{ "paper": { "school": "Nanyang", "year": 2023, "level": "P4", "label": "Weighted Assessment 1 and 2", "source_prefix": "Nanyang 2023 P4 Weighted Assessment 1 and 2", "has_answer_key": true, "notes": "Combined booklet: WA1 (pages 1-6, Q1-9) and WA2 (pages 7-13, Q1-9). WA1 answer key page 15; WA2 answer key pages 16-17. Question numbering restarts at WA2 — sources disambiguated as 'WA1 Q' / 'WA2 Q'." }, "questions": [ { "n": 1, "type_id": 1, "question": "649 × 73 = [?]", "answer0": "722", "answer1": "6490", "answer2": "24 013", "answer3": "47 377", "correct_answer": 3, "skill_id": 116, "difficulty_id": 2, "explanation": "Multiply 649 by 73. 649 × 70 = 45 430 and 649 × 3 = 1947. 45 430 + 1947 = 47 377.", "hints": [ "Split 73 into 70 + 3.", "Add 649 × 70 and 649 × 3." ], "source": "Nanyang 2023 P4 Weighted Assessment 1 and 2 WA1 Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Stem printed with a blank for the product; rendered as a single FIB-style blank inside the MCQ stem. Key: option 4 (47 377)." }, { "n": 2, "type_id": 1, "question": "A number when rounded to the nearest hundred is 56 400. What is the greatest possible whole number?", "answer0": "56 399", "answer1": "56 409", "answer2": "56 449", "answer3": "56 499", "correct_answer": 2, "skill_id": 109, "difficulty_id": 2, "explanation": "Numbers from 56 350 to 56 449 round to 56 400 (nearest hundred). The greatest whole number in this range is 56 449.", "hints": [ "A number rounds to 56 400 if it is from 56 350 up to 56 449.", "Take the largest value in that range." ], "source": "Nanyang 2023 P4 Weighted Assessment 1 and 2 WA1 Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 3 (56 449)." }, { "n": 3, "type_id": 1, "question": "Look at the number pattern.
39 400, 37 400, 37 365, 35 365, 35 330, [?], 33 295
What is the missing number?", "answer0": "33 330", "answer1": "33 365", "answer2": "35 130", "answer3": "35 295", "correct_answer": 0, "skill_id": 108, "difficulty_id": 3, "explanation": "The pattern alternates two operations: subtract 2000, then subtract 35. 39 400 −2000 = 37 400; 37 400 −35 = 37 365; 37 365 −2000 = 35 365; 35 365 −35 = 35 330; 35 330 −2000 = 33 330; 33 330 −35 = 33 295. The missing number is 33 330.", "hints": [ "Look at the differences between consecutive terms.", "The steps alternate between −2000 and −35." ], "source": "Nanyang 2023 P4 Weighted Assessment 1 and 2 WA1 Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "Pattern is text (boxed numbers), reproduced inline; no figure crop required. Key: option 1 (33 330)." }, { "n": 4, "type_id": 2, "question": "What is the remainder when 7294 is divided by 8?", "answer0": "6", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 117, "difficulty_id": 2, "explanation": "7294 ÷ 8 = 911 remainder 6 (911 × 8 = 7288; 7294 − 7288 = 6). The remainder is 6.", "hints": [ "Divide 7294 by 8.", "Multiply the quotient by 8 and subtract from 7294 to find the remainder." ], "source": "Nanyang 2023 P4 Weighted Assessment 1 and 2 WA1 Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 6 (7294 ÷ 8 = 911 R 6)." }, { "n": 5, "type_id": 2, "question": "16 and 64 have exactly five common factors. Three of the common factors are 1, 4 and 16. What are the other two common factors?", "answer0": "2", "answer1": "8", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 113, "difficulty_id": 2, "explanation": "Common factors of 16 and 64 are 1, 2, 4, 8 and 16. Removing the given 1, 4 and 16 leaves 2 and 8.", "hints": [ "List the factors of 16: 1, 2, 4, 8, 16.", "Each factor of 16 also divides 64, so the remaining common factors are 2 and 8." ], "source": "Nanyang 2023 P4 Weighted Assessment 1 and 2 WA1 Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "Two-blank answer (in either order). Key: 2, 8." }, { "n": 6, "type_id": 2, "question": "Find the sum of the first three common multiples of 2 and 6.", "answer0": "36", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 115, "difficulty_id": 2, "explanation": "Common multiples of 2 and 6 are multiples of 6: 6, 12, 18, ... The first three are 6, 12 and 18. Their sum is 6 + 12 + 18 = 36.", "hints": [ "The common multiples of 2 and 6 are the multiples of 6.", "Add the first three: 6 + 12 + 18." ], "source": "Nanyang 2023 P4 Weighted Assessment 1 and 2 WA1 Q6", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 36." }, { "n": 7, "type_id": 2, "question": "Use the 5 digits to form the greatest 5-digit number. The digit in the thousands place is an even number. Use each digit only once.
1, 0, 3, 5, 8", "answer0": "80531", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 106, "difficulty_id": 3, "explanation": "To make the greatest number, place the largest digit first: 8 in the ten-thousands place. The thousands digit must be even; the largest remaining even digit is 0, so put 0 in the thousands place. Arrange the rest in descending order: 5, 3, 1. This gives 80 531.", "hints": [ "Put the biggest digit (8) in the ten-thousands place.", "The thousands digit must be even; the largest available even digit left is 0.", "Arrange the remaining digits 5, 3, 1 in descending order." ], "source": "Nanyang 2023 P4 Weighted Assessment 1 and 2 WA1 Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Digit cards 1, 0, 3, 5, 8 reproduced inline as text; no figure crop required. Key: 80531." }, { "n": 8, "type_id": 2, "question": "Katelyn has two six-sided dice. One is black in colour and one is white in colour. She rolls both dice and adds the two numbers shown on the dice. How many ways can she get a total of 8?", "answer0": "5", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 2, "explanation": "Because the two dice are different colours, order matters. Pairs (black + white) summing to 8: 2+6, 3+5, 4+4, 5+3, 6+2. That is 5 ways.", "hints": [ "The dice are different colours, so 2+6 and 6+2 count separately.", "List every black/white pair that adds to 8." ], "source": "Nanyang 2023 P4 Weighted Assessment 1 and 2 WA1 Q8", "image_needed": false, "image_options": false, "image_file": null, "notes": "Dice picture is decorative only; the count does not depend on the figure. Key: 5." }, { "n": 9, "type_id": 2, "question": "The cost of a dining table was $735. The dining table cost 5 times as much as a dining chair.
(a) How much did the dining chair cost?
(b) How much more did the dining table cost than the dining chair?", "answer0": "147", "answer1": "588", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 2, "explanation": "(a) The chair = table ÷ 5 = $735 ÷ 5 = $147. (b) The difference = chair × 4 = $147 × 4 = $588 (or $735 − $147 = $588).", "hints": [ "The table is 5 units and the chair is 1 unit.", "(a) 1 unit = $735 ÷ 5.", "(b) The difference is 4 units, or table − chair." ], "source": "Nanyang 2023 P4 Weighted Assessment 1 and 2 WA1 Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Two-part word problem. answer0 = part (a) $147, answer1 = part (b) $588. Money plain (no $ in answers). Key: (a) $147, (b) $588." }, { "n": 10, "type_id": 1, "question": "In a group of 120 children, $$\\frac{3}{8}$$ of them are girls. How many girls are there?", "answer0": "15", "answer1": "40", "answer2": "45", "answer3": "75", "correct_answer": 2, "skill_id": 120, "difficulty_id": 2, "explanation": "$$\\frac{3}{8}$$ of 120 = 120 ÷ 8 × 3 = 15 × 3 = 45. There are 45 girls.", "hints": [ "Find one eighth of 120 first: 120 ÷ 8 = 15.", "Multiply by 3." ], "source": "Nanyang 2023 P4 Weighted Assessment 1 and 2 WA2 Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "WA2 Q1. Key: option 3 (45)." }, { "n": 11, "type_id": 1, "question": "In the square grid, the [?] is south-east of the heart.", "answer0": "star", "answer1": "circle", "answer2": "square", "answer3": "triangle", "correct_answer": 0, "skill_id": 142, "difficulty_id": 2, "explanation": "South-east means down and to the right of the heart. The star sits below and to the right of the heart, so the answer is the star.", "hints": [ "North is up; south-east is down and to the right.", "Find the shape that is both below and to the right of the heart." ], "source": "Nanyang 2023 P4 Weighted Assessment 1 and 2 WA2 Q2", "image_needed": true, "image_options": false, "image_file": "q11.png", "image_page": 8, "image_bbox": [ 0.28, 0.1, 0.68, 0.28 ], "image_loc": "5x5 square grid near top of page with heart, circle, star and square in the middle rows and a triangle lower-left, plus a small N compass arrow to the right", "notes": "WA2 Q2. Options are text shape names (not images). Key: option 1 (star). Grid figure needed to answer; compass N arrow included in crop." }, { "n": 12, "type_id": 1, "question": "Finn is facing east at first. He makes a $$\\frac{1}{4}$$ turn clockwise and then turns through an angle of 315° in an anti-clockwise direction. What place is he facing in the end?", "answer0": "Park", "answer1": "Market", "answer2": "Bookshop", "answer3": "Shopping Mall", "correct_answer": 2, "skill_id": 141, "difficulty_id": 3, "explanation": "Start facing east. A $$\\frac{1}{4}$$ turn (90°) clockwise makes him face south. From south, a 315° anti-clockwise turn is the same as a 45° clockwise turn (360° − 315° = 45°), bringing him to face south-west; continuing the standard 8-point reading on this diagram, the place he ends up facing is the Bookshop.", "hints": [ "A quarter turn clockwise from east faces south.", "315° anti-clockwise is the same as 45° clockwise.", "Match the final facing direction to the place shown on the diagram." ], "source": "Nanyang 2023 P4 Weighted Assessment 1 and 2 WA2 Q3", "image_needed": true, "image_options": false, "image_file": "q12.png", "image_page": 9, "image_bbox": [ 0.22, 0.08, 0.82, 0.36 ], "image_loc": "central 'Finn' oval surrounded by nine labelled place boxes (Shopping Mall, Playground, Bookshop, School, Garden, Market, MRT Station, Park) arranged in a 3x3 layout, with a small N compass arrow to the right", "notes": "WA2 Q3. Options are text place names (not images). Key: option 3 (Bookshop). Place-layout diagram needed to map the final direction to a place." }, { "n": 13, "type_id": 0, "question": "Using a protractor and a ruler, draw ∠ABC = 145°. Mark and label the angle. The line AB has been drawn for you.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 140, "difficulty_id": 2, "explanation": "Place the protractor centre at B with AB along the baseline, measure 145°, mark point C and draw BC. ∠ABC = 145°.", "hints": [], "source": "Nanyang 2023 P4 Weighted Assessment 1 and 2 WA2 Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "WA2 Q4. Construction/drawing task (draw and label a 145° angle) — no value or sequence answer; type_id 0, SKIPPED on insert. Answer key shows the constructed angle only." }, { "n": 14, "type_id": 2, "question": "Fei Ming spent $$\\frac{4}{7}$$ of his money on a guitar and had $210 left. How much did he spend on the guitar?", "answer0": "280", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 122, "difficulty_id": 2, "explanation": "He spent $$\\frac{4}{7}$$, so $$\\frac{3}{7}$$ was left = $210. 1 unit ($$\\frac{1}{7}$$) = $210 ÷ 3 = $70. Spent = 4 units = $70 × 4 = $280.", "hints": [ "The fraction left is 1 − $$\\frac{4}{7}$$ = $$\\frac{3}{7}$$, which equals $210.", "Find 1 unit: $210 ÷ 3.", "The guitar cost 4 units." ], "source": "Nanyang 2023 P4 Weighted Assessment 1 and 2 WA2 Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "WA2 Q5. Money plain. Key: $280." }, { "n": 15, "type_id": 2, "question": "Mary bought 4 kg of flour. She used $$\\frac{1}{4}$$ kg of flour to make cupcakes and $$\\frac{2}{5}$$ kg of it to make pizza. How much flour was left? Express your answer as a mixed number.", "answer0": "3 7/20", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 121, "difficulty_id": 2, "explanation": "Used = $$\\frac{1}{4}+\\frac{2}{5}=\\frac{5}{20}+\\frac{8}{20}=\\frac{13}{20}$$ kg. Left = 4 − $$\\frac{13}{20}$$ = 3$$\\frac{20}{20}$$ − $$\\frac{13}{20}$$ = 3$$\\frac{7}{20}$$ kg.", "hints": [ "Add the two fractions used using a common denominator of 20.", "Subtract the total used from 4 kg.", "Express the result as a mixed number." ], "source": "Nanyang 2023 P4 Weighted Assessment 1 and 2 WA2 Q6", "image_needed": false, "image_options": false, "image_file": null, "notes": "WA2 Q6. Mixed-number FIB answer kept plain as '3 7/20'. Key: 3 7/20 kg." }, { "n": 16, "type_id": 2, "question": "Ali painted $$\\frac{2}{9}$$ of a wall on Monday and $$\\frac{2}{3}$$ of the same wall on Tuesday. What fraction of the wall was not painted?", "answer0": "1/9", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 121, "difficulty_id": 2, "explanation": "Painted = $$\\frac{2}{9}+\\frac{2}{3}=\\frac{2}{9}+\\frac{6}{9}=\\frac{8}{9}$$. Not painted = 1 − $$\\frac{8}{9}$$ = $$\\frac{1}{9}$$.", "hints": [ "Convert $$\\frac{2}{3}$$ to ninths.", "Add the two painted fractions, then subtract from 1 (the whole wall)." ], "source": "Nanyang 2023 P4 Weighted Assessment 1 and 2 WA2 Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "WA2 Q7. FIB fraction answer kept plain '1/9'. Key: 1/9." }, { "n": 17, "type_id": 2, "question": "There were 20 balloons at a party. 2 of them were purple, 4 of them were blue, 11 of them were green and the rest were yellow. For each statement, write True or False.
(a) $$\\frac{3}{20}$$ of the balloons were yellow.
(b) $$\\frac{1}{5}$$ of the balloons were blue.
(c) $$\\frac{9}{11}$$ of the balloons were not green.
(d) The fraction of the balloons that were purple is greater than the fraction of the balloons that were blue.", "answer0": "True", "answer1": "True", "answer2": "False", "answer3": "False", "correct_answer": null, "skill_id": 120, "difficulty_id": 3, "explanation": "Yellow = 20 − 2 − 4 − 11 = 3, so yellow = $$\\frac{3}{20}$$ → True. Blue = 4 = $$\\frac{4}{20}=\\frac{1}{5}$$ → True. Not green = 20 − 11 = 9 out of 20 = $$\\frac{9}{20}$$, not $$\\frac{9}{11}$$ → False. Purple $$\\frac{2}{20}$$ is less than blue $$\\frac{4}{20}$$, so 'purple greater than blue' → False.", "hints": [ "First work out how many balloons were yellow.", "Write each colour as a fraction of 20 and simplify.", "Compare carefully — 'not green' is out of 20, not out of 11." ], "source": "Nanyang 2023 P4 Weighted Assessment 1 and 2 WA2 Q8", "image_needed": false, "image_options": false, "image_file": null, "notes": "WA2 Q8. Originally a True/False tick table; converted to a 4-blank FIB where each answer is the True/False verdict in order. Key: True, True, False, False." }, { "n": 18, "type_id": 2, "question": "Sumiko baked some cookies. She gave $$\\frac{1}{6}$$ of the cookies to her siblings and 45 of the cookies to her friends. She had $$\\frac{2}{3}$$ of the cookies left.
(a) How many cookies did she have left?
(b) She packed the leftover cookies into 18 bags. Some bags contained 6 cookies while the rest of the bags contained 12 cookies. How many bags contained 6 cookies?", "answer0": "180", "answer1": "6", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 122, "difficulty_id": 3, "explanation": "(a) She gave away $$\\frac{1}{6}$$ + 45 cookies and had $$\\frac{2}{3}$$ left. Fraction given to siblings + fraction left = $$\\frac{1}{6}+\\frac{4}{6}=\\frac{5}{6}$$, so the 45 cookies given to friends are the remaining $$\\frac{1}{6}$$. Thus 1 unit ($$\\frac{1}{6}$$) = 45, and the $$\\frac{2}{3}$$ = 4 units left = 4 × 45 = 180 cookies. (b) 180 cookies in 18 bags. If all 18 bags held 12, that is 216; the shortfall 216 − 180 = 36 must come from bags holding 6 instead of 12 (each such bag is 6 fewer): 36 ÷ 6 = 6 bags contained 6 cookies.", "hints": [ "(a) Siblings + left = $$\\frac{1}{6}+\\frac{2}{3}=\\frac{5}{6}$$; the 45 friends' cookies are the remaining $$\\frac{1}{6}$$, so 1 unit = 45.", "(a) The amount left is $$\\frac{2}{3}$$ = 4 units.", "(b) Suppose all 18 bags held 12 cookies, compare with 180 and assign the difference to the 6-cookie bags." ], "source": "Nanyang 2023 P4 Weighted Assessment 1 and 2 WA2 Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "WA2 Q9. 'and 45 of the cookies to her friends' in the stem is the printed number 45 (cookies), used in the working. Two-part: answer0 = (a) 180 cookies, answer1 = (b) 6 bags. Key: (a) 180, (b) 6." } ] }