{
"paper": {
"school": "Methodist Girls' School (Primary)",
"year": 2024,
"level": "P6",
"label": "Weighted Assessment 2",
"source_prefix": "MGS 2024 P6 Weighted Assessment 2",
"has_answer_key": false,
"notes": "NO printed answer key in the PDF -- every answer solved by the agent. Single paper, 12 questions (all structured/short-answer). Algebra/fraction/ratio answers rendered as MCQ per spec; tick-table (Q10) is type_id 0."
},
"questions": [
{
"n": 1,
"type_id": 1,
"question": "(a) Express \\(15y - (3 + 4y) + 7y + 20\\) in the simplest form.
(b) Find the value of the expression \\(\\dfrac{7p - 6}{4}\\) when \\(p = 35\\).",
"answer0": "(a) \\(18y + 17\\) (b) 59.75",
"answer1": "(a) \\(18y + 23\\) (b) 59.75",
"answer2": "(a) \\(18y + 17\\) (b) 60.25",
"answer3": "(a) \\(11y + 17\\) (b) 59.75",
"correct_answer": 0,
"skill_id": 239,
"difficulty_id": 2,
"explanation": "(a) \\(15y - 3 - 4y + 7y + 20 = (15 - 4 + 7)y + (20 - 3) = 18y + 17\\). (b) \\(\\dfrac{7(35) - 6}{4} = \\dfrac{245 - 6}{4} = \\dfrac{239}{4} = 59.75\\).",
"hints": ["Remove the brackets carefully (watch the minus sign).", "For (b), substitute p = 35 and simplify."],
"source": "MGS 2024 P6 Weighted Assessment 2 Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "No answer key -- solved. Part (a) is an algebraic expression (not FIB), so the question is rendered as MCQ combining (a) 18y + 17 and (b) 59.75."
},
{
"n": 2,
"type_id": 1,
"question": "(a) Express 0.25% as a fraction in its simplest form.
(b) \\(10 : 6 = [\\;?\\;] : 15\\). What is the missing number in the box?",
"answer0": "(a) \\(\\dfrac{1}{400}\\) (b) 25",
"answer1": "(a) \\(\\dfrac{1}{40}\\) (b) 25",
"answer2": "(a) \\(\\dfrac{1}{400}\\) (b) 9",
"answer3": "(a) \\(\\dfrac{25}{100}\\) (b) 25",
"correct_answer": 0,
"skill_id": 173,
"difficulty_id": 2,
"explanation": "(a) 0.25% = \\(\\dfrac{0.25}{100} = \\dfrac{25}{10000} = \\dfrac{1}{400}\\). (b) \\(\\dfrac{10}{6} = \\dfrac{?}{15}\\) → ? = \\(\\dfrac{10\\times 15}{6} = 25\\).",
"hints": ["Percent means out of 100; clear the decimal.", "For (b), use equivalent ratios."],
"source": "MGS 2024 P6 Weighted Assessment 2 Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "No answer key -- solved. Part (a) is a fraction (not FIB), so rendered as MCQ combining (a) 1/400 and (b) 25."
},
{
"n": 3,
"type_id": 2,
"question": "The pie chart shows the number of red, yellow, blue and green marbles. Half of the marbles are made up of red and green marbles in the ratio of 3 : 2. There are 52 green marbles. How many blue marbles are there? [?]",
"answer0": "65",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 235,
"difficulty_id": 3,
"explanation": "Red : green = 3 : 2 with green = 52, so 1 unit = 26 and red = 78. Red + green = 130 = half the marbles, so total = 260. The other half (130) is yellow + blue. From the pie chart, the blue sector is a right angle (\\(\\dfrac{1}{4}\\) of the whole), so blue = \\(\\dfrac{1}{4}\\times 260 = 65\\).",
"hints": ["Use the 3 : 2 ratio and green = 52 to find the total.", "Read the blue sector's size (right angle = quarter) from the pie chart."],
"source": "MGS 2024 P6 Weighted Assessment 2 Q3",
"image_needed": true,
"image_page": 2,
"image_bbox": [0.5, 0.12, 0.78, 0.32],
"image_loc": "pie chart with Red, Yellow, Blue, Green sectors",
"image_options": false,
"image_file": "q3.png",
"notes": "No answer key -- solved; figure-dependent. Blue = 65 assumes the right-angle mark makes the blue sector a quarter of the pie -- verify the sector sizes against the chart."
},
{
"n": 4,
"type_id": 1,
"question": "At a carnival, the ratio of the number of adults to that of children is 3 : 8. The ratio of the number of boys to the number of girls is 1 : 3. What is the ratio of the number of adults to the number of boys to the number of girls at the carnival?",
"answer0": "3 : 2 : 6",
"answer1": "3 : 1 : 3",
"answer2": "3 : 8 : 24",
"answer3": "3 : 6 : 2",
"correct_answer": 0,
"skill_id": 213,
"difficulty_id": 2,
"explanation": "Take adults = 3, children = 8. Children split as boys : girls = 1 : 3, so boys = \\(\\dfrac{1}{4}\\times 8 = 2\\), girls = \\(\\dfrac{3}{4}\\times 8 = 6\\). Adults : boys : girls = 3 : 2 : 6.",
"hints": ["Children = boys + girls = 8 units.", "Split the 8 children in the ratio 1 : 3."],
"source": "MGS 2024 P6 Weighted Assessment 2 Q4",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "No answer key -- solved. Ratio answer -> MCQ per spec."
},
{
"n": 5,
"type_id": 2,
"question": "Siti bought a pair of rollerblades at a 25% discount and saved $28. What was the price of the rollerblades before the discount? [?]",
"answer0": "112",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 176,
"difficulty_id": 2,
"explanation": "The $28 saved is the 25% discount, so 25% = $28 and 100% = 4 × $28 = $112. The price before discount was $112.",
"hints": ["The amount saved equals the 25% discount.", "Find 100% from 25%."],
"source": "MGS 2024 P6 Weighted Assessment 2 Q5",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "No answer key -- solved. Answer in dollars: $112."
},
{
"n": 6,
"type_id": 2,
"question": "Randy spent 30% of his money on a badminton racket. He spent another $84 on books. In the end, he had 55% of his money left. How much money did Randy have left? [?]",
"answer0": "308",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 175,
"difficulty_id": 3,
"explanation": "He spent 100% − 55% = 45% in total. The racket was 30%, so the books were 15% = $84, giving 1% = $5.60 and 100% = $560. Money left = 55% × $560 = $308.",
"hints": ["The books take up 45% − 30% = 15%.", "Find 100%, then 55% of it."],
"source": "MGS 2024 P6 Weighted Assessment 2 Q6",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "No answer key -- solved. Answer in dollars: $308."
},
{
"n": 7,
"type_id": 1,
"question": "Alison and Blake shared some stickers in the ratio of 1 : 2. Carl had \\(\\dfrac{3}{4}\\) the number of stickers that Blake has. What fraction of the total number of stickers did Blake have?",
"answer0": "\\(\\dfrac{4}{9}\\)",
"answer1": "\\(\\dfrac{2}{9}\\)",
"answer2": "\\(\\dfrac{1}{3}\\)",
"answer3": "\\(\\dfrac{2}{3}\\)",
"correct_answer": 0,
"skill_id": 210,
"difficulty_id": 2,
"explanation": "Take Alison = 1, Blake = 2. Carl = \\(\\dfrac{3}{4}\\times 2 = \\dfrac{3}{2}\\). Total = 1 + 2 + \\(\\dfrac{3}{2}\\) = \\(\\dfrac{9}{2}\\). Blake's fraction = \\(2 \\div \\dfrac{9}{2} = \\dfrac{4}{9}\\).",
"hints": ["Use units: Alison 1, Blake 2.", "Find Carl, then Blake ÷ total."],
"source": "MGS 2024 P6 Weighted Assessment 2 Q7",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "No answer key -- solved. Fraction answer -> MCQ per spec."
},
{
"n": 8,
"type_id": 2,
"question": "Samantha bought some red, yellow and green balls. 130 of the balls were red. 30% of the balls was yellow. She bought 50 more green balls than yellow balls.
(a) How many yellow balls did Samantha buy? [?]
(b) Samantha lost some of her red balls while playing a game. There was a 10% decrease in the number of red balls. How many red balls did she lose? [?]",
"answer0": "135",
"answer1": "13",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 175,
"difficulty_id": 3,
"explanation": "(a) Let total = T. Red 130 + yellow 0.3T + green (0.3T + 50) = T → 180 + 0.6T = T → 0.4T = 180 → T = 450. Yellow = 0.3 × 450 = 135. (b) 10% of 130 red = 13 red balls lost.",
"hints": ["Write all three colours in terms of T and solve.", "10% decrease means lose 10% of the red balls."],
"source": "MGS 2024 P6 Weighted Assessment 2 Q8",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "No answer key -- solved. answer0=(a) yellow balls, answer1=(b) red balls lost."
},
{
"n": 9,
"type_id": 1,
"question": "The bar graph represents the number of students who took part in some activities; each student chose only one activity. The number who chose Basketball was \\(\\dfrac{2}{3}\\) of those who chose Archery. The ratio of those who chose Cycling to Swimming was 5 : 2. Swimming and Cycling together formed 50% of all the students. The information is also shown in a pie chart with sectors labelled W, X, Y and Z.
(a) Match the labels W, X, Y and Z to Archery, Basketball, Cycling and Swimming.
(b) How many students were there altogether?",
"answer0": "(a) Archery = Z, Basketball = Y, Cycling = W, Swimming = X (b) 700",
"answer1": "(a) Archery = W, Basketball = X, Cycling = Y, Swimming = Z (b) 700",
"answer2": "(a) Archery = Z, Basketball = Y, Cycling = W, Swimming = X (b) 600",
"answer3": "(a) Archery = W, Basketball = Y, Cycling = Z, Swimming = X (b) 700",
"correct_answer": 0,
"skill_id": 235,
"difficulty_id": 3,
"explanation": "Cycling + Swimming = \\(\\dfrac{1}{2}\\)T, split 5 : 2 → Cycling = \\(\\dfrac{5}{14}\\)T, Swimming = \\(\\dfrac{1}{7}\\)T. Archery + Basketball = \\(\\dfrac{1}{2}\\)T with Basketball = \\(\\dfrac{2}{3}\\)Archery → Archery = \\(\\dfrac{3}{10}\\)T, Basketball = \\(\\dfrac{1}{5}\\)T. From the bar graph Cycling = 250 = \\(\\dfrac{5}{14}\\)T → T = 700. So Archery = 210, Basketball = 140, Cycling = 250, Swimming = 100. (a) By sector size the largest sector W = Cycling, Z = Archery, Y = Basketball, X = Swimming. (b) Total = 700.",
"hints": ["Use the 5 : 2 split and Cycling = 250 to find the total.", "Order the four counts to match the pie sector sizes."],
"source": "MGS 2024 P6 Weighted Assessment 2 Q9",
"image_needed": true,
"image_page": 6,
"image_bbox": [0.12, 0.18, 0.78, 0.36],
"image_loc": "bar graph (Archery, Basketball, Cycling, Swimming) plus pie chart with sectors W, X, Y, Z",
"image_options": false,
"image_file": "q9.png",
"notes": "No answer key -- solved. (b) total = 700 is confident. (a) the W/X/Y/Z label matching is figure-dependent (depends on the pie sector sizes) -- best-effort mapping by size; verify against the pie chart. Rendered as MCQ because (a) is a label-matching answer."
},
{
"n": 10,
"type_id": 0,
"question": "The pie charts show the number of each type of flower in Garden A and Garden B. The total number of flowers in Garden A is three times the total in Garden B. In Garden B, the number of Tulips is \\(\\dfrac{2}{3}\\) the number of Sunflowers. For each statement, indicate True, False or Not possible to tell.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 236,
"difficulty_id": 3,
"explanation": "Let Garden B total = b, so Garden A total = 3b. In Garden A, Tulip = \\(\\dfrac{1}{3}\\times 3b = b\\). Statement 1 (roses in A = 3 × total of tulips + sunflowers in B): Garden B's rose share is not given, so this is NOT POSSIBLE TO TELL. Statement 2 (fewer roses in A than B): roses in A are more than half of 3b while Garden B has only b flowers total, so roses in A > roses in B — FALSE. Statement 3 (ratio of tulips in A to total flowers in B is 1 : 1): tulips in A = b = total flowers in B — TRUE.",
"hints": ["Let Garden B total = b and Garden A total = 3b.", "Tulips in Garden A = \\(\\dfrac{1}{3}\\) of 3b = b."],
"source": "MGS 2024 P6 Weighted Assessment 2 Q10",
"image_needed": true,
"image_page": 7,
"image_bbox": [0.16, 0.16, 0.74, 0.4],
"image_loc": "two pie charts: Garden A (Tulip 1/3, Sunflower, Rose) and Garden B (Tulip, Sunflower, Rose)",
"image_options": false,
"image_file": "q10.png",
"notes": "No answer key -- solved. True/False/Not-possible tick table -> type_id 0 (skipped on insert). Best-effort answers (figure-dependent): S1 = Not possible to tell, S2 = False, S3 = True. Verify against the pie-chart sector sizes."
},
{
"n": 11,
"type_id": 2,
"question": "The same brand of laundry detergent is sold in 2 shops in 2 sizes; prices before discount are the same at both shops. Shop A: for every 1 big bottle purchased, get 45% discount on 1 small bottle. Shop B: bundle set @ $35 = 2 small bottles + 2 big bottles.
(a) The price of a big bottle before discount is $14.40. Susan bought 1 small bottle and 1 big bottle from Shop A and paid $18.25 altogether. What was the price of the small bottle before discount? [?]
(b) Michelle bought a bundle set from Shop B. What percentage of the amount of money spent in Shop B did she save by buying from Shop B instead of Shop A? Round your answer to 1 decimal place. [?]",
"answer0": "7",
"answer1": "4.3",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 176,
"difficulty_id": 3,
"explanation": "(a) Big = $14.40 (no discount on big). Small after 45% discount = $18.25 − $14.40 = $3.85, which is 55% of the small price, so small before discount = $3.85 ÷ 0.55 = $7. (b) Shop A for 2 big + 2 small: 2 × $14.40 + 2 × (0.55 × $7) = $28.80 + $7.70 = $36.50. Shop B bundle = $35, so Michelle saves $36.50 − $35 = $1.50. As a percentage of the Shop B amount: \\(\\dfrac{1.50}{35}\\times 100\\% \\approx 4.3\\%\\).",
"hints": ["The discount only applies to the small bottle (45% off).", "Compare the Shop A cost of 2 big + 2 small with the $35 bundle."],
"source": "MGS 2024 P6 Weighted Assessment 2 Q11",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "No answer key -- solved. answer0=(a) small bottle price in dollars ($7), answer1=(b) percentage saved (4.3%)."
},
{
"n": 12,
"type_id": 2,
"question": "The figure is formed by a right-angled triangle FGZ, an overlapped square ABCD and rectangle EFGH. The area of the square is 25% of the area of the rectangle. The ratio of the area of the rectangle to that of the triangle is 5 : 3. The shaded area is \\(\\dfrac{1}{3}\\) that of the total area of the square. The square has side 15 cm. What is the area of the figure? [?]",
"answer0": "1590",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 138,
"difficulty_id": 3,
"explanation": "Square area = 15 × 15 = 225 cm². Rectangle = square ÷ 25% = 225 ÷ 0.25 = 900 cm². Triangle = rectangle × \\(\\dfrac{3}{5}\\) = 540 cm². The square overlaps the rectangle; the shaded overlap = \\(\\dfrac{1}{3}\\) × 225 = 75 cm². Area of figure = rectangle + triangle + (square not overlapping) = 900 + 540 + (225 − 75) = 1590 cm².",
"hints": ["Find the rectangle and triangle areas from the square (225 cm²).", "Add the parts but count the overlap (shaded) only once."],
"source": "MGS 2024 P6 Weighted Assessment 2 Q12",
"image_needed": true,
"image_page": 9,
"image_bbox": [0.24, 0.16, 0.78, 0.34],
"image_loc": "figure: square ABCD overlapping rectangle EFGH with right-angled triangle FGZ",
"image_options": false,
"image_file": "q12.png",
"notes": "No answer key -- solved. Overlap (shaded) = 1/3 of square = 75 cm²; total figure = rectangle + triangle + (square − overlap) = 1590 cm². Verify the overlap interpretation against the figure. Answer in cm²."
}
]
}