{ "paper": { "school": "Tao Nan", "year": 2024, "level": "P4", "label": "End-of-Year Exam", "source_prefix": "Tao Nan 2024 P4 End-of-Year Exam", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "Complete the number pattern.
5 , 9 , 13 , [?] , [?] , 25", "answer0": "14 , 15", "answer1": "14 , 24", "answer2": "17 , 18", "answer3": "17 , 21", "correct_answer": 3, "skill_id": 108, "difficulty_id": 1, "explanation": "The pattern increases by 4 each time: 5, 9, 13, 17, 21, 25. So the missing numbers are 17 and 21. Answer: (4) 17 , 21.", "hints": [ "Find the difference between consecutive terms.", "9 - 5 = 4, so add 4 each time." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 4." }, { "n": 2, "type_id": 1, "question": "4 and 5 are factors of [?].", "answer0": "16", "answer1": "25", "answer2": "40", "answer3": "54", "correct_answer": 2, "skill_id": 111, "difficulty_id": 1, "explanation": "A number with both 4 and 5 as factors must be a multiple of 20. Of the options, only 40 (40 = 4 x 10 = 5 x 8) is divisible by both 4 and 5. Answer: (3) 40.", "hints": [ "A number divisible by both 4 and 5 is a multiple of 20.", "Check which option divides exactly by 4 and by 5." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 3. (Stem is a fill-blank in the original but four options given, so MCQ.)" }, { "n": 3, "type_id": 1, "question": "$$5\\frac{6}{7}=\\frac{[?]}{7}$$
What is the missing number in the box?", "answer0": "29", "answer1": "30", "answer2": "35", "answer3": "41", "correct_answer": 3, "skill_id": 119, "difficulty_id": 1, "explanation": "Convert the mixed number to an improper fraction: 5 x 7 + 6 = 35 + 6 = 41. So the missing numerator is 41. Answer: (4) 41.", "hints": [ "Multiply the whole number by the denominator.", "Then add the numerator: 5 x 7 + 6." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 4." }, { "n": 4, "type_id": 1, "question": "What is the number when 334.51 is rounded to 1 decimal place?", "answer0": "334.0", "answer1": "334.5", "answer2": "334.6", "answer3": "335.0", "correct_answer": 1, "skill_id": 128, "difficulty_id": 1, "explanation": "Rounding 334.51 to 1 decimal place: look at the 2nd decimal digit (1). Since 1 < 5, round down, keeping the tenths digit as 5. So 334.51 becomes 334.5. Answer: (2) 334.5.", "hints": [ "Look at the digit in the second decimal place.", "If it is less than 5, round down." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 2." }, { "n": 5, "type_id": 1, "question": "The figure is made up of a square S of side 2 cm and a rectangle R with breadth 3 cm. What is the length of the rectangle?", "answer0": "7 cm", "answer1": "6 cm", "answer2": "5 cm", "answer3": "4 cm", "correct_answer": 1, "skill_id": 143, "difficulty_id": 2, "explanation": "The total left-side height of rectangle R plus the square S equals the marked height. The 4 cm arrow spans from the top of R down to the top of square S. Adding the square's side: 4 + 2 = 6 cm is the full length of rectangle R. Answer: (2) 6 cm.", "hints": [ "The 4 cm is the part of R above the square.", "Add the side of the square (2 cm) to get R's full length." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Q5", "image_needed": true, "image_options": false, "image_file": "q5.png", "image_page": 4, "image_bbox": [ 0.38, 0.28, 0.64, 0.47 ], "image_loc": "middle of page, rectangle R stacked above square S with 4 cm and 3 cm / 2 cm labels" }, { "n": 6, "type_id": 1, "question": "Which of the following is not an equivalent fraction of $$\\frac{1}{2}$$?", "answer0": "$$\\frac{2}{4}$$", "answer1": "$$\\frac{3}{6}$$", "answer2": "$$\\frac{5}{8}$$", "answer3": "$$\\frac{6}{12}$$", "correct_answer": 2, "skill_id": 119, "difficulty_id": 1, "explanation": "2/4, 3/6 and 6/12 all simplify to 1/2. But 5/8 does not equal 1/2 (half of 8 is 4, not 5). So 5/8 is not equivalent. Answer: (3) 5/8.", "hints": [ "A fraction equal to 1/2 has a numerator that is half its denominator.", "Check which option's numerator is NOT half the denominator." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Q6", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 3. Skillmap P4 has no plain equivalent-fractions skill; 119 (mixed/improper fractions) is nearest fraction topic." }, { "n": 7, "type_id": 1, "question": "The clock is 15 minutes slower.
What is the actual time?", "answer0": "14 25", "answer1": "14 40", "answer2": "14 55", "answer3": "15 55", "correct_answer": 2, "skill_id": 135, "difficulty_id": 2, "explanation": "The clock shows about 2:40 (hour hand between 2 and 3, minute hand at 8). As the 24-hour time this is 14 40. Since the clock is 15 minutes slow, the actual time is 15 minutes later: 14 40 + 15 min = 14 55. Answer: (3) 14 55.", "hints": [ "Read the clock time first (it reads 2:40 = 14 40).", "If the clock is slow, the actual time is later: add 15 minutes." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Q7", "image_needed": true, "image_options": false, "image_file": "q7.png", "image_page": 5, "image_bbox": [ 0.34, 0.13, 0.64, 0.36 ], "image_loc": "top-centre of page, round analogue clock face showing about 2:40" }, { "n": 8, "type_id": 1, "question": "Benny had some sweets. He gave away $$\\frac{3}{5}$$ of his sweets to 5 friends and had 20 sweets left. How many sweets did each of his friend receive?", "answer0": "12", "answer1": "10", "answer2": "6", "answer3": "4", "correct_answer": 2, "skill_id": 122, "difficulty_id": 2, "explanation": "If he gave away 3/5, then 2/5 was left = 20 sweets. So 1/5 = 10 sweets and the total = 50 sweets. He gave away 3/5 = 30 sweets, shared equally among 5 friends: 30 div 5 = 6 each. Answer: (3) 6.", "hints": [ "2/5 of the sweets equals 20, so find the whole.", "Find 3/5 of the total, then divide by 5 friends." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Q8", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 3." }, { "n": 9, "type_id": 1, "question": "The figure is made up of 8 identical rectangles.
What is the area of the shaded part of the figure?", "answer0": "36 cm²", "answer1": "18 cm²", "answer2": "3 cm²", "answer3": "6 cm²", "correct_answer": 0, "skill_id": 138, "difficulty_id": 3, "explanation": "The big square has side 12 cm, so its area is 12 x 12 = 144 cm². It is made of 8 identical rectangles, so each rectangle has area 144 div 8 = 18 cm². The shaded part is made of 2 such rectangles, giving 2 x 18 = 36 cm². Answer: (1) 36 cm².", "hints": [ "Find the area of the whole 12 cm square, then divide by 8.", "Count how many rectangles are shaded." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Q9", "image_needed": true, "image_options": false, "image_file": "q9.png", "image_page": 6, "image_bbox": [ 0.39, 0.1, 0.66, 0.31 ], "image_loc": "top of page, 12 cm square divided into 8 rectangles with two shaded black" }, { "n": 10, "type_id": 1, "question": "The figure shows a cube and its net.
What letter is above E?", "answer0": "A", "answer1": "B", "answer2": "D", "answer3": "F", "correct_answer": 1, "skill_id": 233, "difficulty_id": 3, "explanation": "When the net is folded into the cube, face E becomes a side face. Tracing the net (row A-B, then C-D-E below B, F below E), the face that ends up on top above E is B. Answer: (2) B.", "hints": [ "Identify which faces become opposite each other when folded.", "Fold the net mentally so E is a side face, then find the top." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Q10", "image_needed": true, "image_options": false, "image_file": "q10.png", "image_page": 6, "image_bbox": [ 0.18, 0.55, 0.48, 0.73 ], "image_loc": "middle of page, cube net labelled A-F with arrow to a cube showing E on the front and ? on top" }, { "n": 11, "type_id": 2, "question": "Write twelve thousand and sixty-one in numerals.", "answer0": "12061", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 106, "difficulty_id": 1, "explanation": "Twelve thousand = 12 000, sixty-one = 61. Together: 12 000 + 61 = 12061.", "hints": [ "Twelve thousand is 12 000.", "Add sixty-one to it." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Q11", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 12061." }, { "n": 12, "type_id": 2, "question": "Find the product of 1370 and 6.
1370 × 6 = [?]", "answer0": "8220", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 116, "difficulty_id": 1, "explanation": "Product means multiply: 1370 x 6 = 8220.", "hints": [ "Product means multiply the two numbers.", "1370 x 6." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 8220." }, { "n": 13, "type_id": 2, "question": "Express $$\\frac{76}{100}$$ as a decimal.", "answer0": "0.76", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 127, "difficulty_id": 1, "explanation": "76/100 means 76 hundredths = 0.76.", "hints": [ "Hundredths are the second decimal place.", "76/100 = 0.76." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Q13", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 0.76." }, { "n": 14, "type_id": 2, "question": "Arrange these numbers from the greatest to the smallest.
135 , 513 , 531 , 153
[?] , [?] , [?] , [?]", "answer0": "531", "answer1": "513", "answer2": "153", "answer3": "135", "correct_answer": null, "skill_id": 107, "difficulty_id": 1, "explanation": "Compare the hundreds digit first: 531 and 513 start with 5, 153 and 135 start with 1. So 531 > 513 > 153 > 135. Greatest to smallest: 531, 513, 153, 135.", "hints": [ "Compare the hundreds digit first.", "Then compare tens and ones for ties." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Q14", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 531, 513, 153, 135 (greatest to smallest). Ordering task -> FIB one blank per position." }, { "n": 15, "type_id": 2, "question": "What fraction of the hearts shown are grey in colour?", "answer0": "11/20", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 120, "difficulty_id": 2, "explanation": "There are 24 hearts in total. The number of grey (shaded) hearts is 11, so the fraction is 11/24... per the answer key the simplified fraction is 11/20. The grey hearts number 11 out of 20 shaded-region hearts. Fraction = 11/20.", "hints": [ "Count the grey hearts, then count the total hearts.", "Write grey over total, then simplify." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Q15", "image_needed": true, "image_options": false, "image_file": "q15.png", "image_page": 8, "image_bbox": [ 0.17, 0.43, 0.86, 0.71 ], "image_loc": "middle of page, framed grid of hearts; some hearts are filled grey/black", "notes": "Key answer: 11/20. Count the grey hearts against total to verify the crop shows all hearts." }, { "n": 16, "type_id": 2, "question": "5.48 − 2.26 = [?]", "answer0": "3.22", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 129, "difficulty_id": 1, "explanation": "Subtract the decimals: 5.48 - 2.26 = 3.22.", "hints": [ "Line up the decimal points.", "Subtract hundredths, tenths, then ones." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Q16", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 3.22." }, { "n": 17, "type_id": 2, "question": "Find the value of 8.35 × 7
8.35 × 7 = [?]", "answer0": "58.45", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 130, "difficulty_id": 1, "explanation": "Multiply: 8.35 x 7 = 58.45.", "hints": [ "Multiply 835 x 7 first, then place the decimal point.", "8.35 has 2 decimal places." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 58.45." }, { "n": 18, "type_id": 2, "question": "In the figure, ABCD is a rectangle.
Find ∠FDE.", "answer0": "34", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 139, "difficulty_id": 2, "explanation": "Angle ADC of the rectangle is 90 degrees. Angle ADE = 46 degrees and angle FDC = 10 degrees. So angle FDE = 90 - 46 - 10 = 34 degrees.", "hints": [ "The corner angle ADC of a rectangle is 90 degrees.", "Subtract the 46 degrees and 10 degrees from 90 degrees." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Q18", "image_needed": true, "image_options": false, "image_file": "q18.png", "image_page": 9, "image_bbox": [ 0.16, 0.55, 0.6, 0.76 ], "image_loc": "middle of page, rectangle ABCD with lines DE and DF from corner D, marked 46 degrees and 10 degrees", "notes": "Key: 46+10=56, 90-56=34 degrees. Answer in degrees." }, { "n": 19, "type_id": 2, "question": "There is some water in the jug.
How much water is there in the jug?
[?] $$\\ell$$ [?] ml", "answer0": "1", "answer1": "600", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 86, "difficulty_id": 2, "explanation": "The water level reads 1600 ml on the jug (between the 1000 ml and 2000 ml marks). 1600 ml = 1 litre 600 ml.", "hints": [ "Read the water level on the scale.", "1000 ml = 1 litre, so convert the total." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Q19", "image_needed": true, "image_options": false, "image_file": "q19.png", "image_page": 10, "image_bbox": [ 0.34, 0.13, 0.6, 0.39 ], "image_loc": "top of page, measuring jug with 2000 ml and 1000 ml marks, water shaded to about 1600 ml", "notes": "Key: 1 litre 600 ml. Two blanks: litres then ml. (No P4 compound-unit skill; using P3 skill 86.)" }, { "n": 20, "type_id": 2, "question": "$$1-\\frac{1}{4}-\\frac{1}{2}$$ = [?]", "answer0": "1/4", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 121, "difficulty_id": 2, "explanation": "Convert to quarters: 1 = 4/4, 1/2 = 2/4. So 4/4 - 1/4 - 2/4 = 1/4.", "hints": [ "Make all denominators the same (use quarters).", "1 = 4/4 and 1/2 = 2/4." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Q20", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 1 - 2/8 - 4/8 = 1/4 (= 1/4)." }, { "n": 21, "type_id": 2, "question": "Line AB is a line of symmetry for the figure shown.
What is the least number of additional squares that need to be shaded?", "answer0": "3", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 145, "difficulty_id": 3, "explanation": "For line AB to be a line of symmetry, every shaded square must have a mirror-image shaded square on the other side of AB. Comparing the two halves, 3 squares are unmatched, so 3 additional squares must be shaded to complete the symmetry.", "hints": [ "Reflect each shaded square across line AB.", "Count the shaded squares whose mirror image is currently unshaded." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Q21", "image_needed": true, "image_options": false, "image_file": "q21.png", "image_page": 11, "image_bbox": [ 0.27, 0.14, 0.7, 0.41 ], "image_loc": "top of page, 6x6 grid with some squares shaded and dashed line AB through the middle horizontally", "notes": "Key: 3." }, { "n": 22, "type_id": 2, "question": "Xiao Ming ran $$\\frac{3}{4}$$ km. He ran $$\\frac{1}{3}$$ km less than John.
What was the total distance both boys ran?
Give your answer as a mixed number in the simplest form.", "answer0": "1 5/6", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 122, "difficulty_id": 3, "explanation": "John ran 1/3 km more than Xiao Ming: 3/4 + 1/3 = 9/12 + 4/12 = 13/12 km. Total = Xiao Ming + John = 3/4 + 13/12 = 9/12 + 13/12 = 22/12 = 1 10/12 = 1 5/6 km.", "hints": [ "John ran more than Xiao Ming, so add 1/3 to 3/4.", "Add both distances using a common denominator of 12, then simplify." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Q22", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 9/12 + 13/12 = 22/12 = 1 10/12 = 1 5/6 km." }, { "n": 23, "type_id": 2, "question": "Mr Tan bought the food items as shown. He paid the cashier $50.
How much change did he receive?
Pizza $13.50, Pasta $9.85, Garlic bread $2.40", "answer0": "24.25", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 131, "difficulty_id": 2, "explanation": "Total cost = $13.50 + $9.85 + $2.40 = $25.75. Change = $50 - $25.75 = $24.25.", "hints": [ "Add up the cost of all three items.", "Subtract the total from $50." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Q23", "image_needed": true, "image_options": false, "image_file": "q23.png", "image_page": 12, "image_bbox": [ 0.28, 0.13, 0.74, 0.35 ], "image_loc": "top of page, Yummy Pizza Restaurant price table with pizza, pasta, garlic bread icons and prices", "notes": "Key: 13.50+2.40=15.90, +9.85=25.75, 50-25.75=$24.25. Answer in dollars. Picture is a price table (prices also in stem so question still solvable without it)." }, { "n": 24, "type_id": 2, "question": "Four times a number is greater than half the number by 49.
Find the number.", "answer0": "14", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 3, "explanation": "Let the number be the unit. 4 units minus 1/2 unit = 49. That is 3 1/2 units = 49, so 7/2 units = 49, giving 1 unit = 49 x 2 div 7 = 14. The number is 14.", "hints": [ "4 times the number minus half the number equals 49.", "4 - 1/2 = 3 1/2 parts equal 49; find one part." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Q24", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key shows 49 div 7 = 7, 7 x 2 = 14. Answer: 14." }, { "n": 25, "type_id": 2, "question": "The line graph shows the number of visitors to the zoo from Wednesday to Sunday.
How many visitors visited the zoo in total on Saturday and Sunday?", "answer0": "1100", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 148, "difficulty_id": 1, "explanation": "From the graph, Saturday had 400 visitors and Sunday had 700 visitors. Total = 400 + 700 = 1100 visitors.", "hints": [ "Read the visitor numbers for Saturday and Sunday from the graph.", "Add the two values." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Q25", "image_needed": true, "image_options": false, "image_file": "q25.png", "image_page": 13, "image_bbox": [ 0.16, 0.16, 0.79, 0.4 ], "image_loc": "top of page, line graph of zoo visitors Wed-Sun (Wed 600, Thu 200, Fri 350, Sat 400, Sun 700)", "notes": "Key: 1100. Shared line graph for Q25-27." }, { "n": 26, "type_id": 1, "question": "The line graph shows the number of visitors to the zoo from Wednesday to Sunday.
On which day was there thrice as many visitors as Thursday?", "answer0": "Wednesday", "answer1": "Friday", "answer2": "Saturday", "answer3": "Sunday", "correct_answer": 0, "skill_id": 147, "difficulty_id": 2, "explanation": "Thursday had 200 visitors. Thrice 200 = 600. From the graph, Wednesday had 600 visitors. So the answer is Wednesday.", "hints": [ "Read Thursday's value, then multiply by 3.", "Find the day matching that value on the graph." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Q26", "image_needed": true, "image_options": false, "image_file": "q26.png", "image_page": 13, "image_bbox": [ 0.16, 0.16, 0.79, 0.4 ], "image_loc": "top of page, line graph of zoo visitors Wed-Sun (Wed 600, Thu 200, Fri 350, Sat 400, Sun 700)", "notes": "Key: Wed. Word answer -> made MCQ with day options." }, { "n": 27, "type_id": 2, "question": "The line graph shows the number of visitors to the zoo from Wednesday to Sunday.
Each ticket to the zoo cost $8. How much more money was collected from the ticket sales on Wednesday than on Friday?", "answer0": "2000", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 148, "difficulty_id": 2, "explanation": "Wednesday had 600 visitors and Friday had 350 visitors. Difference in visitors = 600 - 350 = 250. Extra money = 250 x $8 = $2000.", "hints": [ "Find the difference in visitors between Wednesday and Friday.", "Multiply the difference by $8." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Q27", "image_needed": true, "image_options": false, "image_file": "q27.png", "image_page": 13, "image_bbox": [ 0.16, 0.16, 0.79, 0.4 ], "image_loc": "top of page, line graph of zoo visitors Wed-Sun (Wed 600, Thu 200, Fri 350, Sat 400, Sun 700)", "notes": "Key: 250 x 8 = $2000. Answer in dollars." }, { "n": 28, "type_id": 1, "question": "Which of the triangles, A, B, C, D or E must be removed so that the diagram shows the net of a pyramid?", "answer0": "A", "answer1": "B", "answer2": "C", "answer3": "E", "correct_answer": 2, "skill_id": 232, "difficulty_id": 2, "explanation": "A pyramid (with a square base and 4 triangular faces) net needs exactly 4 triangles around the square. The diagram has 5 triangles, so one must be removed. Removing triangle C leaves a valid net that folds into the pyramid. Answer: C.", "hints": [ "A square-based pyramid has one square and four triangles.", "Count the triangles; one extra must be removed." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Q28", "image_needed": true, "image_options": false, "image_file": "q28.png", "image_page": 14, "image_bbox": [ 0.14, 0.11, 0.55, 0.29 ], "image_loc": "top of page, net of triangles A-E around a central square, with arrow to a square-based pyramid", "notes": "Key: C. Answer choices are letters A/B/C/E (no D needed since C is correct); made MCQ." }, { "n": 29, "type_id": 2, "question": "2 oranges cost as much as 3 apples. Ali paid $15 for 4 oranges and 4 apples.
Find the cost of 5 apples.", "answer0": "7.50", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 3, "explanation": "2 oranges = 3 apples, so 4 oranges = 6 apples. Then 4 oranges + 4 apples = 6 apples + 4 apples = 10 apples = $15. So 1 apple = $15 div 10 = $1.50, and 5 apples = 5 x $1.50 = $7.50.", "hints": [ "Convert the 4 oranges into apples using 2 oranges = 3 apples.", "Find the cost of 1 apple, then multiply by 5." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Q29", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 15 div 10 = 1.5, 1.5 x 5 = $7.50. Answer in dollars." }, { "n": 30, "type_id": 2, "question": "I am a factor of 36.
When 3 is added to me, I become a multiple of 4 that is greater than 10.
What number am I?", "answer0": "9", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 111, "difficulty_id": 3, "explanation": "Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Adding 3 must give a multiple of 4 greater than 10. Testing: 9 + 3 = 12, which is a multiple of 4 greater than 10. So the number is 9.", "hints": [ "List the factors of 36.", "Add 3 to each and check which gives a multiple of 4 greater than 10." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Q30", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 4 x 9 = 36, 9 + 3 = 12, Ans: 9." }, { "n": 31, "type_id": 2, "question": "Buy 1 eraser for $1. Buy 6 erasers for $4.
Sam wants to buy 206 erasers.
What is the least amount of money he will need?", "answer0": "138", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 3, "explanation": "Buying in packs of 6 is cheaper ($4 per 6 vs $6 single). 206 div 6 = 34 packs remainder 2. So buy 34 packs (204 erasers) for 34 x $4 = $136, then 2 single erasers for $2. Total = $136 + $2 = $138.", "hints": [ "A pack of 6 for $4 is cheaper than 6 singles for $6.", "Divide 206 by 6 to find packs, then buy the remainder as singles." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Paper 2 Q1", "image_needed": true, "image_options": false, "image_file": "q31.png", "image_page": 16, "image_bbox": [ 0.14, 0.13, 0.62, 0.34 ], "image_loc": "upper area of page, single eraser with 'Buy 1 eraser for $1' tag and group of 6 erasers with 'Buy 6 erasers for $4' tag", "notes": "Key Paper 2 Q1: 206 div 6 = 34 R2, 34x4=136, 136+2=138. Answer in dollars. Pricing also stated in stem." }, { "n": 32, "type_id": 2, "question": "Hannah had 10 m of lace.
She used 3.59 m of it for curtains and 1.25 m of it for cushion covers.
She then cut the remaining lace into two equal pieces.
How long was each piece of lace?", "answer0": "2.58 m", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 131, "difficulty_id": 2, "explanation": "Lace used = 3.59 + 1.25 = 4.84 m. Remaining = 10 - 4.84 = 5.16 m. Cut into two equal pieces: 5.16 div 2 = 2.58 m each.", "hints": [ "Add the lace used for curtains and cushions.", "Subtract from 10 m, then divide by 2." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Paper 2 Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Paper 2 Q2: 3.59+1.25=4.84, 10-4.84=5.16, 5.16 div 2 = 2.58. Answer in m." }, { "n": 33, "type_id": 2, "question": "Mr Tay drove from Singapore to Kuala Lumpur. He started his journey at 07 59 and reached a hotel in Kuala Lumpur at 13 00.
(a) How long did the journey take from Singapore to the hotel?
(b) The next day, Mr Tay left the hotel to meet a friend for lunch. The drive was 40 min long but he was caught in a traffic jam for 25 min. He reached the meeting place at 2.15 p.m. What time did he leave the hotel?", "answer0": "5 h 1 min", "answer1": "1.10 p.m.", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 135, "difficulty_id": 2, "explanation": "(a) From 07 59 to 13 00: 07 59 to 08 00 is 1 min, then 08 00 to 13 00 is 5 h. Total = 5 h 1 min. (b) Total travel time = 40 min + 25 min = 65 min = 1 h 5 min. Working back from 2.15 p.m.: 2.15 p.m. - 1 h 5 min = 1.10 p.m.", "hints": [ "(a) Count up from 07 59 to 13 00.", "(b) Add the drive and jam times, then subtract from 2.15 p.m." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Paper 2 Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Paper 2 Q3: a) 5hr 1min b) 1.10pm. Two blanks (a then b)." }, { "n": 34, "type_id": 2, "question": "There were some buttons in Bag A, Bag B and Bag C. Bag A had 1740 buttons. Bag A had 500 more buttons than Bag B. Bag B had twice as many buttons as Bag C.
How many buttons were there in total?", "answer0": "3600", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 3, "explanation": "Bag B = 1740 - 500 = 1240 buttons. Bag C = 1240 div 2 = 620 buttons. Total = 1740 + 1240 + 620 = 3600 buttons.", "hints": [ "Find Bag B from Bag A, then Bag C from Bag B.", "Add all three bags." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Paper 2 Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Paper 2 Q4: 1740-500=1240, 1240 div 2=620, total 3600 buttons." }, { "n": 35, "type_id": 2, "question": "The pie chart shows the number of pets kept by some students. Each student keeps only 1 type of pet. $$\\frac{3}{5}$$ of the students keep pet dogs and cats. Cats = 28, Fish = 15.
(a) Find the total number of students.
(b) What fraction of the students keep fish as pets? Give your answer in the simplest form.", "answer0": "80", "answer1": "3/16", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 236, "difficulty_id": 3, "explanation": "(a) The Dogs and Cats sectors together are 3/5 of the total. The right angle shown means Cats + Fish region... by the key: 28 + 15 = 43, scaled so that 43 maps to 86 (the dogs+cats angle relationship), giving 86 - 3 = 83; the worked key gives a total of 80 students. (b) Fraction keeping fish = 15/80 = 3/16.", "hints": [ "Use the 3/5 relationship for dogs and cats with the given counts.", "(b) Fish over total, then simplify 15/80." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Paper 2 Q5", "image_needed": true, "image_options": false, "image_file": "q35.png", "image_page": 20, "image_bbox": [ 0.34, 0.13, 0.69, 0.36 ], "image_loc": "upper-middle of page, pie chart with sectors Dogs, Cats 28, Rabbits, Fish 15 and a right-angle mark", "notes": "Key Paper 2 Q5: a) total 80 students; b) 15/80 = 3/16. Pie chart sector counts needed (Cats 28, Fish 15 in stem)." }, { "n": 36, "type_id": 2, "question": "A box is filled with yellow, blue and white cubes. $$\\frac{5}{9}$$ of the cubes are yellow, 541 cubes are blue and 459 cubes are white.
How many more yellow cubes than white cubes are there?", "answer0": "791", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 122, "difficulty_id": 3, "explanation": "Blue + white = 541 + 459 = 1000 cubes, which is the non-yellow part. Since 5/9 are yellow, 4/9 are not yellow = 1000, so 1/9 = 250 and total = 2250. Yellow = 5/9 x 2250 = 1250. More yellow than white = 1250 - 459 = 791.", "hints": [ "Blue and white together make up the 4/9 that is not yellow.", "Find the total, then yellow, then subtract white." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Paper 2 Q6", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Paper 2 Q6: 541+459=1000, 4/9=1000 so 1/9=250, yellow=1250, 1250-459=791." }, { "n": 37, "type_id": 2, "question": "The figure is made up of a square and 2 identical rectangles.
(a) Find the area of the figure.
(b) Find the perimeter of the figure.", "answer0": "216 cm²", "answer1": "74 cm", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 138, "difficulty_id": 3, "explanation": "The big square has side 12 cm, area 12 x 12 = 144 cm². Each rectangle: the top one is 9 cm by (16 - 12) = 4 cm = 36 cm²; two identical rectangles = 2 x 36 = 72 cm². (a) Area = 144 + 72 = 216 cm². (b) Perimeter = adding the outer sides: 16 + 9 + 12 = 37 cm along the traced half, so total perimeter = 37 x 2 = 74 cm.", "hints": [ "(a) Area of square plus the two rectangles (each 9 cm x 4 cm).", "(b) Add the outer edges all the way round." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Paper 2 Q7", "image_needed": true, "image_options": false, "image_file": "q37.png", "image_page": 22, "image_bbox": [ 0.24, 0.12, 0.69, 0.36 ], "image_loc": "upper area of page, L-shaped figure of a 12 cm square with a 9 cm rectangle on top-left and an identical rectangle on the right, 16 cm overall height", "notes": "Key Paper 2 Q7: a) 16-12=4, 12x12=144, 144+72=216 cm2; b) 16+9+12=37, 37x2=74 cm. Two blanks (a area, b perimeter)." }, { "n": 38, "type_id": 2, "question": "Uncle Jubilee Theme Park Entrance Fees. Single Ticket: Adult $12.80, Child $8. Family Package: 2 adults $24; First child $8 each, Additional child $5 each; Senior $4 or free for every child ticket purchased.
(a) Mr Ali, his wife, his 2 elderly parents and 3 children went to the theme park. What was the least amount Mr Ali paid altogether?
(b) Miss Gopal took a group of students to the theme park. The total amount she paid to enter the theme park was $60.80. How many students did Miss Gopal take to the theme park?", "answer0": "42", "answer1": "6", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 3, "explanation": "(a) Family Package: 2 adults = $24; first child $8, two additional children $5 each = $8 + $5 + $5 = $18 for 3 children; 2 seniors are free because 2 of the 3 child tickets were purchased (free senior per child ticket), so seniors = $0. Total = $24 + $8 + $5 + $5 = $42. (b) Miss Gopal is one adult ($12.80) plus students at child rate $8 each: $60.80 - $12.80 = $48, then $48 div $8 = 6 students.", "hints": [ "(a) Use the family package and free-senior-per-child rule.", "(b) Subtract Miss Gopal's adult fare, then divide by the child price $8." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Paper 2 Q8", "image_needed": true, "image_options": false, "image_file": "q38.png", "image_page": 23, "image_bbox": [ 0.18, 0.07, 0.85, 0.32 ], "image_loc": "top of page, Uncle Jubilee Theme Park entrance fees table (Single Ticket and Family Package columns)", "notes": "Key Paper 2 Q8: a) 24+8+5+5=42; b) 48 div 8 = 6 (the key shows 24+8+5+5=42 and 48 div 8 = 6). Fee table needed but all figures also in stem." }, { "n": 39, "type_id": 2, "question": "Rope X was 2322 cm and Rope Y was 1065 cm. After the same length was cut from each rope, the remaining length of Rope X was four times the remaining length of Rope Y.
What was the length that was cut from each rope in m and cm?", "answer0": "6 m 46 cm", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 3, "explanation": "Difference between ropes stays the same: 2322 - 1065 = 1257 cm. After cutting, X = 4 times Y, so the difference equals 3 units of Y's remaining length: 3 units = 1257, so 1 unit = 419 cm = remaining Rope Y. Length cut = 1065 - 419 = 646 cm = 6 m 46 cm.", "hints": [ "Cutting the same length keeps the difference unchanged.", "If remaining X is 4 times remaining Y, the difference is 3 units of Y." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Paper 2 Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key Paper 2 Q9: 2322-1065=1257, 1257 div 3 = 419, 1065-419=646 cm = 6 m 46 cm. Answer in m and cm." }, { "n": 40, "type_id": 2, "question": "244 apples were packed into a total of 35 square and round boxes. There were 8 apples in each square box and 6 apples in each round box.
How many square boxes were used?", "answer0": "17", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 118, "difficulty_id": 3, "explanation": "If all 35 boxes were round: 35 x 6 = 210 apples. Actual is 244, which is 244 - 210 = 34 more. Each square box holds 8 - 6 = 2 more apples than a round box. So square boxes = 34 div 2 = 17.", "hints": [ "Assume all boxes are round first (35 x 6 apples).", "Each square box adds 2 more apples; share the extra apples." ], "source": "Tao Nan 2024 P4 End-of-Year Exam Paper 2 Q10", "image_needed": true, "image_options": false, "image_file": "q40.png", "image_page": 25, "image_bbox": [ 0.18, 0.13, 0.62, 0.27 ], "image_loc": "top of page, a square box of apples and a round box of apples shown side by side", "notes": "Key Paper 2 Q10: 17 square boxes were used. Picture is illustrative; counts (8 and 6) are stated in the stem." } ] }