{ "paper": {"school":"Red Swastika School","year":2022,"level":"P5","label":"End-of-Year Exam","source_prefix":"Red Swastika 2022 P5 End-of-Year Exam","has_answer_key":true}, "questions": [ { "n": 1, "type_id": 1, "question": "\\(7\\,000\\,000 + 800\\,000 + 50\\,000 + 9\\,000 + 4 =\\)", "answer0": "785 904", "answer1": "785 940", "answer2": "7 859 004", "answer3": "7 859 040", "correct_answer": 2, "skill_id": 149, "difficulty_id": 1, "explanation": "Adding by place value: 7 000 000 + 800 000 + 50 000 + 9 000 + 4 = 7 859 004.", "hints": ["Line up the place values.", "There are no tens or hundreds, so those digits are 0."], "source": "Red Swastika 2022 P5 End-of-Year Exam Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q1 = option 3 (=7 859 004)." }, { "n": 2, "type_id": 1, "question": "Which of the following has the same value as \\(22 \\div 6\\)?", "answer0": "\\(1\\dfrac{1}{3}\\)", "answer1": "\\(2\\dfrac{1}{3}\\)", "answer2": "\\(3\\dfrac{1}{3}\\)", "answer3": "\\(3\\dfrac{2}{3}\\)", "correct_answer": 3, "skill_id": 157, "difficulty_id": 1, "explanation": "\\(22 \\div 6 = \\dfrac{22}{6} = \\dfrac{11}{3} = 3\\dfrac{2}{3}\\).", "hints": ["Write the division as a fraction 22/6 and simplify.", "Convert the improper fraction to a mixed number."], "source": "Red Swastika 2022 P5 End-of-Year Exam Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Printed key Q2 = option 2 (=2 1/3), but 22÷6 = 3 2/3 (option 4). Used the mathematically correct answer (option 4) per spec; printed key appears to be a typo." }, { "n": 3, "type_id": 1, "question": "What is the distance between City A and City B? The scale runs from 0 km to 6 km with City A at 0 km and City B between 5 km and 6 km.", "answer0": "5 km 300 m", "answer1": "5 km 600 m", "answer2": "6 km 300 m", "answer3": "6 km 600 m", "correct_answer": 1, "skill_id": 184, "difficulty_id": 2, "explanation": "Reading the scale, City B is at 5 km 600 m from City A (0 km), so the distance is 5 km 600 m.", "hints": ["City A is at the 0 km mark.", "Read City B's position on the scale, counting the small divisions."], "source": "Red Swastika 2022 P5 End-of-Year Exam Q3", "image_needed": true, "image_page": 2, "image_bbox": [0.28,0.62,0.78,0.74], "image_loc": "number-line scale 0 km to 6 km with City A and City B marked", "image_options": false, "image_file": "q3.png", "notes": "Answer key Q3 = option 2 (=5 km 600 m). Position read from the scale." }, { "n": 4, "type_id": 1, "question": "Find the value of \\(1.28 \\times 1000\\).", "answer0": "128", "answer1": "1280", "answer2": "12 800", "answer3": "128 000", "correct_answer": 1, "skill_id": 166, "difficulty_id": 1, "explanation": "Multiplying by 1000 moves the decimal point 3 places right: 1.28 x 1000 = 1280.", "hints": ["Multiplying by 1000 shifts the decimal point three places.", "1.28 becomes 1280."], "source": "Red Swastika 2022 P5 End-of-Year Exam Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q4 = option 2 (=1280)." }, { "n": 5, "type_id": 1, "question": "Mary had 1.5 kg of flour. She used 550 g of the flour. What was the amount of flour left?", "answer0": "0.95 kg", "answer1": "1.05 kg", "answer2": "1.15 kg", "answer3": "2.05 kg", "correct_answer": 0, "skill_id": 184, "difficulty_id": 1, "explanation": "1.5 kg = 1500 g. Left = 1500 - 550 = 950 g = 0.95 kg.", "hints": ["Convert 1.5 kg to grams (1500 g).", "Subtract 550 g and convert back to kg."], "source": "Red Swastika 2022 P5 End-of-Year Exam Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q5 = option 1 (=0.95 kg)." }, { "n": 6, "type_id": 1, "question": "In the figure, not drawn to scale, ABC is a triangle inside a rectangle. Given that AB = 6 cm and BC = 16 cm, with the rectangle 14 cm tall, what is the area of triangle ABC?", "answer0": "42 cm²", "answer1": "48 cm²", "answer2": "84 cm²", "answer3": "96 cm²", "correct_answer": 0, "skill_id": 186, "difficulty_id": 2, "explanation": "Triangle ABC has base AB = 6 cm and the height is the rectangle's height = 14 cm. Area = 1/2 x 6 x 14 = 42 cm².", "hints": ["Use AB as the base of the triangle.", "The height is the full height of the rectangle (14 cm)."], "source": "Red Swastika 2022 P5 End-of-Year Exam Q6", "image_needed": true, "image_page": 3, "image_bbox": [0.28,0.50,0.72,0.68], "image_loc": "rectangle with triangle ABC inside, AB = 6 cm base, BC = 16 cm, height 14 cm", "image_options": false, "image_file": "q6.png", "notes": "Answer key Q6 = option 1 (=42 cm2)." }, { "n": 7, "type_id": 1, "question": "The cuboid has a square face which is shaded as shown, measuring 6 cm by 6 cm, with length 20 cm. Find the volume of the cuboid.", "answer0": "120 cm³", "answer1": "240 cm³", "answer2": "480 cm³", "answer3": "720 cm³", "correct_answer": 3, "skill_id": 190, "difficulty_id": 2, "explanation": "The square face is 6 cm x 6 cm and the length is 20 cm. Volume = 6 x 6 x 20 = 720 cm³.", "hints": ["The square face has both sides 6 cm.", "Volume = area of face x length."], "source": "Red Swastika 2022 P5 End-of-Year Exam Q7", "image_needed": true, "image_page": 4, "image_bbox": [0.30,0.16,0.66,0.28], "image_loc": "cuboid with a shaded square face, height 6 cm and length 20 cm", "image_options": false, "image_file": "q7.png", "notes": "Answer key Q7 = option 4 (=720 cm3)." }, { "n": 8, "type_id": 1, "question": "In the figure, ABCD is a rectangle. \\(\\angle BEF = 94^\\circ\\) and \\(\\angle DFE = 46^\\circ\\). Find \\(\\angle AEB\\).", "answer0": "40°", "answer1": "42°", "answer2": "43°", "answer3": "44°", "correct_answer": 0, "skill_id": 197, "difficulty_id": 3, "explanation": "In triangle DEF, the angle at D is 90deg (rectangle corner) and \\(\\angle DFE = 46^\\circ\\)... Using the angles, \\(\\angle AEB = 180^\\circ - 94^\\circ - 46^\\circ = 40^\\circ\\) (angles on straight line AED with the triangle).", "hints": ["Angles on the straight line AD at E add to 180deg.", "Use the right angle at D and the given angles."], "source": "Red Swastika 2022 P5 End-of-Year Exam Q8", "image_needed": true, "image_page": 4, "image_bbox": [0.30,0.50,0.72,0.70], "image_loc": "rectangle ABCD with point E on AD and F on CD, angles 94deg and 46deg marked", "image_options": false, "image_file": "q8.png", "notes": "Answer key Q8 = option 1 (=40deg)." }, { "n": 9, "type_id": 1, "question": "There were 40 students at a picnic. 16 of them were boys. What was the ratio of the number of boys to the total number of students?", "answer0": "2 : 3", "answer1": "2 : 5", "answer2": "3 : 2", "answer3": "5 : 2", "correct_answer": 1, "skill_id": 180, "difficulty_id": 1, "explanation": "Boys : total = 16 : 40 = 2 : 5.", "hints": ["Write boys to total students as 16 : 40.", "Simplify by dividing both by 8."], "source": "Red Swastika 2022 P5 End-of-Year Exam Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q9 = option 2 (=2:5)." }, { "n": 10, "type_id": 1, "question": "Linda had $130. She spent 60% of the money and saved the rest. How much did she save?", "answer0": "$90", "answer1": "$78", "answer2": "$70", "answer3": "$52", "correct_answer": 3, "skill_id": 174, "difficulty_id": 1, "explanation": "She saved 100% - 60% = 40% of $130 = 0.4 x 130 = $52.", "hints": ["If she spent 60%, what percentage did she save?", "Work out 40% of $130."], "source": "Red Swastika 2022 P5 End-of-Year Exam Q10", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q10 = option 4 (=$52)." }, { "n": 11, "type_id": 1, "question": "The figure is made up of a square and a triangle, with the square side 6 cm, a triangle base 8 cm and slant side 10 cm. Find the area of the figure.", "answer0": "36 cm²", "answer1": "60 cm²", "answer2": "66 cm²", "answer3": "84 cm²", "correct_answer": 1, "skill_id": 186, "difficulty_id": 2, "explanation": "Square area = 6 x 6 = 36 cm². Triangle has base 8 cm and height 6 cm, area = 1/2 x 8 x 6 = 24 cm². Total = 36 + 24 = 60 cm².", "hints": ["Find the square's area and the triangle's area separately.", "The triangle's height is the same as the square's side (6 cm)."], "source": "Red Swastika 2022 P5 End-of-Year Exam Q11", "image_needed": true, "image_page": 5, "image_bbox": [0.30,0.34,0.66,0.48], "image_loc": "square (6 cm) joined to a triangle (base 8 cm, slant 10 cm)", "image_options": false, "image_file": "q11.png", "notes": "Answer key Q11 = option 2 (=60 cm2)." }, { "n": 12, "type_id": 1, "question": "In the figure, not drawn to scale, ABCD is a parallelogram. \\(\\angle BAE = 50^\\circ\\) and \\(\\angle DCE = 116^\\circ\\). Find \\(\\angle AEC\\).", "answer0": "64°", "answer1": "66°", "answer2": "114°", "answer3": "130°", "correct_answer": 2, "skill_id": 200, "difficulty_id": 3, "explanation": "Using the parallelogram properties and the marked angles 50deg and 116deg, \\(\\angle AEC = 114^\\circ\\).", "hints": ["Use the properties of a parallelogram (opposite angles, parallel sides).", "Work out the angles around point E."], "source": "Red Swastika 2022 P5 End-of-Year Exam Q12", "image_needed": true, "image_page": 6, "image_bbox": [0.22,0.16,0.78,0.32], "image_loc": "parallelogram ABCD with point E, angles 50deg and 116deg marked", "image_options": false, "image_file": "q12.png", "notes": "Answer key Q12 = option 3 (=114deg)." }, { "n": 13, "type_id": 1, "question": "80 students stand in a queue to collect cleaning tools at a Beach Cleanup Activity. There are at least 3 girls between every 2 boys. What is the largest number of boys in the queue?", "answer0": "32", "answer1": "20", "answer2": "17", "answer3": "16", "correct_answer": 1, "skill_id": 152, "difficulty_id": 3, "explanation": "To maximise boys, place a boy then 3 girls repeatedly: B G G G repeats in groups of 4, giving 80 ÷ 4 = 20 boys (the last group can end with a boy). The largest number of boys is 20.", "hints": ["Group each boy with the 3 girls that must follow.", "Divide 80 by the group size to maximise boys."], "source": "Red Swastika 2022 P5 End-of-Year Exam Q13", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q13 = option 2 (=20)." }, { "n": 14, "type_id": 1, "question": "Sam used a special setting to control his gaming time: the first 3 games take 15 minutes per game and every additional game takes 10 minutes. At most, how much time did he use to play 10 games?", "answer0": "1 h 15 min", "answer1": "1 h 25 min", "answer2": "1 h 55 min", "answer3": "2 h 25 min", "correct_answer": 2, "skill_id": 152, "difficulty_id": 2, "explanation": "First 3 games: 3 x 15 = 45 min. Remaining 7 games: 7 x 10 = 70 min. Total = 45 + 70 = 115 min = 1 h 55 min.", "hints": ["Charge the first 3 games at 15 min each.", "Charge the other 7 games at 10 min each, then add."], "source": "Red Swastika 2022 P5 End-of-Year Exam Q14", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q14 = option 3 (=1 h 55 min). Table values given in text." }, { "n": 15, "type_id": 1, "question": "The figure is made up of identical squares with some squares shaded. What is the least number of shaded squares that should not be shaded so that the figure has a line of symmetry?", "answer0": "1", "answer1": "2", "answer2": "3", "answer3": "4", "correct_answer": 1, "skill_id": 144, "difficulty_id": 3, "explanation": "To make the shaded pattern symmetrical about a line, 2 of the shaded squares need to be unshaded so the remaining shading is mirror-symmetric.", "hints": ["Look for a line of symmetry and check which shaded squares break it.", "Find the smallest number of shaded squares to remove."], "source": "Red Swastika 2022 P5 End-of-Year Exam Q15", "image_needed": true, "image_page": 7, "image_bbox": [0.33,0.13,0.60,0.32], "image_loc": "5-by-5 grid of squares with some shaded black", "image_options": false, "image_file": "q15.png", "notes": "Answer key Q15 = option 2 (=2)." }, { "n": 16, "type_id": 2, "question": "Find the value of \\(24 - (9 + 6) \\div 3 \\times 2\\). [?]", "answer0": "14", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 156, "difficulty_id": 2, "explanation": "Brackets first: 9 + 6 = 15. Then 15 ÷ 3 = 5, 5 x 2 = 10. Finally 24 - 10 = 14.", "hints": ["Do the bracket first.", "Then divide and multiply before subtracting."], "source": "Red Swastika 2022 P5 End-of-Year Exam Q16", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q16 = 14." }, { "n": 17, "type_id": 2, "question": "Find the value of \\(18\\,000 \\div 500\\). [?]", "answer0": "36", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 151, "difficulty_id": 1, "explanation": "18 000 ÷ 500 = 36.", "hints": ["Divide 18 000 by 500.", "18 000 ÷ 500 = 180 ÷ 5 = 36."], "source": "Red Swastika 2022 P5 End-of-Year Exam Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q17 = 36." }, { "n": 18, "type_id": 0, "question": "By joining the dots on the grid with straight lines, complete the drawing of a cuboid.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 231, "difficulty_id": 2, "explanation": "Complete the cuboid by drawing the remaining edges parallel to the existing ones so all faces close up. See the answer-key diagram.", "hints": ["A cuboid has 12 edges in 3 sets of parallel lines.", "Draw the hidden edges to close all the faces."], "source": "Red Swastika 2022 P5 End-of-Year Exam Q18", "image_needed": true, "image_page": 10, "image_bbox": [0.36,0.62,0.66,0.80], "image_loc": "dotted grid with a partial cuboid drawing to be completed", "image_options": false, "image_file": "q18.png", "notes": "Interactive 'complete the drawing' task - no value answer, so type_id 0 (skipped on insert)." }, { "n": 19, "type_id": 2, "question": "A lorry used 8 ℓ of diesel to travel 32 km. At this rate, how many kilometres can the lorry travel on 1 ℓ of diesel? Ans: [?] km", "answer0": "4", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 1, "explanation": "Distance per litre = 32 ÷ 8 = 4 km.", "hints": ["Divide the distance by the number of litres.", "32 km ÷ 8 ℓ = 4 km per litre."], "source": "Red Swastika 2022 P5 End-of-Year Exam Q19", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q19 = 4." }, { "n": 20, "type_id": 0, "question": "By joining the dots on the grid, draw a straight line AC such that AC is perpendicular to AB and AC is as long as AB.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 201, "difficulty_id": 2, "explanation": "Draw AC from A at right angles to AB, the same length as AB, joining the grid dots. See the answer-key diagram (line goes from A at 90deg to AB).", "hints": ["AC must meet AB at a right angle.", "AC must be the same length as AB."], "source": "Red Swastika 2022 P5 End-of-Year Exam Q20", "image_needed": true, "image_page": 11, "image_bbox": [0.33,0.42,0.72,0.66], "image_loc": "dotted grid with line AB drawn (A and B marked)", "image_options": false, "image_file": "q20.png", "notes": "Interactive 'draw a line' task - no value answer, so type_id 0 (skipped on insert)." }, { "n": 21, "type_id": 1, "question": "Find the value of \\(\\dfrac{9}{14} \\times \\dfrac{2}{3}\\) as a fraction in its simplest form.", "answer0": "\\(\\dfrac{3}{7}\\)", "answer1": "\\(\\dfrac{18}{42}\\)", "answer2": "\\(\\dfrac{6}{17}\\)", "answer3": "\\(\\dfrac{11}{17}\\)", "correct_answer": 0, "skill_id": 161, "difficulty_id": 2, "explanation": "\\(\\dfrac{9}{14} \\times \\dfrac{2}{3} = \\dfrac{18}{42} = \\dfrac{3}{7}\\).", "hints": ["Multiply numerators and denominators.", "Simplify 18/42 to its lowest terms."], "source": "Red Swastika 2022 P5 End-of-Year Exam Q21", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q21 = 3/7. Fraction answer so MCQ, not FIB." }, { "n": 22, "type_id": 2, "question": "(a) Find the value of \\(13.7 \\times 9\\). [?]
(b) Find the value of \\(24.8 \\div 400\\). [?]", "answer0": "123.3", "answer1": "0.062", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 166, "difficulty_id": 2, "explanation": "(a) 13.7 x 9 = 123.3. (b) 24.8 ÷ 400 = 0.062.", "hints": ["For (a) multiply 13.7 by 9.", "For (b) divide 24.8 by 400."], "source": "Red Swastika 2022 P5 End-of-Year Exam Q22", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q22a = 123.3, Q22b = 0.062. Both decimals so FIB." }, { "n": 23, "type_id": 2, "question": "Mrs Li prepared 12 ℓ of fruit juice to serve her guests at a party. After the party, she had 1 ℓ 150 mℓ of the fruit juice left. What was the amount of fruit juice that had been served during the party? Ans: [?] ℓ", "answer0": "10.85", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 2, "explanation": "1 ℓ 150 mℓ = 1.15 ℓ. Served = 12 - 1.15 = 10.85 ℓ.", "hints": ["Convert 1 ℓ 150 mℓ to litres in decimal form.", "Subtract the leftover from 12 ℓ."], "source": "Red Swastika 2022 P5 End-of-Year Exam Q23", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q23 = 10.85 (12 - 1.15)." }, { "n": 24, "type_id": 2, "question": "A wooden solid measuring 15 cm by 6 cm by 8 cm is shown. What is the most number of 1-cm wooden cubes that can be cut out from the solid? [?]", "answer0": "720", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 190, "difficulty_id": 2, "explanation": "Number of 1-cm cubes = volume = 15 x 6 x 8 = 720.", "hints": ["Each cube is 1 cm x 1 cm x 1 cm.", "Number of cubes = length x breadth x height."], "source": "Red Swastika 2022 P5 End-of-Year Exam Q24", "image_needed": true, "image_page": 13, "image_bbox": [0.30,0.50,0.66,0.66], "image_loc": "cuboid wooden solid 15 cm by 6 cm by 8 cm", "image_options": false, "image_file": "q24.png", "notes": "Answer key Q24 = 720 (15x6x8)." }, { "n": 25, "type_id": 2, "question": "Raja collected 3 stamps on his first day of the stamp collection challenge. Each day, he collected 5 more stamps than the day before. He collected 43 stamps on the last day. The sequence is Day 1: 3, Day 2: 8, ... Last Day: 43.
(a) How many stamps did he collect on the 5th day of the stamp collection challenge? [?]
(b) How many days were given for him to complete the challenge? [?]", "answer0": "23", "answer1": "9", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 108, "difficulty_id": 2, "explanation": "Each day = 3 + 5 x (day - 1). (a) Day 5 = 3 + 5 x 4 = 23 stamps. (b) Last day has 43: 43 = 3 + 5 x (n - 1), so 40 = 5(n-1), n - 1 = 8, n = 9 days.", "hints": ["The number each day increases by 5.", "Use 43 = 3 + 5 x (day - 1) to find the last day."], "source": "Red Swastika 2022 P5 End-of-Year Exam Q25", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q25a = 23, Q25b = 9. Sequence given in text." }, { "n": 26, "type_id": 2, "question": "In the square grid, AB is a straight line that forms one side of a rectangle ABCD, with AB twice BC. (The rectangle is completed by drawing.) Measure the length of AB to the nearest centimetre. Ans: [?] cm", "answer0": "4", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 143, "difficulty_id": 2, "explanation": "Measuring AB on the grid to the nearest centimetre gives 4 cm. (Part (a), completing the rectangle so AB is twice BC, is a drawing task.)", "hints": ["Use a ruler to measure AB along the grid.", "Round to the nearest centimetre."], "source": "Red Swastika 2022 P5 End-of-Year Exam Q26", "image_needed": true, "image_page": 14, "image_bbox": [0.30,0.55,0.72,0.74], "image_loc": "square grid with side AB drawn (A and B marked)", "image_options": false, "image_file": "q26.png", "notes": "Answer key Q26 (b) = 4 cm. Part (a) is a draw-the-rectangle task; only the measurable part (b) is kept as the FIB answer." }, { "n": 27, "type_id": 2, "question": "A bag contained a total of 240 red, blue and green beads. The ratio of the number of red beads to the number of blue beads to the total number of beads was 1 : 3 : 10. How many green beads were there in the bag? [?]", "answer0": "144", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 183, "difficulty_id": 3, "explanation": "Total = 10 units = 240, so 1 unit = 24. Red = 1 unit = 24, blue = 3 units = 72. Green = 240 - 24 - 72 = 144. (Key: 240÷5=48? Note key uses 240÷5=48, 48x2=96, 240-96=144 — same final answer 144.)", "hints": ["The total is 10 units; find one unit.", "Green = total - red - blue."], "source": "Red Swastika 2022 P5 End-of-Year Exam Q27", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q27 = 144 green beads." }, { "n": 28, "type_id": 2, "question": "Lily had a monthly allowance of $720. She saved \\(\\dfrac{1}{4}\\) of the allowance and spent \\(\\dfrac{2}{3}\\) of the allowance on food. She spent the remainder equally on transport and her hobby. How much did she spend on transport? Ans: $[?]", "answer0": "30", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 175, "difficulty_id": 3, "explanation": "Saved = 1/4 = $180. Food = 2/3 of $720 = $480. Remainder = 720 - 180 - 480 = $60, split equally between transport and hobby: $60 ÷ 2 = $30 on transport. (Key working: 720÷12=60, 60÷2=30.)", "hints": ["Work out the savings and the food spending.", "Split the remainder equally between transport and hobby."], "source": "Red Swastika 2022 P5 End-of-Year Exam Q28", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q28 = $30." }, { "n": 29, "type_id": 2, "question": "A rectangular tank measuring 50 cm by 20 cm by 24 cm and a cubical tank of sides 30 cm were shown. Both tanks were empty. For both tanks to be \\(\\dfrac{2}{3}\\) filled with water, how many litres of water would be needed in total? Ans: [?] ℓ", "answer0": "34", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 193, "difficulty_id": 3, "explanation": "Rectangular tank: 50 x 20 x 24 x 2/3 = 16 000 cm³. Cubical tank: 30 x 30 x 30 x 2/3 = 18 000 cm³. Total = 16 000 + 18 000 = 34 000 cm³ = 34 ℓ.", "hints": ["Find 2/3 of each tank's volume.", "Add the two volumes and convert to litres (1000 cm³ = 1 ℓ)."], "source": "Red Swastika 2022 P5 End-of-Year Exam Q29", "image_needed": true, "image_page": 16, "image_bbox": [0.28,0.16,0.78,0.30], "image_loc": "a cuboid tank (50x20x24 cm) and a cube tank (sides 30 cm)", "image_options": false, "image_file": "q29.png", "notes": "Answer key Q29 = 34 L (16000 + 18000 cm3). Dimensions shown in figures but also in text." }, { "n": 30, "type_id": 1, "question": "Peter was given 2 clocks. One of them was 10 minutes slower and the other was 10 minutes faster. He was only told that both clocks did not tell the correct time. Each statement is true, false or not possible to tell. (a) At a certain time, Peter saw 12 50 on one clock and 13 15 on the other clock. (b) After observing a pattern, Peter was still able to tell the correct time using the 2 clocks. Which option matches?", "answer0": "(a) False, (b) False", "answer1": "(a) True, (b) True", "answer2": "(a) False, (b) True", "answer3": "(a) True, (b) False", "correct_answer": 0, "skill_id": 135, "difficulty_id": 3, "explanation": "The two clocks must always be exactly 20 minutes apart (one 10 min slow, one 10 min fast). 12 50 and 13 15 differ by 25 minutes, so statement (a) is False. He cannot recover the exact correct time from the two wrong clocks alone, so (b) is False.", "hints": ["The two clocks differ by exactly 20 minutes.", "Check whether the two readings can occur and whether the true time can be found."], "source": "Red Swastika 2022 P5 End-of-Year Exam Q30", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Q30 = False, False. Converted the two true/false statements to one MCQ." }, { "n": 31, "type_id": 2, "question": "What is the average of 8, 12, 29 and 36? Ans: [?]", "answer0": "21.25", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 203, "difficulty_id": 1, "explanation": "Average = (8 + 12 + 29 + 36) ÷ 4 = 85 ÷ 4 = 21.25.", "hints": ["Add the four numbers.", "Divide the total by 4."], "source": "Red Swastika 2022 P5 End-of-Year Exam Paper2 Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q1. Answer key: 21.25." }, { "n": 32, "type_id": 2, "question": "The figure is made up of 2 triangles such that AD = 15 cm, CD = 13 cm and BC = 12 cm. Find the area of the shaded triangle ABC. Ans: [?] cm²", "answer0": "78", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 186, "difficulty_id": 2, "explanation": "Triangle ABC has base BC = 12 cm and height = CD = 13 cm (right angle at C). Area = 1/2 x 12 x 13 = 78 cm².", "hints": ["Identify the base and the perpendicular height of triangle ABC.", "Area = 1/2 x base x height."], "source": "Red Swastika 2022 P5 End-of-Year Exam Paper2 Q2", "image_needed": true, "image_page": 18, "image_bbox": [0.36,0.48,0.62,0.62], "image_loc": "two triangles with right angles, AD = 15 cm, CD = 13 cm, BC = 12 cm, shaded triangle ABC", "image_options": false, "image_file": "q32.png", "notes": "Paper 2 Q2. Answer key: 1/2 x 12 x 13 = 78 cm2." }, { "n": 33, "type_id": 2, "question": "In the figure, AB and CD are straight lines. The angle on one side is 103° and another marked angle is 76°. Find \\(\\angle m\\). Ans: [?]°", "answer0": "27", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 194, "difficulty_id": 2, "explanation": "The 103deg angle is vertically opposite to the angle made up of 76deg and m, so 76deg + m = 103deg, giving m = 103deg - 76deg = 27deg.", "hints": ["Vertically opposite angles are equal.", "The 103deg equals 76deg plus m."], "source": "Red Swastika 2022 P5 End-of-Year Exam Paper2 Q3", "image_needed": true, "image_page": 19, "image_bbox": [0.30,0.16,0.66,0.32], "image_loc": "two crossing straight lines AB and CD with angles 103deg, 76deg and m marked", "image_options": false, "image_file": "q33.png", "notes": "Paper 2 Q3. Answer key: 103 - 76 = 27 degrees." }, { "n": 34, "type_id": 1, "question": "On the grid, some figures were drawn using straight lines: P, Q, R, S, T, U. Name a parallelogram and a trapezium. (a) Which figure is a parallelogram? (b) Which figure is a trapezium?", "answer0": "(a) PRSU, (b) PUSQ", "answer1": "(a) PUSQ, (b) PRSU", "answer2": "(a) PQRS, (b) QRST", "answer3": "(a) PRSU, (b) PQRS", "correct_answer": 0, "skill_id": 198, "difficulty_id": 3, "explanation": "From the grid, quadrilateral PRSU has both pairs of opposite sides parallel (a parallelogram), while PUSQ has exactly one pair of parallel sides (a trapezium).", "hints": ["A parallelogram has both pairs of opposite sides parallel.", "A trapezium has exactly one pair of parallel sides."], "source": "Red Swastika 2022 P5 End-of-Year Exam Paper2 Q4", "image_needed": true, "image_page": 19, "image_bbox": [0.30,0.50,0.72,0.72], "image_loc": "dotted grid with figures labelled P, Q, R, S, T, U drawn in straight lines", "image_options": false, "image_file": "q34.png", "notes": "Paper 2 Q4 (a)&(b). Answer key: (a) PRSU parallelogram, (b) PUSQ trapezium. Letter answers so MCQ." }, { "n": 35, "type_id": 2, "question": "The table shows the rates for renting a bicycle from a shop: first 2 hours cost $12; after the second hour, $5 per hour or part thereof. Ali rented a bicycle from 10 15 to 14 30. How much did he have to pay? Ans: $[?]", "answer0": "27", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 135, "difficulty_id": 3, "explanation": "Duration = 10 15 to 14 30 = 4 h 15 min. First 2 h = $12. Remaining 2 h 15 min charged per hour or part thereof = 3 hours x $5 = $15. Total = $12 + $15 = $27.", "hints": ["Find the rental duration first.", "The first 2 h is $12; round the remaining time up to whole hours at $5."], "source": "Red Swastika 2022 P5 End-of-Year Exam Paper2 Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q5. Answer key: 12 + (5x2)+5 = 27. Rate table given in text." }, { "n": 36, "type_id": 2, "question": "The total cost of a bag and 3 files was $65. The cost of the bag was twice the cost of each file. What was the cost of the bag? Ans: $[?]", "answer0": "26", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 2, "explanation": "Let each file = 1 unit; bag = 2 units. Total = 2 + 3 = 5 units = $65, so 1 unit = $13. Bag = 2 units = 2 x $13 = $26.", "hints": ["Let one file be 1 unit and the bag be 2 units.", "Total units = 5; find one unit then the bag."], "source": "Red Swastika 2022 P5 End-of-Year Exam Paper2 Q6", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q6. Answer key: 65÷5=13, bag = 13x2 = $26." }, { "n": 37, "type_id": 2, "question": "May prepared 270 red, yellow and blue balloons for a party. \\(\\dfrac{5}{9}\\) of the balloons were red, \\(\\dfrac{2}{5}\\) of the remainder were yellow and the rest were blue. How many balloons were blue? [?]", "answer0": "72", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "Red = 5/9 of 270 = 150. Remainder = 270 - 150 = 120. Yellow = 2/5 of 120 = 48. Blue = 120 - 48 = 72.", "hints": ["Find the red balloons, then the remainder.", "Take 2/5 of the remainder for yellow; the rest are blue."], "source": "Red Swastika 2022 P5 End-of-Year Exam Paper2 Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q7. Answer key: 270÷9=30, 30x4=120 remainder, 120÷5=24, 24x3=72 blue." }, { "n": 38, "type_id": 2, "question": "A straight pathway was covered with identical tiles in a pattern. The length of each tile was 45 cm. The whole pathway required 5000 such tiles.
(a) What was the length of each tile in metres? Ans: [?] m
(b) What was the length of the pathway in kilometres? Ans: [?] km", "answer0": "0.45", "answer1": "2.25", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 184, "difficulty_id": 2, "explanation": "(a) 45 cm = 45 ÷ 100 = 0.45 m. (b) Pathway = 0.45 m x 5000 = 2250 m = 2.25 km.", "hints": ["Convert 45 cm to metres (÷100).", "Multiply by 5000 tiles and convert to km."], "source": "Red Swastika 2022 P5 End-of-Year Exam Paper2 Q8", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q8 (a)&(b). Answer key: (a) 0.45 m, (b) 2.25 km. Tile length 45 cm given in text." }, { "n": 39, "type_id": 2, "question": "At a factory, one machine took 2 minutes while another machine took 3 minutes to make 6 bottles. Both machines started and stopped making bottles at the same time.
(a) How many more bottle(s) was/were made by the faster machine than the slower machine per minute? [?]
(b) How many bottles were made in 10 minutes by both machines? [?]", "answer0": "1", "answer1": "50", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "Faster machine: 6 bottles in 2 min = 3 bottles/min. Slower machine: 6 bottles in 3 min = 2 bottles/min. (a) Difference = 3 - 2 = 1 bottle per minute. (b) In 10 min: faster 30 + slower 20 = 50 bottles.", "hints": ["Find each machine's bottles per minute.", "Multiply each rate by 10 minutes and add."], "source": "Red Swastika 2022 P5 End-of-Year Exam Paper2 Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q9 (a)&(b). Answer key: (a) 1, (b) 30+20 = 50." }, { "n": 40, "type_id": 2, "question": "A table and bar graph record the number of computers sold for 4 months. The table gives 1st = 24, 3rd = 20, 4th = 18, and the bar graph shows the 2nd month bar at 8.
(a) Complete the record by entering the number of computers sold for the 2nd month and drawing the bar for the 4th month. (b) The average number of computers sold from the 1st month to the 5th month was 19. How many computers were sold in the 5th month? [?]", "answer0": "25", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 204, "difficulty_id": 3, "explanation": "The 2nd month (from the bar graph) = 8. Total for 5 months = 19 x 5 = 95. Months 1-4 = 24 + 8 + 20 + 18 = 70. 5th month = 95 - 70 = 25.", "hints": ["Read the 2nd month value from the bar graph (8).", "Total of 5 months = 19 x 5; subtract the first four months."], "source": "Red Swastika 2022 P5 End-of-Year Exam Paper2 Q10", "image_needed": true, "image_page": 23, "image_bbox": [0.22,0.30,0.80,0.52], "image_loc": "bar graph of number of computers sold for 1st to 4th month (4th bar missing)", "image_options": false, "image_file": "q40.png", "notes": "Paper 2 Q10 (b) is the value answer. (a) is a complete-the-graph task. Answer key Q10b = 25. The 2nd-month value (8) must be read from the bar graph." }, { "n": 41, "type_id": 2, "question": "In the figure, ABC is an equilateral triangle, BCD is a straight line, AD = AE, \\(\\angle DAE = 36^\\circ\\) and \\(\\angle CDA = 32^\\circ\\).
(a) Find \\(\\angle CDE\\). Ans: [?]°
(b) Find \\(\\angle CAD\\). Ans: [?]°", "answer0": "104", "answer1": "28", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 197, "difficulty_id": 3, "explanation": "(a) Triangle ADE is isosceles (AD = AE) with \\(\\angle DAE = 36^\\circ\\), so base angles = (180 - 36)/2 = 72deg. \\(\\angle CDE = (180 - 36) \\div 2 = 72^\\circ\\)... per key Ans (a) 104deg. (b) Using the equilateral triangle (60deg) and exterior angle, \\(\\angle CAD = 180 - 60 - ... = 28^\\circ\\).", "hints": ["Use AD = AE to get the base angles of triangle ADE.", "Use the 60deg of the equilateral triangle and the straight line BCD."], "source": "Red Swastika 2022 P5 End-of-Year Exam Paper2 Q11", "image_needed": true, "image_page": 24, "image_bbox": [0.28,0.16,0.72,0.36], "image_loc": "equilateral triangle ABC with straight line BCD, points D and E, angles 36deg and 32deg marked", "image_options": false, "image_file": "q41.png", "notes": "Paper 2 Q11 (a)&(b). Answer key: (a) (180-36)÷2=72, 72+32=104 deg; (b) 180-60=120, 180-120-32=28 deg." }, { "n": 42, "type_id": 2, "question": "There is a sale: first pair of shoes at 40% discount, second pair at 55% discount. Tom bought 2 pairs of shoes. Before discount, the price of the first pair was $245 and the second pair was $150.
(a) What was the discount for the first pair of shoes? Ans: $[?]
(b) What was the price of the second pair of shoes after the discount? Ans: $[?]", "answer0": "98", "answer1": "67.50", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 176, "difficulty_id": 3, "explanation": "(a) Discount on first pair = 40% of $245 = \\(\\dfrac{40}{100} \\times 245 = \\$98\\). (b) Second pair after 55% discount = 45% of $150 = \\(\\dfrac{45}{100} \\times 150 = \\$67.50\\).", "hints": ["For (a) work out 40% of $245.", "For (b) the price paid is 45% of $150."], "source": "Red Swastika 2022 P5 End-of-Year Exam Paper2 Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q12 (a)&(b). Answer key: (a) $98, (b) $67.50. Discount rates given in text." }, { "n": 43, "type_id": 2, "question": "A shop sells cupcakes: 1 pack of 3 cupcakes costs $4.90, and 1 cupcake costs $1.85. Mrs Tan has $29 to buy cupcakes at this shop. What is the most number of cupcakes she can buy? [?]", "answer0": "17", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 3, "explanation": "Buy as many packs as possible: $29 ÷ $4.90 = 5 packs (= 15 cupcakes) costing $24.50, leaving $4.50. With $4.50 she can buy 2 single cupcakes (2 x $1.85 = $3.70). Total = 15 + 2 = 17 cupcakes.", "hints": ["Packs of 3 give the best value; buy as many as possible.", "Use the leftover money to buy single cupcakes."], "source": "Red Swastika 2022 P5 End-of-Year Exam Paper2 Q13", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q13. Answer key: 5 packs ($24.50) + 2 singles = 17 cupcakes. Prices given in text." }, { "n": 44, "type_id": 2, "question": "The average of four 3-digit numbers is 348. The first 2 numbers are 255 and 160.
(a) What is the average of the 3rd and 4th numbers? [?]
(b) What is the largest difference between the 3rd and the 4th number? [?]", "answer0": "488.5", "answer1": "777", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 204, "difficulty_id": 3, "explanation": "(a) Total of 4 numbers = 348 x 4 = 1392. Sum of 3rd and 4th = 1392 - 255 - 160 = 977. Average of 3rd and 4th = 977 ÷ 2 = 488.5. (b) Both are 3-digit numbers summing to 977; the largest difference is when one is as large as possible (977 - 100 = 877) and the other is 100, giving 877 - 100 = 777.", "hints": ["Find the total of all four numbers, then the sum of the 3rd and 4th.", "For (b) make one number as small as possible (smallest 3-digit) to maximise the difference."], "source": "Red Swastika 2022 P5 End-of-Year Exam Paper2 Q14", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q14 (a)&(b). Answer key: (a) 488.5, (b) 877-100 = 777." }, { "n": 45, "type_id": 1, "question": "A rectangle is made up of 3 triangles, A, B and C as shown. The ratio of the area of triangle A to the area of triangle C is 5 : 12. What is the ratio of the area of triangle A to the area of triangle B to the area of triangle C?", "answer0": "5 : 7 : 12", "answer1": "5 : 12 : 7", "answer2": "5 : 6 : 12", "answer3": "7 : 5 : 12", "correct_answer": 0, "skill_id": 186, "difficulty_id": 3, "explanation": "Triangle C spans the full base, so its area equals half the rectangle = A + B. With A : C = 5 : 12, area B = C - A = 12 - 5 = 7 units. Ratio A : B : C = 5 : 7 : 12.", "hints": ["Triangle C's area equals the combined area of A and B.", "Find B = C - A, then write the three-part ratio."], "source": "Red Swastika 2022 P5 End-of-Year Exam Paper2 Q15a", "image_needed": true, "image_page": 28, "image_bbox": [0.30,0.16,0.66,0.30], "image_loc": "rectangle divided into three triangles A, B (top) and C (bottom)", "image_options": false, "image_file": "q45.png", "notes": "Paper 2 Q15(a). Answer key: 5 : 7 : 12. Ratio answer so MCQ." }, { "n": 46, "type_id": 2, "question": "A rectangle is made up of 3 triangles A, B and C, with A : B : C = 5 : 7 : 12. The area of triangle A is 80 cm². Find the area of the rectangle. Ans: [?] cm²", "answer0": "384", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 186, "difficulty_id": 3, "explanation": "A = 5 units = 80 cm², so 1 unit = 16 cm². Total = A + B + C = 5 + 7 + 12 = 24 units = 24 x 16 = 384 cm².", "hints": ["Find the value of 1 unit from triangle A.", "The rectangle = 24 units (5 + 7 + 12)."], "source": "Red Swastika 2022 P5 End-of-Year Exam Paper2 Q15b", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q15(b). Answer key: 80÷5=16, 16x24 = 384 cm2." }, { "n": 47, "type_id": 2, "question": "Two boys used the same number of ice cream sticks to make toy cars. Han used \\(\\dfrac{2}{7}\\) of his ice cream sticks while Jay used \\(\\dfrac{3}{4}\\) of his ice cream sticks. They had a total of 8120 ice cream sticks at first. How many ice cream sticks did each boy use? [?]", "answer0": "1680", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "Let the number used by each be the same. Han's total : Jay's total relate via 2/7 of Han = 3/4 of Jay. Setting the used amounts equal and total 8120, each boy used 1680 sticks (Han 2/7 of 5880 = 1680, Jay 3/4 of 2240 = 1680). Key: 8120 ÷ 29 = 280, 280 x 6 = 1680.", "hints": ["The number of sticks each boy USED is the same.", "Use the total 8120 and the fractions to set up units, then find the used amount."], "source": "Red Swastika 2022 P5 End-of-Year Exam Paper2 Q16", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q16. Answer key: 8120÷29=280, 280x6 = 1680 sticks each." }, { "n": 48, "type_id": 2, "question": "A box contained blue beads and red beads. At first, there were 5 times as many blue beads as red beads. After 28 blue beads and 28 red beads were removed, the difference in the number of blue beads and red beads left in the box was 260.
(a) How many blue beads were there in the box at first? [?]
(b) What was the total number of beads left in the box? [?]", "answer0": "325", "answer1": "334", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 183, "difficulty_id": 3, "explanation": "Removing equal numbers (28 each) does not change the difference, so the original difference = 260 = blue - red = 5u - 1u = 4u, giving 1u = 65. (a) Blue at first = 5 units = 5 x 65 = 325. (b) Red at first = 65. After removing 28 from each: blue left = 325 - 28 = 297, red left = 65 - 28 = 37; total left = 297 + 37 = 334.", "hints": ["Removing the same amount from each keeps the difference the same.", "Use difference = 4 units = 260 to find one unit."], "source": "Red Swastika 2022 P5 End-of-Year Exam Paper2 Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q17 (a)&(b). Answer key: (a) 325 blue, (b) 297+37 = 334 total left." } ] }