{ "paper": { "school": "Nanyang", "year": 2022, "level": "P4", "label": "Semestral Assessment 2", "source_prefix": "Nanyang 2022 P4 Semestral Assessment 2", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "In which of the following numbers does the digit 6 stand for 600?", "answer0": "4659", "answer1": "6549", "answer2": "5946", "answer3": "9465", "correct_answer": 0, "skill_id": 105, "difficulty_id": 1, "explanation": "Place value of digit 6: in 4659 the 6 is in the hundreds place, so it stands for 600. (6549: 6000; 5946: 6; 9465: 60.) Answer: 4659.", "hints": ["Look at which place each 6 sits in.", "The hundreds digit stands for that digit x 100."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option (1) 4659." }, { "n": 2, "type_id": 1, "question": "Thirty-four thousand and ninety-two in figures is [?].", "answer0": "34 920", "answer1": "34 902", "answer2": "34 092", "answer3": "3492", "correct_answer": 2, "skill_id": 106, "difficulty_id": 1, "explanation": "Thirty-four thousand = 34 000; ninety-two = 92. 34 000 + 92 = 34 092. Answer: 34 092.", "hints": ["Write the thousands part first: 34 000.", "Add ninety-two = 92 into the tens and ones."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option (3) 34 092." }, { "n": 3, "type_id": 1, "question": "Which of the following are common factors of 16 and 24?", "answer0": "1 and 6", "answer1": "2 and 3", "answer2": "3 and 8", "answer3": "4 and 8", "correct_answer": 3, "skill_id": 113, "difficulty_id": 2, "explanation": "Factors of 16: 1,2,4,8,16. Factors of 24: 1,2,3,4,6,8,12,24. Common factors: 1,2,4,8. Only '4 and 8' are both common factors. Answer: 4 and 8.", "hints": ["List the factors of each number.", "A common factor must divide both 16 and 24."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option (4) 4 and 8." }, { "n": 4, "type_id": 1, "question": "What fraction of the shapes are circles?", "answer0": "2/10", "answer1": "2/8", "answer2": "8/10", "answer3": "8/2", "correct_answer": 0, "skill_id": 120, "difficulty_id": 1, "explanation": "The box has 10 shapes: 2 circles and 8 stars. Fraction that are circles = 2/10. Answer: 2/10.", "hints": ["Count the total number of shapes.", "Fraction = number of circles / total shapes."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q4", "image_needed": true, "image_options": false, "image_file": "q4.png", "image_page": 4, "image_bbox": [0.30, 0.11, 0.55, 0.20], "image_loc": "boxed set of 2 circles and 8 stars, just below the question stem near top of page", "notes": "Stem reworded to remove the inline circle symbol; figure shows 2 circles + 8 stars (10 shapes). Key: option (1) 2/10." }, { "n": 5, "type_id": 1, "question": "In which of the following numbers does the digit 4 stand for 4 tenths?", "answer0": "15.45", "answer1": "24.13", "answer2": "37.84", "answer3": "46.21", "correct_answer": 0, "skill_id": 123, "difficulty_id": 2, "explanation": "4 tenths = 0.4, the first digit after the decimal point. In 15.45 the digit 4 is in the tenths place = 0.4. Answer: 15.45.", "hints": ["Tenths is the first place after the decimal point.", "Find the number whose first decimal digit is 4."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option (1) 15.45." }, { "n": 6, "type_id": 1, "question": "In the figure, which angle is smaller than a right angle?", "answer0": "angle w", "answer1": "angle x", "answer2": "angle y", "answer3": "angle z", "correct_answer": 0, "skill_id": 99, "difficulty_id": 2, "explanation": "In the quadrilateral, angle w (bottom-right) is the only acute angle - it is clearly less than 90 degrees, while x, y and z are at least a right angle. Answer: angle w.", "hints": ["A right angle is 90 degrees; an acute angle is smaller.", "Compare each marked angle against a square corner."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q6", "image_needed": true, "image_options": false, "image_file": "q6.png", "image_page": 5, "image_bbox": [0.33, 0.13, 0.73, 0.30], "image_loc": "irregular quadrilateral with angles x (top), y (top-left), z (bottom-left), w (bottom-right)", "notes": "Key: option (1) angle w." }, { "n": 7, "type_id": 1, "question": "Tristal bought 28 identical ovens and a kettle. Each oven cost 5 times as much as the kettle. The kettle cost $65. How much did she pay for all the ovens?", "answer0": "$9165", "answer1": "$9100", "answer2": "$3250", "answer3": "$1820", "correct_answer": 1, "skill_id": 118, "difficulty_id": 2, "explanation": "1 oven = 5 x $65 = $325. 28 ovens = $325 x 28 = $9100. Answer: $9100.", "hints": ["First find the cost of one oven.", "Multiply the cost of one oven by 28."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option (2) $9100." }, { "n": 8, "type_id": 1, "question": "On Tuesday, a factory produced 6 times as many notebooks as on Monday. A total of 4242 notebooks were produced on both days. How many notebooks were produced on Monday?", "answer0": "66", "answer1": "77", "answer2": "606", "answer3": "707", "correct_answer": 2, "skill_id": 118, "difficulty_id": 2, "explanation": "Monday = 1 unit, Tuesday = 6 units, total = 7 units = 4242. 1 unit = 4242 / 7 = 606. Monday produced 606. Answer: 606.", "hints": ["Let Monday be 1 unit; Tuesday is 6 units.", "Total is 7 units = 4242, so divide by 7."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q8", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option (3) 606." }, { "n": 9, "type_id": 1, "question": "Lucy can type 45 words in 1 minute. Lucy takes 10 seconds less than Paul to type the same number of words. How long does Paul take to type 45 words?", "answer0": "50 s", "answer1": "70 s", "answer2": "90 s", "answer3": "110 s", "correct_answer": 1, "skill_id": 133, "difficulty_id": 1, "explanation": "1 minute = 60 s (Lucy's time). Paul takes 10 s more than Lucy: 60 + 10 = 70 s. Answer: 70 s.", "hints": ["Convert 1 minute to seconds.", "Paul is slower, so add 10 seconds to Lucy's time."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option (2) 70 s." }, { "n": 10, "type_id": 1, "question": "The total mass of a box containing 4 identical books and 2 identical calculators was 2.94 kg. The total mass of the box containing 4 such books and 1 such calculator was 2.76 kg. What was the total mass of the box containing 4 such books?", "answer0": "2.48 kg", "answer1": "2.54 kg", "answer2": "2.58 kg", "answer3": "2.62 kg", "correct_answer": 2, "skill_id": 131, "difficulty_id": 3, "explanation": "The extra calculator accounts for 2.94 - 2.76 = 0.18 kg (1 calculator). Box + 4 books = 2.76 - 0.18 = 2.58 kg. Answer: 2.58 kg.", "hints": ["The difference between the two masses is 1 calculator.", "Subtract one calculator's mass from 2.76 kg."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q10", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option (3) 2.58 kg." }, { "n": 11, "type_id": 1, "question": "Peter sells three types of fruit juice. The bar graph shows the number of cups of each type of fruit juice sold by Peter on a particular day. The table shows the price of each cup of fruit juice. How much did Peter collect in total from the sales of fruit juices?", "answer0": "$34", "answer1": "$32", "answer2": "$24", "answer3": "$4", "correct_answer": 1, "skill_id": 104, "difficulty_id": 2, "explanation": "From the bar graph: Watermelon 10 cups, Honeydew 6 cups, Mango 8 cups. Watermelon: 10 x $1 = $10; Honeydew: 6 x $1 = $6; Mango: 8 x $2 = $16. Total = $10 + $6 + $16 = $32. Answer: $32.", "hints": ["Read each bar to get the number of cups.", "Multiply cups by price, then add all three."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q11", "image_needed": true, "image_options": false, "image_file": "q11.png", "image_page": 7, "image_bbox": [0.20, 0.20, 0.82, 0.40], "image_loc": "horizontal bar graph 'Number of cups of fruit juice sold' (Mango 8, Honeydew 6, Watermelon 10) in upper-middle of page", "notes": "Bar graph required for cup counts (price table is reproduced in stem). Watermelon=10, Honeydew=6, Mango=8. Key: option (2) $32." }, { "n": 12, "type_id": 1, "question": "The perimeter of a rectangular grass patch is 12 m. The breadth of the grass patch is 2 m. Find its length.", "answer0": "8 m", "answer1": "6 m", "answer2": "5 m", "answer3": "4 m", "correct_answer": 3, "skill_id": 136, "difficulty_id": 2, "explanation": "Perimeter = 2 x (length + breadth), so length + breadth = 12 / 2 = 6 m. Length = 6 - 2 = 4 m. Answer: 4 m.", "hints": ["Half the perimeter equals length + breadth.", "Subtract the breadth from that half."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "Figure is a plain labelled rectangle (length ?, breadth 2 m) that just restates the given numbers; not needed. Key: option (4) 4 m." }, { "n": 13, "type_id": 1, "question": "Aminah has 198 coins. She has 3 times as many coins as Bob. Charlie has 76 more coins than Bob. Charlie then gave Bob some of his coins such that they both have the same number of coins. How many more coins does Aminah have than Bob now?", "answer0": "66", "answer1": "94", "answer2": "104", "answer3": "160", "correct_answer": 1, "skill_id": 118, "difficulty_id": 3, "explanation": "Bob = 198 / 3 = 66. Charlie = 66 + 76 = 142. Charlie shares equally with Bob: (66 + 142) / 2 = 104 each, so Bob now has 104. Aminah - Bob = 198 - 104 = 94. Answer: 94.", "hints": ["Find Bob's coins from Aminah = 3 x Bob.", "After sharing, Bob and Charlie split their combined total equally."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q13", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option (2) 94." }, { "n": 14, "type_id": 1, "question": "The table shows the number of customers at a restaurant over 4 days. Part of the table was covered by a stain. Day 1 had 30 customers and Day 2 had 45 customers. The number of customers on Day 3 is equal to the total number of customers on Day 1 and Day 2. The total number of customers on all 4 days is 230 when rounded to the nearest ten. What is the greatest possible number of customers on Day 4?", "answer0": "75", "answer1": "80", "answer2": "84", "answer3": "89", "correct_answer": 2, "skill_id": 109, "difficulty_id": 3, "explanation": "Day 3 = 30 + 45 = 75. Days 1-3 = 30 + 45 + 75 = 150. For the 4-day total to round to 230, the total is 225 to 234, so Day 4 is 75 to 84. Greatest is 84. Answer: 84.", "hints": ["Day 3 equals Day 1 + Day 2.", "A total that rounds to 230 lies between 225 and 234; take the largest Day 4."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q14", "image_needed": false, "image_options": false, "image_file": null, "notes": "Day 1 = 30, Day 2 = 45 given in stem; the stain hides Day 3 and Day 4 which are derived. Key: option (3) 84." }, { "n": 15, "type_id": 1, "question": "Jiayi had $13. She bought 2 different items and paid more than $10 for them. The prices were: Calculator $7.80, Stapler $2.10, Comic Book $6.65, Plastic Folder $0.85, Notebook $5.45. Which were the 2 items she bought?", "answer0": "Plastic Folder and Comic Book", "answer1": "Plastic Folder and Stapler", "answer2": "Notebook and Calculator", "answer3": "Comic Book and Notebook", "correct_answer": 3, "skill_id": 129, "difficulty_id": 2, "explanation": "Try each pair: Folder+Comic = $7.50; Folder+Stapler = $2.95; Notebook+Calculator = $13.25 (over $13); Comic+Notebook = $6.65 + $5.45 = $12.10 (more than $10 and within $13). Answer: Comic Book and Notebook.", "hints": ["Add each pair of prices.", "The total must be more than $10 but not more than $13."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q15", "image_needed": false, "image_options": false, "image_file": null, "notes": "Price table reproduced in stem text; no figure needed. Key: option (4) Comic Book and Notebook." }, { "n": 16, "type_id": 2, "question": "Find the product of 3608 and 9.", "answer0": "32472", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 116, "difficulty_id": 1, "explanation": "3608 x 9 = 32 472. Answer: 32 472.", "hints": ["Multiply 3608 by 9 using column multiplication.", "9 x 8 = 72, carry the tens."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q16", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 32 472." }, { "n": 17, "type_id": 2, "question": "Square ABCD is made up of 9 unit squares. What fraction of square ABCD is shaded?", "answer0": "4/9", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 120, "difficulty_id": 1, "explanation": "The 3x3 grid has 9 unit squares; 4 of them are shaded (two in top row, one in middle, one in bottom). Fraction shaded = 4/9. Answer: 4/9.", "hints": ["Count the total small squares (9).", "Count the shaded squares and write as a fraction of 9."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q17", "image_needed": true, "image_options": false, "image_file": "q17.png", "image_page": 13, "image_bbox": [0.40, 0.46, 0.62, 0.62], "image_loc": "3x3 grid square ABCD with 4 black-shaded unit squares, centred below the question", "notes": "Key: 4/9 (4 of 9 unit squares shaded)." }, { "n": 18, "type_id": 2, "question": "How many one-fifths are there in 1 whole?", "answer0": "5", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 119, "difficulty_id": 1, "explanation": "1 whole = 5/5, which is 5 one-fifths. Answer: 5.", "hints": ["Write 1 as a fraction with denominator 5.", "1 = 5/5."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q18", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 5." }, { "n": 19, "type_id": 2, "question": "Express 3/9 in its simplest form.", "answer0": "1/3", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 119, "difficulty_id": 1, "explanation": "Divide numerator and denominator by 3: 3/9 = (3 / 3)/(9 / 3) = 1/3. Answer: 1/3.", "hints": ["Find the common factor of 3 and 9.", "Divide top and bottom by 3."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q19", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 1/3." }, { "n": 20, "type_id": 2, "question": "Express 84/100 as a decimal.", "answer0": "0.84", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 127, "difficulty_id": 1, "explanation": "84/100 = 0.84 (84 hundredths). Answer: 0.84.", "hints": ["Hundredths go two places after the decimal point.", "84 hundredths = 0.84."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q20", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 0.84." }, { "n": 21, "type_id": 2, "question": "Arrange the following numbers in order from the greatest to the smallest. 0.045 , 0.504 , 0.405", "answer0": "0.504", "answer1": "0.405", "answer2": "0.045", "answer3": null, "correct_answer": null, "skill_id": 124, "difficulty_id": 2, "explanation": "Compare tenths first: 0.504 and 0.405 have 5 and 4 tenths, 0.045 has 0 tenths. So 0.504 > 0.405 > 0.045. Greatest to smallest: 0.504, 0.405, 0.045.", "hints": ["Compare the tenths digit first.", "Then the hundredths if tenths are equal."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q21", "image_needed": false, "image_options": false, "image_file": null, "notes": "Ordering FIB, greatest to smallest: 0.504, 0.405, 0.045. Key matches." }, { "n": 22, "type_id": 2, "question": "Round 18.55 to the nearest whole number.", "answer0": "19", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 128, "difficulty_id": 1, "explanation": "The tenths digit is 5, so round up: 18.55 rounds to 19. Answer: 19.", "hints": ["Look at the digit in the tenths place.", "5 or more rounds up."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q22", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 19." }, { "n": 23, "type_id": 2, "question": "Find the value of 6.72 x 7.", "answer0": "47.04", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 130, "difficulty_id": 1, "explanation": "6.72 x 7 = 47.04. (672 x 7 = 4704, then place the decimal two places: 47.04.) Answer: 47.04.", "hints": ["Multiply as whole numbers: 672 x 7.", "Put back two decimal places."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q23", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 47.04." }, { "n": 24, "type_id": 1, "question": "In the figure, name the smallest angle.", "answer0": "angle a", "answer1": "angle b", "answer2": "angle c", "answer3": "angle d", "correct_answer": 1, "skill_id": 140, "difficulty_id": 2, "explanation": "At the point, the marked angle b is the smallest of the four angles a, b, c, d formed by the intersecting lines. Answer: angle b.", "hints": ["The smallest angle has the narrowest opening.", "Compare angles a, b, c and d at the meeting point."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q24", "image_needed": true, "image_options": false, "image_file": "q24.png", "image_page": 15, "image_bbox": [0.33, 0.30, 0.65, 0.52], "image_loc": "two lines crossing at a point with angles a (top), b (right), c (bottom), d (left) marked around the intersection", "notes": "Original is open-ended ('name the smallest angle'); converted to MCQ with the four labelled angles as options so it is gradeable. Key: angle b." }, { "n": 25, "type_id": 2, "question": "The area of a square tile is 49 cm². Find its length.", "answer0": "7", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 137, "difficulty_id": 2, "explanation": "Area of a square = length x length = 49. 7 x 7 = 49, so the length is 7 cm. Answer: 7 cm.", "hints": ["Area of a square = side x side.", "Find the number that multiplied by itself gives 49."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q25", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer in cm. Figure is a decorative shaded square restating 'length ?'; not required for solving. Key: 7." }, { "n": 26, "type_id": 0, "question": "Using a protractor and a ruler, draw angle ABC = 120 degrees. 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": "Construction task: place the protractor centre on B, measure 120 degrees from ray BA, mark the point and draw ray BC, then label angle ABC = 120 degrees.", "hints": ["Centre the protractor on B along BA.", "Measure 120 degrees and draw the second ray."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q26", "image_needed": false, "image_options": false, "image_file": null, "notes": "Drawing/construction task - no value answer; type_id 0 (skipped on insert)." }, { "n": 27, "type_id": 2, "question": "Ravi is at the zoo. He is facing south now. He then turns to face the elephant. What angle has he turned through in the anti-clockwise direction?", "answer0": "225", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 142, "difficulty_id": 3, "explanation": "The 8 animals sit at 45-degree spacings (compass shows N up). Facing south, turning anti-clockwise: each step is 45 degrees. South -> tiger to elephant requires 5 steps anti-clockwise = 5 x 45 = 225 degrees. Answer: 225 degrees.", "hints": ["Each animal is 45 degrees apart around Ravi.", "Count the 45-degree steps from south to the elephant going anti-clockwise."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q27", "image_needed": true, "image_options": false, "image_file": "q27.png", "image_page": 17, "image_bbox": [0.22, 0.18, 0.80, 0.46], "image_loc": "8-point arrangement of zoo animals around 'Ravi' in the centre, with a North arrow to the right", "notes": "Answer in degrees. Key: 225 (8-point compass turn)." }, { "n": 28, "type_id": 1, "question": "Study the square grid. In which direction is Point E from Point C?", "answer0": "North-east", "answer1": "North-west", "answer2": "South-east", "answer3": "South-west", "correct_answer": 1, "skill_id": 142, "difficulty_id": 2, "explanation": "On the grid, E lies above and to the left of C (North arrow points up). Up = North, left = West, so E is North-west of C. Answer: North-west.", "hints": ["Use the North arrow to fix up = North.", "E is higher and to the left of C."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q28", "image_needed": true, "image_options": false, "image_file": "q28.png", "image_page": 18, "image_bbox": [0.20, 0.15, 0.66, 0.42], "image_loc": "8x8 square grid with labelled points A,B,C,D,E,F and a North arrow to the right", "notes": "Original is open-ended direction question; converted to MCQ with 8-point compass options. Key: North-west." }, { "n": 29, "type_id": 2, "question": "ABCD is a rectangle and PQRC is a square. Find angle a + angle b.", "answer0": "69", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 143, "difficulty_id": 3, "explanation": "At C the rectangle corner gives 90 degrees: angle a = 90 - 64 = 26 degrees. The square corner gives 90 degrees: angle b = 90 - 47 = 43 degrees. a + b = 26 + 43 = 69 degrees. Answer: 69 degrees.", "hints": ["Each corner (rectangle and square) is a right angle of 90 degrees.", "Subtract the given angle from 90 for each, then add."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q29", "image_needed": true, "image_options": false, "image_file": "q29.png", "image_page": 19, "image_bbox": [0.28, 0.14, 0.72, 0.30], "image_loc": "rectangle ABCD joined to square PQRC, with angles a, b and given 64 and 47 degrees at corner C", "notes": "Answer in degrees. Key: 69." }, { "n": 30, "type_id": 0, "question": "EF and FG form two sides of a rectangle EFGH on the square grid. Complete the drawing of rectangle EFGH.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 143, "difficulty_id": 2, "explanation": "Construction task: from G draw a segment parallel and equal to FE, and from E draw a segment parallel and equal to FG; their intersection is H, completing rectangle EFGH.", "hints": ["Opposite sides of a rectangle are equal and parallel.", "Translate EF to G to locate H."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q30", "image_needed": false, "image_options": false, "image_file": null, "notes": "Drawing/construction task - no value answer; type_id 0 (skipped on insert)." }, { "n": 31, "type_id": 0, "question": "Complete the figure on the square grid so that it is symmetric about the line of symmetry XY.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 145, "difficulty_id": 2, "explanation": "Construction task: reflect each vertex of the given half across the diagonal line XY and join the reflected points to complete the symmetric figure.", "hints": ["Each point and its mirror image are the same distance from XY.", "Reflect every corner across the dashed line."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q31", "image_needed": false, "image_options": false, "image_file": null, "notes": "Drawing/symmetry-completion task - no value answer; type_id 0 (skipped on insert)." }, { "n": 32, "type_id": 2, "question": "The line graph shows the number of Primary 1 students enrolled in Percy Primary School from Year 2016 to Year 2020. (a) In which two years were the number of Primary 1 students enrolled the same? (b) How many more Primary 1 students were enrolled in Year 2019 than Year 2018?", "answer0": "2016", "answer1": "2020", "answer2": "25", "answer3": null, "correct_answer": null, "skill_id": 147, "difficulty_id": 2, "explanation": "(a) The graph shows 245 students in both 2016 and 2020, so those two years are equal. (b) Year 2019 = 300, Year 2018 = 275; 300 - 275 = 25 more students. Answers: (a) 2016 and 2020; (b) 25.", "hints": ["Find the two points at the same height for part (a).", "Subtract the 2018 value from the 2019 value for part (b)."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q32", "image_needed": true, "image_options": false, "image_file": "q32.png", "image_page": 21, "image_bbox": [0.26, 0.17, 0.80, 0.42], "image_loc": "line graph 'Primary 1 students enrolled in Percy Primary School', years 2016-2020 on x-axis", "notes": "Two-part graph FIB: answer0/1 = the two equal years (2016, 2020), answer2 = difference 25. Key: (a) 2016 & 2020, (b) 25." }, { "n": 33, "type_id": 2, "question": "Sam had a new book to read. He read 3/5 of the new book in the morning and 3/10 of it in the evening. What fraction of the book was left unread?", "answer0": "1/10", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 122, "difficulty_id": 2, "explanation": "3/5 = 6/10. Read = 6/10 + 3/10 = 9/10. Unread = 1 - 9/10 = 1/10. Answer: 1/10.", "hints": ["Convert 3/5 to tenths to add the fractions.", "Subtract the total read from 1 whole."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q33", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 1/10." }, { "n": 34, "type_id": 2, "question": "A farmer planted some trees in a straight row. The trees were planted at an equal distance apart from one another. The distance between the 2nd tree and the 5th tree was 2340 m. What was the distance between the 1st tree and the 10th tree?", "answer0": "7020", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 3, "explanation": "2nd to 5th tree = 3 gaps = 2340 m, so 1 gap = 780 m. 1st to 10th tree = 9 gaps = 9 x 780 = 3 x 2340 = 7020 m. Answer: 7020 m.", "hints": ["Count the gaps between trees, not the trees.", "2nd to 5th = 3 gaps; 1st to 10th = 9 gaps."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q34", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer in m. Key: 7020." }, { "n": 35, "type_id": 2, "question": "The figure is made up of 5 identical squares. The perimeter of the figure is 36 cm. Find the area of the figure.", "answer0": "45", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 138, "difficulty_id": 3, "explanation": "The outline of the figure is made of 12 unit-square sides, so each side = 36 / 12 = 3 cm. Each square area = 3 x 3 = 9 cm². 5 squares = 5 x 9 = 45 cm². Answer: 45 cm².", "hints": ["Count how many square-sides form the perimeter.", "Find one side, square it, then multiply by 5."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q35", "image_needed": true, "image_options": false, "image_file": "q35.png", "image_page": 23, "image_bbox": [0.24, 0.16, 0.47, 0.25], "image_loc": "cross/zig-zag figure made of 5 identical squares, upper-left below the question", "notes": "Answer in cm². Perimeter of the 5-square figure = 12 unit-sides. Key: 45." }, { "n": 36, "type_id": 2, "question": "Container A had 13.5 l of tea. Container B had 4 times as much tea as container A. All the tea in container B was poured into identical bottles. Each bottle then has 3 l of tea. How many such bottles were filled with tea from container B?", "answer0": "18", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 131, "difficulty_id": 2, "explanation": "Container B = 13.5 x 4 = 54 l. Bottles = 54 / 3 = 18. Answer: 18 bottles.", "hints": ["First find the volume in container B.", "Divide by 3 l per bottle."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q36", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 18 bottles." }, { "n": 37, "type_id": 2, "question": "Benny had his dinner from 17 15 to 19 05. After his dinner, he shopped for 2 h 55 min. How much time did he spend on having his dinner and shopping altogether?", "answer0": "4 h 45 min", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 135, "difficulty_id": 2, "explanation": "Dinner from 17 15 to 19 05 = 1 h 50 min. Total = 1 h 50 min + 2 h 55 min = 3 h 105 min = 4 h 45 min. Answer: 4 h 45 min.", "hints": ["Find the dinner duration first (17 15 to 19 05).", "Add the shopping time and convert 60 min to 1 h."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q37", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 4 h 45 min." }, { "n": 38, "type_id": 2, "question": "The figure is made up of a rectangle and a square. The rectangle measures 27 m by 13 m. Find the area of the unshaded part.", "answer0": "270", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 138, "difficulty_id": 3, "explanation": "Rectangle area = 27 x 13 = 351 m². Square side = 27 - 9 - 9 = 9 m, so square area = 9 x 9 = 81 m². Unshaded = 351 - 81 = 270 m². Answer: 270 m².", "hints": ["Find the rectangle's area.", "The square side is 27 minus the two 9 m gaps; subtract its area."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q38", "image_needed": true, "image_options": false, "image_file": "q38.png", "image_page": 25, "image_bbox": [0.33, 0.18, 0.72, 0.36], "image_loc": "rectangle 27 m by 13 m with a shaded square in the centre, 9 m gaps on each side", "notes": "Answer in m². Key: 270." }, { "n": 39, "type_id": 2, "question": "The line graph shows the cost related to the mass of rice sold in a shop. (a) Mr Sim bought 1.5 kg of rice. Mr Wee bought 2 kg of rice. How much more did Mr Wee have to pay than Mr Sim? (b) Mrs Tan spent $20 on rice. Mrs Goh spent $8 less than Mrs Tan on rice. Find the difference between the mass of rice bought by Mrs Tan and Mrs Goh.", "answer0": "$2", "answer1": "2 kg", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 148, "difficulty_id": 3, "explanation": "From the graph, cost is $4 per kg (1 kg=$4, 2 kg=$8...). (a) Mr Sim 1.5 kg = $6, Mr Wee 2 kg = $8; difference = $8 - $6 = $2. (b) Mrs Tan $20 = 5 kg; Mrs Goh $20 - $8 = $12 = 3 kg; difference = 5 - 3 = 2 kg. Answers: (a) $2; (b) 2 kg.", "hints": ["Read the cost for each mass off the line graph.", "For (b) convert each amount of money back to a mass, then subtract."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q39", "image_needed": true, "image_options": false, "image_file": "q39.png", "image_page": 26, "image_bbox": [0.26, 0.14, 0.78, 0.33], "image_loc": "line graph 'Mass of rice sold', cost ($) on y-axis vs mass of rice (kg) on x-axis", "notes": "Two-part FIB: answer0 = $2, answer1 = 2 kg. Key: (a) $2, (b) 2 kg." }, { "n": 40, "type_id": 2, "question": "Michelle and Bridget went shopping with the same amount of money. After Michelle spent $8.80 and Bridget spent $50, Michelle had 5 times as much money left as Bridget. (a) How much money did Michelle have in the end? (b) How much money did Bridget have at first?", "answer0": "$51.50", "answer1": "$60.30", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 3, "explanation": "They started equal. The difference in what they spent is $50 - $8.80 = $41.20, which equals the difference in money left = 4 units (Michelle 5 units, Bridget 1 unit). 4 units = $41.20, 1 unit = $10.30. (a) Michelle's end = 5 units = $51.50. (b) Bridget at first = money left + spent = $10.30 + $50 = $60.30. Answers: (a) $51.50; (b) $60.30.", "hints": ["Equal start means the spending difference equals the leftover difference.", "Michelle's leftover is 5 units, Bridget's is 1 unit."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q40", "image_needed": false, "image_options": false, "image_file": null, "notes": "Two-part FIB: answer0 = $51.50 (Michelle end), answer1 = $60.30 (Bridget at first). Key matches." }, { "n": 41, "type_id": 2, "question": "May and Nina have 274 beads altogether. May and Oliver have 618 beads altogether. The number of beads Oliver has is nine times that of Nina. How many beads does May have?", "answer0": "231", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 3, "explanation": "Oliver - Nina = (May+Oliver) - (May+Nina) = 618 - 274 = 344. Oliver = 9 x Nina, so Oliver - Nina = 8 units = 344, 1 unit (Nina) = 43. May = 274 - Nina = 274 - 43 = 231. Answer: 231 beads.", "hints": ["Subtract the two totals to remove May and get Oliver - Nina.", "Oliver is 9 times Nina, so the difference is 8 units."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q41", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 231 beads." }, { "n": 42, "type_id": 2, "question": "Rope A is 5/6 m shorter than Rope B. Rope C is 1/6 m longer than Rope A. Rope C is 2/3 m long. (a) What is the length of Rope A? (b) What is the length of Rope B? Give your answer in the simplest form.", "answer0": "1/2", "answer1": "1 1/3", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 122, "difficulty_id": 3, "explanation": "(a) Rope A = Rope C - 1/6 = 2/3 - 1/6 = 4/6 - 1/6 = 3/6 = 1/2 m. (b) Rope B = Rope A + 5/6 = 3/6 + 5/6 = 8/6 = 1 2/6 = 1 1/3 m. Answers: (a) 1/2 m; (b) 1 1/3 m.", "hints": ["Rope C is longer than A by 1/6, so A = C - 1/6.", "Rope B is longer than A by 5/6; add and simplify."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q42", "image_needed": false, "image_options": false, "image_file": null, "notes": "Two-part FIB: answer0 = 1/2 (Rope A), answer1 = 1 1/3 (Rope B). Key: (a) 1/2 m, (b) 1 1/3 m." }, { "n": 43, "type_id": 2, "question": "At a bakery, the price of a cupcake was $2 and the price of a tart was $5. Ms Lim paid $38 to buy a total of 13 cupcakes and tarts. How many more cupcakes than tarts did Ms Lim buy?", "answer0": "5", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 3, "explanation": "If all 13 were cupcakes: 13 x $2 = $26. Extra = $38 - $26 = $12. Each swap to a tart adds $5 - $2 = $3, so tarts = $12 / $3 = 4. Cupcakes = 13 - 4 = 9. More cupcakes than tarts = 9 - 4 = 5. Answer: 5.", "hints": ["Assume all 13 are cupcakes and find the shortfall in cost.", "Each tart adds $3; divide to find the number of tarts."], "source": "Nanyang 2022 P4 Semestral Assessment 2 Q43", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 5 (9 cupcakes, 4 tarts)." } ] }