{ "paper": { "school": "Red Swastika", "year": 2024, "level": "P5", "label": "End-of-Year Exam", "source_prefix": "Red Swastika 2024 P5 End-of-Year Exam", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "Which of the following is fifty-four thousand and seventy in numerals?", "answer0": "5470", "answer1": "54 070", "answer2": "54 700", "answer3": "540 070", "correct_answer": 1, "skill_id": 149, "difficulty_id": 1, "explanation": "Fifty-four thousand = 54 000, and seventy = 70. So fifty-four thousand and seventy = 54 000 + 70 = 54 070.", "hints": ["Write 'fifty-four thousand' as 54 000.", "Add seventy (70) to get 54 070."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: option 2 (54 070)." }, { "n": 2, "type_id": 1, "question": "What is the missing number in the box?
\\(\\dfrac{9}{12} = \\dfrac{3}{[\\,?\\,]}\\)", "answer0": "9", "answer1": "8", "answer2": "6", "answer3": "4", "correct_answer": 3, "skill_id": 158, "difficulty_id": 1, "explanation": "\\(\\dfrac{9}{12}\\) simplified: divide numerator and denominator by 3 gives \\(\\dfrac{3}{4}\\). So the missing number is 4.", "hints": ["The numerator goes from 9 to 3, so divide by 3.", "Divide the denominator 12 by 3 as well."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: option 4 (4). Equivalent-fraction box shown as 3/[?]." }, { "n": 3, "type_id": 1, "question": "Arrange the following fractions from the greatest to the smallest.
\\(\\dfrac{2}{3}\\), \\(\\dfrac{5}{6}\\), \\(\\dfrac{7}{12}\\)", "answer0": "\\(\\dfrac{5}{6}\\), \\(\\dfrac{2}{3}\\), \\(\\dfrac{7}{12}\\)", "answer1": "\\(\\dfrac{5}{6}\\), \\(\\dfrac{7}{12}\\), \\(\\dfrac{2}{3}\\)", "answer2": "\\(\\dfrac{7}{12}\\), \\(\\dfrac{5}{6}\\), \\(\\dfrac{2}{3}\\)", "answer3": "\\(\\dfrac{7}{12}\\), \\(\\dfrac{2}{3}\\), \\(\\dfrac{5}{6}\\)", "correct_answer": 0, "skill_id": 158, "difficulty_id": 2, "explanation": "Convert to twelfths: \\(\\dfrac{2}{3}=\\dfrac{8}{12}\\), \\(\\dfrac{5}{6}=\\dfrac{10}{12}\\), \\(\\dfrac{7}{12}=\\dfrac{7}{12}\\). Greatest to smallest: \\(\\dfrac{10}{12}, \\dfrac{8}{12}, \\dfrac{7}{12}\\), i.e. \\(\\dfrac{5}{6}, \\dfrac{2}{3}, \\dfrac{7}{12}\\).", "hints": ["Use a common denominator of 12.", "Larger numerator over 12 means a larger fraction."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: option 1. Fraction-ordering -> MCQ." }, { "n": 4, "type_id": 1, "question": "Round 8.745 to 2 decimal places.", "answer0": "8.70", "answer1": "8.74", "answer2": "8.75", "answer3": "8.80", "correct_answer": 2, "skill_id": 168, "difficulty_id": 1, "explanation": "To round 8.745 to 2 decimal places, look at the 3rd decimal digit (5). Since it is 5, round up the 2nd decimal digit: 8.74 becomes 8.75.", "hints": ["Look at the digit in the thousandths place.", "If it is 5 or more, round the hundredths digit up."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: option 3 (8.75)." }, { "n": 5, "type_id": 1, "question": "Linda baked 200 cookies. She sold 60 of them. What percentage of the cookies Linda baked was sold?", "answer0": "30%", "answer1": "40%", "answer2": "60%", "answer3": "70%", "correct_answer": 0, "skill_id": 171, "difficulty_id": 1, "explanation": "Percentage sold = \\(\\dfrac{60}{200}\\times 100\\% = 30\\%\\).", "hints": ["Write the sold cookies as a fraction of the total: \\(\\dfrac{60}{200}\\).", "Multiply the fraction by 100% to get a percentage."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: option 1 (30%)." }, { "n": 6, "type_id": 1, "question": "A machine takes 3 min to print 4 posters. At the same rate, how long will it take to print 24 posters?", "answer0": "6 min", "answer1": "8 min", "answer2": "12 min", "answer3": "18 min", "correct_answer": 3, "skill_id": 152, "difficulty_id": 1, "explanation": "24 posters is 24 ÷ 4 = 6 times as many as 4 posters. Time = 6 × 3 min = 18 min.", "hints": ["Find how many groups of 4 posters are in 24 posters.", "Multiply that by 3 minutes."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q6", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: option 4 (18 min)." }, { "n": 7, "type_id": 1, "question": "How many minutes are there in 4 hours?", "answer0": "100", "answer1": "120", "answer2": "240", "answer3": "400", "correct_answer": 2, "skill_id": 135, "difficulty_id": 1, "explanation": "1 hour = 60 minutes. 4 hours = 4 × 60 = 240 minutes.", "hints": ["1 hour has 60 minutes.", "Multiply 60 by 4."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: option 3 (240)." }, { "n": 8, "type_id": 1, "question": "AB and CD are straight lines. Which two angles are equal?", "answer0": "∠x and ∠z", "answer1": "∠y and ∠z", "answer2": "∠x and ∠y", "answer3": "∠w and ∠y", "correct_answer": 0, "skill_id": 194, "difficulty_id": 2, "explanation": "∠x and ∠z are vertically opposite angles formed by the two straight lines AB and CD, so they are equal.", "hints": ["Vertically opposite angles are equal.", "Find the pair that lie directly opposite each other at the crossing point."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q8", "image_needed": true, "image_options": false, "image_file": "q8.png", "image_page": 5, "image_bbox": [0.30, 0.13, 0.68, 0.30], "image_loc": "below the question stem, figure of two intersecting straight lines AB and CD with angles w, x, y, z labelled", "notes": "Answer key: option 1 (∠x and ∠z)." }, { "n": 9, "type_id": 1, "question": "The graph shows the number of handphones sold by a shop from June to September.
How many handphones did the shop sell in September?", "answer0": "10", "answer1": "15", "answer2": "25", "answer3": "40", "correct_answer": 2, "skill_id": 148, "difficulty_id": 1, "explanation": "Reading the bar for September on the graph, the bar reaches 25. So 25 handphones were sold in September.", "hints": ["Find the September bar on the graph.", "Read the value on the vertical axis."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q9", "image_needed": true, "image_options": false, "image_file": "q9.png", "image_page": 5, "image_bbox": [0.30, 0.45, 0.82, 0.66], "image_loc": "bar graph below the first line of the stem, months June-September on x-axis, number of handphones on y-axis", "notes": "Answer key: option 3 (25)." }, { "n": 10, "type_id": 1, "question": "There are 78 canned drinks in a carton. 24 of them are mango flavoured and the rest are lychee flavoured. What is the ratio of the number of mango flavoured drinks to the number of lychee flavoured drinks?", "answer0": "4 : 9", "answer1": "9 : 4", "answer2": "4 : 13", "answer3": "9 : 13", "correct_answer": 3, "skill_id": 179, "difficulty_id": 2, "explanation": "Lychee drinks = 78 − 24 = 54. Ratio mango : lychee = 24 : 54 = 4 : 9... check: 24:54 divide by 6 = 4:9. The printed key gives option 4 (9:13). Note: 24:54 simplifies to 4:9 (option 1).", "hints": ["Find the number of lychee drinks: 78 − 24.", "Write mango : lychee and simplify by dividing by the common factor."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q10", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key marks option 4 (9:13), but 24:54 simplifies to 4:9 (option 1). Flagging discrepancy: mathematically correct answer is 4:9 (index 0). correct_answer set to 0 per math; verify against official key." }, { "n": 11, "type_id": 1, "question": "Evan was given $4 pocket money every day from Monday to Friday. He spent $3.20 each day from Monday to Thursday and saved the rest. He spent 30 cents more on Friday. How much did Evan save altogether?", "answer0": "$3.20", "answer1": "$3.70", "answer2": "$4.00", "answer3": "$4.30", "correct_answer": 1, "skill_id": 167, "difficulty_id": 3, "explanation": "Mon-Thu: saved $4 − $3.20 = $0.80 each day, over 4 days = $3.20. Friday he spent $3.20 + $0.30 = $3.50, saved $4 − $3.50 = $0.50. Total saved = $3.20 + $0.50 = $3.70.", "hints": ["Find the daily saving from Monday to Thursday and multiply by 4.", "On Friday he spent 30 cents more, so find Friday's saving separately and add."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q11", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: option 2 ($3.70)." }, { "n": 12, "type_id": 1, "question": "The figure is made up of 3 identical rectangles. The breadth of the rectangle is 3 cm. The perimeter of the figure is 48 cm. What is the length of the rectangle?", "answer0": "36 cm", "answer1": "12 cm", "answer2": "9 cm", "answer3": "4 cm", "correct_answer": 2, "skill_id": 138, "difficulty_id": 3, "explanation": "The two top rectangles lie end to end (each length L, breadth 3) and one rectangle below. Tracing the outline: perimeter = 4L + 6 (in terms of L and the 3 cm breadths) ... using the printed key the length = 9 cm.", "hints": ["Express the perimeter in terms of the length L and breadth 3 cm.", "Set the perimeter expression equal to 48 cm and solve for L."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q12", "image_needed": true, "image_options": false, "image_file": "q12.png", "image_page": 6, "image_bbox": [0.35, 0.55, 0.70, 0.66], "image_loc": "figure of three identical rectangles below the stem, 3 cm breadth marked on the right and ? marking the length at the bottom", "notes": "Answer key: option 3 (9 cm)." }, { "n": 13, "type_id": 1, "question": "A rectangular tank, 10 cm by 5 cm by 24 cm shown is \\(\\dfrac{1}{4}\\) filled with water. How much more water is needed to fill the tank to its brim?", "answer0": "300 cm³", "answer1": "600 cm³", "answer2": "900 cm³", "answer3": "1200 cm³", "correct_answer": 2, "skill_id": 191, "difficulty_id": 2, "explanation": "Tank volume = 10 × 5 × 24 = 1200 cm³. It is \\(\\dfrac{1}{4}\\) full, so \\(\\dfrac{3}{4}\\) is empty. Water needed = \\(\\dfrac{3}{4}\\times 1200 = 900\\) cm³.", "hints": ["Find the full volume: 10 × 5 × 24.", "The tank is 1/4 full, so 3/4 is still needed."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q13", "image_needed": true, "image_options": false, "image_file": "q13.png", "image_page": 7, "image_bbox": [0.33, 0.13, 0.62, 0.33], "image_loc": "3D rectangular tank below the stem, dimensions 10 cm, 5 cm, 24 cm marked, lower quarter shaded for water", "notes": "Answer key: option 3 (900 cm³)." }, { "n": 14, "type_id": 1, "question": "The average number of students in 3 classes is 32. Class A has 37 students while Class B has 3 more students than Class A. What is the number of students in Class C?", "answer0": "19", "answer1": "24", "answer2": "27", "answer3": "96", "correct_answer": 0, "skill_id": 203, "difficulty_id": 2, "explanation": "Total students = 3 × 32 = 96. Class B = 37 + 3 = 40. Class C = 96 − 37 − 40 = 19.", "hints": ["Total = average × number of classes = 32 × 3.", "Subtract Class A and Class B totals to find Class C."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q14", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: option 1 (19)." }, { "n": 15, "type_id": 1, "question": "Devi had some 10-cents, 20-cents and 50-cents coins in a box. There were twice as many 20-cent coins as 50-cent coins in the box. The number of 10-cent coins was the same as the number of 50-cent coins. The total value of all her coins was $23. How many coins were there in the box altogether?", "answer0": "23", "answer1": "46", "answer2": "69", "answer3": "92", "correct_answer": 3, "skill_id": 152, "difficulty_id": 3, "explanation": "Let 50c coins = u, then 10c coins = u and 20c coins = 2u. Value = 50u + 10u + 20(2u) = 50u + 10u + 40u = 100u cents per unit-group = $1 per u. Total $23 means u = 23. Coins = u + u + 2u = 4u = 4 × 23 = 92.", "hints": ["Let the number of 50-cent coins be a unit; express the others in the same unit.", "Find the total value of one set of coins, then divide $23 by it."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q15", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: option 4 (92)." }, { "n": 16, "type_id": 2, "question": "Ali listed the factors of 18.
1, 3, 9, 18
He missed out two factors. What are the two missing factors?
[?] and [?]", "answer0": "2", "answer1": "6", "correct_answer": null, "skill_id": 152, "difficulty_id": 1, "explanation": "The factors of 18 are 1, 2, 3, 6, 9, 18. The listed ones are 1, 3, 9, 18. The missing factors are 2 and 6.", "hints": ["List all numbers that divide 18 exactly.", "Compare your list with 1, 3, 9, 18 to find the missing ones."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q16", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 2 and 6. Order interchangeable but listed smallest first." }, { "n": 17, "type_id": 2, "question": "What is the value of \\(64 - (9 + 11) \\div 5 \\times 2\\)?
[?]", "answer0": "56", "correct_answer": null, "skill_id": 155, "difficulty_id": 2, "explanation": "Brackets first: 9 + 11 = 20. Then \\(20 \\div 5 = 4\\), then \\(4 \\times 2 = 8\\). Finally 64 − 8 = 56.", "hints": ["Do the brackets first.", "Then division and multiplication from left to right, before subtracting."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 56." }, { "n": 18, "type_id": 2, "question": "Find the value of \\(7.8 \\div 3\\).
[?]", "answer0": "2.6", "correct_answer": null, "skill_id": 166, "difficulty_id": 1, "explanation": "\\(7.8 \\div 3 = 2.6\\).", "hints": ["Divide 78 by 3 to get 26.", "Place the decimal point to get 2.6."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q18", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 2.6." }, { "n": 19, "type_id": 0, "question": "In the grid, draw a line parallel to AB and passing through C.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 201, "difficulty_id": 2, "explanation": "Draw a straight line through C that has the same slope (gradient) as AB so it never meets AB. The answer key shows a line through C parallel to AB.", "hints": ["Parallel lines have the same slant.", "Copy the direction of AB but start at point C."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q19", "image_needed": true, "image_options": false, "image_file": "q19.png", "image_page": 10, "image_bbox": [0.22, 0.10, 0.80, 0.46], "image_loc": "dotted grid with line segment AB (A lower-left, B upper-right) and point C above A", "notes": "Interactive draw-a-line task; no value answer -> type_id 0, SKIPPED on insert." }, { "n": 20, "type_id": 1, "question": "Find the value of \\(\\dfrac{4}{9} \\times 5\\). Leave your answer in mixed number.", "answer0": "\\(2\\dfrac{2}{9}\\)", "answer1": "\\(1\\dfrac{2}{9}\\)", "answer2": "\\(\\dfrac{20}{9}\\)", "answer3": "\\(2\\dfrac{1}{9}\\)", "correct_answer": 0, "skill_id": 163, "difficulty_id": 1, "explanation": "\\(\\dfrac{4}{9}\\times 5 = \\dfrac{20}{9} = 2\\dfrac{2}{9}\\).", "hints": ["Multiply the numerator by 5: 4 × 5 = 20.", "Convert \\(\\dfrac{20}{9}\\) to a mixed number (20 ÷ 9 = 2 remainder 2)."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q20", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 2 2/9. Mixed-number answer -> MCQ. Distractors plausible." }, { "n": 21, "type_id": 2, "question": "(a) Three volumes are given: \\(1.3\\,\\ell\\), \\(1\\dfrac{1}{4}\\,\\ell\\), \\(1\\,\\ell\\;33\\,\\text{ml}\\). Which is the smallest?
[?]
(b) How much water is in the container shown? Give your answer in ml.
[?] ml", "answer0": "1 ℓ 33 ml", "answer1": "700", "correct_answer": null, "skill_id": 184, "difficulty_id": 2, "explanation": "(a) Convert all to ml: 1.3 ℓ = 1300 ml; 1¼ ℓ = 1250 ml; 1 ℓ 33 ml = 1033 ml. Smallest is 1 ℓ 33 ml. (b) Each marking = 1000 ml ÷ 10 = 100 ml; water reaches 7 markings, so 7 × 100 ml = 700 ml.", "hints": ["Convert every volume to millilitres to compare.", "For (b) work out the value of each scale marking first."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q21", "image_needed": true, "image_options": false, "image_file": "q21.png", "image_page": 11, "image_bbox": [0.33, 0.45, 0.50, 0.60], "image_loc": "measuring beaker for part (b), 1 litre mark at top, water filled to lower part", "notes": "Answer key: (a) 1L33ml, (b) 700 ml. (a) is a word/label answer kept as text first blank; (b) numeric. Part (a) blank answer is a phrase ' 1 ℓ 33 ml'." }, { "n": 22, "type_id": 2, "question": "Gabriel had 340 Pokemon cards for sale. He sold 35% of them yesterday. How many Pokemon cards did he sell yesterday?
[?]", "answer0": "119", "correct_answer": null, "skill_id": 174, "difficulty_id": 1, "explanation": "35% of 340 = \\(\\dfrac{35}{100}\\times 340 = 119\\). (10% = 34, 30% = 102, 5% = 17, 102 + 17 = 119.)", "hints": ["Find 10% of 340 first.", "Build up to 35% (30% + 5%)."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q22", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 119." }, { "n": 23, "type_id": 1, "question": "Peter is standing at point A facing North. He makes a \\(\\dfrac{1}{4}\\)-turn clockwise. Then he turns through an angle of 135° in an anti-clockwise direction. Which direction will he be facing in the end?", "answer0": "North-West", "answer1": "North-East", "answer2": "South-West", "answer3": "South-East", "correct_answer": 0, "skill_id": 152, "difficulty_id": 2, "explanation": "Start facing North. A \\(\\dfrac{1}{4}\\)-turn clockwise (90°) faces him East. Turning 135° anti-clockwise from East: 90° brings him back to North, a further 45° anti-clockwise gives North-West.", "hints": ["A quarter turn is 90°; clockwise from North gives East.", "From East, go 135° anti-clockwise on the 8-point compass."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q23", "image_needed": true, "image_options": false, "image_file": "q23.png", "image_page": 12, "image_bbox": [0.34, 0.18, 0.62, 0.38], "image_loc": "8-point compass diagram with point A in centre, North up and East to the right marked", "notes": "Paper Q23 has a part (a) direction (key: North-West) and a part (b) complete-the-symmetric-figure (interactive, skipped). Only the direction part is captured here as MCQ. Key (a): North-West." }, { "n": 24, "type_id": 2, "question": "A tank was completely filled with water for a water rationing exercise at 1 p.m. The line graph shows the volume of water in the tank from 1 p.m. to 7 p.m.
(a) What was the capacity of the tank? Give your answer in \\(\\ell\\).
[?]
(b) At what time was the tank \\(\\dfrac{1}{3}\\) filled with water? Give your answer in p.m.
[?]", "answer0": "90", "answer1": "6", "correct_answer": null, "skill_id": 148, "difficulty_id": 2, "explanation": "(a) The capacity is the starting (full) volume at 1 p.m., which the graph reads as 90 ℓ. (b) \\(\\dfrac{1}{3}\\) of 90 ℓ = 30 ℓ. The graph reaches 30 ℓ at 6 p.m.", "hints": ["The tank is full at 1 p.m.; read that value for the capacity.", "Find 1/3 of the capacity, then read the time when the graph reaches it."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q24", "image_needed": true, "image_options": false, "image_file": "q24.png", "image_page": 13, "image_bbox": [0.22, 0.13, 0.80, 0.32], "image_loc": "line graph of volume of water in tank (litres) vs time 1 p.m. to 7 p.m., decreasing line", "notes": "Answer key: (a) 90 (litres), (b) 6 (p.m.). Both numeric; units kept in stem." }, { "n": 25, "type_id": 2, "question": "Keming, Ray and Hassan shared a box of stickers in the ratio 5 : 9 : 3. Ray had 32 stickers more than Keming. How many stickers did the three boys have altogether?
[?]", "answer0": "136", "correct_answer": null, "skill_id": 183, "difficulty_id": 2, "explanation": "Ray − Keming = 9u − 5u = 4u = 32, so 1u = 8. Total = 5u + 9u + 3u = 17u = 17 × 8 = 136.", "hints": ["The difference between Ray's and Keming's units equals 32.", "Find 1 unit, then total the 17 units."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q25", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 17u = 32/4 × 17 = 136." }, { "n": 26, "type_id": 2, "question": "The solid is made up of 11 identical cubes. The side view is as shown. Find the greatest number of unit cube(s) Gopal can add to the solid without changing the front view and side view.
[?]", "answer0": "1", "correct_answer": null, "skill_id": 188, "difficulty_id": 3, "explanation": "Adding cubes only in positions hidden from both the front and side views keeps both views unchanged. The greatest number that can be added is 1.", "hints": ["A cube can be added only where it does not appear in the front or the side outline.", "Look for a hidden gap behind the visible cubes."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q26", "image_needed": true, "image_options": false, "image_file": "q26.png", "image_page": 14, "image_bbox": [0.25, 0.12, 0.82, 0.33], "image_loc": "isometric solid of 11 unit cubes (top/front/side views labelled) and a dot-grid side view to its right", "notes": "Paper Q26 part (a) is draw the front view (interactive, skipped); part (b) is the numeric count. Only part (b) captured. Answer key: (b) 1." }, { "n": 27, "type_id": 2, "question": "ABCD is a square of side 12 cm. It is formed from two rectangles ABGE and EGCD. F is a point on AB and G is a point on BC. Find the area of EFGH. Give your answer in cm².
[?]", "answer0": "72", "correct_answer": null, "skill_id": 186, "difficulty_id": 3, "explanation": "EFGH is a triangle (per key) with EG as base = 12 cm and height = 6 cm (half the square). Area = \\(12 \\times 12 \\times \\dfrac{1}{2} = 12 \\times 6 = 72\\) cm².", "hints": ["EG runs across the full width of the square, 12 cm.", "Use area = 1/2 × base × height."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q27", "image_needed": true, "image_options": false, "image_file": "q27.png", "image_page": 15, "image_bbox": [0.55, 0.14, 0.83, 0.31], "image_loc": "square ABCD with internal lines, points E,F,G,H marked, 4 cm marked near H at bottom", "notes": "Answer key: EFGH = 12 × 12 × 1/2 = 72 cm²." }, { "n": 28, "type_id": 2, "question": "The figure is made up of two identical squares overlapping each other. The overlapped part forms a shaded square with an area of 49 cm². Find the perimeter of the figure. Give your answer in cm.
[?]", "answer0": "84", "correct_answer": null, "skill_id": 186, "difficulty_id": 3, "explanation": "The shaded overlap square has area 49 cm², so its side = 7 cm (since 7 × 7 = 49). The figure's outline equals two big-square perimeters minus the overlap edges; per the key, side + side = 7 + 7 = 14 and perimeter = 14 × 6 = 84 cm.", "hints": ["Find the side of the small shaded square from its area.", "Use the key's relation: 14 × 6 = 84 cm."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q28", "image_needed": true, "image_options": false, "image_file": "q28.png", "image_page": 15, "image_bbox": [0.28, 0.43, 0.70, 0.66], "image_loc": "two tilted identical squares overlapping, shaded small square in the middle of the overlap", "notes": "Answer key: 7 + 7 = 14; 14 × 6 = 84 cm." }, { "n": 29, "type_id": 2, "question": "Ali used 48 tacks to pin his drawings side by side onto a board. How many drawings did he pin altogether?
[?]", "answer0": "23", "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "Drawings pinned side by side share tacks at shared corners. Per the key, (48 − 2) ÷ 2 = 46 ÷ 2 = 23 drawings.", "hints": ["Adjacent drawings share corner tacks.", "Use the relationship (48 − 2) ÷ 2."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q29", "image_needed": true, "image_options": false, "image_file": "q29.png", "image_page": 16, "image_bbox": [0.27, 0.12, 0.85, 0.23], "image_loc": "row of drawings pinned side by side with tacks at corners, dashed gap then a final framed drawing", "notes": "Answer key: (48-2) ÷ 2 = 23." }, { "n": 30, "type_id": 1, "question": "Sam kept some red and blue pens in bags A and B. Bag A contained twice as many pens as bag B. In bag A, \\(\\dfrac{1}{5}\\) of the pens were red pens and the rest were blue pens. In bag B, \\(\\dfrac{1}{3}\\) of the pens were red pens and the rest were blue pens. What fraction of Sam's pens were red?", "answer0": "\\(\\dfrac{11}{45}\\)", "answer1": "\\(\\dfrac{8}{15}\\)", "answer2": "\\(\\dfrac{2}{15}\\)", "answer3": "\\(\\dfrac{13}{45}\\)", "correct_answer": 0, "skill_id": 165, "difficulty_id": 3, "explanation": "Let bag B = 15 units, bag A = 30 units (twice). Red in A = \\(\\dfrac{1}{5}\\times 30 = 6\\); red in B = \\(\\dfrac{1}{3}\\times 15 = 5\\). Total red = 6 + 5 = 11; total pens = 30 + 15 = 45. Fraction red = \\(\\dfrac{11}{45}\\).", "hints": ["Choose a number of pens for bag B that divides by both 5 and 3 (e.g. 15).", "Bag A is twice bag B; add up the red pens over the total pens."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q30", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 30 + 15 = 45 total, 6 + 5 = 11 red, 11/45. Fraction answer -> MCQ. Distractors plausible." }, { "n": 31, "type_id": 2, "question": "In 38 564,
(a) which digit is in the hundreds place? [?]
(b) what is the value of the digit 3? [?]", "answer0": "5", "answer1": "30000", "correct_answer": null, "skill_id": 149, "difficulty_id": 1, "explanation": "(a) In 38 564 the hundreds place digit is 5. (b) The digit 3 is in the ten-thousands place, so its value is 30 000.", "hints": ["Count places from the right: ones, tens, hundreds.", "The digit 3 sits in the ten-thousands column."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q31", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q1. Answer key: (a) 5, (b) 30000." }, { "n": 32, "type_id": 1, "question": "(a) The figure is made up of two squares. What fraction of the figure is shaded?", "answer0": "\\(\\dfrac{1}{4}\\)", "answer1": "\\(\\dfrac{1}{2}\\)", "answer2": "\\(\\dfrac{1}{3}\\)", "answer3": "\\(\\dfrac{3}{8}\\)", "correct_answer": 0, "skill_id": 158, "difficulty_id": 2, "explanation": "The two squares together are divided so the shaded triangle equals one quarter of the whole figure. Answer: \\(\\dfrac{1}{4}\\).", "hints": ["Work out the area of the shaded triangle relative to the whole figure.", "Compare it to the total area of the two squares."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q32", "image_needed": true, "image_options": false, "image_file": "q32.png", "image_page": 18, "image_bbox": [0.28, 0.43, 0.58, 0.58], "image_loc": "two squares side by side with diagonals drawn, a shaded triangle in the lower middle", "notes": "Paper 2 Q2(a). Fraction answer -> MCQ. Answer key: 1/4. Part (b) of paper Q2 is captured separately as the next item." }, { "n": 33, "type_id": 2, "question": "In the number line, what is the decimal represented by A?
[?]", "answer0": "1.25", "correct_answer": null, "skill_id": 123, "difficulty_id": 1, "explanation": "The interval from 1 to 2 is divided into 8 equal parts of 0.125 each. A is at the 2nd mark from 1, so A = 1 + 2 × 0.125 = 1.25.", "hints": ["Count how many equal parts lie between 1 and 2.", "Find the value of one part, then count up to A."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q33", "image_needed": true, "image_options": false, "image_file": "q33.png", "image_page": 18, "image_bbox": [0.25, 0.70, 0.66, 0.80], "image_loc": "number line from 1 to 2 divided into 8 equal parts, marker A near the start", "notes": "Paper 2 Q2(b). Answer key: 1.25." }, { "n": 34, "type_id": 2, "question": "Two numbers add up to 674. Both numbers are 3-digit numbers. What is the greatest possible difference between the two numbers?
[?]", "answer0": "474", "correct_answer": null, "skill_id": 152, "difficulty_id": 2, "explanation": "To make the difference greatest, make one number as small as possible (smallest 3-digit number, 100). The other = 674 − 100 = 574. Difference = 574 − 100 = 474.", "hints": ["Both numbers must be 3-digit, so the smallest one is 100.", "Subtract 100 from 674 for the other number, then find the difference."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q34", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q3. Answer key: 674 − 100 = 574; 574 − 100 = 474." }, { "n": 35, "type_id": 2, "question": "The rate to send letters to a country is: first 20 g costs $0.85, every additional 10 g or part thereof costs $0.25. Ben sent a letter that weighed 43 g. How much did Ben pay for sending the letter? Give your answer in dollars.
$[?]", "answer0": "1.60", "correct_answer": null, "skill_id": 167, "difficulty_id": 2, "explanation": "43 g = first 20 g + 23 g extra. The extra 23 g is 3 lots of 10 g (10 + 10 + 3, part thereof counts as a full block). Cost = $0.85 + 3 × $0.25 = $0.85 + $0.75 = $1.60.", "hints": ["Subtract the first 20 g, then split the rest into 10 g blocks.", "Any leftover part of 10 g counts as a whole block."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q35", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q4. Answer key: 0.85 + 0.25 × 3 = 1.60." }, { "n": 36, "type_id": 2, "question": "The figure shows a square, WXYZ. \\(\\angle UYX\\) is 21° and \\(\\angle WZU\\) is 48°. Find \\(\\angle UZY\\). Give your answer in degrees.
[?]", "answer0": "42", "correct_answer": null, "skill_id": 200, "difficulty_id": 2, "explanation": "In square WXYZ, \\(\\angle WZY = 90°\\). \\(\\angle UZY = \\angle WZY - \\angle WZU = 90° - 48° = 42°\\).", "hints": ["Each corner of a square is 90°.", "Subtract ∠WZU from the 90° corner at Z."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q36", "image_needed": true, "image_options": false, "image_file": "q36.png", "image_page": 20, "image_bbox": [0.36, 0.12, 0.66, 0.30], "image_loc": "square WXYZ with point U inside, lines from Z and Y to U, 48° at Z and 21° at Y marked", "notes": "Paper 2 Q5(a). Answer key: 90 − 48 = 42°. Part (b) circle-the-words is interactive (key: 'is' an isosceles triangle because ∠YUZ is equal to ∠ZYU) and is omitted as a separate question." }, { "n": 37, "type_id": 2, "question": "In a library, books were placed on 40 shelves with equal number of books on each shelf. 6 shelves were removed and the books on these shelves were placed on the remaining 34 shelves. Because of this, the number of books on each shelf increased by 9. What was the number of books on each shelf at first?
[?]", "answer0": "51", "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "The 6 removed shelves' books are spread over 34 shelves, raising each by 9, so total moved = 34 × 9 = 306. These came from 6 shelves, so books per shelf at first = 306 ÷ 6 = 51.", "hints": ["Total extra books on 34 shelves = 34 × 9.", "Those extra books originally sat on the 6 removed shelves; divide by 6."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q37", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q6. Answer key: 9 × 34 = 306; 306 ÷ 6 = 51." }, { "n": 38, "type_id": 2, "question": "Miss Tan decorated a frame, 28 cm long by 16 cm wide, with identical rectangular tiles using the tiling pattern shown. Each tile is 4 cm by 1 cm. How many tiles did Miss Tan use altogether?
[?]", "answer0": "56", "correct_answer": null, "skill_id": 138, "difficulty_id": 2, "explanation": "Number of tiles fitting along length = 28 ÷ 4 = 7; along width = 16 ÷ 4 = 4. Total tiles = 7 × 4 × 2 = 56 (the key uses 28÷4=7, 16÷4=4, 7×4=28, 28×2=56).", "hints": ["Work out how many tile-lengths fit along each side.", "Account for the tiling pattern doubling per the key: ×2."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q38", "image_needed": true, "image_options": false, "image_file": "q38.png", "image_page": 21, "image_bbox": [0.27, 0.47, 0.70, 0.66], "image_loc": "rectangular frame 28 cm by 16 cm filled with brick-like rectangular tile pattern, single 4 cm x 1 cm tile shown at left", "notes": "Paper 2 Q7. Answer key: 28÷4=7, 16÷4=4, 7×4=28, 28×2=56." }, { "n": 39, "type_id": 2, "question": "The mass of a box with 50 identical beads weighs 0.9 kg. When 30 beads are removed, the mass of the box with the remaining beads is 0.54 kg. What is the mass of each bead in kilogram?
[?]", "answer0": "0.012", "correct_answer": null, "skill_id": 167, "difficulty_id": 2, "explanation": "Removing 30 beads reduced the mass by 0.9 − 0.54 = 0.36 kg. So 30 beads weigh 0.36 kg, and each bead = 0.36 ÷ 30 = 0.012 kg.", "hints": ["Find the mass of the 30 beads removed (the drop in total mass).", "Divide that mass by 30."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q39", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q8. Answer key: 0.36 ÷ 30 = 0.012." }, { "n": 40, "type_id": 1, "question": "A shop sells dresses in four different sizes. The table shows the number of dresses sold last Saturday for size S (16), M (49) and XL (47) but not L. The ratio of the total number of dresses sold in size S, M and XL to the number of dresses sold in size L was 4 : 3. Find the ratio of the number of dresses sold in size M to the number of dresses sold in size L. (Give your answer in the simplest form.)", "answer0": "7 : 12", "answer1": "49 : 84", "answer2": "12 : 7", "answer3": "4 : 3", "correct_answer": 0, "skill_id": 179, "difficulty_id": 3, "explanation": "S + M + XL = 16 + 49 + 47 = 112. This is 4 units, so 1 unit = 28; L = 3 units = 84. M : L = 49 : 84 = 7 : 12 (divide by 7).", "hints": ["Add the three known sizes to get the 4-unit total.", "Find L from the ratio, then simplify M : L."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q40", "image_needed": true, "image_options": false, "image_file": "q40.png", "image_page": 22, "image_bbox": [0.27, 0.45, 0.73, 0.55], "image_loc": "table of dress sizes S, M, L, XL and number sold (S=16, M=49, L blank, XL=47)", "notes": "Paper 2 Q9. Ratio answer -> MCQ. Answer key: 49:84 = 7:12." }, { "n": 41, "type_id": 2, "question": "A baker baked some cupcakes for sale on Saturday morning. He sold 65% of the cupcakes on Saturday and found that he had 203 cupcakes left.
(a) How many cupcakes did the baker bake on Saturday morning? [?]
(b) He sold the remaining cupcakes on Sunday at a discount of 20% off the price of $3.50 each. How much were all the cupcakes sold for on Sunday? Give your answer in dollars. $[?]", "answer0": "580", "answer1": "568.40", "correct_answer": null, "skill_id": 175, "difficulty_id": 3, "explanation": "(a) 203 left = 35% of total, so total = \\(\\dfrac{203}{35}\\times 100 = 580\\) cupcakes. (b) Discounted price = $3.50 × 80% = $2.80. The 203 remaining cupcakes sold for 2.80 × 203 = $568.40.", "hints": ["The 203 left over is 100% − 65% = 35% of the total.", "For (b) apply the 20% discount to $3.50 first, then multiply by 203."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q41", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q10. Answer key: (a) 203/35 × 100 = 580; (b) 3.50 × 0.80 = 2.80, 2.80 × 203 = 568.40. Cupcake price tag image is decorative; not required." }, { "n": 42, "type_id": 2, "question": "The graph shows the cost of food delivery a company charges for delivering meals for the first 10 kilometres.
(a) How much would it cost to deliver a meal that is within 2 km? Give your answer in dollars. $[?]
(b) How much does the delivery company charge for every kilometre after 4 km of travel? Give your answer in dollars. $[?]
(c) The delivery man has to drive 9 km to Peggy's house. How much is her delivery charge? Give your answer in dollars. $[?]", "answer0": "3", "answer1": "2.50", "answer2": "20.50", "correct_answer": null, "skill_id": 148, "difficulty_id": 3, "explanation": "(a) The graph starts at $3 for the first 2 km. (b) After 4 km the line rises $2.50 for each extra km (e.g. from $8 at 4 km to $20.50 at 9 km gives 12.50 over 5 km = $2.50/km). (c) At 9 km: 8 + 2.50 × 5 = $20.50.", "hints": ["Read the cost where distance is up to 2 km for part (a).", "Find the steepness (cost rise per km) of the line beyond 4 km, then extend it to 9 km."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q42", "image_needed": true, "image_options": false, "image_file": "q42.png", "image_page": 24, "image_bbox": [0.22, 0.13, 0.80, 0.36], "image_loc": "line graph cost of delivery ($) vs distance (km) up to 10 km, rising straight line", "notes": "Paper 2 Q11. Answer key: (a) $3, (b) $2.50, (c) 18 + 2.5 = $20.50 (line reading)." }, { "n": 43, "type_id": 2, "question": "In the figure, ACG is a triangle and ABEG is a trapezium. BDE is an isosceles triangle and BH is parallel to CG. D and F are points on the straight line CG. \\(\\angle ABH = 41°\\) and \\(\\angle DBC = 31°\\). Find \\(\\angle r\\). Give your answer in degrees.
[?]", "answer0": "36", "correct_answer": null, "skill_id": 197, "difficulty_id": 3, "explanation": "Angles on a straight line at B: ∠p + ∠q + ∠r = 180° − ∠ABH − ∠DBC = 180° − 41° − 31° = 108°. Since 180° − 108° = 72°, and per the key \\(\\angle r = 180° - (72°\\times 2) = 180° - 144° = 36°\\).", "hints": ["Angles on the straight line AC at B sum to 180°.", "Use the isosceles triangle BDE property to find r."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q43", "image_needed": true, "image_options": false, "image_file": "q43.png", "image_page": 25, "image_bbox": [0.27, 0.13, 0.78, 0.36], "image_loc": "triangle ACG with trapezium ABEG and isosceles triangle BDE, angles 41° and 31° at B, angles p, q, r labelled at B", "notes": "Paper 2 Q12(a). Answer key: 180 − (41+31) = 108; 180 − 108 = 72; 180 − 72×2 = 36°. Part (b) true/false table is interactive and omitted." }, { "n": 44, "type_id": 2, "question": "Mrs Chan bought an equal number of pots and pans. The ratio of the cost of a pot to the cost of a pan was 3 : 2. The average price of a pot and a pan was $11.25. Mrs Chan paid $45 less for the pans than the pots. How many pans did Mrs Chan buy?
[?]", "answer0": "10", "correct_answer": null, "skill_id": 205, "difficulty_id": 3, "explanation": "Total of one pot + one pan = 11.25 × 2 = $22.50. The cost difference per pot-pan pair (3 − 2 = 1 unit) is 22.50 ÷ 5 = $4.50. Total difference is $45, so number of pairs = 45 ÷ 4.50 = 10. Hence 10 pans.", "hints": ["The average of a pot and pan times 2 gives one pot + one pan.", "Find the price gap per pot-pan pair, then divide $45 by it."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q44", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q13(a). Answer key: 11.25 × 2 = 22.50; 22.50 ÷ 5 = 4.50; 45 ÷ 4.50 = 10. Part (b) circle-the-words (key: 'more than') is interactive and omitted." }, { "n": 45, "type_id": 2, "question": "The bar graph (Figure 1) shows the number of books sold in a book store from September to November (scale not given). The line graph (Figure 2) shows the number of books left unsold at the end of each month (scale not given).
(a) Based on Figure 1, what fraction of the books sold in the three months were sold in October? [?]
(b) Given that 18 books were sold in the month of November, how many books were sold from September to November? [?]
(c) What was the number of books left unsold in the book store in December? [?]", "answer0": "\\(\\dfrac{1}{2}\\)", "answer1": "144", "answer2": "0", "correct_answer": null, "skill_id": 148, "difficulty_id": 3, "explanation": "(a) From the bar heights (Sep:Oct:Nov = 2:4:1.5 units... per key the October fraction is \\(\\dfrac{1}{2}\\) of total sold). (b) November = 18 books = its bar units; scaling all bars gives total Sep-Nov = 144. (c) The line graph reaches 0 unsold by November and stays 0, so December = 0.", "hints": ["Compare the October bar height to the sum of all three bars for (a).", "Use the November value (18) to find the scale, then total all bars for (b)."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q45", "image_needed": true, "image_options": false, "image_file": "q45.png", "image_page": 27, "image_bbox": [0.20, 0.18, 0.78, 0.62], "image_loc": "Figure 1 bar graph (books sold Sep-Nov) and Figure 2 line graph (books unsold Aug-Dec), stacked vertically", "notes": "Paper 2 Q14. No printed numeric key for this question on the answer-key pages; (a) fraction kept as text label, (b)/(c) numeric. (a) answer 1/2 and (b) 144, (c) 0 are solved by figure reading (Sep:Oct:Nov bars ~ 2:4:1.5 not clear). FLAG: scales not given and key absent for Q14; values estimated from graph proportions — verify before serving. Mixed answer types; consider review." }, { "n": 46, "type_id": 2, "question": "Two children used the same number of ice cream sticks to make toy houses. Don used \\(\\dfrac{6}{7}\\) of his ice cream sticks while Lea used \\(\\dfrac{3}{4}\\) of her ice cream sticks. They had a total of 4350 ice cream sticks at first.
(a) How many ice cream sticks did each of them use? [?]
(b) How many ice cream sticks must Lea give Don so that they will have an equal number of ice cream sticks left? [?]", "answer0": "1740", "answer1": "145", "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "(a) \\(\\dfrac{6}{7}\\) of Don = \\(\\dfrac{3}{4}\\) of Lea (used equal numbers). Common multiple: Don = 7 units of his (6 used), Lea = 8 units of hers (6 used), used = 6 of each unit-set. Don:Lea total units = 7:8 = 15 parts = 4350, so 1 part = 290. Used = 6 × 290 = 1740 each. (b) Don left = 1×290 = 290; Lea left = 2×290 = 580. To equalise: (580+290)÷2 = 435, Lea gives 580 − 435 = 145.", "hints": ["Set Don's used equal to Lea's used to find the unit ratio (7:8).", "For (b) find each child's leftover, then move sticks until equal."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q46", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q16. Answer key: 6/7 D = 3/4 L; 8+7=15; 4350÷15=290; used 6×290=1740. (b) 2u=580, 580+290=870, 870÷2=435, 435−290=145." }, { "n": 47, "type_id": 2, "question": "The figure is made up of two identical right-angled triangles that overlap each other and PQ = 10 cm. The large triangle has height 24 cm and base 14 cm.
(a) Find the length of RS. Give your answer in cm. [?]
(b) Find the area of the shaded part. Give your answer in cm². [?]", "answer0": "14", "answer1": "266", "correct_answer": null, "skill_id": 186, "difficulty_id": 3, "explanation": "(a) The two triangles are identical, so RS equals the base of a triangle = 14 cm. (b) Shaded part = large triangle area minus the small unshaded overlap triangle. Per key: \\(\\dfrac{1}{2}\\times 14 \\times 10 = 70\\); large area-related 14 × 14 = 196 (140 + 56); shaded = 196 + 70 = 266 cm².", "hints": ["The triangles are identical, so use the given base for RS.", "Subtract the overlapping (unshaded) triangle from the relevant total area."], "source": "Red Swastika 2024 P5 End-of-Year Exam Q47", "image_needed": true, "image_options": false, "image_file": "q47.png", "image_page": 31, "image_bbox": [0.30, 0.13, 0.78, 0.31], "image_loc": "two overlapping right-angled triangles, P top, Q where they cross, R and S on the base; 24 cm height and 14 cm base marked", "notes": "Paper 2 Q17. Answer key: (a) 14 cm; (b) 1/2×14×10=70, 14×14=140+56=196, 196+70=266 cm²." } ] }