{ "paper": { "school": "Nanyang Primary School", "year": 2024, "level": "P4", "label": "End-of-Year Exam", "source_prefix": "Nanyang 2024 P4 End-of-Year Exam", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "The value of digit 5 in 75 328 is [?].", "answer0": "50", "answer1": "500", "answer2": "5000", "answer3": "50 000", "correct_answer": 2, "skill_id": 105, "difficulty_id": 1, "explanation": "In 75 328 the digit 5 is in the thousands place, so its value is 5000.", "hints": [ "Identify which place the digit 5 sits in.", "Thousands place value = digit × 1000." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key marks option (3) = 5000." }, { "n": 2, "type_id": 1, "question": "36 258 rounded to the nearest hundred is [?].", "answer0": "36 300", "answer1": "36 260", "answer2": "36 200", "answer3": "36 000", "correct_answer": 0, "skill_id": 109, "difficulty_id": 1, "explanation": "The tens digit is 5, so round up. 36 258 ≈ 36 300 to the nearest hundred.", "hints": [ "Look at the tens digit to decide round up or down.", "5 or more rounds up." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key marks option (1) = 36 300." }, { "n": 3, "type_id": 1, "question": "3 and 4 are factors of [?].", "answer0": "8", "answer1": "18", "answer2": "24", "answer3": "34", "correct_answer": 2, "skill_id": 111, "difficulty_id": 1, "explanation": "A number with both 3 and 4 as factors must be divisible by 12. 24 ÷ 3 = 8 and 24 ÷ 4 = 6, so 24 works.", "hints": [ "Both 3 and 4 must divide the number exactly.", "Check divisibility by 3 and by 4." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key marks option (3) = 24." }, { "n": 4, "type_id": 1, "question": "How many one-thirds are there in 4 wholes?", "answer0": "12", "answer1": "$$\\frac{3}{4}$$", "answer2": "$$1\\frac{1}{3}$$", "answer3": "4", "correct_answer": 0, "skill_id": 119, "difficulty_id": 1, "explanation": "1 whole = $$\\frac{3}{3}$$, so 1 whole has three one-thirds. 4 wholes = 4 × 3 = 12 one-thirds.", "hints": [ "Each whole contains three thirds.", "Multiply 4 by 3." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key marks option (1) = 12." }, { "n": 5, "type_id": 1, "question": "In which of the following does the digit 7 stand for 7 tenths?", "answer0": "13.75", "answer1": "37.68", "answer2": "45.37", "answer3": "71.54", "correct_answer": 0, "skill_id": 123, "difficulty_id": 1, "explanation": "7 tenths = 0.7, the first digit after the decimal point. In 13.75 the 7 is in the tenths place.", "hints": [ "Tenths is the first place after the decimal point.", "Look for 7 immediately after the decimal point." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key marks option (1) = 13.75." }, { "n": 6, "type_id": 1, "question": "Which figure has perpendicular lines?", "answer0": "A", "answer1": "H", "answer2": "N", "answer3": "V", "correct_answer": 1, "skill_id": 100, "difficulty_id": 1, "explanation": "Perpendicular lines meet at right angles (90°). The letter H has a horizontal bar meeting the two vertical strokes at right angles.", "hints": [ "Perpendicular lines meet at a right angle.", "Look for a letter with a square corner." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q6", "image_needed": false, "image_options": false, "image_file": null, "notes": "Options are letters rendered as text (A/H/N/V); no images needed. Key marks option (2) = H." }, { "n": 7, "type_id": 1, "question": "Each figure is made up of 4 identical squares and 2 identical rectangles. Which one has a line of symmetry?", "answer0": "Figure 1", "answer1": "Figure 2", "answer2": "Figure 3", "answer3": "Figure 4", "correct_answer": 3, "skill_id": 145, "difficulty_id": 2, "explanation": "A line of symmetry divides a figure into two mirror-image halves. Figure (4) is symmetric about a vertical line through its centre.", "hints": [ "Imagine folding the figure so the two halves match.", "Check for a vertical or horizontal mirror line." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q7", "image_needed": true, "image_options": true, "image_file": null, "notes": "Image-option MCQ: 4 grid figures made of squares/rectangles. Key marks option (4). Each option needs a crop (q7_opt0..3).", "image_page": 5, "image_bbox": [ 0.26, 0.14, 0.52, 0.55 ], "image_loc": "left-centre of page; four stacked square/rectangle figures labelled (1)-(4)" }, { "n": 8, "type_id": 1, "question": "The figure shows a pyramid. Which of the following is a net of the pyramid?", "answer0": "Net 1", "answer1": "Net 2", "answer2": "Net 3", "answer3": "Net 4", "correct_answer": 1, "skill_id": 232, "difficulty_id": 2, "explanation": "A square-based pyramid has 1 square base and 4 triangular faces. The net showing one square attached to four triangles is option (2).", "hints": [ "Count the faces of the pyramid: 1 square + 4 triangles.", "The correct net has exactly one square and four triangles arranged around it." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q8", "image_needed": true, "image_options": true, "image_file": null, "notes": "Image-option MCQ; the pyramid figure and four candidate nets are pictures. Key marks option (2). Crop pyramid + each option (q8_opt0..3).", "image_page": 6, "image_bbox": [ 0.2, 0.27, 0.5, 0.58 ], "image_loc": "left-centre; the pyramid drawing near top, four net options (1)-(4) below" }, { "n": 9, "type_id": 1, "question": "The area of rectangle B is 56 m². Its length is 8 m. Find the breadth of rectangle B.", "answer0": "6 m", "answer1": "7 m", "answer2": "8 m", "answer3": "9 m", "correct_answer": 1, "skill_id": 136, "difficulty_id": 1, "explanation": "Breadth = area ÷ length = 56 ÷ 8 = 7 m.", "hints": [ "Area = length × breadth.", "Breadth = area ÷ length." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q9", "image_needed": true, "image_options": false, "image_file": "q9.png", "notes": "Figure: rectangle B with 8 m base and unknown breadth marked '?'. Key marks option (2) = 7 m.", "image_page": 7, "image_bbox": [ 0.36, 0.11, 0.64, 0.27 ], "image_loc": "top-centre; rectangle labelled B with 8 m below and ? on right side" }, { "n": 10, "type_id": 1, "question": "A rectangle is divided into 4 identical squares. The perimeter of the rectangle is 80 cm. What is the length of the rectangle?", "answer0": "16 cm", "answer1": "32 cm", "answer2": "48 cm", "answer3": "64 cm", "correct_answer": 1, "skill_id": 96, "difficulty_id": 2, "explanation": "The rectangle is 4 squares long and 1 square wide, so the perimeter = 10 square-sides. 80 ÷ 10 = 8 cm per square side. Length = 4 × 8 = 32 cm.", "hints": [ "A 4-by-1 arrangement has perimeter of 10 side-lengths.", "Find one square's side first, then multiply by 4." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q10", "image_needed": true, "image_options": false, "image_file": "q10.png", "notes": "Figure: rectangle split into 4 equal squares by dashed lines, length marked '?'. Key marks option (2) = 32 cm.", "image_page": 7, "image_bbox": [ 0.36, 0.55, 0.69, 0.66 ], "image_loc": "centre; long rectangle divided into 4 squares with ? above" }, { "n": 11, "type_id": 1, "question": "A square piece of paper as shown in Figure 1 is folded twice into the shape of a smaller square as shown in Figure 3. The area of the smaller square is 9 cm². What is the perimeter of the square piece of paper as shown in Figure 1?", "answer0": "12 cm", "answer1": "18 cm", "answer2": "24 cm", "answer3": "36 cm", "correct_answer": 2, "skill_id": 137, "difficulty_id": 2, "explanation": "Small square area 9 cm², so its side = 3 cm. Folding twice (halving twice) means the original square's side = 2 × 3 = 6 cm. Perimeter = 6 × 4 = 24 cm.", "hints": [ "Area 9 cm² gives a side of 3 cm.", "Each fold halves a dimension; two folds make the original side twice the small one." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q11", "image_needed": true, "image_options": false, "image_file": "q11.png", "notes": "Figure: Figure 1 (big square with fold arrows) → Figure 2 → Figure 3 (small square). Key marks option (3) = 24 cm.", "image_page": 8, "image_bbox": [ 0.29, 0.17, 0.74, 0.26 ], "image_loc": "top-centre; three squares with arrows labelled Figure 1, 2, 3" }, { "n": 12, "type_id": 1, "question": "Jun Kai earned $130 for a day of work. How much did Jun Kai earn for 14 days of work?", "answer0": "$550", "answer1": "$650", "answer2": "$1720", "answer3": "$1820", "correct_answer": 3, "skill_id": 116, "difficulty_id": 1, "explanation": "Total = $130 × 14 = $1820.", "hints": [ "Multiply daily earnings by the number of days.", "130 × 14." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key marks option (4) = $1820." }, { "n": 13, "type_id": 1, "question": "The table shows the number of customers at a drinks stall from Monday to Friday.
Monday: 450, Tuesday: 300, Wednesday: 500, Thursday: 250, Friday: 450.
Which one of the line graphs best represents the information in the table?", "answer0": "Graph 1", "answer1": "Graph 2", "answer2": "Graph 3", "answer3": "Graph 4", "correct_answer": 3, "skill_id": 147, "difficulty_id": 2, "explanation": "Mon and Fri are equal (450); Wed is the highest (500); Thu is the lowest (250); Tue (300) is between. Only graph (4) matches all these points.", "hints": [ "Mon and Fri must be at the same height.", "Wed is the peak and Thu is the lowest point." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q13", "image_needed": true, "image_options": true, "image_file": null, "notes": "Image-option MCQ: four line graphs. Table data given in stem. Key marks option (4). Crop each graph (q13_opt0..3).", "image_page": 9, "image_bbox": [ 0.28, 0.21, 0.62, 0.86 ], "image_loc": "left-centre column; four line graphs labelled (1)-(4) stacked vertically" }, { "n": 14, "type_id": 1, "question": "The pie chart shows the favourite types of food of a group of 60 children. Which statement best represents the data in the pie chart?", "answer0": "Chicken rice is the least favourite food among the children.", "answer1": "The number of children who chose bee hoon is twice the number of children who chose roti prata.", "answer2": "$$\\frac{1}{10}$$ of the children chose fishball noodles as their favourite food.", "answer3": "20 children chose roti prata as their favourite food.", "correct_answer": 3, "skill_id": 235, "difficulty_id": 2, "explanation": "Roti prata = $$\\frac{1}{3}$$ of 60 = 20 children, so (4) is true. (1) is false (chicken rice $$\\frac{5}{12}$$ is the largest). (2) is false (bee hoon 10 is half of roti prata 20). Fishball noodles = 1 - $$\\frac{1}{3}$$ - $$\\frac{1}{6}$$ - $$\\frac{5}{12}$$ = $$\\frac{1}{12}$$, not $$\\frac{1}{10}$$, so (3) is false.", "hints": [ "Find each fraction of 60.", "Roti prata = $$\\frac{1}{3}$$ of 60." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q14", "image_needed": true, "image_options": false, "image_file": "q14.png", "notes": "Figure: pie chart 'Favourite Food' with Roti Prata 1/3, Bee Hoon 1/6, Chicken Rice 5/12, Fishball Noodles. Key marks option (4).", "image_page": 10, "image_bbox": [ 0.27, 0.18, 0.74, 0.5 ], "image_loc": "centre; circular pie chart titled Favourite Food with four labelled sectors" }, { "n": 15, "type_id": 1, "question": "The table shows the prices of tickets for a concert.
Adult: Monday to Friday $31.60, Saturday and Sunday $39.60.
Child: Monday to Friday $15.90, Saturday and Sunday $21.90.
How much does a family of 2 adults and 3 children have to pay for the concert that will be held on a Saturday?", "answer0": "$110.90", "answer1": "$126.60", "answer2": "$144.90", "answer3": "$162.60", "correct_answer": 2, "skill_id": 131, "difficulty_id": 2, "explanation": "Saturday prices: 2 adults = $39.60 × 2 = $79.20; 3 children = $21.90 × 3 = $65.70. Total = $79.20 + $65.70 = $144.90.", "hints": [ "Use the Saturday/Sunday column.", "Add 2 adult tickets and 3 child tickets." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q15", "image_needed": false, "image_options": false, "image_file": null, "notes": "Table read into stem. Key marks option (3) = $144.90." }, { "n": 16, "type_id": 2, "question": "What is the remainder when 1786 is divided by 9? [?]", "answer0": "4", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 117, "difficulty_id": 1, "explanation": "1786 ÷ 9 = 198 remainder 4 (198 × 9 = 1782, 1786 - 1782 = 4).", "hints": [ "Do long division of 1786 by 9.", "The leftover after the last step is the remainder." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q16", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key answer = 4." }, { "n": 17, "type_id": 2, "question": "What fraction of the triangles shown are black in colour? [?]", "answer0": "5/14", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 120, "difficulty_id": 1, "explanation": "There are 14 triangles in total and 5 are black, so the fraction is $$\\frac{5}{14}$$.", "hints": [ "Count the black triangles and the total triangles.", "Fraction = black ÷ total." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q17", "image_needed": true, "image_options": false, "image_file": "q17.png", "notes": "Figure: row of 14 alternating up/down triangles, 5 of them shaded black. Key answer = 5/14 (count verified against key).", "image_page": 13, "image_bbox": [ 0.22, 0.46, 0.69, 0.56 ], "image_loc": "left-centre; horizontal box containing a row of black and white triangles" }, { "n": 18, "type_id": 2, "question": "Express $$\\frac{9}{12}$$ in its simplest form. [?]", "answer0": "3/4", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 78, "difficulty_id": 1, "explanation": "Divide numerator and denominator by 3: $$\\frac{9}{12}=\\frac{3}{4}$$.", "hints": [ "Find the highest common factor of 9 and 12.", "Divide top and bottom by 3." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q18", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key answer = 3/4." }, { "n": 19, "type_id": 2, "question": "Which two of the fractions below are smaller than $$\\frac{1}{2}$$?
$$\\frac{3}{5}$$, $$\\frac{2}{7}$$, $$\\frac{4}{8}$$, $$\\frac{5}{12}$$
[?] and [?]", "answer0": "2/7", "answer1": "5/12", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 79, "difficulty_id": 2, "explanation": "Compare each with $$\\frac{1}{2}$$: $$\\frac{3}{5}=\\frac{6}{10}>\\frac{1}{2}$$; $$\\frac{2}{7}=\\frac{4}{14}<\\frac{7}{14}=\\frac{1}{2}$$; $$\\frac{4}{8}=\\frac{1}{2}$$ (not smaller); $$\\frac{5}{12}<\\frac{6}{12}=\\frac{1}{2}$$. So $$\\frac{2}{7}$$ and $$\\frac{5}{12}$$ are smaller.", "hints": [ "A fraction is less than $$\\frac{1}{2}$$ if its numerator is less than half its denominator.", "Check each fraction against half its denominator." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q19", "image_needed": false, "image_options": false, "image_file": null, "notes": "Two-blank FIB; order of the two answers is interchangeable. Key answers = 2/7 and 5/12." }, { "n": 20, "type_id": 2, "question": "Write the decimal represented by A. [?]", "answer0": "0.83", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 123, "difficulty_id": 2, "explanation": "The number line from 0.8 to 0.9 is split into 10 equal intervals of 0.01 each. A is 3 intervals past 0.8, so A = 0.83.", "hints": [ "Each small interval between 0.8 and 0.9 is 0.01.", "Count the intervals from 0.8 to the arrow A." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q20", "image_needed": true, "image_options": false, "image_file": "q20.png", "notes": "Figure: number line marked 0.8 and 0.9 with arrow A. Key answer = 0.83.", "image_page": 14, "image_bbox": [ 0.18, 0.38, 0.74, 0.49 ], "image_loc": "centre; horizontal number line with arrow labelled A between 0.8 and 0.9" }, { "n": 21, "type_id": 2, "question": "Round 23.45 to the nearest whole number. [?]", "answer0": "23", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 128, "difficulty_id": 1, "explanation": "The first decimal digit is 4, which is less than 5, so round down. 23.45 ≈ 23.", "hints": [ "Look at the tenths digit (4).", "Less than 5 means round down." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q21", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key answer = 23." }, { "n": 22, "type_id": 2, "question": "Arrange these numbers from the smallest to the greatest.
$$\\frac{2}{5}$$, 0.408, 0.048
[?], [?], [?]", "answer0": "0.048", "answer1": "2/5", "answer2": "0.408", "answer3": null, "correct_answer": null, "skill_id": 124, "difficulty_id": 2, "explanation": "$$\\frac{2}{5}=0.4$$. Comparing: 0.048 < 0.4 < 0.408. So smallest to greatest: 0.048, $$\\frac{2}{5}$$, 0.408.", "hints": [ "Convert $$\\frac{2}{5}$$ to a decimal (0.4).", "Then compare 0.048, 0.4 and 0.408." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q22", "image_needed": false, "image_options": false, "image_file": null, "notes": "Ordered FIB (smallest to greatest). Key: 0.048, 2/5, 0.408. Key notes 2/5 must be written as a fraction, not 0.4." }, { "n": 23, "type_id": 2, "question": "6.3 − 0.74 = [?]", "answer0": "5.56", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 129, "difficulty_id": 1, "explanation": "6.30 − 0.74 = 5.56.", "hints": [ "Write 6.3 as 6.30 and line up the decimal points.", "Subtract column by column." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q23", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key answer = 5.56." }, { "n": 24, "type_id": 1, "question": "Name the smallest angle.", "answer0": "∠e", "answer1": "∠f", "answer2": "∠g", "answer3": "∠h", "correct_answer": 1, "skill_id": 139, "difficulty_id": 2, "explanation": "Of the four angles e, f, g and h formed at the point, angle f is visibly the narrowest opening, so it is the smallest angle.", "hints": [ "The smallest angle has the narrowest opening between its two arms.", "Compare the gaps of e, f, g and h." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q24", "image_needed": true, "image_options": false, "image_file": "q24.png", "notes": "Original is open-response naming angle. Converted to MCQ over the four labelled angles e/f/g/h. Key answer = ∠f (option 2). Figure: lines meeting at a point with angles e, f, g, h marked.", "image_page": 15, "image_bbox": [ 0.3, 0.31, 0.62, 0.43 ], "image_loc": "centre; rays from a single point with angles labelled e, f, g, h" }, { "n": 25, "type_id": 2, "question": "ABCD is a rectangle. ∠EBC = 15°. Find ∠ABE. [?]", "answer0": "75", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 143, "difficulty_id": 2, "explanation": "∠ABC is a right angle of the rectangle = 90°. ∠ABE = ∠ABC − ∠EBC = 90° − 15° = 75°.", "hints": [ "A rectangle's corner is 90°.", "∠ABE = 90° − ∠EBC." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q25", "image_needed": true, "image_options": false, "image_file": "q25.png", "notes": "Answer in degrees. Figure: tilted rectangle ABCD with point E on side DC and 15° marked at B. Key answer = 75 (degrees).", "image_page": 15, "image_bbox": [ 0.33, 0.56, 0.66, 0.74 ], "image_loc": "centre; tilted rectangle ABCD with E near D-C and angle 15° at B" }, { "n": 26, "type_id": 2, "question": "The table shows the number of boys and girls in two Primary 4 classes who took part in two sports events, Long Jump and High Jump.
Class 4A: boys Long Jump 9, boys High Jump 11, girls Long Jump ?, girls High Jump 6, Total 40.
Class 4B: boys Long Jump 10, boys High Jump 8, girls Long Jump 10, girls High Jump 14, Total 42.
(a) How many boys in 4B took part in High Jump? (b) How many girls in 4A took part in Long Jump?
(a) [?] (b) [?]", "answer0": "8", "answer1": "14", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 146, "difficulty_id": 2, "explanation": "(a) Read directly from the table: boys in 4B High Jump = 8. (b) 4A total = 40; known = 9 + 11 + 6 = 26; girls in 4A Long Jump = 40 − 26 = 14.", "hints": [ "Part (a) is read straight from the table.", "Part (b): subtract the three known 4A values from the 4A total of 40." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q26", "image_needed": false, "image_options": false, "image_file": null, "notes": "Two-part; table read into stem. Key: (a) 8, (b) 14." }, { "n": 27, "type_id": 2, "question": "Use all the digits 3, 0, 9, 1, 8 to form the smallest 5-digit even number. Each digit can only be used once. [?]", "answer0": "10398", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 106, "difficulty_id": 2, "explanation": "For the smallest 5-digit number the leading digit can't be 0, so use 1. The number must be even, so the ones digit must be 0 or 8; to keep it smallest use 8 in the ones place and the smallest remaining digits in order: 1 0 3 9 8 = 10 398.", "hints": [ "Smallest 5-digit number: smallest non-zero digit goes first.", "Even number: the last digit must be 0 or 8 — choose to keep the rest smallest." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q27", "image_needed": false, "image_options": false, "image_file": null, "notes": "Digit cards given in stem. Key answer = 10 398 (stored without space as 10398)." }, { "n": 28, "type_id": 2, "question": "The difference between two numbers is 1340. The greater number is 5 times the smaller number. What is the greater number? [?]", "answer0": "1675", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 2, "explanation": "Greater = 5 units, smaller = 1 unit, difference = 4 units = 1340, so 1 unit = 1340 ÷ 4 = 335. Greater = 335 × 5 = 1675.", "hints": [ "Let the smaller number be 1 unit; the greater is 5 units.", "The difference of 4 units equals 1340." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q28", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key answer = 1675." }, { "n": 29, "type_id": 2, "question": "Joseph spent $21.95. He spent $3.25 more than Muthu. How much did Joseph and Muthu spend altogether? $[?]", "answer0": "40.65", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 131, "difficulty_id": 2, "explanation": "Muthu spent $21.95 − $3.25 = $18.70. Altogether = $21.95 + $18.70 = $40.65.", "hints": [ "Find Muthu's amount first (Joseph's amount minus $3.25).", "Then add the two amounts." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q29", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer in dollars. Key answer = $40.65." }, { "n": 30, "type_id": 2, "question": "The figure is made up of 2 identical squares and 4 identical rectangles. The length of AB is 45 cm. Find the area of a square. [?] cm²", "answer0": "81", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 138, "difficulty_id": 3, "explanation": "Along AB there are 5 equal lengths (each a square side / short rectangle side), so each = 45 ÷ 5 = 9 cm. The square side is 9 cm, so area of a square = 9 × 9 = 81 cm².", "hints": [ "The 45 cm spans 5 equal segments of 9 cm each.", "Area of square = side × side." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q30", "image_needed": true, "image_options": false, "image_file": "q30.png", "notes": "Answer in cm². Figure: arrangement of 2 squares + 4 rectangles, AB = 45 cm marked, one part marked 9 cm. Key answer = 81 (cm²).", "image_page": 18, "image_bbox": [ 0.25, 0.12, 0.8, 0.28 ], "image_loc": "top; composite figure of squares and rectangles with A and B marked and 45 cm below" }, { "n": 31, "type_id": 0, "question": "Using a protractor and a ruler, draw ∠PQR = 104°. Mark and label the angle. The line QR has been drawn for you.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 140, "difficulty_id": 1, "explanation": "Place the protractor centre on Q with the baseline along QR, mark 104°, then draw QP. ∠PQR = 104°.", "hints": [ "Align the protractor baseline with QR and centre on Q.", "Mark 104° then draw the ray QP." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q31", "image_needed": false, "image_options": false, "image_file": null, "notes": "Interactive draw-with-protractor task; no value/sequence answer, so type_id 0 (skipped on insert). Answer is a constructed 104° angle." }, { "n": 32, "type_id": 0, "question": "In the square grid, line EF and line FG form two sides of a square EFGH. Complete the drawing of square EFGH.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 143, "difficulty_id": 2, "explanation": "EF and FG are two equal adjacent sides meeting at F. Translate E by the vector FG (and G by the vector FE) to locate H, then draw GH and HE to complete square EFGH. Key notes point H must be labelled.", "hints": [ "EFGH is a square, so all sides are equal and meet at right angles.", "Find H so that EH is parallel and equal to FG." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q32", "image_needed": false, "image_options": false, "image_file": null, "notes": "Interactive grid-drawing task (complete the square); type_id 0 (skipped on insert). Answer: locate and label vertex H to complete square EFGH." }, { "n": 33, "type_id": 0, "question": "Complete the symmetric figure with XY as the line of symmetry.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 145, "difficulty_id": 2, "explanation": "Reflect every drawn segment across the diagonal line XY; each grid point's mirror image lies the same number of squares on the opposite side of XY. Join the reflected points to complete the symmetric figure.", "hints": [ "Reflect each vertex across the dashed line XY.", "The mirror image is the same perpendicular distance from XY." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q33", "image_needed": false, "image_options": false, "image_file": null, "notes": "Interactive reflect-and-draw task; type_id 0 (skipped on insert). Answer: the figure reflected across diagonal XY." }, { "n": 34, "type_id": 2, "question": "The line graph shows the number of members in a golf club from 2019 to 2023.
2019: 100, 2020: 150, 2021: 80, 2022: 100, 2023: 180.
(a) During which 1-year period was there a greatest increase in the number of members in the golf club? Year [?] to Year [?]
(b) How many fewer members were there in 2021 than 2020? [?]", "answer0": "2022", "answer1": "2023", "answer2": "70", "answer3": null, "correct_answer": null, "skill_id": 147, "difficulty_id": 2, "explanation": "(a) Increases: 2019→2020 +50, 2022→2023 +80 (others are decreases). The greatest increase is 2022 to 2023. (b) 2020 had 150, 2021 had 80, so 150 − 80 = 70 fewer members.", "hints": [ "Part (a): find the steepest upward segment.", "Part (b): subtract the 2021 value from the 2020 value." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q34", "image_needed": true, "image_options": false, "image_file": "q34.png", "notes": "Three blanks: (a) two year blanks, (b) one. Graph values read into stem. Key: (a) Year 2022 to Year 2023, (b) 70. Figure: line graph 2019-2023.", "image_page": 20, "image_bbox": [ 0.22, 0.16, 0.76, 0.4 ], "image_loc": "upper-centre; line graph titled 'Number of members in a golf club', years 2019-2023 on x-axis" }, { "n": 35, "type_id": 2, "question": "Two types of cardboard are sold at the prices shown. A small cardboard costs $3 and a large cardboard costs $5. Meiling bought a total of 23 cardboards. She paid $85 altogether. How many small cardboards did she buy? [?]", "answer0": "15", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 3, "explanation": "Assume all 23 were large: 23 × $5 = $115. Excess = $115 − $85 = $30. Each small instead of large saves $5 − $3 = $2, so number of small = $30 ÷ $2 = 15.", "hints": [ "Assume all 23 cardboards are large and find the over-estimate.", "Each swap to a small saves $2; divide the excess by 2." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q35", "image_needed": false, "image_options": false, "image_file": null, "notes": "Prices given in stem ($3 small, $5 large). Key answer = 15." }, { "n": 36, "type_id": 2, "question": "The table shows the number of pancakes and tarts sold in a cafe from Friday to Sunday.
Friday: pancakes 45, tarts 42. Saturday: pancakes 52, tarts 33. Sunday: pancakes 48, tarts 51.
(a) On which day were there more tarts sold than pancakes? [?]
(b) Each pancake was sold at $3. How much more money was collected from the sale of the pancakes on Saturday than on Friday? $[?]", "answer0": "Sunday", "answer1": "21", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 148, "difficulty_id": 2, "explanation": "(a) Tarts > pancakes only on Sunday (51 > 48). (b) Saturday pancake sales = 52 × $3 = $156; Friday = 45 × $3 = $135; difference = $156 − $135 = $21.", "hints": [ "Part (a): compare tarts and pancakes for each day.", "Part (b): find each day's pancake takings, then subtract." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q36", "image_needed": false, "image_options": false, "image_file": null, "notes": "Two parts; (a) word answer Sunday (acceptable here as a definite day value), (b) $21. Table read into stem. Key: (a) Sunday, (b) $21." }, { "n": 37, "type_id": 2, "question": "The mass of a box with 5 identical cubes weighed 31.7 kg. 2 cubes were removed from the box. The mass of the box with the remaining number of cubes weighed 20.3 kg. What was the mass of the empty box? [?] kg", "answer0": "3.2", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 131, "difficulty_id": 3, "explanation": "Mass of 2 cubes = 31.7 − 20.3 = 11.4 kg, so 1 cube = 11.4 ÷ 2 = 5.7 kg. Mass of 3 cubes = 5.7 × 3 = 17.1 kg. Empty box = 20.3 − 17.1 = 3.2 kg.", "hints": [ "Removing 2 cubes drops the mass by their weight; find one cube's mass.", "Subtract the mass of the remaining 3 cubes from 20.3 kg." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q37", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer in kg. Key answer = 3.2 kg." }, { "n": 38, "type_id": 2, "question": "James bought an equal number of muffins and cookies for a group of friends. When he gave them 5 muffins each, he had 6 muffins left. When he gave them 7 cookies each, he was short of 4 cookies.
(a) How many muffins and cookies did James buy altogether? [?]
(b) How many friends did James give the muffins and cookies to? [?]", "answer0": "62", "answer1": "5", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 3, "explanation": "Muffins = 5n + 6; cookies = 7n − 4; equal, so 5n + 6 = 7n − 4, giving 2n = 10, n = 5 friends. Muffins = 5×5 + 6 = 31, cookies = 31. (a) Total = 31 + 31 = 62. (b) 5 friends.", "hints": [ "Write muffins as 5 × friends + 6 and cookies as 7 × friends − 4.", "They are equal — solve for the number of friends." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q38", "image_needed": false, "image_options": false, "image_file": null, "notes": "Two parts. Key: (a) 62, (b) 5 friends. (Solved by guess-and-check table in the key.)" }, { "n": 39, "type_id": 2, "question": "The figure is made up of straight lines that meet at right angles. The top-left vertical side is 7 m, the short horizontal step is 7 m wide and 6 m deep, the bottom is 26 m long and the right side is 7 m.
(a) Find the perimeter of the figure. [?] m
(b) Find the area of the figure. [?] cm²", "answer0": "78", "answer1": "224", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 138, "difficulty_id": 3, "explanation": "(a) The total height is 6 + 7 = 13 m. Perimeter = (26 + 13) × 2 = 78 m (sum of the L-shape outline). (b) Split into rectangle A (7 × 6 = 42) and rectangle B (26 × 7 = 182); total area = 42 + 182 = 224 m².", "hints": [ "Part (a): an L-shape has the same perimeter as the enclosing rectangle, (26 + 13) × 2.", "Part (b): cut the L into two rectangles and add their areas." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q39", "image_needed": true, "image_options": false, "image_file": "q39.png", "notes": "Answers: (a) 78 m, (b) area 224 m². NOTE: paper's (b) Ans line is misprinted 'cm²' but figure is in metres; key gives 224 m². Figure: L-shaped right-angled figure with 7 m, 6 m, 26 m, 7 m marked.", "image_page": 25, "image_bbox": [ 0.32, 0.1, 0.74, 0.27 ], "image_loc": "top-centre; L-shaped figure with sides 7 m, 6 m, 26 m, 7 m labelled" }, { "n": 40, "type_id": 2, "question": "There is a rectangular piece of cardboard measuring 23 cm by 19 cm. Danissa pasted a photograph at the centre of the cardboard, leaving a border of 4 cm all around it.
(a) What is the perimeter of the photograph? [?] cm
(b) What is the area of the photograph? [?] cm²", "answer0": "52", "answer1": "165", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 138, "difficulty_id": 2, "explanation": "The 4 cm border removes 8 cm from each dimension. Photo length = 23 − 4 − 4 = 15 cm; photo breadth = 19 − 4 − 4 = 11 cm. (a) Perimeter = (15 + 11) × 2 = 52 cm. (b) Area = 15 × 11 = 165 cm².", "hints": [ "Subtract the 4 cm border from both ends of each side (8 cm total).", "Then use perimeter = (l + b) × 2 and area = l × b." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q40", "image_needed": true, "image_options": false, "image_file": "q40.png", "notes": "Answers: (a) 52 cm, (b) 165 cm². Figure: cardboard 23 cm by 19 cm with central 'photograph' and 4 cm borders marked.", "image_page": 26, "image_bbox": [ 0.28, 0.16, 0.68, 0.38 ], "image_loc": "centre; outer rectangle 23 cm x 19 cm with inner 'photograph' rectangle and 4 cm borders" }, { "n": 41, "type_id": 2, "question": "Mrs Singh baked some cupcakes for a party. $$\\frac{2}{7}$$ of them were chocolate cupcakes, $$\\frac{4}{7}$$ of them were strawberry cupcakes and the rest were vanilla cupcakes. There were 56 strawberry cupcakes.
(a) How many chocolate cupcakes did Mrs Singh bake? [?]
(b) How many more strawberry cupcakes than vanilla cupcakes did Mrs Singh bake? [?]", "answer0": "28", "answer1": "42", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 122, "difficulty_id": 2, "explanation": "Strawberry = $$\\frac{4}{7}$$ = 56, so 1 unit ($$\\frac{1}{7}$$) = 56 ÷ 4 = 14. (a) Chocolate = $$\\frac{2}{7}$$ = 2 × 14 = 28. Vanilla = 1 − $$\\frac{2}{7}$$ − $$\\frac{4}{7}$$ = $$\\frac{1}{7}$$ = 14. (b) Strawberry − vanilla = 56 − 14 = 42 (i.e. 3 units × 14).", "hints": [ "Find 1 unit ($$\\frac{1}{7}$$) from the 56 strawberry cupcakes.", "Chocolate is 2 units; vanilla is the leftover 1 unit." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q41", "image_needed": false, "image_options": false, "image_file": null, "notes": "Two parts. Key: (a) 28, (b) 42." }, { "n": 42, "type_id": 2, "question": "Cassie and Eli had some orange juice at first. Cassie gave $$\\frac{3}{4}$$ ℓ of orange juice to Dayan. Eli then gave Cassie $$\\frac{5}{8}$$ ℓ of orange juice. Cassie had $$\\frac{9}{10}$$ ℓ of orange juice in the end. How much orange juice did Cassie have at first? Express your answer as a mixed number. [?]", "answer0": "1 1/40", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 122, "difficulty_id": 3, "explanation": "Before receiving $$\\frac{5}{8}$$ ℓ, Cassie had $$\\frac{9}{10}-\\frac{5}{8}=\\frac{36}{40}-\\frac{25}{40}=\\frac{11}{40}$$ ℓ. Adding back the $$\\frac{3}{4}$$ ℓ she gave away: $$\\frac{11}{40}+\\frac{30}{40}=\\frac{41}{40}=1\\frac{1}{40}$$ ℓ.", "hints": [ "Work backwards from the $$\\frac{9}{10}$$ ℓ she ended with.", "Subtract what she received, then add back what she gave away." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q42", "image_needed": false, "image_options": false, "image_file": null, "notes": "Part (a) only is a value (mixed number). Part (b) is a tick-the-box T/F/NPTT table — an interactive format with no single value answer, omitted from this FIB. Key: (a) = 1 1/40 ℓ. (Key part-b answers: row1 NPTT, row2 T, row3 F.)" }, { "n": 43, "type_id": 2, "question": "There were 76 more belts than caps at first. After 158 belts and 30 caps were sold, there were 3 times as many caps as belts left.
(a) How many belts were there in the end? [?]
(b) How many caps were there at first? [?]", "answer0": "26", "answer1": "108", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 3, "explanation": "Let caps left = c, belts left = b. Belts were 76 more than caps at first; after selling 158 belts and 30 caps, belts left exceed caps left by 76 − 158 + 30 = −52, i.e. caps left are 52 more than belts left. Also caps left = 3 × belts left, so 2 × belts left = 52, belts left = 26. (a) 26 belts in the end. Caps left = 3 × 26 = 78, so caps at first = 78 + 30 = 108. (b) 108 caps at first.", "hints": [ "Compare belts-left and caps-left using the model: the 76 lead changes by the items sold.", "Caps left = 3 × belts left; find belts left first, then work back to caps at first." ], "source": "Nanyang 2024 P4 End-of-Year Exam Q43", "image_needed": false, "image_options": false, "image_file": null, "notes": "Two parts. Key: (a) 26 belts in the end, (b) 108 caps at first (caps left 78 + 30 sold)." } ] }