{ "paper": { "school": "Pei Chun", "year": 2024, "level": "P5", "label": "End-of-Year Exam", "source_prefix": "Pei Chun 2024 P5 End-of-Year Exam", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "What is the value of the digit 7 in 70 489?", "answer0": "7", "answer1": "70", "answer2": "7000", "answer3": "70 000", "correct_answer": 3, "skill_id": 149, "difficulty_id": 1, "explanation": "The digit 7 is in the ten-thousands place. Its value = 7 × 10 000 = 70 000.", "hints": ["Identify which place the digit 7 sits in.", "70 489: the 7 is in the ten-thousands column."], "source": "Pei Chun 2024 P5 End-of-Year Exam Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 4 (70 000)." }, { "n": 2, "type_id": 1, "question": "What is the missing number?
\\(\\dfrac{8}{12} = \\dfrac{2}{[\\,?\\,]}\\)", "answer0": "8", "answer1": "6", "answer2": "3", "answer3": "4", "correct_answer": 2, "skill_id": 158, "difficulty_id": 1, "explanation": "Simplify \\(\\dfrac{8}{12}\\): divide numerator and denominator by 4 → \\(\\dfrac{2}{3}\\). The missing denominator is 3.", "hints": ["Simplify \\(\\dfrac{8}{12}\\) to a numerator of 2.", "8 ÷ 4 = 2, so 12 ÷ 4 = 3."], "source": "Pei Chun 2024 P5 End-of-Year Exam Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 3 (value 3). Stem uses [?] inside the equivalent-fraction display as part of the printed figure, not an answer blank (this is MCQ)." }, { "n": 3, "type_id": 1, "question": "In 4.312, which digit is in the tenths place?", "answer0": "1", "answer1": "2", "answer2": "3", "answer3": "4", "correct_answer": 2, "skill_id": 158, "difficulty_id": 1, "explanation": "The first digit after the decimal point is the tenths place. In 4.312 that digit is 3.", "hints": ["The tenths place is immediately after the decimal point.", "4.312 → tenths = 3, hundredths = 1, thousandths = 2."], "source": "Pei Chun 2024 P5 End-of-Year Exam Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 3 (digit 3)." }, { "n": 4, "type_id": 1, "question": "How much water is in the container?", "answer0": "150 ml", "answer1": "200 ml", "answer2": "250 ml", "answer3": "300 ml", "correct_answer": 3, "skill_id": 192, "difficulty_id": 2, "explanation": "The beaker is marked to 1 litre with 5 large divisions (each 200 ml). The water level reaches the shaded mark at 300 ml.", "hints": ["Read the scale on the 1 ℓ beaker.", "The water reaches the shaded line; key gives 300 ml."], "source": "Pei Chun 2024 P5 End-of-Year Exam Q4", "image_needed": true, "image_options": false, "image_file": "q4.png", "image_page": 4, "image_bbox": [0.52, 0.07, 0.66, 0.20], "image_loc": "right of the question text, a beaker labelled 1 litre with water shaded near the bottom", "notes": "Key: option 4 (300 ml)." }, { "n": 5, "type_id": 1, "question": "Mdm Aisyah baked 200 cupcakes. She gave 70 cupcakes to her neighbour. What percentage of the cupcakes did she give to her neighbour?", "answer0": "30%", "answer1": "35%", "answer2": "65%", "answer3": "70%", "correct_answer": 1, "skill_id": 171, "difficulty_id": 1, "explanation": "Percentage = \\(\\dfrac{70}{200} \\times 100\\% = 35\\%\\).", "hints": ["Express 70 out of 200 as a fraction.", "\\(\\dfrac{70}{200}\\times100\\% = 35\\%\\)."], "source": "Pei Chun 2024 P5 End-of-Year Exam Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 2 (35%)." }, { "n": 6, "type_id": 1, "question": "The figure shows triangle JKL. Given the base LK, which of the following is its corresponding height?", "answer0": "JK", "answer1": "JM", "answer2": "LJ", "answer3": "NK", "correct_answer": 3, "skill_id": 186, "difficulty_id": 2, "explanation": "The height corresponding to base LK is the perpendicular line from the opposite vertex J to line LK. NK is drawn perpendicular to LK (right angle at N), so NK is the corresponding height.", "hints": ["The height must be perpendicular to the chosen base LK.", "Look for the right-angle mark — NK meets LK at a right angle."], "source": "Pei Chun 2024 P5 End-of-Year Exam Q6", "image_needed": true, "image_options": false, "image_file": "q6.png", "image_page": 4, "image_bbox": [0.2, 0.5, 0.68, 0.68], "image_loc": "triangle JKL with vertex J top-right, base L--K, N on LJ with a right-angle mark, dashed lines to K and M", "notes": "Key: option 4 (NK)." }, { "n": 7, "type_id": 1, "question": "The table shows the temperatures of cities A, B, C and D.
City A: lowest 9°C, highest 19°C.
City B: lowest 14°C, highest 21°C.
City C: lowest 17°C, highest 31°C.
City D: lowest 4°C, highest 26°C.
When Faizal was at some of these cities, the temperature was 10°C. Name the cities.", "answer0": "A and D", "answer1": "B and D", "answer2": "B and C", "answer3": "C and D", "correct_answer": 0, "skill_id": 147, "difficulty_id": 2, "explanation": "10°C must lie between a city's lowest and highest temperature. A: 9 to 19 (yes). D: 4 to 26 (yes). B: 14 to 21 (no, 10 < 14). C: 17 to 31 (no). So the cities are A and D.", "hints": ["10°C must be between the lowest and highest of a city.", "Check each range: only A (9–19) and D (4–26) include 10."], "source": "Pei Chun 2024 P5 End-of-Year Exam Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 1 (A and D). Table transcribed into the stem as text." }, { "n": 8, "type_id": 1, "question": "Which line in the square grid is parallel to AF?", "answer0": "AB", "answer1": "BE", "answer2": "CD", "answer3": "EF", "correct_answer": 2, "skill_id": 100, "difficulty_id": 2, "explanation": "AF has a particular slope on the grid. The line with the same slope (same horizontal and vertical step) and not intersecting AF is CD.", "hints": ["Parallel lines have the same slant on the grid.", "Compare the grid steps of AF with each option; CD matches."], "source": "Pei Chun 2024 P5 End-of-Year Exam Q8", "image_needed": true, "image_options": false, "image_file": "q8.png", "image_page": 5, "image_bbox": [0.24, 0.45, 0.62, 0.66], "image_loc": "square grid with points A, B, C, D, E, F joined into a tilted shape", "notes": "Key: option 3 (CD)." }, { "n": 9, "type_id": 1, "question": "Which fraction is greater than \\(\\dfrac{1}{2}\\)?", "answer0": "\\(\\dfrac{4}{9}\\)", "answer1": "\\(\\dfrac{4}{7}\\)", "answer2": "\\(\\dfrac{3}{8}\\)", "answer3": "\\(\\dfrac{3}{10}\\)", "correct_answer": 1, "skill_id": 159, "difficulty_id": 1, "explanation": "Half of each denominator: \\(\\dfrac{4}{9}\\) (half is 4.5, 4<4.5, less), \\(\\dfrac{4}{7}\\) (half is 3.5, 4>3.5, greater), \\(\\dfrac{3}{8}\\) (half is 4, 3<4, less), \\(\\dfrac{3}{10}\\) (half is 5, less). Only \\(\\dfrac{4}{7}>\\dfrac{1}{2}\\).", "hints": ["A fraction exceeds 1/2 when the numerator is more than half the denominator.", "\\(\\dfrac{4}{7}\\): half of 7 is 3.5, and 4 > 3.5."], "source": "Pei Chun 2024 P5 End-of-Year Exam Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 2 (4/7). Fraction options rendered inline." }, { "n": 10, "type_id": 1, "question": "AB and CD are straight lines. Find \\(\\angle e\\).", "answer0": "43°", "answer1": "44°", "answer2": "46°", "answer3": "49°", "correct_answer": 3, "skill_id": 194, "difficulty_id": 2, "explanation": "Angles on straight line CD at the point sum to 180°: 87° + 44° + \\(\\angle e\\) = 180°. So \\(\\angle e\\) = 180° − 87° − 44° = 49°.", "hints": ["The three angles 87°, e and 44° lie on straight line CD.", "180° − 87° − 44° = 49°."], "source": "Pei Chun 2024 P5 End-of-Year Exam Q10", "image_needed": true, "image_options": false, "image_file": "q10.png", "image_page": 6, "image_bbox": [0.3, 0.34, 0.55, 0.52], "image_loc": "two crossing straight lines AB and CD with 87° at top, e and 44° below", "notes": "Key: option 4 (49°)." }, { "n": 11, "type_id": 1, "question": "Mandy bought a roll of ribbon and used 0.75 m. She cut the remaining ribbon into 10 equal pieces, each 25 cm long. What was the length of the ribbon at first?", "answer0": "1 m", "answer1": "2.5 m", "answer2": "3.25 m", "answer3": "25.75 m", "correct_answer": 2, "skill_id": 167, "difficulty_id": 2, "explanation": "Remaining = 10 × 25 cm = 250 cm = 2.5 m. At first = 2.5 m + 0.75 m = 3.25 m.", "hints": ["Find the remaining length: 10 pieces × 25 cm.", "250 cm = 2.5 m; add the 0.75 m used → 3.25 m."], "source": "Pei Chun 2024 P5 End-of-Year Exam Q11", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 3 (3.25 m)." }, { "n": 12, "type_id": 1, "question": "The ratio of Emily's age to her sister's age is 1 : 3. In 4 years' time, their total age will be 36 years old. What is Emily's age now?", "answer0": "5 years old", "answer1": "7 years old", "answer2": "8 years old", "answer3": "9 years old", "correct_answer": 1, "skill_id": 183, "difficulty_id": 3, "explanation": "In 4 years their total age = 36, so total now = 36 − 4 − 4 = 28. Now the ratio is 1 : 3 (4 units = 28), 1 unit = 7. Emily's age now = 1 unit = 7 years old.", "hints": ["Subtract the 4 years each will gain from the future total of 36.", "Total now = 28; 4 units = 28 so 1 unit = 7; Emily = 1 unit."], "source": "Pei Chun 2024 P5 End-of-Year Exam Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 2 (7 years old)." }, { "n": 13, "type_id": 1, "question": "The average of 4 numbers is 99. The sum of the first 3 numbers is 315. What is the fourth number?", "answer0": "6", "answer1": "81", "answer2": "105", "answer3": "216", "correct_answer": 1, "skill_id": 203, "difficulty_id": 2, "explanation": "Total of 4 numbers = 99 × 4 = 396. Fourth number = 396 − 315 = 81.", "hints": ["Total = average × number of items = 99 × 4.", "396 − 315 = 81."], "source": "Pei Chun 2024 P5 End-of-Year Exam Q13", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 2 (81)." }, { "n": 14, "type_id": 1, "question": "Farmer Lee had some apples and oranges. He sold \\(\\dfrac{1}{3}\\) of the apples and \\(\\dfrac{1}{6}\\) of the oranges. \\(\\dfrac{3}{7}\\) of the fruits sold were oranges. What fraction of the fruits were sold?", "answer0": "\\(\\dfrac{1}{2}\\)", "answer1": "\\(\\dfrac{7}{30}\\)", "answer2": "\\(\\dfrac{23}{30}\\)", "answer3": "\\(\\dfrac{7}{33}\\)", "correct_answer": 1, "skill_id": 165, "difficulty_id": 3, "explanation": "Of the fruits sold, oranges are 3/7 and apples are 4/7. Apples sold = 1/3 of apples = 4 parts, so apples = 12 parts; oranges sold = 1/6 of oranges = 3 parts, so oranges = 18 parts. Total fruit = 12 + 18 = 30 parts; total sold = 4 + 3 = 7 parts. Fraction sold = \\(\\dfrac{7}{30}\\).", "hints": ["Let the fruits sold be split 4 (apples) : 3 (oranges) since 3/7 are oranges.", "Apples = 3 × 4 = 12 parts, oranges = 6 × 3 = 18 parts; sold 7 of 30."], "source": "Pei Chun 2024 P5 End-of-Year Exam Q14", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 2 (7/30). Fraction options rendered inline." }, { "n": 15, "type_id": 1, "question": "John went to a bookshop to buy some stickers. For every 35 stickers that John paid for at the bookshop, he received 5 free stickers. John left the bookshop with 520 stickers. What was the least number of stickers he paid for?", "answer0": "13", "answer1": "65", "answer2": "455", "answer3": "507", "correct_answer": 2, "skill_id": 152, "difficulty_id": 3, "explanation": "Each group = 35 paid + 5 free = 40 stickers. 520 ÷ 40 = 13 complete groups. Paid = 13 × 35 = 455.", "hints": ["Each set of 40 stickers (35 paid + 5 free) repeats.", "520 ÷ 40 = 13 groups; paid = 13 × 35 = 455."], "source": "Pei Chun 2024 P5 End-of-Year Exam Q15", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 3 (455)." }, { "n": 16, "type_id": 2, "question": "Find the largest multiple of 8 that is smaller than 60. [?]", "answer0": "56", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 151, "difficulty_id": 1, "explanation": "Multiples of 8: 48, 56, 64. The largest one below 60 is 56.", "hints": ["List multiples of 8 near 60.", "8 × 7 = 56 (8 × 8 = 64 is too big)."], "source": "Pei Chun 2024 P5 End-of-Year Exam Q16", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 56." }, { "n": 17, "type_id": 2, "question": "Find \\(\\angle m\\) in the figure shown. [?]", "answer0": "157", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 194, "difficulty_id": 2, "explanation": "Angles at a point sum to 360°. \\(\\angle m\\) = 360° − 140° − 63° = 157°.", "hints": ["The angles around the point add up to 360°.", "360° − 140° − 63° = 157°."], "source": "Pei Chun 2024 P5 End-of-Year Exam Q17", "image_needed": true, "image_options": false, "image_file": "q17.png", "image_page": 10, "image_bbox": [0.22, 0.32, 0.52, 0.45], "image_loc": "two lines meeting with marked angles 140° and 63° above, m below", "notes": "Answer in degrees. Key: 157 (360 − 140 − 63)." }, { "n": 18, "type_id": 2, "question": "Round 3.785 to 2 decimal places. [?]", "answer0": "3.79", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 168, "difficulty_id": 1, "explanation": "The 3rd decimal digit is 5, so round up the 2nd decimal: 3.785 → 3.79.", "hints": ["Look at the thousandths digit to decide rounding.", "The digit is 5 → round the hundredths place up: 3.79."], "source": "Pei Chun 2024 P5 End-of-Year Exam Q18", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 3.79." }, { "n": 19, "type_id": 2, "question": "Tim cleaned his room from 9.30 a.m. to 11.15 a.m. How much time did Tim spend cleaning his room? Give your answer in h and min.
[?] h [?] min", "answer0": "1", "answer1": "45", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 135, "difficulty_id": 1, "explanation": "From 9.30 a.m. to 11.30 a.m. is 2 h, but to 11.15 is 15 min less. Easier: 9.30 to 11.15 = 1 h 45 min.", "hints": ["Count from 9.30 to 10.30 (1 h), then 10.30 to 11.15.", "10.30 to 11.15 is 45 min, total 1 h 45 min."], "source": "Pei Chun 2024 P5 End-of-Year Exam Q19", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: Total → 1h 45min. Two blanks (h and min)." }, { "n": 20, "type_id": 2, "question": "There were 440 books on sale. James sold 30% of them. How many books did James sell? [?]", "answer0": "132", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 174, "difficulty_id": 1, "explanation": "30% of 440 = \\(\\dfrac{30}{100}\\times440 = \\dfrac{440\\times30}{100} = \\dfrac{13200}{100} = 132\\).", "hints": ["Find 30% of 440.", "440 × 30 ÷ 100 = 132."], "source": "Pei Chun 2024 P5 End-of-Year Exam Q20", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 132." }, { "n": 21, "type_id": 2, "question": "Water leaks from a tap at a rate of 7 ml per second. At this rate, how much water will leak from the tap in 1 minute? [?]", "answer0": "420", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 1, "explanation": "1 minute = 60 seconds. Water = 7 ml × 60 = 420 ml.", "hints": ["Convert 1 minute to seconds.", "7 ml × 60 s = 420 ml."], "source": "Pei Chun 2024 P5 End-of-Year Exam Q21", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer in ml. Key: 420 ml." }, { "n": 22, "type_id": 2, "question": "The graph shows the temperature of water in a pot from 09 00 to 09 30. For how many minutes was the temperature of the water 50°C and below? [?]", "answer0": "20", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 147, "difficulty_id": 2, "explanation": "From the graph the temperature is 50°C at 09 10 and stays 50°C or below until 09 30. That is 09 10 to 09 30 = 20 minutes.", "hints": ["Find the time when the line first reaches 50°C.", "50°C at 09 10; from 09 10 to 09 30 is 20 min."], "source": "Pei Chun 2024 P5 End-of-Year Exam Q22", "image_needed": true, "image_options": false, "image_file": "q22.png", "image_page": 12, "image_bbox": [0.18, 0.4, 0.82, 0.66], "image_loc": "line graph, temperature (0-100) vs time 09 00 to 09 30, line falling from 95 to about 10", "notes": "Answer in min. Key: 20min." }, { "n": 23, "type_id": 2, "question": "There were 56 children at a party. \\(\\dfrac{2}{7}\\) of them were boys. The rest were girls. How many more girls than boys were there at the party? [?]", "answer0": "24", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 2, "explanation": "Boys = \\(\\dfrac{2}{7}\\times56 = 16\\). Girls = 56 − 16 = 40. More girls than boys = 40 − 16 = 24.", "hints": ["Find the number of boys: 2/7 of 56.", "Boys = 16, girls = 40, difference = 24."], "source": "Pei Chun 2024 P5 End-of-Year Exam Q23", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key working: 7 units = 56, 1 unit = 8, girls = 40, 40 − 16 = 24." }, { "n": 24, "type_id": 1, "question": "Madelyn had \\(\\dfrac{3}{5}\\) kg of flour. She used \\(\\dfrac{1}{3}\\) of the flour for baking. How much flour was she left with?", "answer0": "\\(\\dfrac{2}{5}\\) kg", "answer1": "\\(\\dfrac{1}{5}\\) kg", "answer2": "\\(\\dfrac{2}{15}\\) kg", "answer3": "\\(\\dfrac{4}{15}\\) kg", "correct_answer": 0, "skill_id": 161, "difficulty_id": 2, "explanation": "She kept \\(1-\\dfrac{1}{3}=\\dfrac{2}{3}\\) of the flour. Left = \\(\\dfrac{3}{5}\\times\\dfrac{2}{3}=\\dfrac{6}{15}=\\dfrac{2}{5}\\) kg.", "hints": ["She has 2/3 of the flour left after using 1/3.", "3/5 × 2/3 = 6/15 = 2/5 kg."], "source": "Pei Chun 2024 P5 End-of-Year Exam Q24", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer is a fraction (2/5 kg) → converted to MCQ per FIB-fraction rule. Key: 2/5. Distractors: 1/5 (3/5 used directly), 2/15, 4/15." }, { "n": 25, "type_id": 1, "question": "The square grid shows the positions of points A, B, C, D, E, F and G.
(a) In which direction was Point F from Point B?
(b) Ali stood at one of the points facing F. After he turned 45° anti-clockwise, he faced C. Which point was Ali at?", "answer0": "(a) South-west, (b) A", "answer1": "(a) South-east, (b) A", "answer2": "(a) South-west, (b) D", "answer3": "(a) North-west, (b) E", "correct_answer": 0, "skill_id": 142, "difficulty_id": 3, "explanation": "(a) F is down and to the left of B (using the North arrow), i.e. South-west. (b) The point from which facing F then turning 45° anti-clockwise lands on facing C is point A.", "hints": ["Use the North arrow to read compass directions.", "(a) F is below-left of B → South-west. (b) From A, F is south and C is south-east; a 45° anti-clockwise turn matches."], "source": "Pei Chun 2024 P5 End-of-Year Exam Q25", "image_needed": true, "image_options": false, "image_file": "q25.png", "image_page": 14, "image_bbox": [0.33, 0.07, 0.58, 0.24], "image_loc": "square grid with points A, B, G, F, C, E, D marked, plus a North arrow to the right", "notes": "Directions/letters → MCQ per spec (no word/letter FIB). Key: (a) South-west, (b) A. Note: the North arrow is part of the figure and must be included in the crop." }, { "n": 26, "type_id": 2, "question": "Two numbers add up to 315. One of them is a 2-digit number and the other is a 3-digit number. What is the smallest possible difference between the two numbers? [?]", "answer0": "117", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "To make the difference smallest, make the 2-digit number as large as possible: 99. Then the 3-digit number = 315 − 99 = 216. Difference = 216 − 99 = 117.", "hints": ["The biggest 2-digit number is 99, giving the closest split.", "3-digit = 315 − 99 = 216; 216 − 99 = 117."], "source": "Pei Chun 2024 P5 End-of-Year Exam Q26", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 2-digit 99, 3-digit 216, difference 117." }, { "n": 27, "type_id": 2, "question": "170 students participated in a charity drive. Each student collected 80 plastic bottles. What was the total number of plastic bottles collected by the students? [?]", "answer0": "13600", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 151, "difficulty_id": 1, "explanation": "Total = 170 × 80 = 13 600 bottles.", "hints": ["Multiply the number of students by bottles each.", "170 × 80 = 13 600."], "source": "Pei Chun 2024 P5 End-of-Year Exam Q27", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 13600." }, { "n": 28, "type_id": 2, "question": "The cost of 3 hair bands was the same as the cost of 12 hair clips. Mei Ling bought 3 hair bands. Jessie bought 1 hair band and some hair clips. Both of them spent the same amount of money. How many hair clips did Jessie buy? [?]", "answer0": "8", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "1 hair band = 4 hair clips (since 3 bands = 12 clips). Mei Ling's 3 bands = 12 clips' worth. Jessie's 1 band = 4 clips' worth, so her hair clips = 12 − 4 = 8.", "hints": ["First find how many clips equal 1 band: 12 ÷ 3 = 4.", "Jessie's 1 band = 4 clips; she needs 12 − 4 = 8 more clips."], "source": "Pei Chun 2024 P5 End-of-Year Exam Q28", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 1 hairband = 4 hairclips, clips = 12 − 4 = 8." }, { "n": 29, "type_id": 2, "question": "The figure shows 7 identical cubes which are glued together to form a solid. The whole solid, including the base, is then painted red. How many cubes have exactly four of their faces painted red? [?]", "answer0": "5", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 187, "difficulty_id": 3, "explanation": "Counting each cube's exposed faces (the whole solid including the base is painted): 5 of the 7 cubes have exactly four faces painted red.", "hints": ["A cube glued to others has fewer than 6 faces exposed.", "Count exposed faces for each of the 7 cubes; 5 have exactly 4."], "source": "Pei Chun 2024 P5 End-of-Year Exam Q29", "image_needed": true, "image_options": false, "image_file": "q29.png", "image_page": 16, "image_bbox": [0.28, 0.09, 0.62, 0.24], "image_loc": "isometric drawing of 7 cubes glued into an L/step solid, with Top/Front/Side View arrows", "notes": "Part (a) 'draw the front view' is non-served (drawing); only part (b) count = 5 is captured. Key: b) 5." }, { "n": 30, "type_id": 2, "question": "Hassan had a rectangular piece of paper. He folded it along the dotted lines without overlapping. Find \\(\\angle y\\). [?]", "answer0": "34", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 197, "difficulty_id": 3, "explanation": "The fold makes equal angles. \\(\\angle y\\) = 68° ÷ 2 = 34°.", "hints": ["Folding creates two equal angles from the 68°.", "68° ÷ 2 = 34°."], "source": "Pei Chun 2024 P5 End-of-Year Exam Q30", "image_needed": true, "image_options": false, "image_file": "q30.png", "image_page": 17, "image_bbox": [0.16, 0.12, 0.78, 0.31], "image_loc": "two diagrams: 'Before folding' rectangle with dotted fold lines and 'After folding' shape with 68° and y marked", "notes": "Answer in degrees. Key: y → 68 ÷ 2 = 34." }, { "n": 31, "type_id": 1, "question": "The figure is made up of 3 squares. One square is divided equally into 4 triangles. What fraction of the figure is shaded? Express your answer in its simplest form.", "answer0": "\\(\\dfrac{1}{4}\\)", "answer1": "\\(\\dfrac{1}{3}\\)", "answer2": "\\(\\dfrac{1}{12}\\)", "answer3": "\\(\\dfrac{2}{3}\\)", "correct_answer": 0, "skill_id": 161, "difficulty_id": 2, "explanation": "The figure has 3 equal squares. One square is split into 4 triangles, and the shaded part is 3 of those 4 triangles = \\(\\dfrac{3}{4}\\) of one square. As a fraction of the whole figure: \\(\\dfrac{3}{4}\\div3 = \\dfrac{3}{12} = \\dfrac{1}{4}\\).", "hints": ["The shaded region is part of just one of the 3 squares.", "Shaded = 3/4 of one square = 3/12 of the figure = 1/4."], "source": "Pei Chun 2024 P5 End-of-Year Exam P2 Q1", "image_needed": true, "image_options": false, "image_file": "p2q1.png", "image_page": 19, "image_bbox": [0.3, 0.18, 0.5, 0.31], "image_loc": "three squares forming an L; the top-left square is divided into 4 triangles with 3 shaded", "notes": "Paper 2 Q1. Answer is a fraction (1/4) → MCQ per FIB-fraction rule. Key: 1/4." }, { "n": 32, "type_id": 2, "question": "In the figure, WXZ is a straight line and XZ = ZY. What is the area of triangle WXY? [?]", "answer0": "138", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 186, "difficulty_id": 3, "explanation": "WX is the base. WX = WZ − XZ = 35 − 12 = 23 cm. The height from Y to line WXZ is ZY = 12 cm. Area = \\(\\dfrac{1}{2}\\times23\\times12 = 138\\) cm².", "hints": ["Find WX along the straight line: WZ − XZ.", "Base WX = 23 cm, height = ZY = 12 cm; area = 1/2 × 23 × 12 = 138 cm²."], "source": "Pei Chun 2024 P5 End-of-Year Exam P2 Q2", "image_needed": true, "image_options": false, "image_file": "p2q2.png", "image_page": 19, "image_bbox": [0.16, 0.4, 0.5, 0.64], "image_loc": "triangle WXY, WZ = 35 cm down the left, WY = 37 cm slant, XZ along base with 12 cm marked, X on WZ", "notes": "Answer in cm². Key: 35 − 12 = 23, area = 1/2 × 23 × 12 = 138 cm²." }, { "n": 33, "type_id": 2, "question": "Peter had 3 times as many pens as Siti. They had 228 pens altogether. How many pens did Siti have? [?]", "answer0": "57", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 1, "explanation": "Siti = 1 unit, Peter = 3 units, total = 4 units = 228. Siti = 228 ÷ 4 = 57 pens.", "hints": ["Total = 4 units (1 for Siti, 3 for Peter).", "228 ÷ 4 = 57."], "source": "Pei Chun 2024 P5 End-of-Year Exam P2 Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: Siti → 228 ÷ 4 = 57." }, { "n": 34, "type_id": 1, "question": "7 ℓ of juice was poured into 8 bottles equally. How much juice was there in each bottle? Leave your answer as a fraction or a mixed number.", "answer0": "\\(\\dfrac{7}{8}\\) ℓ", "answer1": "\\(\\dfrac{8}{7}\\) ℓ", "answer2": "\\(1\\dfrac{1}{8}\\) ℓ", "answer3": "\\(\\dfrac{1}{8}\\) ℓ", "correct_answer": 0, "skill_id": 157, "difficulty_id": 2, "explanation": "Each bottle = 7 ÷ 8 = \\(\\dfrac{7}{8}\\) ℓ (also 7000 ml ÷ 8 = 875 ml = 0.875 ℓ).", "hints": ["Divide the total juice by the number of bottles.", "7 ÷ 8 = 7/8 ℓ."], "source": "Pei Chun 2024 P5 End-of-Year Exam P2 Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer is a fraction (7/8 ℓ) → MCQ per FIB-fraction rule. Key: 7/8 L." }, { "n": 35, "type_id": 2, "question": "20 cones were placed equal distance apart along all four sides of a rectangular field. The diagram shows the arrangement of cones along two sides of the rectangular field. The breadth of the rectangular field is 24 m. Find the length of the rectangular field. [?]", "answer0": "56", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "Along the breadth there are 4 cones → 3 gaps, so 1 gap = 24 ÷ 3 = 8 m. Total cones = 20 around the perimeter. Number of cones along one length (counting corners once across the rectangle): cones split so that each long side has (20 ÷ 2 + 2 − 1)... using the key: 6 cones along the length → 6 + 2 − 1 = 7 intervals; length = 7 × 8 = 56 m.", "hints": ["Find one gap from the breadth: 24 ÷ 3 = 8 m.", "Work out the cones along the length, then length = intervals × 8 = 56 m."], "source": "Pei Chun 2024 P5 End-of-Year Exam P2 Q5", "image_needed": true, "image_options": false, "image_file": "p2q5.png", "image_page": 20, "image_bbox": [0.16, 0.42, 0.72, 0.62], "image_loc": "rectangle outline with cones (dots) along the top and right sides, '?' across the top, '24 m' down the right", "notes": "Answer in m. Key: 1 unit = 28÷3... length 7 × 8 = 56 m. Breadth has 4 cones (3 gaps of 8 m)." }, { "n": 36, "type_id": 2, "question": "The table shows the charges for a photocopier service: first 100 copies cost 7 cents per copy; above 100 copies cost 4 cents per copy.
(a) Murali printed 98 copies. How much did he pay?
(b) Aminah printed some copies and paid $8.12 for the photocopying services. How many copies did she print?
(a) $[?]
(b) [?] copies", "answer0": "6.86", "answer1": "128", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 3, "explanation": "(a) 98 copies at 7 cents = 98 × $0.07 = $6.86. (b) First 100 copies cost 100 × $0.07 = $7.00. Remaining paid = $8.12 − $7.00 = $1.12 at 4 cents each = 1.12 ÷ 0.04 = 28. Total = 100 + 28 = 128 copies.", "hints": ["(a) All 98 copies are within the first 100 → 7 cents each.", "(b) Pay $7 for first 100, then $1.12 ÷ $0.04 = 28 more → 128."], "source": "Pei Chun 2024 P5 End-of-Year Exam P2 Q6", "image_needed": false, "image_options": false, "image_file": null, "notes": "Two parts; (a) $6.86, (b) 128 copies. Charge table transcribed into stem." }, { "n": 37, "type_id": 2, "question": "The graph shows the number of coins Jack had in his piggy bank. The number of 50¢ coins is not recorded in the graph. (10¢: 35 coins, 20¢: 45 coins, $1: 40 coins.) \\(\\dfrac{1}{2}\\) of the total number of coins Jack had are 50¢ coins. How much money did Jack have in his piggy bank? [?]", "answer0": "112.50", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "Recorded coins = 35 + 45 + 40 = 120. Since 50¢ coins are half the total, the recorded 120 are the other half, so 50¢ coins = 120. Money: 10¢ → 35 × $0.10 = $3.50; 20¢ → 45 × $0.20 = $9.00; 50¢ → 120 × $0.50 = $60.00; $1 → 40 × $1 = $40.00. Total = 3.50 + 9 + 60 + 40 = $112.50.", "hints": ["The recorded coins (120) make up the half that are not 50¢, so there are 120 fifty-cent coins.", "Add the value of each coin type: $3.50 + $9 + $60 + $40 = $112.50."], "source": "Pei Chun 2024 P5 End-of-Year Exam P2 Q7", "image_needed": true, "image_options": false, "image_file": "p2q7.png", "image_page": 22, "image_bbox": [0.2, 0.12, 0.82, 0.36], "image_loc": "bar graph, number of coins vs coin type (10¢ 35, 20¢ 45, 50¢ blank, $1 40)", "notes": "Answer in dollars. Key: total $112.50 (50¢ coins = 120, the other half)." }, { "n": 38, "type_id": 2, "question": "Gina had 3.06 ℓ of water in a jug. She poured the water into identical cups with some water left in the jug. Each cup had a capacity of 280 ml.
(a) What was the greatest possible number of cups that she could fill completely?
(b) What was the amount of water left in the jug?
(a) [?] cups
(b) [?] ml", "answer0": "10", "answer1": "260", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 192, "difficulty_id": 3, "explanation": "3.06 ℓ = 3060 ml. (a) 3060 ÷ 280 = 10 remainder 260, so 10 cups can be filled completely. (b) Water left = 3060 − 10 × 280 = 3060 − 2800 = 260 ml.", "hints": ["Convert 3.06 ℓ to ml first (3060 ml).", "3060 ÷ 280 = 10 r 260 → 10 cups, 260 ml left."], "source": "Pei Chun 2024 P5 End-of-Year Exam P2 Q8", "image_needed": false, "image_options": false, "image_file": null, "notes": "Two parts: (a) 10 cups, (b) 260 ml." }, { "n": 39, "type_id": 2, "question": "Rosnah spent $739.50 on some pillows and towels. She bought 3 more pillows than towels. A pillow cost $22.50 and a towel cost $9.50.
(a) Find the cost of 3 pillows.
(b) How many towels did she buy?
(a) $[?]
(b) [?] towels", "answer0": "67.50", "answer1": "21", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 3, "explanation": "(a) 3 pillows = 3 × $22.50 = $67.50. (b) The 3 extra pillows cost $67.50, so remaining = $739.50 − $67.50 = $672 spent on equal numbers of pillows and towels. Each pillow+towel pair = $22.50 + $9.50 = $32. Number of towels = 672 ÷ 32 = 21.", "hints": ["(a) Cost of 3 pillows = 3 × $22.50.", "(b) Remove the 3 extra pillows' cost, then divide the rest by ($22.50 + $9.50) = $32 → 21 towels."], "source": "Pei Chun 2024 P5 End-of-Year Exam P2 Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Two parts: (a) $67.50, (b) 21 towels." }, { "n": 40, "type_id": 2, "question": "In the figure, EFG is an equilateral triangle and GH = FH.
(a) Find \\(\\angle EFH\\). (\\(\\angle GHF = 124°\\).)
(b) In the figure, WXYZ is a trapezium and WX // ZY. (\\(\\angle WXY = 130°\\), \\(\\angle XZY = 117°\\).) Find \\(\\angle XWZ\\).
(a) [?]
(b) [?]", "answer0": "32", "answer1": "63", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 197, "difficulty_id": 3, "explanation": "(a) Triangle GHF is isosceles (GH = FH) with \\(\\angle GHF = 124°\\), so \\(\\angle HFG = (180−124)\\div2 = 28°\\). In equilateral EFG, \\(\\angle EFG = 60°\\). So \\(\\angle EFH = 60° − 28° = 32°\\). (b) Since WX // ZY, \\(\\angle XWZ\\) and \\(\\angle WZY\\) are co-interior. Using the trapezium angles, \\(\\angle XWZ = 180° − 117° = 63°\\).", "hints": ["(a) Triangle FHG is isosceles; base angles = (180 − 124)/2 = 28°; EFG = 60°.", "(b) WX // ZY → co-interior angles; ∠XWZ = 180° − 117° = 63°."], "source": "Pei Chun 2024 P5 End-of-Year Exam P2 Q10", "image_needed": true, "image_options": false, "image_file": "p2q10.png", "image_page": 25, "image_bbox": [0.16, 0.08, 0.7, 0.66], "image_loc": "top: equilateral triangle EFG with H inside, 124° marked at H; bottom: trapezium WXYZ with 130° at X and 117° at Z", "notes": "Two angle parts on one page: (a) ∠EFH = 32°, (b) ∠XWZ = 63°. Two figures — crop covers both." }, { "n": 41, "type_id": 2, "question": "Mdm Lee had 480 beads. 45% of her beads were blue and the rest were red. She used 105 red and blue beads to make a necklace. 60% of the remaining beads were red.
(a) How many red beads did she have at first?
(b) How many red beads did she use?
(a) [?]
(b) [?]", "answer0": "264", "answer1": "39", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 175, "difficulty_id": 3, "explanation": "(a) Red = 100% − 45% = 55% of 480 = \\(\\dfrac{55}{100}\\times480 = 264\\) red beads. (b) Remaining beads = 480 − 105 = 375. 60% of remaining are red → red remaining = 60% × 375 = 225. Red used = red at first − red remaining = 264 − 225 = 39.", "hints": ["(a) Red% = 100 − 45 = 55; 55% of 480 = 264.", "(b) Remaining = 375; red remaining = 60% × 375 = 225; red used = 264 − 225 = 39."], "source": "Pei Chun 2024 P5 End-of-Year Exam P2 Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "Two parts: (a) 264 red beads, (b) 39 red beads used. (P2 Q11 is a draw-only grid task — see P2 Q11 entry below, type_id 0.)" }, { "n": 42, "type_id": 2, "question": "Zhi Wei earns $2400 each month. He spends some of his salary and saves the rest. The line graph shows the amount of money he saved each month (Jan $1300, Feb $1700, Mar $2000, Apr $1500, May $1400).
(a) In which month did Zhi Wei spend the most amount of money?
(c) What percentage of his monthly salary did he spend in May? Give your answer correct to the nearest 1%.
(a) [?]
(c) [?]", "answer0": "January", "answer1": "42", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 175, "difficulty_id": 3, "explanation": "(a) He spends most when he saves least; the smallest saving is in January ($1300), so he spent the most in January. (c) In May he saved $1400, so he spent $2400 − $1400 = $1000. Percentage spent = \\(\\dfrac{1000}{2400}\\times100\\% = 41.67\\% \\approx 42\\%\\).", "hints": ["(a) Most spent = least saved; find the lowest point on the graph.", "(c) Spent in May = 2400 − 1400 = 1000; 1000/2400 × 100 ≈ 42%."], "source": "Pei Chun 2024 P5 End-of-Year Exam P2 Q13", "image_needed": true, "image_options": false, "image_file": "p2q13.png", "image_page": 28, "image_bbox": [0.18, 0.12, 0.82, 0.42], "image_loc": "line graph, amount saved ($0-2500) vs months Jan-May, peaking at Mar (2000)", "notes": "Parts (a) January and (c) 42% captured. Part (b) (fraction 5/6) is a separate MCQ entry below to satisfy the FIB-fraction rule." }, { "n": 43, "type_id": 1, "question": "Zhi Wei earns $2400 each month and saves the rest of his salary. In March he saved $2000. What fraction of his monthly salary did he save in March? Give your answer in the simplest form.", "answer0": "\\(\\dfrac{5}{6}\\)", "answer1": "\\(\\dfrac{2}{3}\\)", "answer2": "\\(\\dfrac{3}{4}\\)", "answer3": "\\(\\dfrac{4}{5}\\)", "correct_answer": 0, "skill_id": 158, "difficulty_id": 2, "explanation": "Fraction saved = \\(\\dfrac{2000}{2400} = \\dfrac{20}{24} = \\dfrac{5}{6}\\).", "hints": ["Write savings over salary: 2000/2400.", "Simplify 2000/2400 by 400 → 5/6."], "source": "Pei Chun 2024 P5 End-of-Year Exam P2 Q13b", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q13(b). Answer is a fraction (5/6) → MCQ per FIB-fraction rule. Key: 2000/2400 = 5/6." }, { "n": 44, "type_id": 2, "question": "Mr Tan had some yellow and pink balloons. The ratio of the number of yellow balloons to the number of pink balloons was 2 : 5. There were 36 more pink balloons than yellow balloons. How many pink balloons did Mr Tan have? [?]", "answer0": "60", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 183, "difficulty_id": 2, "explanation": "Yellow : pink = 2 : 5, difference = 5 − 2 = 3 units = 36, so 1 unit = 12. Pink = 5 units = 5 × 12 = 60 balloons.", "hints": ["The difference in ratio units is 5 − 2 = 3.", "3 units = 36 → 1 unit = 12; pink = 5 × 12 = 60."], "source": "Pei Chun 2024 P5 End-of-Year Exam P2 Q14", "image_needed": false, "image_options": false, "image_file": null, "notes": "Part (a) only as FIB. Part (b) answer is a ratio (6:1) → separate MCQ entry below per spec." }, { "n": 45, "type_id": 1, "question": "Mr Tan had yellow and pink balloons in the ratio 2 : 5, with 60 pink and 24 yellow balloons. Mr Tan gave away 50 pink balloons. Find the ratio of the number of yellow balloons to the number of pink balloons in the end. Give your answer in the simplest form.", "answer0": "12 : 5", "answer1": "5 : 12", "answer2": "24 : 10", "answer3": "2 : 1", "correct_answer": 0, "skill_id": 179, "difficulty_id": 3, "explanation": "Yellow = 24, pink after giving away 50 = 60 − 50 = 10. Ratio yellow : pink = 24 : 10 = 12 : 5.", "hints": ["Pink left = 60 − 50 = 10; yellow stays 24.", "24 : 10 simplifies (÷2) to 12 : 5."], "source": "Pei Chun 2024 P5 End-of-Year Exam P2 Q14b", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q14(b). Answer is a ratio (12:5) → MCQ per spec (ratio answers not FIB). Key working: 60 − 50 = 10, yellow 12 × 2 = 24, so 24:10 = 12:5. Distractor 24:10 is the un-simplified form." }, { "n": 46, "type_id": 2, "question": "A rectangular tank measuring 45 cm by 18 cm by 31 cm was filled with 18.8 ℓ of water. When three identical wooden blocks were added into the tank, 620 ml of water overflowed from the tank. What is the volume of one such wooden block? [?]", "answer0": "2310", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 193, "difficulty_id": 3, "explanation": "Tank capacity = 45 × 18 × 31 = 25 110 cm³ = 25.11 ℓ. Water already in = 18.8 ℓ. Empty space = 25.11 − 18.8 = 6.31 ℓ. Total volume the 3 blocks displaced = empty space + overflow = 6.31 ℓ + 0.62 ℓ = 6.93 ℓ = 6930 cm³. One block = 6930 ÷ 3 = 2310 cm³.", "hints": ["Tank volume = 45 × 18 × 31 = 25 110 cm³ = 25.11 ℓ.", "Blocks displace (25.11 − 18.8) + 0.62 = 6.93 ℓ; ÷3 = 2.31 ℓ = 2310 cm³."], "source": "Pei Chun 2024 P5 End-of-Year Exam P2 Q15", "image_needed": true, "image_options": false, "image_file": "p2q15.png", "image_page": 30, "image_bbox": [0.28, 0.13, 0.72, 0.36], "image_loc": "cuboid water tank with dimensions 45 cm (length), 18 cm (depth), 31 cm (height) marked, water shaded", "notes": "Answer in cm³ (2310). Key gives 2.31 L per block = 2310 cm³. Printed key writes '25.11 - 18.8 - 6.31L' meaning the empty space is 6.31 L; total displaced 6.93 L ÷ 3 = 2.31 L." }, { "n": 47, "type_id": 2, "question": "Sunitha had a sum of money. She spent \\(\\dfrac{2}{3}\\) of it on a television set, \\(\\dfrac{1}{2}\\) of her remaining money on a washing machine and another $52 on a coffee table. She had \\(\\dfrac{1}{12}\\) of her money left. How much money did she have at first? [?]", "answer0": "624", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "After the TV she has \\(\\dfrac{1}{3}\\) left. The washing machine took \\(\\dfrac{1}{2}\\) of that = \\(\\dfrac{1}{6}\\) of the whole, leaving \\(\\dfrac{1}{6}\\). She then spent $52 and was left with \\(\\dfrac{1}{12}\\). So \\(\\dfrac{1}{6} - \\dfrac{1}{12} = \\dfrac{1}{12}\\) of her money = $52. Therefore total = 52 × 12 = $624.", "hints": ["Washing machine = 1/2 of the 1/3 remaining = 1/6 of total; leftover before coffee table = 1/6.", "1/6 − 1/12 = 1/12 = $52, so total = 52 × 12 = $624."], "source": "Pei Chun 2024 P5 End-of-Year Exam P2 Q16", "image_needed": false, "image_options": false, "image_file": null, "notes": "Part (b) only as FIB (answer $624). Part (a) fraction 1/6 → separate MCQ entry below per FIB-fraction rule." }, { "n": 48, "type_id": 1, "question": "Sunitha spent \\(\\dfrac{2}{3}\\) of her money on a television set and \\(\\dfrac{1}{2}\\) of her remaining money on a washing machine. What fraction of her money did she spend on the washing machine? Give your answer in the simplest form.", "answer0": "\\(\\dfrac{1}{6}\\)", "answer1": "\\(\\dfrac{1}{2}\\)", "answer2": "\\(\\dfrac{1}{3}\\)", "answer3": "\\(\\dfrac{2}{3}\\)", "correct_answer": 0, "skill_id": 161, "difficulty_id": 2, "explanation": "After the TV, \\(1-\\dfrac{2}{3}=\\dfrac{1}{3}\\) remained. The washing machine took \\(\\dfrac{1}{2}\\) of this: \\(\\dfrac{1}{2}\\times\\dfrac{1}{3}=\\dfrac{1}{6}\\) of her money.", "hints": ["Remaining after TV = 1/3 of total.", "1/2 × 1/3 = 1/6."], "source": "Pei Chun 2024 P5 End-of-Year Exam P2 Q16a", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q16(a). Answer is a fraction (1/6) → MCQ per FIB-fraction rule. Key: 2/12 = 1/6." }, { "n": 49, "type_id": 2, "question": "Ming En used black and white triangles to form some patterns. For each pattern the number of triangles follows: Pattern 1 → 0 white, 1 black, 1 total; Pattern 2 → 1 white, 3 black, 4 total; Pattern 3 → 3 white, 6 black, 9 total; Pattern 4 → 6 white, 10 black, 16 total.
(b) What is the total number of triangles needed to form Pattern 43?
(c) How many white triangles are needed to form Pattern 67?
(b) [?]
(c) [?]", "answer0": "1849", "answer1": "2211", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "(b) Total number of triangles in Pattern n = n × n. Pattern 43 → 43 × 43 = 1849. (c) Number of white triangles in Pattern n = (n − 1) × \\(\\dfrac{n}{2}\\)... using the key's relation, white in Pattern 67 = 67 × 33 = 2211 (66 ÷ 2 = 33, then × 67).", "hints": ["(b) Total triangles in Pattern n = n²; 43² = 1849.", "(c) White triangles in Pattern 67: 67 × 33 = 2211 (66/2 = 33)."], "source": "Pei Chun 2024 P5 End-of-Year Exam P2 Q17", "image_needed": true, "image_options": false, "image_file": "p2q17.png", "image_page": 32, "image_bbox": [0.22, 0.11, 0.78, 0.22], "image_loc": "four triangle patterns (Pattern 1 to 4) made of black and white small triangles, increasing in size", "notes": "Parts (b) 1849 and (c) 2211 captured as FIB. Part (a) 'complete the table for Pattern 5' is a table-fill drawing task → separate type_id 0 entry below. Key: total = n², white(67) = 67 × 33 = 2211." }, { "n": 50, "type_id": 0, "question": "Mei Yan drew a triangle ABC in a square grid. (a) Triangle BCD is an isosceles triangle with an area that is twice the area of triangle ABC. Draw triangle BCD on the grid such that triangle BCD does not overlap with triangle ABC. (b) Mei Yan drew another triangle X in a square grid. Draw a parallelogram with the same perimeter as X. Label the parallelogram Y.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 201, "difficulty_id": 3, "explanation": "Drawing task on a square grid — no single numeric answer. (a) Draw isosceles triangle BCD sharing base BC with double the area of ABC, not overlapping. (b) Draw a parallelogram Y with the same perimeter as triangle X.", "hints": [], "source": "Pei Chun 2024 P5 End-of-Year Exam P2 Q11", "image_needed": true, "image_options": false, "image_file": "p2q11.png", "image_page": 26, "image_bbox": [0.24, 0.1, 0.78, 0.78], "image_loc": "two square dot grids: top with triangle ABC drawn, bottom with triangle X drawn", "notes": "type_id 0 (draw-on-grid task, no value answer) → skipped on insert. Key answer is a diagram only." }, { "n": 51, "type_id": 0, "question": "Ming En used black and white triangles to form patterns. Complete the table for Pattern 5 (number of white triangles, number of black triangles, and total number of triangles).", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 2, "explanation": "Pattern 5: white triangles = 10, black triangles = 15, total triangles = 25 (5 × 5 = 25). This is a table-completion task on the printed paper.", "hints": [], "source": "Pei Chun 2024 P5 End-of-Year Exam P2 Q17a", "image_needed": false, "image_options": false, "image_file": null, "notes": "type_id 0 (fill the printed table — three cells, not a single served answer) → skipped on insert. Key: Pattern 5 → 10 white, 15 black, 25 total." } ] }