{ "paper": { "school": "CHIJ St Nicholas Girls' School (Primary)", "year": 2023, "level": "P6", "label": "Weighted Assessment 2", "source_prefix": "St Nicholas 2023 P6 Weighted Assessment 2", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 2, "question": "A fruit seller sold some apples, mangoes and oranges in the ratio 7 : 3 : 6. He sold 336 apples, mangoes and oranges altogether. How many oranges did the fruit seller sell? [?]", "answer0": "126", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 213, "difficulty_id": 1, "explanation": "Method: total units then find the orange share.
Total units = 7 + 3 + 6 = 16.
1 unit = 336 ÷ 16 = 21 oranges.
Oranges = 6 units = 21 × 6 = 126.", "hints": ["Add the ratio parts to get the total number of units.", "Divide 336 by the total units to find the value of 1 unit, then multiply by the orange parts (6)."], "source": "St Nicholas 2023 P6 Weighted Assessment 2 Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 126." }, { "n": 2, "type_id": 2, "question": "A cubical tank of edge 56 cm was \\(\\dfrac{1}{7}\\) filled with water at first. Water flowed from a tap into the tank at a rate of 4.5 ℓ per minute. Find the volume of water in the tank after 15 minutes. [?] ml", "answer0": "92588", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 191, "difficulty_id": 2, "explanation": "Method: initial volume + water added.
Initial water height = 56 × \\(\\dfrac{1}{7}\\) = 8 cm, so initial volume = 8 × 56 × 56 = 25088 cm³.
Water added = 4.5 ℓ = 4500 ml per minute; in 15 minutes = 4500 × 15 = 67500 ml (cm³).
Total = 67500 + 25088 = 92588 ml.", "hints": ["1/7 of the tank is filled — find the initial volume = 1/7 of (56 × 56 × 56), i.e. 8 × 56 × 56.", "Convert 4.5 ℓ to ml (1 ℓ = 1000 ml), multiply by 15 minutes, then add the initial volume."], "source": "St Nicholas 2023 P6 Weighted Assessment 2 Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "1 ml = 1 cm³. Answer key: 92588 ml." }, { "n": 3, "type_id": 2, "question": "The figure is made up of a rhombus ABEG and a square BCDF.
(a) Name an obtuse angle. [?]
(b) Find ∠x. [?]°
(c) Find ∠y. [?]°", "answer0": "∠y", "answer1": "52", "answer2": "105", "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 2, "explanation": "(a) ∠y is an obtuse angle (it works out to 105°, greater than 90°).
(b) ∠x: angles on a straight line at E — 180 − 128 = 52°.
(c) ∠y: in triangle FEG, the angle at E inside = ∠x + 23 = 52 + 23 = 75°; ∠y is on a straight line with this, so ∠y = 180 − 75 = 105°.", "hints": ["An obtuse angle is between 90° and 180°; the 128° and y angles are candidates — the key names ∠y.", "∠x = 180° − 128° (angles on a straight line). For ∠y, use the angle (∠x + 23°) and angles on a straight line."], "source": "St Nicholas 2023 P6 Weighted Assessment 2 Q3", "image_needed": true, "image_options": false, "image_file": "q3.png", "image_page": 4, "image_bbox": [0.20, 0.20, 0.72, 0.42], "image_loc": "rhombus ABEG and square BCDF figure near top of the page, below the question stem", "notes": "Answer key: (a) ∠Y obtuse, (b) x = 52°, (c) y = 105°. (a) accepts ∠y / ∠BGE; angle answers are integers so FIB is used." }, { "n": 4, "type_id": 2, "question": "Jia Hui's salary was \\(\\dfrac{4}{7}\\) of Aishah's salary. Jia Hui spent $729. Aishah did not spend any money. In the end, the amount of money Jia Hui had left to the amount of money Aishah had was 2 : 5. How much was Jia Hui's salary? $[?]", "answer0": "2430", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 214, "difficulty_id": 3, "explanation": "Method: make Aishah a common base.
Start: Jia Hui : Aishah = 4 : 7.
End ratio (Jia Hui left) : Aishah = 2 : 5. Make Aishah the same in both: 4 : 7 × 5 = 20 : 35; 2 : 5 × 7 = 14 : 35.
The drop in Jia Hui's units = 20 − 14 = 6 units = $729 spent, so 1 unit = 729 ÷ 6 = $121.50.
Jia Hui's salary = 20 units = 121.5 × 20 = $2430.", "hints": ["Aishah's amount never changes — rewrite both ratios so Aishah's part is the same number (e.g. 35).", "The change in Jia Hui's units equals the $729 she spent; find 1 unit, then her original salary (20 units)."], "source": "St Nicholas 2023 P6 Weighted Assessment 2 Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer is money $2430 (whole dollars) — FIB. Answer key: $2430." }, { "n": 5, "type_id": 2, "question": "Shanti wanted to buy a sofa set. The sofa set in Shop A was sold at a 5% discount and the similar sofa set in Shop B was sold at a 20% discount. Both shops sold the sofa set at the same price before discount.
To buy the sofa set in Shop A, Shanti would need $150 more than what she had. Shanti bought the sofa set in Shop B and had $300 left.
(a) What was the price of the sofa set before discount? $[?]
(b) How much money did Shanti have at first? $[?]", "answer0": "3000", "answer1": "2700", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 209, "difficulty_id": 3, "explanation": "(a) Shop A price = 95% of full price; Shop B price = 80% of full price. The difference between what she'd need at A and at B is $150 + $300 = $450, which equals (95% − 80%) = 15% of the full price.
15% → $450, so 1% → $30, full price = 30 × 100 = $3000.
(b) Shop B price = 80% of 3000 = $2400. She had $300 left after paying, so she had 2400 + 300 = $2700 at first.", "hints": ["Shop A costs 95% and Shop B costs 80% of the full price; the gap (95% − 80% = 15%) corresponds to $150 + $300 = $450.", "Find the full price from 15% = $450, then Shop B's price (80%), then add the $300 she had left."], "source": "St Nicholas 2023 P6 Weighted Assessment 2 Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: (a) $3000, (b) $2700." }, { "n": 6, "type_id": 2, "question": "The figure is formed by three identical circles with centres A, C and E. ABEF and BCDE are identical squares of side 10 cm. AC and FD are straight lines. (Take π = 3.14)
(a) Find the total area of the shaded parts. [?] cm²
(b) Find the perimeter of the shaded parts. [?] cm", "answer0": "714", "answer1": "188.4", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 222, "difficulty_id": 3, "explanation": "(a) Radius = 10 cm. Unshaded inside each square pair: half a square (\\(\\dfrac{1}{2}\\)×10×10 = 50) and a quarter circle (\\(\\dfrac{1}{4}\\)×3.14×10×10 = 78.5), so the white bite per region = 78.5 − 50 = 28.5 cm². Area of one full circle = 3.14×10×10 = 314; three circles = 314×3 = 942. Subtract the white bites: 28.5×8 = 228; shaded area = 942 − 228 = 714 cm².
(b) Perimeter: circumference of one circle = 3.14×20 = 62.8 cm; the shaded boundary = 62.8×3 = 188.4 cm.", "hints": ["Each circle has radius 10 cm (square side). Find the area of three full circles, then subtract the white overlap pieces.", "For the perimeter, the outer boundary equals 3 full circumferences; use C = π × diameter = 3.14 × 20."], "source": "St Nicholas 2023 P6 Weighted Assessment 2 Q6", "image_needed": true, "image_options": false, "image_file": "q6.png", "image_page": 7, "image_bbox": [0.28, 0.15, 0.62, 0.36], "image_loc": "three overlapping shaded circles figure (centres A, C, E) near top of page, below the question stem", "notes": "Answers are decimals — FIB. Answer key: (a) 714 cm², (b) 188.4 cm." }, { "n": 7, "type_id": 2, "question": "The line graph shows the mass of newspapers a class collected at the end of each month for 6 months.
(a) In which month was the increase in the mass of newspapers collected the greatest? [?]
(b) Find the percentage decrease in the mass of newspapers collected from March to April. [?]%
(c) The collection of newspapers continued until December. In February, the class collected \\(\\dfrac{2}{9}\\) of the total mass of newspapers collected. What was the total mass of the newspapers collected from January to December? [?] kg", "answer0": "June", "answer1": "47", "answer2": "78.3", "answer3": null, "correct_answer": null, "skill_id": 209, "difficulty_id": 2, "explanation": "(a) Compare monthly increases: Jan→Feb 17.4−13.2 = 4.2; Feb→Mar 20−17.4 = 2.6; Apr→May 12.6−10.6 = 2; May→Jun 21.4−12.6 = 8.8. Greatest increase is in June.
(b) March = 20 kg, April = 10.6 kg; decrease = 20 − 10.6 = 9.4 kg; percentage = \\(\\dfrac{9.4}{20}\\) × 100 = 47%.
(c) February mass = 17.4 kg = \\(\\dfrac{2}{9}\\) of the total, so 1/9 = 17.4 ÷ 2 = 8.7 kg; total = 8.7 × 9 = 78.3 kg.", "hints": ["(a) Work out the rise between each pair of consecutive months and pick the largest; (b) percentage decrease = decrease ÷ original (March) × 100.", "(c) February's reading is 2/9 of the whole; find 1/9 (half of February), then multiply by 9."], "source": "St Nicholas 2023 P6 Weighted Assessment 2 Q7", "image_needed": true, "image_options": false, "image_file": "q7.png", "image_page": 8, "image_bbox": [0.16, 0.12, 0.85, 0.55], "image_loc": "line graph of newspaper mass (kg) vs month Jan–Jun, below the question stem on the page", "notes": "(a) answers 'June' (greatest increase 8.8 kg, May→June). (b) 47%, (c) 78.3 kg — all FIB. Readings from graph: Jan 13.2, Feb 17.4, Mar 20, Apr 10.6, May 12.6, Jun 21.4." }, { "n": 8, "type_id": 2, "question": "Basheer drew some identical rectangles along a straight line on a piece of paper to form the figure as shown. Each rectangle has a length of 7.2 cm and a breadth of 5 cm. The shaded squares are the overlapping parts. Each shaded square has a side of 2.4 cm.
(a) What was the length of the figure formed by Basheer using 4 such rectangles? [?] cm
(b) Find the area of the figure which was formed by using 4 such rectangles. [?] cm²
(c) Basheer continued to draw more rectangles along the straight line. The distance between the first rectangle and the last rectangle was 290.4 cm. How many rectangles did he draw altogether? [?]", "answer0": "21.6", "answer1": "126.72", "answer2": "60", "answer3": null, "correct_answer": null, "skill_id": 138, "difficulty_id": 3, "explanation": "Each rectangle is 7.2 cm long; consecutive rectangles overlap by 2.4 cm, so each new rectangle adds 7.2 − 2.4 = 4.8 cm.
(a) 4 rectangles: 4.8 + 4.8 + 4.8 + 7.2 = 21.6 cm.
(b) Total area of 4 rectangles = 7.2 × 5 × 4 = 144 cm². Each overlap square = 2.4 × 2.4 = 5.76 cm²; there are 3 overlaps = 5.76 × 3 = 17.28 cm² counted twice. Area = 144 − 17.28 = 126.72 cm².
(c) Distance first→last = 290.4 cm. Each step (gap) = 4.8 cm after removing one final rectangle's 7.2: 290.4 − 7.2 = 283.2; 283.2 ÷ 4.8 = 59 steps; rectangles = 59 + 1 = 60.", "hints": ["Overlap is 2.4 cm, so each extra rectangle adds 7.2 − 2.4 = 4.8 cm to the length.", "(b) Add up 4 rectangle areas then subtract the 3 overlapping squares (counted twice). (c) Subtract one rectangle length from 290.4, divide by 4.8, then add 1."], "source": "St Nicholas 2023 P6 Weighted Assessment 2 Q8", "image_needed": true, "image_options": false, "image_file": "q8.png", "image_page": 10, "image_bbox": [0.15, 0.18, 0.85, 0.40], "image_loc": "row of overlapping rectangles along a straight line with shaded overlap squares; dimensions 2.4 cm, 7.2 cm, 5 cm labelled, below the stem", "notes": "Answer key: (a) 21.6 cm, (b) 126.72 cm², (c) 60." }, { "n": 9, "type_id": 1, "question": "Mr Ho had a box of red, blue and green pens. \\(\\dfrac{1}{5}\\) of the pens were red, \\(\\dfrac{1}{4}\\) of the pens were blue and the rest were green pens. The cost of each pen is shown in the table. He sold all the pens and collected $1141.
Red: $1.20 Blue: $1.60 Green: $1.80
What fraction of the pens were green?", "answer0": "\\(\\dfrac{11}{20}\\)", "answer1": "\\(\\dfrac{9}{20}\\)", "answer2": "\\(\\dfrac{2}{9}\\)", "answer3": "\\(\\dfrac{1}{2}\\)", "correct_answer": 0, "skill_id": 209, "difficulty_id": 2, "explanation": "Green fraction = 1 − \\(\\dfrac{1}{5}\\) − \\(\\dfrac{1}{4}\\). Using a common denominator of 20: \\(\\dfrac{1}{5}=\\dfrac{4}{20}\\), \\(\\dfrac{1}{4}=\\dfrac{5}{20}\\). Green = 1 − \\(\\dfrac{4}{20}\\) − \\(\\dfrac{5}{20}\\) = \\(\\dfrac{20-9}{20}\\) = \\(\\dfrac{11}{20}\\).", "hints": ["Add the red and blue fractions using a common denominator (20), then subtract from 1 whole.", "1 − 1/5 − 1/4 = 1 − 4/20 − 5/20."], "source": "St Nicholas 2023 P6 Weighted Assessment 2 Q9 (a)", "image_needed": false, "image_options": false, "image_file": null, "notes": "Part (a) only. Answer is a fraction → MCQ. Answer key: 11/20. Pen-cost table folded into stem text." }, { "n": 10, "type_id": 2, "question": "Mr Ho had a box of red, blue and green pens. \\(\\dfrac{1}{5}\\) of the pens were red, \\(\\dfrac{1}{4}\\) of the pens were blue and the rest were green pens. Each red pen costs $1.20, each blue pen costs $1.60 and each green pen costs $1.80. He sold all the pens and collected $1141. How many pens did Mr Ho sell altogether? [?]", "answer0": "700", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 209, "difficulty_id": 3, "explanation": "Take total pens as 20 units: red = 4 units, blue = 5 units, green = 11 units.
Cost of 20 units = 4×$1.20 + 5×$1.60 + 11×$1.80 = 4.8 + 8 + 19.8 = $32.60.
$1141 ÷ $32.60 = 35, so 1 unit = 35 pens. Total pens = 35 × 20 = 700.", "hints": ["Let the total be 20 units (4 red, 5 blue, 11 green) and find the cost of one set of 20 units.", "Divide $1141 by the cost of 20 units to get the value of 1 unit, then multiply by 20."], "source": "St Nicholas 2023 P6 Weighted Assessment 2 Q9 (b)", "image_needed": false, "image_options": false, "image_file": null, "notes": "Part (b). Answer is a whole-number count → FIB. Answer key: 700." }, { "n": 11, "type_id": 2, "question": "Mr Ho had a box of red, blue and green pens. \\(\\dfrac{1}{5}\\) of the pens were red, \\(\\dfrac{1}{4}\\) of the pens were blue and the rest were green pens. Each red pen costs $1.20, each blue pen costs $1.60 and each green pen costs $1.80. Daphne bought 2 red pens and 4 green pens with \\(\\dfrac{2}{7}\\) of her pocket money. She bought blue pens with all her remaining pocket money. How many blue pens did Daphne buy? [?]", "answer0": "15", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 209, "difficulty_id": 3, "explanation": "Cost of 2 red + 4 green = 2×$1.20 + 4×$1.80 = $2.40 + $7.20 = $9.60. This is \\(\\dfrac{2}{7}\\) of her pocket money, so \\(\\dfrac{1}{7}\\) = 9.60 ÷ 2 = $4.80. Remaining money = 7 − 2 = 5 sevenths = 4.80 × 5 = $24. Blue pens cost $1.60 each: 24 ÷ 1.60 = 15 blue pens.", "hints": ["Find the cost of 2 red + 4 green pens; this equals 2/7 of her money, so 1/7 is half of that.", "Work out the remaining 5/7 in dollars, then divide by the price of a blue pen ($1.60)."], "source": "St Nicholas 2023 P6 Weighted Assessment 2 Q9 (c)", "image_needed": false, "image_options": false, "image_file": null, "notes": "Part (c). Answer is a whole-number count → FIB. Answer key: 15." } ] }