{
 "paper": {
  "school": "Methodist Girls' School (Primary)",
  "year": 2024,
  "level": "P4",
  "label": "Weighted Assessment 2",
  "source_prefix": "MGS 2024 P4 Weighted Assessment 2",
  "has_answer_key": true
 },
 "questions": [
  {
   "n": 1,
   "type_id": 1,
   "question": "What fraction of the shapes in the box are △ ?",
   "answer0": "$$\\frac{5}{12}$$",
   "answer1": "$$\\frac{5}{7}$$",
   "answer2": "$$\\frac{7}{12}$$",
   "answer3": "$$\\frac{7}{5}$$",
   "correct_answer": 2,
   "skill_id": 120,
   "difficulty_id": 1,
   "explanation": "Count the shapes in the box: there are 12 shapes in total, of which 7 are triangles. So the fraction that are triangles is $$\\frac{7}{12}$$.",
   "hints": [
    "Count the total number of shapes in the box.",
    "Count how many of them are triangles, then write triangles over total."
   ],
   "source": "MGS 2024 P4 Weighted Assessment 2 Q1",
   "image_needed": true,
   "image_options": false,
   "image_file": "q1.png",
   "image_page": 1,
   "image_bbox": [
    0.49,
    0.49,
    0.7,
    0.58
   ],
   "image_loc": "box of triangle/heart shapes, right of the question on page 1",
   "notes": "Count to verify: 12 shapes total, 7 triangles. Answer key = option (3) = 7/12."
  },
  {
   "n": 2,
   "type_id": 1,
   "question": "$$1-\\frac{2}{5}-\\frac{1}{6}$$ = ______",
   "answer0": "$$\\frac{3}{11}$$",
   "answer1": "$$\\frac{13}{30}$$",
   "answer2": "$$\\frac{17}{30}$$",
   "answer3": "$$\\frac{8}{11}$$",
   "correct_answer": 1,
   "skill_id": 121,
   "difficulty_id": 2,
   "explanation": "Use a common denominator of 30: $$1=\\frac{30}{30}$$, $$\\frac{2}{5}=\\frac{12}{30}$$, $$\\frac{1}{6}=\\frac{5}{30}$$. So $$\\frac{30}{30}-\\frac{12}{30}-\\frac{5}{30}=\\frac{13}{30}$$.",
   "hints": [
    "Find a common denominator for 5 and 6 (it is 30).",
    "Convert 1 to $$\\frac{30}{30}$$ and subtract both fractions."
   ],
   "source": "MGS 2024 P4 Weighted Assessment 2 Q2",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Answer key = option (2) = 13/30."
  },
  {
   "n": 3,
   "type_id": 1,
   "question": "Ravi drank $$\\frac{3}{4}$$ $$\\ell$$ of water. His sister drank $$\\frac{1}{5}$$ $$\\ell$$ less water than he did. How much water did they drink altogether?",
   "answer0": "$$1\\frac{7}{10}$$ $$\\ell$$",
   "answer1": "$$1\\frac{3}{10}$$ $$\\ell$$",
   "answer2": "$$\\frac{19}{20}$$ $$\\ell$$",
   "answer3": "$$\\frac{11}{20}$$ $$\\ell$$",
   "correct_answer": 1,
   "skill_id": 122,
   "difficulty_id": 2,
   "explanation": "Sister drank $$\\frac{3}{4}-\\frac{1}{5}=\\frac{15}{20}-\\frac{4}{20}=\\frac{11}{20}$$ litre. Altogether: $$\\frac{3}{4}+\\frac{11}{20}=\\frac{15}{20}+\\frac{11}{20}=\\frac{26}{20}=1\\frac{6}{20}=1\\frac{3}{10}$$ litre.",
   "hints": [
    "First find how much the sister drank by subtracting $$\\frac{1}{5}$$ from $$\\frac{3}{4}$$.",
    "Then add Ravi's amount and his sister's amount together."
   ],
   "source": "MGS 2024 P4 Weighted Assessment 2 Q3",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Answer key = option (2) = 1 3/10 litre."
  },
  {
   "n": 4,
   "type_id": 1,
   "question": "A class of students is put into two groups, A and B. The bar graph shows the number of boys and girls in each group.<br>What fraction of the class are boys?",
   "answer0": "$$\\frac{1}{5}$$",
   "answer1": "$$\\frac{4}{15}$$",
   "answer2": "$$\\frac{7}{15}$$",
   "answer3": "$$\\frac{3}{4}$$",
   "correct_answer": 2,
   "skill_id": 148,
   "difficulty_id": 2,
   "explanation": "From the stacked bar graph: Group A has 8 girls and 2 boys (total 10); Group B has 4 girls and 1 boy (total 5). Total students = 15, total boys = 2 + 1 = 7 ... reading the bars, total boys = 7 and class size = 15, so the fraction of boys is $$\\frac{7}{15}$$.",
   "hints": [
    "Read the boys portion and the girls portion of each group's bar.",
    "Add up all the boys, divide by the total number of students."
   ],
   "source": "MGS 2024 P4 Weighted Assessment 2 Q4",
   "image_needed": true,
   "image_options": false,
   "image_file": "q4.png",
   "image_page": 2,
   "image_bbox": [
    0.2,
    0.4,
    0.8,
    0.64
   ],
   "image_loc": "horizontal stacked bar graph 'Students in a Class' in the middle of page 2",
   "notes": "Answer key = option (3) = 7/15. Total boys = 7, total class = 15 (stacked Girls+Boys bars per group)."
  },
  {
   "n": 5,
   "type_id": 2,
   "question": "364 × 27 = [?]",
   "answer0": "9828",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 116,
   "difficulty_id": 1,
   "explanation": "364 × 27 = 364 × 20 + 364 × 7 = 7280 + 2548 = 9828.",
   "hints": [
    "Multiply 364 by 7, then by 20.",
    "Add the two partial products."
   ],
   "source": "MGS 2024 P4 Weighted Assessment 2 Q5",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Answer key = 9828."
  },
  {
   "n": 6,
   "type_id": 2,
   "question": "8974 ÷ 8 = [?]",
   "answer0": "1121 R6",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 117,
   "difficulty_id": 1,
   "explanation": "8974 ÷ 8: 8 into 89 is 11 r1; bring down 7 → 17, 8 into 17 is 2 r1; bring down 4 → 14, 8 into 14 is 1 r6. Quotient = 1121 remainder 6.",
   "hints": [
    "Use long division by 8.",
    "Track the remainder at each step; the final remainder is 6."
   ],
   "source": "MGS 2024 P4 Weighted Assessment 2 Q6",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Answer key = 1121 R6 (1121 remainder 6)."
  },
  {
   "n": 7,
   "type_id": 2,
   "question": "What is the mixed number represented by the letter A in the number line?",
   "answer0": "2 3/4",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 119,
   "difficulty_id": 2,
   "explanation": "The interval from 2 to 3 is divided into 4 equal parts (quarters). The letter A is at the 3rd mark past 2, so it represents $$2\\frac{3}{4}$$.",
   "hints": [
    "Count how many equal parts are between 2 and 3.",
    "Count how many of those parts A is past the 2 mark."
   ],
   "source": "MGS 2024 P4 Weighted Assessment 2 Q7",
   "image_needed": true,
   "image_options": false,
   "image_file": "q7.png",
   "image_page": 3,
   "image_bbox": [
    0.13,
    0.71,
    0.78,
    0.83
   ],
   "image_loc": "number line from 1 to 3 with arrow A near the lower part of page 3",
   "notes": "Answer key = 2 3/4. FIB answer kept plain."
  },
  {
   "n": 8,
   "type_id": 2,
   "question": "$$1\\frac{5}{8}$$ = $$\\frac{[?]}{8}$$ What is the missing value in the box?",
   "answer0": "13",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 119,
   "difficulty_id": 1,
   "explanation": "Convert the mixed number to an improper fraction: $$1\\frac{5}{8}=\\frac{1\\times8+5}{8}=\\frac{13}{8}$$. So the missing value is 13.",
   "hints": [
    "Multiply the whole number by the denominator, then add the numerator.",
    "1 × 8 + 5 = 13."
   ],
   "source": "MGS 2024 P4 Weighted Assessment 2 Q8",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Answer key = 13 (1×8+5=13)."
  },
  {
   "n": 9,
   "type_id": 2,
   "question": "Arrange the fractions in decreasing order.<br>$$\\frac{7}{3}$$ , $$\\frac{11}{5}$$ , $$2\\frac{2}{5}$$",
   "answer0": "2 2/5",
   "answer1": "7/3",
   "answer2": "11/5",
   "answer3": null,
   "correct_answer": null,
   "skill_id": 119,
   "difficulty_id": 2,
   "explanation": "Convert to decimals/like values: $$\\frac{7}{3}\\approx2.33$$, $$\\frac{11}{5}=2.2$$, $$2\\frac{2}{5}=2.4$$. In decreasing order: $$2\\frac{2}{5}$$, $$\\frac{7}{3}$$, $$\\frac{11}{5}$$.",
   "hints": [
    "Convert each fraction to a decimal or to a common denominator.",
    "Largest comes first when arranging in decreasing order."
   ],
   "source": "MGS 2024 P4 Weighted Assessment 2 Q9",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Answer key = 2 2/5 (greatest), 7/3, 11/5. Three blanks in decreasing order."
  },
  {
   "n": 10,
   "type_id": 2,
   "question": "There are 56 flowers in a basket. $$\\frac{2}{7}$$ of the flowers are roses. How many roses are there in the basket?",
   "answer0": "16",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 120,
   "difficulty_id": 2,
   "explanation": "7 units = 56, so 1 unit = 56 ÷ 7 = 8. Roses = 2 units = 8 × 2 = 16.",
   "hints": [
    "Find how many flowers make up 1 unit (one seventh).",
    "Multiply that by 2 to get $$\\frac{2}{7}$$ of the flowers."
   ],
   "source": "MGS 2024 P4 Weighted Assessment 2 Q10",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Answer key = 16 roses."
  },
  {
   "n": 11,
   "type_id": 2,
   "question": "The line graph shows the amount of water in a water dispenser measured hourly on a certain day, from 9 a.m. to 4 p.m.<br>(a) How much water was taken from the dispenser from 9 a.m. to 10 a.m.? Answer in $$\\ell$$.<br>(b) During which 1-hour period was the most amount of water taken from the dispenser? Give the period as [?] to [?].",
   "answer0": "3",
   "answer1": "12 p.m.",
   "answer2": "1 p.m.",
   "answer3": null,
   "correct_answer": null,
   "skill_id": 147,
   "difficulty_id": 2,
   "explanation": "(a) At 9 a.m. the volume is 22 L and at 10 a.m. it is 19 L, so water taken = 22 − 19 = 3 L. (b) The steepest drop is from 12 p.m. (about 16 L) to 1 p.m. (about 8 L), a fall of about 8 L, the largest 1-hour decrease. So the most water was taken from 12 p.m. to 1 p.m.",
   "hints": [
    "Subtract the 10 a.m. reading from the 9 a.m. reading for part (a).",
    "For part (b), look for the steepest downward slope between two consecutive hours."
   ],
   "source": "MGS 2024 P4 Weighted Assessment 2 Q11",
   "image_needed": true,
   "image_options": false,
   "image_file": "q11.png",
   "image_page": 5,
   "image_bbox": [
    0.16,
    0.11,
    0.8,
    0.42
   ],
   "image_loc": "line graph of 'Volume of water (litres)' vs time 9 a.m.–4 p.m. near the top of page 5",
   "notes": "Answer key: (a) 22-19 = 3 L; (b) 12pm to 1pm. Three blanks: 3, 12 p.m., 1 p.m."
  },
  {
   "n": 12,
   "type_id": 2,
   "question": "James planted a seedling and recorded its height at the start of each week over 5 weeks, using a table and a line graph. The height of the seedling is not shown on the scale of the line graph.<br>Week 1: 2 cm, Week 2: 6 cm, Week 3: 11 cm, Week 4: ?, Week 5: 17 cm, Week 6: 18 cm.<br>(a) What was the height of the seedling recorded at the start of Week 4? Answer in cm.<br>(b) The statement 'The height of the seedling increased by 16 cm over the 5 weeks.' is either true, false or not possible to tell. State True, False or Not possible to tell.",
   "answer0": "15",
   "answer1": "True",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 147,
   "difficulty_id": 2,
   "explanation": "(a) Reading the line graph between Week 3 (11 cm) and Week 5 (17 cm), the Week 4 point is at 15 cm. (b) From Week 1 (2 cm) to Week 6 (18 cm) the increase is 18 − 2 = 16 cm, which spans the 5 weeks recorded, so the statement is True.",
   "hints": [
    "Read the Week 4 point off the line graph (it lies between the Week 3 and Week 5 values).",
    "For (b), subtract the first height from the last height: 18 − 2."
   ],
   "source": "MGS 2024 P4 Weighted Assessment 2 Q12",
   "image_needed": true,
   "image_options": false,
   "image_file": "q12.png",
   "image_page": 6,
   "image_bbox": [
    0.16,
    0.2,
    0.78,
    0.48
   ],
   "image_loc": "line graph 'Height of seedling (cm)' across Week 1–Week 6 in the upper-middle of page 6",
   "notes": "Answer key: (a) 15 cm; (b) True. Table values are part of the stem; graph image still needed for part (a). Two blanks: 15, True."
  },
  {
   "n": 13,
   "type_id": 2,
   "question": "Kenneth cycled home from school. After completing $$\\frac{7}{10}$$ of the journey, he still needed to cycle another 480 m to reach home. What was the distance between Kenneth's home and his school?",
   "answer0": "1600 m",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 122,
   "difficulty_id": 3,
   "explanation": "The remaining part of the journey is $$1-\\frac{7}{10}=\\frac{3}{10}$$, which equals 480 m. So 3 units = 480 m, 1 unit = 480 ÷ 3 = 160 m. Whole journey = 10 units = 160 × 10 = 1600 m.",
   "hints": [
    "Find the fraction of the journey that the 480 m represents (1 − 7/10).",
    "Use it to find 1 unit, then multiply up to the whole journey."
   ],
   "source": "MGS 2024 P4 Weighted Assessment 2 Q13",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Answer key: 3u = 480, 1u = 160, 10u = 1600 m."
  },
  {
   "n": 14,
   "type_id": 2,
   "question": "Denise, Emily and Fred scored a total of 4490 points in a game. Denise scored 3 times as many points as Emily. Fred scored 550 points less than Denise. How many points did Fred score?",
   "answer0": "1610",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 118,
   "difficulty_id": 3,
   "explanation": "Let Emily = 1 unit, then Denise = 3 units, Fred = 3 units − 550. Total: 1u + 3u + 3u − 550 = 4490, so 7u = 4490 + 550 = 5040, 1u = 5040 ÷ 7 = 720. Denise = 3 × 720 = 2160. Fred = 2160 − 550 = 1610.",
   "hints": [
    "Let Emily be 1 unit; write Denise and Fred in terms of units.",
    "Add the 550 back to the total to make whole units, then divide by 7."
   ],
   "source": "MGS 2024 P4 Weighted Assessment 2 Q14",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Answer key: 4490 + 550 = 5040; 5040 ÷ 7 = 720; 720 × 3 = 2160; 2160 − 550 = 1610."
  },
  {
   "n": 15,
   "type_id": 2,
   "question": "Arthur and Ben had the same number of stickers at first. After Arthur gave 72 stickers to Caleb, Ben had 4 times as many stickers as Arthur.<br>(a) How many stickers did Arthur have left?<br>(b) Caleb gave $$\\frac{4}{9}$$ of the stickers he received from Arthur to his friends and kept the rest. How many stickers did Caleb keep for himself?",
   "answer0": "24",
   "answer1": "40",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 118,
   "difficulty_id": 3,
   "explanation": "(a) Arthur and Ben started equal. After Arthur gives away 72, Ben = 4 × Arthur. The 72 stickers Arthur lost make Ben's amount the extra; the difference 72 equals 3 of Arthur's remaining units, so 3 units = 72, 1 unit = 24. Arthur had 24 stickers left. (b) Caleb received 72 stickers. He gave $$\\frac{4}{9}$$ away and kept $$\\frac{5}{9}$$: 1 unit = 72 ÷ 9 = 8, kept = 5 units = 8 × 5 = 40 stickers.",
   "hints": [
    "For (a): Ben stays the same while Arthur drops by 72; Ben = 4 × Arthur means the gap of 72 is 3 of Arthur's parts.",
    "For (b): Caleb received 72; he kept $$\\frac{5}{9}$$ of them."
   ],
   "source": "MGS 2024 P4 Weighted Assessment 2 Q15",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Answer key: (a) 3u = 72, 1u = 24; (b) 9u = 72, 1u = 8, 5u = 40. Two blanks: 24, 40."
  }
 ]
}