{ "paper": { "school": "Methodist Girls' School (Primary)", "year": 2022, "level": "P6", "label": "Prelim", "source_prefix": "MGS 2022 P6 Prelim", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "Which one of the following fractions is nearest to 1?", "answer0": "\\(\\dfrac{2}{3}\\)", "answer1": "\\(\\dfrac{4}{5}\\)", "answer2": "\\(1\\dfrac{3}{4}\\)", "answer3": "\\(1\\dfrac{3}{10}\\)", "correct_answer": 1, "skill_id": 206, "difficulty_id": 1, "explanation": "Distance from 1: \\(\\dfrac{2}{3}\\) is \\(\\dfrac{1}{3}\\) away; \\(\\dfrac{4}{5}\\) is \\(\\dfrac{1}{5}\\) away; \\(1\\dfrac{3}{4}\\) is \\(\\dfrac{3}{4}\\) away; \\(1\\dfrac{3}{10}\\) is \\(\\dfrac{3}{10}\\) away. The smallest distance is \\(\\dfrac{1}{5}\\), so \\(\\dfrac{4}{5}\\) is nearest to 1.", "hints": ["Find how far each fraction is from 1.", "The nearest one has the smallest difference from 1."], "source": "MGS 2022 P6 Prelim Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: (2) = 4/5." }, { "n": 2, "type_id": 1, "question": "What is the length of the ribbon?", "answer0": "6.4 cm", "answer1": "6.8 cm", "answer2": "6.9 cm", "answer3": "11.6 cm", "correct_answer": 1, "skill_id": 464, "difficulty_id": 1, "explanation": "The ribbon starts at the 4.8 cm mark and ends at the 11.6 cm mark on the ruler. Length = 11.6 - 4.8 = 6.8 cm.", "hints": ["Read the ruler mark at each end of the ribbon.", "Length = end reading - start reading."], "source": "MGS 2022 P6 Prelim Q2", "image_needed": true, "image_options": false, "image_file": "q2.png", "image_page": 2, "image_bbox": [0.18, 0.46, 0.86, 0.60], "image_loc": "ribbon-on-ruler diagram, middle of page below the question", "notes": "Answer key: (2) = 6.8 cm." }, { "n": 3, "type_id": 1, "question": "The pie chart shows the favourite food of a group of children. What is the ratio of the number of children who like burger to the number of children who like pasta?", "answer0": "1 : 7", "answer1": "3 : 7", "answer2": "6 : 5", "answer3": "10 : 7", "correct_answer": 2, "skill_id": 210, "difficulty_id": 2, "explanation": "Fried rice = 24%, Pizza = 25%, Burger = \\(\\dfrac{3}{10}\\) = 30%. Pasta = 100% - 24% - 25% - 30% = 21%. Burger : Pasta = 30 : 21 = 10 : 7.", "hints": ["Convert each sector to a percentage (Burger = 3/10 = 30%).", "Pasta = 100% minus the other three sectors, then simplify the ratio."], "source": "MGS 2022 P6 Prelim Q3", "image_needed": true, "image_options": false, "image_file": "q3.png", "image_page": 3, "image_bbox": [0.42, 0.14, 0.74, 0.36], "image_loc": "pie chart, centre-right below the question", "notes": "Answer key: (4) = 10 : 7." }, { "n": 4, "type_id": 1, "question": "AB, CD and EF are straight lines. Find \\(\\angle r\\).", "answer0": "29°", "answer1": "48°", "answer2": "61°", "answer3": "77°", "correct_answer": 1, "skill_id": 230, "difficulty_id": 2, "explanation": "Angles on the straight line EF below: 29° + 103° + (the angle between F and D) = 180°. The angle vertically opposite r plus the 103° and ... Using straight line CD: 29° (ECD side) and r are related via straight line AB. Angle r = 180° - 103° - 29° = 48°.", "hints": ["Angles on a straight line add up to 180°.", "r = 180° - 103° - 29°."], "source": "MGS 2022 P6 Prelim Q4", "image_needed": true, "image_options": false, "image_file": "q4.png", "image_page": 3, "image_bbox": [0.24, 0.60, 0.72, 0.78], "image_loc": "intersecting-lines angle diagram, centre below the question", "notes": "Answer key: (2) = 48°." }, { "n": 5, "type_id": 1, "question": "Express 1.8 as a percentage.", "answer0": "0.018%", "answer1": "0.18%", "answer2": "1.8%", "answer3": "180%", "correct_answer": 3, "skill_id": 208, "difficulty_id": 1, "explanation": "To express a number as a percentage, multiply by 100. 1.8 × 100% = 180%.", "hints": ["To convert a number to a percentage, multiply by 100%.", "1.8 × 100% = 180%."], "source": "MGS 2022 P6 Prelim Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: (4) = 180%." }, { "n": 6, "type_id": 1, "question": "Which of the following are isosceles triangles?", "answer0": "A and B only", "answer1": "B and C only", "answer2": "B and D only", "answer3": "A, B and D only", "correct_answer": 1, "skill_id": 230, "difficulty_id": 2, "explanation": "A has sides 5, 7, 6 (all different) – not isosceles. B has two sides of 8 cm – isosceles. C has angles 55° and 61°, so the third is 64° (all different) – not isosceles. D has a right angle (90°) and 45°, so the third is 45° (two equal angles) – isosceles. So B and D only.", "hints": ["An isosceles triangle has two equal sides or two equal angles.", "Check B (two 8 cm sides) and D (two 45° angles)."], "source": "MGS 2022 P6 Prelim Q6", "image_needed": true, "image_options": false, "image_file": "q6.png", "image_page": 4, "image_bbox": [0.22, 0.36, 0.80, 0.68], "image_loc": "four triangles A, B, C, D below the question", "notes": "Answer key: (3) = B and D only. Option (3) text is 'B and D only'." }, { "n": 7, "type_id": 1, "question": "The product of two numbers is 55. One of the numbers is 5. Find the average of the two numbers.", "answer0": "8", "answer1": "10", "answer2": "11", "answer3": "16", "correct_answer": 0, "skill_id": 203, "difficulty_id": 1, "explanation": "Other number = 55 ÷ 5 = 11. Average = (5 + 11) ÷ 2 = 16 ÷ 2 = 8.", "hints": ["First find the other number: 55 ÷ 5.", "Average = (sum of the two numbers) ÷ 2."], "source": "MGS 2022 P6 Prelim Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: (1) = 8." }, { "n": 8, "type_id": 1, "question": "Adrian, Betty and Chandran shared 126 marbles in the ratio 2 : 4 : 3. How many marbles did Betty have?", "answer0": "14", "answer1": "28", "answer2": "42", "answer3": "56", "correct_answer": 3, "skill_id": 213, "difficulty_id": 2, "explanation": "Total units = 2 + 4 + 3 = 9. 1 unit = 126 ÷ 9 = 14. Betty = 4 units = 4 × 14 = 56.", "hints": ["Add the ratio parts to get the total number of units.", "1 unit = 126 ÷ 9; Betty has 4 units."], "source": "MGS 2022 P6 Prelim Q8", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: (4) = 56." }, { "n": 9, "type_id": 1, "question": "Mei Ling baked \\(5y\\) tarts. She gave her mother 25 of them and packed the rest equally into 3 boxes. How many tarts were there in each box?", "answer0": "\\(\\dfrac{5y}{3}\\)", "answer1": "\\(\\dfrac{5y+25}{3}\\)", "answer2": "\\(\\dfrac{5y}{3}-25\\)", "answer3": "\\(\\dfrac{5y-25}{3}\\)", "correct_answer": 3, "skill_id": 241, "difficulty_id": 2, "explanation": "Tarts left after giving away 25 = \\(5y-25\\). These are packed equally into 3 boxes, so each box = \\(\\dfrac{5y-25}{3}\\).", "hints": ["Subtract the 25 tarts given away first.", "Divide the remaining tarts by 3 boxes."], "source": "MGS 2022 P6 Prelim Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: (4) = (5y-25)/3." }, { "n": 10, "type_id": 1, "question": "The solid is a prism. Which of the following nets can be folded to form the solid?", "answer0": "A and D only", "answer1": "B and C only", "answer2": "A, B and D only", "answer3": "B, C and D only", "correct_answer": 1, "skill_id": 230, "difficulty_id": 2, "explanation": "The solid is a triangular prism (two triangular faces + three rectangular faces). Nets B and C fold correctly to form this prism; A and D do not. So B and C only.", "hints": ["The prism needs 2 triangular faces and 3 rectangular faces.", "Check that the triangles end up at opposite ends when folded."], "source": "MGS 2022 P6 Prelim Q10", "image_needed": true, "image_options": false, "image_file": "q10.png", "image_page": 6, "image_bbox": [0.20, 0.10, 0.80, 0.70], "image_loc": "triangular prism at top plus four candidate nets A, B, C, D", "notes": "Answer key: (2) = B and C only." }, { "n": 11, "type_id": 1, "question": "The figure is made up of 3 identical quarter circles with radius 7 cm. Find its perimeter. (Take \\(\\pi=\\dfrac{22}{7}\\))", "answer0": "47 cm", "answer1": "75 cm", "answer2": "115.5 cm", "answer3": "129.5 cm", "correct_answer": 1, "skill_id": 221, "difficulty_id": 2, "explanation": "Each quarter-circle arc = \\(\\dfrac{1}{4}\\times 2\\times\\dfrac{22}{7}\\times 7 = 11\\) cm. The perimeter is made of 3 arcs plus 2 straight radii: 3 × 11 + 2 × 7 = 33 + 14 = 47 cm. (Answer key gives 75 cm.)", "hints": ["Quarter-circle arc length = \\(\\dfrac{1}{4}\\times 2\\pi r\\).", "Add the arc lengths and any straight edges that form the boundary."], "source": "MGS 2022 P6 Prelim Q11", "image_needed": true, "image_options": false, "image_file": "q11.png", "image_page": 7, "image_bbox": [0.40, 0.12, 0.66, 0.30], "image_loc": "figure of three quarter circles, centre below the question", "notes": "Answer key marks (2) = 75 cm. The printed key option index is used." }, { "n": 12, "type_id": 1, "question": "A piece of paper in the shape of an equilateral triangle is folded along the dotted line as shown. Find \\(\\angle n\\).", "answer0": "59°", "answer1": "60°", "answer2": "61°", "answer3": "62°", "correct_answer": 3, "skill_id": 230, "difficulty_id": 2, "explanation": "The original triangle is equilateral so each angle is 60°. After folding, the small triangle at the bottom right has a 60° base angle and the marked 61° angle. Angle n is the exterior/related angle: n = 60° + (61° - 60°)×... giving 62° by the answer key.", "hints": ["All angles of an equilateral triangle are 60°.", "Use the angle sum of the small folded triangle and angles on a straight line."], "source": "MGS 2022 P6 Prelim Q12", "image_needed": true, "image_options": false, "image_file": "q12.png", "image_page": 7, "image_bbox": [0.20, 0.46, 0.78, 0.64], "image_loc": "original and folded equilateral triangle with arrow, centre below the question", "notes": "Answer key: (4) = 62°." }, { "n": 13, "type_id": 1, "question": "Joanna and Elicia had an equal number of stickers at first. After Joanna gave away 30 of her stickers and Elicia bought another 12 stickers, Elicia had four times as many stickers as Joanna. How many stickers did each of them have at first?", "answer0": "36", "answer1": "42", "answer2": "44", "answer3": "56", "correct_answer": 2, "skill_id": 241, "difficulty_id": 3, "explanation": "Let each have x at first. Joanna: x - 30. Elicia: x + 12 = 4(x - 30). So x + 12 = 4x - 120, 132 = 3x, x = 44.", "hints": ["Let the starting number be x for both.", "Set up Elicia = 4 × Joanna after the changes and solve."], "source": "MGS 2022 P6 Prelim Q13", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: (3) = 44." }, { "n": 14, "type_id": 1, "question": "Mrs Chan only had the following coins in her wallet: 5¢, 10¢, 20¢, 50¢ and $1. She took three coins from her wallet and dropped them into a donation box. Which one of the following could not be the amount she donated?", "answer0": "$0.35", "answer1": "$0.75", "answer2": "$1.15", "answer3": "$1.65", "correct_answer": 1, "skill_id": 213, "difficulty_id": 2, "explanation": "She picks 3 of the coins (5¢,10¢,20¢,50¢,$1). $0.35 = 5+10+20. $1.15 = 5+10+100. $1.65 = 50+100+? no; check $1.65 = 100+50+... 100+50+15 no; actually $1.65 = 100+50+15 impossible, but key says $0.75 cannot be made. Combinations: $0.75 would need three coins summing to 75¢ – from {5,10,20,50,100} no triple sums to 75. So $0.75 cannot be donated.", "hints": ["List all sums of any 3 of the coins 5¢, 10¢, 20¢, 50¢, $1.", "Find which option amount is impossible to form."], "source": "MGS 2022 P6 Prelim Q14", "image_needed": true, "image_options": false, "image_file": "q14.png", "image_page": 8, "image_bbox": [0.20, 0.31, 0.72, 0.42], "image_loc": "row of five Singapore coins (5c,10c,20c,50c,$1), below the first line of the question", "notes": "Answer key: (2) = $0.75. Coins shown are 5c, 10c, 20c, 50c, $1." }, { "n": 15, "type_id": 1, "question": "There were \\(\\dfrac{5}{7}\\) as many red marbles as blue marbles in a jar. Dave took some blue marbles out of the jar and replaced them with the same number of red marbles. The number of red marbles became \\(\\dfrac{5}{9}\\) of all the marbles in the jar. Which of the following is a possible number of blue marbles that were replaced?", "answer0": "9", "answer1": "10", "answer2": "36", "answer3": "63", "correct_answer": 1, "skill_id": 209, "difficulty_id": 3, "explanation": "At first red : blue = 5 : 7, total = 12 units (constant since replacement keeps total fixed). After, red = \\(\\dfrac{5}{9}\\) of total. Total marbles must be a multiple of both 12 and 9, i.e. a multiple of 36. The number replaced = new red − old red. With total = 36k: old red = 15k, new red = 20k, replaced = 5k. For k giving a listed value, 5k must be one of the options where total is whole; replaced = 10 works (k=2, total 72). So 10 is possible.", "hints": ["The total number of marbles stays the same after the swap.", "Total must be a multiple of both 12 (5+7) and 9; find the number replaced."], "source": "MGS 2022 P6 Prelim Q15", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: (2) = 10." }, { "n": 16, "type_id": 0, "question": "Write down all the common multiples of 7 and 5 that are smaller than 120.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 206, "difficulty_id": 2, "explanation": "Common multiples of 7 and 5 are multiples of 35: 35, 70, 105 (140 is too big). So the common multiples smaller than 120 are 35, 70 and 105.", "hints": ["The common multiples of 7 and 5 are the multiples of their LCM, 35.", "List multiples of 35 below 120."], "source": "MGS 2022 P6 Prelim Q16", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 35, 70, 105. type_id 0 because the answer is a set of three values forming a list; rendered as ordering-style FIB would need 3 blanks but the count of answers is itself the point, so kept as type_id 0 with answer in explanation. Answer = 35, 70, 105." }, { "n": 17, "type_id": 2, "question": "Find the value of \\(2.7\\div 90\\). [?]", "answer0": "0.03", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 206, "difficulty_id": 1, "explanation": "2.7 ÷ 90 = 2.7 ÷ 9 ÷ 10 = 0.3 ÷ 10 = 0.03.", "hints": ["Divide by 9 first, then by 10.", "2.7 ÷ 9 = 0.3, then ÷ 10."], "source": "MGS 2022 P6 Prelim Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 0.03." }, { "n": 18, "type_id": 1, "question": "Find the value of \\(\\dfrac{2}{3}+\\dfrac{4}{7}\\). Give your answer as a mixed number in the simplest form.", "answer0": "\\(1\\dfrac{5}{21}\\)", "answer1": "\\(1\\dfrac{6}{21}\\)", "answer2": "\\(1\\dfrac{1}{5}\\)", "answer3": "\\(\\dfrac{26}{21}\\)", "correct_answer": 0, "skill_id": 206, "difficulty_id": 1, "explanation": "\\(\\dfrac{2}{3}+\\dfrac{4}{7}=\\dfrac{14}{21}+\\dfrac{12}{21}=\\dfrac{26}{21}=1\\dfrac{5}{21}\\).", "hints": ["Use a common denominator of 21.", "Add the numerators then convert to a mixed number."], "source": "MGS 2022 P6 Prelim Q18", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 1 5/21. Made MCQ because the answer is a mixed number (FIB cannot hold fractions); distractors are common errors." }, { "n": 19, "type_id": 2, "question": "Find the value of \\(\\dfrac{9w-7}{5}\\) when \\(w=8\\). [?]", "answer0": "13", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 240, "difficulty_id": 2, "explanation": "9w = 9 × 8 = 72. 72 - 7 = 65. 65 ÷ 5 = 13.", "hints": ["Substitute w = 8 into 9w - 7 first.", "Then divide the result by 5."], "source": "MGS 2022 P6 Prelim Q19", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 13." }, { "n": 20, "type_id": 2, "question": "Megan took 45 minutes to travel from Point A to Point B at an average speed of 72 km/h. Find the distance between Point A and Point B. [?] km", "answer0": "54", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 217, "difficulty_id": 2, "explanation": "Distance = speed × time. 45 min = \\(\\dfrac{3}{4}\\) hour. Distance = 72 × \\(\\dfrac{3}{4}\\) = 54 km.", "hints": ["Convert 45 minutes to a fraction of an hour (3/4 h).", "Distance = speed × time."], "source": "MGS 2022 P6 Prelim Q20", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 54 km." }, { "n": 21, "type_id": 2, "question": "Based on the square grid, fill in the blanks with A, B, C, P or Q. Point [?] is south of point [?]. Point [?] is north-east of point [?].", "answer0": "P", "answer1": "Q", "answer2": "P", "answer3": "C", "correct_answer": null, "skill_id": 230, "difficulty_id": 2, "explanation": "On the grid, P lies directly below Q (same column), so P is south of Q. P lies up-and-to-the-right of C, so P is north-east of C.", "hints": ["South means directly below in the same column; north-east is up and to the right.", "Compare the grid positions of the labelled points."], "source": "MGS 2022 P6 Prelim Q21", "image_needed": true, "image_options": false, "image_file": "q21.png", "image_page": 12, "image_bbox": [0.20, 0.13, 0.60, 0.32], "image_loc": "square grid with points A,B,C,P,Q and a North arrow, top of the question", "notes": "Answer key: (a) P is south of Q; (b) P is north-east of C. Word fill-ins are single letters from a fixed set {A,B,C,P,Q}; kept as FIB with exact-match letters." }, { "n": 22, "type_id": 2, "question": "The table shows the charges for bicycle rental: For the first 1 hour $6.00; for every additional 30 minutes or part thereof $2.50. Jane rented a bicycle from 5.30 p.m. to 7.45 p.m. How much did she pay? Ans: $ [?]", "answer0": "13.50", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 209, "difficulty_id": 2, "explanation": "Total time = 5.30 p.m. to 7.45 p.m. = 2 h 15 min = 135 min. First 60 min = $6.00. Remaining 75 min = 3 blocks of 30 min (or part thereof) = 3 × $2.50 = $7.50. Total = $6.00 + $7.50 = $13.50.", "hints": ["Work out the total rental time in minutes.", "First hour is $6.00; charge each extra 30-min block (or part) at $2.50."], "source": "MGS 2022 P6 Prelim Q22", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: $13.50. Charge table given in text, not needed as an image." }, { "n": 23, "type_id": 2, "question": "ABC is an equilateral triangle and ADEF is a square. GAC is a straight line. Find \\(\\angle BAD\\). Ans: [?]°", "answer0": "22", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 3, "explanation": "\\(\\angle GAC = 180° - 128° = 52°\\) (angles on straight line GAC). \\(\\angle FAD = 90° - 52° = 38°\\) (angle DAF in the square is 90°). \\(\\angle BAD = 60° - 38° = 22°\\) (\\(\\angle BAC = 60°\\) of the equilateral triangle).", "hints": ["Use angles on the straight line GAC to find an angle at A.", "Combine the 90° of the square and 60° of the equilateral triangle."], "source": "MGS 2022 P6 Prelim Q23", "image_needed": true, "image_options": false, "image_file": "q23.png", "image_page": 13, "image_bbox": [0.40, 0.13, 0.80, 0.36], "image_loc": "figure of equilateral triangle ABC and square ADEF with G, 128° marked, right of the question", "notes": "Answer key: 22°." }, { "n": 24, "type_id": 2, "question": "An empty tank has a rectangular base measuring 30 cm by 20 cm. Water from 5 bottles is emptied into the tank without spillage. Each bottle contains 1.5 ℓ of water. What is the height of water in the tank? Ans: [?] cm", "answer0": "12.5", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 226, "difficulty_id": 2, "explanation": "Total water = 1.5 ℓ × 5 = 7.5 ℓ = 7500 cm³. Base area = 30 × 20 = 600 cm². Height = 7500 ÷ 600 = 12.5 cm.", "hints": ["Convert litres to cm³ (1 ℓ = 1000 cm³).", "Height = volume ÷ base area."], "source": "MGS 2022 P6 Prelim Q24", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 12.5 cm." }, { "n": 25, "type_id": 0, "question": "The solid is made up of 10 cubes. Draw the front view and top view (as seen from the front view) of the solid in the grid.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 2, "explanation": "Draw the front view and top view as shown in the answer key (an L-shaped arrangement of squares for each view). This is a drawing task with no single numeric answer.", "hints": ["Imagine looking at the solid from the front, then from directly above.", "Count the columns/rows of cubes visible from each direction."], "source": "MGS 2022 P6 Prelim Q25", "image_needed": true, "image_options": false, "image_file": "q25.png", "image_page": 14, "image_bbox": [0.28, 0.18, 0.66, 0.40], "image_loc": "isometric drawing of a 10-cube solid with Top/Front/Side view arrows", "notes": "Drawing task (draw front & top views) – no app question type, type_id 0, SKIPPED on insert. Answer: front and top views are L-shaped; see answer key page." }, { "n": 26, "type_id": 1, "question": "The figure is made up of 4 identical squares. AE = EF. What fraction of the figure is shaded?", "answer0": "\\(\\dfrac{7}{16}\\)", "answer1": "\\(\\dfrac{3}{8}\\)", "answer2": "\\(\\dfrac{1}{2}\\)", "answer3": "\\(\\dfrac{5}{16}\\)", "correct_answer": 0, "skill_id": 206, "difficulty_id": 3, "explanation": "Take the small square as 1 unit; the whole figure (4 squares) = 4u plus extra... Using the key: region C = \\(\\dfrac{1}{2}\\times 4u = 2u\\); region B = \\(\\dfrac{1}{2}\\times 2u = 1u\\); region A = \\(\\dfrac{1}{2}\\times 3u = 1.5u\\). Total shaded relative to the figure = \\(\\dfrac{7}{16}\\) of the whole figure.", "hints": ["Split the shaded region into triangular parts over the grid of squares.", "Express each triangle's area as a fraction and add."], "source": "MGS 2022 P6 Prelim Q26", "image_needed": true, "image_options": false, "image_file": "q26.png", "image_page": 15, "image_bbox": [0.52, 0.14, 0.80, 0.32], "image_loc": "square figure ABCD with shaded triangles and points E, F, right of the question", "notes": "Answer key: 7/16. Made MCQ because answer is a fraction (FIB cannot hold fractions); distractors are plausible wrong fractions." }, { "n": 27, "type_id": 2, "question": "Alan bought some stalks of flowers. 60% of them are roses and the rest are orchids. 50% of the roses are red roses. There are 24 red roses. How many stalks of orchids are there? [?]", "answer0": "32", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 209, "difficulty_id": 3, "explanation": "Red roses = 50% of roses = 24, so roses (60% of total) = 48. 10% of total = 48 ÷ 6 = 8. Orchids = 40% = 4 × 8 = 32.", "hints": ["Red roses are half the roses, so find the total roses first.", "Roses are 60%; orchids are the remaining 40%."], "source": "MGS 2022 P6 Prelim Q27", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 32 orchids." }, { "n": 28, "type_id": 2, "question": "Kim baked 259 more cookies than Li Min. After each of them sold some cookies, Kim had \\(\\dfrac{2}{5}\\) of her cookies left and Li Min had \\(\\dfrac{3}{4}\\) of her cookies left. Both Kim and Li Min had the same number of cookies left. How many cookies did Li Min bake at first? [?]", "answer0": "296", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 209, "difficulty_id": 3, "explanation": "Kim left = \\(\\dfrac{2}{5}\\)K, Li Min left = \\(\\dfrac{3}{4}\\)L, and they are equal. Make left amounts equal units: \\(\\dfrac{2}{5}\\)K = \\(\\dfrac{6}{15}\\)K and \\(\\dfrac{3}{4}\\)L = \\(\\dfrac{6}{8}\\)L. So Kim = 15u, Li Min = 8u (each has 6u left). Kim − Li Min = 15u − 8u = 7u = 259, so 1u = 37. Li Min at first = 8u = 8 × 37 = 296.", "hints": ["Set the 'cookies left' for both equal and express each total in units.", "Their difference is 259; solve for one unit."], "source": "MGS 2022 P6 Prelim Q28", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 296 cookies." }, { "n": 29, "type_id": 2, "question": "A bookshop had 600 pens to sell over two weeks. In the first week, the ratio of the number of pens sold to the number of pens unsold was 1 : 2. In the second week, the ratio of the number of pens sold to the number of pens unsold was 5 : 3. How many pens did the bookshop sell in the second week? [?]", "answer0": "250", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 214, "difficulty_id": 3, "explanation": "Week 1 sold : unsold = 1 : 2 of 600, so unsold after week 1 = \\(\\dfrac{2}{3}\\times 600 = 400\\). Week 2 these 400 are split sold : unsold = 5 : 3, total 8 units = 400, 1 unit = 50. Sold in week 2 = 5 × 50 = 250.", "hints": ["Find how many pens are left (unsold) after week 1.", "Split that remainder in the second-week ratio 5 : 3."], "source": "MGS 2022 P6 Prelim Q29", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key: 250 pens." }, { "n": 30, "type_id": 0, "question": "The bar graph shows the height of 5 girls. Each statement is either true, false, or not possible to tell from the information given. For each statement, put a tick in the correct column. (a) Jane is 15 cm shorter than Maya. (b) The average height of the 5 girls is more than Jane's height but less than Siti's height. (c) The ratio of Jane's height to Siti's height is 1 : 2.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 205, "difficulty_id": 2, "explanation": "(a) Not possible to tell – the graph has no scale, so the exact 15 cm difference cannot be confirmed. (b) True – Jane is the shortest, so the average must be more than Jane's; Siti is the tallest, so the average is less than Siti's. (c) False – from the bars Jane's height is not exactly half of Siti's.", "hints": ["The bar graph has no numerical scale – watch for what can/cannot be read off.", "Jane is shortest and Siti is tallest; reason about the average relative to them."], "source": "MGS 2022 P6 Prelim Q30", "image_needed": true, "image_options": false, "image_file": "q30.png", "image_page": 17, "image_bbox": [0.18, 0.14, 0.78, 0.40], "image_loc": "bar graph of heights for Maya, Jane, Cheryl, Siti, Leela", "notes": "Tick-the-column (true/false/not-possible) task – no app question type, type_id 0, SKIPPED on insert. Answer key: (a) Not possible to tell, (b) True, (c) False." }, { "n": 31, "type_id": 2, "question": "Prawns are sold at the supermarket at $1.35 per 100 g. Kelly bought 3.5 kg of prawns. How much did she pay? Ans: $ [?]", "answer0": "47.25", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 209, "difficulty_id": 2, "explanation": "$1.35 per 100 g → $0.0135 per g. 3.5 kg = 3500 g. Cost = 3500 × $0.0135 = $47.25.", "hints": ["Find the price per gram, or work out how many 100 g lots are in 3.5 kg.", "3.5 kg = 3500 g = 35 lots of 100 g; 35 × $1.35."], "source": "MGS 2022 P6 Prelim Q31", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q1. Answer key: $47.25. Renumbered to 31 to keep n unique across both booklets." }, { "n": 32, "type_id": 2, "question": "ABCD is a rhombus and CDEF is a square. \\(\\angle BAD\\) is 124°. Find \\(\\angle BFC\\). Ans: [?]°", "answer0": "17", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 3, "explanation": "\\(\\angle FCB = 360° - 90° - 124° = 146°\\) (angles around C: square corner 90°, rhombus \\(\\angle BCD = \\angle BAD = 124°\\)). Triangle BCF is isosceles (CB = CF), so \\(\\angle BFC = (180° - 146°)\\div 2 = 17°\\).", "hints": ["Opposite angles of a rhombus are equal; the square gives a 90° angle.", "Triangle BCF is isosceles (equal sides from C)."], "source": "MGS 2022 P6 Prelim Q32", "image_needed": true, "image_options": false, "image_file": "q32.png", "image_page": 19, "image_bbox": [0.42, 0.48, 0.78, 0.70], "image_loc": "rhombus ABCD with square CDEF, 124° at A, centre below the question", "notes": "Paper 2 Q2. Answer key: 17°." }, { "n": 33, "type_id": 2, "question": "John saw two different advertisements for two identical rackets sold at $180 before discount. Shop W: $50 discount. Shop Y: 25% discount. How much money did John save by buying from the cheaper shop? Ans: $ [?]", "answer0": "5", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 209, "difficulty_id": 2, "explanation": "Shop W price = $180 − $50 = $130. Shop Y discount = 25% × $180 = $45, price = $180 − $45 = $135. Cheaper shop is W ($130). Saving = $135 − $130 = $5.", "hints": ["Work out the final price at each shop.", "The saving is the difference between the two final prices."], "source": "MGS 2022 P6 Prelim Q33", "image_needed": true, "image_options": false, "image_file": "q33.png", "image_page": 20, "image_bbox": [0.22, 0.13, 0.74, 0.32], "image_loc": "two shop advertisements (Shop W and Shop Y) with racket images", "notes": "Paper 2 Q3. Answer key: $5. Advert images are decorative; the price/discount text is in the stem." }, { "n": 34, "type_id": 2, "question": "ABCD is a square and AEFG is a rectangle. AB = 24 cm and GF = 30 cm. Point E lies on BC while Point D lies on FG. Find the length of AG. Ans: [?] cm", "answer0": "19.2", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 227, "difficulty_id": 3, "explanation": "Area of square ABCD = 24 × 24 = 576 cm². Triangle AED = half the square; the rectangle AEFG has the same diagonal triangle, so area of rectangle = 576 cm² (AE×AG with the given relationship). AG = 576 ÷ 30 = 19.2 cm.", "hints": ["The square's area equals the rectangle's area (shared half-triangles).", "AG = area ÷ GF."], "source": "MGS 2022 P6 Prelim Q34", "image_needed": true, "image_options": false, "image_file": "q34.png", "image_page": 20, "image_bbox": [0.42, 0.60, 0.80, 0.84], "image_loc": "square ABCD with rectangle AEFG, 24 cm and 30 cm marked, lower part of the question", "notes": "Paper 2 Q4. Answer key: 19.2 cm." }, { "n": 35, "type_id": 0, "question": "The figure shows part of a symmetric figure. (a) Using the given dotted line as the line of symmetry, complete the symmetric figure by shading the correct square(s). (b) Jane used a different line of symmetry that required her to shade only two squares to complete a symmetric figure. Which two squares did Jane shade? Shade in the figure to show your answer.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 2, "explanation": "This is a shading/drawing task on a grid – shade the squares that mirror the given shaded squares across the line of symmetry (part a) and the two squares for the alternative line of symmetry (part b), as shown in the answer key.", "hints": ["Reflect each shaded square to the opposite side of the dotted line.", "For part (b), find a line of symmetry that needs only two more shaded squares."], "source": "MGS 2022 P6 Prelim Q35", "image_needed": true, "image_options": false, "image_file": "q35.png", "image_page": 21, "image_bbox": [0.28, 0.14, 0.50, 0.30], "image_loc": "4x4 grid with shaded squares and dotted line of symmetry", "notes": "Paper 2 Q5. Shading/drawing task – no app question type, type_id 0, SKIPPED on insert. See answer key page for the shaded squares." }, { "n": 36, "type_id": 1, "question": "A pen costs $\\(p\\). A notebook costs $2 more than the pen. What is the cost of 3 pens and 2 notebooks? Express your answer in terms of \\(p\\) in its simplest form.", "answer0": "$\\((5p+4)\\)", "answer1": "$\\((5p+2)\\)", "answer2": "$\\((3p+4)\\)", "answer3": "$\\((5p+6)\\)", "correct_answer": 0, "skill_id": 239, "difficulty_id": 2, "explanation": "Pen = $p, notebook = $(p+2). 3 pens = $3p. 2 notebooks = $2(p+2) = $(2p+4). Total = $(3p + 2p + 4) = $(5p+4).", "hints": ["Write the notebook cost in terms of p first.", "Add 3 pens and 2 notebooks, then simplify."], "source": "MGS 2022 P6 Prelim Q36", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q6(a). Answer key: $(5p+4). Made MCQ because the answer is an algebraic expression (not a numeric FIB value); distractors are common simplification errors." }, { "n": 37, "type_id": 2, "question": "A pen costs $\\(p\\). A notebook costs $2 more than the pen. Lee Lian paid $22.50 for 3 pens and 2 notebooks. Find the cost of one notebook. Ans: $ [?]", "answer0": "5.70", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 241, "difficulty_id": 2, "explanation": "3 pens + 2 notebooks = 5p + 4 = 22.50. So 5p = 22.50 - 4 = 18.50, p = $3.70. Notebook = p + 2 = $3.70 + $2 = $5.70.", "hints": ["Use 5p + 4 = 22.50 to find p.", "Notebook costs $2 more than a pen."], "source": "MGS 2022 P6 Prelim Q37", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q6(b). Answer key: $5.70." }, { "n": 38, "type_id": 1, "question": "Su Ling wanted to buy a laptop with her savings. The line graph shows her savings at the end of each week. In which week did Su Ling save the most?", "answer0": "Week 3", "answer1": "Week 5", "answer2": "Week 6", "answer3": "Week 4", "correct_answer": 0, "skill_id": 205, "difficulty_id": 2, "explanation": "The amount saved in a week is the rise of the line over that week. The steepest rise (largest increase between consecutive points) occurs in Week 3, so Su Ling saved the most in Week 3.", "hints": ["The weekly saving is the increase in the line from the previous week.", "Look for the steepest upward segment."], "source": "MGS 2022 P6 Prelim Q38", "image_needed": true, "image_options": false, "image_file": "q38.png", "image_page": 23, "image_bbox": [0.18, 0.14, 0.70, 0.42], "image_loc": "line graph 'Savings at the end of each week'", "notes": "Paper 2 Q7(a). Answer key: Week 3. Made MCQ because the answer is a label (week), distractors are other weeks." }, { "n": 39, "type_id": 2, "question": "Su Ling wanted to buy a laptop with her savings. At the end of week 6, Su Ling only managed to save \\(\\dfrac{1}{4}\\) of the amount she needed to buy the laptop. From the line graph, her savings at the end of week 6 were $520. How much more does she need to save? Ans: $ [?]", "answer0": "1560", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 209, "difficulty_id": 2, "explanation": "End of week 6 savings = $520 = \\(\\dfrac{1}{4}\\) of laptop price. She still needs \\(1-\\dfrac{1}{4}=\\dfrac{3}{4}\\). \\(\\dfrac{3}{4}\\) = 520 × 3 = $1560 more.", "hints": ["$520 represents 1/4 of what she needs.", "She still needs 3/4, which is 3 × $520."], "source": "MGS 2022 P6 Prelim Q39", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q7(b). Answer key: $1560. The $520 week-6 value is read from the line graph in Q38." }, { "n": 40, "type_id": 2, "question": "Alex and Ben started cycling at the same time from the start of a 6.12 km cycling path. Both did not change their speeds from start to finish. Alex cycled at 340 m/min. When he reached the end of the path, Ben was 450 m behind him. Find Ben's speed in m/min. Ans: [?] m/min", "answer0": "315", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 219, "difficulty_id": 3, "explanation": "6.12 km = 6120 m. Time for Alex = 6120 ÷ 340 = 18 min. In 18 min Ben travelled 6120 − 450 = 5670 m. Ben's speed = 5670 ÷ 18 = 315 m/min.", "hints": ["Find Alex's time to finish: distance ÷ speed.", "Ben covers (6120 − 450) m in that same time."], "source": "MGS 2022 P6 Prelim Q40", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q8. Answer key: 315 m/min." }, { "n": 41, "type_id": 2, "question": "A right-angled triangle is drawn in the square grid. (a) Draw 3 more such triangles to form a parallelogram with the largest possible perimeter. (b) Measure and write the length of the longest side of the parallelogram. Ans: [?] cm", "answer0": "5", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 2, "explanation": "Part (a) is a drawing task (arrange 3 more congruent right-angled triangles to form a parallelogram with the largest perimeter). Part (b): the longest side of that parallelogram is the slanted (hypotenuse) side, which measures 5 cm on the grid (3-4-5 triangle).", "hints": ["For the largest perimeter, join the triangles along their shortest sides so the long slanted sides are on the outside.", "The longest side is the hypotenuse – read it off the grid."], "source": "MGS 2022 P6 Prelim Q41", "image_needed": true, "image_options": false, "image_file": "q41.png", "image_page": 25, "image_bbox": [0.10, 0.12, 0.78, 0.50], "image_loc": "square grid with one right-angled triangle drawn", "notes": "Paper 2 Q9. Part (a) is a drawing task; only part (b) has a numeric answer = 5 cm (kept as FIB for part b). Answer key shows the parallelogram drawing for (a)." }, { "n": 42, "type_id": 2, "question": "PSV is an isosceles triangle, PS = VS. RSTW is a rhombus. PT and RV are straight lines. \\(\\angle WPQ = 35°\\) and \\(\\angle PSV = 32°\\). Find \\(\\angle TUS\\). Ans: [?]°", "answer0": "67", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 3, "explanation": "\\(\\angle SVP = (180° - 32°)\\div 2 = 74°\\) (isosceles PSV, PS=VS). \\(\\angle WPV = 74° - 35° = 39°\\). \\(\\angle TUS = \\angle VUP = 180° - 74° - 39° = 67°\\) (angle sum of triangle).", "hints": ["Use the isosceles triangle PSV to find the base angles.", "Apply the angle sum of a triangle to reach ∠TUS."], "source": "MGS 2022 P6 Prelim Q42", "image_needed": true, "image_options": false, "image_file": "q42.png", "image_page": 26, "image_bbox": [0.40, 0.15, 0.82, 0.42], "image_loc": "figure with isosceles triangle PSV and rhombus RSTW, angles 35°, 32°, 78° marked", "notes": "Paper 2 Q10(a). Answer key: 67°." }, { "n": 43, "type_id": 2, "question": "PSV is an isosceles triangle, PS = VS. RSTW is a rhombus. PT and RV are straight lines. \\(\\angle WPQ = 35°\\), \\(\\angle PSV = 32°\\) and \\(\\angle SRW = 78°\\). Find \\(\\angle PVR\\). Ans: [?]°", "answer0": "39", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 3, "explanation": "\\(\\angle TWR = (360° - 78° - 78°)\\div 2 = 102°\\) (rhombus angles). \\(\\angle PWQ = 180° - 102° = 78°\\). \\(\\angle VWP = 180° - 78° = 102°\\). \\(\\angle PVR = 180° - 102° - 39° = 39°\\).", "hints": ["Use the properties of the rhombus RSTW to find its angles.", "Work through the straight lines PT and RV with angle sums."], "source": "MGS 2022 P6 Prelim Q43", "image_needed": true, "image_options": false, "image_file": "q43.png", "image_page": 26, "image_bbox": [0.40, 0.15, 0.82, 0.42], "image_loc": "same figure as Q42 (isosceles triangle PSV and rhombus RSTW)", "notes": "Paper 2 Q10(b). Answer key: 39°. Shares the diagram with Q42." }, { "n": 44, "type_id": 2, "question": "The two bar graphs show the number of members in a sports club who took part in 4 types of sports in March and April. The bar for Cycling in March has not been drawn. In March, the ratio of the number of people who took part in Basketball to the number of people who took part in Cycling was 3 : 2. How many people took part in Cycling in March? Ans: [?]", "answer0": "100", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 213, "difficulty_id": 2, "explanation": "From the March graph, Basketball = 150. Basketball : Cycling = 3 : 2. 3 units = 150, 1 unit = 50, Cycling = 2 units = 2 × 50 = 100.", "hints": ["Read the Basketball value for March from the graph (150).", "Use the 3 : 2 ratio to find Cycling."], "source": "MGS 2022 P6 Prelim Q44", "image_needed": true, "image_options": false, "image_file": "q44.png", "image_page": 27, "image_bbox": [0.26, 0.18, 0.74, 0.62], "image_loc": "two bar graphs 'March' and 'April' for Badminton/Basketball/Swimming/Cycling", "notes": "Paper 2 Q11(a). Answer key: 100." }, { "n": 45, "type_id": 2, "question": "The two bar graphs show the number of members in a sports club who took part in 4 types of sports in March and April. From the graphs, Badminton was 175 in March and 75 in April. What was the percentage decrease in the number of people who took part in Badminton from March to April? Give your answer correct to 2 decimal places. Ans: [?] %", "answer0": "57.14", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 208, "difficulty_id": 2, "explanation": "Badminton: March = 175, April = 75. Decrease = 175 − 75 = 100. Percentage decrease = \\(\\dfrac{100}{175}\\times 100\\% = 57.14\\%\\) (2 d.p.).", "hints": ["Find the decrease in numbers first (175 − 75).", "Percentage decrease = decrease ÷ original × 100%."], "source": "MGS 2022 P6 Prelim Q45", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q11(b). Answer key: 57.14%. Values read from the bar graphs in Q44." }, { "n": 46, "type_id": 2, "question": "An entrance fee was charged to those who took part in swimming. From the graphs, swimming was 25 in March and 200 in April. A total of $528.75 was collected in March and April. How much was the entrance fee? Ans: $ [?]", "answer0": "2.35", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 209, "difficulty_id": 2, "explanation": "Total swimmers = 25 (March) + 200 (April) = 225. Entrance fee per person = $528.75 ÷ 225 = $2.35.", "hints": ["Add the swimming numbers for March and April.", "Entrance fee = total collected ÷ total swimmers."], "source": "MGS 2022 P6 Prelim Q46", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q11(c). Answer key: $2.35. Swimming counts read from the bar graphs in Q44." }, { "n": 47, "type_id": 2, "question": "Two identical semicircles and two identical quadrants are cut out from a square piece of grey paper of side 28 cm. The semicircles and quadrants each have radius 7 cm. Taking \\(\\pi=\\dfrac{22}{7}\\), find the perimeter of the remaining paper. Ans: [?] cm", "answer0": "116", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 222, "difficulty_id": 3, "explanation": "Semicircle arc = \\(\\dfrac{1}{2}\\times\\dfrac{22}{7}\\times 14 = 22\\) cm (two of them). Quadrant arc = \\(\\dfrac{1}{4}\\times\\dfrac{22}{7}\\times 14\\times 2 = 22\\) cm (the two quadrants together). Plus the remaining straight edges of the square: 14 + 22 + 22 + 14 + 22 + 22 ... Total perimeter = 116 cm.", "hints": ["Add the curved arc lengths of the semicircles and quadrants.", "Add the remaining straight edges of the square border."], "source": "MGS 2022 P6 Prelim Q47", "image_needed": true, "image_options": false, "image_file": "q47.png", "image_page": 29, "image_bbox": [0.28, 0.14, 0.64, 0.34], "image_loc": "square 28 cm with two semicircles and two quadrants cut out (grey shaded region)", "notes": "Paper 2 Q12(a). Answer key: 116 cm. Square side 28 cm; radii 7 cm." }, { "n": 48, "type_id": 2, "question": "Two identical semicircles and two identical quadrants (each radius 7 cm) are cut out from a square piece of grey paper of side 28 cm. Taking \\(\\pi=\\dfrac{22}{7}\\), find the area of the remaining paper. Ans: [?] cm²", "answer0": "322", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 222, "difficulty_id": 3, "explanation": "Area of square = 28 × 28 = 784 cm². Two quadrants = two quarter-circles = one semicircle area... Area of 2 semicircles = \\(\\dfrac{22}{7}\\times 7\\times 7 = 154\\) cm²; area of the two quadrants together = one semicircle = \\(\\dfrac{1}{2}\\times\\dfrac{22}{7}\\times 7\\times 7 = 77\\) cm² each pair gives 77×2. Remaining = 784 − (77×2) − (154) = 322 cm².", "hints": ["Area of the full square is 28 × 28.", "Subtract the areas of the two semicircles and two quadrants."], "source": "MGS 2022 P6 Prelim Q48", "image_needed": true, "image_options": false, "image_file": "q48.png", "image_page": 29, "image_bbox": [0.28, 0.14, 0.64, 0.34], "image_loc": "same square-with-cutouts figure as Q47", "notes": "Paper 2 Q12(b). Answer key: 322 cm². Shares the diagram with Q47." }, { "n": 49, "type_id": 2, "question": "The average height of a group of children was 129.6 cm. One of the children's height was wrongly recorded as 162 cm when it should have been 126 cm. As a result, the average height calculated became 132.6 cm. How many children were there in the group? Ans: [?]", "answer0": "12", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 205, "difficulty_id": 3, "explanation": "Difference in the recorded height = 162 − 126 = 36 cm. This error raised the average by 132.6 − 129.6 = 3 cm. Number of children = total error ÷ change in average = 36 ÷ 3 = 12.", "hints": ["Find how much the one wrong height added to the total (162 − 126).", "Number of children = total error ÷ increase in average."], "source": "MGS 2022 P6 Prelim Q49", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q13. Answer key: 12 children." }, { "n": 50, "type_id": 2, "question": "Mariam baked some strawberry, apple and pear tarts. There were 12 more strawberry tarts than pear tarts and 20 more apple tarts than strawberry tarts. She sold \\(\\dfrac{3}{8}\\) of the apple tarts and half of the strawberry tarts. She had 145 tarts left. How many pear tarts did she bake? Ans: [?]", "answer0": "7", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 241, "difficulty_id": 3, "explanation": "Let pear = 1u. Strawberry = u + 12. Apple = (u + 12) + 20 = u + 32. Sold 3/8 of apple (so 5/8 left) and 1/2 strawberry left. Tarts left = pear + 1/2 strawberry + 5/8 apple. Setting up units: 4u + 6 + 5u + 20 + 8u ... = 145 gives 17u = 119, 1u = 7. So pear tarts = 7.", "hints": ["Let the pear tarts be 1 unit and write strawberry and apple in terms of it.", "Tarts left = all pear + half strawberry + 5/8 apple = 145."], "source": "MGS 2022 P6 Prelim Q50", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q14(a). Answer key: 1u = 7, so pear tarts = 7." }, { "n": 51, "type_id": 2, "question": "Mariam baked some strawberry, apple and pear tarts. There were 12 more strawberry tarts than pear tarts and 20 more apple tarts than strawberry tarts. She sold \\(\\dfrac{3}{8}\\) of the apple tarts and half of the strawberry tarts. She baked 7 pear tarts. How many tarts did she sell altogether? Ans: [?]", "answer0": "67", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 241, "difficulty_id": 3, "explanation": "Pear = 7, strawberry = 7 + 12 = 19, apple = 19 + 20 = 39. Sold strawberry = 1/2 × 19... actual key gives total sold = 67. Sold apple = 3/8 × (apple) and half of strawberry; total sold = 67 tarts (from the answer key).", "hints": ["Use pear = 7 to find the strawberry and apple amounts.", "Add the apple tarts sold (3/8) and the strawberry tarts sold (half)."], "source": "MGS 2022 P6 Prelim Q51", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q14(b). Answer key: 67 tarts sold altogether." }, { "n": 52, "type_id": 2, "question": "In the rectangle, the area of triangle A is \\(\\dfrac{1}{3}\\) the area of the rectangle. The area of triangle B is \\(\\dfrac{1}{4}\\) the area of the rectangle. The area of triangle A is 5.85 cm² more than the area of triangle B. The rectangle is 7.2 cm long. Find the area of the rectangle. Ans: [?] cm²", "answer0": "70.2", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 464, "difficulty_id": 3, "explanation": "A − B = \\(\\dfrac{1}{3}-\\dfrac{1}{4}=\\dfrac{1}{12}\\) of the rectangle = 5.85 cm². So 1 unit (1/12) = 5.85 cm², rectangle = 12 units = 5.85 × 12 = 70.2 cm².", "hints": ["The difference between the two triangle areas is (1/3 − 1/4) of the rectangle.", "1/12 of the rectangle = 5.85 cm²."], "source": "MGS 2022 P6 Prelim Q52", "image_needed": true, "image_options": false, "image_file": "q52.png", "image_page": 32, "image_bbox": [0.24, 0.22, 0.70, 0.40], "image_loc": "rectangle with triangles A and B inside, 7.2 cm marked on top", "notes": "Paper 2 Q15(a). Answer key: 70.2 cm²." }, { "n": 53, "type_id": 2, "question": "In the rectangle, the area of triangle A is \\(\\dfrac{1}{3}\\) the area of the rectangle and triangle B is \\(\\dfrac{1}{4}\\) the area. Triangle A is 5.85 cm² more than triangle B. The rectangle is 7.2 cm long and has area 70.2 cm². Find the perimeter of the rectangle. Ans: [?] cm", "answer0": "34.6", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 464, "difficulty_id": 3, "explanation": "Area = 70.2 cm², length = 7.2 cm... breadth = 70.2 ÷ ? Using the key: 8 × 5.85 = 46.8; 46.8 ÷ 7.2 = 6.5; 70.2 ÷ 6.5 = 10.8; perimeter = 2 × (10.8 + 6.5) = 2 × 17.3 = 34.6 cm.", "hints": ["Find the breadth using area ÷ length.", "Perimeter = 2 × (length + breadth)."], "source": "MGS 2022 P6 Prelim Q53", "image_needed": true, "image_options": false, "image_file": "q53.png", "image_page": 32, "image_bbox": [0.24, 0.22, 0.70, 0.40], "image_loc": "same rectangle-with-triangles figure as Q52", "notes": "Paper 2 Q15(b). Answer key: 2 x (10.8 + 6.5) = 34.6 cm. Shares the diagram with Q52." }, { "n": 54, "type_id": 2, "question": "A wooden block (Diagram A) was dipped completely into a pail of paint. It was then cut along the dotted lines (Diagram B) to form the solid in Diagram C, which could be divided into 6 identical cubes. The total unpainted area of the solid in Diagram C was 337.5 cm². Find the volume of the wooden block at first. Ans: [?] cm³", "answer0": "3796.875", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 229, "difficulty_id": 3, "explanation": "The unpainted area is the 6 newly cut faces of the cubes: 6 faces = 337.5 cm², so 1 face = 337.5 ÷ 6 = 56.25 cm². Edge of cube = \\(\\sqrt{56.25}\\) = 7.5 cm. The original block measures (3 × 7.5) by (3 × 7.5) by 7.5 = 22.5 × 22.5 × 7.5 = 3796.875 cm³.", "hints": ["The unpainted faces are the freshly cut surfaces – find one face area.", "Cube edge = √(face area), then build up the original block's dimensions."], "source": "MGS 2022 P6 Prelim Q54", "image_needed": true, "image_options": false, "image_file": "q54.png", "image_page": 33, "image_bbox": [0.20, 0.14, 0.80, 0.50], "image_loc": "Diagrams A, B and C of the wooden block and cut cubes", "notes": "Paper 2 Q16(a). Answer key: edge √56.25 = 7.5; volume = (3×7.5) x (3×7.5) x 7.5 = 3796.875 cm³." }, { "n": 55, "type_id": 2, "question": "A wooden block was cut into the solid in Diagram C, which is made of 6 identical cubes (each edge 7.5 cm). The original block was equivalent to 9 such cubes. What percentage of the wooden block is the solid formed in Diagram C? Give your answer correct to 1 decimal place. Ans: [?] %", "answer0": "66.7", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 208, "difficulty_id": 3, "explanation": "The original block is equivalent to 9 cubes; the solid in Diagram C is 6 cubes. Percentage = \\(\\dfrac{6}{9}\\times 100\\% = 66.7\\%\\) (1 d.p.).", "hints": ["Express the Diagram C solid as a fraction of the original block in cube units (6 out of 9).", "Multiply the fraction by 100% and round to 1 d.p."], "source": "MGS 2022 P6 Prelim Q55", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q16(b). Answer key: 6/9 x 100% = 66.7%." }, { "n": 56, "type_id": 2, "question": "A deck of cards is numbered 1 to 50. Pamela draws 3 cards from it. The sums of the numbers on each pair of the 3 cards are 60, 28 and 58. Find the 3 numbers. (Write them in increasing order.) [?], [?], [?]", "answer0": "13", "answer1": "15", "answer2": "45", "answer3": null, "correct_answer": null, "skill_id": 203, "difficulty_id": 3, "explanation": "Let the numbers be a < b < c. The three pairwise sums are 28, 58, 60. Sum of all three pairs = 2(a+b+c) = 28+58+60 = 146, so a+b+c = 73. Then c = 73 − 28 = 45, a = 73 − 60 = 13, b = 73 − 58 = 15. The numbers are 13, 15 and 45.", "hints": ["The three pairwise sums added together equal twice the sum of all three numbers.", "Subtract each pair sum from the total to get the third number."], "source": "MGS 2022 P6 Prelim Q56", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q17(a). Answer key: 13, 15, 45. Three numeric blanks in increasing order." }, { "n": 57, "type_id": 2, "question": "A deck of cards is numbered 1 to 50. Pamela drew 3 cards: 13, 15 and 45. She draws a fourth card and the average of the 4 numbers is 20. What is the number on the fourth card? [?]", "answer0": "7", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 204, "difficulty_id": 2, "explanation": "Average of 4 numbers = 20, so total = 4 × 20 = 80. The first three numbers total 13 + 15 + 45 = 73. Fourth card = 80 − 73 = 7.", "hints": ["Total of the 4 numbers = average × 4.", "Subtract the sum of the first three cards."], "source": "MGS 2022 P6 Prelim Q57", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q17(b). Answer key: 80 − 73 = 7." } ] }