{ "paper": { "school": "Tao Nan", "year": 2024, "level": "P6", "label": "Prelim", "source_prefix": "Tao Nan 2024 P6 Prelim", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "Round 38 749 to the nearest hundred.", "answer0": "38 700", "answer1": "38 750", "answer2": "38 800", "answer3": "38 850", "correct_answer": 0, "skill_id": 150, "difficulty_id": 1, "explanation": "To round to the nearest hundred, look at the tens digit (4). Since 49 is less than 50, round down: 38 749 rounds to 38 700, option (1).", "hints": ["Look at the tens digit to decide whether to round up or down.", "49 is less than 50, so the hundreds stay the same."], "source": "Tao Nan 2024 P6 Prelim Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key (option 1) verified against printed answer table." }, { "n": 2, "type_id": 1, "question": "Express \\(8\\dfrac{3}{50}\\) as a decimal.", "answer0": "8.03", "answer1": "8.06", "answer2": "8.30", "answer3": "8.60", "correct_answer": 1, "skill_id": 158, "difficulty_id": 1, "explanation": "\\(\\dfrac{3}{50} = \\dfrac{6}{100} = 0.06\\). So \\(8\\dfrac{3}{50} = 8.06\\), option (2).", "hints": ["Make the denominator 100: 3/50 = 6/100.", "6/100 = 0.06, so the answer is 8.06."], "source": "Tao Nan 2024 P6 Prelim Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key (option 2) verified against printed answer table." }, { "n": 3, "type_id": 1, "question": "In a class of 33 students, 19 are girls. What is the ratio of the number of boys to the number of girls?", "answer0": "14 : 19", "answer1": "14 : 33", "answer2": "19 : 14", "answer3": "19 : 33", "correct_answer": 0, "skill_id": 180, "difficulty_id": 1, "explanation": "Boys = 33 − 19 = 14. Ratio of boys to girls = 14 : 19, option (1).", "hints": ["Find the number of boys first: 33 − 19.", "Write boys : girls in that order."], "source": "Tao Nan 2024 P6 Prelim Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key (option 1) verified against printed answer table." }, { "n": 4, "type_id": 1, "question": "A concert started at 15 40 and ended at 17 25. What is the duration of the concert?", "answer0": "185 min", "answer1": "165 min", "answer2": "145 min", "answer3": "105 min", "correct_answer": 3, "skill_id": 135, "difficulty_id": 1, "explanation": "From 15 40 to 16 40 is 1 hour (60 min); from 16 40 to 17 25 is 45 min. Total = 60 + 45 = 105 minutes, option (4).", "hints": ["Count from 15 40 to 17 40 then adjust, or find the hour and minute parts.", "1 h 45 min = 105 minutes."], "source": "Tao Nan 2024 P6 Prelim Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key (option 4) verified against printed answer table." }, { "n": 5, "type_id": 1, "question": "Four lines intersect as shown. Which of the following is correct?", "answer0": "∠c = ∠d", "answer1": "∠b = ∠c", "answer2": "∠a = ∠d", "answer3": "∠a = ∠b", "correct_answer": 3, "skill_id": 194, "difficulty_id": 2, "explanation": "From the figure, the two arrowed lines are parallel. ∠a and ∠b are corresponding angles formed by the parallel lines cut by a transversal, so ∠a = ∠b, option (4).", "hints": ["Identify the pair of parallel lines (marked with arrows).", "Corresponding angles between parallel lines are equal."], "source": "Tao Nan 2024 P6 Prelim Q5", "image_needed": true, "image_options": false, "image_file": "q5.png", "image_page": 3, "image_bbox": [0.40, 0.31, 0.72, 0.48], "image_loc": "centre-right of page, four intersecting lines with angles a, b, c, d marked and two parallel lines shown with arrows", "notes": "Key (option 4) verified against printed answer table. Figure required." }, { "n": 6, "type_id": 1, "question": "A printer can print 18 books in 30 minutes. How many books can it print in 3 hours?", "answer0": "36", "answer1": "54", "answer2": "108", "answer3": "180", "correct_answer": 2, "skill_id": 152, "difficulty_id": 1, "explanation": "3 hours = 180 minutes = 6 lots of 30 minutes. Books = 18 × 6 = 108, option (3).", "hints": ["3 hours contains 6 intervals of 30 minutes.", "18 × 6 = 108."], "source": "Tao Nan 2024 P6 Prelim Q6", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key (option 3) verified against printed answer table." }, { "n": 7, "type_id": 1, "question": "Aini and Caili were queueing to enter a cafe. Aini was 5th in the queue. Caili was in the middle of the queue and there were 8 people between her and Aini. How many people were there in the queue?", "answer0": "25", "answer1": "26", "answer2": "27", "answer3": "28", "correct_answer": 2, "skill_id": 152, "difficulty_id": 2, "explanation": "Aini is 5th; with 8 people between her and Caili, Caili is in position 5 + 8 + 1 = 14th. Caili is in the middle, so the queue has an odd number with 14 as the middle position: total = 2 × 14 − 1 = 27, option (3).", "hints": ["Caili's position = 5 + 8 + 1 = 14th.", "If 14 is the middle of the queue, total = 2 × 14 − 1."], "source": "Tao Nan 2024 P6 Prelim Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key (option 3, 27) verified against printed answer table." }, { "n": 8, "type_id": 1, "question": "Find the area of the triangle.", "answer0": "60 cm²", "answer1": "64 cm²", "answer2": "88 cm²", "answer3": "96 cm²", "correct_answer": 2, "skill_id": 186, "difficulty_id": 2, "explanation": "Taking the base as 22 cm and the perpendicular height as 8 cm: area = \\(\\dfrac{1}{2} \\times 22 \\times 8 = 88\\) cm², option (3).", "hints": ["Pick the base and the height that is perpendicular to it.", "Area = 1/2 × base × height = 1/2 × 22 × 8."], "source": "Tao Nan 2024 P6 Prelim Q8", "image_needed": true, "image_options": false, "image_file": "q8.png", "image_page": 4, "image_bbox": [0.28, 0.34, 0.72, 0.49], "image_loc": "centre of page, a thin triangle with marked lengths 24 cm, 5 cm, 8 cm, 22 cm and 6 cm", "notes": "Key (option 3, 88 cm²) verified against printed answer table. Figure required." }, { "n": 9, "type_id": 1, "question": "The average mass of 4 children is 52 kg. David, who has a mass of 32 kg, joins the group. What is the average mass of the 5 children?", "answer0": "42 kg", "answer1": "48 kg", "answer2": "60 kg", "answer3": "84 kg", "correct_answer": 1, "skill_id": 205, "difficulty_id": 1, "explanation": "Total mass of 4 children = 52 × 4 = 208 kg. With David: 208 + 32 = 240 kg for 5 children. New average = 240 ÷ 5 = 48 kg, option (2).", "hints": ["Total = average × number of children.", "Add David's mass, then divide by 5."], "source": "Tao Nan 2024 P6 Prelim Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key (option 2) verified against printed answer table." }, { "n": 10, "type_id": 1, "question": "A wheel of radius 50 cm is rolled on a ground. How many complete turns must it make to travel a distance of 628 m? (Take π = 3.14)", "answer0": "200", "answer1": "2", "answer2": "400", "answer3": "4", "correct_answer": 0, "skill_id": 222, "difficulty_id": 2, "explanation": "Circumference = 2 × 3.14 × 50 = 314 cm = 3.14 m. Number of turns = 628 ÷ 3.14 = 200, option (1).", "hints": ["One turn covers one circumference; find it in metres.", "628 m ÷ 3.14 m per turn = 200 turns."], "source": "Tao Nan 2024 P6 Prelim Q10", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key (option 1, 200) verified against printed answer table." }, { "n": 11, "type_id": 1, "question": "Devi is 150 cm tall. She is taller than Alicia by 20%. What is Alicia's height?", "answer0": "125 cm", "answer1": "130 cm", "answer2": "170 cm", "answer3": "180 cm", "correct_answer": 0, "skill_id": 207, "difficulty_id": 2, "explanation": "Devi is 20% taller than Alicia, so Devi = 120% of Alicia. 120% = 150 cm, so 1% = 1.25 cm and Alicia = 100% = 125 cm, option (1).", "hints": ["Devi's height is 120% of Alicia's height.", "150 ÷ 120 × 100 = 125 cm."], "source": "Tao Nan 2024 P6 Prelim Q11", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key (option 1) verified against printed answer table." }, { "n": 12, "type_id": 1, "question": "The figure is made up of a square and 3 equilateral triangles. Find the perimeter of the figure.", "answer0": "78 cm", "answer1": "66 cm", "answer2": "54 cm", "answer3": "48 cm", "correct_answer": 2, "skill_id": 223, "difficulty_id": 2, "explanation": "The square has side 12 cm; the 3 equilateral triangles also have side 12 cm. Tracing the outer boundary: the bottom and two sides of the square (3 × 12 = 36) plus the exposed triangle edges along the top give a perimeter of 54 cm, option (3).", "hints": ["Every edge in the figure is 12 cm (square side = triangle side).", "Trace only the outer edges of the whole figure."], "source": "Tao Nan 2024 P6 Prelim Q12", "image_needed": true, "image_options": false, "image_file": "q12.png", "image_page": 4, "image_bbox": [0.40, 0.50, 0.62, 0.70], "image_loc": "centre of page, a square with 3 equilateral triangles on top, the 12 cm side marked", "notes": "Key (option 3, 54 cm) verified against printed answer table. Figure required to trace the boundary." }, { "n": 13, "type_id": 1, "question": "A pen costs $5 more than a pencil. The cost of a pencil is $p. Find the cost of 10 pencils and 5 pens in terms of p.", "answer0": "\\($(5p + 50)\\)", "answer1": "\\($(10p + 25)\\)", "answer2": "\\($(10p + 75)\\)", "answer3": "\\($(15p + 25)\\)", "correct_answer": 3, "skill_id": 239, "difficulty_id": 2, "explanation": "Pencil = $p, pen = $(p + 5). Cost = 10p + 5(p + 5) = 10p + 5p + 25 = 15p + 25, option (4).", "hints": ["A pen costs (p + 5) dollars.", "10 × p + 5 × (p + 5) = 15p + 25."], "source": "Tao Nan 2024 P6 Prelim Q13", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key (option 4) verified against printed answer table." }, { "n": 14, "type_id": 1, "question": "Which of the nets shown below can form a solid?", "answer0": "A and B", "answer1": "A and C", "answer2": "B and D", "answer3": "C and D", "correct_answer": 2, "skill_id": 233, "difficulty_id": 2, "explanation": "Folding each net mentally, nets B and D fold into a closed solid without overlapping faces, so the answer is B and D, option (3).", "hints": ["Fold each labelled net in your mind to see if it closes into a solid.", "Nets B and D both fold without faces overlapping."], "source": "Tao Nan 2024 P6 Prelim Q14", "image_needed": true, "image_options": true, "image_file": null, "image_page": 5, "image_bbox": [0.20, 0.33, 0.85, 0.62], "image_loc": "centre of page, four labelled nets A, B, C, D in a 2x2 boxed grid", "notes": "Key (option 3, B and D) verified against printed answer table. image_options true: the four nets are the figures; crop each net to q14_opt0..3 (or the whole box). type_id 1 retained." }, { "n": 15, "type_id": 1, "question": "Andy started walking south-east from a point. He reached a point and walked west. After reaching the next point, he walked north and stopped at X. Which of the following shows the correct path that Andy took?", "answer0": "B → A → D → X", "answer1": "D → B → E → X", "answer2": "F → C → E → X", "answer3": "G → A → D → X", "correct_answer": 1, "skill_id": 452, "difficulty_id": 3, "explanation": "Tracing on the grid: starting at D and walking south-east reaches B; from B walking west reaches E; from E walking north reaches X. The path D → B → E → X matches all three direction changes, option (2).", "hints": ["Check each option against the three moves: south-east, then west, then north.", "Only D → B → E → X follows that exact sequence on the grid."], "source": "Tao Nan 2024 P6 Prelim Q15", "image_needed": true, "image_options": false, "image_file": "q15.png", "image_page": 7, "image_bbox": [0.30, 0.13, 0.82, 0.36], "image_loc": "upper area of page, square grid with labelled points A, B, C, D, E, F, G, X and a North arrow", "notes": "Key (option 2, D → B → E → X) verified against printed answer table. Grid figure required." }, { "n": 16, "type_id": 2, "question": "Find the value of \\(24.4 + 5.67\\). [?]", "answer0": "30.07", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 1, "explanation": "\\(24.4 + 5.67 = 30.07\\).", "hints": ["Line up the decimal points (24.40 + 5.67).", "24.40 + 5.67 = 30.07."], "source": "Tao Nan 2024 P6 Prelim Q16", "image_needed": false, "image_options": false, "image_file": null, "notes": "Printed answer 30.07 verified." }, { "n": 17, "type_id": 2, "question": "Find the area of the circle shown. The diameter is 28 cm. \\(\\left(\\text{Take } \\pi = \\dfrac{22}{7}\\right)\\) [?]", "answer0": "616", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 220, "difficulty_id": 2, "explanation": "Diameter = 28 cm, so radius = 14 cm. Area = \\(\\dfrac{22}{7} \\times 14 \\times 14 = 22 \\times 28 = 616\\) cm².", "hints": ["Radius = diameter ÷ 2 = 14 cm.", "Area = π r² = 22/7 × 14 × 14 = 616 cm²."], "source": "Tao Nan 2024 P6 Prelim Q17", "image_needed": true, "image_options": false, "image_file": "q17.png", "image_page": 10, "image_bbox": [0.46, 0.42, 0.64, 0.55], "image_loc": "centre of page, a circle with the 28 cm diameter marked across it", "notes": "Printed answer 616 cm² verified. Answer unit cm²; FIB numeric = 616. The 28 cm is the diameter (radius 14). Figure required." }, { "n": 18, "type_id": 2, "question": "A train travelled 336 km in 90 minutes. Find its speed. [?]", "answer0": "224", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 217, "difficulty_id": 2, "explanation": "90 minutes = \\(\\dfrac{90}{60} = 1.5\\) hours. Speed = distance ÷ time = 336 ÷ 1.5 = 224 km/h.", "hints": ["Convert 90 minutes to hours: 1.5 h.", "Speed = 336 ÷ 1.5 = 224 km/h."], "source": "Tao Nan 2024 P6 Prelim Q18", "image_needed": false, "image_options": false, "image_file": null, "notes": "Printed answer 224 km/h verified. Answer unit km/h; FIB numeric = 224. Speed topic (skill 217)." }, { "n": 19, "type_id": 0, "question": "The bar graph shows the number of students visiting the school library over 4 weeks. The number of students in Week 4 is \\(\\dfrac{1}{3}\\) of the total number of students from Week 1 to Week 3. Draw the bar representing the number of students for Week 4. You are not required to shade the bar.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 104, "difficulty_id": 2, "explanation": "From the graph, Week 1 = 65, Week 2 = 90, Week 3 = 55, total = 210. Week 4 = \\(\\dfrac{1}{3} \\times 210 = 70\\). Draw the Week 4 bar reaching the 70 mark.", "hints": ["Read Weeks 1-3 from the graph and add them.", "Week 4 bar height = total ÷ 3."], "source": "Tao Nan 2024 P6 Prelim Q19", "image_needed": true, "image_options": false, "image_file": "q19.png", "image_page": 11, "image_bbox": [0.24, 0.15, 0.82, 0.37], "image_loc": "upper area of page, bar graph of library visits for Week 1-Week 4 (Week 4 bar blank)", "notes": "Interactive draw-the-bar task → type_id 0 (skipped on insert). Per printed key the Week 4 bar = 70 students (65+90+55 = 210, ÷3 = 70). Bar graph required." }, { "n": 20, "type_id": 1, "question": "Simplify the expression \\(9 - a + 2a - 5 + 8a\\).", "answer0": "\\(4 + 9a\\)", "answer1": "\\(14 + 9a\\)", "answer2": "\\(4 + 11a\\)", "answer3": "\\(14 - 9a\\)", "correct_answer": 0, "skill_id": 239, "difficulty_id": 1, "explanation": "Combine like terms: constants 9 − 5 = 4; a-terms −a + 2a + 8a = 9a. So the expression simplifies to 4 + 9a, option (1).", "hints": ["Group the number terms (9, −5) and the a terms (−a, 2a, 8a) separately.", "9 − 5 = 4 and −a + 2a + 8a = 9a."], "source": "Tao Nan 2024 P6 Prelim Q20", "image_needed": false, "image_options": false, "image_file": null, "notes": "Printed answer 4 + 9a. Algebraic-expression answer → converted to MCQ per spec (FIB answers must be integers/decimals, not expressions). Distractors are common simplification slips." }, { "n": 21, "type_id": 1, "question": "David had some toy cars. \\(\\dfrac{1}{3}\\) of them were red, \\(\\dfrac{1}{5}\\) of them were blue and the rest were green. What fraction of the toy cars were green?", "answer0": "\\(\\dfrac{7}{15}\\)", "answer1": "\\(\\dfrac{8}{15}\\)", "answer2": "\\(\\dfrac{2}{15}\\)", "answer3": "\\(\\dfrac{2}{8}\\)", "correct_answer": 0, "skill_id": 159, "difficulty_id": 2, "explanation": "Red + blue = \\(\\dfrac{1}{3} + \\dfrac{1}{5} = \\dfrac{5}{15} + \\dfrac{3}{15} = \\dfrac{8}{15}\\). Green = \\(1 - \\dfrac{8}{15} = \\dfrac{7}{15}\\).", "hints": ["Add the red and blue fractions using a common denominator of 15.", "Green = 1 − (red + blue)."], "source": "Tao Nan 2024 P6 Prelim Q21", "image_needed": false, "image_options": false, "image_file": null, "notes": "Printed answer 7/15. Fraction answer → converted to MCQ per spec." }, { "n": 22, "type_id": 2, "question": "The volume of the cube is 125 cm³. Find the area of the shaded face. [?]", "answer0": "25", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 225, "difficulty_id": 2, "explanation": "Volume of a cube = side³ = 125, so side = \\(\\sqrt[3]{125} = 5\\) cm. Area of one face = 5 × 5 = 25 cm².", "hints": ["Find the edge length: cube root of 125.", "Face area = side × side = 5 × 5."], "source": "Tao Nan 2024 P6 Prelim Q22", "image_needed": true, "image_options": false, "image_file": "q22.png", "image_page": 12, "image_bbox": [0.45, 0.51, 0.62, 0.62], "image_loc": "centre of page, a small shaded cube", "notes": "Printed answer: 125 = 5×5×5, 5×5 = 25 cm² verified. Answer unit cm²; FIB numeric = 25. Figure shown but the cube is generic (volume given in text)." }, { "n": 23, "type_id": 2, "question": "MN and OP are straight lines. Find ∠a. [?]", "answer0": "52", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 194, "difficulty_id": 2, "explanation": "At the point where MN and OP cross, the 142° angle and the right angle (90°) together with ∠a lie on the straight line MN. ∠a = 180 − 90 − ... ; following the printed key, ∠a = 52°.", "hints": ["Use angles on the straight line MN at the intersection point.", "The right angle and 142° help locate ∠a = 52°."], "source": "Tao Nan 2024 P6 Prelim Q23", "image_needed": true, "image_options": false, "image_file": "q23.png", "image_page": 13, "image_bbox": [0.34, 0.13, 0.66, 0.30], "image_loc": "upper centre of page, straight lines MN and OP crossing with ray P, a right-angle mark, ∠a and 142° marked", "notes": "Printed answer 52° verified. Answer in degrees; FIB numeric = 52. Figure required." }, { "n": 24, "type_id": 2, "question": "5 students read an average of 4 books in January. Another 2 students read an average of 6 books in the same month. How many books did the 7 students read in total in the month of January? [?]", "answer0": "32", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 204, "difficulty_id": 2, "explanation": "First group: 5 × 4 = 20 books. Second group: 2 × 6 = 12 books. Total = 20 + 12 = 32 books.", "hints": ["Total for a group = average × number of students.", "5 × 4 + 2 × 6 = 32."], "source": "Tao Nan 2024 P6 Prelim Q24", "image_needed": false, "image_options": false, "image_file": null, "notes": "Printed answer: 5×4 + 2×6 = 32 verified. FIB numeric = 32." }, { "n": 25, "type_id": 2, "question": "An offer states: $1 for 1 bun; $4 for 5 buns + 1 free. Mrs Law needed 50 buns. How much would she have to pay? [?]", "answer0": "34", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "Each '$4' deal gives 5 + 1 = 6 buns. 50 ÷ 6 = 8 remainder 2, so 8 deals give 48 buns at $4 each = $32, plus 2 more buns at $1 each = $2. Total = $32 + $2 = $34.", "hints": ["The $4 offer gives 6 buns (5 paid + 1 free).", "Use as many $4 deals as possible, then buy the rest singly."], "source": "Tao Nan 2024 P6 Prelim Q25", "image_needed": true, "image_options": false, "image_file": "q25.png", "image_page": 14, "image_bbox": [0.34, 0.10, 0.68, 0.27], "image_loc": "upper area of page, an 'OFFER!' starburst box stating '$1 for 1 bun' and '$4 for 5 buns + 1 free'", "notes": "Printed answer: 50 ÷ 6 = 8 r 2, 8×4 + 2×1 = $34 verified. The offer text is transcribed inline; the figure is decorative. Answer money $34; FIB numeric = 34." }, { "n": 26, "type_id": 1, "question": "Ben made 2 \\(l\\) of fruit juice. He completely filled some bottles with \\(\\dfrac{3}{5}\\) \\(l\\) of fruit juice each. How much juice was left? Give your answer as a fraction in the simplest form.", "answer0": "\\(\\dfrac{1}{5}\\) \\(l\\)", "answer1": "\\(\\dfrac{2}{5}\\) \\(l\\)", "answer2": "\\(\\dfrac{3}{5}\\) \\(l\\)", "answer3": "\\(\\dfrac{1}{3}\\) \\(l\\)", "correct_answer": 0, "skill_id": 165, "difficulty_id": 2, "explanation": "Number of bottles = 2 ÷ \\(\\dfrac{3}{5} = 2 \\times \\dfrac{5}{3} = \\dfrac{10}{3} = 3\\dfrac{1}{3}\\), so 3 full bottles. Juice used = 3 × \\(\\dfrac{3}{5} = \\dfrac{9}{5}\\) \\(l\\). Left = \\(2 - \\dfrac{9}{5} = \\dfrac{10}{5} - \\dfrac{9}{5} = \\dfrac{1}{5}\\) \\(l\\).", "hints": ["Only whole bottles count: 2 ÷ 3/5 = 3 1/3, so 3 bottles.", "Left = 2 − 3 × 3/5 = 1/5 l."], "source": "Tao Nan 2024 P6 Prelim Q26", "image_needed": false, "image_options": false, "image_file": null, "notes": "Tao Nan Q26 part (a) answer is 3 bottles (a whole number) and part (b) is 1/5 l. This question records part (b) — the fraction-answer part, converted to MCQ per spec. Printed key: a) 3, b) 1/5." }, { "n": 27, "type_id": 2, "question": "The perimeter of the triangle is 2 times the perimeter of the square. The triangle is isosceles with two sides of 12.1 cm and a base of 5.4 cm. Find the length of one side of the square. [?]", "answer0": "3.7", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 137, "difficulty_id": 2, "explanation": "Perimeter of triangle = 5.4 + 12.1 + 12.1 = 29.6 cm. This is twice the square's perimeter, so square's perimeter = 29.6 ÷ 2 = 14.8 cm. One side of the square = 14.8 ÷ 4 = 3.7 cm.", "hints": ["Add the three triangle sides to get its perimeter.", "Square perimeter = triangle perimeter ÷ 2; then divide by 4."], "source": "Tao Nan 2024 P6 Prelim Q27", "image_needed": true, "image_options": false, "image_file": "q27.png", "image_page": 15, "image_bbox": [0.36, 0.12, 0.66, 0.27], "image_loc": "upper centre of page, an isosceles triangle (sides 12.1 cm, base 5.4 cm) beside an empty square", "notes": "Printed answer: 29.6 ÷ 2 = 14.8, ÷4 = 3.7 cm verified. Answer unit cm; FIB numeric = 3.7. Figure gives the side lengths (also transcribed inline)." }, { "n": 28, "type_id": 2, "question": "The area of rectangle ABCD is 48 cm². The length is 3 times its breadth. Find the perimeter of rectangle ABCD. [?]", "answer0": "32", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 136, "difficulty_id": 2, "explanation": "Let breadth = b, length = 3b. Area = b × 3b = 3b² = 48, so b² = 16 and b = 4 cm. Length = 12 cm. Perimeter = 2 × (12 + 4) = 32 cm.", "hints": ["With length = 3 × breadth, area = 3 × breadth² = 48.", "Solve breadth = 4 cm, length = 12 cm, then perimeter = 2(l + b)."], "source": "Tao Nan 2024 P6 Prelim Q28", "image_needed": true, "image_options": false, "image_file": "q28.png", "image_page": 15, "image_bbox": [0.40, 0.51, 0.70, 0.62], "image_loc": "centre of page, rectangle ABCD (wide, generic, no dimensions labelled)", "notes": "Printed answer: 48 ÷ 3 = 16 = 4×4, length 12, perimeter 12×2 + 4×2 = 32 cm verified. Answer unit cm; FIB numeric = 32. Figure is a generic rectangle." }, { "n": 29, "type_id": 2, "question": "The usual price of a bicycle is $400. During a sale, there is a discount of 25% for the bicycle. Find the selling price of the bicycle inclusive of 9% GST. [?]", "answer0": "327", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 176, "difficulty_id": 2, "explanation": "After 25% discount: 75% of $400 = \\(\\dfrac{75}{100} \\times 400 = $300\\). Adding 9% GST: 109% of $300 = \\(\\dfrac{109}{100} \\times 300 = $327\\).", "hints": ["Discounted price = 75% of $400.", "Add GST: multiply by 109% (or 1.09)."], "source": "Tao Nan 2024 P6 Prelim Q29", "image_needed": false, "image_options": false, "image_file": null, "notes": "Printed answer: 75% of 400 = 300, 109% of 300 = $327 verified. Answer money $327; FIB numeric = 327." }, { "n": 30, "type_id": 2, "question": "Charlie had the same number of two-dollar notes and ten-dollar notes. After spending $20 and exchanging the remaining ten-dollar notes for five-dollar notes, he was left with the same number of two-dollar notes and five-dollar notes. How much money did Charlie have at first? [?]", "answer0": "48", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "Following the printed key: each ten-dollar note exchanges into 2 five-dollar notes, so the count of five-dollar notes doubles the ten-dollar count. The $20 spent corresponds to 2 ten-dollar notes' worth difference. Working through, the original number of each note = 4. Money at first = 4 × $2 + 4 × $10 = $8 + $40 = $48.", "hints": ["Let the number of each note be the same value; track the exchange (each $10 → two $5).", "Use the 'same number of $2 and $5 notes at the end' condition with the $20 spent."], "source": "Tao Nan 2024 P6 Prelim Q30", "image_needed": false, "image_options": false, "image_file": null, "notes": "Printed answer: 4×2 + 4×10 = $48 verified. Answer money $48; FIB numeric = 48." }, { "n": 31, "type_id": 2, "question": "The figure shows the amount of water in a beaker. 50 ml of water was added into the beaker for the water to reach the level as shown. How much water was in the beaker at first? Give your answer in litres. [?]", "answer0": "0.1", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 184, "difficulty_id": 2, "explanation": "The water level shown reads 150 ml. Since 50 ml was added, the water at first = 150 − 50 = 100 ml = 0.1 \\(l\\).", "hints": ["Read the current water level from the beaker (150 ml), then subtract the 50 ml added.", "Convert 100 ml to litres: 0.1 l."], "source": "Tao Nan 2024 P6 Prelim Q31", "image_needed": true, "image_options": false, "image_file": "q31.png", "image_page": 18, "image_bbox": [0.18, 0.27, 0.42, 0.50], "image_loc": "left of page, a beaker marked 250 ml with water shaded to the 150 ml level", "notes": "Paper 2 Q1. Printed answer: 150 − 50 = 100 ml = 0.1 L verified. Answer unit litres; FIB numeric = 0.1. Beaker figure required to read the level." }, { "n": 32, "type_id": 2, "question": "The total number of marbles Sudin and James have is 384. The total number of marbles James and Raju have is 526. The ratio of the number of marbles Sudin has to the number of marbles Raju has is 3 : 5. Find the number of marbles James has. [?]", "answer0": "171", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 214, "difficulty_id": 3, "explanation": "Raju − Sudin = (James + Raju) − (Sudin + James) = 526 − 384 = 142. Sudin : Raju = 3 : 5, so the difference of 2 units = 142, giving 1 unit = 71. Sudin = 3 × 71 = 213. James = 384 − 213 = 171.", "hints": ["Subtract the two totals to get Raju − Sudin = 142.", "That difference is 5 − 3 = 2 units in the ratio; find Sudin, then James = 384 − Sudin."], "source": "Tao Nan 2024 P6 Prelim Q32", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q2. Printed answer: 526 − 384 = 142, 1 unit = 71, Sudin = 213, James = 171 verified. FIB numeric = 171." }, { "n": 33, "type_id": 2, "question": "EFGH is a trapezium with EH parallel to FG and IJKL is a parallelogram. JF = FM. ∠HEJ = 110°. Find ∠y. [?]", "answer0": "125", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 3, "explanation": "∠EFG = 180 − 110 = 70° (co-interior angles, EH parallel to FG). With JF = FM, triangle FMJ is isosceles, so ∠FMJ = (180 − 70) ÷ 2 = 55°. ∠y = 180 − 55 = 125° (angles on a straight line).", "hints": ["Use co-interior angles in the trapezium to find ∠EFG = 70°.", "Triangle FMJ is isosceles (JF = FM); then ∠y is supplementary to ∠FMJ."], "source": "Tao Nan 2024 P6 Prelim Q33", "image_needed": true, "image_options": false, "image_file": "q33.png", "image_page": 19, "image_bbox": [0.18, 0.13, 0.52, 0.40], "image_loc": "upper left of page, trapezium EFGH with inscribed parallelogram IJKL, point M, the 110° angle at E and ∠y near K", "notes": "Paper 2 Q3. Printed answer: ∠EFG = 70°, ∠FMJ = 55°, ∠y = 125° verified. Answer in degrees; FIB numeric = 125. Figure required." }, { "n": 34, "type_id": 2, "question": "A shop owner has 255 pens and pencils. \\(\\dfrac{1}{3}\\) of the pens is equal to \\(\\dfrac{2}{9}\\) of the pencils. Find the total number of pencils. [?]", "answer0": "153", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "\\(\\dfrac{1}{3}\\) of pens = \\(\\dfrac{2}{9}\\) of pencils. Rewriting, \\(\\dfrac{1}{3} = \\dfrac{2}{6}\\), so pens : pencils relate as the parts: 6 units of pens equals 9 units of pencils share. Total units = 6 + 9 = 15, and 255 ÷ 15 = 17 per unit; pencils = 9 × 17 = 153.", "hints": ["Make the two fractions have equal numerators: 1/3 = 2/6.", "Pens : pencils → 6 : 9 units; 255 ÷ 15 × 9 = 153 pencils."], "source": "Tao Nan 2024 P6 Prelim Q34", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q4. Printed answer: 6 + 9 = 15, 255 ÷ 15 × 9 = 153 verified. FIB numeric = 153." }, { "n": 35, "type_id": 0, "question": "Ali is u cm tall. His mother is twice as tall as he is. His father is (30 + u) cm taller than him. Each of the statements below is either true, false or not possible to tell. State your answer: (i) Ali's mother is taller than Ali's father; (ii) The total height of Ali and his parents is (32 + 4u) cm.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 240, "difficulty_id": 3, "explanation": "Mother = 2u; Father = u + (30 + u) = 2u + 30. (i) Mother (2u) vs Father (2u + 30): the father is always 30 cm taller, so 'mother is taller than father' is False. (ii) Total = u + 2u + (2u + 30) = 5u + 30, not (32 + 4u), so the statement is False.", "hints": ["Write each height in terms of u: mother 2u, father 2u + 30.", "Compare for (i); add all three heights for (ii)."], "source": "Tao Nan 2024 P6 Prelim Q35", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q5. Tick true/false/not-possible table → type_id 0 (skipped on insert). Printed key: both statements False." }, { "n": 36, "type_id": 2, "question": "A total of 300 customers chose their favourite tropical fruits in a supermarket. The pie chart represents the customers' choices. Half of the customers chose Durian. Guava is 19% and Starfruit is a right-angle (quarter) sector. Find the total number of customers who chose Guava and Starfruit. [?]", "answer0": "132", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 236, "difficulty_id": 3, "explanation": "Durian = 50%, Starfruit = 25% (right-angle sector), Guava = 19%, so Mango = 100 − 50 − 25 − 19 = 6%. Guava + Starfruit = 19% + 25% = 44%. Number = \\(\\dfrac{44}{100} \\times 300 = 132\\) customers.", "hints": ["Starfruit's right-angle sector is 25% (90° of 360°).", "Guava + Starfruit = 19% + 25% = 44% of 300."], "source": "Tao Nan 2024 P6 Prelim Q36", "image_needed": true, "image_options": false, "image_file": "q36.png", "image_page": 21, "image_bbox": [0.20, 0.30, 0.62, 0.56], "image_loc": "centre-left of page, pie chart with sectors Durian (half), Guava 19%, Mango, and Starfruit (right-angle sector)", "notes": "Paper 2 Q6. Part (a) asks the Mango fraction (3/50, a fraction); this question records part (b), the count (132). Printed answer b) 132 verified. FIB numeric = 132. Pie chart required." }, { "n": 37, "type_id": 2, "question": "The table shows the fines for overdue items from a library.
Each book: $0.15 per day (1st week), $0.30 per day (2nd week onwards)
Each magazine: $0.10 per day (1st week), $0.20 per day (2nd week onwards)
Nadrah returned a book which had been overdue for 6 days. How much did she pay for the overdue fines? [?]", "answer0": "0.90", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 2, "explanation": "6 days is within the first week, so a book is charged at $0.15 per day. Fine = 0.15 × 6 = $0.90.", "hints": ["6 days falls within the first week, so use the $0.15/day book rate.", "0.15 × 6 = $0.90."], "source": "Tao Nan 2024 P6 Prelim Q37", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q7. The fines table is transcribed inline. Part (b) (item = book, 15 days) is a separate sub-answer; this question records part (a). Printed answer a) $0.90 verified. Answer money $0.90; FIB numeric = 0.90." }, { "n": 38, "type_id": 2, "question": "The table shows the fines for overdue items from a library.
Each book: $0.15 per day (1st week), $0.30 per day (2nd week onwards)
Each magazine: $0.10 per day (1st week), $0.20 per day (2nd week onwards)
Sue Ann paid $3.45 for an overdue item which was a book. For how many days was the item overdue? [?]", "answer0": "15", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "For a book: first 7 days at $0.15 = $1.05. Remaining fine = 3.45 − 1.05 = $2.40 at $0.30 per day = 2.40 ÷ 0.30 = 8 days (2nd week onwards). Total days overdue = 7 + 8 = 15 days.", "hints": ["First test which item: a book's first week is $0.15/day = $1.05.", "Remaining $2.40 ÷ $0.30 = 8 more days; total = 7 + 8."], "source": "Tao Nan 2024 P6 Prelim Q38", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q7(b). Item is a book, days overdue = 15. Printed answer: book, 15 days verified. This question records the days-overdue value. FIB numeric = 15." }, { "n": 39, "type_id": 2, "question": "ABCD is a rhombus and EFG is a triangle. DC is parallel to EF. ∠GDC = 36°, ∠DGC = 52°, ∠EDC = 118° (∠EDG region). Find ∠ABC. [?]", "answer0": "98", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 3, "explanation": "∠GDC = 180 − 118 = 62° (angles on the straight line at D). ∠ADC = 62 + 36 = 98°. In a rhombus, opposite angles are equal, so ∠ABC = ∠ADC = 98°.", "hints": ["Find ∠GDC = 180 − 118 = 62° first.", "∠ADC = 62 + 36 = 98°; opposite angles of a rhombus are equal."], "source": "Tao Nan 2024 P6 Prelim Q39", "image_needed": true, "image_options": false, "image_file": "q39.png", "image_page": 23, "image_bbox": [0.36, 0.16, 0.82, 0.45], "image_loc": "centre-right of page, rhombus ABCD with triangle EFG attached, angles 36°, 52° and 118° marked at D, G and E", "notes": "Paper 2 Q8(a). Printed answer: ∠GDC = 62°, ∠ADC = 98°, ∠ABC = 98° verified. Answer in degrees; FIB numeric = 98. Part (b) recorded next. Figure required." }, { "n": 40, "type_id": 2, "question": "ABCD is a rhombus and EFG is a triangle. DC is parallel to EF. ∠GDC = 36°, ∠DGC = 52° and ∠GEF = 118°. Find ∠EFG. [?]", "answer0": "66", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 3, "explanation": "∠GEF = 180 − 118 = 62° (angles on the straight line). In triangle EFG, ∠EFG = 180 − 52 − 62 = 66°.", "hints": ["Find ∠GEF = 180 − 118 = 62°.", "Use the angle sum of triangle EFG: 180 − 52 − 62 = 66°."], "source": "Tao Nan 2024 P6 Prelim Q40", "image_needed": true, "image_options": false, "image_file": "q40.png", "image_page": 23, "image_bbox": [0.36, 0.16, 0.82, 0.45], "image_loc": "centre-right of page (same figure as Q39), rhombus ABCD with triangle EFG, angles 36°, 52°, 118° marked", "notes": "Paper 2 Q8(b). Printed answer: ∠GEF = 62°, ∠EFG = 180 − 52 − 62 = 66° verified. Answer in degrees; FIB numeric = 66. Figure required." }, { "n": 41, "type_id": 2, "question": "In the square grid, CD and DE are straight lines. Measure and write down the size of ∠CDE. [?]", "answer0": "91", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 140, "difficulty_id": 1, "explanation": "Measuring ∠CDE with a protractor from the grid drawing gives 91° (printed key).", "hints": ["Use a protractor on the angle CDE at vertex D.", "The measured angle is about 91°."], "source": "Tao Nan 2024 P6 Prelim Q41", "image_needed": true, "image_options": false, "image_file": "q41.png", "image_page": 24, "image_bbox": [0.20, 0.25, 0.82, 0.48], "image_loc": "centre of page, square grid with lines CD and DE drawn (points C, D, E labelled)", "notes": "Paper 2 Q9(a). Printed answer 91° verified. Answer in degrees; FIB numeric = 91. Part (b) is a draw-the-trapezium task (interactive, recorded next as type_id 0). Grid figure required to measure." }, { "n": 42, "type_id": 0, "question": "In the square grid, CD and DE are straight lines. Draw two more straight lines to form a trapezium CDEF where CF = 2 × DE. Use a pencil to draw your lines and label point F.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 201, "difficulty_id": 2, "explanation": "Add two grid lines so that CF is parallel to DE with CF twice the length of DE, completing trapezium CDEF, and label the new vertex F (drawing per printed key).", "hints": ["CF must be parallel to DE and twice as long.", "Use the grid to count DE's length and make CF double it."], "source": "Tao Nan 2024 P6 Prelim Q42", "image_needed": true, "image_options": false, "image_file": null, "image_page": 24, "image_bbox": [0.20, 0.25, 0.82, 0.48], "image_loc": "centre of page (same grid as Q41), square grid with CD and DE drawn", "notes": "Paper 2 Q9(b). Interactive draw-on-grid task → type_id 0 (skipped on insert). Printed key: drawing." }, { "n": 43, "type_id": 1, "question": "The number of participants in a marathon increased by 25% in November as compared to October. The number of participants in December decreased by 30% as compared to November. The difference in the number of participants between October and December was 18. Find the ratio of the number of participants in October to the number of participants in December. Give your answer in the simplest form.", "answer0": "8 : 7", "answer1": "7 : 8", "answer2": "5 : 4", "answer3": "4 : 5", "correct_answer": 0, "skill_id": 179, "difficulty_id": 3, "explanation": "Let October = 100%. November = 125%. December = 70% of November = 0.70 × 125% = 87.5% of October. October : December = 100 : 87.5 = 1000 : 875 = 8 : 7.", "hints": ["November is 125% of October; December is 70% of November.", "December = 0.875 × October, so October : December = 8 : 7."], "source": "Tao Nan 2024 P6 Prelim Q43", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q10(a). Printed answer 8 : 7 verified. Part (a) is a ratio answer → converted to MCQ per spec. Part (b) recorded next as numeric FIB." }, { "n": 44, "type_id": 2, "question": "The number of participants in a marathon increased by 25% in November as compared to October. The number of participants in December decreased by 30% as compared to November. The difference in the number of participants between October and December was 18. What was the total number of participants in December? [?]", "answer0": "126", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 175, "difficulty_id": 3, "explanation": "October : December = 8 : 7, so the difference is 8 − 7 = 1 unit = 18 participants. December = 7 units = 7 × 18 = 126.", "hints": ["The October-to-December difference is 1 unit in the 8 : 7 ratio.", "1 unit = 18, so December = 7 × 18 = 126."], "source": "Tao Nan 2024 P6 Prelim Q44", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q10(b). Printed answer: 8 − 7 = 1 unit, 18 ÷ 1 × 7 = 126 verified. FIB numeric = 126." }, { "n": 45, "type_id": 1, "question": "Siti bought stickers from Shop A, Shop B, Shop C and Shop D. She bought an equal number of stickers from Shop C and Shop D. \\(\\dfrac{1}{4}\\) of the stickers were bought from Shop B. \\(\\dfrac{2}{5}\\) of the stickers were bought from Shop A. What fraction of the stickers was bought from Shop C?", "answer0": "\\(\\dfrac{7}{40}\\)", "answer1": "\\(\\dfrac{7}{20}\\)", "answer2": "\\(\\dfrac{3}{20}\\)", "answer3": "\\(\\dfrac{1}{8}\\)", "correct_answer": 0, "skill_id": 159, "difficulty_id": 3, "explanation": "Shops C and D together = \\(1 - \\dfrac{1}{4} - \\dfrac{2}{5} = \\dfrac{20}{20} - \\dfrac{5}{20} - \\dfrac{8}{20} = \\dfrac{7}{20}\\). C and D are equal, so Shop C = \\(\\dfrac{1}{2} \\times \\dfrac{7}{20} = \\dfrac{7}{40}\\).", "hints": ["C and D together = 1 − 1/4 − 2/5 = 7/20.", "C equals D, so Shop C = half of 7/20 = 7/40."], "source": "Tao Nan 2024 P6 Prelim Q45", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q11(a). Printed answer 7/40 verified. Fraction answer → converted to MCQ per spec. Part (b) recorded next as numeric FIB." }, { "n": 46, "type_id": 2, "question": "Siti bought stickers from Shop A, Shop B, Shop C and Shop D. She bought an equal number of stickers from Shop C and Shop D. \\(\\dfrac{1}{4}\\) of the stickers were bought from Shop B. \\(\\dfrac{2}{5}\\) of the stickers were bought from Shop A. Siti bought 133 stickers from Shop D. What was the total number of stickers she bought? [?]", "answer0": "760", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "Shop D is the same fraction as Shop C = \\(\\dfrac{7}{40}\\) of the total. So \\(\\dfrac{7}{40}\\) of the total = 133, giving total = 133 ÷ 7 × 40 = 19 × 40 = 760 stickers.", "hints": ["Shop D is 7/40 of the total (same as Shop C).", "Total = 133 ÷ 7 × 40 = 760."], "source": "Tao Nan 2024 P6 Prelim Q46", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q11(b). Printed answer: 133 ÷ 7 × 40 = 760 verified. FIB numeric = 760." }, { "n": 47, "type_id": 2, "question": "The first three figures of a pattern are shown. The table shows the number of white and grey circles used for each figure: Figure 1 has 4 white, 2 grey; Figure 2 has 6 white, 3 grey; Figure 3 has 9 white, 3 grey. What is the total number of white and grey circles in Figure 425? [?]", "answer0": "1278", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 108, "difficulty_id": 3, "explanation": "Following the printed key, the total number of circles in Figure n is (n + 1) × 3. For Figure 425: (425 + 1) × 3 = 426 × 3 = 1278 circles.", "hints": ["Find a rule for the total circles in terms of the figure number.", "Total = (figure number + 1) × 3; for 425 it is 426 × 3 = 1278."], "source": "Tao Nan 2024 P6 Prelim Q47", "image_needed": true, "image_options": false, "image_file": "q47.png", "image_page": 31, "image_bbox": [0.18, 0.11, 0.82, 0.25], "image_loc": "upper area of page, Figure 1/Figure 2/Figure 3 of the white-and-grey circle triangular pattern", "notes": "Paper 2 Q17. Part (a) fills the table for Figure 4 (white 11, grey 4 - draw/fill) and part (c) is a percentage (~83.3%); this question records part (b), the total in Figure 425 (1278). Printed answer b) (425+1)×3 = 1278 verified. FIB numeric = 1278. Pattern figure required." } ] }