{ "paper": { "school": "Raffles Girls' Primary School", "year": 2023, "level": "P6", "label": "Weighted Assessment 2", "source_prefix": "Raffles 2023 P6 Weighted Assessment 2", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 2, "question": "\\(18 : [?] = 3 : 4\\)", "answer0": "24", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 213, "difficulty_id": 1, "explanation": "In equivalent ratios, the multiplier is 18 ÷ 3 = 6. So the missing number = 4 × 6 = 24. Answer: 24.", "hints": ["The two ratios are equivalent, so find what 3 was multiplied by to get 18.", "18 ÷ 3 = 6, so multiply 4 by the same factor."], "source": "Raffles 2023 P6 Weighted Assessment 2 Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q1 confirms: 18÷3=6, 4×6=24." }, { "n": 2, "type_id": 1, "question": "There are 60 marbles in a box. 16 marbles are blue and the rest are green. What is the ratio of the number of blue marbles to the number of green marbles? Give your answer in the simplest form.", "answer0": "4 : 11", "answer1": "11 : 4", "answer2": "4 : 15", "answer3": "16 : 60", "correct_answer": 0, "skill_id": 212, "difficulty_id": 1, "explanation": "Green = 60 − 16 = 44. Blue : Green = 16 : 44 = 4 : 11. Answer: 4 : 11.", "hints": ["First find the number of green marbles: 60 − 16.", "Write blue : green, then divide both by their common factor."], "source": "Raffles 2023 P6 Weighted Assessment 2 Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Ratio answer → MCQ. Answer key Q2 confirms 16:44 = 4:11." }, { "n": 3, "type_id": 2, "question": "In the figure, O is the centre of the circle with a diameter of 12 cm. Find the area of the shaded part. (Take \\(\\pi = 3.14\\)) [?]", "answer0": "84.78", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 222, "difficulty_id": 2, "explanation": "Radius = 12 ÷ 2 = 6 cm. The shaded part is three-quarters of the circle. Area = \\(\\dfrac{3}{4} \\times 3.14 \\times 6 \\times 6\\) = 84.78 cm². Answer: 84.78 cm².", "hints": ["The diameter is 12 cm, so the radius is 6 cm.", "The unshaded quarter is removed, so the shaded part is 3/4 of the whole circle area \\(\\pi r^2\\)."], "source": "Raffles 2023 P6 Weighted Assessment 2 Q3", "image_needed": true, "image_options": false, "image_file": "q3.png", "image_page": 3, "image_bbox": [0.16, 0.15, 0.45, 0.33], "image_loc": "left side of page, below the question text: a circle with centre O and a small unshaded quarter (top-right), the rest shaded", "notes": "Answer unit is cm². Answer key Q3 confirms 3/4 × 3.14 × 6 × 6 = 84.78 cm²." }, { "n": 4, "type_id": 2, "question": "The figure is made up of a square and a quadrant. The length of the square is 42 cm. Find the perimeter of the shaded part. (Take \\(\\pi = \\dfrac{22}{7}\\)) [?]", "answer0": "159", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 223, "difficulty_id": 2, "explanation": "The quadrant has radius = 42 ÷ 2 = 21 cm. Arc of the quadrant = \\(\\dfrac{1}{4} \\times \\dfrac{22}{7} \\times 2 \\times 21\\) = 33 cm. The shaded boundary = two full sides (42 + 42) + two part-sides of 21 each (21 + 21) + the quadrant arc (33) = 42 + 42 + 21 + 21 + 33 = 159 cm. Answer: 159 cm.", "hints": ["The quadrant is cut from one corner of the square; its radius is half the side, 21 cm.", "Add the straight edges of the shaded part to the curved quarter-arc length."], "source": "Raffles 2023 P6 Weighted Assessment 2 Q4", "image_needed": true, "image_options": false, "image_file": "q4.png", "image_page": 3, "image_bbox": [0.15, 0.5, 0.42, 0.71], "image_loc": "left side of page, below the question: a shaded square with a white quarter-circle cut from the bottom-right corner", "notes": "Answer unit is cm. Answer key Q4 confirms 42+21+33+21+42 = 159 cm." }, { "n": 5, "type_id": 2, "question": "The ratio of the number of men to women to children at a concert was 5 : 12 : 8. There were 1200 people at the concert altogether. How many children were at the concert? [?]", "answer0": "384", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 213, "difficulty_id": 2, "explanation": "Total units = 5 + 12 + 8 = 25 units = 1200. 1 unit = 1200 ÷ 25 = 48. Children = 8 units = 8 × 48 = 384. Answer: 384.", "hints": ["Add the ratio parts to find the total number of units.", "Find the value of 1 unit, then multiply by the children's share (8 units)."], "source": "Raffles 2023 P6 Weighted Assessment 2 Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q5 confirms 25u=1200, u=48, 8u=384." }, { "n": 6, "type_id": 1, "question": "In a fruit stall, \\(\\dfrac{2}{7}\\) of the number of apples is equal to \\(\\dfrac{1}{6}\\) of the number of oranges. What is the ratio of the number of apples to the number of oranges?", "answer0": "7 : 12", "answer1": "12 : 7", "answer2": "2 : 6", "answer3": "1 : 3", "correct_answer": 0, "skill_id": 212, "difficulty_id": 2, "explanation": "\\(\\dfrac{2}{7}\\) of apples = \\(\\dfrac{1}{6}\\) of oranges. So \\(\\dfrac{2A}{7} = \\dfrac{O}{6}\\), giving 12A = 7O, so A : O = 7 : 12. Answer: 7 : 12.", "hints": ["Set up the equation \\(\\dfrac{2}{7}\\)A = \\(\\dfrac{1}{6}\\)O and cross-multiply.", "Rearrange to compare A and O directly."], "source": "Raffles 2023 P6 Weighted Assessment 2 Q6", "image_needed": false, "image_options": false, "image_file": null, "notes": "Ratio answer → MCQ. Answer key Q6 confirms 7:12." }, { "n": 7, "type_id": 2, "question": "Figure ACDF is made up of a square and a rectangle. The ratio of the length of AB to the length of BC is 1 : 2. The perimeter of rectangle ACDF is 160 cm. Find the area of square ABEF. [?]", "answer0": "400", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 223, "difficulty_id": 2, "explanation": "Let AB = 1 unit, BC = 2 units, so AC = 3 units (the length) and the width AF = AB = 1 unit. Perimeter of ACDF = 2 × (3u + 1u) = 8 units = 160 cm, so 1 unit = 20 cm. Square ABEF has side 20 cm, area = 20 × 20 = 400 cm². Answer: 400 cm².", "hints": ["The width of the figure equals AB (the side of the square), and the length AC = AB + BC.", "Express the perimeter in units, find 1 unit, then square the side of ABEF."], "source": "Raffles 2023 P6 Weighted Assessment 2 Q7", "image_needed": true, "image_options": false, "image_file": "q7.png", "image_page": 5, "image_bbox": [0.22, 0.15, 0.68, 0.27], "image_loc": "centre of page, below the question: rectangle ACDF with vertices A,B,C across the top and F,E,D across the bottom; B-E divides it into square ABEF and a rectangle", "notes": "Answer unit is cm². Answer key Q7 confirms 8u=160, u=20, 20×20=400 cm²." }, { "n": 8, "type_id": 2, "question": "The ratio of the number of pies to the number of buns at a bakery was 8 : 3. After 203 pies were sold, the ratio of the number of pies to the number of buns became 3 : 2. How many buns were there at the bakery? [?]", "answer0": "174", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 214, "difficulty_id": 3, "explanation": "The number of buns does not change. Let buns = 3 units (so pies = 8 units at first). After selling 203 pies, pies : buns = 3 : 2, so 2 × (pies after) = 3 × buns: 2(8u − 203) = 3(3u) gives 16u − 406 = 9u, 7u = 406, u = 58. Buns = 3u = 174. Answer: 174.", "hints": ["The number of buns stays the same before and after the sale.", "Set the buns to a fixed number of units in both ratios and form an equation from the second ratio."], "source": "Raffles 2023 P6 Weighted Assessment 2 Q8", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q8 worked 7u=203→u=29→6u=174 but printed '124', an arithmetic typo (6×29=174). Correct buns = 174." }, { "n": 9, "type_id": 2, "question": "A plot of land is divided into three rectangular fields of equal width. JM = 42 m and JK = 46 m. The fields are fenced using 252 m of fencing, indicated by the dashed lines in the figure. Find the length of ML. [?]", "answer0": "38", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 223, "difficulty_id": 3, "explanation": "The three fields have equal width = 42 ÷ 3 = 14 m. The fencing (dashed lines) total 252 m. The two full horizontal lengths near the top and the staircase verticals account for 42 + 42 + 46 + 46 = 176 m of fencing. The remaining fencing = 252 − 176 = 76 m forms the two equal lengths along the bottom, so ML = 76 ÷ 2 = 38 m. Answer: 38 m.", "hints": ["Each field's width is 42 ÷ 3 m; work out which edges the dashed fencing covers.", "Subtract the known fenced lengths from 252 m, then split the remainder."], "source": "Raffles 2023 P6 Weighted Assessment 2 Q9", "image_needed": true, "image_options": false, "image_file": "q9.png", "image_page": 6, "image_bbox": [0.13, 0.18, 0.55, 0.43], "image_loc": "left side of page, below the question: a staircase-shaped figure with corners J,K (top, 46 m apart), 42 m down the left side to M, and L at bottom with '?' marking ML", "notes": "Answer unit is m. Answer key Q9: 252−176=76 (printed '786', a typo), 76÷2=38 m." }, { "n": 10, "type_id": 2, "question": "Salim baked some cookies. He ate \\(\\dfrac{1}{4}\\) of the cookies. The rest of the cookies were given to Alex, Bala and Caili in the ratio of 9 : 5 : 4. The number of cookies Alex received was 145 more than the number of cookies Caili received. How many cookies did Salim bake? [?]", "answer0": "696", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 214, "difficulty_id": 3, "explanation": "Alex − Caili = 9u − 4u = 5u = 145, so 1 unit = 29 cookies. The rest given away = 9 + 5 + 4 = 18 units. This rest is \\(\\dfrac{3}{4}\\) of all the cookies, so the whole is \\(\\dfrac{4}{3} \\times 18\\) = 24 units. Total baked = 24 × 29 = 696. Answer: 696.", "hints": ["Use Alex − Caili = 145 to find the value of one ratio unit.", "The 18 units given away are 3/4 of all the cookies; scale up to the whole."], "source": "Raffles 2023 P6 Weighted Assessment 2 Q10", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q10 confirms 5u=145, u=29, 24u=696." }, { "n": 11, "type_id": 2, "question": "Lily has a piece of square paper, PQRS. She folded the paper into 2 equal halves along PR. She then cut off the corners along XY. Find the area of the remaining paper. [?]", "answer0": "96", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 223, "difficulty_id": 3, "explanation": "The square PQRS has side 12 cm, area = 12 × 12 = 144 cm². PX = 4 cm, so the cut leaves XQ = 12 − 4 = 8 cm. On the folded paper the cut removes a right triangle with legs 6 and 8 (XY runs from X down to Y on QR), area = \\(\\dfrac{6 \\times 8}{2}\\) = 24 cm²; unfolding doubles this to 24 × 2 = 48 cm² removed. Remaining area = 144 − 48 = 96 cm². Answer: 96 cm².", "hints": ["Find the full area of the 12 cm square first.", "Work out the triangular piece cut off on the folded (half) paper, then double it before subtracting."], "source": "Raffles 2023 P6 Weighted Assessment 2 Q11", "image_needed": true, "image_options": false, "image_file": "q11.png", "image_page": 8, "image_bbox": [0.13, 0.16, 0.85, 0.37], "image_loc": "upper half of page: two diagrams - 'Before folding' square PQRS (12 cm) with diagonal PR, and 'After folding' triangle with PX = 4 cm and cut line XY", "notes": "Answer unit is cm². Answer key Q11 confirms 12×12=144, cut 6×8÷2=24, ×2=48, 144−48=96 cm²." }, { "n": 12, "type_id": 1, "question": "Alan, Ben, and Chandra shared the cost of a present for their cousin. Alan paid \\(\\dfrac{1}{5}\\) of the total amount. Ben paid \\(\\dfrac{3}{5}\\) of the total amount Alan and Chandra paid. What is the ratio of the amount Alan paid to the total amount Ben and Chandra paid? Give your answer in the simplest form.", "answer0": "1 : 4", "answer1": "4 : 1", "answer2": "1 : 5", "answer3": "1 : 3", "correct_answer": 0, "skill_id": 210, "difficulty_id": 2, "explanation": "Alan paid \\(\\dfrac{1}{5}\\) of the total, so Ben and Chandra together paid the remaining \\(\\dfrac{4}{5}\\). Alan : (Ben + Chandra) = \\(\\dfrac{1}{5} : \\dfrac{4}{5}\\) = 1 : 4. Answer: 1 : 4.", "hints": ["If Alan paid 1/5 of the total, what fraction did Ben and Chandra pay together?", "Compare Alan's 1/5 with the rest, 4/5."], "source": "Raffles 2023 P6 Weighted Assessment 2 Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "Part (a) only (ratio → MCQ). Part (b) split into Q12b. Answer key Q12(a) confirms 1:4." }, { "n": 13, "type_id": 2, "question": "Alan, Ben, and Chandra shared the cost of a present for their cousin. Alan paid \\(\\dfrac{1}{5}\\) of the total amount. Ben paid \\(\\dfrac{3}{5}\\) of the total amount Alan and Chandra paid. Given that the present cost $224, how much did Chandra pay for the present? [?]", "answer0": "95.20", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 214, "difficulty_id": 3, "explanation": "Let the total be 5 units; Alan = 1 unit, so Ben + Chandra = 4 units. Ben = \\(\\dfrac{3}{5}\\) of (Alan + Chandra). Take the total as 40 small units: Alan = 8, Ben + Chandra = 32. Ben = \\(\\dfrac{3}{5}\\)(Alan + Chandra) gives Ben = 15, so Chandra = 32 − 15 = 17 units. Total $224 = 40 units, so 1 unit = $5.60 and Chandra = 17 × $5.60 = $95.20. Answer: $95.20.", "hints": ["Use the same units as part (a); the total is 5 (or 40) units.", "Express Ben as 3/5 of (Alan + Chandra) to find Chandra's units, then scale to $224."], "source": "Raffles 2023 P6 Weighted Assessment 2 Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "This is Q12 part (b); money answer ($95.20) → FIB decimal. Answer key Q12(b) confirms 40u=224, 17u=$95.20." }, { "n": 14, "type_id": 2, "question": "The figure is made up of 5 equilateral triangles and a circle. O is the centre of the circle with diameter 30 cm. (a) Find the circumference of the circle. (Take \\(\\pi = 3.14\\)) [?]", "answer0": "94.2", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 220, "difficulty_id": 1, "explanation": "Circumference = \\(\\pi \\times d\\) = 3.14 × 30 = 94.2 cm. Answer: 94.2 cm.", "hints": ["Circumference = \\(\\pi \\times\\) diameter.", "Multiply 3.14 by 30."], "source": "Raffles 2023 P6 Weighted Assessment 2 Q13", "image_needed": true, "image_options": false, "image_file": "q14.png", "image_page": 10, "image_bbox": [0.36, 0.07, 0.68, 0.28], "image_loc": "top-centre of page: a circle with centre O and a diameter line, with 5 equilateral triangles arranged in a zig-zag along the diameter; lower part shaded", "notes": "This is Q13 part (a). Answer unit is cm. Answer key Q13(a) confirms 3.14×30=94.2 cm." }, { "n": 15, "type_id": 2, "question": "The figure is made up of 5 equilateral triangles and a circle. O is the centre of the circle with diameter 30 cm. (b) Find the perimeter of the shaded part. Round your answer to the nearest centimetre. (Take \\(\\pi = 3.14\\)) [?]", "answer0": "107", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 222, "difficulty_id": 3, "explanation": "The shaded boundary is the lower semicircular arc plus the two radii along the diameter. Semicircle arc = 94.2 ÷ 2 = 47.1 cm. The two straight parts along the diameter total 30 + 30 = 60 cm... the shaded perimeter = 47.1 + 30 + 30 = 107.1 cm, which rounds to 107 cm. Answer: 107 cm.", "hints": ["Half the circumference gives the curved part of the shaded boundary.", "Add the straight edges along the diameter, then round to the nearest cm."], "source": "Raffles 2023 P6 Weighted Assessment 2 Q13", "image_needed": true, "image_options": false, "image_file": "q15.png", "image_page": 10, "image_bbox": [0.36, 0.07, 0.68, 0.28], "image_loc": "top-centre of page (same figure as Q14): circle with centre O, diameter line and 5 equilateral triangles; lower region shaded", "notes": "This is Q13 part (b). Answer unit is cm. Answer key Q13(b) confirms 47.1+30+30=107.1 ≈ 107 cm." } ] }