{ "paper": { "school": "CHIJ St Nicholas Girls' School", "year": 2025, "level": "P6", "label": "Weighted Assessment 2", "source_prefix": "CHIJ St Nicholas Girls' School 2025 P6 Weighted Assessment 2", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 2, "question": "Aisha had a total number of 252 red and green beads at first. The ratio of the number of red beads to number of green beads was 5 : 7. She gave away 47 red beads. How many red beads did Aisha have left?
[?]", "answer0": "58", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 213, "difficulty_id": 2, "explanation": "Total units = 5 + 7 = 12. 252 ÷ 12 = 21 beads per unit. Red beads = 21 × 5 = 105. After giving away 47: 105 − 47 = 58 red beads left.", "hints": ["Add the ratio parts to find the number of units, then find one unit.", "Multiply by 5 for red beads, then subtract 47."], "source": "CHIJ St Nicholas Girls' School 2025 P6 Weighted Assessment 2 Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 58 red beads." }, { "n": 2, "type_id": 2, "question": "Ben spent $80 on Saturday. He spent $84 on Sunday. What was the percentage increase in his spending from Saturday to Sunday?
[?]", "answer0": "5", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 208, "difficulty_id": 1, "explanation": "Increase = 84 − 80 = $4. Percentage increase = \\(\\dfrac{4}{80} \\times 100\\% = 5\\%\\).", "hints": ["Find the increase in dollars first.", "Divide the increase by the original amount, then multiply by 100."], "source": "CHIJ St Nicholas Girls' School 2025 P6 Weighted Assessment 2 Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 5%. Answer given as a percentage." }, { "n": 3, "type_id": 2, "question": "The figure is made up of four identical rectangles with a breadth of 5 cm and a square with an area of 225 cm². Find the total area of the 4 rectangles.
[?]", "answer0": "400", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 223, "difficulty_id": 2, "explanation": "Square area 225 cm² means each side = 15 cm (15 × 15 = 225). The length of each rectangle = 15 + 5 = 20 cm. One rectangle = 20 × 5 = 100 cm². Four rectangles = 100 × 4 = 400 cm².", "hints": ["Find the side of the square from its area.", "The rectangle length equals the square side plus the breadth; find one rectangle then multiply by 4."], "source": "CHIJ St Nicholas Girls' School 2025 P6 Weighted Assessment 2 Q3", "image_needed": true, "image_options": false, "image_file": "q3.png", "image_page": 3, "image_bbox": [0.36, 0.16, 0.62, 0.34], "image_loc": "left-middle of page; square (225 cm²) framed by four rectangles, 5 cm marked at top-left", "notes": "Key: 400 cm². Answer in cm²." }, { "n": 4, "type_id": 2, "question": "QSTU is a parallelogram. RQS is an isosceles triangle. QR = QS, RQU and PQS are straight lines. \\(\\angle PQU = 35°\\).
(a) Find \\(\\angle QRS\\). [?]
(b) Find \\(\\angle STU\\). [?]", "answer0": "72.5", "answer1": "145", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 3, "explanation": "(a) \\(\\angle RQS = \\angle PQU = 35°\\) (vertically opposite). Triangle RQS is isosceles with QR = QS, so \\(\\angle QRS = \\angle QSR = (180° − 35°) ÷ 2 = 72.5°\\). (b) In parallelogram QSTU, \\(\\angle STU = \\angle SQU = 180° − 35° = 145°\\).", "hints": ["Use vertically opposite angles to find ∠RQS, then split the remaining angle equally in the isosceles triangle.", "Opposite angles of a parallelogram are equal; ∠STU equals ∠SQU."], "source": "CHIJ St Nicholas Girls' School 2025 P6 Weighted Assessment 2 Q4", "image_needed": true, "image_options": false, "image_file": "q4.png", "image_page": 4, "image_bbox": [0.18, 0.2, 0.72, 0.4], "image_loc": "upper-middle of page; parallelogram QSTU with triangle RQS and line P through Q, 35° marked at Q", "notes": "Key: (a) 72.5°, (b) 145°. Part (c) of the printed paper (circle is/is not a trapezium and is/is not parallel) is interactive circling and is omitted. Answers in degrees." }, { "n": 5, "type_id": 2, "question": "Great Singapore Sale! Buy first refrigerator at 20% discount. Buy second refrigerator at 40% discount. Sue paid $1120 for two refrigerators during the Great Singapore Sale. How much would she have had to pay for the two refrigerators when there was no sale?
[?]", "answer0": "1600", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 207, "difficulty_id": 3, "explanation": "First fridge sale price = 100% − 20% = 80% of its usual price; second = 100% − 40% = 60%. If both usual prices were equal, total paid = 80% + 60% = 140% of one usual price = $1120, so 100% = $1120 ÷ 140 × 100 = $800 each, and two at full price = 200% = \\(\\dfrac{1120}{140} \\times 200 = \\$1600\\).", "hints": ["Write each fridge's sale price as a percentage of its usual price (80% and 60%).", "The two sale prices total 140% → $1120; scale to 200% for the no-sale total."], "source": "CHIJ St Nicholas Girls' School 2025 P6 Weighted Assessment 2 Q5", "image_needed": true, "image_options": false, "image_file": "q5.png", "image_page": 5, "image_bbox": [0.2, 0.11, 0.82, 0.27], "image_loc": "top of page; 'Great Singapore Sale!' poster with two refrigerators and discount labels (20% and 40%)", "notes": "Key: $1600. The two refrigerators are taken as having equal usual price. Answer in dollars." }, { "n": 6, "type_id": 2, "question": "The shaded figure is formed by 3 straight lines and 6 identical quarter circles. Take \\(\\pi = 3.14\\). The figure is 16 cm wide and 9 cm tall.
(a) What is the radius of each quarter circle? [?]
(b) Find the area of the shaded figure. [?]
(c) Find the perimeter of the shaded figure. [?]", "answer0": "3", "answer1": "101.61", "answer2": "54.26", "answer3": null, "correct_answer": null, "skill_id": 221, "difficulty_id": 3, "explanation": "(a) Three quarter circles stack along the 9 cm height, so radius = 9 ÷ 3 = 3 cm. (b) Per the key, the shaded area = 101.61 cm². (c) Straight edges: 16 − 3 = 13, 9 − 3 = 3, and 16 − 3 − 3 − 3 = 7, giving 13 + 6 + 7. Curved part = 6 quarter circles = \\(6 \\times \\dfrac{1}{4} \\times 3.14 \\times 2 \\times 3 = 28.26\\) cm. Perimeter = 28.26 + 13 + 6 + 7 = 54.26 cm.", "hints": ["Three quarter-circle radii fit along the 9 cm side to find the radius.", "Perimeter combines the straight edges with the arc lengths of the six quarter circles."], "source": "CHIJ St Nicholas Girls' School 2025 P6 Weighted Assessment 2 Q6", "image_needed": true, "image_options": false, "image_file": "q6.png", "image_page": 6, "image_bbox": [0.24, 0.16, 0.64, 0.33], "image_loc": "upper-middle of page; shaded rectangle 16 cm by 9 cm with quarter-circle bites along the edges", "notes": "Key: (a) 3 cm, (b) 101.61 cm², (c) 54.26 cm. Answers: radius in cm, area in cm², perimeter in cm." }, { "n": 7, "type_id": 1, "question": "Mrs Koh had some red pens and 280 blue pens. She sold 50 red pens and 30% of the blue pens. After that, the ratio of the number of red pens to blue pens Mrs Koh had left was 3 : 7. (a) How many blue pens did Mrs Koh sell? (b) What fraction of the red pens were sold? Give your answer in the simplest form.", "answer0": "\\(\\dfrac{25}{67}\\)", "answer1": "\\(\\dfrac{50}{134}\\)", "answer2": "\\(\\dfrac{25}{42}\\)", "answer3": "\\(\\dfrac{50}{84}\\)", "correct_answer": 0, "skill_id": 213, "difficulty_id": 3, "explanation": "(a) Blue pens sold = \\(280 \\times \\dfrac{30}{100} = 84\\). (b) Blue pens left = 280 − 84 = 196 = 7 units, so 1 unit = 28 and red pens left = 3 × 28 = 84. Total red at first = 84 + 50 = 134. Fraction of red pens sold = \\(\\dfrac{50}{134} = \\dfrac{25}{67}\\).", "hints": ["Find 30% of 280 for the blue pens sold.", "Use the 3 : 7 ratio with the blue pens left to find red pens left, add back the 50 sold, then form the fraction."], "source": "CHIJ St Nicholas Girls' School 2025 P6 Weighted Assessment 2 Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Part (a) answer is 84 (stated in explanation). Part (b) answer is a fraction (25/67) so the question is rendered as MCQ on the final-answer part. Key: (a) 84, (b) 25/67." }, { "n": 8, "type_id": 2, "question": "Black and white tiles are used to form figures that follow a pattern. The table shows the number of white tiles and black tiles for the first four figures: Figure 1 — 1 white, 3 black, 4 total; Figure 2 — 3 white, 6 black, 9 total; Figure 3 — 7 white, 9 black, 16 total; Figure 4 — 13 white, 12 black, 25 total; Figure 5 — total 36.
(a) Complete the table for Figure 5: number of white tiles [?] and number of black tiles [?].
(b) Find the total number of white and black tiles in Figure 10. [?]
(c) Which figure number has 133 white tiles? [?]", "answer0": "21", "answer1": "15", "answer2": "121", "answer3": "12", "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "Total for Figure n = (n + 1)². (a) Figure 5 total = 36, black tiles = 3 × 5 = 15, so white = 36 − 15 = 21. (b) Figure 10 total = (10 + 1)² = 11 × 11 = 121. (c) White tiles grow 1, 3, 7, 13, 21, 31, 43, 57, 73, 91, 111, 133 → 133 white tiles occur at Figure 12.", "hints": ["Total tiles for Figure n is (n + 1)²; black tiles are 3 × n.", "List the white-tile counts figure by figure until you reach 133."], "source": "CHIJ St Nicholas Girls' School 2025 P6 Weighted Assessment 2 Q8", "image_needed": true, "image_options": false, "image_file": "q8.png", "image_page": 9, "image_bbox": [0.18, 0.13, 0.82, 0.25], "image_loc": "top of page; Figures 1 to 4 of the growing black-and-white tile pyramids", "notes": "Key: (a) white 21, black 15; (b) 121; (c) Figure 12. Four blanks in order: Fig5 white, Fig5 black, Fig10 total, figure number." }, { "n": 9, "type_id": 2, "question": "At first, Mr Singh had some eggs. He sold \\(\\dfrac{4}{9}\\) of his eggs and gave away 36 eggs. He had \\(\\dfrac{1}{2}\\) of the eggs left and he put them on 30 trays. Some trays had 10 eggs while the rest had 12 eggs.
(a) How many eggs were put on the 30 trays? [?]
(b) How many trays had 10 eggs? [?]
(c) Special Offer: Buy 12 eggs, get 2 more eggs free. Mrs Toh took home 56 eggs with the special offer. She paid $2.80 less with the special offer. What was the price of 12 eggs without the special offer? [?]", "answer0": "324", "answer1": "18", "answer2": "4.20", "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "(a) Eggs left = total − sold − given away. \\(1 − \\dfrac{4}{9} − \\dfrac{1}{2} = \\dfrac{18}{18} − \\dfrac{8}{18} − \\dfrac{9}{18} = \\dfrac{1}{18}\\) of the total = 36 eggs given away, so total = 36 × 18 = 648, and the eggs on trays = \\(\\dfrac{1}{2}\\) of 648 = 324. (b) If all 30 trays held 12, that would be 12 × 30 = 360; actual is 324, a shortfall of 360 − 324 = 36. Each 10-egg tray is 12 − 10 = 2 fewer, so 36 ÷ 2 = 18 trays had 10 eggs. (c) With the offer, 56 eggs = buying 4 lots of 12 (12 + 12 = 24 eggs per two-pack pattern → 56 ÷ 14 = 4 paid dozens). The $2.80 saving spread over 8 free eggs is $2.80 ÷ 8 = $0.35 per egg, so 12 eggs without the offer = 0.35 × 12 = $4.20.", "hints": ["Find the fraction of eggs given away (1 − 4/9 − 1/2) and equate it to 36 to get the total.", "For (b) assume all trays held 12 and use the shortfall; for (c) work out the price per egg from the $2.80 saving."], "source": "CHIJ St Nicholas Girls' School 2025 P6 Weighted Assessment 2 Q9", "image_needed": true, "image_options": false, "image_file": "q9.png", "image_page": 11, "image_bbox": [0.33, 0.12, 0.68, 0.27], "image_loc": "top of page 11; 'Special Offer' box with an egg carton — Buy 12 eggs, get 2 more eggs free (relates to part c)", "notes": "Key: (a) 324 eggs, (b) 18 trays, (c) $4.20. Three blanks in order. Part (c) figure (egg-carton special offer) is on page 11." } ] }