{
  "paper": {
    "school": "Raffles Girls' Primary School",
    "year": 2023,
    "level": "P6",
    "label": "Weighted Assessment 1",
    "source_prefix": "Raffles 2023 P6 Weighted Assessment 1",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 2,
      "question": "What is the missing number in the box?<br>$3\\,000\\,000 + 10\\,000 + [?] + 8 = 3\\,014\\,008$",
      "answer0": "4000",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 149,
      "difficulty_id": 1,
      "explanation": "Method: subtract the known parts from the total. $3\\,014\\,008 - 3\\,000\\,000 - 10\\,000 - 8 = 4\\,000$. The missing number is 4000.",
      "hints": ["Add up the parts you already know: 3 000 000 + 10 000 + 8.", "Subtract that sum from 3 014 008."],
      "source": "Raffles 2023 P6 Weighted Assessment 1 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Place value to millions. Answer key: 4000."
    },
    {
      "n": 2,
      "type_id": 2,
      "question": "Use all the digits 4, 5, 6, 8 to form the greatest number between 5 000 and 6 000.<br>[?]",
      "answer0": "5864",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 149,
      "difficulty_id": 1,
      "explanation": "Method: the number must be between 5000 and 6000, so the thousands digit is 5. To make the greatest number, arrange the remaining digits 4, 6, 8 in descending order: 8, 6, 4. Greatest number = 5864.",
      "hints": ["The number is between 5000 and 6000, so it must start with 5.", "Arrange the leftover digits 4, 6, 8 from largest to smallest."],
      "source": "Raffles 2023 P6 Weighted Assessment 1 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 5864."
    },
    {
      "n": 3,
      "type_id": 2,
      "question": "How many halves are there in \\(5\\dfrac{1}{2}\\)?<br>[?]",
      "answer0": "11",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 206,
      "difficulty_id": 1,
      "explanation": "Method: divide by one half. \\(5\\dfrac{1}{2} \\div \\dfrac{1}{2} = \\dfrac{11}{2} \\times \\dfrac{2}{1} = 11\\). There are 11 halves.",
      "hints": ["Convert the mixed number to an improper fraction: \\(\\dfrac{11}{2}\\).", "Counting halves means dividing by \\(\\dfrac{1}{2}\\)."],
      "source": "Raffles 2023 P6 Weighted Assessment 1 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 5½ ÷ ½ = 11."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Arrange these fractions from the smallest to the largest.<br>\\(2\\dfrac{1}{2}\\) , \\(\\dfrac{13}{5}\\) , \\(2\\dfrac{3}{7}\\)",
      "answer0": "\\(2\\dfrac{3}{7}\\) , \\(2\\dfrac{1}{2}\\) , \\(\\dfrac{13}{5}\\)",
      "answer1": "\\(2\\dfrac{1}{2}\\) , \\(\\dfrac{13}{5}\\) , \\(2\\dfrac{3}{7}\\)",
      "answer2": "\\(\\dfrac{13}{5}\\) , \\(2\\dfrac{1}{2}\\) , \\(2\\dfrac{3}{7}\\)",
      "answer3": "\\(2\\dfrac{3}{7}\\) , \\(\\dfrac{13}{5}\\) , \\(2\\dfrac{1}{2}\\)",
      "correct_answer": 0,
      "skill_id": 158,
      "difficulty_id": 2,
      "explanation": "Method: convert each to a decimal. \\(2\\dfrac{1}{2}=2.5\\); \\(\\dfrac{13}{5}=2.6\\); \\(2\\dfrac{3}{7}\\approx2.43\\). Smallest to largest: \\(2\\dfrac{3}{7}\\), \\(2\\dfrac{1}{2}\\), \\(\\dfrac{13}{5}\\).",
      "hints": ["Change each fraction to a decimal to compare them easily.", "\\(\\dfrac{3}{7}\\approx0.43\\), which is smaller than \\(\\dfrac{1}{2}\\)."],
      "source": "Raffles 2023 P6 Weighted Assessment 1 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Ordering of fractions/mixed numbers -> MCQ (fraction answers). Answer key order smallest->largest: 2 3/7, 2 1/2, 13/5."
    },
    {
      "n": 5,
      "type_id": 2,
      "question": "Mr Ravi bought some boxes of chocolates. Each box contained 12 chocolates. The total number of chocolates Mr Ravi bought was more than 50 but fewer than 100. Mr Ravi ate 7 chocolates and gave the rest equally to each of his 5 children. How many chocolates did each child get?<br>[?]",
      "answer0": "13",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "Method: the total is a multiple of 12 between 50 and 100 (60, 72, 84, 96). After eating 7 the rest must divide exactly by 5. $72 - 7 = 65$ and $65 \\div 5 = 13$. Each child got 13 chocolates.",
      "hints": ["List the multiples of 12 between 50 and 100: 60, 72, 84, 96.", "After removing 7, the remaining number must be divisible by 5."],
      "source": "Raffles 2023 P6 Weighted Assessment 1 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Total = 72 (the only valid multiple of 12). Answer key: 13."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "Fill in the boxes with the correct mathematical symbols. Each symbol can only be used once. The symbols are $+$ , $-$ , $\\times$ , $\\div$ .<br>$56 \\;\\square\\; 4 + 3 \\;\\square\\; 8 = 38$",
      "answer0": "$\\div$ and $\\times$",
      "answer1": "$\\times$ and $\\div$",
      "answer2": "$+$ and $-$",
      "answer3": "$-$ and $+$",
      "correct_answer": 0,
      "skill_id": 155,
      "difficulty_id": 2,
      "explanation": "Method: test the symbols using order of operations. $56 \\div 4 + 3 \\times 8 = 14 + 24 = 38$. So the first box is $\\div$ and the second box is $\\times$.",
      "hints": ["Remember to do multiplication and division before addition.", "Try making the two terms add up to 38: one part 14, the other 24."],
      "source": "Raffles 2023 P6 Weighted Assessment 1 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Symbol fill-in -> MCQ. Answer key: 56 ÷ 4 + 3 × 8 = 38."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "Eva spent \\(\\dfrac{1}{7}\\) of her savings on a gift for her brother. Then, she spent \\(\\dfrac{2}{3}\\) of the remainder on a school bag. What fraction of her savings had she left? Give your answer in the simplest form.",
      "answer0": "\\(\\dfrac{2}{7}\\)",
      "answer1": "\\(\\dfrac{4}{7}\\)",
      "answer2": "\\(\\dfrac{1}{3}\\)",
      "answer3": "\\(\\dfrac{6}{21}\\)",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "Method: after the gift, the remainder is \\(1-\\dfrac{1}{7}=\\dfrac{6}{7}\\). She spent \\(\\dfrac{2}{3}\\) of that on the bag, leaving \\(\\dfrac{1}{3}\\) of the remainder. Fraction left \\(=\\dfrac{1}{3}\\times\\dfrac{6}{7}=\\dfrac{6}{21}=\\dfrac{2}{7}\\).",
      "hints": ["After the gift, \\(\\dfrac{6}{7}\\) of the savings is left.", "Spending \\(\\dfrac{2}{3}\\) of the remainder leaves \\(\\dfrac{1}{3}\\) of it."],
      "source": "Raffles 2023 P6 Weighted Assessment 1 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Fraction answer -> MCQ. Answer key: 2/7."
    },
    {
      "n": 8,
      "type_id": 2,
      "question": "Terry had 3 times as many $2-notes as $5-notes. He had $385 altogether. How many $5-notes did Terry have?<br>[?]",
      "answer0": "35",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 213,
      "difficulty_id": 2,
      "explanation": "Method: let the number of $5-notes be 1 unit, so the $2-notes are 3 units. Value of 1 group = $5 + 3 \\times $2 = $5 + $6 = $11. Number of $5-notes = $385 \\div $11 = 35.",
      "hints": ["For every one $5-note there are three $2-notes.", "One group is worth $5 + 3 × $2 = $11; divide $385 by $11."],
      "source": "Raffles 2023 P6 Weighted Assessment 1 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer key: 6U + 5U = 385, U = 385 ÷ 11 = 35."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "Aminah had an equal number of sunflowers and roses. She gave away \\(\\dfrac{3}{5}\\) of the sunflowers and some roses. In the end, she was left with \\(\\dfrac{1}{4}\\) of the total number of flowers. What fraction of the roses did she give away?",
      "answer0": "\\(\\dfrac{9}{10}\\)",
      "answer1": "\\(\\dfrac{3}{5}\\)",
      "answer2": "\\(\\dfrac{1}{4}\\)",
      "answer3": "\\(\\dfrac{7}{10}\\)",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Method: let sunflowers = roses = 10 units each, total 20 units. She kept \\(\\dfrac{2}{5}\\) of the sunflowers = 4 units. She was left with \\(\\dfrac{1}{4}\\) of 20 = 5 units in total, so roses left = 5 - 4 = 1 unit. Roses given away = 10 - 1 = 9 units. Fraction of roses given away = \\(\\dfrac{9}{10}\\).",
      "hints": ["Let the sunflowers and roses each be 10 units so the total is 20 units.", "Sunflowers left = \\(\\dfrac{2}{5}\\) of 10; total left = \\(\\dfrac{1}{4}\\) of 20. The difference is the roses left."],
      "source": "Raffles 2023 P6 Weighted Assessment 1 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Fraction answer -> MCQ. Answer key: 18/20 = 9/10."
    },
    {
      "n": 10,
      "type_id": 0,
      "question": "There are some pink, black and green beads in a container. \\(\\dfrac{2}{5}\\) of the beads are pink. There are more black beads than green beads. Each of the statements below is either true, false or not possible to tell from the information given. (a) There are fewer green beads than pink beads. (b) If \\(\\dfrac{1}{8}\\) of the pink beads are used, there will be more black beads than pink beads left.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Pink = 2/5; black + green = 3/5 with black > green. (a) Black + green = 3/5 and black > green means green < 3/10, which is less than pink (2/5 = 4/10), so 'fewer green than pink' is True. (b) Using 1/8 of pink leaves 7/8 of 2/5 = 14/40 = 7/20 pink; black is between 3/10 (12/40) and just under 3/5; cannot be determined, so Not possible to tell.",
      "hints": ["Pink is 2/5; the black and green together make up the other 3/5.", "Statement (b) depends on the exact number of black beads, which is not given."],
      "source": "Raffles 2023 P6 Weighted Assessment 1 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Interactive true/false/not-possible-to-tell table -> type_id 0 (skipped on insert). Answer key: (a) True, (b) Not possible to tell."
    },
    {
      "n": 11,
      "type_id": 2,
      "question": "Tim and Jerry were paid a total of $8568 for selling tickets. Tim was paid $5304 more than Jerry. (a) How much was Tim paid for selling the tickets? $[?]<br>(b) Tim and Jerry were paid based on the number of tickets they sold. Tim sold 3 times as many tickets as Jerry. Tim was paid $5 more than Jerry for selling each ticket. How many tickets did Tim sell? [?]",
      "answer0": "6936",
      "answer1": "408",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "(a) Difference is $5304, total $8568. Jerry = (8568 - 5304) ÷ 2 = 3264 ÷ 2 = $1632; Tim = 1632 + 5304 = $6936. (b) Tim sold 3 times as many tickets, so Tim's price per ticket = 6936 ÷ (3 units) per Jerry's units; per-ticket pay difference is $5. Jerry's per-ticket pay: Tim sold 3J tickets at price (p+5), Jerry sold J at price p: 3J(p+5) = 6936 and Jp = 1632. From key: 6936 ÷ 3 = 2312, 2312 - 1632 = 680, 680 ÷ 5 = 136 (= Jerry's tickets J), Tim's tickets = 136 × 3 = 408.",
      "hints": ["(a) Subtract the difference from the total, halve it to get Jerry's pay, then add the difference back for Tim.", "(b) Compare Tim's pay split into 3 equal ticket-groups against Jerry's pay; the $680 gap over $5 per ticket gives Jerry's ticket count."],
      "source": "Raffles 2023 P6 Weighted Assessment 1 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Multi-part FIB (a) $6936, (b) 408 tickets. Answer key: a) 6936; b) 408."
    },
    {
      "n": 12,
      "type_id": 2,
      "question": "Ruth needs 90 pieces of ribbons each of length \\(\\dfrac{4}{5}\\) m to decorate a room. Ribbon is sold in rolls of 10 m each. (a) What is the maximum number of pieces of ribbon she can get from a roll of 10 m? [?]<br>(b) What is the least number of rolls of ribbon that Ruth needs to buy? [?]",
      "answer0": "12",
      "answer1": "8",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "(a) From one 10 m roll, number of \\(\\dfrac{4}{5}\\) m pieces = \\(10 \\div \\dfrac{4}{5} = 10 \\times \\dfrac{5}{4} = 12.5\\); the maximum whole pieces is 12. (b) She needs 90 pieces; 90 ÷ 12 = 7.5, so she must buy 8 whole rolls.",
      "hints": ["(a) Divide 10 m by \\(\\dfrac{4}{5}\\) m, then round DOWN to a whole piece.", "(b) Divide 90 pieces by the 12 pieces per roll, then round UP."],
      "source": "Raffles 2023 P6 Weighted Assessment 1 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Multi-part FIB (a) 12 pieces, (b) 8 rolls. Answer key: a) 12; b) 90 ÷ 12 = 7.5 ~ 8."
    },
    {
      "n": 13,
      "type_id": 2,
      "question": "Ahmad used sticks to form the following figures. The table shows the number of triangles and sticks for the first three figures: Figure 1 has 2 triangles and 8 sticks; Figure 2 has 4 triangles and 15 sticks; Figure 3 has 6 triangles and 22 sticks. (a) Complete the table for Figure 4: number of triangles [?] and number of sticks [?].<br>(b) A figure in the pattern has a total of 2507 sticks. What is the Figure Number? [?]",
      "answer0": "8",
      "answer1": "29",
      "answer2": "358",
      "answer3": null,
      "correct_answer": null,
      "skill_id": 237,
      "difficulty_id": 3,
      "explanation": "(a) Triangles go up by 2 each figure: Figure 4 = 8 triangles. Sticks go up by 7 each figure (8, 15, 22, ...): Figure 4 = 22 + 7 = 29 sticks. (b) Number of sticks = 7 × Figure Number + 1. So 2507 - 1 = 2506; 2506 ÷ 7 = 358. The Figure Number is 358.",
      "hints": ["Triangles increase by 2 each time; sticks increase by 7 each time.", "Sticks = 7 × (Figure Number) + 1. Subtract 1 from 2507, then divide by 7."],
      "source": "Raffles 2023 P6 Weighted Assessment 1 Q13",
      "image_needed": true,
      "image_options": false,
      "image_file": "q13.png",
      "image_page": 9,
      "image_bbox": [0.24, 0.10, 0.78, 0.23],
      "image_loc": "top of page below the question text: three stick figures labelled Figure 1, Figure 2, Figure 3",
      "notes": "Answer-key working uses 2499 ÷ 7 = 357, 357 + 1 = 358 (treating the first stick separately); both give Figure 358. Sticks formula 7n+1. Answer key: a) 8, 29; b) 358."
    }
  ]
}