{
  "paper": {
    "school": "Red Swastika",
    "year": 2022,
    "level": "P5",
    "label": "Weighted Assessment 1",
    "source_prefix": "Red Swastika 2022 P5 Weighted Assessment 1",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "Which of the following is five million, four hundred and nine thousand and six in figures?",
      "answer0": "5 009 406",
      "answer1": "5 049 006",
      "answer2": "5 409 006",
      "answer3": "5 490 006",
      "correct_answer": 2,
      "skill_id": 149,
      "difficulty_id": 1,
      "explanation": "Five million = 5 000 000; four hundred and nine thousand = 409 000; six = 6. Sum: 5 000 000 + 409 000 + 6 = 5 409 006. Answer: 5 409 006 (option 3).",
      "hints": ["Break the number into millions, thousands and ones.", "409 thousand is written as 409 000, not 049 000."],
      "source": "Red Swastika 2022 P5 Weighted Assessment 1 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 3."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "What is the value of 704 000 ÷ 200?",
      "answer0": "352",
      "answer1": "3520",
      "answer2": "35 200",
      "answer3": "352 000",
      "correct_answer": 1,
      "skill_id": 151,
      "difficulty_id": 1,
      "explanation": "704 000 ÷ 200 = 704 000 ÷ 2 ÷ 100 = 352 000 ÷ 100 = 3520. Answer: 3520 (option 2).",
      "hints": ["Divide by 2 first, then by 100.", "Dividing by 100 moves the digits two places."],
      "source": "Red Swastika 2022 P5 Weighted Assessment 1 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 2."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "Which of the following has the same value as \\(\\dfrac{2}{5}\\)?",
      "answer0": "0.2",
      "answer1": "0.4",
      "answer2": "0.5",
      "answer3": "2.5",
      "correct_answer": 1,
      "skill_id": 158,
      "difficulty_id": 1,
      "explanation": "\\(\\dfrac{2}{5}=\\dfrac{4}{10}=0.4\\). Answer: 0.4 (option 2).",
      "hints": ["Make the denominator 10.", "\\(\\dfrac{2}{5}=\\dfrac{4}{10}\\)."],
      "source": "Red Swastika 2022 P5 Weighted Assessment 1 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 2."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "What is the value of \\(\\dfrac{4}{14} \\times \\dfrac{2}{3}\\)?",
      "answer0": "\\(\\dfrac{3}{7}\\)",
      "answer1": "\\(\\dfrac{4}{7}\\)",
      "answer2": "\\(\\dfrac{1}{21}\\)",
      "answer3": "\\(\\dfrac{4}{21}\\)",
      "correct_answer": 3,
      "skill_id": 161,
      "difficulty_id": 2,
      "explanation": "\\(\\dfrac{4}{14}=\\dfrac{2}{7}\\). Then \\(\\dfrac{2}{7}\\times\\dfrac{2}{3}=\\dfrac{4}{21}\\). Answer: \\(\\dfrac{4}{21}\\) (option 4).",
      "hints": ["Simplify \\(\\dfrac{4}{14}\\) to \\(\\dfrac{2}{7}\\) first.", "Multiply numerators and denominators."],
      "source": "Red Swastika 2022 P5 Weighted Assessment 1 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 4."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "Which of the following pairs shows the correct base and its related height for finding the area of triangle ACD?",
      "answer0": "Base CE, Height AE",
      "answer1": "Base CD, Height AD",
      "answer2": "Base AB, Height BD",
      "answer3": "Base AC, Height BD",
      "correct_answer": 3,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "For triangle ACD, AC is the base (straight line through A, B, C) and the height is the perpendicular from D to AC, which is BD (D sits below B with BD vertical to AC). So base AC, height BD. Answer: option 4.",
      "hints": ["The height must be perpendicular to the chosen base.", "From vertex D, the perpendicular to AC is BD."],
      "source": "Red Swastika 2022 P5 Weighted Assessment 1 Q5",
      "image_needed": true,
      "image_options": false,
      "image_file": "q5.png",
      "image_page": 3,
      "image_bbox": [0.27, 0.45, 0.74, 0.62],
      "image_loc": "triangle figure ACD with point E below D, middle of page above the options table",
      "notes": "Key: option 4. Figure only (the answer-choice table is text, kept in options)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "What is the value if you add the largest 4-digit even number to 4000?",
      "answer0": "5000",
      "answer1": "13 000",
      "answer2": "13 998",
      "answer3": "13 999",
      "correct_answer": 2,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "The largest 4-digit even number is 9998. 9998 + 4000 = 13 998. Answer: 13 998 (option 3).",
      "hints": ["Largest 4-digit number is 9999; the largest even one is 9998.", "Add 4000."],
      "source": "Red Swastika 2022 P5 Weighted Assessment 1 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 3."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "Jenny bought 100 apples. She ate 20 apples and packed the rest of them into bags of 5. Which equation represents the number of bags of apples she had after packing?",
      "answer0": "100 − 20 ÷ 5",
      "answer1": "100 + 20 ÷ 5",
      "answer2": "(100 − 20) ÷ 5",
      "answer3": "(100 + 20) ÷ 5",
      "correct_answer": 2,
      "skill_id": 156,
      "difficulty_id": 2,
      "explanation": "Remaining apples = 100 − 20 = 80, packed into bags of 5: 80 ÷ 5. The subtraction must be done first, so brackets are needed: (100 − 20) ÷ 5. Answer: option 3.",
      "hints": ["First find how many apples are left.", "Use brackets so the subtraction happens before dividing."],
      "source": "Red Swastika 2022 P5 Weighted Assessment 1 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 3."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "PQR and EFG are identical right-angled triangles. The total area of the shaded parts is 230 cm². Find the area of the <b>unshaded</b> part.",
      "answer0": "35 cm²",
      "answer1": "40 cm²",
      "answer2": "70 cm²",
      "answer3": "80 cm²",
      "correct_answer": 0,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Each triangle has area \\(\\dfrac{1}{2}\\times20\\times15=150\\) cm²; two identical triangles total 300 cm². The two triangles overlap; shaded = total of both triangles minus the overlap counted differently. Shaded parts = 230 cm², so the overlapping (unshaded) region = (sum of both triangles − shaded) shared. 300 − 230 = 70 is the overlap counted once; the unshaded middle triangle = 300 − 230 = 70, but it is double-covered, so unshaded = 300 − 230 − 70 = 35 cm². Answer: 35 cm² (option 1).",
      "hints": ["Each triangle area = \\(\\dfrac{1}{2}\\times20\\times15=150\\) cm².", "The unshaded middle region is shared by both triangles; account for it once."],
      "source": "Red Swastika 2022 P5 Weighted Assessment 1 Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q8.png",
      "image_page": 4,
      "image_bbox": [0.30, 0.50, 0.72, 0.70],
      "image_loc": "two overlapping right-angled triangles PQR (20 cm) and EFG (15 cm) on base line Q-G-R-F, middle of page",
      "notes": "Key: option 1 (35 cm²)."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "\\(\\dfrac{2}{5}\\) of Jim's savings is equal to \\(\\dfrac{4}{9}\\) of Max's savings.<br>Jim has $30 more than Max.<br>How much money does Max have?",
      "answer0": "$150",
      "answer1": "$270",
      "answer2": "$300",
      "answer3": "$570",
      "correct_answer": 1,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "\\(\\dfrac{2}{5}\\)Jim = \\(\\dfrac{4}{9}\\)Max. Make numerators equal: \\(\\dfrac{2}{5}=\\dfrac{4}{10}\\), so \\(\\dfrac{4}{10}\\)Jim = \\(\\dfrac{4}{9}\\)Max, giving \\(\\dfrac{Jim}{Max}=\\dfrac{10}{9}\\). The difference 10u − 9u = 1u = $30, so 1u = $300... rather Jim:Max = 10:9, difference 1u = $30. Max = 9u = 9 × $30 = $270. Answer: $270 (option 2).",
      "hints": ["Rewrite \\(\\dfrac{2}{5}\\) as \\(\\dfrac{4}{10}\\) so both numerators are 4.", "Then Jim:Max = 10:9; the 1-unit difference is $30."],
      "source": "Red Swastika 2022 P5 Weighted Assessment 1 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: option 2 ($270). Jim:Max=10:9, 1u=$30, Max=9u=$270."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "The rectangle is divided into 4 triangles. The areas of triangles A, B and C are 400 cm², 325 cm² and 150 cm² respectively. Find the area of triangle D.",
      "answer0": "75 cm²",
      "answer1": "175 cm²",
      "answer2": "225 cm²",
      "answer3": "250 cm²",
      "correct_answer": 2,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "In a rectangle split by its two diagonals into 4 triangles, opposite triangles are equal in area and the two pairs each sum to half the rectangle: A + C = B + D. So D = A + C − B = 400 + 150 − 325 = 225 cm². Answer: 225 cm² (option 3).",
      "hints": ["Opposite triangles' areas: A + C = B + D (each pair = half the rectangle).", "D = 400 + 150 − 325."],
      "source": "Red Swastika 2022 P5 Weighted Assessment 1 Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 5,
      "image_bbox": [0.30, 0.40, 0.68, 0.62],
      "image_loc": "rectangle divided by two diagonals into 4 triangles A (top), B (right), C (bottom), D (left), middle of page",
      "notes": "Key: option 3 (225 cm²)."
    },
    {
      "n": 11,
      "type_id": 2,
      "question": "Find the value of 4 + 5 × (60 − 30) ÷ 10. [?]",
      "answer0": "19",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 155,
      "difficulty_id": 2,
      "explanation": "Brackets first: 60 − 30 = 30. Then 5 × 30 = 150; 150 ÷ 10 = 15. Finally 4 + 15 = 19. Answer: 19.",
      "hints": ["Do the brackets first, then × and ÷ from left to right.", "Add last."],
      "source": "Red Swastika 2022 P5 Weighted Assessment 1 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key working: =4+5×30÷10 =4+150÷10 =4+15 =19."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "Find the missing fraction in the box: \\(1\\dfrac{7}{12} - \\square = \\dfrac{11}{12}\\).",
      "answer0": "\\(\\dfrac{8}{12}\\)",
      "answer1": "\\(\\dfrac{2}{3}\\)",
      "answer2": "\\(\\dfrac{7}{12}\\)",
      "answer3": "\\(\\dfrac{5}{12}\\)",
      "correct_answer": 1,
      "skill_id": 160,
      "difficulty_id": 2,
      "explanation": "\\(1\\dfrac{7}{12}=\\dfrac{19}{12}\\). Missing = \\(\\dfrac{19}{12}-\\dfrac{11}{12}=\\dfrac{8}{12}=\\dfrac{2}{3}\\). Answer: \\(\\dfrac{2}{3}\\).",
      "hints": ["Convert \\(1\\dfrac{7}{12}\\) to \\(\\dfrac{19}{12}\\).", "Subtract \\(\\dfrac{11}{12}\\) then simplify."],
      "source": "Red Swastika 2022 P5 Weighted Assessment 1 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer is a fraction (2/3) -> converted to MCQ per spec. Key: 8/12 = 2/3. Correct option = 2/3 (index 1)."
    },
    {
      "n": 13,
      "type_id": 2,
      "question": "Jack is 5 years old. His mother is 45 years old. In how many years' time will Jack's mother be 3 times as old as Jack? [?]",
      "answer0": "15",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "The age gap stays 45 − 5 = 40 years. When mother is 3 times Jack's age, the gap (40) equals 2 times Jack's age, so Jack is 40 ÷ 2 = 20. That is in 20 − 5 = 15 years' time. Answer: 15 years.",
      "hints": ["The age difference (40 years) never changes.", "When mother = 3×Jack, the difference = 2×Jack's new age."],
      "source": "Red Swastika 2022 P5 Weighted Assessment 1 Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key working: 45−5=40; 40÷2=20; 20−5=15."
    },
    {
      "n": 14,
      "type_id": 2,
      "question": "A pencil case cost $6 more than a water bottle. Mrs Tan paid $28 for a pencil case and a water bottle. Find the cost of a water bottle. [?]",
      "answer0": "11",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "Remove the extra $6: 28 − 6 = 22 represents two water bottles. So one water bottle = 22 ÷ 2 = $11. Answer: $11.",
      "hints": ["Subtract the $6 difference from the total first.", "Then split the remainder between the two equal bottles."],
      "source": "Red Swastika 2022 P5 Weighted Assessment 1 Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer is money $11; FIB whole-number. Key: (28−6)÷2 = $11."
    },
    {
      "n": 15,
      "type_id": 2,
      "question": "Abby, Ben and Carole had some marbles. Ben and Carole had a total of 360 marbles. Abby and Carole had a total of 450 marbles. Ben had half of the number of marbles Abby had. How many marbles did Carole have? [?]",
      "answer0": "270",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Abby + Carole − (Ben + Carole) = 450 − 360 = 90, so Abby − Ben = 90. Since Ben = half of Abby, Abby − ½Abby = ½Abby = 90, giving Abby = 180 and Ben = 90. Then Carole = 360 − Ben = 360 − 90 = 270. Answer: 270 marbles.",
      "hints": ["Subtract the two totals to get Abby − Ben.", "Use Ben = half of Abby to find each, then Carole = 360 − Ben."],
      "source": "Red Swastika 2022 P5 Weighted Assessment 1 Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key working printed as 450−360=90 then 360−90=270. Carole = 270."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Square WXYZ is made up of four identical triangles and a small square. The area of the small square is 4 cm². Find the area of square WXYZ. [?]",
      "answer0": "100",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Each identical right-angled triangle has legs 8 cm and 6 cm, so area = \\(\\dfrac{1}{2}\\times8\\times6=24\\) cm². Four triangles = 4 × 24 = 96 cm². Add the small square (4 cm²): 96 + 4 = 100 cm². Answer: 100 cm².",
      "hints": ["Area of one triangle = \\(\\dfrac{1}{2}\\times8\\times6\\).", "Four triangles plus the small square give the whole big square."],
      "source": "Red Swastika 2022 P5 Weighted Assessment 1 Q16",
      "image_needed": true,
      "image_options": false,
      "image_file": "q16.png",
      "image_page": 8,
      "image_bbox": [0.30, 0.20, 0.70, 0.34],
      "image_loc": "square WXYZ split into 4 triangles + small square, beside a right triangle labelled 8 cm and 6 cm, upper area of page",
      "notes": "Answer is whole-number cm² (100), units cm². Key: 4×24=96; 96+4=100 cm²."
    },
    {
      "n": 17,
      "type_id": 1,
      "question": "Alice had \\(\\dfrac{4}{5}\\) m of ribbon. She cut 4 pieces of ribbon of equal length from it and there was some ribbon left. Each piece that was cut was \\(\\dfrac{1}{8}\\) of the ribbon she had at first.<br>(a) Find the length of each piece of the ribbon cut.<br>(b) Find the total length of the 4 pieces of ribbon that was cut.",
      "answer0": "(a) \\(\\dfrac{1}{10}\\) m, (b) \\(\\dfrac{4}{10}\\) m (\\(=\\dfrac{2}{5}\\) m)",
      "answer1": "(a) \\(\\dfrac{1}{8}\\) m, (b) \\(\\dfrac{1}{2}\\) m",
      "answer2": "(a) \\(\\dfrac{1}{5}\\) m, (b) \\(\\dfrac{4}{5}\\) m",
      "answer3": "(a) \\(\\dfrac{4}{40}\\) m, (b) \\(\\dfrac{4}{8}\\) m",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "(a) Each piece = \\(\\dfrac{1}{8}\\) of \\(\\dfrac{4}{5}\\) m = \\(\\dfrac{1}{8}\\times\\dfrac{4}{5}=\\dfrac{4}{40}=\\dfrac{1}{10}\\) m. (b) Total of 4 pieces = 4 × \\(\\dfrac{1}{10}=\\dfrac{4}{10}=\\dfrac{2}{5}\\) m.",
      "hints": ["Each piece is \\(\\dfrac{1}{8}\\) of \\(\\dfrac{4}{5}\\) m — multiply the fractions.", "Multiply that length by 4 for the total."],
      "source": "Red Swastika 2022 P5 Weighted Assessment 1 Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answers are fractions (1/10 m, 4/10 m) -> per spec made MCQ. Key: a) 1/10 m, b) 4/10 m. Correct = option 1 (index 0)."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "Mrs Chong had some flowers in her garden. \\(\\dfrac{2}{3}\\) of the flowers were roses. \\(\\dfrac{1}{4}\\) of the remainder was tulips and the rest were lilies. There were 55 more roses than lilies.<br>(a) How many flowers did Mrs Chong have altogether? [?]<br>(b) How many lilies were there in the garden? [?]",
      "answer0": "132",
      "answer1": "33",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Roses = \\(\\dfrac{2}{3}\\); remainder = \\(\\dfrac{1}{3}\\). Tulips = \\(\\dfrac{1}{4}\\) of remainder = \\(\\dfrac{1}{12}\\); lilies = rest of remainder = \\(\\dfrac{3}{4}\\times\\dfrac{1}{3}=\\dfrac{3}{12}=\\dfrac{1}{4}\\). Using twelfths: roses = \\(\\dfrac{8}{12}\\), lilies = \\(\\dfrac{3}{12}\\). Difference = \\(\\dfrac{5}{12}\\) of total = 55, so 1 unit (\\(\\dfrac{1}{12}\\)) = 11 and total = 12 × 11 = 132. (a) 132 flowers. (b) Lilies = 3 units = 3 × 11 = 33.",
      "hints": ["Express roses and lilies over a common 12 parts.", "The 55-flower difference equals 5 of those parts."],
      "source": "Red Swastika 2022 P5 Weighted Assessment 1 Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key working: a) 5u=55, u=11, 12u=132; b) 3u=11×3=33. Both answers whole numbers."
    }
  ]
}