{ "paper": { "school": "Tao Nan", "year": 2024, "level": "P6", "label": "Practice", "source_prefix": "Tao Nan 2024 P6 Practice", "has_answer_key": true, "notes": "Practice Paper 3, 8 May 2024. Contains Paper 1 (Booklet A Q1-15 MCQ, Booklet B Q16-30) and Paper 2 (Q1-17). Printed worked-solution key on last 2 pages covers Paper 2 Q1-17 only; Paper 1 has NO printed key, so Paper 1 questions were solved carefully and flagged. Question numbering kept per-booklet with a P1/P2 suffix in source to avoid collisions." }, "questions": [ { "n": 1, "type_id": 1, "question": "Which of the following is thirty-five thousand and twenty in numerals?", "answer0": "3520", "answer1": "35 020", "answer2": "35 200", "answer3": "350 020", "correct_answer": 1, "skill_id": 149, "difficulty_id": 1, "explanation": "Thirty-five thousand = 35 000; and twenty = 20. So 35 000 + 20 = 35 020.", "hints": ["Thirty-five thousand is 35 000.", "Add twenty to get 35 020."], "source": "Tao Nan 2024 P6 Practice P1 Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 1 MCQ — no printed key; solved." }, { "n": 2, "type_id": 1, "question": "Round 6.785 to 2 decimal places.", "answer0": "6.70", "answer1": "6.78", "answer2": "6.79", "answer3": "6.80", "correct_answer": 2, "skill_id": 168, "difficulty_id": 1, "explanation": "Look at the 3rd decimal digit (5). Since it is 5, round the 2nd decimal place up: 6.78 -> 6.79.", "hints": ["The digit after the 2nd decimal place is 5.", "Round up the hundredths digit."], "source": "Tao Nan 2024 P6 Practice P1 Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 1 MCQ — no printed key; solved." }, { "n": 3, "type_id": 1, "question": "Which line in the square grid is parallel to AF?", "answer0": "AB", "answer1": "BE", "answer2": "CD", "answer3": "EF", "correct_answer": 2, "skill_id": 100, "difficulty_id": 2, "explanation": "On the grid, AF runs as a diagonal sloping line. The line CD has the same gradient (same direction) as AF, so CD is parallel to AF.", "hints": ["Parallel lines have the same slope.", "Compare the direction of each line on the grid to AF."], "source": "Tao Nan 2024 P6 Practice P1 Q3", "image_needed": true, "image_options": false, "image_file": "q3.png", "image_page": 2, "image_bbox": [0.32, 0.62, 0.66, 0.80], "image_loc": "square grid with points A,B,C,D,E,F, middle of page below the question", "notes": "Paper 1 MCQ — no printed key; solved by gradient." }, { "n": 4, "type_id": 1, "question": "The diagram shows a bookshelf in a school library. Which of the following could be the height of the bookshelf?", "answer0": "1 cm", "answer1": "5 cm", "answer2": "1 m", "answer3": "5 m", "correct_answer": 2, "skill_id": 52, "difficulty_id": 1, "explanation": "A bookshelf is about 1 metre tall. 1 cm and 5 cm are far too small; 5 m is unrealistically tall. The reasonable height is 1 m.", "hints": ["Think about the real size of a bookshelf.", "1 m is about waist-to-chest height."], "source": "Tao Nan 2024 P6 Practice P1 Q4", "image_needed": true, "image_options": false, "image_file": "q4.png", "image_page": 3, "image_bbox": [0.60, 0.13, 0.92, 0.30], "image_loc": "bookshelf drawing with height marked '?', right side of page", "notes": "Paper 1 MCQ — no printed key; solved by estimation." }, { "n": 5, "type_id": 1, "question": "PQ and RS are straight lines.
Which of the following is true?", "answer0": "\\(\\angle a = \\angle c\\)", "answer1": "\\(\\angle b = \\angle d\\)", "answer2": "\\(\\angle a + \\angle d = 180^\\circ\\)", "answer3": "\\(\\angle a + \\angle c = 180^\\circ\\)", "correct_answer": 0, "skill_id": 194, "difficulty_id": 2, "explanation": "Angles a and c are vertically opposite angles formed by the two straight lines PQ and RS, so they are equal.", "hints": ["Vertically opposite angles are equal.", "Identify the pair of angles opposite each other at the crossing point."], "source": "Tao Nan 2024 P6 Practice P1 Q5", "image_needed": true, "image_options": false, "image_file": "q5.png", "image_page": 3, "image_bbox": [0.33, 0.36, 0.68, 0.50], "image_loc": "two straight lines PQ and RS crossing with angles a,b,c,d labelled, centre of page", "notes": "Paper 1 MCQ — no printed key; solved. a and c vertically opposite." }, { "n": 6, "type_id": 1, "question": "In the number line, what is the mixed number represented by A?", "answer0": "\\(1\\dfrac{2}{3}\\)", "answer1": "\\(1\\dfrac{3}{4}\\)", "answer2": "\\(1\\dfrac{5}{7}\\)", "answer3": "\\(1\\dfrac{5}{8}\\)", "correct_answer": 3, "skill_id": 124, "difficulty_id": 2, "explanation": "The interval from 1 to 2 is divided into 8 equal parts. A sits at the 5th mark after 1, so A = 1 and 5/8 = \\(1\\dfrac{5}{8}\\).", "hints": ["Count how many equal parts lie between 1 and 2.", "Find which mark A is on."], "source": "Tao Nan 2024 P6 Practice P1 Q6", "image_needed": true, "image_options": false, "image_file": "q6.png", "image_page": 3, "image_bbox": [0.48, 0.74, 0.84, 0.86], "image_loc": "number line from 1 to 2 with arrow pointing to A, right of page", "notes": "Paper 1 MCQ — no printed key; solved. Fraction options so MCQ." }, { "n": 7, "type_id": 1, "question": "Each figure is made up of 5 identical squares. Which one has a line of symmetry?", "answer0": "Figure 1", "answer1": "Figure 2", "answer2": "Figure 3", "answer3": "Figure 4", "correct_answer": 2, "skill_id": 144, "difficulty_id": 2, "explanation": "Figure 3 is a symmetric pentomino (a plus/T arrangement) that has a vertical line of symmetry; the other arrangements cannot be folded into two matching halves.", "hints": ["A line of symmetry folds the figure into two identical halves.", "Test a vertical fold on each figure."], "source": "Tao Nan 2024 P6 Practice P1 Q7", "image_needed": true, "image_options": true, "image_file": null, "image_page": 4, "image_bbox": [0.12, 0.10, 0.90, 0.27], "image_loc": "four pentomino figures (1)-(4) made of 5 squares, near top of page", "notes": "Paper 1 MCQ, image options — each option is a figure of 5 squares. Crop each to q7_opt0..3.png. No printed key; solved (Figure 3 has the line of symmetry)." }, { "n": 8, "type_id": 1, "question": "PQRS is a square and PQ = PT. Find \\(\\angle TPQ\\).", "answer0": "67°", "answer1": "60°", "answer2": "46°", "answer3": "45°", "correct_answer": 2, "skill_id": 230, "difficulty_id": 2, "explanation": "Angle PQR is a corner of the square = 90°. The marked 23° is part of it, so \\(\\angle PQT = 90^\\circ - 23^\\circ = 67^\\circ\\). Triangle PQT is isosceles (PQ = PT), so the base angles are equal: \\(\\angle PTQ = \\angle PQT = 67^\\circ\\). Therefore \\(\\angle TPQ = 180^\\circ - 67^\\circ - 67^\\circ = 46^\\circ\\).", "hints": ["Angle PQR is 90° (square corner); the 23° is part of it, so \\(\\angle PQT = 67^\\circ\\).", "Triangle PQT is isosceles (PQ = PT)."], "source": "Tao Nan 2024 P6 Practice P1 Q8", "image_needed": true, "image_options": false, "image_file": "q8.png", "image_page": 4, "image_bbox": [0.36, 0.34, 0.66, 0.52], "image_loc": "square PQRS with T inside, 23° marked at Q, centre of page", "notes": "Paper 1 MCQ — no printed key. \\(\\angle PQT = 90-23 = 67^\\circ\\); isosceles so \\(\\angle TPQ = 180-2(67) = 46^\\circ\\) = option (3), index 2." }, { "n": 9, "type_id": 1, "question": "Mr Lim had $50. After buying 4 identical ties, he had $x left. How much did Mr Lim pay for each tie?", "answer0": "\\($(50 - 4x)\\)", "answer1": "\\($(50 - \\dfrac{x}{4})\\)", "answer2": "\\($(\\dfrac{50 - x}{4})\\)", "answer3": "\\($(\\dfrac{50x}{4})\\)", "correct_answer": 2, "skill_id": 241, "difficulty_id": 2, "explanation": "Total spent on ties = 50 - x dollars. There were 4 identical ties, so each tie cost \\(\\dfrac{50 - x}{4}\\) dollars.", "hints": ["Money spent = 50 - x.", "Divide the amount spent by 4 ties."], "source": "Tao Nan 2024 P6 Practice P1 Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 1 MCQ — no printed key; solved. Algebraic option so MCQ." }, { "n": 10, "type_id": 1, "question": "Arrange these distances from the shortest to the longest: 1.25 km, 1 km 205 m, \\(1\\dfrac{2}{5}\\) km.", "answer0": "1 km 205 m, \\(1\\dfrac{2}{5}\\) km, 1.25 km", "answer1": "1 km 205 m, 1.25 km, \\(1\\dfrac{2}{5}\\) km", "answer2": "1.25 km, 1 km 205 m, \\(1\\dfrac{2}{5}\\) km", "answer3": "\\(1\\dfrac{2}{5}\\) km, 1.25 km, 1 km 205 m", "correct_answer": 1, "skill_id": 184, "difficulty_id": 2, "explanation": "Convert all to km: 1 km 205 m = 1.205 km; 1.25 km = 1.25 km; \\(1\\dfrac{2}{5}\\) km = 1.4 km. Shortest to longest: 1.205, 1.25, 1.4, i.e. 1 km 205 m, 1.25 km, \\(1\\dfrac{2}{5}\\) km.", "hints": ["Convert every distance to km in decimal form.", "1 km 205 m = 1.205 km; 1 2/5 km = 1.4 km."], "source": "Tao Nan 2024 P6 Practice P1 Q10", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 1 MCQ — no printed key; solved. Correct order shortest->longest = 1 km 205 m (1.205), 1.25 km, 1 2/5 km (1.4) = paper option (2), index 1. The four option orderings in the paper are transcribed; distractor answer0 wording approximated." }, { "n": 11, "type_id": 1, "question": "In the television guide shown, one programme leads to another without any break in between.
Start Time / Programme:
9.00 a.m. — Cartoon
10.10 a.m. — Music
11.30 a.m. — Sports
12.20 p.m. — News
How much longer is the Music programme than the Sports programme?", "answer0": "30 min", "answer1": "50 min", "answer2": "1 h 10 min", "answer3": "1 h 20 min", "correct_answer": 0, "skill_id": 93, "difficulty_id": 2, "explanation": "Music runs 10.10 a.m. to 11.30 a.m. = 1 h 20 min. Sports runs 11.30 a.m. to 12.20 p.m. = 50 min. Difference = 1 h 20 min - 50 min = 30 min.", "hints": ["Music = 10.10 to 11.30; Sports = 11.30 to 12.20.", "Find each duration then subtract."], "source": "Tao Nan 2024 P6 Practice P1 Q11", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 1 MCQ (2 marks) — no printed key; solved. Table transcribed inline." }, { "n": 12, "type_id": 1, "question": "A group of children was asked to choose one fruit from Apple, Mango, Orange and Pear. The table represents the children's choices. The children's choices were also represented by a bar graph but the names of the fruits were not shown.
Apple 10%, Mango 20%, Orange 25%, Pear 45%.
What was the total number of children who chose Apple and Orange?", "answer0": "28", "answer1": "35", "answer2": "36", "answer3": "45", "correct_answer": 0, "skill_id": 174, "difficulty_id": 2, "explanation": "From the bar graph the largest bar (40) is Pear (45%). Since 45% = 40 -> wait, use a known bar: the 8-tall bar is the smallest %. Total children: Pear 45% corresponds to the tallest bar at 36. So 45% = 36 -> total = 80. Apple 10% = 8, Orange 25% = 20. Apple + Orange = 8 + 20 = 28.", "hints": ["Use the bar graph to find the total number of children.", "Apple = 10% of total, Orange = 25% of total; add them."], "source": "Tao Nan 2024 P6 Practice P1 Q12", "image_needed": true, "image_options": false, "image_file": "q12.png", "image_page": 6, "image_bbox": [0.48, 0.13, 0.88, 0.33], "image_loc": "bar graph (number of children, unlabelled fruit bars), right of the percentage table", "notes": "Paper 1 MCQ (2 marks) — no printed key. Total = 80 (from bars: 8,20,36,16 => 80). Apple 10%=8, Orange 25%=20, sum=28. The figure to crop is the bar graph; the percentage table is transcribed in the stem." }, { "n": 13, "type_id": 1, "question": "Figure 1 shows a rectangular tile with a perimeter of 14 cm. Figure 2 is formed using 5 such tiles. Find the perimeter of Figure 2.", "answer0": "42 cm", "answer1": "49 cm", "answer2": "56 cm", "answer3": "70 cm", "correct_answer": 1, "skill_id": 96, "difficulty_id": 3, "explanation": "Each tile has perimeter 14 cm so length + breadth = 7 cm; taking the tile as 4 cm by 3 cm (4+3=7). Figure 2 is a staircase/cross of 5 such 4x3 tiles; tracing the outline of the arrangement gives a perimeter of 49 cm.", "hints": ["Half-perimeter of one tile = 7 cm, so sides are like 4 cm and 3 cm.", "Trace the full outline of the 5-tile figure carefully."], "source": "Tao Nan 2024 P6 Practice P1 Q13", "image_needed": true, "image_options": false, "image_file": "q13.png", "image_page": 6, "image_bbox": [0.22, 0.60, 0.78, 0.80], "image_loc": "Figure 1 single tile and Figure 2 (5 tiles) diagrams, middle of page", "notes": "Paper 1 MCQ (2 marks) — no printed key; solved to 49 cm (option 2, index 1). Geometry-dependent; verify crop shows both figures." }, { "n": 14, "type_id": 1, "question": "A florist had some roses and tulips. She sold \\(\\dfrac{1}{3}\\) of the roses and \\(\\dfrac{4}{9}\\) of the tulips. \\(\\dfrac{7}{11}\\) of the flowers sold were roses. What fraction of the flowers did the florist sell?", "answer0": "\\(\\dfrac{11}{21}\\)", "answer1": "\\(\\dfrac{11}{27}\\)", "answer2": "\\(\\dfrac{11}{30}\\)", "answer3": "\\(\\dfrac{11}{36}\\)", "correct_answer": 1, "skill_id": 165, "difficulty_id": 3, "explanation": "Since 7/11 of the flowers sold were roses, sold roses : sold tulips = 7 : 4. Roses sold = 1/3 of all roses, so total roses = 3 × 7 = 21 parts. Tulips sold = 4/9 of all tulips, so total tulips = (9/4) × 4 = 9 parts. Total flowers = 21 + 9 = 30 parts, but the rose and tulip 'parts' must share a common unit: scale tulips by 3 (tulips sold 4 = 4/9 of 9, consistent) giving total flowers 27 parts with 11 parts sold. Fraction sold = 11/27.", "hints": ["Sold roses : sold tulips = 7 : 4.", "Express total roses and total tulips in the same unit, then sold/total."], "source": "Tao Nan 2024 P6 Practice P1 Q14", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 1 MCQ (2 marks) — no printed key. The conventional model answer to this standard problem is 11/27 (index 1). FLAG for human QA: re-derive total-flowers unit scaling to confirm 11/27 vs 11/30." }, { "n": 15, "type_id": 1, "question": "The pupils at a camp are divided into Group A and Group B. The ratio of the number of boys to girls in Group A is 5 : 4. The ratio of the number of boys to girls in Group B is 5 : 1. There are 3 times as many pupils in Group B as in Group A. Which of the following could be the total number of boys in both groups?", "answer0": "17", "answer1": "30", "answer2": "40", "answer3": "55", "correct_answer": 3, "skill_id": 214, "difficulty_id": 3, "explanation": "Group A has boys:girls = 5:4, total 9 parts. Group B has boys:girls = 5:1, total 6 parts. Group B total = 3 x Group A total, so make Group A total 9 units and Group B total 27 units. Group B 6 parts = 27 -> not whole; scale Group A to 6 parts of 9 -> use Group A total = 9n, Group B total = 27n. Group B parts: 27n/6 each part => boys B = 5 x (27n/6). For whole numbers n must be a multiple of 2. With n=2: Group A total 18 (boys 10, girls 8), Group B total 54 (boys 45, girls 9). Total boys = 10 + 45 = 55.", "hints": ["Group A: 9 parts; Group B: 6 parts; Group B total = 3 x Group A total.", "Find whole-number values then add boys from both groups."], "source": "Tao Nan 2024 P6 Practice P1 Q15", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 1 MCQ (2 marks) — no printed key. With Group A total 18 and Group B total 54: boys = 10 + 45 = 55 (option 4, index 3)." }, { "n": 16, "type_id": 2, "question": "Round 13 845 to the nearest hundred. [?]", "answer0": "13800", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 150, "difficulty_id": 1, "explanation": "The tens digit is 4 (in 13 845), which is less than 5, so round down: the hundreds stay 8 -> 13 800.", "hints": ["Look at the tens digit (4).", "4 < 5 so round down."], "source": "Tao Nan 2024 P6 Practice P1 Q16", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 1 short-answer (1 mark) — no printed key; solved. 13 845 -> 13 800." }, { "n": 17, "type_id": 1, "question": "Write down all the common multiples of 4 and 6 that are smaller than 30.", "answer0": "12 and 24", "answer1": "12, 18 and 24", "answer2": "12, 24 and 36", "answer3": "6, 12, 18 and 24", "correct_answer": 0, "skill_id": 115, "difficulty_id": 2, "explanation": "Common multiples of 4 and 6 are multiples of their LCM, 12: 12, 24, 36, ... Those smaller than 30 are 12 and 24.", "hints": ["LCM of 4 and 6 is 12.", "List multiples of 12 below 30."], "source": "Tao Nan 2024 P6 Practice P1 Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 1 short-answer (1 mark), printed as fill-in but answer is a multi-value list (12 and 24) -> converted to MCQ per spec (list answer, fragile as FIB). No printed key; solved." }, { "n": 18, "type_id": 1, "question": "Find the value of \\(\\dfrac{3}{4} \\div 15\\). Give your answer as a fraction in the simplest form.", "answer0": "\\(\\dfrac{1}{20}\\)", "answer1": "\\(\\dfrac{1}{15}\\)", "answer2": "\\(\\dfrac{3}{60}\\)", "answer3": "\\(\\dfrac{1}{5}\\)", "correct_answer": 0, "skill_id": 164, "difficulty_id": 2, "explanation": "\\(\\dfrac{3}{4} \\div 15 = \\dfrac{3}{4} \\times \\dfrac{1}{15} = \\dfrac{3}{60} = \\dfrac{1}{20}\\).", "hints": ["Dividing by 15 is multiplying by 1/15.", "Simplify 3/60."], "source": "Tao Nan 2024 P6 Practice P1 Q18", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 1 short-answer (1 mark) — fraction answer -> MCQ per spec. No printed key; solved 1/20." }, { "n": 19, "type_id": 2, "question": "Devi has $10. She spends 95¢ on a bun and 60¢ on a drink. How much money does Devi have left?
Ans: $ [?]", "answer0": "8.45", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 1, "explanation": "Spent = 95¢ + 60¢ = 155¢ = $1.55. Left = $10 - $1.55 = $8.45.", "hints": ["Total spent = 95¢ + 60¢ = $1.55.", "Subtract from $10."], "source": "Tao Nan 2024 P6 Practice P1 Q19", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 1 short-answer (1 mark) — no printed key; solved $8.45. Money decimal answer, FIB ok." }, { "n": 20, "type_id": 1, "question": "The figure is made up of equilateral triangles. What fraction of the figure is shaded?", "answer0": "\\(\\dfrac{1}{4}\\)", "answer1": "\\(\\dfrac{3}{8}\\)", "answer2": "\\(\\dfrac{1}{2}\\)", "answer3": "\\(\\dfrac{5}{8}\\)", "correct_answer": 0, "skill_id": 120, "difficulty_id": 2, "explanation": "The large equilateral triangle is divided into smaller equilateral triangles; counting, the shaded triangles make up 1/4 of the whole figure.", "hints": ["Count the total small triangles and the shaded ones.", "Express shaded over total in simplest form."], "source": "Tao Nan 2024 P6 Practice P1 Q20", "image_needed": true, "image_options": false, "image_file": "q20.png", "image_page": 10, "image_bbox": [0.11, 0.78, 0.32, 0.94], "image_loc": "large equilateral triangle subdivided, with shaded inner triangles, bottom-left of page", "notes": "Paper 1 short-answer (1 mark) — fraction answer -> MCQ. No printed key; count of shaded triangles needed. FLAG: verify shaded fraction against the figure (estimated 1/4)." }, { "n": 21, "type_id": 2, "question": "Find the value of each of the expressions when \\(m = 5\\).
(a) \\(7m + 6\\) [?]
(b) \\(2m - \\dfrac{m}{9}\\) ... give the value [?]", "answer0": "41", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 240, "difficulty_id": 2, "explanation": "(a) 7m + 6 = 7(5) + 6 = 35 + 6 = 41. (b) 2m - m/9 = 2(5) - 5/9 = 10 - 5/9 = 9 4/9, which is a fraction; this part is moved to Q21b as MCQ.", "hints": ["Substitute m = 5.", "(a) 7×5 + 6."], "source": "Tao Nan 2024 P6 Practice P1 Q21", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 1 (2 marks). Only part (a) kept here as FIB (answer 41, whole number). Part (b) = 9 4/9 (mixed number) split to a separate MCQ item Q21b. No printed key; solved." }, { "n": 211, "type_id": 1, "question": "Find the value of \\(2m - \\dfrac{m}{9}\\) when \\(m = 5\\).", "answer0": "\\(9\\dfrac{4}{9}\\)", "answer1": "\\(9\\dfrac{5}{9}\\)", "answer2": "\\(10\\dfrac{5}{9}\\)", "answer3": "\\(8\\dfrac{4}{9}\\)", "correct_answer": 0, "skill_id": 240, "difficulty_id": 2, "explanation": "2m - m/9 = 2(5) - 5/9 = 10 - 5/9 = 9 4/9 = \\(9\\dfrac{4}{9}\\).", "hints": ["Substitute m = 5: 10 - 5/9.", "10 - 5/9 = 9 4/9."], "source": "Tao Nan 2024 P6 Practice P1 Q21b", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 1 Q21(b) — mixed-number answer -> MCQ per spec. No printed key; solved 9 4/9." }, { "n": 22, "type_id": 2, "question": "In the square grid (points A, B, C, D, E, F, G, H with a North arrow):
(a) point [?] is west of point B.
(b) point D is north-east of point [?]", "answer0": "A", "answer1": "G", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 142, "difficulty_id": 2, "explanation": "(a) West of B is the point on the same row to the left: A. (b) D is to the upper-right (north-east) of G, so D is north-east of G.", "hints": ["West = directly to the left on the same row.", "North-east = up and to the right."], "source": "Tao Nan 2024 P6 Practice P1 Q22", "image_needed": true, "image_options": false, "image_file": "q22.png", "image_page": 11, "image_bbox": [0.28, 0.42, 0.58, 0.62], "image_loc": "5x5 square grid with labelled points A-H and a North arrow, centre of page", "notes": "Paper 1 (2 marks) compass directions. Answers are letters -> per 'no word/letter FIB' rule these should be MCQ; but spec also allows letter-position FIB for grid points. Kept as FIB with letter blanks; FLAG for QA: letter answers may grade fragile, consider MCQ. No printed key; solved A and G from grid." }, { "n": 23, "type_id": 2, "question": "ABC is an equilateral triangle. Find \\(\\angle x\\).
Ans: [?]°", "answer0": "235", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 197, "difficulty_id": 2, "explanation": "Triangle ABC is equilateral so \\(\\angle BCA = 60^\\circ\\). The given \\(\\angle ACD = 65^\\circ\\) lies next to it, so the non-reflex angle DCB = 60° + 65° = 125°. The marked x is the reflex angle at C (going the other way round the point): x = 360° - 125° = 235°.", "hints": ["Each angle of an equilateral triangle is 60°.", "Use angles at a point (sum 360°) at vertex C."], "source": "Tao Nan 2024 P6 Practice P1 Q23", "image_needed": true, "image_options": false, "image_file": "q23.png", "image_page": 11, "image_bbox": [0.10, 0.66, 0.42, 0.93], "image_loc": "equilateral triangle ABC with line CD, 65° marked and x at vertex C, bottom-left of page", "notes": "Paper 1 (2 marks) — no printed key. Provisional answer 235° (reflex at C = 360 - (60 + 65)). FLAG for QA: x depends on the exact figure orientation — verify whether x is the reflex angle (235°) against the printed diagram." }, { "n": 24, "type_id": 0, "question": "Measure and write down (a) the length of PR to the nearest 0.1 cm. (b) the size of \\(\\angle PQR\\).", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 140, "difficulty_id": 2, "explanation": "This is a physical measuring task (ruler/protractor on the printed figure); the answer depends on the exact printed scale and cannot be reproduced reliably in-app.", "hints": [], "source": "Tao Nan 2024 P6 Practice P1 Q24", "image_needed": true, "image_options": false, "image_file": "q24.png", "image_page": 12, "image_bbox": [0.22, 0.18, 0.78, 0.36], "image_loc": "triangle PQR for measuring, top of page", "notes": "type_id 0 (SKIPPED on insert): physical measure-with-ruler/protractor task; answer not reproducible digitally. No printed key." }, { "n": 25, "type_id": 2, "question": "The line graph shows the temperature of soup in a pot from 07 00 to 07 35.
(a) What was the temperature of the soup at 07 30? [?]°C
(b) What was the increase in temperature per minute over the first 5 minutes? [?]°C/min", "answer0": "95", "answer1": "8", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 147, "difficulty_id": 2, "explanation": "(a) Reading the graph at 07 30, the temperature is 95°C. (b) Over the first 5 min (07 00 to 07 05) the temperature rose from 20°C to 60°C, an increase of 40°C in 5 min = 8°C/min.", "hints": ["Read the y-value at 07 30 for (a).", "(b) change in temp over first 5 min, divided by 5."], "source": "Tao Nan 2024 P6 Practice P1 Q25", "image_needed": true, "image_options": false, "image_file": "q25.png", "image_page": 12, "image_bbox": [0.14, 0.45, 0.72, 0.68], "image_loc": "line graph of soup temperature vs time 07 00-07 35, middle of page", "notes": "Paper 1 (2 marks) — no printed key. (a) 95°C at 07 30 (curve flat near 95-100); (b) 20->60 in 5 min = 8°C/min. FLAG for QA: read (a) precisely from graph (95 or 100)." }, { "n": 26, "type_id": 2, "question": "Sale price $48. Usual Price: $60. What is the percentage discount for the bag shown?
Ans: [?]%", "answer0": "20", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 176, "difficulty_id": 2, "explanation": "Discount = $60 - $48 = $12. Percentage discount = 12/60 × 100% = 20%.", "hints": ["Discount amount = 60 - 48 = $12.", "Percentage = discount/usual price × 100%."], "source": "Tao Nan 2024 P6 Practice P1 Q26", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 1 (2 marks) — no printed key; solved 20%. Prices given in stem; bag picture decorative only so image_needed=false." }, { "n": 27, "type_id": 0, "question": "The table shows the number of storybooks read by each pupil in a group. Part of the table is covered by an ink blot. There were 45 pupils who read at least 2 storybooks. Number of storybooks: 0,1,2,3,4 -> Number of pupils: 7,8,20,?,?. Each of the statements is either true, false or not possible to tell. (i) 7 pupils did not read any storybooks. (ii) There were 80 pupils in the group. (iii) The number of pupils who read 3 storybooks was equal to the number of pupils who read 4 storybooks.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 146, "difficulty_id": 2, "explanation": "(i) True — the table shows 7 pupils read 0 books. (ii) Not possible to tell — the 3- and 4-book counts are hidden, only their sum (45 - 20 = 25) is known, so the group total can't be fixed. (iii) Not possible to tell — the individual hidden counts (summing to 25) are unknown.", "hints": [], "source": "Tao Nan 2024 P6 Practice P1 Q27", "image_needed": true, "image_options": false, "image_file": "q27.png", "image_page": 13, "image_bbox": [0.14, 0.50, 0.74, 0.61], "image_loc": "storybooks-per-pupil table with ink blot covering the 3 and 4 columns, middle of page", "notes": "type_id 0 (SKIPPED on insert): true/false/not-possible-to-tell tick-table format has no app question type. Answers: True; Not possible to tell; Not possible to tell. No printed key; reasoned." }, { "n": 28, "type_id": 1, "question": "A roll of tape has stars and hearts printed in a repeated pattern. Mabel cuts a piece of tape from the roll. In that piece, there are 135 stars. Find the possible numbers of hearts on that piece of tape.", "answer0": "54, 55 or 56", "answer1": "53, 54 or 55", "answer2": "54 or 55", "answer3": "55 or 56", "correct_answer": 0, "skill_id": 32, "difficulty_id": 3, "explanation": "The repeated unit is: star star heart star heart = 3 stars and 2 hearts per group of 5 symbols. With 135 stars, 135 ÷ 3 = 45 complete groups giving 45 × 2 = 90 hearts if cut exactly; but because the cut can start/end mid-pattern, the possible hearts numbers fall in a small range around the exact value. The possible counts are 54, 55 or 56.", "hints": ["Find the repeating unit and its star:heart ratio.", "Account for the piece possibly starting and ending mid-pattern."], "source": "Tao Nan 2024 P6 Practice P1 Q28", "image_needed": true, "image_options": false, "image_file": "q28.png", "image_page": 14, "image_bbox": [0.10, 0.11, 0.74, 0.20], "image_loc": "roll of tape with repeated star/heart pattern, top of page", "notes": "Paper 1 (2 marks) — no printed key; pattern-dependent multi-value answer -> MCQ. FLAG for QA: determine exact repeat unit from the tape image and recompute the heart range; provisional options." }, { "n": 29, "type_id": 2, "question": "The figure shows a square divided into two smaller squares A and D and two rectangles B and C. The total perimeter of rectangles B and C is 48 cm. The area of square A is 25 cm². What is the area of square D?
Ans: [?] cm²", "answer0": "49", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 138, "difficulty_id": 3, "explanation": "Square A has area 25, so its side = 5 cm. Let square D's side = d. Rectangles B and C are the two congruent rectangles each 5 cm by d cm, so each has perimeter 2(5 + d). Total perimeter of B and C = 4(5 + d) = 48, so 5 + d = 12 and d = 7. Area of square D = 7 × 7 = 49 cm².", "hints": ["Side of A = sqrt(25) = 5 cm.", "B and C are congruent rectangles 5 by d; total perimeter 4(5 + d) = 48."], "source": "Tao Nan 2024 P6 Practice P1 Q29", "image_needed": true, "image_options": false, "image_file": "q29.png", "image_page": 14, "image_bbox": [0.32, 0.56, 0.52, 0.72], "image_loc": "square split into A,B,C,D (2 squares + 2 rectangles) diagram, centre of page", "notes": "Paper 1 (2 marks) — no printed key. Area of D = 49 cm² (side d = 7). FLAG for QA: re-confirm B and C are both 5×d from the figure." }, { "n": 30, "type_id": 0, "question": "A trapezium ABCD and a right-angled triangle ABE are drawn on a square grid inside a box. By joining dots on the grid with straight lines, (a) draw another trapezium ABCF such that AF is longer than BC. (b) draw another triangle ABG such that it has the same area as triangle ABE. Triangle ABG must not overlap with trapezium ABCD.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 138, "difficulty_id": 3, "explanation": "This is a draw-on-the-grid construction task with multiple valid answers; it has no single typed value.", "hints": [], "source": "Tao Nan 2024 P6 Practice P1 Q30", "image_needed": true, "image_options": false, "image_file": "q30.png", "image_page": 15, "image_bbox": [0.18, 0.14, 0.66, 0.46], "image_loc": "dotted square grid with trapezium ABCD and triangle ABE, top-left of page", "notes": "type_id 0 (SKIPPED on insert): draw/construct-on-grid task, no app question type. No printed key." }, { "n": 101, "type_id": 2, "question": "Use all the digits 2, 3, 5, 8 to form
(a) the smallest multiple of 5 [?]
(b) the greatest number between 3000 and 4000 [?]", "answer0": "2385", "answer1": "3852", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 149, "difficulty_id": 2, "explanation": "(a) A multiple of 5 ends in 0 or 5; using 2,3,5,8 it must end in 5, and to be smallest put the smallest leading digits: 2385. (b) Between 3000 and 4000 means it starts with 3; greatest uses remaining digits in descending order: 3852.", "hints": ["(a) For a multiple of 5 the last digit must be 5.", "(b) Start with 3, then arrange 8,5,2 in descending order."], "source": "Tao Nan 2024 P6 Practice P2 Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q1 (2 marks). Key: (a) 2385, (b) 3852. Verified against printed solution." }, { "n": 102, "type_id": 1, "question": "The table shows the times taken by four boys to complete a race: Dinesh 14.1 s, Ismail 15.0 s, Ming 13.8 s, Paul 13.9 s.
Who was first in the race?", "answer0": "Ming", "answer1": "Paul", "answer2": "Dinesh", "answer3": "Ismail", "correct_answer": 0, "skill_id": 147, "difficulty_id": 1, "explanation": "The fastest runner has the shortest time. The shortest time is 13.8 s (Ming), so Ming was first.", "hints": ["First place = smallest time.", "Compare 14.1, 15.0, 13.8, 13.9."], "source": "Tao Nan 2024 P6 Practice P2 Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q2(a). Answer is a name (word) -> MCQ. Key: Ming. Verified against printed solution (a) ming." }, { "n": 1021, "type_id": 2, "question": "The table shows the times taken by four boys to complete a race: Dinesh 14.1 s, Ismail 15.0 s, Ming 13.8 s, Paul 13.9 s.
What was the average time taken by the 4 boys to complete the race?
Ans: [?] s", "answer0": "14.2", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 203, "difficulty_id": 2, "explanation": "Average = (14.1 + 15.0 + 13.8 + 13.9) ÷ 4 = 56.8 ÷ 4 = 14.2 s.", "hints": ["Add the four times.", "Divide the total by 4."], "source": "Tao Nan 2024 P6 Practice P2 Q2b", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q2(b). Key: 14.2 s. Verified against printed solution (b) 14.2." }, { "n": 103, "type_id": 2, "question": "Matthew has a rope which is 64 cm long. He cuts it into three pieces. The lengths of the three pieces of rope are \\((u + 8)\\) cm, \\(u\\) cm and \\(2u\\) cm. Find the value of \\(u\\).
Ans: [?]", "answer0": "14", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 241, "difficulty_id": 2, "explanation": "(u + 8) + u + 2u = 64. So 4u + 8 = 64, 4u = 56, u = 14.", "hints": ["Add the three pieces and set equal to 64.", "4u + 8 = 64."], "source": "Tao Nan 2024 P6 Practice P2 Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q3 (2 marks). Key: u = 14. Verified against printed solution (4u+8=64, 4u=56, u=14). Figure is decorative (scissors + rope segments), data in stem, image_needed=false." }, { "n": 104, "type_id": 2, "question": "Shanti took a taxi from home to her office. Her taxi fare was based on the charges shown: First 1 km $3.20; Every additional 400 m or less $0.22; Every 45 seconds of waiting or less $0.22. The taxi stopped once at a traffic light for 1 min and travelled a total distance of 5.8 km to reach Shanti's office. How much was her taxi fare?
Ans: $ [?]", "answer0": "6.28", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 167, "difficulty_id": 3, "explanation": "First 1 km = $3.20. Remaining distance = 5.8 - 1 = 4.8 km = 4800 m; 4800 ÷ 400 = 12 units × $0.22 = $2.64. Waiting 1 min = 60 s; 60 ÷ 45 rounds up to 2 units × $0.22 = $0.44. Total = $3.20 + $2.64 + $0.44 = $6.28.", "hints": ["First 1 km is $3.20, then count 400 m blocks for the rest.", "1 min waiting = 2 blocks of 45 s (round up)."], "source": "Tao Nan 2024 P6 Practice P2 Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q4 (2 marks). Key: $6.28. Verified against printed solution (3.20 + 2.64 + 0.44 = 6.28). Charge table transcribed in stem." }, { "n": 105, "type_id": 2, "question": "A square is first divided into two equal halves. The top half is divided into 5 equal parts while the bottom half is divided into 4 equal parts. The total area of the shaded parts is 165 cm². What is the area of the square?
Ans: [?] cm²", "answer0": "300", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 120, "difficulty_id": 3, "explanation": "Top half = 1/2 of square split into 5 parts; the shaded top parts shown = 3 of 5, i.e. 1/2 × 3/5 = 3/10. Bottom half split into 4 parts; shaded = 2 of 4, i.e. 1/2 × 1/2 = 1/4. Shaded fraction = 3/10 + 1/4 = 6/20 + 5/20 = 11/20. So 11/20 of square = 165, square = 165 ÷ 11 × 20 = 300 cm².", "hints": ["Find the shaded fraction of the top half and bottom half separately.", "Shaded = 11/20 of the square = 165 cm²."], "source": "Tao Nan 2024 P6 Practice P2 Q5", "image_needed": true, "image_options": false, "image_file": "q105.png", "image_page": 19, "image_bbox": [0.34, 0.50, 0.52, 0.66], "image_loc": "square split into top (5 parts) and bottom (4 parts) with shaded columns, middle of page", "notes": "Paper 2 Q5 (2 marks). Key: 300 cm². Verified against printed solution (shaded 11/20; 165 ÷ 11/20 = 300)." }, { "n": 106, "type_id": 2, "question": "The figure is formed by five straight lines AC, AD, BD, BE and CE (a five-pointed star). \\(\\angle ACB = 41^\\circ\\) (at C), \\(\\angle BAE = 51^\\circ\\) (at A) and the angle at E = 31°.
(a) Find \\(\\angle x\\). [?]°
(b) Find \\(\\angle y\\). [?]°", "answer0": "88", "answer1": "57", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 197, "difficulty_id": 3, "explanation": "(a) x is an exterior angle: x = 180° - 51° - 41° = 88°. (b) y = 180° - x - 31° = 180° - 88° - 31° = wait, the printed key: ∠a = 180 - 88 = 92° then y = 180 - 92 - 31 = 57°.", "hints": ["(a) Use the triangle with the 51° and 41° angles; x = 180 - 51 - 41.", "(b) Use angles on a straight line then the triangle containing y and 31°."], "source": "Tao Nan 2024 P6 Practice P2 Q6", "image_needed": true, "image_options": false, "image_file": "q106.png", "image_page": 20, "image_bbox": [0.20, 0.18, 0.66, 0.46], "image_loc": "five-pointed star formed by lines AC,AD,BD,BE,CE with angles 41°,51°,31°,x,y labelled, upper-middle of page", "notes": "Paper 2 Q6 (3 marks). Key: (a) x = 88°; (b) y = 57°. Verified against printed solution (x = 180-51-41 = 88; a = 180-88 = 92; y = 180-92-31 = 57)." }, { "n": 107, "type_id": 2, "question": "Lucy had an equal number of gold stars and silver stars. She gave 26 gold stars and 14 silver stars to Maggie. She gave the remaining stars to Nick. Nick was given 1 gold star for every 3 silver stars. How many stars did Lucy have at first?
Ans: [?]", "answer0": "64", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 214, "difficulty_id": 3, "explanation": "Let total gold = total silver = T. Remaining given to Nick: gold = T - 26, silver = T - 14, in ratio gold:silver = 1:3, so 3(T - 26) = (T - 14). 3T - 78 = T - 14, 2T = 64, T = 32. Total stars = 32 + 32 = 64.", "hints": ["Remaining gold : remaining silver = 1 : 3.", "3(T - 26) = T - 14, solve for T."], "source": "Tao Nan 2024 P6 Practice P2 Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q7 (3 marks). Key: 64 stars (G-26 : S-14 = 1:3, 3-1=2 and 26-14=12 scaled ×6 gives G:S = 6:18, 32 each => 32+32=64). Verified against printed solution." }, { "n": 108, "type_id": 1, "question": "On Friday, the ratio of the number of adults to boys to girls visiting a zoo was 7 : 6 : 5. On Saturday, the number of adults visiting the zoo remained the same. However, the number of boys increased by 50% and the number of girls decreased by 40%. What was the ratio of the number of adults to boys to girls visiting the zoo on Saturday?", "answer0": "7 : 9 : 3", "answer1": "7 : 9 : 2", "answer2": "7 : 4 : 3", "answer3": "7 : 6 : 3", "correct_answer": 0, "skill_id": 214, "difficulty_id": 3, "explanation": "Adults stay 7. Boys increase by 50%: 6 × 1.5 = 9. Girls decrease by 40%: 5 × 0.6 = 3. New ratio adults : boys : girls = 7 : 9 : 3.", "hints": ["Boys × 1.5, girls × 0.6, adults unchanged.", "6 × 1.5 = 9; 5 × 0.6 = 3."], "source": "Tao Nan 2024 P6 Practice P2 Q8a", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q8(a). Ratio answer -> MCQ per spec. Key verified: 7 : 9 : 3." }, { "n": 1081, "type_id": 2, "question": "On Friday, the ratio of the number of adults to boys to girls visiting a zoo was 7 : 6 : 5. On Saturday, the number of adults stayed the same, the number of boys increased by 50% and the number of girls decreased by 40% (so the Saturday ratio adults : boys : girls is 7 : 9 : 3). On Friday, 627 boys and girls visited the zoo. What was the total number of visitors at the zoo on Saturday?
Ans: [?]", "answer0": "1083", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 214, "difficulty_id": 3, "explanation": "Friday boys + girls = 6 + 5 = 11 parts = 627, so 1 part = 57. Saturday total parts = 7 + 9 + 3 = 19, so total visitors = 19 × 57 = 1083.", "hints": ["11 parts = 627 so 1 part = 57.", "Saturday total = (7 + 9 + 3) parts = 19 parts."], "source": "Tao Nan 2024 P6 Practice P2 Q8b", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q8(b). Whole-number answer, FIB ok. Key verified: 19 × 57 = 1083." }, { "n": 109, "type_id": 2, "question": "ABCD is a rhombus. DFB and DECG are straight lines. \\(\\angle DAB = 106^\\circ\\) (at A) and the angle at E (\\(\\angle FEC\\)) = 54°.
(a) Find \\(\\angle ABD\\). [?]°
(b) Find \\(\\angle GCB\\). [?]°
(c) Find \\(\\angle EFB\\). [?]°", "answer0": "37", "answer1": "74", "answer2": "163", "answer3": null, "correct_answer": null, "skill_id": 230, "difficulty_id": 3, "explanation": "(a) In rhombus, triangle ABD is isosceles (AB = AD) with apex \\(\\angle DAB = 106^\\circ\\); base angles \\(\\angle ABD = (180^\\circ - 106^\\circ) ÷ 2 = 37^\\circ\\). (b) \\(\\angle ADC = 180^\\circ - 106^\\circ = 74^\\circ\\) (co-interior); \\(\\angle GCB = 74^\\circ\\) (corresponding/property). (c) \\(\\angle FDE = 180^\\circ - 106^\\circ - 37^\\circ = 37^\\circ\\); \\(\\angle DFE = 180^\\circ - 37^\\circ - 126^\\circ = 17^\\circ\\); \\(\\angle EFB = 180^\\circ - 17^\\circ = 163^\\circ\\).", "hints": ["(a) Triangle ABD is isosceles with apex 106°.", "(c) Work through triangle DEF then angles on a straight line."], "source": "Tao Nan 2024 P6 Practice P2 Q9", "image_needed": true, "image_options": false, "image_file": "q109.png", "image_page": 23, "image_bbox": [0.18, 0.12, 0.70, 0.36], "image_loc": "rhombus ABCD with straight lines DFB and DECG, 106° at A and 54° marked, upper part of page", "notes": "Paper 2 Q9. Key verified: (a) 37°, (b) 74°, (c) 163°. Three whole-degree blanks, FIB ok." }, { "n": 110, "type_id": 2, "question": "Shops A and B sell files of four colours. The bar graphs show the number of files sold by each shop in January. The bar for the number of yellow files sold by Shop A has not been drawn. Shop A: Blue 150, Green 175, Red 25. Shop B: Blue 125, Green 175, Red 200, Yellow 75.
(a) Half of the files sold by Shop A were yellow files. How many yellow files did Shop A sell? [?]
(c) In February, Shop B sold 105 more blue files than the number of blue files sold in January. What was the percentage increase in the number of blue files sold by Shop B from January to February? [?]%", "answer0": "350", "answer1": "84", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 175, "difficulty_id": 3, "explanation": "(a) Non-yellow files for Shop A = Blue 150 + Green 175 + Red 25 = 350. Half of all Shop A files were yellow, so yellow = the other half = 350. (c) Shop B January blue = 125; increase 105 -> 105/125 × 100% = 84%.", "hints": ["(a) If yellow is half, yellow equals the sum of the other three colours.", "(c) Percentage increase = increase ÷ original × 100%."], "source": "Tao Nan 2024 P6 Practice P2 Q10", "image_needed": true, "image_options": false, "image_file": "q110.png", "image_page": 24, "image_bbox": [0.12, 0.18, 0.80, 0.38], "image_loc": "two bar graphs Shop A and Shop B (files by colour), upper part of page", "notes": "Paper 2 Q10. Key verified: (a) 350; (c) 84%. Part (b) ('Which colour(s) of files did Shop A sell more than Shop B?' answer Blue) is a word answer; omitted from the two FIB blanks here. FLAG for QA: part (b) = Blue (make a separate MCQ if desired). Bar values read from graphs." }, { "n": 111, "type_id": 2, "question": "The photocopying rates of two machines, P and Q, are: P: 2 pages per second; Q: 7 pages every 5 seconds. Both machines were used to make a copy of a set of notes which had been divided into Part 1 and Part 2. Machine P took 7 minutes to photocopy Part 1 and Machine Q took 8 minutes to photocopy Part 2.
(a) How many pages were there altogether in the set of notes? [?]
(b) Another copy of the same set of notes was made using Machine Q only. How many minutes did Machine Q take? [?]", "answer0": "1512", "answer1": "18", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "(a) P: 2 pages/s × 60 = 120 pages/min; Part 1 = 7 × 120 = 840 pages. Q: 7 pages / 5 s = 84 pages/min; Part 2 = 8 × 84 = 672 pages. Total = 840 + 672 = 1512 pages. (b) Q rate = 84 pages/min; 1512 ÷ 84 = 18 min.", "hints": ["Convert each rate to pages per minute.", "(a) Part1 (P) + Part2 (Q); (b) total ÷ Q's rate."], "source": "Tao Nan 2024 P6 Practice P2 Q11", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q11. Key verified: (a) 1512 pages; (b) 18 min. Machine pictures decorative; rates in stem. image_needed=false." }, { "n": 112, "type_id": 2, "question": "The figure is formed by two identical circles with centres at A and C. ABCD is a square and the length of AB is 15 cm. (Take \\(\\pi = 3.14\\))
(a) Find the perimeter of the unshaded part. [?] cm
(b) Find the total area of the shaded parts. [?] cm²", "answer0": "47.1", "answer1": "1156.5", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 222, "difficulty_id": 3, "explanation": "Radius = AB = 15 cm. (a) The unshaded part is a lens/leaf formed by two 90° arcs: perimeter = 2 × (90/360 × 2 × 3.14 × 15) = 2 × (1/4 × 2 × 3.14 × 15) = 2 × 23.55 = 47.1 cm. (b) Shaded = total of two circles minus the two unshaded quarter-overlap pieces. Per the printed working: shaded = 1059.75 + 96.75 = 1156.5 cm².", "hints": ["Radius = 15 cm; unshaded outline is two quarter-circle arcs.", "(b) Combine the large shaded circle parts with the leftover segments per the working."], "source": "Tao Nan 2024 P6 Practice P2 Q12", "image_needed": true, "image_options": false, "image_file": "q112.png", "image_page": 26, "image_bbox": [0.12, 0.12, 0.46, 0.30], "image_loc": "two overlapping identical circles (centres A and C) with shaded regions, B at top and D at bottom, upper-left of page", "notes": "Paper 2 Q12. Key verified from printed working: (a) 47.1 cm; (b) total shaded = 1059.75 + 96.75 = 1156.5 cm²." }, { "n": 113, "type_id": 2, "question": "Mr Lim had blue pens and red pens for sale. He sold 270 blue pens. 25% of the pens sold were red.
(a) How many blue pens and red pens did Mr Lim sell altogether? [?]
(b) He sold 40% of his pens. 30% of the pens left unsold were blue. How many red pens did Mr Lim have at first? [?]", "answer0": "360", "answer1": "468", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 209, "difficulty_id": 3, "explanation": "(a) Blue sold 270 = 75% of pens sold (since 25% were red). Total sold = 270 ÷ 75 × 100 = 360. (b) Sold 360 = 40% of all pens, so total pens = 900; unsold = 540. 30% of unsold were blue = 162 blue unsold; remaining unsold red = 540 - 162 = 378. Red pens at first = red sold + red unsold = (25% of 360 = 90)... printed working: 378 + 25/100 × 360 = 378 + 90 = 468.", "hints": ["(a) 270 blue = 75% of sold pens.", "(b) Total pens from 'sold 360 = 40%'; red at first = red unsold + red sold."], "source": "Tao Nan 2024 P6 Practice P2 Q13", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q13. Key verified: (a) 360; (b) 468 (270×100/75 = 360 total sold; 360×100/40 = 900 total; 900-360 = 540 unsold; 70% of 540 = 378 unsold red; 378 + 25%×360 = 378 + 90 = 468)." }, { "n": 114, "type_id": 2, "question": "Andy saved a total of $108 in coins in his coin box. \\(\\dfrac{2}{3}\\) of all the coins saved were one-dollar coins. There were 3 times as many one-dollar coins as fifty-cent coins. The remaining coins were twenty-cent coins. How many coins did Andy save in his coin box altogether?
Ans: [?]", "answer0": "135", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 209, "difficulty_id": 3, "explanation": "Let total coins = 1 whole = units. One-dollar = 2/3 (=6/9). Fifty-cent = one-third of one-dollar count = 2/9. Twenty-cent = remaining = 1 - 6/9 - 2/9 = 1/9. So per 9 units: $1 × 6 + $0.50 × 2 + $0.20 × 1 = $6 + $1 + $0.20 = $7.20 per 9 coins. $108 ÷ $7.20 = 15 groups. Total coins = 15 × 9 = 135.", "hints": ["One-dollar : fifty-cent : twenty-cent counts = 6 : 2 : 1 (out of 9).", "Value per group of 9 coins = $7.20; 108 ÷ 7.20 = 15 groups."], "source": "Tao Nan 2024 P6 Practice P2 Q14", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q14 (3 marks). Key verified from printed working: counts ratio 6:2:1 of 9; $108 ÷ $7.20 = 1.5 × 10 × 9 = 135 coins." }, { "n": 115, "type_id": 2, "question": "Cassie hung some identical rings vertically. The thickness of each ring was 1 cm. One ring's outer height is 9 cm; when overlapped, each extra ring adds part of its height (overlap shown).
(a) What was the distance from the top of the 1st ring to the bottom of the 4th ring? [?] cm
(b) The distance from the top of the 1st ring to the bottom of the last ring was 198 cm. How many rings did Cassie hang altogether? [?]", "answer0": "30", "answer1": "28", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 32, "difficulty_id": 3, "explanation": "First ring = 9 cm. Each additional ring adds 7 cm (9 - 2 × 1 cm overlap on the connecting thickness). (a) 4 rings = 9 + 7 + 7 + 7 = 30 cm. (b) 198 cm: (198 - 9) ÷ 7 = 189 ÷ 7 = 27 additional rings; total = 27 + 1 = 28 rings.", "hints": ["First ring contributes 9 cm; each later ring adds 7 cm.", "(b) (198 - 9) ÷ 7 then + 1."], "source": "Tao Nan 2024 P6 Practice P2 Q15", "image_needed": true, "image_options": false, "image_file": "q115.png", "image_page": 29, "image_bbox": [0.18, 0.12, 0.66, 0.36], "image_loc": "single ring (9 cm, 1 cm thick) and a vertical chain of overlapping rings with '?' height, upper part of page", "notes": "Paper 2 Q15. Key verified: (a) 9+7+7+7 = 30 cm; (b) (198-9)/7 = 27, 27+1 = 28 rings." }, { "n": 116, "type_id": 2, "question": "In Figure 1, PQRS is a rectangular piece of paper. PQ = 25 cm and PS = 15 cm. After 6 identical triangles are cut out from the paper, the remaining paper is shown in Figure 2. The area of the remaining paper is 279 cm².
(a) What is the area of each triangle that was cut out? [?] cm²
(b) The perimeter of Figure 2 is 54 cm longer than the perimeter of Figure 1. What is the perimeter of each triangle? [?] cm", "answer0": "16", "answer1": "19", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 138, "difficulty_id": 3, "explanation": "(a) Rectangle area = 25 × 15 = 375 cm². Removed = 375 - 279 = 96 cm² over 6 triangles, so each = 96 ÷ 6 = 16 cm². (b) Perimeter of Figure 1 = 2(25 + 15) = 80 cm. Figure 2 perimeter = 80 + 54 = 134 cm. The added length comes from the two slanted sides of each cut triangle (the base lies along the original edge): 134 - 80 = 54 added = sum of the extra sides. Per the printed working: 134 - 25 - 25 = 84; 84 ÷ 6 = 14 cm (the two slant sides per triangle total 14); base = 15 ÷ 3 = 5 cm; perimeter of each triangle = 14 + 5 = 19 cm.", "hints": ["(a) (375 - 279) ÷ 6.", "(b) Find Figure 2 perimeter (80 + 54), then work out each triangle's three sides."], "source": "Tao Nan 2024 P6 Practice P2 Q16", "image_needed": true, "image_options": false, "image_file": "q116.png", "image_page": 30, "image_bbox": [0.14, 0.16, 0.80, 0.32], "image_loc": "Figure 1 (solid rectangle PQRS 25×15) and Figure 2 (rectangle with 6 triangular notches), upper part of page", "notes": "Paper 2 Q16. Key verified from printed working: (a) 16 cm²; (b) 19 cm (slant pair 14 + base 5)." }, { "n": 117, "type_id": 2, "question": "Mrs Wu spent \\(\\dfrac{1}{6}\\) of her money on a dress and 2 blouses. The dress cost 3 times as much as each blouse. Mrs Wu spent \\(\\dfrac{3}{4}\\) of her remaining money on a watch. She spent $220.50 more on the watch than on the dress.
(a) What fraction of Mrs Wu's money was spent on each blouse? [?]
(b) How much money did Mrs Wu have at first? [?]", "answer0": "\\(\\dfrac{1}{30}\\)", "answer1": "420", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "(a) Dress + 2 blouses = 1/6 of money. Dress = 3 blouse-units, so 3 + 2 = 5 blouse-units = 1/6, each blouse = 1/6 ÷ 5 = 1/30 of her money. (b) Dress = 3/30 = 1/10 of money. Remaining after 1/6 = 5/6; watch = 3/4 × 5/6 = 5/8. Watch - dress = 5/8 - 1/10 = 25/40 - 4/40 = 21/40 of money = $220.50. So money = 220.50 ÷ 21 × 40 = $10.50 × 40 = $420.", "hints": ["(a) Dress = 3 units, blouse = 1 unit; 5 units = 1/6.", "(b) Watch fraction - dress fraction = 21/40 = $220.50."], "source": "Tao Nan 2024 P6 Practice P2 Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "Paper 2 Q17. (a) fraction answer 1/30 -> per spec should be MCQ; (b) $420 (money, FIB ok). Key verified from printed working: each blouse = 1/30; watch = 5/8, dress = 1/10, diff 21/40 = 220.50, money = 220.50 ÷ 21 × 40 = $420. FLAG for QA: split (a) into MCQ with fraction options; keep (b) FIB $420." } ] }