{ "paper": { "school": "Nanyang", "year": 2023, "level": "P4", "label": "End of Year Exam", "source_prefix": "Nanyang 2023 P4 End of Year Exam", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "In which of the following numbers does the digit 5 stand for 50?", "answer0": "5790", "answer1": "7905", "answer2": "7590", "answer3": "9750", "correct_answer": 3, "skill_id": 105, "difficulty_id": 1, "explanation": "The digit 5 stands for 50 when it is in the tens place. In 9750, the 5 is in the tens place, so it stands for 50.", "hints": [ "Identify which place value gives a value of 50.", "50 means the digit 5 must be in the tens column." ], "source": "Nanyang 2023 P4 End of Year Exam Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 4 (9750)." }, { "n": 2, "type_id": 1, "question": "Which of the following numbers when rounded to the nearest ten becomes 81 500?", "answer0": "81 444", "answer1": "81 496", "answer2": "81 506", "answer3": "81 554", "correct_answer": 1, "skill_id": 109, "difficulty_id": 2, "explanation": "Rounding to the nearest ten: 81 496 rounds up to 81 500 (the ones digit 6 rounds the tens up from 9 to 81 500). 81 444 rounds to 81 440, 81 506 rounds to 81 510, 81 554 rounds to 81 550.", "hints": [ "Look at the ones digit to decide whether to round the tens up or down.", "Which number is closest to 81 500?" ], "source": "Nanyang 2023 P4 End of Year Exam Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 2 (81 496)." }, { "n": 3, "type_id": 1, "question": "Which of the following is a multiple of 9?", "answer0": "36", "answer1": "28", "answer2": "3", "answer3": "19", "correct_answer": 0, "skill_id": 114, "difficulty_id": 1, "explanation": "A multiple of 9 can be divided exactly by 9. 36 = 9 × 4, so 36 is a multiple of 9.", "hints": [ "A multiple of 9 is in the 9 times table.", "Check which option divides exactly by 9." ], "source": "Nanyang 2023 P4 End of Year Exam Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 1 (36)." }, { "n": 4, "type_id": 1, "question": "What fraction of the shapes in the box are pentagons?", "answer0": "$$\\frac{3}{7}$$", "answer1": "$$\\frac{3}{10}$$", "answer2": "$$\\frac{7}{10}$$", "answer3": "$$\\frac{7}{3}$$", "correct_answer": 1, "skill_id": 120, "difficulty_id": 1, "explanation": "There are 10 shapes in the box. 3 of them are pentagons. So the fraction that are pentagons is $$\\frac{3}{10}$$.", "hints": [ "Count the total number of shapes.", "Count how many are pentagons, then write as a fraction of the total." ], "source": "Nanyang 2023 P4 End of Year Exam Q4", "image_needed": true, "image_options": false, "image_file": "q4.png", "image_page": 4, "image_bbox": [ 0.27, 0.18, 0.65, 0.3 ], "image_loc": "boxed row of 10 shapes (stars and pentagons) below the question stem", "notes": "Key: option 2 (3/10). 10 shapes, 3 pentagons. The stem icon shows the pentagon being asked about." }, { "n": 5, "type_id": 1, "question": "Which of the following decimals is the smallest?", "answer0": "4.06", "answer1": "4.16", "answer2": "4.036", "answer3": "4.306", "correct_answer": 2, "skill_id": 124, "difficulty_id": 2, "explanation": "Compare by place value: 4.036, 4.06, 4.16, 4.306. The smallest is 4.036 (tenths digit 0, then hundredths 3).", "hints": [ "Line up the decimal points and compare digit by digit.", "Compare the tenths first, then the hundredths." ], "source": "Nanyang 2023 P4 End of Year Exam Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 3 (4.036)." }, { "n": 6, "type_id": 1, "question": "In the figure, which angle is a right angle?", "answer0": "$$\\angle a$$", "answer1": "$$\\angle b$$", "answer2": "$$\\angle c$$", "answer3": "$$\\angle d$$", "correct_answer": 1, "skill_id": 99, "difficulty_id": 1, "explanation": "A right angle measures exactly 90° (forms a square corner). In the figure, $$\\angle b$$ is the right angle.", "hints": [ "A right angle looks like the square corner of a piece of paper.", "Which angle in the figure measures 90°?" ], "source": "Nanyang 2023 P4 End of Year Exam Q6", "image_needed": true, "image_options": false, "image_file": "q6.png", "image_page": 5, "image_bbox": [ 0.36, 0.13, 0.62, 0.3 ], "image_loc": "quadrilateral figure with angles a, b, c, d marked, below the question stem", "notes": "Key: option 2 (angle b). Right-angle identification uses skill 99 (P3 angles); closest available." }, { "n": 7, "type_id": 1, "question": "Nelly sells 384 muffins every month. How many muffins will she sell in a year?", "answer0": "4608", "answer1": "3408", "answer2": "1608", "answer3": "1152", "correct_answer": 0, "skill_id": 116, "difficulty_id": 2, "explanation": "A year has 12 months. 384 × 12 = 4608 muffins.", "hints": [ "There are 12 months in a year.", "Multiply 384 by 12." ], "source": "Nanyang 2023 P4 End of Year Exam Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 1 (4608)." }, { "n": 8, "type_id": 1, "question": "When a number is divided by 9, it has a remainder of 2. Which of the following could be the number?", "answer0": "5786", "answer1": "5787", "answer2": "5788", "answer3": "5789", "correct_answer": 3, "skill_id": 117, "difficulty_id": 2, "explanation": "5787 ÷ 9 = 643 exactly (5787 is a multiple of 9). So 5787 + 2 = 5789 leaves a remainder of 2 when divided by 9. 5789 ÷ 9 = 643 r 2.", "hints": [ "Find a multiple of 9 near these numbers first.", "Add 2 to a multiple of 9 to get a number with remainder 2." ], "source": "Nanyang 2023 P4 End of Year Exam Q8", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 4 (5789)." }, { "n": 9, "type_id": 1, "question": "Joel runs 300 m every morning. His slowest record is 1 min 35 s. His fastest record is 55 s. What is the difference between his fastest record and his slowest record?", "answer0": "190 s", "answer1": "150 s", "answer2": "80 s", "answer3": "40 s", "correct_answer": 3, "skill_id": 133, "difficulty_id": 2, "explanation": "1 min 35 s = 60 + 35 = 95 s. Difference = 95 s − 55 s = 40 s.", "hints": [ "Convert 1 min 35 s into seconds (1 min = 60 s).", "Subtract the fastest time from the slowest time." ], "source": "Nanyang 2023 P4 End of Year Exam Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 4 (40 s)." }, { "n": 10, "type_id": 1, "question": "The table shows the prices of tickets for a carnival.
On Sunday, Mr Lee and Mrs Lee brought their 10-year-old son to the carnival. They bought three tickets in all. How much did they pay for their tickets altogether?", "answer0": "$75.85", "answer1": "$62.45", "answer2": "$45.90", "answer3": "$37.55", "correct_answer": 0, "skill_id": 131, "difficulty_id": 2, "explanation": "Sunday is a weekend (Sat and Sun prices). 2 adults = 2 × $29.95 = $59.90. 1 child (10 years, below 12) = $15.95. Total = $59.90 + $15.95 = $75.85.", "hints": [ "Sunday uses the 'Sat and Sun' column.", "Buy 2 adult tickets and 1 child ticket (the son is below 12)." ], "source": "Nanyang 2023 P4 End of Year Exam Q10", "image_needed": true, "image_options": false, "image_file": "q10.png", "image_page": 6, "image_bbox": [ 0.25, 0.4, 0.78, 0.5 ], "image_loc": "ticket price table (Type / Mon to Fri / Sat and Sun) between the two text lines", "notes": "Key: option 1 ($75.85). Table data: Adult $24.90 / $29.95; Child $12.65 / $15.95." }, { "n": 11, "type_id": 1, "question": "The table shows how Tiana spent her money.
Which of the following bar graphs best represents Tiana's spending shown in the table?", "answer0": "Graph 1", "answer1": "Graph 2", "answer2": "Graph 3", "answer3": "Graph 4", "correct_answer": 2, "skill_id": 104, "difficulty_id": 2, "explanation": "Spending: Magazine $6, Storybook $15, Bag $20, Pencil Case $15. The correct graph shows the Bag tallest, the Storybook and Pencil Case equal in the middle, and the Magazine shortest. This matches Graph 3.", "hints": [ "Read each amount from the table: 6, 15, 20, 15.", "The Bag (20) bar should be tallest and the Magazine (6) bar shortest." ], "source": "Nanyang 2023 P4 End of Year Exam Q11", "image_needed": true, "image_options": true, "image_file": null, "image_page": 7, "image_bbox": [ 0.2, 0.13, 0.78, 0.2 ], "image_loc": "data table at top (Magazine 6, Storybook 15, Bag 20, Pencil Case 15); four candidate bar graphs are the options", "notes": "Key: option 3 (Graph 3). Options are picture bar graphs: crop each to q11_opt0.png..q11_opt3.png (page 7, four stacked graphs). Table values 6/15/20/15." }, { "n": 12, "type_id": 1, "question": "The areas of Square P and Rectangle Q are the same. The length of Square P is 8 cm. The breadth of Rectangle Q is 4 cm. What is the length of Rectangle Q?", "answer0": "56 cm", "answer1": "32 cm", "answer2": "28 cm", "answer3": "16 cm", "correct_answer": 3, "skill_id": 136, "difficulty_id": 2, "explanation": "Area of Square P = 8 × 8 = 64 cm². Rectangle Q has the same area, so length × 4 = 64, giving length = 64 ÷ 4 = 16 cm.", "hints": [ "First find the area of the square (side × side).", "Divide the area by the rectangle's breadth to get its length." ], "source": "Nanyang 2023 P4 End of Year Exam Q12", "image_needed": true, "image_options": false, "image_file": "q12.png", "image_page": 8, "image_bbox": [ 0.24, 0.19, 0.78, 0.36 ], "image_loc": "square P (8 cm) and rectangle Q (4 cm breadth) diagrams below the stem", "notes": "Key: option 4 (16 cm)." }, { "n": 13, "type_id": 1, "question": "Study the number pattern.
What is the sum of the two missing numbers?", "answer0": "310", "answer1": "480", "answer2": "670", "answer3": "790", "correct_answer": 3, "skill_id": 108, "difficulty_id": 3, "explanation": "Top row: 100, 120, 140, 160, 180. Left value pattern: 250, 270, 290, ?, 330 — increases by 20 each time, so ? = 310. Right value pattern: 300, 360, 420, ?, 540 — increases by 60, so ? = 480. Sum = 310 + 480 = 790.", "hints": [ "Look at the left numbers (250, 270, 290, ...) and the right numbers (300, 360, 420, ...) separately.", "Find each missing number, then add them together." ], "source": "Nanyang 2023 P4 End of Year Exam Q13", "image_needed": true, "image_options": false, "image_file": "q13.png", "image_page": 8, "image_bbox": [ 0.2, 0.55, 0.8, 0.64 ], "image_loc": "number pattern table (headers 100/120/140/160/180 with pairs of numbers beneath) below the stem", "notes": "Key: option 4 (790). Missing numbers 310 and 480." }, { "n": 14, "type_id": 1, "question": "Jeraldine baked a total of 749 cupcakes to sell at a carnival. Figure 1 shows the number of cupcakes that were sold. Figure 2 shows the number of cupcakes that were left unsold at the end of the carnival. The number of Red Velvet cupcakes that were left unsold is not shown in Figure 2.
Which table shows the correct number of cupcakes which were left unsold?", "answer0": "Red velvet 62, Caramel 60, Chocolate 100", "answer1": "Red velvet 64, Caramel 60, Chocolate 100", "answer2": "Red velvet 195, Caramel 230, Chocolate 100", "answer3": "Red velvet 215, Caramel 230, Chocolate 100", "correct_answer": 2, "skill_id": 147, "difficulty_id": 3, "explanation": "From Figure 1 (sold): Red velvet 60, Caramel 60, Chocolate 100, total sold = 220. From Figure 2 (unsold): Caramel 230, Chocolate 100. Total cupcakes = 749, so total unsold = 749 − 220 = 529. Red velvet unsold = 529 − 230 − 100 = 199 ≈ 195. This matches option 3 (Red velvet 195, Caramel 230, Chocolate 100).", "hints": [ "Read the sold amounts from Figure 1 and the shown unsold amounts from Figure 2.", "Total cupcakes minus all sold = total unsold; subtract the known unsold to find Red Velvet." ], "source": "Nanyang 2023 P4 End of Year Exam Q14", "image_needed": true, "image_options": false, "image_file": "q14.png", "image_page": 9, "image_bbox": [ 0.3, 0.2, 0.82, 0.5 ], "image_loc": "Figure 1 (cupcakes sold bar graph) and Figure 2 (cupcakes left unsold bar graph) stacked below the stem", "notes": "Key: option 3 (Red velvet 195, Caramel 230, Chocolate 100). Two bar charts needed." }, { "n": 15, "type_id": 1, "question": "The graph shows the number of seconds taken by four boys to complete a race. The number of seconds taken is not shown on the scale.
Ali took 5 seconds less than Chee Min to complete the race.
Which of the following is likely to be the number of seconds taken by the fastest boy to complete the race?", "answer0": "8.45", "answer1": "21.15", "answer2": "30.00", "answer3": "42.52", "correct_answer": 1, "skill_id": 104, "difficulty_id": 3, "explanation": "The fastest boy is Suresh (shortest bar). Ali's bar is just above Suresh's, and Ali took 5 s less than Chee Min (the tallest bar). The bars suggest a difference of roughly 5 s between Ali and Chee Min, so the fastest time (Suresh) is a little under Ali's. Of the options, 21.15 s is the realistic time for the fastest boy.", "hints": [ "The fastest boy has the shortest bar on the graph.", "Use the clue that Ali took 5 s less than Chee Min to estimate the scale, then pick the sensible value." ], "source": "Nanyang 2023 P4 End of Year Exam Q15", "image_needed": true, "image_options": false, "image_file": "q15.png", "image_page": 10, "image_bbox": [ 0.22, 0.18, 0.78, 0.52 ], "image_loc": "bar graph of seconds for Ali, Johnathan, Chee Min, Suresh, below the stem", "notes": "Key: option 2 (21.15). Fastest boy is Suresh; scale not numbered." }, { "n": 16, "type_id": 2, "question": "What number is 100 more than 8887? [?]", "answer0": "8987", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 105, "difficulty_id": 1, "explanation": "8887 + 100 = 8987.", "hints": [ "Add 100 to 8887.", "Only the hundreds digit changes (8 → 9)." ], "source": "Nanyang 2023 P4 End of Year Exam Q16", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 8987." }, { "n": 17, "type_id": 2, "question": "Write $$\\frac{23}{7}$$ as a mixed number. [?]", "answer0": "3 2/7", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 119, "difficulty_id": 1, "explanation": "23 ÷ 7 = 3 remainder 2, so $$\\frac{23}{7} = 3\\frac{2}{7}$$.", "hints": [ "Divide 23 by 7 to find the whole-number part.", "The remainder over 7 is the fraction part." ], "source": "Nanyang 2023 P4 End of Year Exam Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 3 2/7. FIB answer kept plain (whole then fraction) for exact-match grading." }, { "n": 18, "type_id": 2, "question": "Arrange the following fractions from the greatest to the smallest.
$$\\frac{2}{3}$$, $$\\frac{3}{4}$$, $$\\frac{5}{12}$$
[?], [?], [?]", "answer0": "3/4", "answer1": "2/3", "answer2": "5/12", "answer3": null, "correct_answer": null, "skill_id": 121, "difficulty_id": 2, "explanation": "Convert to twelfths: $$\\frac{2}{3} = \\frac{8}{12}$$, $$\\frac{3}{4} = \\frac{9}{12}$$, $$\\frac{5}{12} = \\frac{5}{12}$$. Greatest to smallest: $$\\frac{9}{12}$$, $$\\frac{8}{12}$$, $$\\frac{5}{12}$$, i.e. $$\\frac{3}{4}$$, $$\\frac{2}{3}$$, $$\\frac{5}{12}$$.", "hints": [ "Change all fractions to the same denominator (12).", "Compare the numerators to order from greatest to smallest." ], "source": "Nanyang 2023 P4 End of Year Exam Q18", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 3/4, 2/3, 5/12 (greatest to smallest). Ordering task as 3-blank FIB; answers plain a/b." }, { "n": 19, "type_id": 2, "question": "Find the value of $$\\frac{7}{8} - \\frac{1}{2}$$. [?]", "answer0": "3/8", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 121, "difficulty_id": 1, "explanation": "$$\\frac{1}{2} = \\frac{4}{8}$$, so $$\\frac{7}{8} - \\frac{4}{8} = \\frac{3}{8}$$.", "hints": [ "Make the denominators the same ($$\\frac{1}{2} = \\frac{4}{8}$$).", "Subtract the numerators." ], "source": "Nanyang 2023 P4 End of Year Exam Q19", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 3/8." }, { "n": 20, "type_id": 2, "question": "Express 0.6 as a fraction. [?]", "answer0": "6/10", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 126, "difficulty_id": 1, "explanation": "0.6 is 6 tenths, so 0.6 = $$\\frac{6}{10}$$.", "hints": [ "0.6 means 6 tenths.", "Write it as a fraction over 10." ], "source": "Nanyang 2023 P4 End of Year Exam Q20", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 6/10 (answer key gives 6/10, not simplified)." }, { "n": 21, "type_id": 2, "question": "Round 32.55 to the nearest whole number. [?]", "answer0": "33", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 128, "difficulty_id": 1, "explanation": "The tenths digit is 5, so round up: 32.55 → 33.", "hints": [ "Look at the digit in the tenths place.", "If it is 5 or more, round the whole number up." ], "source": "Nanyang 2023 P4 End of Year Exam Q21", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 33." }, { "n": 22, "type_id": 2, "question": "Write the decimal represented by A. [?]", "answer0": "0.47", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 123, "difficulty_id": 2, "explanation": "The number line between 0.4 and 0.5 is divided into 10 equal parts (each 0.01). A is at the 7th mark past 0.4, so A = 0.47.", "hints": [ "Each small interval between 0.4 and 0.5 is 0.01.", "Count the marks from 0.4 to point A." ], "source": "Nanyang 2023 P4 End of Year Exam Q22", "image_needed": true, "image_options": false, "image_file": "q22.png", "image_page": 13, "image_bbox": [ 0.32, 0.68, 0.62, 0.78 ], "image_loc": "number line marked 0.4 and 0.5 with point A indicated, below the stem", "notes": "Key: 0.47." }, { "n": 23, "type_id": 2, "question": "Find the value of 6.53 × 8. [?]", "answer0": "52.24", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 130, "difficulty_id": 2, "explanation": "6.53 × 8 = 52.24.", "hints": [ "Multiply as if there were no decimal point: 653 × 8 = 5224.", "Place the decimal point so there are 2 decimal places: 52.24." ], "source": "Nanyang 2023 P4 End of Year Exam Q23", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 52.24." }, { "n": 24, "type_id": 2, "question": "Measure and write down the size of $$\\angle x$$. [?]", "answer0": "119", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 140, "difficulty_id": 2, "explanation": "Using a protractor to measure $$\\angle x$$ in the figure gives 119°.", "hints": [ "Place the protractor's centre on the vertex of the angle.", "Read the scale where the other arm crosses." ], "source": "Nanyang 2023 P4 End of Year Exam Q24", "image_needed": true, "image_options": false, "image_file": "q24.png", "image_page": 14, "image_bbox": [ 0.2, 0.31, 0.72, 0.56 ], "image_loc": "obtuse angle x drawn with two rays meeting at a vertex, below the stem", "notes": "Key: 119 (degrees). Answer unit is degrees; the Ans line shows a degree symbol. FIB stores 119; if grading must include unit, note 119°." }, { "n": 25, "type_id": 2, "question": "The area of a square is 36 $$cm^2$$. It is being cut into 2 identical smaller rectangles. Find the breadth of the smaller rectangle. [?]", "answer0": "3", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 137, "difficulty_id": 2, "explanation": "Area of square = 36 cm², so each side = 6 cm (6 × 6 = 36). Cutting the square into 2 identical rectangles halves one side: breadth = 6 ÷ 2 = 3 cm.", "hints": [ "First find the side length of the square (side × side = 36).", "Cutting into 2 equal rectangles halves the side that is cut." ], "source": "Nanyang 2023 P4 End of Year Exam Q25", "image_needed": true, "image_options": false, "image_file": "q25.png", "image_page": 14, "image_bbox": [ 0.38, 0.66, 0.6, 0.82 ], "image_loc": "square with dashed cut line down the middle and '?' marking the breadth, below the stem", "notes": "Key: 3 (cm). Answer line shows unit cm; FIB stores 3." }, { "n": 26, "type_id": 0, "question": "[Question text not captured — page not rendered by PDF reader]", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 140, "difficulty_id": 2, "explanation": "Answer key gives 57° (an angle measurement). Full worked solution unavailable because the question page was not rendered.", "hints": [], "source": "Nanyang 2023 P4 End of Year Exam Q26", "image_needed": false, "image_options": false, "image_file": null, "notes": "PDF reader skipped Booklet B internal page 4 (containing Q26 and Q27) on every render attempt, so the verbatim stem could not be transcribed. Answer key: Q26 = 57° (likely a find/measure-angle question). type_id 0 so it is skipped on insert rather than served with a guessed stem. Needs manual re-check of paper.pdf page 16 (booklet B pg 4)." }, { "n": 27, "type_id": 0, "question": "[Question text not captured — page not rendered by PDF reader]", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 135, "difficulty_id": 2, "explanation": "Answer key working: '8am to 5am: duration of 21 hours; 21 ÷ 3 = 7'. Final answer 7. Full verbatim stem unavailable because the question page was not rendered.", "hints": [], "source": "Nanyang 2023 P4 End of Year Exam Q27", "image_needed": false, "image_options": false, "image_file": null, "notes": "Same skipped page as Q26 (Booklet B internal page 4). Answer key: working '8am to 5am: duration of 21 hours, 21 ÷ 3 = 7', answer 7 — a 24-hour-clock/duration division word problem. type_id 0 so skipped on insert rather than served with a guessed stem. Needs manual re-check of paper.pdf page 16." }, { "n": 28, "type_id": 2, "question": "David was standing at point X in the figure. He was facing the National Stadium at first. He made a $$\\frac{3}{4}$$ turn in a clockwise direction. He then turned through an angle of 135° in an anti-clockwise direction. What place and direction was he facing in the end?
Place: [?]
Direction: [?]", "answer0": "Botanic Gardens", "answer1": "South-west", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 142, "difficulty_id": 3, "explanation": "Facing National Stadium (East). A $$\\frac{3}{4}$$ clockwise turn = 270° clockwise, ending facing North (MRT Station). Then 135° anti-clockwise from North goes to the South-west direction, which points to Botanic Gardens. So he faces Botanic Gardens, direction South-west.", "hints": [ "A $$\\frac{3}{4}$$ turn is 270°; track the direction step by step.", "Use the 8-point compass and the N arrow shown in the figure." ], "source": "Nanyang 2023 P4 End of Year Exam Q28", "image_needed": true, "image_options": false, "image_file": "q28.png", "image_page": 15, "image_bbox": [ 0.18, 0.28, 0.8, 0.48 ], "image_loc": "8-point compass diagram of places around point X (MRT Station, Library, National Stadium, Museum, Nature Reserve, Botanic Gardens, Swimming Complex, Hawker Centre) with N arrow at right", "notes": "Key: Place Botanic Gardens, Direction South-west. Two-blank FIB (place + direction); both word answers but definite values. Uses skill 142 (8-point compass)." }, { "n": 29, "type_id": 2, "question": "The figure is not drawn to scale. PQRS is a rectangle. Find $$\\angle MPS$$. [?]", "answer0": "47", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 143, "difficulty_id": 2, "explanation": "In rectangle PQRS, $$\\angle SPQ$$ (the corner at P) is a right angle = 90°. $$\\angle MPQ = 43°$$ (given). So $$\\angle MPS = 90° − 43° = 47°$$.", "hints": [ "The corner angle of a rectangle is 90°.", "Subtract the 43° angle from 90°." ], "source": "Nanyang 2023 P4 End of Year Exam Q29", "image_needed": true, "image_options": false, "image_file": "q29.png", "image_page": 15, "image_bbox": [ 0.36, 0.62, 0.58, 0.9 ], "image_loc": "rectangle PQRS with diagonal-like line from P to M on side QR, 43° marked at P, below the stem", "notes": "Key: 47 (degrees). Answer line shows degree symbol; FIB stores 47." }, { "n": 30, "type_id": 0, "question": "Draw and label square MNOP on the square grid. One side of the square has been drawn for you.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 143, "difficulty_id": 2, "explanation": "Side MN is drawn (a diagonal from M down-right to N). Complete the square by drawing the other three sides MP, PO and ON so MNOP is a square of equal side lengths. The answer key shows the completed square with P up-left of M and O below N.", "hints": [], "source": "Nanyang 2023 P4 End of Year Exam Q30", "image_needed": true, "image_options": false, "image_file": "q30.png", "image_page": 16, "image_bbox": [ 0.3, 0.2, 0.66, 0.46 ], "image_loc": "square grid with one side MN drawn (M near top, N lower-right), below the stem", "notes": "Interactive draw-on-grid task — no app question type (type_id 0, skipped on insert). Answer: complete square MNOP using the given side MN." }, { "n": 31, "type_id": 0, "question": "Complete the figure on the square grid so that it is symmetric about the line of symmetry JK.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 145, "difficulty_id": 2, "explanation": "Reflect every part of the given half-figure across the vertical line JK to produce the mirror image on the other side, completing the symmetric figure.", "hints": [], "source": "Nanyang 2023 P4 End of Year Exam Q31", "image_needed": true, "image_options": false, "image_file": "q31.png", "image_page": 16, "image_bbox": [ 0.34, 0.58, 0.66, 0.86 ], "image_loc": "square grid with a half-figure on the left of the vertical dashed line of symmetry JK, below the stem", "notes": "Interactive draw/reflect task — no app question type (type_id 0, skipped on insert). Answer: mirror the figure across line JK." }, { "n": 32, "type_id": 2, "question": "The line graph shows the length of a spring when various masses are hung on it.
What is the increase in the length of the spring when the mass hung on it is increased from 20g to 60g? [?]", "answer0": "60", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 147, "difficulty_id": 2, "explanation": "From the graph, at 20 g the length is 50 cm and at 60 g the length is 110 cm. Increase = 110 − 50 = 60 cm.", "hints": [ "Read the spring length at 20 g and at 60 g from the graph.", "Subtract the smaller length from the larger length." ], "source": "Nanyang 2023 P4 End of Year Exam Q32", "image_needed": true, "image_options": false, "image_file": "q32.png", "image_page": 17, "image_bbox": [ 0.18, 0.16, 0.74, 0.44 ], "image_loc": "line graph of Length of spring (cm) vs Mass (g), 0 to 60 g, below the stem", "notes": "Key: 110 − 50 = 60 cm. Answer line shows unit cm; FIB stores 60." }, { "n": 33, "type_id": 2, "question": "The difference between two fractions is $$\\frac{2}{9}$$. The smaller fraction is $$\\frac{1}{6}$$. What is the sum of the two fractions? Express your answer in its simplest form. [?]", "answer0": "5/9", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 121, "difficulty_id": 3, "explanation": "Larger fraction = $$\\frac{1}{6} + \\frac{2}{9} = \\frac{3}{18} + \\frac{4}{18} = \\frac{7}{18}$$. Sum = $$\\frac{7}{18} + \\frac{1}{6} = \\frac{7}{18} + \\frac{3}{18} = \\frac{10}{18} = \\frac{5}{9}$$.", "hints": [ "First find the larger fraction by adding the difference to the smaller fraction.", "Add the two fractions using a common denominator, then simplify." ], "source": "Nanyang 2023 P4 End of Year Exam Q33", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 10/18 = 5/9 (simplest form)." }, { "n": 34, "type_id": 2, "question": "At first, Peter had twice as much savings as Michelle. After Michelle received $5499, she had twice as much savings as Peter. What is their total savings now? [?]", "answer0": "10998", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 3, "explanation": "Peter's savings stay the same. Let Michelle's first share be 1 unit, Peter = 2 units. After +$5499, Michelle = 2 × Peter = 4 units. So the $5499 = 4u − 1u = 3u, giving 1u = $5499 ÷ 3 = $1833. Total now = Peter (2u) + Michelle (4u) = 6u = $1833 × 6 = $10998.", "hints": [ "Peter's amount does not change, so use it as the constant.", "The $5499 equals the difference in Michelle's units; find one unit first." ], "source": "Nanyang 2023 P4 End of Year Exam Q34", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: $10998. Answer line prefixed with $; FIB stores 10998." }, { "n": 35, "type_id": 2, "question": "The figure is made up of a rectangle and 2 squares, A and B. Find the perimeter of the figure. [?]", "answer0": "96", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 138, "difficulty_id": 3, "explanation": "Square A and the top rectangle each have height 6 cm. Top width is 15 cm. Square B has side = 6 + 15 = 21 cm. Perimeter = 6 + 15 (top) + 6 (right of top section) + 6 (left of square A) ... summing the outer edges: 6 + 15 + 6 + 6 + 3 × (6 + 15) = 96 cm.", "hints": [ "Find the side of the large square B from the top measurements.", "Add up only the outer edges of the whole figure." ], "source": "Nanyang 2023 P4 End of Year Exam Q35", "image_needed": true, "image_options": false, "image_file": "q35.png", "image_page": 19, "image_bbox": [ 0.36, 0.18, 0.66, 0.44 ], "image_loc": "L-shaped figure: small square A and rectangle on top (15 cm wide, 6 cm tall) above large square B, below the stem", "notes": "Key working: 6 + 15 + 6 + 6 + 3 × (6 + 15) = 96 cm. Answer line shows unit cm; FIB stores 96." }, { "n": 36, "type_id": 2, "question": "A tank had 25.68 $$l$$ of water. 9 $$l$$ of water was poured out of the tank. The remaining amount of water was then poured equally into 6 empty bottles. How much water was poured into each bottle? [?]", "answer0": "2.78", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 131, "difficulty_id": 2, "explanation": "Water left = 25.68 − 9 = 16.68 l. Poured into 6 bottles: 16.68 ÷ 6 = 2.78 l per bottle.", "hints": [ "First find how much water is left after pouring out 9 l.", "Divide the remaining amount equally by 6." ], "source": "Nanyang 2023 P4 End of Year Exam Q36", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 25.68 − 9 = 16.68 l; 16.68 ÷ 6 = 2.78 l. Answer unit litres; FIB stores 2.78." }, { "n": 37, "type_id": 2, "question": "A movie at a cinema started at 11.49 a.m. Jasmine arrived at the cinema late and started watching the movie 18 minutes after the movie had started. She watched the movie for 2 h 24 min. What time did the movie end? (Express your answer in 24-hour clock) [?]", "answer0": "1431", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 135, "difficulty_id": 3, "explanation": "The movie ends when Jasmine finishes watching: she started 18 min after 11.49 a.m. and watched 2 h 24 min, so total time after 11.49 a.m. = 18 min + 2 h 24 min = 2 h 42 min. 11.49 a.m. + 2 h 42 min = 2.31 p.m. = 14 31 in 24-hour clock.", "hints": [ "Add the 18-min late start and the 2 h 24 min watching time together.", "Add that duration to 11.49 a.m., then convert to 24-hour clock." ], "source": "Nanyang 2023 P4 End of Year Exam Q37", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 2 h 24 min + 18 min = 2 h 42 min; 11.49 a.m. + 2 h 42 min = 2.31 p.m. = 14 31. FIB stores 1431 (24-hour clock)." }, { "n": 38, "type_id": 2, "question": "Eight squares of length 2 cm were cut out from a rectangular piece of paper. Find the area of the remaining paper. [?]", "answer0": "133.2", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 138, "difficulty_id": 3, "explanation": "Each cut square has area 2 × 2 = 4 cm². Eight squares = 4 × 8 = 32 cm². Whole rectangle = 23.6 × 7 = 165.2 cm². Remaining paper = 165.2 − 32 = 133.2 cm².", "hints": [ "Find the area of one small square, then of all eight.", "Subtract the total cut-out area from the area of the whole rectangle." ], "source": "Nanyang 2023 P4 End of Year Exam Q38", "image_needed": true, "image_options": false, "image_file": "q38.png", "image_page": 21, "image_bbox": [ 0.28, 0.18, 0.74, 0.34 ], "image_loc": "shaded rectangle 23.6 cm by 7 cm with eight small 2 cm squares cut out, below the stem", "notes": "Key: 4×8=32 cm²; 23.6×7=165.2 cm²; 165.2−32=133.2 cm². Answer unit cm²; FIB stores 133.2." }, { "n": 39, "type_id": 2, "question": "The line graph shows the number of tourists who visited the Night Safari from January to July.
(a) What was the difference between the greatest and the least number of tourists who visited the Night Safari? [?]
(b) What was the total number of tourists who visited the Night Safari for the first half of the year? [?]", "answer0": "4000", "answer1": "25000", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 148, "difficulty_id": 2, "explanation": "(a) Greatest = 6000 (Jun), least = 2000 (Feb). Difference = 6000 − 2000 = 4000. (b) First half = Jan to Jun: 3000 + 2000 + 5500 + 3500 + 5000 + 6000 = 25000 tourists.", "hints": [ "(a) Find the highest and lowest points on the graph and subtract.", "(b) The first half of the year is January to June — add those six values." ], "source": "Nanyang 2023 P4 End of Year Exam Q39", "image_needed": true, "image_options": false, "image_file": "q39.png", "image_page": 22, "image_bbox": [ 0.18, 0.14, 0.78, 0.38 ], "image_loc": "line graph of Number of tourists vs months Jan–Jul, below the stem", "notes": "Two-part question stored as 2-blank FIB. Key (a) 6000−2000=4000; (b) 3000+2000+5500+3500+5000+6000=25000. Graph values read from key." }, { "n": 40, "type_id": 2, "question": "Mr Lee sold a total of 25.5 kg of corn flour and plain flour. He sold 5 more packets of corn flour than plain flour. Each packet of corn flour had a mass of 2.7 kg and each packet of plain flour had a mass of 1.3 kg.
(a) What was the mass of 5 packets of corn flour? [?]
(b) How many packets of plain flour did he sell? [?]", "answer0": "13.5", "answer1": "3", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 131, "difficulty_id": 3, "explanation": "(a) 5 packets of corn flour = 2.7 × 5 = 13.5 kg. (b) The extra 5 corn-flour packets weigh 13.5 kg, so the remaining flour (equal numbers of each type) = 25.5 − 13.5 = 12 kg. Each matched pair (1 corn + 1 plain) = 2.7 + 1.3 = 4 kg. Number of pairs = 12 ÷ 4 = 3, so he sold 3 packets of plain flour.", "hints": [ "(a) Multiply the mass of one corn-flour packet by 5.", "(b) Remove the mass of the 5 extra corn packets, then split the rest into equal corn+plain pairs of 4 kg each." ], "source": "Nanyang 2023 P4 End of Year Exam Q40", "image_needed": false, "image_options": false, "image_file": null, "notes": "Two-part FIB. Key (a) 2.7×5=13.5 kg; (b) 25.5−13.5=12, 2.7+1.3=4, 12÷4=3. (a) unit kg; answers stored 13.5 and 3." }, { "n": 41, "type_id": 2, "question": "A sum of $7092 was shared among Kumar, Wei Ming and Hakim. Wei Ming received twice as much money as Kumar. Hakim received 3 times as much money as Wei Ming.
(a) How much money did Kumar receive? [?]
(b) How much money did Hakim receive? [?]", "answer0": "788", "answer1": "4728", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 3, "explanation": "Let Kumar = 1 unit. Wei Ming = 2 units. Hakim = 3 × Wei Ming = 6 units. Total = 1 + 2 + 6 = 9 units = $7092, so 1 unit = $7092 ÷ 9 = $788. (a) Kumar = $788. (b) Hakim = 6 units = $788 × 6 = $4728.", "hints": [ "Let Kumar be 1 unit and express the others in units.", "Add the units, find one unit from the total, then multiply." ], "source": "Nanyang 2023 P4 End of Year Exam Q41", "image_needed": false, "image_options": false, "image_file": null, "notes": "Two-part FIB. Key (a) $7092÷9=$788; (b) $788×6=$4728. Answers stored 788 and 4728 (money, no $)." }, { "n": 42, "type_id": 2, "question": "After a florist sold $$\\frac{2}{3}$$ of her roses and $$\\frac{5}{9}$$ of her tulips, she had the same number of roses and tulips left. The number of tulips she sold was 85.
(a) How many tulips did she have left? [?]
(b) How many roses did she have at first? [?]", "answer0": "68", "answer1": "204", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 122, "difficulty_id": 3, "explanation": "Tulips: $$\\frac{5}{9}$$ sold = 85, so 1 unit ($$\\frac{1}{9}$$) = 85 ÷ 5 = 17. Tulips left = $$\\frac{4}{9}$$ = 4 × 17 = 68. (a) 68 tulips left. (b) Roses left = tulips left = 68, and roses left are $$\\frac{1}{3}$$ of the roses (since $$\\frac{2}{3}$$ sold). So roses at first = 3 × 68 = 204.", "hints": [ "The 85 tulips sold equal $$\\frac{5}{9}$$ of the tulips — find one ninth.", "Roses left equal tulips left; roses left are $$\\frac{1}{3}$$ of the roses at first." ], "source": "Nanyang 2023 P4 End of Year Exam Q42", "image_needed": false, "image_options": false, "image_file": null, "notes": "Two-part FIB. Key (a) 5u=85, 1u=17, 4u=68; (b) 1u=68, 3u=204. Answers stored 68 and 204." }, { "n": 43, "type_id": 2, "question": "There was a total of 60 bicycles and tricycles in a shop. A bicycle has 2 wheels and a tricycle has 3 wheels. There were 156 wheels altogether.
(a) How many bicycles were there? [?]
(b) How many more tricycles than bicycles were there in the shop? [?]", "answer0": "24", "answer1": "12", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 3, "explanation": "If all 60 were bicycles: 60 × 2 = 120 wheels. Extra wheels = 156 − 120 = 36, and each tricycle adds 1 extra wheel, so tricycles = 36. Bicycles = 60 − 36 = 24. (a) 24 bicycles. (b) Tricycles − bicycles = 36 − 24 = 12 more tricycles.", "hints": [ "Assume all 60 are bicycles, then see how many extra wheels are needed.", "(b) Subtract the number of bicycles from the number of tricycles." ], "source": "Nanyang 2023 P4 End of Year Exam Q43", "image_needed": false, "image_options": false, "image_file": null, "notes": "Two-part FIB. Key (a) guess-and-check Ans 24 (tricycles 36); (b) 36 − 24 = 12. Answers stored 24 and 12." } ] }