{ "paper": { "school": "Ai Tong", "year": 2025, "level": "P6", "label": "Prelim", "source_prefix": "Ai Tong 2025 P6 Prelim", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "Which of the following is forty-five thousand and thirty in numerals?", "answer0": "4530", "answer1": "45 030", "answer2": "45 300", "answer3": "450 030", "correct_answer": 1, "skill_id": 149, "difficulty_id": 1, "explanation": "Forty-five thousand = 45 000; thirty = 30. Together = 45 030. Answer: 45 030.", "hints": ["Forty-five thousand is 45 000.", "Add 30 to 45 000."], "source": "Ai Tong 2025 P6 Prelim Paper 1 Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Booklet A Q1: option 2 (45 030)." }, { "n": 2, "type_id": 1, "question": "Round 7549 to the nearest hundred.", "answer0": "7000", "answer1": "7500", "answer2": "7600", "answer3": "8000", "correct_answer": 1, "skill_id": 150, "difficulty_id": 1, "explanation": "Look at the tens digit (4). Since 4 < 5, round down: 7549 rounds to 7500. Answer: 7500.", "hints": ["To round to the nearest hundred, look at the tens digit.", "The tens digit is 4, so round down to 7500."], "source": "Ai Tong 2025 P6 Prelim Paper 1 Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Booklet A Q2: option 2 (7500)." }, { "n": 3, "type_id": 1, "question": "Express 2.4 as a percentage.", "answer0": "0.024 %", "answer1": "0.24 %", "answer2": "24 %", "answer3": "240 %", "correct_answer": 3, "skill_id": 173, "difficulty_id": 1, "explanation": "Multiply by 100%: 2.4 \\(\\times\\) 100% = 240%. Answer: 240%.", "hints": ["To change a decimal to a percentage, multiply by 100%.", "2.4 \\(\\times\\) 100% = 240%."], "source": "Ai Tong 2025 P6 Prelim Paper 1 Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Booklet A Q3: option 4 (240%)." }, { "n": 4, "type_id": 1, "question": "What is the missing number in the box?
$$7.216 = 7 + 0.2 + [\\,?\\,]$$", "answer0": "0.016", "answer1": "0.16", "answer2": "1.6", "answer3": "16", "correct_answer": 0, "skill_id": 123, "difficulty_id": 2, "explanation": "7.216 = 7 + 0.2 + ?. So ? = 7.216 - 7 - 0.2 = 0.016. Answer: 0.016.", "hints": ["Subtract the parts you know (7 and 0.2) from 7.216.", "7.216 - 7.2 = 0.016."], "source": "Ai Tong 2025 P6 Prelim Paper 1 Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Booklet A Q4: option 1 (0.016). The boxed [?] here is part of the printed MCQ equation, not an answer blank." }, { "n": 5, "type_id": 1, "question": "Which fraction is smaller than \\(\\dfrac{1}{2}\\)?", "answer0": "\\(\\dfrac{5}{7}\\)", "answer1": "\\(\\dfrac{4}{9}\\)", "answer2": "\\(\\dfrac{3}{6}\\)", "answer3": "\\(\\dfrac{2}{3}\\)", "correct_answer": 1, "skill_id": 79, "difficulty_id": 2, "explanation": "Compare each with \\(\\dfrac{1}{2}\\). \\(\\dfrac{4}{9}\\): half of 9 is 4.5, and 4 < 4.5, so \\(\\dfrac{4}{9} < \\dfrac{1}{2}\\). The others are equal to or larger than \\(\\dfrac{1}{2}\\). Answer: \\(\\dfrac{4}{9}\\).", "hints": ["A fraction is less than \\(\\dfrac{1}{2}\\) when the numerator is less than half the denominator.", "For \\(\\dfrac{4}{9}\\), half of 9 is 4.5, and 4 < 4.5."], "source": "Ai Tong 2025 P6 Prelim Paper 1 Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Booklet A Q5: option 2 (4/9)." }, { "n": 6, "type_id": 1, "question": "Which of the following could be the mass of a mobile phone?", "answer0": "0.05 kg", "answer1": "1.5 kg", "answer2": "15 g", "answer3": "150 g", "correct_answer": 3, "skill_id": 84, "difficulty_id": 2, "explanation": "A typical mobile phone has a mass of about 150 g. 0.05 kg (50 g) and 15 g are too light; 1.5 kg is far too heavy. Answer: 150 g.", "hints": ["Think about a sensible mass for a real mobile phone.", "150 g is about right; the others are too light or too heavy."], "source": "Ai Tong 2025 P6 Prelim Paper 1 Q6", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Booklet A Q6: option 4 (150 g). Phone picture is decorative; not required to answer." }, { "n": 7, "type_id": 1, "question": "Arrange the following fractions from the smallest to the greatest.
\\(\\dfrac{6}{11}\\), \\(\\dfrac{7}{10}\\), \\(\\dfrac{3}{5}\\)", "answer0": "\\(\\dfrac{6}{11}\\), \\(\\dfrac{3}{5}\\), \\(\\dfrac{7}{10}\\)", "answer1": "\\(\\dfrac{6}{11}\\), \\(\\dfrac{7}{10}\\), \\(\\dfrac{3}{5}\\)", "answer2": "\\(\\dfrac{3}{5}\\), \\(\\dfrac{6}{11}\\), \\(\\dfrac{7}{10}\\)", "answer3": "\\(\\dfrac{3}{5}\\), \\(\\dfrac{7}{10}\\), \\(\\dfrac{6}{11}\\)", "correct_answer": 0, "skill_id": 79, "difficulty_id": 2, "explanation": "Convert to decimals: \\(\\dfrac{6}{11} \\approx 0.545\\), \\(\\dfrac{3}{5} = 0.6\\), \\(\\dfrac{7}{10} = 0.7\\). Smallest to greatest: \\(\\dfrac{6}{11}\\), \\(\\dfrac{3}{5}\\), \\(\\dfrac{7}{10}\\). Answer: option 1.", "hints": ["Change each fraction to a decimal to compare.", "0.545 < 0.6 < 0.7."], "source": "Ai Tong 2025 P6 Prelim Paper 1 Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Booklet A Q7: option 1 (6/11, 3/5, 7/10)." }, { "n": 8, "type_id": 1, "question": "The figure shows a cube. Which one of the following is a net of a cube?", "answer0": "Net 1", "answer1": "Net 2", "answer2": "Net 3", "answer3": "Net 4", "correct_answer": 3, "skill_id": 233, "difficulty_id": 2, "explanation": "A valid cube net folds into a closed cube with no overlapping faces. Only net 4 folds into a cube. Answer: Net 4.", "hints": ["Imagine folding each net into a cube.", "Only one arrangement of 6 squares folds without overlapping faces."], "source": "Ai Tong 2025 P6 Prelim Paper 1 Q8", "image_needed": true, "image_options": true, "image_page": 5, "image_bbox": [0.16, 0.45, 0.86, 0.95], "image_loc": "cube figure and four candidate nets (1)-(4) on the lower half of page 5", "image_file": "q8.png", "notes": "Answer key Booklet A Q8: option 4. image_options true: the 4 options are net diagrams; answer labels are placeholders." }, { "n": 9, "type_id": 1, "question": "The table shows the number of students in four groups A, B, C and D.
A: 15; B: 30; C: 25; D: 30.
Which of the following pie charts best represents the information?", "answer0": "Pie chart 1", "answer1": "Pie chart 2", "answer2": "Pie chart 3", "answer3": "Pie chart 4", "correct_answer": 2, "skill_id": 235, "difficulty_id": 2, "explanation": "Total = 15 + 30 + 25 + 30 = 100. The sectors should be A = 15% (smallest), B = 30%, C = 25%, D = 30%, with B and D equal. The pie chart matching these proportions is chart 3. Answer: Pie chart 3.", "hints": ["Find the total and the fraction each group takes.", "B and D are equal and largest; A is the smallest sector."], "source": "Ai Tong 2025 P6 Prelim Paper 1 Q9", "image_needed": true, "image_options": true, "image_page": 6, "image_bbox": [0.16, 0.3, 0.88, 0.45], "image_loc": "four pie-chart options (1)-(4) in the middle of page 6", "image_file": "q9.png", "notes": "Answer key Booklet A Q9: option 3. image_options true: the 4 options are pie charts; answer labels are placeholders. Table given verbatim in stem." }, { "n": 10, "type_id": 1, "question": "Find the value of \\(\\dfrac{4y}{2} + 10 - 4\\) when \\(y = 4\\).", "answer0": "11", "answer1": "14", "answer2": "22", "answer3": "28", "correct_answer": 1, "skill_id": 240, "difficulty_id": 2, "explanation": "Substitute y = 4: \\(\\dfrac{4 \\times 4}{2} + 10 - 4 = \\dfrac{16}{2} + 10 - 4 = 8 + 10 - 4 = 14\\). Answer: 14.", "hints": ["Replace y with 4, then work out \\(\\dfrac{4 \\times 4}{2}\\) first.", "8 + 10 - 4 = 14."], "source": "Ai Tong 2025 P6 Prelim Paper 1 Q10", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Booklet A Q10: option 2 (14)." }, { "n": 11, "type_id": 1, "question": "Amelia used identical unit cubes to build a solid. She drew the top and side views of the solid. Which of the following could be the solid built by Amelia?", "answer0": "Solid 1", "answer1": "Solid 2", "answer2": "Solid 3", "answer3": "Solid 4", "correct_answer": 2, "skill_id": 188, "difficulty_id": 3, "explanation": "Match each candidate solid's top view and side view to the given views. Only solid 3 produces both the given top view and side view. Answer: Solid 3.", "hints": ["Check that each solid gives BOTH the given top view and side view.", "Only one solid matches both views."], "source": "Ai Tong 2025 P6 Prelim Paper 1 Q11", "image_needed": true, "image_options": true, "image_page": 7, "image_bbox": [0.12, 0.1, 0.86, 0.85], "image_loc": "top and side views plus four 3D solid options (1)-(4) on page 7", "image_file": "q11.png", "notes": "Answer key Booklet A Q11: option 3. image_options true: the 4 options are 3D solids; crop the whole region including the given top/side views." }, { "n": 12, "type_id": 1, "question": "Hassan spent 35% of his monthly allowance on food and \\(\\dfrac{2}{5}\\) of the remaining allowance on transport. What percentage of his allowance was left?", "answer0": "65%", "answer1": "61%", "answer2": "39%", "answer3": "25%", "correct_answer": 2, "skill_id": 175, "difficulty_id": 3, "explanation": "After food, 100% - 35% = 65% remains. Transport = \\(\\dfrac{2}{5}\\) of 65% = 26%. Left = 65% - 26% = 39%. Answer: 39%.", "hints": ["65% remains after food.", "Transport takes \\(\\dfrac{2}{5}\\) of that 65%; subtract it from 65%."], "source": "Ai Tong 2025 P6 Prelim Paper 1 Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Booklet A Q12: option 3 (39%)." }, { "n": 13, "type_id": 1, "question": "The figure is made up of two identical semicircles with radius of 21 m. Find the perimeter of the figure in terms of \\(\\pi\\).", "answer0": "\\(21\\pi\\) m", "answer1": "\\((21\\pi + 21)\\) m", "answer2": "\\(42\\pi\\) m", "answer3": "\\((42\\pi + 42)\\) m", "correct_answer": 2, "skill_id": 221, "difficulty_id": 2, "explanation": "Each semicircle has radius 21 m, so its curved arc = \\(\\dfrac{1}{2} \\times 2\\pi \\times 21 = 21\\pi\\) m. The figure is two such semicircle arcs joined (an S-shape), so total perimeter = 21\\(\\pi\\) + 21\\(\\pi\\) = 42\\(\\pi\\) m. Answer: \\(42\\pi\\) m.", "hints": ["The arc of one semicircle (radius 21) is \\(\\dfrac{1}{2} \\times 2\\pi \\times 21 = 21\\pi\\).", "The figure is made of two such arcs; add them."], "source": "Ai Tong 2025 P6 Prelim Paper 1 Q13", "image_needed": true, "image_options": false, "image_page": 8, "image_bbox": [0.3, 0.42, 0.68, 0.62], "image_loc": "S-shaped figure of two semicircles with 21 m radius marked, middle of page 8", "image_file": "q13.png", "notes": "Answer key Booklet A Q13: option 3 (42 pi m)." }, { "n": 14, "type_id": 1, "question": "Jack drew three triangles to form a figure. The areas of the triangles were in the ratio 1 : 8 : 12. He then shaded some parts of the figure. What is the ratio of the total area of the shaded parts to the area of the figure?", "answer0": "5 : 12", "answer1": "5 : 21", "answer2": "7 : 12", "answer3": "2 : 3", "correct_answer": 0, "skill_id": 183, "difficulty_id": 3, "explanation": "The three triangle areas are 1, 8 and 12 units (total 21). From the figure, the shaded region is the smallest triangle (1) plus the part of the 8-triangle outside the 1-triangle, etc.; the shaded total works out to 5 units against the figure's 12 units (the outer 12-triangle), giving 5 : 12. Answer: 5 : 12.", "hints": ["Use the area units 1, 8 and 12 from the ratio.", "Add up the shaded units and compare with the area of the whole figure."], "source": "Ai Tong 2025 P6 Prelim Paper 1 Q14", "image_needed": true, "image_options": false, "image_page": 9, "image_bbox": [0.28, 0.16, 0.66, 0.36], "image_loc": "nested triangles figure with shaded parts, upper part of page 9", "image_file": "q14.png", "notes": "Answer key Booklet A Q14: option 1 (5 : 12)." }, { "n": 15, "type_id": 1, "question": "4 years ago, the ratio of Calvin's age to Lina's age is 2 : 7. In 8 years' time, Calvin's age will be \\(\\dfrac{2}{5}\\) of Lina's age. How old is Calvin now?", "answer0": "10 years old", "answer1": "18 years old", "answer2": "22 years old", "answer3": "30 years old", "correct_answer": 2, "skill_id": 183, "difficulty_id": 3, "explanation": "4 years ago Calvin : Lina = 2 : 7, so Calvin = 2u and Lina = 7u then. In 8 years' time (12 years after that point) Calvin = 2u + 12, Lina = 7u + 12, and 2u + 12 = \\(\\dfrac{2}{5}\\)(7u + 12). Solving: 5(2u + 12) = 2(7u + 12); 10u + 60 = 14u + 24; 4u = 36; u = 9... so Calvin 4 years ago = 18, Calvin now = 18 + 4 = 22. Answer: 22 years old.", "hints": ["Let Calvin = 2u and Lina = 7u for 4 years ago.", "Write both ages 'in 8 years' time' and use the \\(\\dfrac{2}{5}\\) relation to solve for u, then add 4 for Calvin's age now."], "source": "Ai Tong 2025 P6 Prelim Paper 1 Q15", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Booklet A Q15: option 3 (22 years old)." }, { "n": 16, "type_id": 2, "question": "What is the value of \\(30 - (8 + 16) \\div 3 \\times 2\\)? Ans: [?]", "answer0": "14", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 155, "difficulty_id": 2, "explanation": "Brackets first: 8 + 16 = 24. Then \\(\\div\\) and \\(\\times\\) left to right: 24 \\(\\div\\) 3 = 8; 8 \\(\\times\\) 2 = 16. Then subtract: 30 - 16 = 14. Answer: 14.", "hints": ["Do the bracket first, then divide and multiply from left to right.", "Subtract from 30 last."], "source": "Ai Tong 2025 P6 Prelim Paper 1 Q16", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Booklet B Q16: = 30 - 16 = 14." }, { "n": 17, "type_id": 2, "question": "In the figure, EOH, FOJ and GOK are straight lines. \\(\\angle EOF = 31^\\circ\\) and \\(\\angle KOH = 96^\\circ\\). Find \\(\\angle GOF\\). Ans: [?]°", "answer0": "65", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 194, "difficulty_id": 2, "explanation": "\\(\\angle GOF\\) and \\(\\angle KOH\\) are vertically opposite-related through the straight lines. Using the key: \\(\\angle GOF = 96^\\circ - 31^\\circ = 65^\\circ\\). Answer: 65°.", "hints": ["Use vertically opposite angles and angles on a straight line.", "\\(\\angle GOF = \\angle KOH - \\angle EOF = 96^\\circ - 31^\\circ\\)."], "source": "Ai Tong 2025 P6 Prelim Paper 1 Q17", "image_needed": true, "image_options": false, "image_page": 13, "image_bbox": [0.12, 0.42, 0.55, 0.66], "image_loc": "three intersecting straight lines through O with E, F, G, H, J, K labelled, middle-left of page 13", "image_file": "q17.png", "notes": "Answer key Booklet B Q17: 96 - 31 = 65." }, { "n": 18, "type_id": 2, "question": "Find the average of 15, 17, 0 and 4. Ans: [?]", "answer0": "9", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 203, "difficulty_id": 1, "explanation": "Average = total \\(\\div\\) number of items. Total = 15 + 17 + 0 + 4 = 36; 36 \\(\\div\\) 4 = 9. Answer: 9.", "hints": ["Add all four numbers.", "Divide the total by 4."], "source": "Ai Tong 2025 P6 Prelim Paper 1 Q18", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Booklet B Q18: 36 / 4 = 9." }, { "n": 19, "type_id": 2, "question": "A ribbon was cut into two pieces in the ratio 3 : 5. The length of the longer piece was 35 cm. What was the length of the ribbon at first? Ans: [?] cm", "answer0": "56", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 182, "difficulty_id": 2, "explanation": "The longer piece (5 parts) = 35 cm, so 1 part = 35 \\(\\div\\) 5 = 7 cm. The shorter piece (3 parts) = 7 \\(\\times\\) 3 = 21 cm. Total = 35 + 21 = 56 cm. Answer: 56 cm.", "hints": ["The longer piece is 5 parts = 35 cm, so 1 part = 7 cm.", "Add both pieces (8 parts) for the whole ribbon."], "source": "Ai Tong 2025 P6 Prelim Paper 1 Q19", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Booklet B Q19: 35/5=7; 7x3=21; 21+35=56 cm." }, { "n": 20, "type_id": 2, "question": "In the figure, WXYZ is a rectangle. Measure and write down the height of Triangle XMZ when MZ is the base. Ans: [?] cm", "answer0": "2.9", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 185, "difficulty_id": 2, "explanation": "Measure the perpendicular distance from vertex X to the base MZ with a ruler. The height = 2.9 cm. Answer: 2.9 cm.", "hints": ["The height is measured perpendicular to the base MZ.", "Use a ruler to measure from X straight to line MZ."], "source": "Ai Tong 2025 P6 Prelim Paper 1 Q20", "image_needed": true, "image_options": false, "image_page": 14, "image_bbox": [0.18, 0.5, 0.78, 0.82], "image_loc": "rectangle WXYZ with triangle XMZ, lower half of page 14", "image_file": "q20.png", "notes": "Answer key Booklet B Q20: 2.9 cm (measured)." }, { "n": 21, "type_id": 1, "question": "The bar graph shows the time taken by 5 children to complete a race.
(a) Who was the fastest runner?", "answer0": "Arif", "answer1": "Caili", "answer2": "Elvin", "answer3": "Ben", "correct_answer": 0, "skill_id": 104, "difficulty_id": 2, "explanation": "The fastest runner took the least time, which is the shortest bar. Arif's bar is the shortest, so Arif was the fastest. Answer: Arif.", "hints": ["Fastest = least time = shortest bar.", "Find the child with the shortest bar."], "source": "Ai Tong 2025 P6 Prelim Paper 1 Q21a", "image_needed": true, "image_options": false, "image_page": 15, "image_bbox": [0.18, 0.2, 0.82, 0.5], "image_loc": "horizontal bar graph of race times for Arif, Ben, Caili, Dan, Elvin, upper part of page 15", "image_file": "q21.png", "notes": "Answer key Booklet B Q21a: Arif. Made MCQ; correct option 1." }, { "n": 22, "type_id": 2, "question": "The bar graph shows the time taken by 5 children to complete a race. Dan took 64 s and Elvin took 48 s.
(b) How much longer did Dan take than Elvin to complete the race? Ans: [?] s", "answer0": "16", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 104, "difficulty_id": 2, "explanation": "Read both bars: Dan = 64 s, Elvin = 48 s. Difference = 64 - 48 = 16 s. Answer: 16 s.", "hints": ["Read the time for Dan and for Elvin from the graph.", "Subtract Elvin's time from Dan's time."], "source": "Ai Tong 2025 P6 Prelim Paper 1 Q21b", "image_needed": true, "image_options": false, "image_page": 15, "image_bbox": [0.18, 0.2, 0.82, 0.5], "image_loc": "same race-times bar graph, upper part of page 15", "image_file": "q22.png", "notes": "Answer key Booklet B Q21b: 64 - 48 = 16 s. Shares figure with Q21." }, { "n": 23, "type_id": 2, "question": "A solid cuboid of height 21 cm has a square base of side 9 cm. What is its volume? Ans: [?] cm³", "answer0": "1701", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 190, "difficulty_id": 2, "explanation": "Volume = base area \\(\\times\\) height = (9 \\(\\times\\) 9) \\(\\times\\) 21 = 81 \\(\\times\\) 21 = 1701 cm³. Answer: 1701 cm³.", "hints": ["Square base area = 9 \\(\\times\\) 9.", "Multiply the base area by the height 21."], "source": "Ai Tong 2025 P6 Prelim Paper 1 Q22", "image_needed": true, "image_options": false, "image_page": 16, "image_bbox": [0.56, 0.1, 0.82, 0.27], "image_loc": "tall cuboid with 21 cm height and 9 cm base, upper-right of page 16", "image_file": "q23.png", "notes": "Answer key Booklet B Q22: 9 x 9 x 21 = 1701 cm³." }, { "n": 24, "type_id": 1, "question": "In the figure, rectangle WXYZ is made up of 8 identical smaller rectangles. What fraction of rectangle WXYZ is shaded? Express your answer in the simplest form.", "answer0": "\\(\\dfrac{5}{8}\\)", "answer1": "\\(\\dfrac{3}{8}\\)", "answer2": "\\(\\dfrac{1}{2}\\)", "answer3": "\\(\\dfrac{5}{16}\\)", "correct_answer": 0, "skill_id": 120, "difficulty_id": 2, "explanation": "The shaded area equals the area of the big rectangle minus the unshaded triangles, which together with the smaller rectangles works out to 5 of the 8 equal parts. So shaded = \\(\\dfrac{5}{8}\\). Answer: \\(\\dfrac{5}{8}\\).", "hints": ["The rectangle is split into 8 equal smaller rectangles.", "Work out how many of the 8 equal parts are shaded (8 - 3 = 5)."], "source": "Ai Tong 2025 P6 Prelim Paper 1 Q23", "image_needed": true, "image_options": false, "image_page": 16, "image_bbox": [0.5, 0.5, 0.86, 0.66], "image_loc": "rectangle WXYZ of 8 smaller rectangles with shaded regions, lower half of page 16", "image_file": "q24.png", "notes": "Answer key Booklet B Q23: 8 - 3 = 5 shaded = 5/8. Fraction answer so converted to MCQ; correct option 1." }, { "n": 25, "type_id": 2, "question": "A triangular piece of paper ABC is folded along the dotted line as shown. AB = AC. The angle at A before folding is 60° and after folding an angle of 14° is shown. Find \\(\\angle p\\). Ans: [?]°", "answer0": "46", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 197, "difficulty_id": 3, "explanation": "Triangle ABC is isosceles (AB = AC) with apex 60°, so the base angles are (180° - 60°) \\(\\div\\) 2 = ... using the key: 180° - 120° - 14° = 46°. So \\(\\angle p = 46^\\circ\\). Answer: 46°.", "hints": ["Use the isosceles triangle and the angle sum of a triangle.", "Subtract the known angles from 180° following the fold (180 - 120 - 14 = 46)."], "source": "Ai Tong 2025 P6 Prelim Paper 1 Q24", "image_needed": true, "image_options": false, "image_page": 17, "image_bbox": [0.18, 0.13, 0.82, 0.36], "image_loc": "before-and-after folding diagrams of triangle ABC, upper part of page 17", "image_file": "q25.png", "notes": "Answer key Booklet B Q24: 180-60=120; 180-120-14=46; (final answer for angle p = 46). The key's extra lines 180-46=134, 134/2=67 relate to a different sub-angle; angle p = 46." }, { "n": 26, "type_id": 1, "question": "Jen wants to spend the least amount of money to buy 25 muffins. Each muffin is sold at $\\(n\\). There is a special offer: buy 2 muffins and get 1 muffin free. How much will she pay for the muffins? Express your answer in terms of \\(n\\).", "answer0": "$17n", "answer1": "$25n", "answer2": "$16n", "answer3": "$18n", "correct_answer": 0, "skill_id": 239, "difficulty_id": 3, "explanation": "With 'buy 2 get 1 free', every 3 muffins cost the price of 2, i.e. $2n. For 24 muffins = 8 groups of 3 = 8 \\(\\times\\) $2n = $16n (24 muffins). The 25th muffin is paid in full = $n. Total = $16n + $n = $17n. Answer: $17n.", "hints": ["Every group of 3 muffins costs $2n (one is free).", "24 muffins = 8 groups ($16n); add the 25th muffin at full price $n."], "source": "Ai Tong 2025 P6 Prelim Paper 1 Q25", "image_needed": true, "image_options": false, "image_page": 17, "image_bbox": [0.21, 0.62, 0.74, 0.78], "image_loc": "muffin special-offer box ($n each; buy 2 get 1 free), lower part of page 17", "image_file": "q26.png", "notes": "Answer key Booklet B Q25: $2n -> 3 muffins; $16n -> 24; +1 muffin $n; $17n -> 25. Algebraic answer so converted to MCQ; correct option 1. Offer also described in stem." }, { "n": 27, "type_id": 2, "question": "In the square grid, AB and BC are straight lines. Measure and write down the size of \\(\\angle ABC\\). Ans: [?]°", "answer0": "141", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 140, "difficulty_id": 2, "explanation": "Measure the angle at B between BA and BC with a protractor. \\(\\angle ABC = 141^\\circ\\). Answer: 141°.", "hints": ["Place the protractor centre at B.", "Read the angle between BA and BC."], "source": "Ai Tong 2025 P6 Prelim Paper 1 Q26a", "image_needed": true, "image_options": false, "image_page": 18, "image_bbox": [0.2, 0.42, 0.82, 0.65], "image_loc": "square grid with lines AB and BC (A, B, C labelled), middle of page 18", "image_file": "q27.png", "notes": "Answer key Booklet B Q26a: 141°. Part (b) 'complete the parallelogram and label D' is an interactive drawing task and is omitted." }, { "n": 28, "type_id": 2, "question": "Three beakers are filled with some water. The first beaker reads 1 \\(\\ell\\), the second reads 1 \\(\\ell\\), and the third reads 400 ml.
What is the total volume of water in the three beakers? Ans: [?] l", "answer0": "1.95", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 184, "difficulty_id": 2, "explanation": "Read each beaker: 1000 ml (to the 1 l line, but water is below the mark) + 750 ml + 200 ml. Using the key readings: 1000 + 750 + 200 = 1950 ml = 1.95 \\(\\ell\\). Answer: 1.95 l.", "hints": ["Read each beaker's water level carefully (it may be below the marked line).", "Add the three volumes in ml, then convert to litres (1000 ml = 1 l)."], "source": "Ai Tong 2025 P6 Prelim Paper 1 Q27", "image_needed": true, "image_options": false, "image_page": 19, "image_bbox": [0.18, 0.13, 0.82, 0.3], "image_loc": "three beakers with water levels marked, upper part of page 19", "image_file": "q28.png", "notes": "Answer key Booklet B Q27: 1000 + 750 + 200 = 1950 ml = 1.95 l. Beaker readings must come from the figure (1 l mark, 1 l mark, 400 ml mark are the scale labels)." }, { "n": 29, "type_id": 2, "question": "In the figure, ABCD is a trapezium with AD // BC. BCF is an isosceles triangle. EFC is a straight line. The angle at A is 114° and the angle at F is 80°. Find \\(\\angle ABF\\). Ans: [?]°", "answer0": "26", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 3, "explanation": "Using angles on the straight line EFC: 180° - 114° = 66°. Then \\(\\angle ABF = 66^\\circ - 40^\\circ = 26^\\circ\\) (using the isosceles triangle's 40° base angle). Answer: 26°.", "hints": ["Find the angle next to 114° on the straight line (180 - 114).", "Use the isosceles triangle to subtract its base angle (40°)."], "source": "Ai Tong 2025 P6 Prelim Paper 1 Q28", "image_needed": true, "image_options": false, "image_page": 19, "image_bbox": [0.4, 0.5, 0.8, 0.78], "image_loc": "trapezium ABCD with triangle BCF and labelled angles, lower-right of page 19", "image_file": "q29.png", "notes": "Answer key Booklet B Q28: 180-114=66; 66-40=26." }, { "n": 30, "type_id": 2, "question": "The figure is made up of two identical right-angled triangles overlapping each other. XY = 3 cm and PQ is a straight line. The vertical side is 8 cm and PX base is 5 cm. Find the area of the shaded part. Ans: [?] cm²", "answer0": "32.5", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 186, "difficulty_id": 3, "explanation": "Using the key: one triangle's horizontal length 8 - 3 = 5 with the overlap; the shaded area = the larger triangle part (5 \\(\\times\\) 5 = 25) plus the small triangle \\(\\dfrac{1}{2} \\times 3 \\times 5 = 7.5\\), giving 25 + 7.5 = 32.5 cm². Answer: 32.5 cm².", "hints": ["Split the shaded region into a rectangle-like part and a triangle.", "Add the two parts (25 + 7.5)."], "source": "Ai Tong 2025 P6 Prelim Paper 1 Q29", "image_needed": true, "image_options": false, "image_page": 20, "image_bbox": [0.2, 0.13, 0.82, 0.34], "image_loc": "two overlapping right-angled triangles with shaded part, upper part of page 20", "image_file": "q30.png", "notes": "Answer key Booklet B Q29: 8-3=5; 5x5=25; 1/2 x 3 x 5 = 7.5; 25 + 7.5 = 32.5 cm²." }, { "n": 31, "type_id": 2, "question": "A shop had some bags for sale. After selling 28 bags in the morning and \\(\\dfrac{5}{8}\\) of the remaining bags in the afternoon, \\(\\dfrac{1}{4}\\) of the bags were left unsold. How many bags were sold altogether? Ans: [?]", "answer0": "63", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "After the morning, \\(\\dfrac{5}{8}\\) of the remaining is sold, leaving \\(\\dfrac{3}{8}\\) of the remaining, which equals \\(\\dfrac{1}{4}\\) of the total. Working from the key: \\(\\dfrac{1}{4}\\) of total = \\(\\dfrac{3}{8}\\) of remaining; matching units, 4 units = 12 (so the morning 28 corresponds to 4 units), giving 28 \\(\\div\\) 4 = 7 per unit; 7 \\(\\times\\) 5 = 35 sold in the afternoon; total sold = 35 + 28 = 63. Answer: 63.", "hints": ["After 28 are sold, \\(\\dfrac{3}{8}\\) of the rest is left, which is \\(\\dfrac{1}{4}\\) of the whole.", "Match units to find the value of one unit, then add morning and afternoon sales."], "source": "Ai Tong 2025 P6 Prelim Paper 1 Q30", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Booklet B Q30: 1 - 5/8 = 3/8; 1/4 -> 3/8 scaled to 4/4 -> 12/8; 4p->12; 12-8=4; 28/4=7; 7x5=35; 35+28=63." }, { "n": 32, "type_id": 2, "question": "The table shows the water charges.
Volume of water: First 40 m³ at $1.40 per m³; each additional m³ at $? per m³.
Mr Chan paid $89 for using 60 m³ of water. How much did he pay per cubic metre for water consumption more than 40 m³? Ans: $[?]", "answer0": "1.65", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 3, "explanation": "Cost of the first 40 m³ = 1.40 \\(\\times\\) 40 = $56. Remaining cost = $89 - $56 = $33 for the extra 60 - 40 = 20 m³. Rate = $33 \\(\\div\\) 20 = $1.65 per m³. Answer: $1.65.", "hints": ["Work out the cost of the first 40 m³ at $1.40 each.", "Subtract from $89, then divide by the extra 20 m³."], "source": "Ai Tong 2025 P6 Prelim Paper 2 Q1", "image_needed": true, "image_options": false, "image_page": 23, "image_bbox": [0.12, 0.18, 0.86, 0.3], "image_loc": "water-charges table near top of page 23", "image_file": "q32.png", "notes": "Answer key Paper 2 Q1: 1.40x40=56; 89-56=33; 60-40=20; 33/20=$1.65. Table values also given verbatim in stem." }, { "n": 33, "type_id": 2, "question": "Deena had 2.07 kg of flour at first. She used 459 g of it. How many kilograms of flour was left? Ans: [?] kg", "answer0": "1.611", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 2, "explanation": "Convert to the same unit: 2.07 kg = 2070 g. Left = 2070 - 459 = 1611 g = 1.611 kg. Answer: 1.611 kg.", "hints": ["Change 2.07 kg to grams (2070 g).", "Subtract 459 g, then convert back to kg."], "source": "Ai Tong 2025 P6 Prelim Paper 2 Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Paper 2 Q2: 2070 - 459 = 1611 g = 1.611 kg." }, { "n": 34, "type_id": 2, "question": "The line graph shows the growth of a plant over 4 weeks. The height at Week 1 was 14 cm and at Week 3 was 56 cm. What was the percentage increase in the height of the plant from Week 1 to Week 3? Ans: [?]%", "answer0": "300", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 208, "difficulty_id": 3, "explanation": "Increase = 56 - 14 = 42 cm. Percentage increase = \\(\\dfrac{42}{14} \\times 100\\% = 300\\%\\). Answer: 300%.", "hints": ["Read the Week 1 and Week 3 heights from the graph (14 cm and 56 cm).", "Percentage increase = increase \\(\\div\\) Week 1 height \\(\\times\\) 100%."], "source": "Ai Tong 2025 P6 Prelim Paper 2 Q3", "image_needed": true, "image_options": false, "image_page": 24, "image_bbox": [0.16, 0.3, 0.78, 0.6], "image_loc": "line graph of plant height over Week 0 to Week 4, middle of page 24", "image_file": "q34.png", "notes": "Answer key Paper 2 Q3: 56-14=42; 42/14 x 100% = 300%." }, { "n": 35, "type_id": 2, "question": "Triangle ABC is an isosceles triangle that lies within a figure made up of a semicircle and a rectangle. AB = AC. The rectangle is 9 m wide and 15 m tall. Find the area of Triangle ABC. Ans: [?] m²", "answer0": "123.75", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 186, "difficulty_id": 3, "explanation": "The base BC = 15 m (the rectangle's height). The height of the triangle from A to BC = the rectangle width 9 m plus the semicircle radius. Using the key: 15 \\(\\div\\) 2 = 7.5 (radius); height = 7.5 + 9 = 16.5 m. Area = \\(\\dfrac{1}{2} \\times 16.5 \\times 15 = 123.75\\) m². Answer: 123.75 m².", "hints": ["The semicircle radius is half the rectangle's 15 m side.", "Triangle height = rectangle width + radius; area = \\(\\dfrac{1}{2} \\times\\) height \\(\\times\\) base (15)."], "source": "Ai Tong 2025 P6 Prelim Paper 2 Q4", "image_needed": true, "image_options": false, "image_page": 25, "image_bbox": [0.28, 0.13, 0.7, 0.34], "image_loc": "semicircle-and-rectangle figure with triangle ABC (9 m, 15 m marked), upper part of page 25", "image_file": "q35.png", "notes": "Answer key Paper 2 Q4: 15/2=7.5; 7.5+9=16.5; 1/2 x 16.5 x 15 = 123.75 m²." }, { "n": 36, "type_id": 2, "question": "The figure is formed using 2 squares and 2 equilateral triangles. The perimeter of the figure is 120 cm. PQ is a straight line. What is the length of PQ? Ans: [?] cm", "answer0": "24", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 195, "difficulty_id": 3, "explanation": "All sides of the squares and equilateral triangles are equal. The perimeter of the figure is made of equal-length sides, and PQ spans the same number of these unit sides such that 5 \\(\\times\\) PQ-unit relations give: 5 units along PQ = 120 cm worth... using the key: 5 PQ-units relate to the perimeter so PQ = 120 \\(\\div\\) 5 = 24 cm. Answer: 24 cm.", "hints": ["Every side (square or triangle) has the same length.", "Express the perimeter in terms of that common side, then find PQ."], "source": "Ai Tong 2025 P6 Prelim Paper 2 Q5", "image_needed": true, "image_options": false, "image_page": 26, "image_bbox": [0.26, 0.13, 0.66, 0.45], "image_loc": "figure of 2 squares and 2 equilateral triangles with P and Q marked, upper part of page 26", "image_file": "q36.png", "notes": "Answer key Paper 2 Q5: 5 PQ = 120 cm; 120/5 = 24 cm." }, { "n": 37, "type_id": 1, "question": "A group of students were asked to choose their favourite fruit. The result was a pie chart. Pear is 35%, Mango is \\(\\dfrac{1}{5}\\). Half of the number of students chose mango or orange.
(a) What fraction of the students chose apple as their favourite fruit? Express your answer in its simplest form.", "answer0": "\\(\\dfrac{3}{20}\\)", "answer1": "\\(\\dfrac{1}{5}\\)", "answer2": "\\(\\dfrac{7}{20}\\)", "answer3": "\\(\\dfrac{3}{10}\\)", "correct_answer": 0, "skill_id": 173, "difficulty_id": 3, "explanation": "Mango + Orange = half = 50%. Mango = \\(\\dfrac{1}{5}\\) = 20%, so Orange = 50% - 20% = 30%. Pear = 35%. Apple = 100% - 35% - 20% - 30% = 15% = \\(\\dfrac{15}{100} = \\dfrac{3}{20}\\). Answer: \\(\\dfrac{3}{20}\\).", "hints": ["Mango and Orange together are 50%; Mango is 20%, so find Orange.", "Apple = 100% - pear - mango - orange, then simplify the fraction."], "source": "Ai Tong 2025 P6 Prelim Paper 2 Q6a", "image_needed": true, "image_options": false, "image_page": 27, "image_bbox": [0.28, 0.18, 0.6, 0.4], "image_loc": "favourite-fruit pie chart (Apple, Pear 35%, Mango 1/5, Orange), upper part of page 27", "image_file": "q37.png", "notes": "Answer key Paper 2 Q6a: 50-35=15... actually orange 30, apple 15% = 3/20. Fraction answer so converted to MCQ; correct option 1." }, { "n": 38, "type_id": 0, "question": "A group of students were asked to choose their favourite fruit. Pear is 35%, Mango is \\(\\dfrac{1}{5}\\), Orange is 30% and Apple is 15%.
(b) Each of the statements below is either true, false or not possible to tell. Indicate your answer.
Statement 1: More students chose orange than pear as their favourite fruit.
Statement 2: 20 students chose mango as their favourite fruit.
Statement 3: More students were surveyed and all of them chose mango. The percentage who chose apple remained the same.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 235, "difficulty_id": 3, "explanation": "Statement 1: Orange 30% < Pear 35%, so 'more chose orange than pear' is FALSE. Statement 2: no total number is given, so NOT POSSIBLE TO TELL. Statement 3: if more students all chose mango, mango's share rises and apple's share would fall, so 'apple percentage stayed the same' is FALSE.", "hints": ["Compare orange (30%) and pear (35%) for statement 1.", "For statement 2, ask whether the total number of students is known."], "source": "Ai Tong 2025 P6 Prelim Paper 2 Q6b", "image_needed": false, "image_options": false, "image_file": null, "notes": "Interactive tick-the-box true/false/not-possible task; type_id 0 (skipped on insert). Answer key Paper 2 Q6b: S1 False, S2 Not possible to tell, S3 False." }, { "n": 39, "type_id": 2, "question": "Figure 1 shows an empty container with a rectangular base area of 30 cm² and height 7.8 cm. The container was filled with some water. Figure 2 (front view) shows the water at height 4.6 cm; Figure 3 (turned upside down) shows the water at height 5.5 cm. What is the capacity of the container? Ans: [?] cm³", "answer0": "207", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 193, "difficulty_id": 3, "explanation": "Using the key: the water volume gives base \\(\\times\\) 4.6 = 30 \\(\\times\\) 4.6 = 138 cm³ for the lower part, and the narrower top section adds 2.3 \\(\\times\\) 30 = 69 cm³ (from the 7.8, 4.6, 5.5 readings). Capacity = 138 + 69 = 207 cm³. Answer: 207 cm³.", "hints": ["Use the base area 30 cm² with the water heights from the two views.", "Add the volumes of the two sections (138 + 69)."], "source": "Ai Tong 2025 P6 Prelim Paper 2 Q7", "image_needed": true, "image_options": false, "image_page": 28, "image_bbox": [0.16, 0.07, 0.82, 0.52], "image_loc": "Figure 1 container plus Figure 2 and Figure 3 front views, upper half of page 28", "image_file": "q39.png", "notes": "Answer key Paper 2 Q7: 4.6 x 30 = 138; 2.3 x 30 = 69; 138 + 69 = 207 cm³." }, { "n": 40, "type_id": 2, "question": "JKLM is a rhombus. KLN and KLO are triangles. LM = MN. The angle 21° is at L (inside) and the angle 72° is at J.
(a) Find \\(\\angle LOK\\). Ans: [?]°", "answer0": "21", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 3, "explanation": "Using the key: \\(\\angle LOK = 180^\\circ - 108^\\circ - 51^\\circ = 21^\\circ\\) (108° from the rhombus angle and 51° from the triangle). Answer: 21°.", "hints": ["Use the rhombus angle and the triangle angle sum.", "\\(\\angle LOK = 180^\\circ - 108^\\circ - 51^\\circ\\)."], "source": "Ai Tong 2025 P6 Prelim Paper 2 Q8a", "image_needed": true, "image_options": false, "image_page": 29, "image_bbox": [0.28, 0.1, 0.78, 0.45], "image_loc": "rhombus JKLM with triangles and N, O points, upper part of page 29", "image_file": "q40.png", "notes": "Answer key Paper 2 Q8a: angle LOK = 180-108-51 = 21." }, { "n": 41, "type_id": 2, "question": "JKLM is a rhombus. KLN and KLO are triangles. LM = MN.
(b) Find \\(\\angle LNM\\). Ans: [?]°", "answer0": "27", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 197, "difficulty_id": 3, "explanation": "Using the key: \\(\\angle LMK = 180^\\circ - 126^\\circ = 54^\\circ\\); since LM = MN the triangle LMN is isosceles, so \\(\\angle LNM = 54^\\circ \\div 2 = 27^\\circ\\). Answer: 27°.", "hints": ["Find \\(\\angle LMK\\) first (180° - 126°).", "Triangle LMN is isosceles (LM = MN), so its base angles are equal."], "source": "Ai Tong 2025 P6 Prelim Paper 2 Q8b", "image_needed": true, "image_options": false, "image_page": 29, "image_bbox": [0.28, 0.1, 0.78, 0.45], "image_loc": "same rhombus JKLM figure, upper part of page 29", "image_file": "q41.png", "notes": "Answer key Paper 2 Q8b: angle LMK = 180-126 = 54; angle LNM = 54/2 = 27. Shares figure with Q40." }, { "n": 42, "type_id": 2, "question": "Kai read part of a book in the morning. The ratio of the number of pages he read to the number of pages that were unread was 6 : 5. After reading another 195 pages of the book in the afternoon, Kai still had 10% of the book unread. How many pages were there in the book? Ans: [?]", "answer0": "550", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 214, "difficulty_id": 3, "explanation": "Morning read : unread = 6 : 5, so read = \\(\\dfrac{6}{11}\\) and unread = \\(\\dfrac{5}{11}\\). In the end unread = 10%, so read overall = 90%. Using the key: convert 6 : 5 and the 10% to a common 110 units (read 60 : unread 50, end 99 : 11). The 195 pages = 99 - 60 = 39 units; 195 \\(\\div\\) 39 = 5 per unit; total = 5 \\(\\times\\) 110 = 550 pages. Answer: 550.", "hints": ["Write the morning ratio as parts of 11, and the final unread as 10%.", "Find the units the 195 afternoon pages represent, then scale to the whole book."], "source": "Ai Tong 2025 P6 Prelim Paper 2 Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Paper 2 Q9: 6:5 -> 60:50; end 90:10 -> 99:11; 99-60=39 -> 195; 195/39=5; 5x110 = 550 pages." }, { "n": 43, "type_id": 1, "question": "Town X and Town Y were 455 km apart. Sam left Town X for Town Y at a constant speed of 85 km/h. At the same time, Dan left Town Y for Town X along the same route at a constant speed of 90 km/h. How long had they travelled when they met each other? Express your answer in h and min.", "answer0": "2 h 36 min", "answer1": "2 h 6 min", "answer2": "2 h 30 min", "answer3": "2 h 60 min", "correct_answer": 0, "skill_id": 219, "difficulty_id": 3, "explanation": "They move towards each other, so combined speed = 85 + 90 = 175 km/h. Time = 455 \\(\\div\\) 175 = 2.6 h. 0.6 h = \\(\\dfrac{60}{100} \\times 60 = 36\\) min. So 2.6 h = 2 h 36 min. Answer: 2 h 36 min.", "hints": ["Add the two speeds (they travel toward each other).", "Time = distance \\(\\div\\) combined speed; convert the decimal part of the hour to minutes."], "source": "Ai Tong 2025 P6 Prelim Paper 2 Q10", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Paper 2 Q10: 85+90=175; 455/175=2.6 h; 0.6 h = 36 min; 2 h 36 min. Time format answer so converted to MCQ; correct option 1." }, { "n": 44, "type_id": 2, "question": "A fruit seller had some mangoes. He sold \\(\\dfrac{2}{5}\\) of them and donated 104 of them. He was left with \\(\\dfrac{1}{3}\\) of the mangoes and packed them into 24 bags. Some bags contained 4 mangoes each while the rest contained 6 mangoes each.
(a) How many mangoes were packed? Ans: [?]", "answer0": "130", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "Sold \\(\\dfrac{2}{5}\\) = \\(\\dfrac{6}{15}\\); remaining after selling = \\(\\dfrac{9}{15}\\). Left (packed) = \\(\\dfrac{1}{3}\\) = \\(\\dfrac{5}{15}\\), so donated = \\(\\dfrac{9}{15} - \\dfrac{5}{15} = \\dfrac{4}{15}\\) = 104 mangoes. So \\(\\dfrac{1}{15}\\) = 104 \\(\\div\\) 4 = 26; packed = \\(\\dfrac{5}{15}\\) = 26 \\(\\times\\) 5 = 130. Answer: 130.", "hints": ["Write everything in fifteenths: sold \\(\\dfrac{6}{15}\\), packed \\(\\dfrac{5}{15}\\).", "The donated 104 mangoes = \\(\\dfrac{4}{15}\\); find one fifteenth, then the packed amount."], "source": "Ai Tong 2025 P6 Prelim Paper 2 Q11a", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Paper 2 Q11a: 2/5=6/15; remaining 9/15; 9/15-5/15=4/15=104; 104/4=26; 26x5=130." }, { "n": 45, "type_id": 2, "question": "A fruit seller packed his remaining mangoes into 24 bags. Some bags contained 4 mangoes each while the rest contained 6 mangoes each. He packed 130 mangoes in total.
(b) How many bags contained 6 mangoes each? Ans: [?]", "answer0": "17", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "Assume all 24 bags held 4 mangoes: 24 \\(\\times\\) 4 = 96 mangoes. The extra 130 - 96 = 34 mangoes come from bags that hold 2 more each (6 - 4 = 2). Number of 6-mango bags = 34 \\(\\div\\) 2 = 17. Answer: 17.", "hints": ["Assume every bag had 4 mangoes (24 \\(\\times\\) 4 = 96).", "Each 6-mango bag adds 2 extra; divide the surplus by 2."], "source": "Ai Tong 2025 P6 Prelim Paper 2 Q11b", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Paper 2 Q11b: 24x4=96; 130-96=34; 6-4=2; 34/2=17." }, { "n": 46, "type_id": 2, "question": "The figure is made up of four identical quarter circles, two identical squares of sides 14 cm and a rectangle of breadth 19 cm. Four identical semicircles lie within the figure.
(a) Find the perimeter of the unshaded part. (Take \\(\\pi = 3.14\\)) Ans: [?] cm", "answer0": "169.88", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 222, "difficulty_id": 3, "explanation": "Using the key: the semicircle diameter = 7 + 14 = 21 cm; one full circle circumference = 21 \\(\\times\\) 3.14 = 65.94 cm; two of these = 131.88 cm. Add the two straight edges of 19 cm (sum 38 cm): 131.88 + 38 = 169.88 cm. Answer: 169.88 cm.", "hints": ["Find the curved lengths using the semicircle/quarter-circle radii (diameter 21 cm).", "Add the straight sides (the 19 cm edges) to the curved parts."], "source": "Ai Tong 2025 P6 Prelim Paper 2 Q12a", "image_needed": true, "image_options": false, "image_page": 33, "image_bbox": [0.28, 0.1, 0.66, 0.35], "image_loc": "stadium-shaped figure with quarter circles, squares (14 cm) and semicircles, upper part of page 33", "image_file": "q46.png", "notes": "Answer key Paper 2 Q12a: diameter 7+14=21; 21x3.14=65.94; x2=131.88; +38 = 169.88 cm." }, { "n": 47, "type_id": 2, "question": "The figure is made up of four identical quarter circles, two identical squares of sides 14 cm and a rectangle of breadth 19 cm. Four identical semicircles lie within the figure.
(b) Find the area of the shaded parts. (Take \\(\\pi = 3.14\\)) Ans: [?] cm²", "answer0": "315.07", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 222, "difficulty_id": 3, "explanation": "Using the key: quarter-circle area = \\(\\dfrac{1}{4} \\times 14 \\times 14 \\times 3.14 = 153.86\\) cm²; square area 14 \\(\\times\\) 14 = 196 cm². For one square region: 196 + 153.86 + 153.86 = 503.72, minus the inner circle 10.5 \\(\\times\\) 10.5 \\(\\times\\) 3.14 = 346.185, giving 157.535; times 2 (two regions) = 315.07 cm². Answer: 315.07 cm².", "hints": ["Build each shaded region from the square plus quarter-circle pieces, then subtract the inner circle.", "Double the result for the two identical shaded regions."], "source": "Ai Tong 2025 P6 Prelim Paper 2 Q12b", "image_needed": true, "image_options": false, "image_page": 33, "image_bbox": [0.28, 0.1, 0.66, 0.35], "image_loc": "same stadium-shaped composite figure, upper part of page 33", "image_file": "q47.png", "notes": "Answer key Paper 2 Q12b: 1/4x14x14x3.14=153.86; 196+153.86+153.86=503.72; 10.5x10.5x3.14=346.185; 503.72-346.185=157.535; x2=315.07 cm². Shares figure with Q46." }, { "n": 48, "type_id": 2, "question": "Two rectangular tanks, Tank A and Tank B, are shown. Tank A is 48 cm by 20 cm by 36 cm; Tank B is 60 cm by 10 cm by 45 cm. At first, Tank A was \\(\\dfrac{1}{3}\\)-filled with water and Tank B was empty.
(a) What was the volume of water in Tank A at first? Ans: [?] cm³", "answer0": "11520", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 193, "difficulty_id": 2, "explanation": "Tank A capacity = 48 \\(\\times\\) 20 \\(\\times\\) 36 = 34 560 cm³. Water = \\(\\dfrac{1}{3}\\) of that = \\(\\dfrac{1}{3} \\times 34\\,560 = 11\\,520\\) cm³. Answer: 11 520 cm³.", "hints": ["Find Tank A's full volume (48 \\(\\times\\) 20 \\(\\times\\) 36).", "Take \\(\\dfrac{1}{3}\\) of it."], "source": "Ai Tong 2025 P6 Prelim Paper 2 Q13a", "image_needed": true, "image_options": false, "image_page": 34, "image_bbox": [0.12, 0.1, 0.86, 0.32], "image_loc": "Tank A and Tank B diagrams with dimensions, upper part of page 34", "image_file": "q48.png", "notes": "Answer key Paper 2 Q13a: 1/3 x 48 x 20 x 36 = 11520 cm³." }, { "n": 49, "type_id": 2, "question": "Two rectangular tanks, Tank A (48 cm by 20 cm by 36 cm) and Tank B (60 cm by 10 cm by 45 cm). Tank A started \\(\\dfrac{1}{3}\\)-filled (11 520 cm³) and Tank B empty.
(b) Both taps were then turned on at the same time. Water from both taps flowed at the same rate of 2.4 litres per minute. How long did it take for the height of the water in both tanks to be the same? Ans: [?] min", "answer0": "8", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 193, "difficulty_id": 3, "explanation": "Tank A base = 48 \\(\\times\\) 20 = 960 cm²; Tank B base = 60 \\(\\times\\) 10 = 600 cm². Each tap adds 2.4 \\(\\ell\\) = 2400 cm³ per min. Tank A starts with water height 12 cm (11 520 \\(\\div\\) 960). Heights rise at 2400 \\(\\div\\) 960 = 2.5 cm/min (A) and 2400 \\(\\div\\) 600 = 4 cm/min (B). B catches up to A's height; the height gap closes at 4 - 2.5 = 1.5 cm/min, starting 12 cm apart, so time = 12 \\(\\div\\) 1.5 = 8 min. Answer: 8 min.", "hints": ["Find each tank's base area, then how fast the water height rises in each (rate \\(\\div\\) base area).", "Tank B's height rises faster; the starting height gap (12 cm) closes at the difference in rise rates."], "source": "Ai Tong 2025 P6 Prelim Paper 2 Q13b", "image_needed": true, "image_options": false, "image_page": 34, "image_bbox": [0.12, 0.1, 0.86, 0.32], "image_loc": "same Tank A and Tank B diagrams, upper part of page 34", "image_file": "q49.png", "notes": "Answer key Paper 2 Q13b: A base 960, B base 600; height-rise diff 4 - 2.5 = 1.5 cm/min; 12/1.5 = 8 min. Shares figure with Q48." }, { "n": 50, "type_id": 2, "question": "In the figure, ABCD is a square. ABE is an equilateral triangle and DECF is a trapezium. DE is parallel to FC, and FDA is a straight line.
(a) Find \\(\\angle DEC\\). Ans: [?]°", "answer0": "150", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 3, "explanation": "Using the key: angles around E sum to 360°; \\(\\angle B = 30^\\circ\\) (from the square and equilateral triangle), so the base angles are (180° - 30°) \\(\\div\\) 2 = 75°. Then \\(\\angle DEC = 360^\\circ - 75^\\circ - 75^\\circ - 60^\\circ = 150^\\circ\\) (the key writes 300 - 75 - 75 = 150). Answer: 150°.", "hints": ["Use the equilateral triangle (60°) and square (90°) angles around point E.", "Angles around E add to 360°; subtract the known angles."], "source": "Ai Tong 2025 P6 Prelim Paper 2 Q14a", "image_needed": true, "image_options": false, "image_page": 35, "image_bbox": [0.28, 0.1, 0.66, 0.36], "image_loc": "square ABCD with equilateral triangle ABE and trapezium DECF, upper part of page 35", "image_file": "q50.png", "notes": "Answer key Paper 2 Q14a: angle B = 30; base angles 75; angle DEC = 300 - 75 - 75 = 150." }, { "n": 51, "type_id": 2, "question": "In the figure, ABCD is a square. ABE is an equilateral triangle and DECF is a trapezium. DE is parallel to FC, and FDA is a straight line.
(b) Find \\(\\angle DFC\\). Ans: [?]°", "answer0": "75", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 3, "explanation": "Using the key: 180° - 150° = 30°; 30° \\(\\div\\) 2 = 15°; 90° + 15° = 105°; \\(\\angle DFC = 180^\\circ - 105^\\circ = 75^\\circ\\). Answer: 75°.", "hints": ["Use the trapezium with DE // FC and the angle found in part (a).", "Co-interior and straight-line angles combine to give \\(\\angle DFC\\)."], "source": "Ai Tong 2025 P6 Prelim Paper 2 Q14b", "image_needed": true, "image_options": false, "image_page": 35, "image_bbox": [0.28, 0.1, 0.66, 0.36], "image_loc": "same square-and-trapezium figure, upper part of page 35", "image_file": "q51.png", "notes": "Answer key Paper 2 Q14b: 180-150=30; 30/2=15; 90+15=105; angle DFC = 180-105 = 75. Shares figure with Q50." }, { "n": 52, "type_id": 2, "question": "Selvi used rods to form figures that follow a pattern. The first four figures use 7, 10, 12 and 15 rods respectively.
(a) What is the difference between the number of rods used for Figure 7 and Figure 9? Ans: [?]", "answer0": "5", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 32, "difficulty_id": 3, "explanation": "The pattern alternates adding 3 then 2 (7, 10, 12, 15, 17, 20, 22, 25, 27, ...). Figure 7 = 22 rods, Figure 9 = 27 rods. Difference = 27 - 22 = 5. Answer: 5.", "hints": ["Continue the pattern of rod counts (7, 10, 12, 15, ...).", "Find Figure 7 and Figure 9 counts, then subtract."], "source": "Ai Tong 2025 P6 Prelim Paper 2 Q15a", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Paper 2 Q15a: 27 - 22 = 5. Pattern figure shown but the rod counts are given in the table verbatim." }, { "n": 53, "type_id": 2, "question": "Selvi used rods to form figures that follow a pattern. The first four figures use 7, 10, 12 and 15 rods respectively.
(b) How many rods would she use for Figure 99? Ans: [?]", "answer0": "252", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 32, "difficulty_id": 3, "explanation": "Using the key: pair up figures so each step of two figures adds 5 rods (e.g. Fig 1 = 7, Fig 3 = 12, ...). For Figure 99 (an odd figure): (99 - 1) \\(\\div\\) 2 = 49 steps of 5 rods from Figure 1's 7 rods: 49 \\(\\times\\) 5 = 245; 245 + 7 = 252. Answer: 252.", "hints": ["Group the odd-numbered figures: each adds 5 rods every two figure numbers.", "From Figure 1 (7 rods), add 5 for each pair of steps up to Figure 99."], "source": "Ai Tong 2025 P6 Prelim Paper 2 Q15b", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Paper 2 Q15b: (99-1)/2 = 49; 49 x 5 = 245; 245 + 7 = 252." }, { "n": 54, "type_id": 1, "question": "Three girls, Mabel, Candy and Lilian, had the same number of coins. Mabel had only twenty-cent coins. Candy and Lilian each had a mix of twenty-cent and one-dollar coins. Candy had 36 one-dollar coins while Lilian had 13 one-dollar coins.
(a) Of the three girls, who had the least and who had the most amount of money?", "answer0": "Least: Mabel, Most: Candy", "answer1": "Least: Candy, Most: Mabel", "answer2": "Least: Lilian, Most: Candy", "answer3": "Least: Mabel, Most: Lilian", "correct_answer": 0, "skill_id": 211, "difficulty_id": 2, "explanation": "All three have the same number of coins. The more one-dollar coins (worth more than twenty-cent coins) a girl has, the more money she has. Mabel has zero one-dollar coins (least money); Candy has 36 (the most one-dollar coins, so most money). Answer: Least Mabel, Most Candy.", "hints": ["Same total coins, but one-dollar coins are worth more than twenty-cent coins.", "More one-dollar coins means more money: Mabel has none, Candy has the most."], "source": "Ai Tong 2025 P6 Prelim Paper 2 Q16a", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Paper 2 Q16a: Least Mabel, Most Candy. Made MCQ; correct option 1." }, { "n": 55, "type_id": 2, "question": "Three girls had the same number of coins. Mabel had only twenty-cent coins. Candy had 36 one-dollar coins (and twenty-cent coins). Lilian had 13 one-dollar coins.
(b) Candy used half of her one-dollar coins and some of her twenty-cent coins to buy a book that cost $20.40. How many twenty-cent coins did Candy use? Ans: [?]", "answer0": "12", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 211, "difficulty_id": 3, "explanation": "Half of Candy's 36 one-dollar coins = 18 coins = $18. The rest of the $20.40 came from twenty-cent coins: $20.40 - $18 = $2.40. Number of twenty-cent coins = $2.40 \\(\\div\\) $0.20 = 12. Answer: 12.", "hints": ["Half of 36 one-dollar coins is $18.", "The remaining cost ($20.40 - $18) is paid in twenty-cent coins; divide by $0.20."], "source": "Ai Tong 2025 P6 Prelim Paper 2 Q16b", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Paper 2 Q16b: 36/2=18; 20.40-18=2.40; 2.40/0.20=12." }, { "n": 56, "type_id": 2, "question": "Three girls had the same number of coins. Mabel had only twenty-cent coins. Candy had 36 one-dollar coins. Lilian had 13 one-dollar coins (and twenty-cent coins). Each girl had 30 coins in total.
(c) What was the difference in the total value of Mabel and Lilian's coins? Ans: $[?]", "answer0": "10.40", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 211, "difficulty_id": 3, "explanation": "Using the key (each girl has 30 coins): Mabel = 30 twenty-cent coins = 30 \\(\\times\\) $0.20 = $6. Lilian = 13 one-dollar coins + (30 - 13 = 17) twenty-cent coins = $13 + 17 \\(\\times\\) $0.20 = $13 + $3.40 = $16.40. Difference = $16.40 - $6 = $10.40. Answer: $10.40.", "hints": ["Work out Mabel's total (all twenty-cent coins) and Lilian's total (13 dollars + the rest in twenty-cent coins).", "Subtract the smaller total from the larger."], "source": "Ai Tong 2025 P6 Prelim Paper 2 Q16c", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Paper 2 Q16c: Mabel 30x0.20=$6; Lilian 13 dollars + 17x0.20=$3.40 = $16.40; 16.40-6 = $10.40." }, { "n": 57, "type_id": 2, "question": "There were 16 more students in Team A than in Team B in a competition. \\(\\dfrac{1}{4}\\) of the students in Team A and \\(\\dfrac{3}{7}\\) of the students in Team B were girls. The number of boys was twice the number of girls in the competition. How many boys were there altogether? Ans: [?]", "answer0": "160", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 214, "difficulty_id": 3, "explanation": "Using the key: in Team A girls : boys : total = 1 : 3 : 4, doubled to 2 : 6 : 8. In Team B girls : boys : total = 3 : 4 : 7. The total difference of 1 unit (8 - 7) corresponds to the 16 more students, so 1 unit = 16; total students = 10 units... boys = 10 \\(\\times\\) 16 = 160. Answer: 160.", "hints": ["Write each team's girls : boys : total ratio from the fractions given.", "Match the units so Team A and Team B share the same unit, using the 16-student difference."], "source": "Ai Tong 2025 P6 Prelim Paper 2 Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "Answer key Paper 2 Q17b: A 1:3:4 -> 2:6:8; B 3:4:7; 8-7=1 -> 1u=16; 10u = 160 boys." } ] }