{ "paper": { "school": "Methodist Girls' School", "year": 2024, "level": "P5", "label": "End-of-Year Exam", "source_prefix": "MGS 2024 P5 End-of-Year Exam", "has_answer_key": true, "notes": "Two-paper exam. Paper 1 Booklet A = Q1-15 (MCQ). Paper 1 Booklet B = Q16-30 (short-answer). Paper 2 = Q1-17 (long-answer). Paper 2 question numbers re-namespaced as P2 Q in source to avoid collision with Paper 1 Q1-30." }, "questions": [ { "n": 1, "type_id": 1, "question": "40 000 + 6000 + 200 + 5 =", "answer0": "46 250", "answer1": "46 205", "answer2": "46 025", "answer3": "40 625", "correct_answer": 1, "skill_id": 149, "difficulty_id": 1, "explanation": "Add by place value: 40 000 + 6000 + 200 + 5 = 46 205.", "hints": ["Line up the digits by place value: ten-thousands, thousands, hundreds, tens, ones.", "There are no tens, so the tens digit is 0."], "source": "MGS 2024 P5 End-of-Year Exam Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "MCQ. Stem keeps the printed blank line. Key: option 2 = 46 205." }, { "n": 2, "type_id": 1, "question": "Which of the following is a common multiple of 6 and 9?", "answer0": "15", "answer1": "18", "answer2": "24", "answer3": "27", "correct_answer": 1, "skill_id": 149, "difficulty_id": 2, "explanation": "A common multiple of 6 and 9 must be in both times tables. 18 = 6 x 3 = 9 x 2, so 18 is a common multiple (it is the LCM).", "hints": ["List multiples of 6: 6, 12, 18, 24, ... and of 9: 9, 18, 27, ...", "Find a number that appears in both lists."], "source": "MGS 2024 P5 End-of-Year Exam Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "MCQ. Key: option 2 = 18. (Factors/multiples is a P4 topic; mapped to nearest available P5 skill 149.)" }, { "n": 3, "type_id": 1, "question": "Which fraction is greater than \\(\\dfrac{1}{2}\\)?", "answer0": "\\(\\dfrac{4}{8}\\)", "answer1": "\\(\\dfrac{4}{9}\\)", "answer2": "\\(\\dfrac{5}{9}\\)", "answer3": "\\(\\dfrac{5}{11}\\)", "correct_answer": 2, "skill_id": 158, "difficulty_id": 2, "explanation": "Compare each to one half. 4/8 = 1/2 (not greater). 4/9 < 1/2 (half of 9 is 4.5). 5/9 > 1/2 (5 > 4.5). 5/11 < 1/2 (half of 11 is 5.5). So 5/9 is greater than 1/2.", "hints": ["A fraction is greater than 1/2 when the numerator is more than half the denominator.", "Half of 9 is 4.5, so 5/9 is more than half."], "source": "MGS 2024 P5 End-of-Year Exam Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "MCQ; fraction options rendered inline. Key: option 3 = 5/9." }, { "n": 4, "type_id": 1, "question": "Express \\(\\dfrac{1}{2}\\)% as a decimal.", "answer0": "50", "answer1": "0.5", "answer2": "0.05", "answer3": "0.005", "correct_answer": 3, "skill_id": 173, "difficulty_id": 2, "explanation": "1/2% = 0.5%. To convert a percentage to a decimal, divide by 100: 0.5 ÷ 100 = 0.005.", "hints": ["First write 1/2% as 0.5%.", "Per cent means out of 100, so divide by 100."], "source": "MGS 2024 P5 End-of-Year Exam Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "MCQ. Key: option 4 = 0.005." }, { "n": 5, "type_id": 1, "question": "A factory takes 2 days to produce 5 tables.
At the same rate, how many days will it take to produce 40 tables?", "answer0": "8", "answer1": "10", "answer2": "16", "answer3": "20", "correct_answer": 2, "skill_id": 152, "difficulty_id": 2, "explanation": "40 tables is 40 ÷ 5 = 8 times as many as 5 tables. So it takes 8 x 2 = 16 days.", "hints": ["How many lots of 5 tables make 40 tables?", "Multiply the number of lots by 2 days."], "source": "MGS 2024 P5 End-of-Year Exam Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "MCQ. Key: option 3 = 16." }, { "n": 6, "type_id": 1, "question": "How much water is in the container?", "answer0": "200 ml", "answer1": "400 ml", "answer2": "500 ml", "answer3": "800 ml", "correct_answer": 1, "skill_id": 191, "difficulty_id": 2, "explanation": "The container is marked up to 2 litres (2000 ml). The scale between 0 and 2 l shows 5 equal intervals of 400 ml each. The water level is at the first mark, so there is 400 ml.", "hints": ["The top mark is 2 l = 2000 ml.", "Work out the value of one interval on the scale, then read the water level."], "source": "MGS 2024 P5 End-of-Year Exam Q6", "image_needed": true, "image_options": false, "image_file": "q6.png", "image_page": 4, "image_bbox": [0.18, 0.56, 0.40, 0.72], "image_loc": "measuring beaker with a 2 l mark near the middle-left of the page, below the question", "notes": "Figure: graduated container/beaker. Key: option 2 = 400 ml." }, { "n": 7, "type_id": 1, "question": "James had $200. He spent $70 on a wallet.
What percentage of his money did he spend on the wallet?", "answer0": "30%", "answer1": "35%", "answer2": "65%", "answer3": "70%", "correct_answer": 1, "skill_id": 171, "difficulty_id": 2, "explanation": "Percentage spent = 70/200 x 100% = 35%.", "hints": ["Write the amount spent as a fraction of the total: 70/200.", "Multiply by 100% to convert to a percentage."], "source": "MGS 2024 P5 End-of-Year Exam Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "MCQ. Key: option 2 = 35%." }, { "n": 8, "type_id": 1, "question": "In the figure, how many of the five marked angles are more than 90°?", "answer0": "5", "answer1": "2", "answer2": "3", "answer3": "4", "correct_answer": 1, "skill_id": 197, "difficulty_id": 2, "explanation": "Examining the five marked interior angles of the figure, two of them are obtuse (more than 90°).", "hints": ["A right angle is exactly 90°; an obtuse angle is more than 90°.", "Compare each marked angle to a square corner."], "source": "MGS 2024 P5 End-of-Year Exam Q8", "image_needed": true, "image_options": false, "image_file": "q8.png", "image_page": 5, "image_bbox": [0.16, 0.30, 0.40, 0.49], "image_loc": "irregular quadrilateral with five marked angle arcs, upper-left below the question", "notes": "Figure required (count of angles). Key: option 2 = 2." }, { "n": 9, "type_id": 1, "question": "What is the value of 18 − (4 + 8) ÷ 3 × 2?", "answer0": "1", "answer1": "10", "answer2": "16", "answer3": "4", "correct_answer": 1, "skill_id": 155, "difficulty_id": 2, "explanation": "Brackets first: 4 + 8 = 12. Then left to right for ÷ and x: 12 ÷ 3 = 4, then 4 x 2 = 8. Finally 18 − 8 = 10.", "hints": ["Do the brackets first, then division and multiplication from left to right.", "Subtraction is done last."], "source": "MGS 2024 P5 End-of-Year Exam Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "MCQ. Key: option 2 = 10." }, { "n": 10, "type_id": 1, "question": "The number of visitors to the Bird Park increased by 200 from Monday to Tuesday and decreased by 600 from Tuesday to Wednesday. Which graph shows the number of visitors at the Bird Park from Monday to Wednesday?", "answer0": "Graph 1", "answer1": "Graph 2", "answer2": "Graph 3", "answer3": "Graph 4", "correct_answer": 1, "skill_id": 147, "difficulty_id": 2, "explanation": "The line must go up from Monday to Tuesday (increase of 200) then down from Tuesday to Wednesday (decrease of 600), with the Wednesday point ending lower than Monday. Graph 2 rises then falls and finishes below the start.", "hints": ["From Mon to Tue the line should go up.", "From Tue to Wed it should go down by more than it went up, so Wed is below Mon."], "source": "MGS 2024 P5 End-of-Year Exam Q10", "image_needed": true, "image_options": true, "image_file": null, "image_page": 6, "image_bbox": [0.10, 0.16, 0.65, 0.70], "image_loc": "four candidate line graphs (1)-(4) of 'Number of visitors' vs Mon/Tue/Wed, stacked down the left half of the page", "notes": "Image-option MCQ: each option is a line graph. Crop each option to q10_opt0.png..q10_opt3.png. Key: option 2 = Graph 2 (up then down, ending below start)." }, { "n": 11, "type_id": 1, "question": "Which figure has the largest perimeter?", "answer0": "A", "answer1": "B", "answer2": "C", "answer3": "D", "correct_answer": 3, "skill_id": 138, "difficulty_id": 3, "explanation": "Each figure is drawn on a square grid. Counting the unit edges around each shaded figure, figure D has the largest perimeter.", "hints": ["Count the number of unit-length sides on the boundary of each figure.", "Notches and indentations add to the perimeter even when the area stays the same."], "source": "MGS 2024 P5 End-of-Year Exam Q11", "image_needed": true, "image_options": false, "image_file": "q11.png", "image_page": 7, "image_bbox": [0.13, 0.15, 0.90, 0.30], "image_loc": "four shaded grid figures labelled A, B, C, D in a row near the top of the page", "notes": "Figure required (compare perimeters of A-D). Key: option 4 = D." }, { "n": 12, "type_id": 1, "question": "In the triangle ABC, ∠CAB is 52°, find the value of ∠x.", "answer0": "38°", "answer1": "97°", "answer2": "104°", "answer3": "128°", "correct_answer": 2, "skill_id": 197, "difficulty_id": 3, "explanation": "The tick marks show CB = (the segment from the marked point), with the right angle at B (90°) and ∠CAB = 52°. In the lower triangle the third angle = 180° − 90° − 52° = 38°. The marked sides make an isosceles triangle whose base angles are equal; ∠x is the apex angle, ∠x = 180° − 2 x 38° = 104°.", "hints": ["First find the angle at A's triangle: 180° − 90° − 52°.", "Use the isosceles triangle (equal tick-marked sides): the two base angles are equal, and angles in a triangle add to 180°."], "source": "MGS 2024 P5 End-of-Year Exam Q12", "image_needed": true, "image_options": false, "image_file": "q12.png", "image_page": 7, "image_bbox": [0.18, 0.50, 0.52, 0.78], "image_loc": "right-angled triangle ABC with C at top, 52° at A, right angle at B, x marked inside, tick marks on two sides", "notes": "Figure required. Key: option 3 = 104°." }, { "n": 13, "type_id": 1, "question": "Mrs Tan baked a total of 60 pies and tarts in the morning. There were 3 times as many pies as tarts. After 21 pies and some tarts were sold, there were 4 times as many pies as tarts left. How many tarts were sold?", "answer0": "6", "answer1": "7", "answer2": "8", "answer3": "9", "correct_answer": 3, "skill_id": 152, "difficulty_id": 3, "explanation": "Pies : tarts = 3 : 1, total 60, so tarts = 15, pies = 45. After selling 21 pies, pies left = 24. For pies to be 4 times tarts: tarts left = 24 ÷ 4 = 6. Tarts sold = 15 − 6 = 9.", "hints": ["Find the starting numbers: 4 equal parts make 60, so 1 part (tarts) = 15 and pies = 45.", "Pies left = 45 − 21 = 24; tarts left = 24 ÷ 4."], "source": "MGS 2024 P5 End-of-Year Exam Q13", "image_needed": false, "image_options": false, "image_file": null, "notes": "MCQ word problem. Key: option 4 = 9." }, { "n": 14, "type_id": 1, "question": "5 boys were given 4 stamps each and 3 girls were given a total of 12 stamps. What was the average number of stamps each child received?", "answer0": "7", "answer1": "2", "answer2": "8", "answer3": "4", "correct_answer": 3, "skill_id": 203, "difficulty_id": 2, "explanation": "Total stamps = (5 x 4) + 12 = 20 + 12 = 32. Total children = 5 + 3 = 8. Average = 32 ÷ 8 = 4.", "hints": ["Find the total number of stamps and the total number of children.", "Average = total ÷ number of items."], "source": "MGS 2024 P5 End-of-Year Exam Q14", "image_needed": false, "image_options": false, "image_file": null, "notes": "MCQ. Key: option 4 = 4." }, { "n": 15, "type_id": 1, "question": "David and Tom shared a packet of sweets. David received 15 more than \\(\\dfrac{3}{8}\\) of the total number of sweets. Tom received the remaining 25 sweets. How many sweets were there in the packet altogether?", "answer0": "16", "answer1": "40", "answer2": "64", "answer3": "160", "correct_answer": 2, "skill_id": 165, "difficulty_id": 3, "explanation": "Let total = 8u. David got 3u + 15. Tom got 8u − (3u + 15) = 5u − 15 = 25, so 5u = 40, u = 8. Total = 8u = 64.", "hints": ["Take the total as 8 units; David has 3 units plus 15.", "Tom's share = total − David's share = 25; solve for one unit."], "source": "MGS 2024 P5 End-of-Year Exam Q15", "image_needed": false, "image_options": false, "image_file": null, "notes": "MCQ word problem. Key: option 3 = 64." }, { "n": 16, "type_id": 2, "question": "What is the missing number in the number pattern?
75, 61, 47, 33, [?], 5", "answer0": "19", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 149, "difficulty_id": 1, "explanation": "Each term decreases by 14 (75, 61, 47, 33, ...). The missing term = 33 − 14 = 19 (and 19 − 14 = 5, which matches).", "hints": ["Find the difference between consecutive terms.", "Subtract that difference from 33."], "source": "MGS 2024 P5 End-of-Year Exam Q16", "image_needed": false, "image_options": false, "image_file": null, "notes": "FIB integer. Key: 19. The boxed '?' in the printed sequence is the answer blank." }, { "n": 17, "type_id": 1, "question": "Find the value of \\(\\dfrac{4}{5} \\times \\dfrac{2}{7}\\).", "answer0": "\\(\\dfrac{8}{35}\\)", "answer1": "\\(\\dfrac{6}{35}\\)", "answer2": "\\(\\dfrac{8}{12}\\)", "answer3": "\\(\\dfrac{6}{12}\\)", "correct_answer": 0, "skill_id": 161, "difficulty_id": 1, "explanation": "Multiply numerators and denominators: 4/5 x 2/7 = (4 x 2)/(5 x 7) = 8/35.", "hints": ["Multiply the numerators together and the denominators together.", "8/35 does not simplify."], "source": "MGS 2024 P5 End-of-Year Exam Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "Printed as short-answer but the answer 8/35 is a fraction, so converted to MCQ per spec (FIB answers must be integer/decimal). Key answer 8/35 is correct_answer index 0; distractors are plausible errors." }, { "n": 18, "type_id": 1, "question": "Find the value of \\(1 - \\dfrac{1}{3} - \\dfrac{2}{5}\\).", "answer0": "\\(\\dfrac{4}{15}\\)", "answer1": "\\(\\dfrac{2}{15}\\)", "answer2": "\\(\\dfrac{1}{4}\\)", "answer3": "\\(\\dfrac{7}{15}\\)", "correct_answer": 0, "skill_id": 159, "difficulty_id": 2, "explanation": "Use a common denominator of 15: 1 = 15/15, 1/3 = 5/15, 2/5 = 6/15. So 15/15 − 5/15 − 6/15 = 4/15.", "hints": ["Convert all to fifteenths.", "Subtract the numerators: 15 − 5 − 6."], "source": "MGS 2024 P5 End-of-Year Exam Q18", "image_needed": false, "image_options": false, "image_file": null, "notes": "Printed short-answer; answer 4/15 is a fraction so converted to MCQ. Key: 4/15 = index 0." }, { "n": 19, "type_id": 2, "question": "Express \\(\\dfrac{5}{8}\\) as a decimal.
[?]", "answer0": "0.625", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 158, "difficulty_id": 2, "explanation": "5/8 means 5 ÷ 8 = 0.625.", "hints": ["Divide the numerator by the denominator: 5 ÷ 8.", "8 goes into 5.000..."], "source": "MGS 2024 P5 End-of-Year Exam Q19", "image_needed": false, "image_options": false, "image_file": null, "notes": "FIB decimal. Key: 0.625." }, { "n": 20, "type_id": 1, "question": "Arrange these distances from the shortest to the longest: 1.35 km, \\(1\\dfrac{3}{5}\\) km, 1 km 305 m.", "answer0": "1 km 305 m, 1.35 km, \\(1\\dfrac{3}{5}\\) km", "answer1": "1.35 km, 1 km 305 m, \\(1\\dfrac{3}{5}\\) km", "answer2": "\\(1\\dfrac{3}{5}\\) km, 1.35 km, 1 km 305 m", "answer3": "1 km 305 m, \\(1\\dfrac{3}{5}\\) km, 1.35 km", "correct_answer": 0, "skill_id": 184, "difficulty_id": 2, "explanation": "Convert all to km: 1.35 km, 1 3/5 km = 1.6 km, 1 km 305 m = 1.305 km. Ordering smallest to largest: 1.305 km (1 km 305 m), 1.35 km, 1.6 km (1 3/5 km). So: 1 km 305 m, 1.35 km, 1 3/5 km.", "hints": ["Write every distance in kilometres as a decimal.", "1 km 305 m = 1.305 km and 1 3/5 km = 1.6 km."], "source": "MGS 2024 P5 End-of-Year Exam Q20", "image_needed": false, "image_options": false, "image_file": null, "notes": "Ordering task; one option contains a mixed number (1 3/5 km), so kept as MCQ (the printed answer requires a mixed-number term that cannot be a clean FIB). Key order: 1 km 305 m, 1.35 km, 1 3/5 km = index 0." }, { "n": 21, "type_id": 2, "question": "In the figure, AFC and BFD are straight lines. Find ∠CFE.
[?]°", "answer0": "26", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 194, "difficulty_id": 2, "explanation": "∠AFB = 48° and ∠AFB is vertically opposite ∠DFC, so ∠DFC = 48°. ∠DFE = 22° is part of ∠DFC, so ∠CFE = ∠DFC − ∠DFE = 48° − 22° = 26°.", "hints": ["Vertically opposite angles are equal, so the angle opposite 48° is also 48°.", "Subtract the 22° angle from that 48° angle."], "source": "MGS 2024 P5 End-of-Year Exam Q21", "image_needed": true, "image_options": false, "image_file": "q21.png", "image_page": 12, "image_bbox": [0.16, 0.20, 0.58, 0.42], "image_loc": "two crossing straight lines through point F: A-F-C horizontal, B-F-D, with 48° at top-left and 22° below, E to the lower right", "notes": "FIB integer (degrees). Answer line on the paper has a degree symbol after the blank. Key: 26." }, { "n": 22, "type_id": 2, "question": "6000 ml of water was poured into 5 containers equally. How many litres of water were there in one container?
[?] l", "answer0": "1.2", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 191, "difficulty_id": 2, "explanation": "6000 ml ÷ 5 = 1200 ml = 1.2 l.", "hints": ["Divide 6000 ml by 5 to find one container.", "Convert ml to litres: 1000 ml = 1 l."], "source": "MGS 2024 P5 End-of-Year Exam Q22", "image_needed": false, "image_options": false, "image_file": null, "notes": "FIB decimal in litres. Answer line on paper has 'l' unit. Key: 1.2." }, { "n": 23, "type_id": 2, "question": "(a) Gopal listed the factors of 36: 1, 2, 3, 4, 6, 18, 36. He missed out two factors. What were the two missing factors? [?] and [?]
(b) Write down all the common factors of 20 and 32. [?]", "answer0": "9", "answer1": "12", "answer2": "1, 2, 4", "answer3": null, "correct_answer": null, "skill_id": 149, "difficulty_id": 2, "explanation": "(a) Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The two missing from Gopal's list are 9 and 12. (b) Factors of 20: 1, 2, 4, 5, 10, 20; factors of 32: 1, 2, 4, 8, 16, 32. Common factors = 1, 2, 4.", "hints": ["For (a), list every factor pair of 36: 1x36, 2x18, 3x12, 4x9, 6x6.", "For (b), find numbers that divide both 20 and 32 exactly."], "source": "MGS 2024 P5 End-of-Year Exam Q23", "image_needed": false, "image_options": false, "image_file": null, "notes": "Multi-part FIB. Part (a) two integer blanks (9, 12); part (b) a small set of common factors '1, 2, 4' entered as one blank. Factors/multiples is a P4 topic; mapped to nearest P5 skill 149. Key: 9 and 12; common factors 1, 2, 4." }, { "n": 24, "type_id": 2, "question": "The figure is formed using 4 squares and 4 equilateral triangles. The length of the straight line AB is 20 cm. Find the perimeter of the figure.
[?] cm", "answer0": "100", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 138, "difficulty_id": 2, "explanation": "AB spans 5 equal side-lengths along the figure, so each side = 20 ÷ 5 = 4 cm. All squares and equilateral triangles share this 4 cm side. The perimeter is made up of 25 such 4 cm sides... using the paper's working: perimeter = 20 cm x 5 = 100 cm.", "hints": ["AB lies along 5 equal edges, so each edge = 20 ÷ 5 = 4 cm.", "Count how many of these equal edges form the outline of the whole figure."], "source": "MGS 2024 P5 End-of-Year Exam Q24", "image_needed": true, "image_options": false, "image_file": "q24.png", "image_page": 13, "image_bbox": [0.16, 0.62, 0.50, 0.80], "image_loc": "composite figure of 4 squares and 4 equilateral triangles with dashed line AB across the middle", "notes": "FIB integer (cm). Key: 100 (per printed solution: 20 x 5)." }, { "n": 25, "type_id": 2, "question": "The graph shows the fare a taxi company charges for the first 10 kilometres.
(a) How much is the taxi fare for the first kilometre? $[?]
(b) Alan paid $20 for his taxi ride. What was the distance he travelled? [?] km", "answer0": "4", "answer1": "8", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 147, "difficulty_id": 2, "explanation": "(a) Reading the line graph, the fare for the first 1 km is $4. (b) Find $20 on the fare axis and read across to the curve, then down to the distance axis: 8 km.", "hints": ["For (a) read the fare value at distance = 1 km.", "For (b) find $20 on the vertical axis and read off the matching distance."], "source": "MGS 2024 P5 End-of-Year Exam Q25", "image_needed": true, "image_options": false, "image_file": "q25.png", "image_page": 14, "image_bbox": [0.16, 0.14, 0.82, 0.40], "image_loc": "line graph of Taxi fare ($) vs Distance (km) with points labelled (4, 8, 12, 20, 32) up to 10 km", "notes": "Multi-part FIB; both answers are whole numbers. Key (a) $4, (b) 8 km." }, { "n": 26, "type_id": 2, "question": "The table shows the local postage rates in Singapore.
First 30 g: $0.30; Next 50 g: $0.50; Every additional 40 g or less: $0.60.
Mr Lim needs to send a parcel that weighs 138 g. How much does he need to pay? $[?]", "answer0": "2", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 2, "explanation": "First 30 g: $0.30. Next 50 g (to 80 g): $0.50. Remaining 138 − 80 = 58 g charged in blocks of 40 g or less: 40 g = $0.60 and the final 18 g = $0.60. Total = 0.30 + 0.50 + 0.60 + 0.60 = $2.00.", "hints": ["Charge the first 30 g, then the next 50 g.", "The remaining 58 g needs two blocks of 'up to 40 g'."], "source": "MGS 2024 P5 End-of-Year Exam Q26", "image_needed": false, "image_options": false, "image_file": null, "notes": "Table transcribed into stem; no figure crop needed. FIB money. Key: $2 (entered as 2)." }, { "n": 27, "type_id": 2, "question": "Ken cut out three identical right-angled triangles. He joined them to form a figure ABCD. CD = 6 cm and AD = 5 cm. The perimeter of the figure is 18 cm. Find the area of the figure ABCD.
[?] cm²", "answer0": "18", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 186, "difficulty_id": 3, "explanation": "Each triangle has legs that match. AB = 18 − 6 − 5 − 5 − 3 = 4 cm (the shorter leg). Area of 1 right-angled triangle = 1/2 x 4 x 3 = 6 cm². The figure is made of 3 congruent triangles, so area = 6 x 3 = 18 cm².", "hints": ["Use the perimeter to find the missing side: 18 − 6 − 5 − 5 − 3.", "Area of one right-angled triangle = 1/2 x base x height; multiply by 3."], "source": "MGS 2024 P5 End-of-Year Exam Q27", "image_needed": true, "image_options": false, "image_file": "q27.png", "image_page": 15, "image_bbox": [0.16, 0.60, 0.45, 0.82], "image_loc": "figure ABCD made of three right-angled triangles, D top with 5 cm to A, 6 cm down DC, B at bottom", "notes": "FIB integer (cm²). Key: 18." }, { "n": 28, "type_id": 2, "question": "In the figure, QTS and PTR are straight lines. PQ = QR = RS. ∠PTS = 115° and ∠RST = 25°. Find ∠PQT.
[?]°", "answer0": "75", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 197, "difficulty_id": 3, "explanation": "∠QRT (= ∠QRP at the straight line, equal to base angle of triangle RST opposite) : ∠QRT = 180° − 115° − 25° = 40°. Triangle PQR is isosceles (PQ = QR) so ∠QPR = ∠QRP = 40°. ∠PQT = 180° − 40° − 40° − 25° = 75°. (Alternatively ∠QTP = 180° − 115° = 65°, then ∠PQT = 180° − 40° − 65° = 75°.)", "hints": ["Find ∠QRT using the straight line and the 25° angle: 180° − 115° − 25°.", "Use the equal sides (isosceles triangles) and the angle sum of 180° in a triangle."], "source": "MGS 2024 P5 End-of-Year Exam Q28", "image_needed": true, "image_options": false, "image_file": "q28.png", "image_page": 16, "image_bbox": [0.14, 0.13, 0.55, 0.27], "image_loc": "figure with Q top-left, R top-right, T at the crossing of QTS and PTR, 115° at T, 25° at S, P lower-left", "notes": "FIB integer (degrees). Key: 75." }, { "n": 29, "type_id": 2, "question": "Three friends shared the total cost of 48 apples in the ratio 5 : 2 : 1. The apples are sold at 12 apples for $10. What was the cost for the largest share? $[?]", "answer0": "25", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 183, "difficulty_id": 3, "explanation": "48 apples cost: 48 ÷ 12 = 4 lots, 4 x $10 = $40. The ratio 5 : 2 : 1 has 5 + 2 + 1 = 8 units = $40, so 1 unit = $5. Largest share = 5 units = 5 x $5 = $25.", "hints": ["First find the total cost of 48 apples using 12 apples for $10.", "Divide the total cost into 8 equal units (5 + 2 + 1) and take 5 units."], "source": "MGS 2024 P5 End-of-Year Exam Q29", "image_needed": true, "image_options": false, "image_file": "q29.png", "image_page": 16, "image_bbox": [0.60, 0.62, 0.82, 0.80], "image_loc": "bag of apples with a '$10' price tag and caption '12 apples for $10', lower-right of page", "notes": "FIB money. The '12 apples for $10' caption is part of the figure; transcribed into the stem so it works without the image. Key: $25." }, { "n": 30, "type_id": 2, "question": "Mary had a new bottle of fish food. She feeds an equal amount of fish food to her fishes each day. At the end of the 18th day, \\(\\dfrac{1}{7}\\) of the bottle was left. At the end of the 19th day, the amount of food left was 200 g. What was the amount of fish food left in the bottle at the end of the 5th day?
[?] g", "answer0": "1600", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "6/7 of the bottle was used in 18 days, so 1/7 lasts 18 ÷ 6 = 3 days. The whole bottle lasts 3 x 7 = 21 days. From day 18 (1/7 left) to day 19, the food drops from 1/7 to 200 g... the amount used in 2 days = the 18th-to-end portion. Using the paper: 2 days → 200 g remaining after day 19 means 100 g per day. Whole bottle = 21 x 100 = 2100 g. At end of day 5, food used = 5 x 100 = 500 g, so food left = 2100 − 500 = 1600 g. (Equivalently 21 − 5 = 16 days of food left, 16 x 100 g = 1600 g.)", "hints": ["6/7 used in 18 days means 1/7 lasts 3 days, so the bottle lasts 21 days.", "Work out the food used per day, then the food left after 5 days."], "source": "MGS 2024 P5 End-of-Year Exam Q30", "image_needed": false, "image_options": false, "image_file": null, "notes": "FIB integer (g). Key: 1600." }, { "n": 31, "type_id": 2, "question": "The usual price of a watch was $780. During a sale, it was sold at 20% discount. How much was the discount?
$[?]", "answer0": "156", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 176, "difficulty_id": 2, "explanation": "Discount = 20/100 x $780 = $156.", "hints": ["20% means 20 out of every 100.", "Find 20% of $780."], "source": "MGS 2024 P5 End-of-Year Exam P2 Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q1. FIB money. Key: $156." }, { "n": 32, "type_id": 2, "question": "Daniel, Ivan and Sean shared 456 marbles in the ratio of 12 : 5 : 2. What was the total number of marbles Ivan and Sean had?
[?]", "answer0": "168", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 183, "difficulty_id": 2, "explanation": "Total units = 12 + 5 + 2 = 19. 19 units = 456, so 1 unit = 456 ÷ 19 = 24. Ivan and Sean = (5 + 2) units = 7 x 24 = 168.", "hints": ["Add the ratio parts: 12 + 5 + 2 = 19 units.", "Find 1 unit, then add Ivan's 5 units and Sean's 2 units."], "source": "MGS 2024 P5 End-of-Year Exam P2 Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q2. FIB integer. Key: 168." }, { "n": 33, "type_id": 2, "question": "In the figure, VWXZ is a square. XYZ is an equilateral triangle. Find ∠WZY.
[?]°", "answer0": "105", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 197, "difficulty_id": 3, "explanation": "In square VWXZ, ∠WZX = 90°. Diagonal ZX splits... ∠WZX = (180 − 90) ÷ 2 = 45° (the diagonal of the square makes 45° at Z). XYZ is equilateral so ∠XZY = 60°. ∠WZY = 45° + 60° = 105°.", "hints": ["The diagonal of a square makes a 45° angle with its side at the corner.", "An equilateral triangle has all angles 60°; add the two angles at Z."], "source": "MGS 2024 P5 End-of-Year Exam P2 Q3", "image_needed": true, "image_options": false, "image_file": "p2q3.png", "image_page": 20, "image_bbox": [0.13, 0.15, 0.45, 0.27], "image_loc": "square VWXZ on the left (V top-left, Z top-right, W bottom-left, X bottom) with equilateral triangle XYZ attached, Y to the right", "notes": "Paper 2 Q3. FIB integer (degrees). Key: 105." }, { "n": 34, "type_id": 2, "question": "PQR is a triangle. Find the sum of angles a, b, c and d.
[?]°", "answer0": "298", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 197, "difficulty_id": 3, "explanation": "A line from Q splits triangle PQR into two triangles. In each triangle the three angles sum to 180°, so the six angles total 2 x 180° = 360°. Angle P (31°) appears in both small triangles' totals as part of the 360°, but a, b, c, d are the other four angles plus the two at the split point... Using the paper's method: a + b + c + d = 2 x 180° − 2 x 31° = 360° − 62° = 298°.", "hints": ["The cevian from Q creates two triangles; their angles total 2 x 180°.", "Subtract the two 31° contributions at P: 2 x 180° − 2 x 31°."], "source": "MGS 2024 P5 End-of-Year Exam P2 Q4", "image_needed": true, "image_options": false, "image_file": "p2q4.png", "image_page": 20, "image_bbox": [0.14, 0.50, 0.52, 0.66], "image_loc": "triangle PQR with a line from Q to base PR; 31° at P, angles a and d near Q, b at the foot, c at R", "notes": "Paper 2 Q4. FIB integer (degrees). Key: 298." }, { "n": 35, "type_id": 0, "question": "Mr and Mrs Soh had different amounts of money. Mr Soh gave 1/4 of his money to Abel. Mrs Soh gave 1/2 of her money to Betsy. For each statement, state whether it is True, False, or Not possible to tell. (a) Abel and Betsy received 3/4 of the total amount of money Mr and Mrs Soh had. (b) Abel and Betsy received the same amount of money from Mr and Mrs Soh.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "(a) False — you cannot just add 1/4 and 1/2 because they are fractions of different (unknown, unequal) totals. (b) Not possible to tell — the actual amounts depend on how much Mr and Mrs Soh each had, which is unknown.", "hints": ["The fractions are of two different wholes that are not equal.", "Without knowing the actual amounts, you cannot compare the gifts."], "source": "MGS 2024 P5 End-of-Year Exam P2 Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q5. True/False/Not-possible-to-tell tick-table — no app question type; type_id 0 (skipped on insert). Key: (a) False, (b) Not possible to tell." }, { "n": 36, "type_id": 2, "question": "Ali and Eva had the same amount of money at first. Later on, Ali received another $550 and Eva spent $260. Ali had 4 times as much money as Eva in the end. How much money did each of them have at first?
$[?]", "answer0": "530", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "Let each start with the same amount. End: Ali = start + 550, Eva = start − 260, and Ali = 4 x Eva. The difference between Ali and Eva at the end = 550 + 260 = $810, which equals 3 units (since Ali = 4u, Eva = 1u). 1u = 810 ÷ 3 = $270 = Eva's end amount. Start = Eva end + 260 = 270 + 260 = $530.", "hints": ["The gap between them at the end = 550 + 260 = $810.", "Ali is 4 times Eva, so the gap is 3 units; find 1 unit then work back to the start."], "source": "MGS 2024 P5 End-of-Year Exam P2 Q6", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q6. They had the SAME amount at first, so one FIB blank. Key: $530 each." }, { "n": 37, "type_id": 2, "question": "John built a solid made up of 9 unit cubes. He placed the solid into a rectangular box measuring 7 units by 4 units by 5 units, then packed the box full by adding more unit cubes. What is the smallest number of unit cubes that John added into the box?
[?]", "answer0": "131", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 190, "difficulty_id": 2, "explanation": "Box volume = 7 x 4 x 5 = 140 unit cubes. The solid already occupies 9 unit cubes, so cubes added = 140 − 9 = 131. (Part (a), drawing the top view, is an interactive draw task and is not served; only the numeric part (b) is captured here.)", "hints": ["Find the total number of unit cubes the box holds: 7 x 4 x 5.", "Subtract the 9 cubes already in the solid."], "source": "MGS 2024 P5 End-of-Year Exam P2 Q7", "image_needed": true, "image_options": false, "image_file": "p2q7.png", "image_page": 23, "image_bbox": [0.30, 0.41, 0.62, 0.58], "image_loc": "rectangular box drawing labelled 7 units, 4 units, 5 units (lower diagram of the question)", "notes": "Paper 2 Q7. Part (a) 'draw the top view' is interactive (not captured). Captured part (b): smallest cubes added = 131. FIB integer." }, { "n": 38, "type_id": 2, "question": "Mrs Lim worked as a sales promoter from February to May. The number of pots she sold was: Feb 58, Mar 47, Apr 69, May unknown. A bonus is given to Mrs Lim if she sells an average of 75 or more pots for any 3 months. What is the least number of pots that she must sell in May to qualify for the bonus?
[?]", "answer0": "98", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 203, "difficulty_id": 3, "explanation": "To average 75 over 3 months the 3-month total must be 75 x 3 = 225. The best 3 months including May are Apr + a strong May plus the larger of the earlier months. Using the paper: total needed = 225, and the two best other months are Apr (69) and Feb (58), so least May = 225 − (58 + 69) = 98.", "hints": ["An average of 75 over 3 months needs a 3-month total of 75 x 3 = 225.", "Pair May with the two highest other months (Feb 58 and Apr 69), then May = 225 − (58 + 69)."], "source": "MGS 2024 P5 End-of-Year Exam P2 Q8", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q8. Table transcribed into stem. FIB integer. Key: 98." }, { "n": 39, "type_id": 1, "question": "Customers who purchased a laptop at a computer fair each received a free item: a printer, a camera, a scanner, or a pair of headphones. The bar graph shows the choices (the camera bar is not shown): Printer 56, Scanner 24, Headphones 40. What is the ratio of the number of customers who chose printers to the number who chose scanners? Give your answer in the simplest form.", "answer0": "7 : 3", "answer1": "3 : 7", "answer2": "56 : 24", "answer3": "14 : 6", "correct_answer": 0, "skill_id": 179, "difficulty_id": 2, "explanation": "Printer : Scanner = 56 : 24. Divide both by their highest common factor 8: 56 ÷ 8 = 7 and 24 ÷ 8 = 3, giving 7 : 3.", "hints": ["Write the ratio printer to scanner: 56 : 24.", "Divide both numbers by 8 to simplify."], "source": "MGS 2024 P5 End-of-Year Exam P2 Q9", "image_needed": true, "image_options": false, "image_file": "p2q9.png", "image_page": 25, "image_bbox": [0.16, 0.17, 0.74, 0.36], "image_loc": "bar graph 'Number of Customers' vs Printer/Camera/Scanner/Headphones with the Camera bar blank", "notes": "Paper 2 Q9 part (a). Answer 7 : 3 is a ratio, so this part is an MCQ. Bar values read from graph: printer 56, scanner 24, headphones 40 (consistent with key). Part (b) captured separately below as an integer FIB. Key: 7 : 3 = index 0." }, { "n": 50, "type_id": 2, "question": "Customers who purchased a laptop at a computer fair each received a free item: a printer, a camera, a scanner, or a pair of headphones. The bar graph shows the choices (the camera bar is not shown): Printer 56, Scanner 24, Headphones 40. \\(\\dfrac{3}{8}\\) of the customers chose cameras. How many customers chose cameras?
[?]", "answer0": "72", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 174, "difficulty_id": 3, "explanation": "The shown bars (printer + scanner + headphones) = 56 + 24 + 40 = 120, which is 5/8 of all customers (since cameras are 3/8). 1/8 = 120 ÷ 5 = 24, so cameras = 3/8 = 3 x 24 = 72.", "hints": ["The three known bars make up 5/8 of all customers (cameras are 3/8).", "Find 1/8 = 120 ÷ 5, then take 3/8."], "source": "MGS 2024 P5 End-of-Year Exam P2 Q9", "image_needed": true, "image_options": false, "image_file": "p2q9.png", "image_page": 25, "image_bbox": [0.16, 0.17, 0.74, 0.36], "image_loc": "bar graph 'Number of Customers' vs Printer/Camera/Scanner/Headphones with the Camera bar blank", "notes": "Paper 2 Q9 part (b). Integer FIB. Shares the p2q9 bar-graph figure. Key: 72." }, { "n": 40, "type_id": 2, "question": "Mary and Nancy had 540 stickers. Mary gave \\(\\dfrac{2}{5}\\) of her stickers to Nancy. Then, Nancy gave \\(\\dfrac{1}{4}\\) of her total number of stickers to Mary. In the end, they had an equal number of stickers. How many stickers did Mary give to Nancy?
[?]", "answer0": "120", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "In the end each has 540 ÷ 2 = 270. Working backwards, Mary's stickers at first (before giving away 2/5, i.e. 3/5 remained then received some back) was 270 + (270 ÷ 3) ... per the paper: Mary's stickers at first = 270 + (270 ÷ ... ) leading to Mary's original 3/5 portion logic, giving Mary first = 300, of which 2/5 = ... The printed key gives stickers Mary gave to Nancy = (180 ÷ 3) x 2 = 120.", "hints": ["In the end each girl has 540 ÷ 2 = 270 stickers.", "Work backwards through Nancy's 1/4 gift, then Mary's 2/5 gift, to find Mary's original amount."], "source": "MGS 2024 P5 End-of-Year Exam P2 Q10", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q10. FIB integer. Key per printed working: 120 stickers given to Nancy." }, { "n": 41, "type_id": 2, "question": "A rectangular tank measuring 50 cm by 28 cm by 30 cm was \\(\\dfrac{3}{5}\\) filled with water at first. Nathan poured some water from the rectangular tank into a 20-cm cubical tank and filled it completely. (a) How much water was left in the rectangular tank? Give your answer in litres. [?] l
(b) Then, he filled 12 identical bottles to the brim with water and poured all the water from the 12 bottles into the rectangular tank. There was 31 litres of water in the rectangular tank in the end. What is the capacity of each bottle? Give your answer in litres. [?] l", "answer0": "17.2", "answer1": "1.15", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 193, "difficulty_id": 3, "explanation": "(a) Water at first = 3/5 x 50 x 28 x 30 = 25 200 cm³. Cubical tank = 20 x 20 x 20 = 8000 cm³. Water left = 25 200 − 8000 = 17 200 cm³ = 17.2 l. (b) Water from 12 bottles = 31 − 17.2 = 13.8 l. Each bottle = 13.8 ÷ 12 = 1.15 l.", "hints": ["Volume = length x breadth x height; 1000 cm³ = 1 litre.", "For (b) the bottles added 31 − 17.2 litres; divide by 12."], "source": "MGS 2024 P5 End-of-Year Exam P2 Q11", "image_needed": true, "image_options": false, "image_file": "p2q11.png", "image_page": 27, "image_bbox": [0.18, 0.18, 0.74, 0.34], "image_loc": "rectangular tank (50 cm x 28 cm x 30 cm) with arrow to a 20 cm cube", "notes": "Paper 2 Q11. Tank dimensions transcribed into stem. Two FIB decimal blanks. Key (a) 17.2 l, (b) 1.15 l." }, { "n": 42, "type_id": 1, "question": "At a concert, \\(\\dfrac{4}{9}\\) of the audience were adults. \\(\\dfrac{3}{4}\\) of the children were boys. What fraction of the audience were girls?", "answer0": "\\(\\dfrac{5}{36}\\)", "answer1": "\\(\\dfrac{5}{12}\\)", "answer2": "\\(\\dfrac{15}{36}\\)", "answer3": "\\(\\dfrac{1}{4}\\)", "correct_answer": 0, "skill_id": 161, "difficulty_id": 3, "explanation": "Children = 1 − 4/9 = 5/9 of the audience. Girls = 1/4 of the children (since 3/4 are boys) = 1/4 x 5/9 = 5/36 of the audience.", "hints": ["Find the fraction that are children: 1 − 4/9.", "Girls are 1/4 of the children; multiply 1/4 x 5/9."], "source": "MGS 2024 P5 End-of-Year Exam P2 Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q12 part (a). Answer 5/36 is a fraction, so this part is an MCQ. (Part (b) below is a separate integer FIB.) Key: 5/36 = index 0." }, { "n": 43, "type_id": 2, "question": "At a concert, \\(\\dfrac{4}{9}\\) of the audience were adults and \\(\\dfrac{3}{4}\\) of the children were boys. Girls made up \\(\\dfrac{5}{36}\\) of the audience. There were 350 more boys than girls. How many people were there at the concert?
[?]", "answer0": "1260", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "Boys = 3/4 of children = 3/4 x 5/9 = 15/36 of the audience; girls = 5/36. Boys − girls = 15/36 − 5/36 = 10/36 = 10 units of 1/36. 10 units = 350, so 1 unit = 35. Whole audience = 36 units = 36 x 35 = 1260.", "hints": ["Boys are 15/36 and girls 5/36 of the audience, a difference of 10/36.", "10 of these 1/36-units equal 350; find 1 unit then multiply by 36."], "source": "MGS 2024 P5 End-of-Year Exam P2 Q13", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q12 part (b), captured as its own integer FIB. Restates the fraction result from part (a) so it stands alone. Key: 1260." }, { "n": 44, "type_id": 2, "question": "In the figure, Point C is on line DE. ∠ABE = 81° and ∠BED = 27°. AB = BC and BD = DC (equal sides marked). ∠ADB = 90°. (a) Find ∠BCE. [?]°
(b) Find ∠ACD. [?]°", "answer0": "132", "answer1": "12", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 197, "difficulty_id": 3, "explanation": "(a) In triangle ABD with right angle at D, ∠ABD = 60° (so triangle ABC equal sides give base angles), and ∠CBE = 81° − 60° = 21°. In triangle BCE: ∠BCE = 180° − (27° + 21°) = 132°. (b) ∠BCD = 180° − 132° = 48° (angles on line DE at C). Triangle BCD is isosceles giving ∠ACD = 60° − 48° = 12°.", "hints": ["Use the equal-side (isosceles) markings and the right angle at D.", "For (a) work in triangle BCE: 180° − (27° + ∠CBE). For (b) use angles on the straight line DE at C."], "source": "MGS 2024 P5 End-of-Year Exam P2 Q14", "image_needed": true, "image_options": false, "image_file": "p2q14.png", "image_page": 30, "image_bbox": [0.14, 0.12, 0.45, 0.36], "image_loc": "figure with B at top, A left, D and C on line going down to E at bottom; 81° at B, 27° at E, equal-side tick marks", "notes": "Paper 2 Q13. Multi-part FIB, two integer degree blanks. Key (a) 132°, (b) 12°. (Note: this is question 13 on Paper 2; n re-namespaced sequentially.)" }, { "n": 45, "type_id": 2, "question": "The total cost of a dress and a skirt was $239. Mrs Chen wanted to buy the dress but she was short of $40. In the end, she bought the skirt and had $25 left. (a) How much more did the dress cost than the skirt? $[?]
(b) How much money did Mrs Chen have at first? $[?]", "answer0": "65", "answer1": "112", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "(a) She was $40 short of the dress but had $25 left after the skirt, so dress − skirt = 40 + 25 = $65. (b) skirt = (239 − 65) ÷ 2 = $87; money at first = skirt cost + $25 left = 87 + 25 = $112.", "hints": ["The dress cost (her money + $40); the skirt cost (her money − $25). The difference is 40 + 25.", "Use total $239 and the $65 difference to find the skirt, then add the $25 left."], "source": "MGS 2024 P5 End-of-Year Exam P2 Q15", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q14. Two integer money FIB blanks. Key (a) $65, (b) $112." }, { "n": 46, "type_id": 2, "question": "The figure shows 2 overlapping identical squares in Rectangle WXYZ. The area of Rectangle WXYZ is 768 cm². (a) What fraction of the Rectangle WXYZ is unshaded? Give your answer in the simplest form.
(b) What is the perimeter of the shaded part? [?] cm", "answer0": "96", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 138, "difficulty_id": 3, "explanation": "(b) The rectangle is divided into 12 equal small squares, each of area 768 ÷ 12 = 64 cm², so each side = 8 cm. The shaded figure's boundary is made of 12 such 8 cm edges, giving perimeter = 12 x 8 = 96 cm. (Part (a), the unshaded fraction 5/12, is a fraction answer and is captured separately as an MCQ in the next entry.)", "hints": ["Each small square has area 768 ÷ 12 = 64 cm², so its side is 8 cm.", "Count the number of 8 cm edges around the shaded part, then multiply."], "source": "MGS 2024 P5 End-of-Year Exam P2 Q16", "image_needed": true, "image_options": false, "image_file": "p2q16.png", "image_page": 32, "image_bbox": [0.22, 0.13, 0.58, 0.30], "image_loc": "Rectangle WXYZ containing two overlapping tilted shaded squares (W top-left, X top-right, Z bottom-left, Y bottom-right)", "notes": "Paper 2 Q15. Captured part (b) perimeter = 96 cm (integer FIB). Part (a) fraction 5/12 captured separately below as an MCQ." }, { "n": 47, "type_id": 1, "question": "The figure shows 2 overlapping identical squares in Rectangle WXYZ, divided into 12 equal small triangles. What fraction of the Rectangle WXYZ is unshaded? Give your answer in the simplest form.", "answer0": "\\(\\dfrac{5}{12}\\)", "answer1": "\\(\\dfrac{7}{12}\\)", "answer2": "\\(\\dfrac{1}{2}\\)", "answer3": "\\(\\dfrac{5}{6}\\)", "correct_answer": 0, "skill_id": 120, "difficulty_id": 3, "explanation": "The rectangle is split into 12 equal parts. Counting the unshaded parts gives 5 out of 12, so the unshaded fraction = 5/12 (already in simplest form).", "hints": ["The rectangle divides into 12 equal triangular parts.", "Count the unshaded parts out of 12."], "source": "MGS 2024 P5 End-of-Year Exam P2 Q16a", "image_needed": true, "image_options": false, "image_file": "p2q16.png", "image_page": 32, "image_bbox": [0.22, 0.13, 0.58, 0.30], "image_loc": "Rectangle WXYZ with two overlapping shaded squares; same figure as P2 Q16", "notes": "Paper 2 Q15 part (a). Answer 5/12 is a fraction, so this part is an MCQ. Shares the q16 figure. Key: 5/12 = index 0." }, { "n": 48, "type_id": 2, "question": "Amy had a number of 50-cent coins and 20-cent coins in the ratio of 5 : 4. After she removed \\(\\dfrac{1}{2}\\) of the 50-cent coins, the total number of coins was reduced to 208. (a) How many of each type of coin did Amy have in the end? 50-cent coins: [?] 20-cent coins: [?]
(b) What was the total value of the coins in the end? $[?]", "answer0": "80", "answer1": "128", "answer2": "65.60", "answer3": null, "correct_answer": null, "skill_id": 183, "difficulty_id": 3, "explanation": "(a) 50-cent : 20-cent = 5 : 4. After removing half the 50-cent coins, those become 2.5 units. Total = 2.5u + 4u = 6.5u = 208, so 1u = 32. 50-cent coins left = 2.5 x 32 = 80; 20-cent coins = 4 x 32 = 128. (b) Total value = (80 x $0.50) + (128 x $0.20) = $40 + $25.60 = $65.60.", "hints": ["After removing half the 50-cent coins they are 2.5 units; total left = 2.5u + 4u = 6.5u = 208.", "For (b) multiply each count by its coin value and add."], "source": "MGS 2024 P5 End-of-Year Exam P2 Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q16. Three blanks: 50-cent (80), 20-cent (128), total value ($65.60). All numeric, FIB. Key per printed solution." }, { "n": 49, "type_id": 2, "question": "Sunshine factory was required to produce 2160 toys. The factory owned Machine A which produces 3 toys per minute. (a) How many hours would it take to produce the required number of toys using Machine A? [?] h
(b) To shorten production time, Machine B was purchased. It produces 7 toys every 3 minutes. With Machine A and B used at the same time, how much time would the company save to produce the same number of toys? Give your answer in hours. [?] h", "answer0": "12", "answer1": "5.25", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "(a) Machine A: 3 toys/min, so 2160 ÷ 3 = 720 min = 12 hours. (b) Machine A in 1 hour = 180 toys; Machine B = 7 every 3 min = 140 toys/hour. Together = 180 + 140 = 320 toys/hour. Time together = 2160 ÷ 320 = 6.75 hours (6 3/4 h). Time saved = 12 − 6.75 = 5.25 hours (5 1/4 h).", "hints": ["For (a) 2160 ÷ 3 minutes, then convert minutes to hours.", "For (b) find the combined toys-per-hour rate (180 + 140), the new time, then subtract from 12 hours."], "source": "MGS 2024 P5 End-of-Year Exam P2 Q18", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q17. Two FIB decimal/whole blanks (hours). Key (a) 12 h, (b) 5.25 h (= 5 1/4 h, expressed as decimal so it stays a valid FIB)." } ] }