{
 "paper": {
  "school": "Paya Lebar Methodist Girls' School (Primary)",
  "year": 2023,
  "level": "P4",
  "label": "Weighted Assessment 2",
  "source_prefix": "PLMGS 2023 P4 Weighted Assessment 2",
  "has_answer_key": true
 },
 "questions": [
  {
   "n": 1,
   "type_id": 1,
   "question": "Which of the following is a common multiple of 4 and 7?",
   "answer0": "36",
   "answer1": "28",
   "answer2": "14",
   "answer3": "12",
   "correct_answer": 1,
   "skill_id": 115,
   "difficulty_id": 1,
   "explanation": "A common multiple of 4 and 7 must be in both times tables. Multiples of 7: 7, 14, 21, 28... Multiples of 4: 4, 8, 12, ..., 28. 28 = 4 × 7 is a common multiple. Answer: 28.",
   "hints": [
    "List the multiples of 4 and the multiples of 7.",
    "Look for a number that appears in both lists. 4 × 7 = 28."
   ],
   "source": "PLMGS 2023 P4 Weighted Assessment 2 Q1",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Answer key: option 2 (28)."
  },
  {
   "n": 2,
   "type_id": 1,
   "question": "Which figure has a line of symmetry?",
   "answer0": "Figure 1",
   "answer1": "Figure 2",
   "answer2": "Figure 3",
   "answer3": "Figure 4",
   "correct_answer": 0,
   "skill_id": 145,
   "difficulty_id": 1,
   "explanation": "A line of symmetry divides a figure into two matching halves that are mirror images. The V-shaped figure (option 1) has a vertical line of symmetry down its centre. The L, K and N shapes do not. Answer: Figure 1.",
   "hints": [
    "Imagine folding each figure in half so the two halves match exactly.",
    "The V shape folds onto itself along a vertical line."
   ],
   "source": "PLMGS 2023 P4 Weighted Assessment 2 Q2",
   "image_needed": true,
   "image_options": true,
   "image_file": null,
   "image_page": 1,
   "image_bbox": [
    0.15,
    0.55,
    0.65,
    0.82
   ],
   "image_loc": "lower-left of page 1: four labelled figures (1) V, (2) L, (3) K, (4) N arranged in a 2x2 block",
   "notes": "Answer key: option 1. Image-option MCQ — each option is a figure; crop q2_opt0..3. Option1=V, option2=L, option3=K, option4=N."
  },
  {
   "n": 3,
   "type_id": 1,
   "question": "In 23.41, which digit is in the tenths place?",
   "answer0": "1",
   "answer1": "2",
   "answer2": "3",
   "answer3": "4",
   "correct_answer": 3,
   "skill_id": 123,
   "difficulty_id": 1,
   "explanation": "In a decimal, the first digit after the decimal point is the tenths place. In 23.41, the digit right after the point is 4. Answer: 4.",
   "hints": [
    "The tenths place is the first digit to the right of the decimal point.",
    "23.41 → 4 is in the tenths place, 1 is in the hundredths place."
   ],
   "source": "PLMGS 2023 P4 Weighted Assessment 2 Q3",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Answer key: option 4 (digit 4)."
  },
  {
   "n": 4,
   "type_id": 1,
   "question": "Arrange the following from the smallest to the greatest.<br>$$\\frac{1}{5}$$, 0.83, $$\\frac{7}{100}$$",
   "answer0": "$$\\frac{1}{5}$$, $$\\frac{7}{100}$$, 0.83",
   "answer1": "$$\\frac{7}{100}$$, 0.83, $$\\frac{1}{5}$$",
   "answer2": "$$\\frac{7}{100}$$, $$\\frac{1}{5}$$, 0.83",
   "answer3": "0.83, $$\\frac{7}{100}$$, $$\\frac{1}{5}$$",
   "correct_answer": 2,
   "skill_id": 124,
   "difficulty_id": 2,
   "explanation": "Convert all to decimals: $$\\frac{1}{5}$$ = 0.20, 0.83 = 0.83, $$\\frac{7}{100}$$ = 0.07. Ordering smallest to greatest: 0.07 < 0.20 < 0.83, so $$\\frac{7}{100}$$, $$\\frac{1}{5}$$, 0.83. Answer: option 3.",
   "hints": [
    "Convert every value to a decimal to compare them.",
    "$$\\frac{1}{5}$$=0.2 and $$\\frac{7}{100}$$=0.07; then order 0.07, 0.2, 0.83."
   ],
   "source": "PLMGS 2023 P4 Weighted Assessment 2 Q4",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Answer key: option 3."
  },
  {
   "n": 5,
   "type_id": 1,
   "question": "A rectangular cardboard measures 35 cm by 24 cm. A picture is pasted on it, leaving a border of 3 cm around it. Find the area of the picture.",
   "answer0": "672 cm²",
   "answer1": "609 cm²",
   "answer2": "576 cm²",
   "answer3": "522 cm²",
   "correct_answer": 3,
   "skill_id": 138,
   "difficulty_id": 2,
   "explanation": "The 3 cm border is on every side, so it removes 2 × 3 = 6 cm from each dimension. Picture length = 35 − 6 = 29 cm; picture width = 24 − 6 = 18 cm. Area = 29 × 18 = 522 cm². Answer: 522 cm².",
   "hints": [
    "The border takes 3 cm off both ends of each side, so subtract 6 cm from each dimension.",
    "Picture = (35−6) × (24−6) = 29 × 18."
   ],
   "source": "PLMGS 2023 P4 Weighted Assessment 2 Q5",
   "image_needed": true,
   "image_options": false,
   "image_file": "q5.png",
   "image_page": 3,
   "image_bbox": [
    0.28,
    0.13,
    0.62,
    0.31
   ],
   "image_loc": "upper-middle of page 3: shaded rectangle with inner 'Picture' rectangle, 24 cm height, 35 cm width, 3 cm border labels",
   "notes": "Answer key: option 4 (522 cm²)."
  },
  {
   "n": 6,
   "type_id": 1,
   "question": "Andy had 204 balloons. $$\\frac{2}{3}$$ of the balloons were blue and the rest were grey and white. There were 3 times as many grey balloons as white balloons. How many white balloons were there?",
   "answer0": "17",
   "answer1": "68",
   "answer2": "102",
   "answer3": "136",
   "correct_answer": 0,
   "skill_id": 122,
   "difficulty_id": 3,
   "explanation": "Blue = $$\\frac{2}{3}$$ × 204 = 136. Grey and white together = 204 − 136 = 68. Grey is 3 times white, so the 68 splits into 3 + 1 = 4 equal parts. White = 68 ÷ 4 = 17. Answer: 17.",
   "hints": [
    "First find the blue balloons, then the grey-and-white total.",
    "Grey = 3 × white means 4 equal parts; white is 1 part of the remaining balloons."
   ],
   "source": "PLMGS 2023 P4 Weighted Assessment 2 Q6",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Answer key: option 1 (17)."
  },
  {
   "n": 7,
   "type_id": 2,
   "question": "(a) Write twenty thousand and sixty-four in numerals. [?]<br>(b) Round 3459 to the nearest thousand. [?]",
   "answer0": "20064",
   "answer1": "3000",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 109,
   "difficulty_id": 1,
   "explanation": "(a) Twenty thousand = 20 000, plus sixty-four = 64, giving 20 064. (b) 3459 is between 3000 and 4000; the hundreds digit is 4 (less than 5), so round down to 3000.",
   "hints": [
    "(a) Twenty thousand is 20 000; add the sixty-four.",
    "(b) Look at the hundreds digit to decide whether to round up or down to the nearest thousand."
   ],
   "source": "PLMGS 2023 P4 Weighted Assessment 2 Q7",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Answer key: a) 20064, b) 3000."
  },
  {
   "n": 8,
   "type_id": 2,
   "question": "Find the value of<br>(a) $$\\frac{2}{3}$$ + $$\\frac{5}{9}$$. Express your answer as a mixed number. [?]<br>(b) $$\\frac{7}{8}$$ − $$\\frac{5}{6}$$ [?]",
   "answer0": "1 2/9",
   "answer1": "1/24",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 121,
   "difficulty_id": 2,
   "explanation": "(a) $$\\frac{2}{3}$$=$$\\frac{6}{9}$$; $$\\frac{6}{9}$$+$$\\frac{5}{9}$$=$$\\frac{11}{9}$$=$$1\\frac{2}{9}$$. (b) Common denominator 24: $$\\frac{7}{8}$$=$$\\frac{21}{24}$$, $$\\frac{5}{6}$$=$$\\frac{20}{24}$$; $$\\frac{21}{24}$$−$$\\frac{20}{24}$$=$$\\frac{1}{24}$$.",
   "hints": [
    "Make the denominators the same before adding or subtracting.",
    "(a) use ninths; (b) use a denominator of 24."
   ],
   "source": "PLMGS 2023 P4 Weighted Assessment 2 Q8",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Answer key: a) 11/9 = 1 2/9, b) 1/24. FIB answers kept plain: '1 2/9' and '1/24'."
  },
  {
   "n": 9,
   "type_id": 2,
   "question": "Part of a scale is shown. Write the values of A and B.<br>A = [?]<br>B = [?]",
   "answer0": "1.84",
   "answer1": "2.0",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 124,
   "difficulty_id": 2,
   "explanation": "The scale runs from 1.7 to 2.1 with main marks every 0.1; each small interval between two of them is 0.02 (5 parts per 0.1). A sits 2 small marks past 1.8, so A = 1.8 + 0.04 = 1.84. B sits at the mark for 2.0. Answer: A = 1.84, B = 2.0.",
   "hints": [
    "Work out the value of each small division on the number line first.",
    "Count the small marks from the nearest labelled value to A and to B."
   ],
   "source": "PLMGS 2023 P4 Weighted Assessment 2 Q9",
   "image_needed": true,
   "image_options": false,
   "image_file": "q9.png",
   "image_page": 5,
   "image_bbox": [
    0.16,
    0.1,
    0.72,
    0.18
   ],
   "image_loc": "top of page 5: horizontal number-line scale labelled 1.7, 1.8, 1.9, 2.1 with arrows marking points A and B",
   "notes": "Answer key: A = 1.84, B = 2.0."
  },
  {
   "n": 10,
   "type_id": 2,
   "question": "The prices of cupcakes sold by Delicious Bakery are listed. 1 cupcake costs $5, with an offer 'Buy 3 and Get 4th one free'. Mr Phua wants to buy 17 cupcakes. What is the least amount he has to pay for the cupcakes that are on offer? $[?]",
   "answer0": "65",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 118,
   "difficulty_id": 2,
   "explanation": "With 'buy 3 get the 4th free', every group of 4 cupcakes is paid as 3. 17 cupcakes = 4 groups of 4 (16 cupcakes) + 1 extra. The 4 groups need 4 × 3 = 12 paid cupcakes; the extra 1 is paid. Paid cupcakes = 12 + 1 = 13. Cost = 13 × $5 = $65.",
   "hints": [
    "In each set of 4 cupcakes you only pay for 3.",
    "Find how many full sets of 4 are in 17, then count the leftover cupcakes."
   ],
   "source": "PLMGS 2023 P4 Weighted Assessment 2 Q10",
   "image_needed": true,
   "image_options": false,
   "image_file": "q10.png",
   "image_page": 5,
   "image_bbox": [
    0.2,
    0.49,
    0.68,
    0.65
   ],
   "image_loc": "middle of page 5: bordered offer box showing '1 cupcake for $5', an 'Offer Price!' star and 'Buy 3 and Get 4th one free' with cupcake icons",
   "notes": "Answer key: (12 + 1) × $5 = $65. FIB answer plain '65' (dollar sign in stem)."
  },
  {
   "n": 11,
   "type_id": 0,
   "question": "Complete the symmetric figure with KL as the line of symmetry.",
   "answer0": null,
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 144,
   "difficulty_id": 2,
   "explanation": "Reflect every point of the given partial figure across the diagonal line of symmetry KL onto the grid; the completed figure is the original shape together with its mirror image, forming a figure symmetric about KL.",
   "hints": [
    "Reflect each vertex of the drawn shape across the dashed line KL.",
    "Distances from KL must be equal on both sides."
   ],
   "source": "PLMGS 2023 P4 Weighted Assessment 2 Q11",
   "image_needed": true,
   "image_options": false,
   "image_file": "q11.png",
   "image_page": 6,
   "image_bbox": [
    0.18,
    0.13,
    0.7,
    0.52
   ],
   "image_loc": "upper area of page 6: square grid with a diagonal dashed line of symmetry from K (top-left) to L (bottom-right) and a partial triangular figure drawn",
   "notes": "Draw/reflection task on a grid — no value answer; type_id 0, skipped on insert. Answer key shows the completed reflected figure."
  },
  {
   "n": 12,
   "type_id": 2,
   "question": "Ray walked $$5\\frac{3}{4}$$ km. He walked $$\\frac{2}{5}$$ km less than John. What was the total distance they had walked? Express your answer in the simplest form. [?] km",
   "answer0": "11 9/10",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 122,
   "difficulty_id": 3,
   "explanation": "Ray walked $$5\\frac{3}{4}$$ km. John walked $$\\frac{2}{5}$$ km more than Ray: John = $$5\\frac{3}{4}$$ + $$\\frac{2}{5}$$. Using twentieths, $$5\\frac{15}{20}$$ + $$\\frac{8}{20}$$ = $$6\\frac{3}{20}$$. Total = Ray + John = $$5\\frac{15}{20}$$ + $$6\\frac{3}{20}$$ = $$11\\frac{18}{20}$$ = $$11\\frac{9}{10}$$ km.",
   "hints": [
    "John walked MORE than Ray (Ray walked less), so add $$\\frac{2}{5}$$ to Ray's distance to get John's.",
    "Add Ray's and John's distances using a denominator of 20, then simplify."
   ],
   "source": "PLMGS 2023 P4 Weighted Assessment 2 Q12",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Answer key: (5 15/20 + 5 15/20) + 8/20 = 11 18/20 = 11 9/10. FIB answer plain '11 9/10'."
  },
  {
   "n": 13,
   "type_id": 2,
   "question": "Tracy had 3485 badges and Ryan had 1096 badges. Tracy gave some badges to Ryan. In the end, Ryan had twice as many badges as Tracy.<br>(a) How many badges did Tracy have in the end? [?]<br>(b) How many badges did Tracy give to Ryan? [?]",
   "answer0": "1527",
   "answer1": "1958",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 118,
   "difficulty_id": 3,
   "explanation": "Total badges stay the same: 3485 + 1096 = 4581. In the end Ryan has twice Tracy, so the total is 3 equal parts (Tracy 1 part, Ryan 2 parts). (a) Tracy's final amount = 4581 ÷ 3 = 1527. (b) Badges given = Tracy's start − Tracy's end = 3485 − 1527 = 1958.",
   "hints": [
    "The total number of badges does not change when Tracy gives some to Ryan.",
    "End ratio Tracy : Ryan = 1 : 2, so split the total into 3 parts; Tracy keeps 1 part."
   ],
   "source": "PLMGS 2023 P4 Weighted Assessment 2 Q13",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Answer key: a) 4581 ÷ 3 = 1527, b) 3485 − 1527 = 1958."
  },
  {
   "n": 14,
   "type_id": 2,
   "question": "The figure is made up of 2 squares, X and Z, and a rectangle, Y. The area of square X is 81 m². The perimeter of rectangle Y is 26 m.<br>(a) Find the length of square X. [?] m<br>(b) Find the area of square Z. [?] m²",
   "answer0": "9",
   "answer1": "16",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 138,
   "difficulty_id": 3,
   "explanation": "(a) Square X has area 81 m², so its length = √81 = 9 m (9 × 9 = 81). (b) Rectangle Y shares the 9 m side of X as its length. Perimeter of Y = 26 m, so length + breadth = 26 ÷ 2 = 13; breadth = 13 − 9 = 4 m. Square Z has the same side as Y's breadth = 4 m, so area of Z = 4 × 4 = 16 m².",
   "hints": [
    "(a) The side of a square is the number that multiplies by itself to give the area.",
    "(b) Y's longer side equals X's side (9 m); use the perimeter 26 m to find the other side, which is Z's side."
   ],
   "source": "PLMGS 2023 P4 Weighted Assessment 2 Q14",
   "image_needed": true,
   "image_options": false,
   "image_file": "q14.png",
   "image_page": 8,
   "image_bbox": [
    0.26,
    0.16,
    0.62,
    0.37
   ],
   "image_loc": "upper-middle of page 8: composite figure with square X (top, '?' marking its side), rectangle Y below-left and square Z below-right",
   "notes": "Answer key: a) 81 = 9×9 = 9 m, b) 26 − (9+9) = 8, 8 ÷ 2 = 4, 4×4 = 16 m²."
  }
 ]
}