 172.", "hints": ["Work backwards: Group Y's original size = 121 - 35.", "Both groups equal at 86, so total = 86 x 2 = 172."], "source": "CHIJ St Nicholas Girls' 2025 P6 WA1 Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: Q2 = 172 pupils. [2 marks]" }, { "n": 3, "type_id": 2, "question": "In the figure, ABCD is a parallelogram. DGC and HGC are triangles. Given that CE and DF are straight lines, find \\(\\angle GHC\\).
[?]°", "answer0": "62", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 200, "difficulty_id": 3, "explanation": "\\(\\angle BAD = \\angle BCH = 102°\\) (opposite angles / co-interior). \\(\\angle GCH = 102° - 49° = 53°\\). \\(\\angle EGF = \\angle DGC = 82°\\) (vertically opposite). \\(\\angle HGC = 82° - 17° = 65°\\). In triangle GHC, \\(\\angle GHC = 180° - 53° - 65° = 62°\\). Answer: 62°.", "hints": ["Use parallelogram angle properties and vertically opposite angles at G.", "In triangle GHC, the three angles sum to 180°: ∠GHC = 180° - 53° - 65° = 62°."], "source": "CHIJ St Nicholas Girls' 2025 P6 WA1 Q3", "image_needed": true, "image_options": false, "image_file": "q3.png", "image_page": 3, "image_bbox": [0.20, 0.15, 0.60, 0.40], "image_loc": "parallelogram ABCD with lines CE and DF crossing at G, angles 82°, 102°, 17°, 49° marked, upper-left of page", "notes": "Key: Q3 = 62°. [2 marks]" }, { "n": 4, "type_id": 2, "question": "The bar graph shows the types of pies sold in a bakery in a day. (a) How many banana pies were sold? (b) The ratio of the number of cream pies sold to the number of apple pies sold was 3 : 4. There were 8 more custard pies sold than apple pies sold. How many apple pies and custard pies were sold?
(a) [?] (b) apple [?], custard [?]", "answer0": "70", "answer1": "64", "answer2": "72", "answer3": null, "correct_answer": null, "skill_id": 181, "difficulty_id": 2, "explanation": "(a) Reading the banana bar gives 70 pies. (b) Cream : apple = 3 : 4 and cream = 48 (from graph), so 1 unit = 48 ÷ 3 = 16 and apple = 4 x 16 = 64. Custard = apple + 8 = 64 + 8 = 72. Answers: (a) 70, (b) apple = 64, custard = 72.", "hints": ["Read the banana bar directly for part (a).", "Use the 3 : 4 ratio with cream = 48 to find apple, then add 8 for custard."], "source": "CHIJ St Nicholas Girls' 2025 P6 WA1 Q4", "image_needed": true, "image_options": false, "image_file": "q4.png", "image_page": 4, "image_bbox": [0.18, 0.21, 0.76, 0.46], "image_loc": "bar graph of number of pies sold for Cream, Apple, Banana, Pumpkin, Custard, upper part of page", "notes": "Key: Q4(a) = 140? No — key says (a) banana = 70 from graph; cream = 48. Note: answer key for Q4 not on solution sheet for (a); from graph banana = 70, cream = 48 used in (b). (a) 70, (b) apple 64, custard 72. The 'complete the bar graph' drawing portion is omitted (interactive)." }, { "n": 5, "type_id": 2, "question": "Martha had 2 pieces of wire. Each of them measured 40 cm. She bent one wire into a square and the other wire into a rectangle with a length of 17 cm. There was no wire left. (a) What was the area of the square? (b) What was the breadth of the rectangle?
(a) [?] cm² (b) [?] cm", "answer0": "100", "answer1": "3", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 464, "difficulty_id": 2, "explanation": "(a) Square: each side = 40 ÷ 4 = 10 cm, area = 10 x 10 = 100 cm². (b) Rectangle perimeter 40 cm: 2 x (17 + breadth) = 40, so 17 + breadth = 20, breadth = 20 - 17 = 3 cm. Answers: (a) 100 cm², (b) 3 cm.", "hints": ["The square's perimeter is 40 cm, so each side is 40 ÷ 4.", "Rectangle: 2 x (length + breadth) = 40; breadth = 20 - 17 = 3 cm."], "source": "CHIJ St Nicholas Girls' 2025 P6 WA1 Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: Q5(a) = 100 cm², (b) = 3 cm. Part (c) handled as separate MCQ entry (n=6) because the answer is a ratio. [1+1 marks]" }, { "n": 6, "type_id": 1, "question": "Martha had 2 pieces of wire, each 40 cm. One was bent into a square (area 100 cm²) and the other into a rectangle 17 cm by 3 cm (area 51 cm²). Find the ratio of the total area of the square and the rectangle to the area of the rectangle.", "answer0": "151 : 51", "answer1": "100 : 51", "answer2": "151 : 100", "answer3": "51 : 151", "correct_answer": 0, "skill_id": 180, "difficulty_id": 2, "explanation": "Area of rectangle = 17 x 3 = 51 cm². Total area = 100 + 51 = 151 cm². Ratio of total area to rectangle area = 151 : 51. Answer: 151 : 51.", "hints": ["Rectangle area = 17 x 3 = 51 cm²; total = square + rectangle = 151 cm².", "Ratio total : rectangle = 151 : 51."], "source": "CHIJ St Nicholas Girls' 2025 P6 WA1 Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "This is Q5(c) of the paper, served as MCQ because the answer is a ratio. Key: 151 : 51. Distractor options added. [1 mark]" }, { "n": 7, "type_id": 2, "question": "ACD is an equilateral triangle and AC = BC. BD is a straight line. (a) Find \\(\\angle ABD\\). (b) Find \\(\\angle AED\\).
(a) [?]° (b) [?]°", "answer0": "30", "answer1": "75", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 197, "difficulty_id": 3, "explanation": "(a) \\(\\angle ACB = 90° + 60° = 150°\\) (right angle at C plus the equilateral 60°). Since AC = BC, triangle ABC is isosceles: \\(\\angle CAB = \\angle CBA = (180° - 90°) ÷ 2 = 45°\\). And \\(\\angle BDC = \\angle DBC = (180° - 150°) ÷ 2 = 15°\\). So \\(\\angle ABD = 45° - 15° = 30°\\). (b) \\(\\angle ADE = 60° - 15° = 45°\\); in triangle AED, \\(\\angle AED = 180° - 60° - 45° = 75°\\). Answers: (a) 30°, (b) 75°.", "hints": ["Use the equilateral triangle's 60° angles and the isosceles triangle AC = BC.", "(a) ∠ABD = 45° - 15° = 30°; (b) ∠AED = 75°."], "source": "CHIJ St Nicholas Girls' 2025 P6 WA1 Q6", "image_needed": true, "image_options": false, "image_file": "q7.png", "image_page": 6, "image_bbox": [0.18, 0.14, 0.58, 0.31], "image_loc": "equilateral triangle ACD with point B, right angle at C and angle marked at B, upper-left of page", "notes": "Paper Q6. Key: (a) 30° [3 marks], (b) 75° [1 mark]." }, { "n": 8, "type_id": 2, "question": "At a camp, \\(\\dfrac{6}{11}\\) of the pupils are girls. \\(\\dfrac{3}{4}\\) of the girls do not wear spectacles and 48 boys wear spectacles. Altogether there are 90 pupils who wear spectacles. (a) What is the total number of boys at the camp? (b) How many boys do not wear spectacles?
(a) [?] (b) [?]", "answer0": "140", "answer1": "92", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "(a) Girls who wear spectacles = total spectacle-wearers - boys who wear spectacles = 90 - 48 = 42. These 42 are \\(\\dfrac{1}{4}\\) of the girls (since \\(\\dfrac{3}{4}\\) do not), so total girls = 42 x 4 = 168. Girls are \\(\\dfrac{6}{11}\\) of pupils, so 1 unit (\\(\\dfrac{1}{11}\\)) = 168 ÷ 6 = 28, total pupils = 28 x 11 = 308. Boys = 308 - 168 = 140. (b) Boys who do not wear spectacles = 140 - 48 = 92. Answers: (a) 140, (b) 92.", "hints": ["Girls who wear spectacles = 90 - 48 = 42, and that is 1/4 of all girls.", "Find total girls (168), then total pupils, then boys = 140; non-spectacle boys = 140 - 48 = 92."], "source": "CHIJ St Nicholas Girls' 2025 P6 WA1 Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper Q7. Key: (a) 140 boys [3 marks], (b) 92 boys [1 mark]." }, { "n": 9, "type_id": 2, "question": "Two rectangular tanks, A and B, are shown. Tank A measures 60 cm by 16 cm by 21 cm; Tank B measures 40 cm by 12 cm by 21 cm. At first, \\(\\dfrac{1}{7}\\) of Tank A was filled with water and Tank B was empty. (a) What was the volume of water in Tank A at first?
[?] ml", "answer0": "2880", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 191, "difficulty_id": 2, "explanation": "Volume of Tank A = 60 x 16 x 21 = 20160 cm³ = 20160 ml. Water = \\(\\dfrac{1}{7}\\) x 20160 = 2880 ml. Answer: 2880 ml.", "hints": ["Find the full volume of Tank A: 60 x 16 x 21.", "Water = 1/7 of 20160 = 2880 ml."], "source": "CHIJ St Nicholas Girls' 2025 P6 WA1 Q8", "image_needed": true, "image_options": false, "image_file": "q9.png", "image_page": 8, "image_bbox": [0.16, 0.13, 0.72, 0.33], "image_loc": "two rectangular tanks A (60 x 16 x 21 cm) and B (40 x 12 x 21 cm) with taps, top of page", "notes": "Paper Q8(a). Key: 2880 ml. [2 marks]" }, { "n": 10, "type_id": 2, "question": "Two rectangular tanks: Tank A is 60 cm by 16 cm by 21 cm; Tank B is 40 cm by 12 cm by 21 cm. At first \\(\\dfrac{1}{7}\\) of Tank A was filled and Tank B was empty. Both taps were turned on at the same time, water from both taps flowed at the same rate. After Tank B was fully filled with water, Tank A took another 7.5 min to be filled to the brim. How much water flowed into Tank A in 1 minute?
[?] ml", "answer0": "960", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 193, "difficulty_id": 3, "explanation": "Tank A volume = 20160 ml; it already held 2880 ml, so it needs 20160 - 2880 = 17280 ml more. Tank B volume = 40 x 12 x 21 = 10080 ml. While both taps run at the same rate, by the time Tank B is full (10080 ml into B), the same 10080 ml went into A. After that, A needs 17280 - 10080 = 7200 ml more, taking 7.5 min. So Tank A's tap rate = 7200 ÷ 7.5 = 960 ml/min. Answer: 960 ml.", "hints": ["Tank A still needs 17280 ml; both taps deliver equal volumes until B is full (10080 ml each).", "Remaining for A = 7200 ml in 7.5 min, so rate = 7200 ÷ 7.5 = 960 ml/min."], "source": "CHIJ St Nicholas Girls' 2025 P6 WA1 Q8", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper Q8(b). Key: 960 ml. [3 marks]" }, { "n": 11, "type_id": 2, "question": "At a shop, rolls of ribbon were sold at $7 each. For every 3 rolls of ribbon bought, customers were given one roll free. Last Friday, some customers bought either 1 roll or 3 rolls of ribbon. The shopkeeper collected a total amount of $1925 from the sale of ribbons and gave away 65 rolls free. How many customers bought only one roll of ribbon?
[?]", "answer0": "80", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "Each free roll corresponds to a customer who bought 3 rolls, so 65 customers bought 3 rolls = 65 x 3 = 195 rolls, costing 195 x $7 = $1365. Money from single-roll buyers = $1925 - $1365 = $560. Each pays $7, so single-roll customers = $560 ÷ $7 = 80. Answer: 80.", "hints": ["65 free rolls means 65 customers bought 3 rolls each.", "Subtract their spending from $1925, then divide by $7."], "source": "CHIJ St Nicholas Girls' 2025 P6 WA1 Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper Q9(a). Key: 80 customers. [3 marks]" }, { "n": 12, "type_id": 2, "question": "At a shop, rolls of ribbon were sold at $7 each. For every 3 rolls of ribbon bought, customers were given one roll free. Lenice used pieces of ribbons, each of length 110 cm, to tie 25 parcels. Ribbon was sold in rolls of 300 cm each. What was the least amount of money that Lenice paid for the rolls of ribbon?
$[?]", "answer0": "70", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 3, "explanation": "Total ribbon needed = 25 x 110 = 2750 cm. Each roll is 300 cm, but only 2 full 110 cm pieces fit per roll (220 cm; 300 - 220 = 80 cm left, not enough for a third). So rolls needed = 25 ÷ 2 = 12.5, round up to 13 rolls. With the 'buy 3 get 1 free' offer, paying for 3 gives 4: 13 rolls means paying for ceil obtained via offer. To get 13 rolls she pays for 10 (10 paid + 3 free = 13). Cost = 10 x $7 = $70. Answer: $70.", "hints": ["Each 300 cm roll yields only two 110 cm pieces, so 25 parcels need 13 rolls.", "With buy-3-get-1-free, 13 rolls cost 10 paid rolls x $7 = $70."], "source": "CHIJ St Nicholas Girls' 2025 P6 WA1 Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper Q9(b). Key: $70. [2 marks]. THE END." } ] }