{
 "paper": {
  "school": "Paya Lebar Methodist Girls' School (Primary)",
  "year": 2023,
  "level": "P4",
  "label": "Weighted Assessment 1",
  "source_prefix": "PLMGS 2023 P4 Weighted Assessment 1",
  "has_answer_key": true
 },
 "questions": [
  {
   "n": 1,
   "type_id": 1,
   "question": "What is the value of 4 thousands + 2 hundreds + 6 ones?",
   "answer0": "4260",
   "answer1": "4206",
   "answer2": "4062",
   "answer3": "4026",
   "correct_answer": 1,
   "skill_id": 105,
   "difficulty_id": 1,
   "explanation": "4 thousands = 4000, 2 hundreds = 200, 6 ones = 6. There are 0 tens. 4000 + 200 + 0 + 6 = 4206.",
   "hints": [
    "Write each part in expanded form: 4000, 200, 6.",
    "There are no tens, so the tens digit is 0."
   ],
   "source": "PLMGS 2023 P4 Weighted Assessment 1 Q1",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 2 (4206)."
  },
  {
   "n": 2,
   "type_id": 1,
   "question": "What is the missing number in the box?<br>$$6\\frac{2}{5}$$ = $$\\frac{[?]}{5}$$",
   "answer0": "12",
   "answer1": "22",
   "answer2": "30",
   "answer3": "32",
   "correct_answer": 3,
   "skill_id": 119,
   "difficulty_id": 1,
   "explanation": "Convert the mixed number to an improper fraction. $$6\\frac{2}{5}$$ = $$\\frac{(6\\times5)+2}{5}$$ = $$\\frac{32}{5}$$, so the missing number is 32.",
   "hints": [
    "Multiply the whole number by the denominator: 6 × 5 = 30.",
    "Add the numerator: 30 + 2 = 32."
   ],
   "source": "PLMGS 2023 P4 Weighted Assessment 1 Q2",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Stem shows equation 6 2/5 = [?]/5 inline. Key: option 4 (32)."
  },
  {
   "n": 3,
   "type_id": 1,
   "question": "There are 9345 men and 8704 women in a stadium. What is the total number of people in the stadium? Round this number to the nearest 100.",
   "answer0": "18 000",
   "answer1": "18 040",
   "answer2": "18 050",
   "answer3": "18 100",
   "correct_answer": 0,
   "skill_id": 109,
   "difficulty_id": 2,
   "explanation": "Total = 9345 + 8704 = 18 049. Rounding 18 049 to the nearest 100: the tens digit is 4 (less than 5), so round down to 18 000.",
   "hints": [
    "First add: 9345 + 8704 = 18 049.",
    "Look at the tens digit to decide rounding to the nearest 100."
   ],
   "source": "PLMGS 2023 P4 Weighted Assessment 1 Q3",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 1 (18 000)."
  },
  {
   "n": 4,
   "type_id": 1,
   "question": "Mindy had $$\\frac{4}{5}$$ kg of flour at first. After she had used some of the flour to make noodles, she had $$\\frac{1}{3}$$ kg of flour left. How much flour did she use to make noodles?",
   "answer0": "$$\\frac{3}{15}$$ kg",
   "answer1": "$$\\frac{7}{15}$$ kg",
   "answer2": "$$\\frac{3}{8}$$ kg",
   "answer3": "$$\\frac{5}{8}$$ kg",
   "correct_answer": 1,
   "skill_id": 121,
   "difficulty_id": 2,
   "explanation": "Flour used = flour at first − flour left = $$\\frac{4}{5}$$ − $$\\frac{1}{3}$$. Common denominator 15: $$\\frac{12}{15}$$ − $$\\frac{5}{15}$$ = $$\\frac{7}{15}$$ kg.",
   "hints": [
    "Used = started with − left over.",
    "Make the denominators the same (use 15) before subtracting."
   ],
   "source": "PLMGS 2023 P4 Weighted Assessment 1 Q4",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key: option 2 (7/15 kg)."
  },
  {
   "n": 5,
   "type_id": 1,
   "question": "Find ∠AOB.",
   "answer0": "65°",
   "answer1": "75°",
   "answer2": "115°",
   "answer3": "125°",
   "correct_answer": 2,
   "skill_id": 140,
   "difficulty_id": 2,
   "explanation": "OB lies along the protractor base (the 0° line on the right). Ray OA passes through the 115° mark on the outer scale measured from OB, so ∠AOB = 115°.",
   "hints": [
    "Start counting from the arm that lies on the 0° baseline.",
    "Read the scale that begins at 0° at arm OB."
   ],
   "source": "PLMGS 2023 P4 Weighted Assessment 1 Q5",
   "image_needed": true,
   "image_options": false,
   "image_file": "q5.png",
   "image_page": 3,
   "image_bbox": [
    0.27,
    0.42,
    0.78,
    0.66
   ],
   "image_loc": "centre of page 3, protractor with rays OA (up-left) and OB (right) below the question",
   "notes": "Protractor diagram needed. Key: option 3 (115°)."
  },
  {
   "n": 6,
   "type_id": 1,
   "question": "KLMN is a rectangle. Find ∠t.",
   "answer0": "10°",
   "answer1": "25°",
   "answer2": "30°",
   "answer3": "45°",
   "correct_answer": 2,
   "skill_id": 143,
   "difficulty_id": 2,
   "explanation": "In rectangle KLMN, the interior angle at N (∠KNM) is 90°. The diagonal NL splits it into 60° and ∠t, so 60° + t = 90°, giving t = 30°.",
   "hints": [
    "Each corner of a rectangle is a right angle (90°).",
    "The two angles at N add up to 90°."
   ],
   "source": "PLMGS 2023 P4 Weighted Assessment 1 Q6",
   "image_needed": true,
   "image_options": false,
   "image_file": "q6.png",
   "image_page": 4,
   "image_bbox": [
    0.18,
    0.16,
    0.7,
    0.42
   ],
   "image_loc": "upper area of page 4, tilted rectangle KLMN with diagonal NL and 60° / t angles marked at corner N",
   "notes": "Rectangle diagram needed. Key: option 3 (30°)."
  },
  {
   "n": 7,
   "type_id": 2,
   "question": "(a) In the number pattern below, what is the missing number in the box?<br>78 082 , [?] , 82 082 , 84 082 , 86 082<br>(b) Andy listed the factors of 12: 1, 2, 4, 12. He missed out two factors. What were the two missing factors? [?] and [?]",
   "answer0": "80082",
   "answer1": "3",
   "answer2": "6",
   "answer3": null,
   "correct_answer": null,
   "skill_id": 108,
   "difficulty_id": 1,
   "explanation": "(a) The pattern increases by 2000 each step (82 082 − 80 082 = 2000). The missing term = 78 082 + 2000 = 80 082. (b) Factors of 12 are 1, 2, 3, 4, 6, 12. The listed set 1, 2, 4, 12 leaves out 3 and 6.",
   "hints": [
    "(a) Find the constant difference between consecutive terms.",
    "(b) List every number that divides 12 exactly, then see which are missing."
   ],
   "source": "PLMGS 2023 P4 Weighted Assessment 1 Q7",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Two-part FIB combined: 7a missing pattern term, 7b two missing factors. Key: a) 80082, b) 3 and 6."
  },
  {
   "n": 8,
   "type_id": 2,
   "question": "Arrange the following in decreasing order.<br>$$\\frac{11}{4}$$ , $$1\\frac{1}{6}$$ , 1 , $$\\frac{8}{3}$$<br>[?] , [?] , [?] , [?]",
   "answer0": "11/4",
   "answer1": "8/3",
   "answer2": "1 1/6",
   "answer3": "1",
   "correct_answer": null,
   "skill_id": 119,
   "difficulty_id": 2,
   "explanation": "Convert to a common form: $$\\frac{11}{4}$$ = 2.75, $$\\frac{8}{3}$$ ≈ 2.67, $$1\\frac{1}{6}$$ ≈ 1.17, 1 = 1. Decreasing order: $$\\frac{11}{4}$$, $$\\frac{8}{3}$$, $$1\\frac{1}{6}$$, 1.",
   "hints": [
    "Change each number to a decimal (or same denominator) to compare.",
    "Decreasing means largest first."
   ],
   "source": "PLMGS 2023 P4 Weighted Assessment 1 Q8",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Ordering FIB, one blank per position, decreasing order. FIB answers kept plain (11/4, 8/3, 1 1/6, 1). Key: 11/4, 8/3, 1 1/6, 1."
  },
  {
   "n": 9,
   "type_id": 2,
   "question": "The diagram shows some places around the playground in a park. Study the map of the park to answer the questions.<br>(a) In which direction is the pond from the playground? [?]<br>(b) James is standing at the playground and he faces south. He wants to leave the park. How many degrees must he turn anticlockwise to face the exit? [?]°",
   "answer0": "South-west",
   "answer1": "90",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 142,
   "difficulty_id": 2,
   "explanation": "(a) On the compass map the pond sits down-left of the playground, i.e. to the south-west. (b) Facing south, the exit is to the east of the playground. Turning anticlockwise from south, south → east is a 90° turn (south → west → north → east would be the long way; the question's key gives 90° measuring south to east anticlockwise via the direct quarter turn).",
   "hints": [
    "(a) Use the North arrow to fix the directions on the map.",
    "(b) Compare the south direction with the direction of the exit; a quarter turn is 90°."
   ],
   "source": "PLMGS 2023 P4 Weighted Assessment 1 Q9",
   "image_needed": true,
   "image_options": false,
   "image_file": "q9.png",
   "image_page": 6,
   "image_bbox": [
    0.15,
    0.23,
    0.72,
    0.5
   ],
   "image_loc": "upper-middle of page 6, hand-drawn park map with North arrow, toilet, playground, Exit, pond and shelter",
   "notes": "Park-map figure needed. Two-blank FIB. Key: a) South-west, b) 90°."
  },
  {
   "n": 10,
   "type_id": 0,
   "question": "In the square grid below, line DE has been drawn. It forms one side of a square DEFG. Complete the drawing of the square DEFG within the grid. Label the points F and G.",
   "answer0": null,
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 143,
   "difficulty_id": 2,
   "explanation": "DE goes 2 right and 2 up. Each remaining side is perpendicular and equal in length. From E go 2 right, 2 down to F; from F go 2 left, 2 down to G; G connects back to D, forming square DEFG (a tilted square with side equal to DE).",
   "hints": [
    "Each side of a square is equal in length and meets at right angles.",
    "Turn 90° at E to find F, keeping the same length as DE."
   ],
   "source": "PLMGS 2023 P4 Weighted Assessment 1 Q10",
   "image_needed": true,
   "image_options": false,
   "image_file": "q10.png",
   "image_page": 7,
   "image_bbox": [
    0.18,
    0.27,
    0.74,
    0.54
   ],
   "image_loc": "upper-middle of page 7, square grid with diagonal line DE drawn (D lower-left, E upper-right)",
   "notes": "Interactive draw-on-grid task (complete and label square DEFG); type_id 0, skipped on insert. Answer per key: complete square DEFG with F above/right and G as shown in answer-key sketch."
  },
  {
   "n": 11,
   "type_id": 2,
   "question": "Mr Chen bought 6 similar dining chairs for $1428. A sofa cost 10 times as much as a dining chair. How much did the sofa cost?<br>$[?]",
   "answer0": "2380",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 118,
   "difficulty_id": 2,
   "explanation": "Cost of 1 dining chair = $1428 ÷ 6 = $238. The sofa costs 10 times as much = 10 × $238 = $2380.",
   "hints": [
    "First find the cost of one chair by dividing.",
    "Then multiply by 10 for the sofa."
   ],
   "source": "PLMGS 2023 P4 Weighted Assessment 1 Q11",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Answer in dollars. Key: $2380."
  },
  {
   "n": 12,
   "type_id": 2,
   "question": "Fiona and Janet had a total of 126 cookies at first. After Janet gave away $$\\frac{1}{3}$$ of the cookies she had, she had 4 times as many cookies as Fiona. How many cookies did Janet have at first?<br>[?]",
   "answer0": "108",
   "answer1": null,
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 122,
   "difficulty_id": 3,
   "explanation": "After giving away $$\\frac{1}{3}$$, Janet keeps $$\\frac{2}{3}$$ of her cookies, which equals 4 times Fiona's. The total 126 is unchanged. Take Fiona as 1 unit, so Janet's remaining = 4 units and Janet's original = 6 units (since $$\\frac{2}{3}$$ of original = 4 units → original = 6 units). Total units = 6 + 1 = 7 = 126, so 1 unit = 18. Janet at first = 6 × 18 = 108.",
   "hints": [
    "Keeping after giving away 1/3 means 2/3 of her cookies remain.",
    "Use units: Janet's original is 6 units, Fiona is 1 unit, total 7 units = 126."
   ],
   "source": "PLMGS 2023 P4 Weighted Assessment 1 Q12",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Key working: 7u = 126, 1u = 18, 6u = 108. Key: 108."
  },
  {
   "n": 13,
   "type_id": 2,
   "question": "Alan made some lime juice on Monday and Tuesday. He made $$\\frac{7}{8}$$ $$l$$ of lime juice on Monday. He made $$\\frac{2}{5}$$ $$l$$ more lime juice on Monday than Tuesday.<br>(a) How much lime juice did he make on Tuesday?<br>(b) What was the total amount of lime juice that he had made on both days? Give your answer in the simplest form.<br>(a) [?]<br>(b) [?]",
   "answer0": "19/40",
   "answer1": "1 7/20",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 122,
   "difficulty_id": 3,
   "explanation": "(a) Tuesday = Monday − $$\\frac{2}{5}$$ = $$\\frac{7}{8}$$ − $$\\frac{2}{5}$$. Common denominator 40: $$\\frac{35}{40}$$ − $$\\frac{16}{40}$$ = $$\\frac{19}{40}$$ $$l$$. (b) Total = Monday + Tuesday = $$\\frac{35}{40}$$ + $$\\frac{19}{40}$$ = $$\\frac{54}{40}$$ = $$1\\frac{14}{40}$$ = $$1\\frac{7}{20}$$ $$l$$.",
   "hints": [
    "(a) Tuesday is less than Monday by 2/5; subtract using denominator 40.",
    "(b) Add Monday and Tuesday, then simplify the fraction."
   ],
   "source": "PLMGS 2023 P4 Weighted Assessment 1 Q13",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Two-part FIB in litres. FIB answers plain (19/40 and 1 7/20). Key: a) 19/40 l, b) 1 7/20 l."
  },
  {
   "n": 14,
   "type_id": 2,
   "question": "Marilyn has some lollipops. If she packs them into bags of 7, she will be short of 1 lollipop. If she packs them into bags of 5, she will have 2 extra lollipops.<br>(a) What is the least number of lollipops that Marilyn has?<br>(b) Marilyn decides to pack all her lollipops into bags of 5. How many more lollipops does she need to fill up the last bag of 5 lollipops?<br>(a) [?]<br>(b) [?]",
   "answer0": "27",
   "answer1": "3",
   "answer2": null,
   "answer3": null,
   "correct_answer": null,
   "skill_id": 115,
   "difficulty_id": 3,
   "explanation": "(a) 'Short of 1' in bags of 7 means the number is 1 less than a multiple of 7: 6, 13, 20, 27, ... '2 extra' in bags of 5 means 2 more than a multiple of 5: 7, 12, 17, 22, 27, ... The least common value is 27. (b) 27 ÷ 5 = 5 remainder 2, so the last bag has 2 lollipops; she needs 5 − 2 = 3 more to fill it.",
   "hints": [
    "(a) List 'multiples of 7 minus 1' and 'multiples of 5 plus 2' and find the first common number.",
    "(b) Find the remainder when 27 is divided by 5, then subtract from 5."
   ],
   "source": "PLMGS 2023 P4 Weighted Assessment 1 Q14",
   "image_needed": false,
   "image_options": false,
   "image_file": null,
   "notes": "Two-part FIB. Key working: multiples of 7 minus 1 (6,13,20,27); multiples of 5 plus 2 (7,12,17,22,27) → 27. Key: a) 27, b) 3."
  }
 ]
}